Handbook of Research on Systems Biology Applications in Medicine

Handbook of Research on Systems Biology Applications in Medicine Andriani Daskalaki Max Planck Institute for Molecular Genetics, Berlin, Germany

Volume I

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Published in the United States of America by Information Science Reference (an imprint of IGI Global) 701 E. Chocolate Avenue, Suite 200 Hershey PA 17033 Tel: 717-533-8845 Fax: 717-533-8661 E-mail: [email protected] Web site: http://www.igi-global.com and in the United Kingdom by Information Science Reference (an imprint of IGI Global) 3 Henrietta Street Covent Garden London WC2E 8LU Tel: 44 20 7240 0856 Fax: 44 20 7379 0609 Web site: http://www.eurospanbookstore.com Copyright © 2009 by IGI Global. All rights reserved. No part of this publication may be reproduced, stored or distributed in any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identi.cation purposes only . Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress Cataloging-in-Publication Data Handbook of research on systems biology applications in medicine / Andriani Daskalaki, editor. p. ; cm. Includes bibliographical references and index. Summary: “This book highlights the use of systems approaches including genomic, cellular, proteomic, metabolomic, bioinformatics, molecular, and biochemical, to address fundamental questions in complex diseases like cancer diabetes but also in ageing”--Provided by publisher. ISBN 978-1-60566-076-9 (h/c) 1. Biological control systems--Handbooks, manuals, etc. 2. Medicine--Research--Handbooks, manuals, etc. I. Daskalaki, Andriani. [DNLM: 1. Systems Biology--methods. 2. Models, Theoretical. QU 26.5 H2367 2009] R852.H36 2009 610.72--dc22 2008020863 British Cataloguing in Publication Data A Cataloguing in Publication record for this book is available from the British Library. All work contributed to this book set is original material. The views expressed in this book are those of the authors, but not necessarily of the publisher.

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Editorial Advisory Board

Ralf Herwig Max Planck Institute for Molecular Genetics, Germany Chuchuka Enwemeka New York Institute of Technology, USA Christoph Wierling Max Planck Institute for Molecular Genetics, Germany Elisabeth Maschke-Dutz Max Planck Institute for Molecular Genetics, Germany James Adjaye Max Planck Institute for Molecular Genetics, Germany Athina Lazakidou University of Piraeus, Greece Sofia Kossida Academy of Athens, Greece Melpomeni Lazakidou General Hospital Salzburg, Austria Anastasia Kastania Athens University, Greece

List of Contributors

Abdeljaoued-Tej, Ines / ESSAI-UR Algorithmes et Structures, Tunisia............................................ 377 Adolphs, Julia / Freie Universität Berlin, Germany.......................................................................... 573 Ahmed, Jessica / Charité Universitaetsmedizin Berlin, Germany..................................................... 423 Albrecht, Daniela / Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany.......................................................................................... 403 Al.eri, Roberta / CNR - Institute for Biomedical Technologies, Italy and CILEA, Italy................... 476 Argyropoulos, Christos / University of Pittsburgh Medical Center, USA......................................... 221 Bagos, Pantelis G. / University of Central Greece, and University of Athens, Greece.............. 167, 182 Baumann, Marc / Biomedicum, Helsinki University, Finland........................................................... 694 Benkahla, Alia / Institut Pasteur de Tunis, Tunisia............................................................................ 377 Benovoy, David / McGill University and Genome Québec Innovation Centre, Canada................... 262 Beuthan, Jürgen / Charité Universitaetsmedizin Berlin, Germany................................................... 673 Boutayeb, Abdesslam / Faculté des sciences Oujda-Morocco, Morocco.................................. 798, 809 Brakhage, Axel A. / Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany and Friedrich Schiller University (FSU), Germany........ 403 Brazhe, Alexey R. / Technical University of Denmark, Denmark and Moscow State University, Russia.............................................................................................................................................. 656 Brazhe, Nadezda A. / Technical University of Denmark, Denmark and Moscow State University, Russia.............................................................................................................................................. 656 Bryan, Kenneth / University College Dublin (UCD), Ireland........................................................... 826 Cho, Kwang-Hyun / Korea Advanced Institute of Science and Technology (KAIST), Korea.............. 11 Clevert, Djork-Arné / Charité Universitaetsmedizin Berlin, Germany and Johannes Kepler University Linz, Austria................................................................................................................... 251 Cunningham, Pádraig / University College Dublin (UCD), Ireland................................................ 826 Daskalaki, Andriani / Max Planck Institute for Molecular Genetics, Germany............................... 643 Daskalakis, Antonis / University of Patras, Greece........................................................................... 221 de Bono, Bernard / European Bioinformatics Institute, UK and University of Malta, Malta........... 714 de Carvalho Lima Lobato, Ana Katerine / Federal University of Rio Grande do Norte, Brazil and Potiguar University, Brazil....................................................................................................... 458 Dellagi, Koussay / Institut Pasteur de Tunis, Tunisia......................................................................... 377 Derouich, Mohamed / Faculté des sciences Oujda-Morocco, Morocco.................................... 798, 809 Desai, Prerak / Utah State University, USA....................................................................................... 278

Deu.hard, Peter / Zuse Institute Berlin, Germany; Freie Universität Berlin, Germany; and DFG Research Center Matheon, Germany............................................................................................... 759 DiFranco, Matthew / University College Dublin (UCD), Ireland..................................................... 826 Dressler, Cathrin / Laser- und Medizin-Technologie GmbH, Berlin, Germany................................. 673 Esposti, F. / Politecnico di Milano, Italy............................................................................................. 541 Evelo, C.T.A. / University of Maastricht, The Netherlands................................................................ 339 Flack, L.K. / University of Queensland, Australia............................................................................. 209 Foley, Ross / University College Dublin (UCD), Ireland................................................................... 826 Gallagher, William M. / University College Dublin (UCD), Ireland................................................ 826 Georgiev, G. / Institute of Mechanics and Biomechanics, Bulgaria..................................................... 27 Ghazal, Peter / University of Edinburgh Medical School, Scotland and Centre for Systems Biology at Edinburgh, Scotland.......................................................................................................... 1 Gillies, Duncan / Imperial College London, UK................................................................................ 516 Gopalakrishnan, Vanathi / University of Pittsburgh, USA............................................................... 126 Guizani-Tabbane, Lamia / Institut Pasteur de Tunis, Tunisia........................................................... 377 Guthke, Reinhard / Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany.......................................................................................... 403 Hache, Hendrik / Max Planck Institute for Molecular Genetics, Germany....................................... 497 Hamblin, Michael R. / Massachusetts General Hospital - Boston, USA; Harvard Medical School, USA; and Harvard-MIT Division of Health Sciences and Technology, USA.................................. 588 Hamodrakas, Stavros J. / University of Athens, Greece........................................................... 167, 182 Hossbach, Julia / Charité Universitaetsmedizin Berlin, Germany..................................................... 423 Kleffe, Jürgen / Charité Universitaetsmedizin Berlin, Germany....................................................... 291 Kniemeyer, Olaf / Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany........................................................................................... 403 Kossida, Sophia / Biomedical Research Foundation of the Academy of Athens, Greece and Biomedicum, Helsinki University, Finland...................................................................................... 694 Kotev, V. / Institute of Mechanics and Biomechanics, Bulgaria........................................................... 27 Kowald, Axel / Medizinisches Proteom Center (MPC), Ruhr-Universität Bochum, Germany.......... 312 Kuznetsov, Andrew / Freiburg University, Germany........................................................................... 97 Kwan, Tony / McGill University and Genome Québec Innovation Centre, Canada......................... 262 Lambin, P. / GROW Research Institute, University of Maastricht, The Netherlands........................ 339 Maffezzoli, A. / Politecnico di Milano, Italy....................................................................................... 541 Majewski, Jacek / McGill University and Genome Québec Innovation Centre, Canada.................. 262 Makrantonaki, Evgenia / Dessau Medical Center, Germany and Charité Universitaetsmedizin Berlin, Germany............................................................................................................................... 331 Maksimov, Georgy V. / Moscow State University, Russia................................................................. 656 Maschke-Dutz, Elisabeth / Max Planck Institute for Molecular Genetics, Germany......................... 74 Mavituna, Ferda / The University of Manchester, UK....................................................................... 458 McLachlan, G.J. / University of Queensland, Australia.................................................................... 209 Meinel, Thomas / Max Planck Institute for Molecular Genetics, Germany...................................... 143 Mendoza, Luis / Universidad Nacional Autónoma de México, Mexico............................................. 530 Milanesi, Luciano / CNR - Institute for Biomedical Technologies, Italy........................................... 476 Miled, Slimane Ben / Institut Pasteur de Tunis, Tunisia and ENIT-LAMSIN, Tunisia...................... 377 Minet, Olaf / Charité Universitaetsmedizin Berlin, Germany............................................................ 673 Mishra, Alok / Imperial College London, UK.................................................................................... 516

Moschopoulos, Charalampos / Biomedical Research Foundation of the Academy of Athens, Greece....694 Mosekilde, Erik / Technical University of Denmark, Denmark......................................................... 656 Mulrane, Laoighse / University College Dublin (UCD), Ireland...................................................... 826 Munoz-Hernandez, Raul / The University of Manchester, UK......................................................... 458 Nikiforidis, George / University of Patras, Greece............................................................................ 221 Nikolov, S. / Institute of Mechanics and Biomechanics, Bulgaria........................................................ 27 Numata, Jorge / Freie Universität Berlin, Germany.......................................................................... 731 Orešič, Matej / VTT Technical Research Centre of Finland, Finland................................................ 354 Pavlov, Alexey N. / Saratov State University, Russia......................................................................... 656 Petrov, V. / Institute of Mechanics and Biomechanics, Bulgaria.......................................................... 27 Pham, Tuan D. / James Cook University, Australia........................................................................... 117 Preissner, Robert / Charité Universitaetsmedizin Berlin, Germany.................................................. 423 Rasche, Axel / Max-Planck-Institute for Molecular Genetics, Germany................................... 251, 361 Reinecke, Isabel / Zuse Institute Berlin, Germany............................................................................. 759 Rexhepaj, Elton / University College Dublin (UCD), Ireland........................................................... 826 Sakellaropoulos, George / University of Patras, Greece................................................................... 221 Santiago-Cortés, Elizabeth / Universidad Nacional Autónoma de México, Mexico........................ 530 Seigneuric, R. / GROW Research Institute, University of Maastricht, The Netherlands................... 339 Sgourakis, Nikolaos G. / Rensselaer Polytechnic Institute, USA...................................................... 167 Signorini, M.G. / Politecnico di Milano, Italy.................................................................................... 541 Sosnovtseva, Olga V. / Technical University of Denmark, Denmark................................................. 656 Sreenath, Sree / Case Systems Biology Initiative, Case Western Reserve University, USA................. 11 Starmans, M.H.W. / GROW Research Institute, University of Maastricht, The Netherlands........... 339 Stier, Heike / Charité Universitaetsmedizin Berlin, Germany............................................................ 291 Theodosiou, Athina / Biomedical Research Foundation of the Academy of Athens, Greece............. 694 van Erk, A. / University of Maastricht, The Netherlands................................................................... 339 van Riel, N.A.W. / Eindhoven University of Technology, The Netherlands....................................... 339 Vicini, Paolo / University of Washington, USA................................................................................... 556 Vidal-Puig, Antonio / Institute of Metabolic Science, Addenbrooke’s Hospital, UK......................... 354 Watson, R. William / University College Dublin (UCD), Ireland..................................................... 826 Weimer, Bart / Utah State University, USA........................................................................................ 278 Wellstead, Peter / The Hamilton Institute, National University of Maynooth, Ireland........................ 11 Wolkenhauer, Olaf / University of Rostock, Germany......................................................................... 11 Wouters, B.G. / GROW Research Institute, University of Maastricht, The Netherlands................... 339 Wrede, Paul / Charité Universitaetsmedizin Berlin, Germany.......................................... 291, 423, 438 Wruck, Wasco / Max Planck Institute for Molecular Genetics, Germany......................................... 239 Zabarylo, Urszula / Charité Universitaetsmedizin Berlin, Germany................................................ 673 Zouboulis, Christos C. / Dessau Medical Center, Germany and Charité Universitaetsmedizin Berlin, Germany............................................................................................................................... 331

Table of Contents

Foreword . .......................................................................................................................................xxxiii Preface . ............................................................................................................................................ xxxv Acknowledgment . ................................................................................................................................ xl Volume I Section I Basic Concepts in Medical Systems Biology Chapter I Pathway Biology Approach to Medicine ................................................................................................ 1 Peter Ghazal, University of Edinburgh Medical School, Scotland and Centre for Systems Biology at Edinburgh, Scotland Chapter II Systems and Control Theory for Medical Systems Biology . ............................................................... 11 Peter Wellstead, The Hamilton Institute, National University of Maynooth, Ireland Sree Sreenath, Case Systems Biology Initiative, Case Western Reserve University, USA Kwang-Hyun Cho, Korea Advanced Institute of Science and Technology (KAIST), Korea Olaf Wolkenhauer, University of Rostock, Germany Chapter III Mathematical Description of Time Delays in Pathways Cross Talk . ................................................... 27 S. Nikolov, Institute of Mechanics and Biomechanics, Bulgaria V. Petrov, Institute of Mechanics and Biomechanics, Bulgaria V. Kotev, Institute of Mechanics and Biomechanics, Bulgaria G. Georgiev, Institute of Mechanics and Biomechanics, Bulgaria Chapter IV Deterministic Modeling in Medicine .................................................................................................... 74 Elisabeth Maschke-Dutz, Max Planck Institute for Molecular Genetics, Germany

Chapter V Synthetic Biology as a Proof of Systems Biology ................................................................................ 97 Andrew Kuznetsov, Freiburg University, Germany Section II Advanced Computational Methods for Systems Biology Chapter VI Computational Models for the Analysis of Modern Biological Data ................................................. 117 Tuan D. Pham, James Cook University, Australia Chapter VII Computer Aided Knowledge Discovery in Biomedicine ................................................................... 126 Vanathi Gopalakrishnan, University of Pittsburgh, USA Section III Genomics and Bioinformatics for Systems Biology Chapter VIII Function and Homology of Proteins Similar in Sequence: Phylogenetic Profiling . .......................... 143 Thomas Meinel, Max Planck Institute for Molecular Genetics, Germany Chapter IX Computational Methods for the Prediction of GPCRs Coupling Selectivity ..................................... 167 Nikolaos G. Sgourakis, Rensselaer Polytechnic Institute, USA Pantelis G. Bagos, University of Central Greece, and University of Athens, Greece Stavros J. Hamodrakas, University of Athens, Greece Chapter X Bacterial β-Barrel Outer Membrane Proteins: A Common Structural Theme Implicated in a Wide Variety of Functional Roles ................................................................................................ 182 Pantelis G. Bagos, University of Central Greece, and University of Athens, Greece Stavros J. Hamodrakas, University of Athens, Greece Section IV Experimental Techniques for Systems Biology Chapter XI Clustering Methods for Gene-Expression Data .................................................................................. 209 L.K. Flack, University of Queensland, Australia G.J. McLachlan, University of Queensland, Australia

Chapter XII Uncovering Fine Structure in Gene Expression Profile by Maximum Entropy Modeling of cDNA Microarray Images and Kernel Density Methods ............................................................... 221 George Sakellaropoulos, University of Patras, Greece Antonis Daskalakis, University of Patras, Greece George Nikiforidis, University of Patras, Greece Christos Argyropoulos, University of Pittsburgh Medical Center, USA Chapter XIII Gene Expression Profiling with the BeadArrayTM Platform ............................................................... 239 Wasco Wruck, Max Planck Institute for Molecular Genetics, Germany Chapter XIV The Affymetrix GeneChip® Microarray Platform .............................................................................. 251 Djork-Arné Clevert, Charité Universitaetsmedizin Berlin, Germany and Johannes Kepler University Linz, Austria Axel Rasche, Max-Planck-Institute for Molecular Genetics, Germany Chapter XV Alternative Isoform Detection Using Exon Arrays . ........................................................................... 262 Jacek Majewski, McGill University and Genome Québec Innovation Centre, Canada David Benovoy, McGill University and Genome Québec Innovation Centre, Canada Tony Kwan, McGill University and Genome Québec Innovation Centre, Canada Chapter XVI Gene Expression in Microbial Systems for Growth and Metabolism ................................................ 278 Prerak Desai, Utah State University, USA Bart Weimer, Utah State University, USA Chapter XVII Alternative Splicing and Disease ........................................................................................................ 291 Heike Stier, Charité Universitaetsmedizin Berlin, Germany Paul Wrede, Charité Universitaetsmedizin Berlin, Germany Jürgen Kleffe, Charité Universitaetsmedizin Berlin, Germany Section V Systems Biology and Aging Chapter XVIII Mathematical Modeling of the Aging Process . .................................................................................. 312 Axel Kowald, Medizinisches Proteom Center (MPC), Ruhr-Universität Bochum, Germany

Chapter XIX The Sebaceous Gland: A Model of Hormonal Aging ......................................................................... 331 Evgenia Makrantonaki, Dessau Medical Center, Germany and Charité Universitaetsmedizin Berlin, Germany Christos C. Zouboulis, Dessau Medical Center, Germany and Charité Universitaetsmedizin Berlin, Germany Section VI Systems Biology Applications in Medicine Chapter XX Systems Biology Applied to Cancer Research ................................................................................... 339 R. Seigneuric, GROW Research Institute, University of Maastricht, The Netherlands N.A.W. van Riel, Eindhoven University of Technology, The Netherlands M.H.W. Starmans, GROW Research Institute, University of Maastricht, The Netherlands A. van Erk, University of Maastricht, The Netherlands C.T.A. Evelo, University of Maastricht, The Netherlands B.G. Wouters, GROW Research Institute, University of Maastricht, The Netherlands P. Lambin, GROW Research Institute, University of Maastricht, The Netherlands Chapter XXI Systems Biology Strategies in Studies of Energy Homeostasis In Vivo ............................................. 354 Matej Orešič, VTT Technical Research Centre of Finland, Finland Antonio Vidal-Puig, Institute of Metabolic Science, Addenbrooke’s Hospital, UK Chapter XXII Approaching Type 2 Diabetes Mellitus by Systems Biology ............................................................. 361 Axel Rasche, Max-Planck-Institute for Molecular Genetics, Germany Chapter XXIII Systems Biology and Infectious Diseases .......................................................................................... 377 Alia Benkahla, Institut Pasteur de Tunis, Tunisia Lamia Guizani-Tabbane, Institut Pasteur de Tunis, Tunisia Ines Abdeljaoued-Tej, ESSAI-UR Algorithmes et Structures, Tunisia Slimane Ben Miled, Institut Pasteur de Tunis, Tunisia and ENIT-LAMSIN, Tunisia Koussay Dellagi, Institut Pasteur de Tunis, Tunisia

Chapter XXIV Systems Biology of Human-Pathogenic Fungi . ................................................................................. 403 Daniela Albrecht, Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany Reinhard Guthke, Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany Olaf Kniemeyer, Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany Axel A. Brakhage, Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany and Friedrich Schiller University (FSU), Germany

Volume II Section VII Systems Biology and Drug Design Chapter XXV Development of Specific Gamma Secretase Inhibitors ...................................................................... 423 Jessica Ahmed, Charité Universitaetsmedizin Berlin, Germany Julia Hossbach, Charité Universitaetsmedizin Berlin, Germany Paul Wrede, Charité Universitaetsmedizin Berlin, Germany Robert Preissner, Charité Universitaetsmedizin Berlin, Germany Chapter XXVI In Machina Systems for the Rational De Novo Peptide Design ......................................................... 438 Paul Wrede, Charité Universitaetsmedizin Berlin, Germany Chapter XXVII Applications of Metabolic Flux Balancing in Medicine . ................................................................... 458 Ferda Mavituna, The University of Manchester, UK Raul Munoz-Hernandez, The University of Manchester, UK Ana Katerine de Carvalho Lima Lobato, Federal University of Rio Grande do Norte, Brazil and Potiguar University, Brazil Section VIII Data Integration and Data Mining Chapter XXVIII Multi-Level Data Integration and Data Mining in Systems Biology . ................................................ 476 Roberta Al.eri, CNR - Institute for Biomedical T echnologies, Italy and CILEA, Italy Luciano Milanesi, CNR - Institute for Biomedical Technologies, Italy

Chapter XXIX Methods for Reverse Engineering of Gene Regulatory Networks ..................................................... 497 Hendrik Hache, Max Planck Institute for Molecular Genetics, Germany Chapter XXX Data Integration for Regulatory Gene Module Discovery . ................................................................ 516 Alok Mishra, Imperial College London, UK Duncan Gillies, Imperial College London, UK Chapter XXXI Discrete Networks as a Suitable Approach for the Analysis of Genetic Regulation .......................... 530 Elizabeth Santiago-Cortés, Universidad Nacional Autónoma de México, Mexico Luis Mendoza, Universidad Nacional Autónoma de México, Mexico Chapter XXXII Investigating the Collective Behavior of Neural Networks: A Review of Signal Processing Approaches . ..................................................................................... 541 A. Maffezzoli, Politecnico di Milano, Italy F. Esposti, Politecnico di Milano, Italy M.G. Signorini, Politecnico di Milano, Italy Chapter XXXIII The System for Population Kinetics: Open Source Software for Population Analysis ...................... 556 Paolo Vicini, University of Washington, USA Section IX Systems Biology in Photochemical Processes Chapter XXXIV Photosynthesis: How Proteins Control Excitation Energy Transfer ................................................... 573 Julia Adolphs, Freie Universität Berlin, Germany Chapter XXXV Photodynamic Therapy: A Systems Biology Approach . .................................................................... 588 Michael R. Hamblin, Massachusetts General Hospital - Boston, USA; Harvard Medical School, USA; and Harvard-MIT Division of Health Sciences and Technology, USA Chapter XXXVI Modeling of Porphyrin Metabolism with PyBioS .............................................................................. 643 Andriani Daskalaki, Max Planck Institute for Molecular Genetics, Germany

Section X Modeling Cellular Physiology Chapter XXXVII Interference Microscopy for Cellular Studies . ................................................................................... 656 Alexey R. Brazhe, Technical University of Denmark, Denmark and Moscow State University, Russia Nadezda A. Brazhe, Technical University of Denmark, Denmark and Moscow State University, Russia Alexey N. Pavlov, Saratov State University, Russia Georgy V. Maksimov, Moscow State University, Russia Erik Mosekilde, Technical University of Denmark, Denmark Olga V. Sosnovtseva, Technical University of Denmark, Denmark Chapter XXXVIII Fluorescence Imaging of Mitochondrial Long-Term Depolarization in Cancer Cells Exposed to Heat-Stress ....................................................................................................................... 673 Cathrin Dressler, Laser- und Medizin-Technologie GmbH, Berlin, Germany Olaf Minet, Charité Universitaetsmedizin Berlin, Germany Urszula Zabarylo, Charité Universitaetsmedizin Berlin, Germany Jürgen Beuthan, Charité Universitaetsmedizin Berlin, Germany Section XI Tools for Molecular Networks Chapter XXXIX Protein Interactions and Diseases ....................................................................................................... 694 Athina Theodosiou, Biomedical Research Foundation of the Academy of Athens, Greece Charalampos Moschopoulos, Biomedical Research Foundation of the Academy of Athens, Greece Marc Baumann, Biomedicum, Helsinki University, Finland Sophia Kossida, Biomedical Research Foundation of the Academy of Athens, Greece and Biomedicum, Helsinki University, Finland Chapter XL The Breadth and Depth of BioMedical Molecular Networks: The Reactome Perspective ................ 714 Bernard de Bono, European Bioinformatics Institute, UK and University of Malta, Malta

Section XII Mathematical Modeling Approaches Chapter XLI Entropy and Thermodynamics in Biomolecular Simulation .............................................................. 731 Jorge Numata, Freie Universität Berlin, Germany Chapter XLII Model Development and Decomposition in Physiology .................................................................... 759 Isabel Reinecke, Zuse Institute Berlin, Germany Peter Deuflhard, Zuse Institute Berlin, Germany; Freie Universität Berlin, Germany; and DFG Research Center Matheon, Germany Chapter XLIII A Pandemic Avian Influenza Mathematical Model ............................................................................ 798 Mohamed Derouich, Faculté des sciences Oujda-Morocco, Morocco Abdesslam Boutayeb, Faculté des sciences Oujda-Morocco, Morocco Chapter XLIV Dengue Fever: A Mathematical Model with Immunization Program . ............................................... 809 Mohamed Derouich, Faculté des sciences Oujda-Morocco, Morocco Abdesslam Boutayeb, Faculté des sciences Oujda-Morocco, Morocco Section XIII Data Processing in Histopathology Chapter XLV Automated Image Analysis Approaches in Histopathology ............................................................... 826 Ross Foley, University College Dublin (UCD), Ireland Matthew DiFranco, University College Dublin (UCD), Ireland Kenneth Bryan, University College Dublin (UCD), Ireland Elton Rexhepaj, University College Dublin (UCD), Ireland Laoighse Mulrane, University College Dublin (UCD), Ireland R. William Watson, University College Dublin (UCD), Ireland Pádraig Cunningham, University College Dublin (UCD), Ireland William M. Gallagher, University College Dublin (UCD), Ireland

Detailed Table of Contents

Foreword . .......................................................................................................................................xxxiii Preface . ............................................................................................................................................ xxxv Acknowledgment . ................................................................................................................................ xl Volume I Section I Basic Concepts in Medical Systems Biology Chapter I Pathway Biology Approach to Medicine ................................................................................................ 1 Peter Ghazal, University of Edinburgh Medical School, Scotland and Centre for Systems Biology at Edinburgh, Scotland Systems biology provides a new approach to studying, analyzing and ultimately controlling biological processes. Biological pathways represent a key sub-system level of organization that seamlessly perform complex information processing and control tasks. The aim of pathway biology is to map and understand the cause-effect relationships and dependencies associated with the complex interactions of biological networks and systems. Drugs that therapeutically modulate the biological processes of disease are often developed with limited knowledge of the underlying complexity of their specific targets. Considering the combinatorial complexity from the outset might help identify potential causal relationships that could lead to a better understanding of the drug-target biology as well as provide new biomarkers for modeling diagnosis and treatment response in patients. This chapter discusses the use of a pathway biology approach to modeling biological processes, providing a new framework for experimental medicine in the post-genomic era. Chapter II Systems and Control Theory for Medical Systems Biology . ............................................................... 11 Peter Wellstead, The Hamilton Institute, National University of Maynooth, Ireland Sree Sreenath, Case Systems Biology Initiative, Case Western Reserve University, USA Kwang-Hyun Cho, Korea Advanced Institute of Science and Technology (KAIST), Korea Olaf Wolkenhauer, University of Rostock, Germany

In this chapter the authors describe systems and control theory concepts for systems biology and the corresponding implications for medicine. The context for a systems approach to the life sciences is outlined, followed by a brief history of systems and control theory. The technical aspects of systems and control theory are then described in a way oriented toward their biological and medical application. This description is then used as a reference base against which to indicate specific areas where systems and control theory aspects of systems biology have strong medical implications. Chapter III Mathematical Description of Time Delays in Pathways Cross Talk . ................................................... 27 S. Nikolov, Institute of Mechanics and Biomechanics, Bulgaria V. Petrov, Institute of Mechanics and Biomechanics, Bulgaria V. Kotev, Institute of Mechanics and Biomechanics, Bulgaria G. Georgiev, Institute of Mechanics and Biomechanics, Bulgaria In this chapter the authors investigate how the inclusion of time delay alters the dynamic properties of (a) delayed protein cross talk model, (b) time delay model of RNA silencing (RNA interference), and (c) time delay in ERK and STAT interaction. The consequences of a time delay on the dynamics of those systems are analyzed using Hopf’s theorem and Lyapunov-Andronov theory. The analytical calculations predict that time delay acts as a key bifurcation parameter, which is confirmed by numerical simulations. Chapter IV Deterministic Modeling in Medicine .................................................................................................... 74 Elisabeth Maschke-Dutz, Max Planck Institute for Molecular Genetics, Germany This chapter describes the basic mathematical methods for the deterministic kinetic modeling of biochemical systems. Mathematical analysis methods, the respective algorithms, and appropriate tools and resources, as well as established standards for data exchange, model representations, and definitions are presented. The methods comprise time-course simulations, steady-state search, parameter scanning, and metabolic control analysis among others. An application is demonstrated using a test-case model that describes parts of the extrinsic apoptosis pathway and a small example network demonstrates an implementation of metabolic control analysis. Chapter V Synthetic Biology as a Proof of Systems Biology ................................................................................ 97 Andrew Kuznetsov, Freiburg University, Germany Biologists have used a reductionist approach to investigate the essence of life. In previous years, scientific disciplines have merged with the aim of studying life on a global scale in terms of molecules and their interactions. Based on high-throughput measurements, Systems Biology adopts mathematical modeling and computational simulation to reconstruct natural biological systems. Synthetic Biology seeks to engineer artificial biological systems starting from standard molecular compounds coding in DNA. Can Systems and Synthetic Biology be combined with the idea of creating a new science—SYS Biology—that will not demarcate natural and artificial realities? What will this approach bring to medicine?

Section II Advanced Computational Methods for Systems Biology Chapter VI Computational Models for the Analysis of Modern Biological Data ................................................. 117 Tuan D. Pham, James Cook University, Australia Computational models have been playing a significant role for the computer-based analysis of biological and biomedical data. Given the recent availability of genomic sequences, microarray gene expression, and proteomic data, there is an increasing demand for developing and applying advanced computational techniques for exploring these types of data. For example, functional interpretation of gene expression data, deciphering of how genes and proteins work together in pathways and networks, and extracting and analyzing phenotypic features of mitotic cells for high throughput screening of novel anti-mitotic drugs. Successful applications of advanced computational algorithms to solving modern life-science problems will make significant impacts on several important and promising issues related to genomic medicine, molecular imaging, and the scientific knowledge of the genetic basis of diseases. This chapter reviews the fusion of engineering, computer science, and information sciences with biology and medicine, to address some latest technical developments in the computational analyses of modern biological data: microarray gene expression data, mass spectrometry data, and bioimaging. Chapter VII Computer Aided Knowledge Discovery in Biomedicine ................................................................... 126 Vanathi Gopalakrishnan, University of Pittsburgh, USA This chapter provides a perspective on three important collaborative areas in systems biology research that represent biological problems of clinical significance. The first area deals with macromolecular crystallization, which is a crucial step in protein structure determination. The second deals with proteomic biomarker discovery from high-throughput mass spectral technologies, while the third area is protein structure prediction and complex fold recognition from sequence and prior knowledge of structure properties. For each area, successful case studies are revisited from the perspective of computer-aided knowledge discovery using machine learning and statistical methods. Information about protein sequence, structure, and function is slowly accumulating in standardized forms within databases. Methods are needed to maximize the use of this prior information for prediction and analysis purposes. This chapter provides insights into such methods by which information available in existing databases can be processed and combined with systems biology expertise to expedite biomedical discoveries Section III Genomics and Bioinformatics for Systems Biology Chapter VIII Function and Homology of Proteins Similar in Sequence: Phylogenetic Profiling . .......................... 143 Thomas Meinel, Max Planck Institute for Molecular Genetics, Germany

The calculation of sequence similarity is an easily feasible way to compute protein comparisons. The comparison of complete proteomes touches one of the earliest topics in bioinformatics—the biologically meaningful organization of proteins in protein families. Several approaches that interpret function or evolutionary aspects of proteins from sequence similarity are reviewed. In particular, this reflects the arsenal of techniques introduced until now. Phylogenetic profiling, a method that compares a set of genes or proteins by their presence or absence across a given set of organisms, is also presented in this chapter. Proteins in a functional context, for example, a pathway or a protein complex, are represented by identical or similar phylogenetic profiles. The detection of functional contexts by phylogenetic profiling is playing a prospective role as an analytic tool also in systems biology. Already established tools for phylogenetic profiling as well as particular biological examples based on the SYSTERS protein family data set are presented. Chapter IX Computational Methods for the Prediction of GPCRs Coupling Selectivity ..................................... 167 Nikolaos G. Sgourakis, Rensselaer Polytechnic Institute, USA Pantelis G. Bagos, University of Central Greece, and University of Athens, Greece Stavros J. Hamodrakas, University of Athens, Greece GPCRs comprise a wide and diverse class of eukaryotic transmembrane proteins with well-established pharmacological significance. As a consequence of recent genome projects, there is a wealth of information at the sequence level that lacks any functional annotation. These receptors, often quoted as orphan GPCRs, could potentially lead to novel drug targets. However, typical experiments that aim at elucidating their function are hampered by the lack of knowledge on their selective coupling partners at the interior of the cell, the G-proteins. Up-to-date computational efforts to predict properties of GPCRs have been focused mainly on the ligand-binding specificity, while the aspect of coupling has been less studied. Here, we present the main motivations, drawbacks, and results from the application of bioinformatics techniques to predict the coupling specificity of GPCRs to G-proteins, and discuss the application of the most successful methods in both experimental works that focus on a single receptor and large-scale genome annotation studies. Chapter X Bacterial β-Barrel Outer Membrane Proteins: A Common Structural Theme Implicated in a Wide Variety of Functional Roles ................................................................................................ 182 Pantelis G. Bagos, University of Central Greece, and University of Athens, Greece Stavros J. Hamodrakas, University of Athens, Greece β-barrel outer membrane proteins constitute the second and less studied class of transmembrane proteins. They are present exclusively in the outer membrane of Gram-negative bacteria and presumably in the outer membrane of mitochondria and chloroplasts. During the last few years, remarkable advances have been made towards the understanding of their functional and structural features. It is now well-known that β-barrels are performing a large variety of biologically important functions for the bacterial cell. Such functions include acting as specific or non-specific channels, receptors for various compounds, enzymes, translocation channels, structural and adhesion proteins. These functional roles are of great importance for the survival of the bacterial cell under various environmental conditions or for the pathogenic proper-

ties expressed by these organisms. We review in this chapter the currently available literature regarding the structure and function of bacterial outer membrane proteins. We emphasize the functional diversity expressed by a common structural motif such as the β-barrel, and we provide evidence from the current literature for dozens of newly discovered families of transmembrane β-barrels. Section IV Experimental Techniques for Systems Biology Chapter XI Clustering Methods for Gene-Expression Data .................................................................................. 209 L.K. Flack, University of Queensland, Australia G.J. McLachlan, University of Queensland, Australia Clustering methods are used to place items in natural patterns or convenient groups. They can be used to place genes into clusters, with the genes placed in clusters having similar expression patterns across the tissue samples of interest. They can also be used to cluster tissues into groups on the basis of their gene profiles. Some of the methods used are hierarchical agglomerative clustering, k-means clustering, self organizing maps, and model-based methods. This chapter’s focus is on using mixtures of multivariate normal distributions to provide model-based clusterings of tissue samples and of genes. Chapter XII Uncovering Fine Structure in Gene Expression Profile by Maximum Entropy Modeling of cDNA Microarray Images and Kernel Density Methods ............................................................... 221 George Sakellaropoulos, University of Patras, Greece Antonis Daskalakis, University of Patras, Greece George Nikiforidis, University of Patras, Greece Christos Argyropoulos, University of Pittsburgh Medical Center, USA The presentation and interpretation of microarray-based genome-wide gene expression profiles as complex biological entities are considered to be problematic due to their featureless, dense nature. Furthermore microarray images are characterized by significant background noise, but the effects of the latter on the holistic interpretation of gene expression profiles remains under-explored. We hypothesize that a framework combining Bayesian methodology for background adjustment in microarray images with model-free modeling tools, may serve the dual purpose of data and model reduction, exposing hitherto hidden features of gene expression profiles. Within the proposed framework, microarray image restoration and noise adjustment is facilitated by a class of prior Maximum Entropy distributions. The resulting gene expression profiles are non-parametrically modeled by kernel density methods, which not only normalize the data, but facilitate the generation of reduced mathematical descriptions of biological variability as mixture models. Chapter XIII Gene Expression Profiling with the BeadArrayTM Platform ............................................................... 239 Wasco Wruck, Max Planck Institute for Molecular Genetics, Germany

This chapter describes the application of the BeadArrayTM technology for gene expression profiling. It introduces the BeadArrayTM technology, shows possible approaches for data analysis, and demonstrates to the reader how the technology performs in comparison to alternative microarray platforms. With this technique, results of high quality can be achieved so that many researchers consider employing it for their projects. It can be expected that it will gain a lot in importance in the future. The author hopes that this resumé will introduce researchers to this novel way of performing gene expression experiments, thus giving them a profound base for judging which technology to employ. Chapter XIV The Affymetrix GeneChip® Microarray Platform .............................................................................. 251 Djork-Arné Clevert, Charité Universitaetsmedizin Berlin, Germany and Johannes Kepler University Linz, Austria Axel Rasche, Max-Planck-Institute for Molecular Genetics, Germany Readers shall find a quick introduction with recommendations into the Preprocessing of Affymetrix GeneChip® microarrays. In the rapidly growing field of microarrays, gene expression, especially the Affymetrix GeneChip arrays, is an established technology present for over ten years on the market. Used in biomedical research, the mass of information demands statistics for its analysis. This chapter presents the particular design of GeneChip arrays, where much research has already been invested and some validation resources for the comparison of the methods are available. For a basic understanding of the preprocessing we emphasize the steps–namely: back­ground correction, normalization, perfect match correction, summarization–coup­led with alternative probe-gene assignments. Combined with a recommendation of successful methods, a first use of the new technology becomes possible. Chapter XV Alternative Isoform Detection Using Exon Arrays . ........................................................................... 262 Jacek Majewski, McGill University and Genome Québec Innovation Centre, Canada David Benovoy, McGill University and Genome Québec Innovation Centre, Canada Tony Kwan, McGill University and Genome Québec Innovation Centre, Canada Eukaryotic genes have the ability to produce several distinct products from a single genomic locus. Recent developments in microarray technology allow monitoring of such isoform variation at a genome-wide scale. In our research, we have used Affymetrix Exon Arrays to detect variation in alternative splicing, initiation of transcription, and poly-adenylation among humans. We demonstrated that such variation is common in human populations and has an underlying genetic component. Here, we use our study to illustrate the use of Exon Arrays to detect alternative isoforms, to outline the analysis involved, and to point out potential problems that may be encountered by researchers using this technology. Chapter XVI Gene Expression in Microbial Systems for Growth and Metabolism ................................................ 278 Prerak Desai, Utah State University, USA Bart Weimer, Utah State University, USA Systems biology is increasingly underpinning our concept of microbial physiology. However, the tools needed for this approach produce such large data sets that we become paralyzed trying to link the data

with the biological interpretation. Often, microbiologists are forced to use unfamiliar statistical tools that require computer science skills that are beyond our experience. Therefore, the analysis phase prohibits the full integration of the tools associated with the burgeoning genome sequences that are publicly available. Mining the genomes for hidden gems of metabolic content is on the verge of exploding with new tools for metabolic flux predictions. However, experimental evidence to verify the models is not keeping pace. Merging bioinformatics with “-omics” tools to verify the metabolic models will be highlighted. The goal of this chapter is to provide an overview of “-omics” tools to study microbial metabolism that is accessible to a newcomer to microbial systems biology; yet, provide some new linking growth with genetic regulation information that will appeal to experienced physiologists. A systems biology context will be the underpinnings of this submission to link the growth (cell division) and survival (non-culturable) with metabolism and metabolic changes. Chapter XVII Alternative Splicing and Disease ........................................................................................................ 291 Heike Stier, Charité Universitaetsmedizin Berlin, Germany Paul Wrede, Charité Universitaetsmedizin Berlin, Germany Jürgen Kleffe, Charité Universitaetsmedizin Berlin, Germany Alternative splicing is an important part of the regular process of gene expression. It controls time and tissue dependent expression of specific splice forms and depends on the correct function of about 60 splicing factor proteins of which many are the product of alternative splicing itself. It is therefore not surprising that even minor sequence disturbances can cause mis-spliced gene products with pathological effects. We survey some common diseases which can be traced back to a malfunction of alternative splicing, including cystic fibrosis, beta-thalassemia, spinal muscular atrophy, and cancer. Cancer also often results from even mis-spliced splicing factors leading to randomly spliced non-functional isoforms of several genes. Section V Systems Biology and Aging Chapter XVIII Mathematical Modeling of the Aging Process . .................................................................................. 312 Axel Kowald, Medizinisches Proteom Center (MPC), Ruhr-Universität Bochum, Germany Aging is a complex biological phenomenon that practically affects all multicellular eukaryotes. It is manifested by an ever increasing mortality risk, which finally leads to the death of the organism. Modern hygiene and medicine has led to an amazing increase in average life expectancy over the last 150 years. However, the underlying biochemical mechanisms of the aging process are still poorly understood. However, a better understanding of these mechanisms is increasingly important, since the growing fraction of elderly people in the population confronts our society with completely new and challenging problems. The aim of this chapter is to provide an overview of the aging process, discuss how it relates to system biological concepts, and explain how mathematical modeling can improve our understanding of biochemical processes involved in the aging process. We concentrate on the modeling of stochastic effects

that become important when the number of involved entities (molecules, organelles, cells) is very small and the reaction rates are low. This is the case for the accumulation of defective mitochondria, which we describe mathematically in detail. In recent years, several tools became available for stochastic modeling, therefore we also provide a brief description of the most important ones. Of course, mitochondria are not the only target of modeling efforts in aging research. Therefore, the chapter concludes with a brief survey of other interesting computational models in this field of research. Chapter XIX The Sebaceous Gland: A Model of Hormonal Aging ......................................................................... 331 Evgenia Makrantonaki, Dessau Medical Center, Germany and Charité Universitaetsmedizin Berlin, Germany Christos C. Zouboulis, Dessau Medical Center, Germany and Charité Universitaetsmedizin Berlin, Germany This chapter introduces an in vitro model as a means of studying human hormonal aging. For this purpose, human sebaceous gland cells were maintained under a hormone-substituted environment consisting of growth factors and sex steroids in concentrations corresponding to those circulating in young and postmenopausal women. The authors suggest that hormone decline, occurring with age, may play a significant role not only in the maintenance of skin homeostasis, but also in the initiation of aging. Furthermore, skin, the largest organ of the body, offers an alternative approach to understanding the molecular mechanisms underlining the aging process. Section VI Systems Biology Applications in Medicine Chapter XX Systems Biology Applied to Cancer Research ................................................................................... 339 R. Seigneuric, GROW Research Institute, University of Maastricht, The Netherlands N.A.W. van Riel, Eindhoven University of Technology, The Netherlands M.H.W. Starmans, GROW Research Institute, University of Maastricht, The Netherlands A. van Erk, University of Maastricht, The Netherlands C.T.A. Evelo, University of Maastricht, The Netherlands B.G. Wouters, GROW Research Institute, University of Maastricht, The Netherlands P. Lambin, GROW Research Institute, University of Maastricht, The Netherlands Complex diseases such as cancer have multiple origins and are therefore difficult to understand and cure. Highly parallel technologies such as DNA microarrays are now available. They provide a data deluge which needs to be mined for relevant information and integrated to existing knowledge at different scales. Systems Biology is a recent field which intends to overcome these challenges by combining different disciplines and provide an analytical framework. Some of these challenges are discussed in this chapter.

Chapter XXI Systems Biology Strategies in Studies of Energy Homeostasis In Vivo ............................................. 354 Matej Orešič, VTT Technical Research Centre of Finland, Finland Antonio Vidal-Puig, Institute of Metabolic Science, Addenbrooke’s Hospital, UK In this chapter the authors report on their experience with analysis and modeling of data obtained from studies of animal models related to obesity and metabolic syndrome. The complex interactions of genetic and environmental factors contributing to the failure of energy balance that lead to obesity, as well as tight systemic regulation to maintain energy homeostasis, require application of the systems biology strategy at the physiological level. In vivo systems offer the possibility of investigating not only the effects of specific genetic modifications or treatments in selected tissues and organs, but also to elucidate compensatory allostatic mechanisms induced to maintain the homeostasis of the whole system. A key challenge for systems biology is to characterize different systems’ responses in the context of activated pathways. One possible strategy is based on reconstruction of tissue specific pathways using lipidomics, or metabolomics in general, in combination with proteomic and transcriptomic profiles. This approach was applied to an obese mouse model and revealed activation of multiple liver pathways that may lead to metabolic products that may impair insulin sensitivity. Chapter XXII Approaching Type 2 Diabetes Mellitus by Systems Biology ............................................................. 361 Axel Rasche, Max-Planck-Institute for Molecular Genetics, Germany We acquired new computational and experimental prospects to seek insight and cure for millions of afflicted persons with an ancient malady. Type 2 diabetes mellitus (T2DM) is a complex disease with a network of interactions among several tissues and a multifactorial pathogenesis. Research conducted in human and multiple animal models has strongly focused on genetics so far. High-throughput experimentation techniques, such as microarrays, provide new tools to amend current knowledge. By integrating those results, the aim is to develop a systems biology model assisting the diagnosis and treatment. Beside experimentation techniques and platforms, or rather general concepts for a new term in biology and medicine, this chapter joins the conceptions with a rather actual medical challenge. It outlines current results and envisions a possible alley to the comprehension of T2DM Chapter XXIII Systems Biology and Infectious Diseases .......................................................................................... 377 Alia Benkahla, Institut Pasteur de Tunis, Tunisia Lamia Guizani-Tabbane, Institut Pasteur de Tunis, Tunisia Ines Abdeljaoued-Tej, ESSAI-UR Algorithmes et Structures, Tunisia Slimane Ben Miled, Institut Pasteur de Tunis, Tunisia and ENIT-LAMSIN, Tunisia Koussay Dellagi, Institut Pasteur de Tunis, Tunisia This chapter reports a variety of molecular biology informatics and mathematical methods that model the cell response to pathogens. First, the authors the main steps of the immune response, then list the high throughput biotechnologies, generating a wealth of information on the infected cell and some of the immune related databases. Last, they explain how to extract meaningful information from these sources. The modeling aspect is divided into modeling molecular interaction and regulatory networks, through

dynamic Boolean and Bayesian models, and modeling biochemical networks and regulatory networks, through Differential/Difference Equations. The interdisciplinary approach explains how to construct a model that mimics the cell’s dynamics and can predict the evolution and the outcome of infection. Chapter XXIV Systems Biology of Human-Pathogenic Fungi . ................................................................................. 403 Daniela Albrecht, Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany Reinhard Guthke, Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany Olaf Kniemeyer, Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany Axel A. Brakhage, Leibniz Institute for Natural Product Research and Infection Biology Hans-Knoell-Institute (HKI), Germany and Friedrich Schiller University (FSU), Germany This chapter describes a holistic approach in order to understand the molecular biology and infection process of human-pathogenic fungi. It comprises the whole process of analyzing transcriptomic and proteomic data. Starting with biological background, information on Aspergillus fumigatus and Candida albicans, two of the most important fungal pathogens, are given. Afterwards, techniques to create transcriptome and proteome data are described. The chapter continues by explaining methods for data processing and analysis. It shows the need for, and problems with data integration as well as the role of standards, ontologies, and databases. General aspects of these three major topics are explained and connected to the research on human-pathogenic fungi. Finally, the near future of this research topic is highlighted. This chapter aims to provide an overview on analyses of data from different cellular levels of human-pathogenic fungi. It describes their integration and application of systems biology methodologies.

Volume II Section VII Systems Biology and Drug Design Chapter XXV Development of Specific Gamma Secretase Inhibitors ...................................................................... 423 Jessica Ahmed, Charité Universitaetsmedizin Berlin, Germany Julia Hossbach, Charité Universitaetsmedizin Berlin, Germany Paul Wrede, Charité Universitaetsmedizin Berlin, Germany Robert Preissner, Charité Universitaetsmedizin Berlin, Germany Secretases are aspartic proteases, which specifically trim important, medically relevant targets like the amyloid-precursor protein (APP) or the Notch-receptor. Therefore, changes in their activity can lead to dramatic diseases like M. Alzheimer caused by aggregation of peptidic fragments. On the other hand, the secretases are interesting targets for molecular therapy of the multiple myeloma, because in this case, the over-expressed Notch-receptor does not emerge into the native conformation until the cleavage by the

gamma secretase occurs. In this chatper, the authors focus on a novel methodology of structure-based drug development that is feasible without prior knowledge of the target structure—analogy modelling. This combination of similarity screening, fold recognition, ligand-supported modelling, and docking is exemplarily illustrated for the structure of the membranal gamma secretase and specific inhibitors Chapter XXVI In Machina Systems for the Rational De Novo Peptide Design ......................................................... 438 Paul Wrede, Charité Universitaetsmedizin Berlin, Germany Peptides fulfill many tasks in controlling and regulating cellular functions. They are key molecules in systems biology. There is a great demand in science and industry for a fast search of innovative peptide structures. In this chapter, a combination of a computer-based guided search of novel peptides in sequence space with their biological experimental validation is introduced. The computer-based search uses an evolutionary algorithm, including artificial neural networks, as fitness function and a mutation operator, called the PepHarvester. Optimization occurs during 100 iterations. This system, called DARWINIZER, is applied in the de novo design of neutralizing peptides against auto antibodies from DCM (dilatative cardiomyopathy) patients. Another approach is the optimization of peptide sequences by an ant colony optimization process. This biologically-oriented system identified several novel weak binding T-cell epitopes. Chapter XXVII Applications of Metabolic Flux Balancing in Medicine . ................................................................... 458 Ferda Mavituna, The University of Manchester, UK Raul Munoz-Hernandez, The University of Manchester, UK Ana Katerine de Carvalho Lima Lobato, Federal University of Rio Grande do Norte, Brazil and Potiguar University, Brazil Recently, metabolic flux analysis (MFA) has attracted great interest for researchers in metabolic engineering. The objective of MFA is to identify the factors and mechanisms responsible to improve cell metabolism or properties. This approach has been widely used for the quantification of intracellular fluxes in metabolism of bacteria, yeast, filamentous fungi, and animal cells. The ease of formulation, versatility in use and general spectrum of application, has made the metabolic flux analysis method a potential approach for the analysis of metabolic physiology and the design of optimal bioprocesses. This chapter is divided in six topics: Streptomyces and antibiotic production; Review of metabolic engineering and metabolic flux analysis; Basic concepts of metabolic flux analysis; Reconstruction of Streptomyces metabolism; Metabolic modelling and Applications of metabolic flux analysis for antibiotic production in Streptomyces. Section VIII Data Integration and Data Mining Chapter XXVIII Multi-Level Data Integration and Data Mining in Systems Biology . ................................................ 476 Roberta Alfieri, CNR - Institute for Biomedical Technologies, Italy and CILEA, Italy Luciano Milanesi, CNR - Institute for Biomedical Technologies, Italy

The availability of a large number of specific resources especially for the experimental researchers is something difficult for users who tried to explore gene, protein, and pathway data for the first time. This chapter finally aims to highlight the complexity in the systems biology data, providing an overview of the data integration and mining approaches in the context of systems biology with some specific example for the Cell Cycle database and the Cell Cycle models simulation. Chapter XXIX Methods for Reverse Engineering of Gene Regulatory Networks ..................................................... 497 Hendrik Hache, Max Planck Institute for Molecular Genetics, Germany In this chapter we discuss and compare different methods and applications for reverse engineering of gene regulatory networks developed in recent years. Inferring gene networks from different kinds of experimental data are a challenging task that emerged, especially with the development of high throughput technologies. Various computational methods based on diverse principles were introduced to identify new regulations among genes. The mathematical aspects of the models are highlighted and the applications are mentioned. Chapter XXX Data Integration for Regulatory Gene Module Discovery . ................................................................ 516 Alok Mishra, Imperial College London, UK Duncan Gillies, Imperial College London, UK By integrating data from various sources, this chapter introduces the techniques that have been used to identify the genetic regulatory modules. Data relating to the functioning of individual genes can be drawn from many different and diverse experimental techniques. Each piece of data provides information on a specific aspect of the cell regulation process. The chapter argues that integration of these diverse types of data is essential in order to identify biologically relevant regulatory modules. A concise review of the different integration techniques is presented, together with a critical discussion of their pros and cons. A very large number of research papers have been published on this topic, and the authors hope that this chapter will present the reader with a high-level view of the area, elucidating the research issues and underlining the importance of data integration in modern bioinformatics. Chapter XXXI Discrete Networks as a Suitable Approach for the Analysis of Genetic Regulation .......................... 530 Elizabeth Santiago-Cortés, Universidad Nacional Autónoma de México, Mexico Luis Mendoza, Universidad Nacional Autónoma de México, Mexico Biological systems are composed of multiple interacting elements; in particular, genetic regulatory networks are formed by genes and their interactions mediated by transcription factors. The establishment of such networks is critical to guarantee the reliability of transcriptional performance in any organism. The study of genetic regulatory networks as dynamical systems is a helpful methodology to understand the transcriptional behavior of the genome. From a number of theoretical studies, it is known that networks present a complex dynamical behavior that includes stability, redundancy, homeostasis, and multistationarity. In this chapter we present some particular biological processes modeled as discrete networks to show that the theoretical properties of networks have a clear biological interpretation.

Chapter XXXII Investigating the Collective Behavior of Neural Networks: A Review of Signal Processing Approaches . ..................................................................................... 541 A. Maffezzoli, Politecnico di Milano, Italy F. Esposti, Politecnico di Milano, Italy M.G. Signorini, Politecnico di Milano, Italy In this chapter, authors review main methods, approaches, and models for the analysis of neuronal network data. In particular, the analysis concerns data from neurons cultivated on Micro Electrode Arrays (MEA), a technology that allows the analysis of large ensemble of cells for long period recordings. The goal is to introduce the reader to the MEA technology and its significance in both theoretical and practical aspects of neurophysiology. The chapter analyzes two different approaches to the MEA data analysis: the statistical methods, mainly addressed to the network activity description, and the system theory methods, more dedicated to the network modeling. Finally authors present two original methods, introduced independently. The first method involves innovative techniques in order to globally quantify the degree of synchronization and inter-dependence on the entire neural network. The second is a new geometrical transformation performing very fast whole-network analysis: this method is useful for singling out collective-network behaviors with a low-cost computational effort. The chapter has the aim of providing an overview of methods dedicated to the quantitative analysis of neural network activity measured through MEA technology. Until now many efforts were devoted to biological aspects of this problem without taking in to account the computational and methodological signal processing questions. This is precisely what we tried to do by our contribution that we hope could be a starting point in an interdisciplinary cooperative research approach. Chapter XXXIII The System for Population Kinetics: Open Source Software for Population Analysis ...................... 556 Paolo Vicini, University of Washington, USA Population kinetic analysis (population kinetics) is an increasingly important tool for modeling and analyzing biomedical kinetic (that is, time-dependent, or time series) data affected by an unfavorable signal-to-noise ratio and relatively short duration. This chapter describes the philosophy behind the SPK, its components, and its current implementation as a Web service available at http://spk.rfpk.washington. edu. The SPK is first and foremost an open source product, and as such, it builds on the availability of many open source tools. This in turn allows for a very flexible modular structure and rapid deployment of new features and user documentation. With the open source release of the SPK, it is our hope that this software tool will turn into a collaborative effort spanning many user communities and developers associated with population kinetic analysis. Section IX Systems Biology in Photochemical Processes Chapter XXXIV Photosynthesis: How Proteins Control Excitation Energy Transfer ................................................... 573 Julia Adolphs, Freie Universität Berlin, Germany

This chapter introduces the theory of optical spectra and excitation energy transfer of light harvesting complexes in photosynthesis. The light energy absorbed by protein bound pigments in these complexes is transferred via an exciton mechanism to the photosynthetic reaction center where it drives the photochemical reactions. The protein holds the pigments in optimal orientation for excitation energy transfer and creates an energy sink by shifting the local transition energies of the pigments. In this way, the excitation energy is directed with high efficiency (close to 100 %) to the reaction center. In the present chapter, this energy transfer is studied theoretically. Based on crystal structure data the excitonic couplings are calculated taking into account also the polarizability of the protein. The local transition energies are obtained by two independent methods and are used to predict the orientation of the FMO protein relative to the reaction center. Chapter XXXV Photodynamic Therapy: A Systems Biology Approach . .................................................................... 588 Michael R. Hamblin, Massachusetts General Hospital - Boston, USA; Harvard Medical School, USA; and Harvard-MIT Division of Health Sciences and Technology, USA This chapter focus on studies of PDT that have employed a systems biology approach. Many cell pathways and signaling systems are engaged after PDT and although many of these cellular changes have been elucidated by traditional biochemical and cell biology techniques, the newer technologies of “-omics” are increasingly being brought to bear on this problem. In particular, these technologies involve the use of gene-expression micro-arrays. We will cover protective responses induced by PDT that include activation of transcription factors, heat shock proteins, antioxidant enzymes, and antiapoptotic pathways. Elucidation of these mechanisms might result in the design of more effective combination strategies to improve the antitumor efficacy of PDT. Chapter XXXVI Modeling of Porphyrin Metabolism with PyBioS .............................................................................. 643 Andriani Daskalaki, Max Planck Institute for Molecular Genetics, Germany Physiological and biochemical evidence indicates that flow of substrates into the porphyrin pathway is controlled by the synthesis of d–aminolevulinic acid (ALA), the first committed precursor of the porphyrin pathway. The basis of the selectivity of ALA-based (Photodynamic Therapy) PDT or (Photodynamic Diagnosis) PDD has been correlated with the metabolic rate of the cells or with the differential expression of enzymes along the heme biosynthetic pathway. Although light is required to trigger the synthesis of ALA and the differentiation of chloroplasts (Reinbothe and Reinbothe, 1996), a feedback inhibition of ALA synthesis by an end product of the porphyrin pathway is thought to be involved in the regulation of influx into the pathway. Both the nature of the product and the mechanism involved in effecting feedback inhibition remain unknown. Thus, the modeling of the porphyrin pathway may fill this void and allow researchers to address this question of long-standing importance.

Section X Modeling Cellular Physiology Chapter XXXVII Interference Microscopy for Cellular Studies . ................................................................................... 656 Alexey R. Brazhe, Technical University of Denmark, Denmark and Moscow State University, Russia Nadezda A. Brazhe, Technical University of Denmark, Denmark and Moscow State University, Russia Alexey N. Pavlov, Saratov State University, Russia Georgy V. Maksimov, Moscow State University, Russia Erik Mosekilde, Technical University of Denmark, Denmark Olga V. Sosnovtseva, Technical University of Denmark, Denmark This chapter describes the application of interference microscopy and double-wavelet analysis to the non-invasive study of cell structure and function. We present different techniques of phase and interference microscopy and discuss how variations in the intrinsic optical properties of a cell can be related to the intracellular processes. Particular emphasis is given to the newly developed phase modulation laser interference microscope. We show how this setup, combined with wavelet analysis of the obtained data series, can be applied to live cell imaging and to investigate the rhythmic intracellular processes and their mutual interactions. We hope that the discussion will contribute to the understanding and learning of new methods for non-invasive investigation of intracellular processes. Chapter XXXVIII Fluorescence Imaging of Mitochondrial Long-Term Depolarization in Cancer Cells Exposed to Heat-Stress ....................................................................................................................... 673 Cathrin Dressler, Laser- und Medizin-Technologie GmbH, Berlin, Germany Olaf Minet, Charité Universitaetsmedizin Berlin, Germany Urszula Zabarylo, Charité Universitaetsmedizin Berlin, Germany Jürgen Beuthan, Charité Universitaetsmedizin Berlin, Germany This chapter deals with the stress response of mitochondria to heat which is the central agent of thermotherapy. Thermotherapies function by inducing lethal heat inside target tissues. Spatial and temporal instabilities of temperature distributions in targets require optimized treatment protocols and reliable temperature-control methods during thermotherapies. Since solid cancers present predominant targets to thermotherapy, we analyzed hyperthermic stress-induced effects on mitochondrial transmembrane potentials in breast cancer cells (MX1). Heat sensitivities and stress reactions might be extremely different among different tissue species and tissue dignities; it is very important to investigate tissue-specific stress responses systematically. Even though this chapter will provide little information, only to the enlightenment of systemic cellular heat stress mechanisms, it may contribute to deepening the basic knowledge about systemic stress responses. In addition, the data presented here might support optimizing of treatment protocols applied during thermotherapy, particularly LITT and hyperthermia.

Section XI Tools for Molecular Networks Chapter XXXIX Protein Interactions and Diseases ....................................................................................................... 694 Athina Theodosiou, Biomedical Research Foundation of the Academy of Athens, Greece Charalampos Moschopoulos, Biomedical Research Foundation of the Academy of Athens, Greece Marc Baumann, Biomedicum, Helsinki University, Finland Sophia Kossida, Biomedical Research Foundation of the Academy of Athens, Greece and Biomedicum, Helsinki University, Finland The direct connection of proteomics with human diseases is now unquestionable and proteomics have become a scientific section of great research interest. In this chapter, we present a detailed description of the nature of protein interactions and describe the more important methodologies that are being used for their detection. The authors review the mechanisms leading to diseases and involving protein interactions, and refer to specific diseases such as Huntington’s disease and cancer. Finally, we give an overview of the most popular computational methods which are used for the prediction or the healing of the diseases. Chapter XL The Breadth and Depth of BioMedical Molecular Networks: The Reactome Perspective ................ 714 Bernard de Bono, European Bioinformatics Institute, UK and University of Malta, Malta From a genetic perspective, disease can be interpreted in terms of a variation in molecular sequence or expression (dose) that impairs normal physiological function. To understand thoroughly the knock-on effect such pathological changes may have, it is crucial to map out the physiological relationship affected genes maintain with their functional neighbors. The goal of the Reactome project is to build such a network knowledgebase for all human genes. Constructing a map of such extent and scope requires a considerable range of expertise, so this project collaborates with field experts to integrate their pathway knowledge into a single quality-checked human model. This resource dataset is systematically crossreferenced to major molecular and literature databases, and is accessible to the community in a number of well-established formats. As an evolving network systems resource, Reactome is also starting to provide increasingly powerful and robust tools to investigate tissue-specific biology and steer targeted drug design. Section XII Mathematical Modeling Approaches Chapter XLI Entropy and Thermodynamics in Biomolecular Simulation .............................................................. 731 Jorge Numata, Freie Universität Berlin, Germany Thermodynamics is one of the best established notions in science. Some recent work in biomolecular modeling has sacrificed its rigor in favor of trendy empirical methods. Even in cases when physics-based

energy functions are used, entropy is forgotten or left “for later versions”. This text gives an overview of the utility of a more rigorous treatment of thermodynamics at the molecular level to understand protein folding and receptor-ligand binding. It begins with an intuitive explanation of thermodynamics: enthalpy is the quantity of energy, while entropy stands for its quality. Recent advances in entropy from information theory and physical chemistry are outlined as they apply to biological thermodynamics. A reliable calculation of equilibrium constants for elementary reactions among biochemical metabolites and kinetic rates of enzymes from first principles would be an invaluable advance for the field of systems biology. The methods presented in this chapter carry such potential. Chapter XLII Model Development and Decomposition in Physiology .................................................................... 759 Isabel Reinecke, Zuse Institute Berlin, Germany Peter Deuflhard, Zuse Institute Berlin, Germany; Freie Universität Berlin, Germany; and DFG Research Center Matheon, Germany Some model development concepts can be used for mathematical modeling in physiology as well as a graph theoretical approach for a decomposition technique in order to simplify parameter estimation. These methods are presented on the basis of a complex mathematical model for the human menstrual cycle. First, some modeling fundamentals are introduced and applied to the model development of the human menstrual cycle. Then it is shown how a complex mathematical model in physiology can be handled if a large number of parameters are used in the model where the parameter values are not known for the most part. A method is presented to divide the model into smaller, disjoint model parts in order to simplify parameter estimation. At the same time, it is shown how this technique works in the case of the human menstrual cycle. The principles for model development and decomposition can be used for other physiological models as well. Chapter XLIII A Pandemic Avian Influenza Mathematical Model ............................................................................ 798 Mohamed Derouich, Faculté des sciences Oujda-Morocco, Morocco Abdesslam Boutayeb, Faculté des sciences Oujda-Morocco, Morocco Worldwide, seasonal outbreaks of influenza affect millions of people, killing about 500,000 individuals every year. Human influenza viruses are classified into three serotypes: A, B, and C. Only influenza A viruses can infect and multiply in avian species. During the last decades, important avian influenza epidemics have occurred. So far, the epidemics among birds have been transmitted to humans, but the most feared problem is the risk of pandemics that may be caused by person-to-person transmission. The present mathematical model deals with the dynamics of human infection by avian influenza both in birds and in humans. Stability analysis is carried out and the behavior of the disease is illustrated by simulation with different parameters values. Chapter XLIV Dengue Fever: A Mathematical Model with Immunization Program . ............................................... 809 Mohamed Derouich, Faculté des sciences Oujda-Morocco, Morocco Abdesslam Boutayeb, Faculté des sciences Oujda-Morocco, Morocco

Dengue fever is a re-emergent disease affecting more than 100 countries. Its incidence has increased fourfold since 1970 and nearly half the world population is now at risk. In the present paper, a mathematical model with immunization is proposed to simulate the succession of two epidemics with variable human populations. Stability of the equilibrium points is carried out and simulation is given for different parameters settings. Section XIII Data Processing in Histopathology Chapter XLV Automated Image Analysis Approaches in Histopathology ............................................................... 826 Ross Foley, University College Dublin (UCD), Ireland Matthew DiFranco, University College Dublin (UCD), Ireland Kenneth Bryan, University College Dublin (UCD), Ireland Elton Rexhepaj, University College Dublin (UCD), Ireland Laoighse Mulrane, University College Dublin (UCD), Ireland R. William Watson, University College Dublin (UCD), Ireland Pádraig Cunningham, University College Dublin (UCD), Ireland William M. Gallagher, University College Dublin (UCD), Ireland The field of histopathology has encountered a key transition point, with the progressive move towards the use of digital slides and automated image analysis approaches. This chapter discusses the various methods and techniques involved in the automation of image analysis in histopathology. Important concepts and techniques are explained in the five main areas of workflow within image analysis in histopathology; data acquisition, the digital image, image pre-processing, segmentation and machine learning. Furthermore, examples of the application of these concepts and techniques in histopathological research are then given.

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Foreword

Systems biology has been in the focus of intense public and private research in recent years evoking high expectations and hopes with regard to the solution of emerging problems in the health care sector. The notion of systems biology is rather broad agglomerating mathematical and computational methods, experimental techniques and biomedical applications. At its core, systems biology aims at the explanation of physiology and disease from the level of interacting components such as molecular pathways, regulatory networks, cells, organs and, ultimately, the entire organism. This is complementary to the single-protein (-target) approach that had been the primary research paradigm for a long time condensed in the term “reductionism”. However, with the increasing amount and heterogeneity of data generated by modern experimental techniques and the increasing power of computational hardware, it has become evident that such reductionism can no longer be maintained as the primary research paradigm. The essential tool of systems biology research is the computer. With the use of computational methods systems biology aims at an understanding of biological processes using mathematical models of different granularity. The purpose of these models is the generation of in silico predictions, for example on the state of a particular disease or the effect of the therapy on the individual patient. With the use of data integration methods systems biology utilises a comprehensive experimental read-out on different levels of cellular information in order to fit the parameters in these models. And, finally, at the intersection of several key research disciplines systems biology links these mathematical models to practically relevant research questions and contributes to the generation and testing of hypotheses and the planning of experiments. These new approaches are about to revolutionize our knowledge on disease mechanisms and on the interpretation of data from high-throughput technologies. Systems biology approaches are necessary in several respects. First, with respect to the increasing complexity of research, it is very likely that systems biology contributes to the formulation and solution of new paradigms able to describe the underlying complex biological problems. Secondly, with respect to the increasing complexity of experimental techniques, new problems arise that must be solved by integration rules. For example, in practice often several laboratories are working with different experimental techniques at the same research question. A fundamental challenge is thus to search through the exhaustive set of data and extract meaningful information. Thirdly, with respect to these increasing demands on the mathematical modelling it becomes more and more evident that the development of computational modelling approaches itself must be connected much closer to the experimental observations in order to proof usefulness and relevant predictive power of these approaches. Having acknowledged that systems biology holds such high promises for future biomedical research, I am delighted to write the Foreword to this “Handbook of Research on Systems Biology Applications in Medicine” as its scope and content provide both, students and researchers, from various disciplines with a broad introduction of systems biology methodologies and show their usefulness on a multitude of applications.

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The book targets systems biology on a rather practical level from two directions – from an experimental and a methodological direction. The experimental path contributes articles that highlight applications in important problem domains, for example human diseases such as cancer, type-2 diabetes mellitus, infectious diseases, influenza and ageing, among others, as well as in specific processes such as apoptosis and photosynthesis and with respect to specific experimental techniques such as chip analyses, interference microscopy, proteinprotein interactions, synthetic biology, de novo peptide design and photodynamic therapy. The reader approaching the book from this path will find in-depth descriptions of these biological phenomena, of the practical problems in analysing these phenomena along with a description of computational solutions for these analyses. The methodological path contributes articles that describe multivariate statistical methods such as clustering, gene expression analysis, normalisation methods as well as analysis methods for kinetic models such as metabolic flux analysis, metabolic control analysis among others and, additionally data integration methods in terms of experimental data, pathways and mathematical models. The reader approaching the book from this path will find introduction and description of relevant computational methods and a demonstration how these methods are applied to practical problems. Taken together both paths allow researchers from different disciplines to catch a common basis. In summary, by presenting such a broad mixture of articles the book gives relevant insights into the different research disciplines that are touched by systems biology such as mathematics, biology, chemistry, medicine and information theory. Students and researchers from these fields might get interested in a specialisation towards this new discipline. On the other hand, researchers coming from the systems biology field will get valuable information on real practical problems and potential approaches to these problems that could benefit from systems biology methods. Thus, the book gives both sides a good starting point to walk on further on this fascinating new road. Ralf Herwig Group Leader, Max-Planck-Institute for Molecular Genetics March 2008 Ralf Herwig studied physics and mathematics at the Technical and the Free University Berlin and finished his PhD in 2001 on clustering methods for gene expression data. He was awarded for the Heinz-Billing-Price for Scientific Computation of the Max-Planck Society in 1999 and was an honor student of the American Academy of Achievement in 2000. Since 2001 he is group leader at the Max-Planck-Institute for Molecular Genetics. His research focuses on multivariate statistical methods, data integration systems and computational modelling. Ralf Herwig has contributed to 50 scientific publications and was coauthor of the first textbook on systems biology in 2005.

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Preface

Systems biology integrates theoretical and experimental research and applies to various areas related to medicine. However, a few things are known in the medical profession about the theories and techniques behind systems biology. In the future, as systems biology techniques progress, it may become possible to study complex diseases at a multitude of levels within the cell, from transcriptional changes, to changes in metabolic flux through genetic pathways. Complete genome sequencing of hundreds of pathogenic and model organisms in the past decade has provided the information required for studies of gene function. Functional genomics and proteomics approaches, when combined with computational biology and the emerging discipline of systems biology, finally allow us to begin comprehensive mapping of cellular and molecular networks and pathways. However, one of the main difficulties we still face is how best to integrate these disparate data sources and use them to better understand, diagnose, and treat biological systems during disease. The systems biology approach of integrating protein expression data with clinical data such as histopathology, clinical functional measurements, medical imaging scores, patient demographics, and clinical outcome provides a powerful tool for linking biomarker expression with biological processes that can be segmented and linked to disease presentation. Systems biology and new technologies enable predictive and preventative medicine. This biology is revolutionizing the field of medical research and creating a new breed of medical researchers.Systems biology yields insights that may aid in the treatment of cancer by combining different disciplines and providing an analytical framework. The existence of heterogeneity of treatment effects is apparent when evaluating patient response to a drug in clinical trials and in clinical practice. Adverse drug reactions are being linked to enzymatic deficiencies or mutations. Therefore one of the great challenges for 21st century medicine is to deliver effective therapies that allow clinicians to choose the correct drug, dose, or intervention for any patient before the start of therapy. (Meyer and Zanger, 1997; Eichelbaum and Burk, 2001; Srivastava, 2003, Nicholson J. K., 2006). The creation of detailed maps of “signaling networks” linkages between various pathways of genes and proteins that resemble complicated wiring diagrams (Hahn C and Weinberg R.A., 2002), provide a better understanding of the disease at a molecular level. Many diseases can be explained by defects in pathways, and new treatments often involve finding drugs that correct those defects. This approach can result to a more individualized, and potentially more effective approach to diagnosis and treatment. Some of these challenges, as well as the development of systems biology techniques and platforms for translating genomic and pathway research into clinical healthcare are discussed in this the handbook. Systems biology provides us with a common language for both describing and modelling the integrated action of regulatory networks at many levels of biological organization from the subcellular through the cell, tissue, and organ, right up to the whole organism. Molecular epidemiology concerns the measurement of the fundamental biochemical factors that underlie population disease demography

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and understanding the health of different nations. This subject naturally lends it to systems biology approaches. Hence, systems biology is certain to play a major role in the future of both the development of personalized medicine and in molecular epidemiological studies. To access the latest research related to the applications of systems biology in medicine, I decided one year ago to launch a handbook project where researchers from all over the world would assist me in providing the necessary coverage of each respective discipline in systems biology. The primary objective of this project was to define the technologies, terms, and acronyms related to the systems biology and its medical applications. The handbook will highlight the use of systems approaches including genomic, cellular, proteomic, metabolomic, bioinformatics, molecular, and biochemical, to address fundamental questions in complex diseases like cancer and diabetes, also in ageing.

Organisa ti on of the H andb ook The handbook is roughly divided into 13 sections. Section I, “Basic Concepts in Medical Systems Biology,” introduces the readers to some basic concepts in the field of systems biology, and the systematic study of complex interactions in biological systems in order to understand better the entirety of processes that happen in diseases as cancer and diabetes. A cellular network can be modeled mathematically using methods coming from chemical kinetics and control theory. Due to the large number of parameters, variables and constraints in cellular networks, numerical and computational techniques are often used. This Section contains 5 chapters. Chapter I and II introduce the basic concepts in medical systems biology. Chapter I discusses the use of a pathway biology approach to modelling biological processes, providing a new framework for experimental medicine. Chapter II presents principles used in medical systems biology and describe systems and control theory concepts for systems biology and the corresponding implications for medicine. Chapter III describes the inclusion of time delay in pathway cross talk models. Chapter IV explains how deterministic modelling is applied to systems biology. Chapter V introduces Synthetic Biology, as an engineering approach to Systems Biology. Section II, “Advanced Computational Methods for Systems Biology” serves as a comprehensive introduction to computational methods supporting systems biology research.This part introduces advanced computational methods related to systems biology. Chapter VI describes technical developments in the computational analyses of modern biological data: microarray gene expression data, mass spectrometry data, and bioimaging. Chapter VII provides a perspective on three important collaborative areas in systems biology research, macromolecular crystallization, proteomic biomarker discovery from high-throughput mass spectral technologies and protein structure prediction and complex fold recognition. Section III “Genomics and Bioinformatics for Systems Biology” provides examples of genomics and bioinformatics applications supporting systems biology research. Chapter VIII describes methods for sequence similarity calculation as well as detection of functional contexts by phylogenetic profiling. Chapter IX provide insight into the application of computational tools to calculate the coupling specificity of important receptors like G-protein coupled receptors (GPCRs), which could present novel drug targets. Chapter X describes the importance of identifying Bacterial β-barrel outer membrane proteins in the completely sequenced genomes as these proteins could serve as potential targets for drugs or vaccines. Section IV describes “Experimental Techniques for Systems Biology” Clustering methods are used to study specific problems in genomics, such as the analysis of time-course experiments. Therefore,

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Chapter XI is focused on model-based clusterings of tissue samples and of genes. Chapter XII propose a novel theoretical framework for data and model reduction of gene expression profiles generated by microarray experiments. Chapter XIII introduces the BeadArrayTM technology for gene expression profiling, shows possible approaches for data analysis and demonstrates to the reader how the technology performs in comparison to alternative microarray platforms. The authors in Chapter XIV provide a basic understanding of the gene expression data processing with the Affymetrix Technology. Chapter XV illustrate the use of Exon Arrays to detect alternative isoforms, and point out potential problems that may be encountered by researchers using this technology. Chapter XVI focuses on microbial metabolism from a systems biology perspective. Chapter XVII introduces the aspects of alternative splicing in human disease, and its investigation by means of computational large-scale analyses. In Section V, “Systems Biology and Aging”, Chapter XVIII introduces an in vitro model as a means of studying human hormonal aging. In addition, Chapter XIX provide an overview of the aging process, discuss how it relates to system biological concepts and explain how mathematical modelling can improve our understanding of biochemical processes involved in the aging process. Section VI, “Systems Biology Applications in Medicine” has been streamlined to focus on the topics most relevant to applications of systems biology in medical problems. In Chapter XXI the authors report on their experience with analysis and modelling of data obtained from studies of animal models related to obesity and metabolic syndrome. Chapter XXII describes modelling approaches in Type 2 Diabetes mellitus. The authors in Chapter XXIII list the high throughput biotechnologies generating a wealth of information on the infected cell and some of the immune related databases and finally explain how to extract meaningful information from these sources. Chapter XXIV describes the integration of data from different cellular levels of human-pathogenic fungi and the application of systems biology methodologies. Section VII, “Systems Biology and Drug Design”, provides a thorough overview of novel methodologies in medical research. Chapter XXV focus on a novel methodology of structure-based drug development feasible without prior knowledge of the target structure: analogy modelling. Chapter XXVI introduce a combination of a computer based guided search of novel peptides in sequence space with their biological experimental validation. Chapter XXVII describe metabolic modelling and applications of metabolic flux analysis for antibiotic production. Section VIII, “Data Integration and Data Mining,” confer an understanding of data integration processes in systems biology.Chapter XXVIII describe data integration and data mining techniques in the context of systems biology studies. Chapter XXIX compare different methods and applications for reverse engineering of gene regulatory networks developed in recent years. Data relating to the functioning of individual genes can be drawn from many different and diverse experimental techniques. Chapter XXX introduces the techniques that have been used to identify the genetic regulatory modules by integrating data from various sources.Chapter XXXI presents some particular biological processes modeled as discrete networks to show that the theoretical properties of networks have a clear biological interpretation. In Chapter XXXII the authors review main methods, approaches and models for the analysis of neuronal network data. Chapter XXXIII describes the philosophy behind the SPK tool for Population kinetic analysis (population kinetics) for modelling and analyzing biomedical kinetic, its components and its current implementation as a web service. The evolution of photosynthesis is driven by selection of genes for photochemical energy conversion that is robust and, yet effective, in a fluctuating light environment. The dynamic regulation of photosynthesis relies on an interplay of multiple sensory, transmission and executive modules that can be studied by the tools of systems biology (Csete and Doyle 2002). Therefore, Section IX, “Systems Biology in Photochemical Processes” is focused on Photochemistry and its applications, highlighting

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the new understanding of the genetics of PDT. Chapter XXXIV introduces the theory of optical spectra and excitation energy transfer of light harvesting complexes in photosynthesis. Chapter XXXV focus on studies of Photodynamic Therapy (PDT) that have employed a systems biology approach. Both the nature of the product and the mechanism involved in effecting feedback inhibition remain unknown. Thus, the modelling of porphyrin pathway introduced in Chapter 36 may fill this void and allow researchers to address these questions of importance. Section X, “Modeling Cellular Physiology” deals with the study of cellular microstructures in biology by microscopy. Chapter XXXVII describes the application of interference microscopy and doublewavelet analysis to the non-invasive study of cell structure and function. Chapter XXXVIII deals with the stress response of mitochondria to heat which is the central agent of thermotherapy. Section XI, “Tools for Molecular Networks,” includes two chapters. Chapter XXXIX reviews the mechanisms leading to diseases and involving protein interactions and refers to specific diseases such as Huntington’s disease and cancer. Chapter XL introduce a network systems resource, Reactome which is also starting to provide powerful and robust tools to investigate tissue-specific biology and steer targeted drug design. Section XII, “Mathematical Modeling Approaches,” includes mathematical modeling that allows us to link epidemiology, physiology and physics to systems biology. Chapter XLI gives an overview of the utility of a more rigorous treatment of thermodynamics at the molecular level to understand protein folding and receptor-ligand binding. Chapter XLII introduces some modelling fundamentals that are applied to the model development of the human menstrual cycle. Chapter XLIII describes mathematical model which deals with the dynamics of human infection by avian influenza both in birds and in humans. Chapter XLIV presents a mathematical model with immunization is proposed to simulate the succession of two epidemics with variable human populations. Section XIII, “Data Processing in Histopathology”, presents automated image analysis approaches which can serve as a valuable aide to clinical pathologists and systems biology researchers in the domain of histopathology. Chapter XLV discusses some of the most important techniques and given examples of their use in the area up to now. The handbook covers basic biological and mathematical concepts important for systems biology. The chapters are oriented to describe the relation between basic science and medical issues. Topics that are covered in this handbook are (a) Foundations of systems biology (2) Pathophysiology of complex diseases and systems biology approach to therapy. The Handbook of Research on Systems Biology Applications in Medicine contains over three hundred pages of information and more than hundred figures. Besides having the traditional text, this information source also has a glossary of terms and definitions, contributions from more than 90 international experts, in-depth analysis of issues, concepts, new trends, and advanced technologies. This handbook allows the inclusion of more than 100 high-quality illustrations. While providing the information that is critical to an understanding of the basic of systems biology, this edition focuses more directly and extensively than ever on applications of medical systems biology. The diverse and comprehensive coverage of multiple disciplines in the field of systems biology in this handbook will contribute to a better understanding all topics, research, and discoveries in this evolving, significant field of study. This handbook provides information for both science and biotechnology researchers and also medical doctors in obtaining a greater understanding of the concepts, issues, problems, trends, challenges and opportunities related to this field of study. In shaping this book, I committed myself to making the textbook as useful as possible to students and advanced researchers coping with the demands of modern medical research. I hope will make the Handbook of Research on Systems Biology Applications in Medicine a helpful tool-not only for the student

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who needs an expert source of basic knowledge in systems biology, but also for the advanced medical researcher who needs clear, concise, and balanced information on which to conduct his research Thanks to a very hard-working advisory editorial board of scientists, excellent authors who fulfilled our invitations, and a very efficient publisher providing clear procedures and practices for a quality production, readers may now enjoy Chapters on some of the major ideas that have concerned systems biology applications in medicine. Andriani Daskalaki Max Planck Institute, Berlin, Germany July 2008

R eferences Csete, M.E., Doyle, J.C. (2002). Reverse Engineering of Biological Complexity. Science, 295: 16641669. Eichelbaum M, Burk O (2001) CYP3A (2001). Genetics in drug metabolism. Nat Med, 7: 285–288. Hahn C. and Weinberg Robert A. (2002). A Subway Map of Cancer Pathways. Nature Reviews Cancer. Klipp E. Klipp E., Herwig R., Kowald A., Wierling C., Lehrach H. (2005). Systems Biology in Practice: Concepts, Implementation and Applications. Nicholson J. K. (2006). Global systems biology, personalized medicine and molecular epidemiology Mol Syst Biol, 2, 52 Meyer UA, Zanger UM (1997). Molecular mechanisms of genetic polymorphisms of drug metabolism. Annu Rev Pharmacol Toxicol, 37, 269–296 Srivastava P. (2003). Drug metabolism and individualized medicine. Curr Drug Metab, 4, 33–44

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Acknowledgment

The editor sincerely acknowledges the help of all persons involved in the collation and review process of this handbook, without whose support the project would not have been satisfactorily completed. Deep appreciation and gratitude is due to Prof. Dr. Hans Lehrach, Director of the Department of Vertebrate Genomics Max-Planck-Institut) for giving me tha opportunity to work in the field of systems biology and generating the idea of this book. I have received generous encouragement and assistance from all staff members of the bioinformatics group. Special thanks go to Dr. Ralf Herwig for his generous encouragement and assistance. I wish to express my appreciation to my colleagues, who, as experts in their fields, have helped us with constructive criticism and helpful suggestions. I acknowledge especially the contributions of the following individuals: Prof Peter Wellstead, Christoph Wierling, and Elisabeth Maschke-Schutz. Most of the authors of chapters included in this handbook also served as referees for chapters written by other authors. Thanks go to all those who provided constructive and comprehensive reviews. However, some of the reviewers must be mentioned as their reviews set the benchmark. Reviewers who provided the most comprehensive, critical and constructive comments include: Dr. Athina Lazakidou from the University of Piraeus, Dr. Sophia Kossida from the Foundation of Biomedical Research; and Dr. Cathrin Dressler from Laser- und Medizin-Technologie GmbH, Berlin. Special thanks also go to the publishing team at IGI Global, whose contributions throughout the whole process from inception of the initial idea to final publication have been invaluable. In particular to Julia Mosemann, who continuously prodded via e-mail for keeping the project on schedule and to Mehdi Khosrow-Pour, whose enthusiasm motivated me to initially accept his invitation for taking on this project. I would also like to thank Dr. Sophia Kossida, who read a semi-final draft of the manuscript and provided helpful suggestions for enhancing its content. And last but not least, my father, Dimitirios Daskalaki, for his unfailing support and encouragement during the months it took to give birth to this book. In closing, I wish to thank all of the authors for their insights and excellent contributions to this handbook. Andriani Daskalaki, PhD Max Planck Institute, Berlin, Germany July 2008

Section I

Basic Concepts in Medical Systems Biology



Chapter I

Pathway Biology Approach to Medicine Peter Ghazal University of Edinburgh Medical School, Scotland, and Centre for Systems Biology at Edinburgh, Scotland

abstract Systems biology provides a new approach to studying, analyzing, and ultimately controlling biological processes. Biological pathways represent a key sub-system level of organization that seamlessly perform complex information processing and control tasks. The aim of pathway biology is to map and understand the cause-effect relationships and dependencies associated with the complex interactions of biological networks and systems. Drugs that therapeutically modulate the biological processes of disease are often developed with limited knowledge of the underlying complexity of their specific targets. Considering the combinatorial complexity from the outset might help identify potential causal relationships that could lead to a better understanding of the drug-target biology as well as provide new biomarkers for modelling diagnosis and treatment response in patients. This chapter discusses the use of a pathway biology approach to modelling biological processes and providing a new framework for experimental medicine in the post-genomic era.

INTR OD UCTI ON An increasing number of biological experiments and more recently clinical based studies are being conducted using large-scale genomic, proteomic and metabolomic techniques which generate high-dimensional data sets. Such approaches require the adoption of both hypothesis and data driven strategies in the analysis and interpretation of results. In particular, data-mining and pattern recognition methodologies have proven particularly useful in this field. The increasing amount of information available from high-throughput experiments has initiated a move from focussed, single gene and protein investigations

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Pathway Biology Approach to Medicine

to the study of multiple component interactions. Vitally, when the output from high dimensional data is integrated with the wealth of information from previously published investigations, the assembly of known and novel network characteristics is possible. The cause-effect association and annotation of multiple genes and gene products by such methods can aptly be described as pathway biology. Pathway data is variously categorised in terms of metabolic pathways, molecular interactions, gene regulatory networks, signalling pathways and which, are often represented differently and in isolation. In recent years there has been an increasing effort in representing biological pathways using computer science based methodologies. These efforts include databases that aim to curate pathways, such as KEGG (Kanehisa et al., 2006), Reactome (Joshi-Tope et al., 2005), aMAZE (Lemer et al., 2004) or PATIKA (Dogrusoz et al., 2005); databases of experimentally and computationally derived protein interactions, such as MPPI (Pagel et al., 2005) and DIP (Salwinski et al., 2004); or tools that aim to extract pathway information from the scientific literature, examples include PathwayAssist (Nikitin et al., 2003) and Ingenuity Pathway Analysis (Ingenuity Systems). However, a common factor in all these resources is the need to describe pathways visually in order to understand their complexity In this regard a biological interaction network based on electronic circuitry diagrams provided an informative approach and aims to provide a compact description of the entity relationships in a pathway (Kohn, 1999; Kohn et al., 2006). Kitano et al have extended this approach by introducing a simple notational system for state transitions (Funahashi et al 2003) for the representation of process flow in signalling pathways (Kitano, 2003, Kitano et al 2005). While considerable advances are being made there will be an increasing need to ensure that such pathway descriptions remain intuitive to biologists in general, involving logic and, in particular, an integrative view of molecular interactions, gene regulatory networks and signalling pathways while maintaining compliance with a more formal description of biological processes. This has been the primary motivation behind the Edinburgh Process Notation which uses and exends core aspects of the Kitano notation (Moodie et al, 2006). Collectively, these efforts have been and are part of a community wide effort to develop graphical notation standards (www. sbgn.org). To date much of this work has focussed on experimental cell signalling based systems and little work has been conducted regarding physiological systems and using clinical data. Here, we discuss a practical guide to a pathway biology approach in medicine. The intended aim is to help translate systems biology from bench science to medical research and ultimately toward clinical use. We particularly put forward the use of logic as a strategy for studying pathways and present arguments for the suitability of logical models for the analysis of clinically derived data.

Litera t ure and da t a mining: st amp c ollecting The first task at hand is toward the acquisition of pathway information. In this regard information relating to the components and interactions of pathways need to be compiled, integrated and visualised using research synthesis methodology (Cooper and Hedges 1994). This generally follows a four stage process: i.



A literature review should be undertaken to identify relevant pathway components and interactions. This can be performed using standard Entrez PubMed queries involving keywords, author searches and the use of Boolean operators. A variety of tools can also be used to facilitate this process, e.g. PDQ wizard (Grimes et al 2006). A manual review of the resultant articles is an es-

Pathway Biology Approach to Medicine

sential undertaking to ensure relevance and accuracy. The literature set should be classified on whether interactions can be attributed to a species (human or mouse), cell type (macrophage or dendritic cell) and technique used to identify the interaction. ii. The next step is to extend the literature search using a data mining approach. This can use a combination of open resources and proprietary software. These resources include but not limited to KEGG (www.genome.jp/kegg/), HPRD (www.hprd.org), Chilibot (www.chilibot.net), Pathway Assist (www.ariadnegenomics.com) and Ingenuity Pathway Analysis (Ingenuity Systems, USA), and can be used to reinforce established molecular interactions and identify new signalling components or interactions. In general they provide an online resource of curated, text-mined and experimental information on protein-protein and protein-gene interactions for producing networks of molecular interaction. iii. A graphical representation of components of the pathway can be achieved by a variety of packages yEd (www.yworks.com), EPE (Sorokin et al 2006), Cell Designer (Funahashi et al 2003) using preferably the SBGN notation. It should be noted that the resulting diagrams represent a ‘consensus’ view of a pathway and should not be taken as a canonical pathway. iv. Lastly a database model for the storage, analysis and sharing of pathway data is essential and under certain cases will need to be linked to anonymised clinical data. Curation of pathway information into a database allows for data browsing, querying, analysing and downloading. Several approaches to the storage and analysis of network interaction data have been published (Bader at al 2003, Hermjakob et al 2004, Joshi-Tope et al 2005) however this area is still in its infancy and will likely see further development in the future. Most notably, none to date have been shown to be extensible to the integration of clinical data. In this regard it is important to note that clinical data from subjects should be stored in separate databases that are fully compliant to confidentiality and data protection law.

Figure 1.



Pathway Biology Approach to Medicine

Mode lling: f orma lizing dependencies The above exercise, particularly the graphical representation, provides an excellent starting point for capturing known knowledge around pathways. However, these diagrams remain essentially pictorial in nature and include a varietal range of fine and course grained information. As such they are not yet sufficiently developed to move seamlessly toward mathematical translation. Thus a key challenge to systems level studies of pathways still remains with how best to model them and this is not an insignificant step. In general, pathway modeling requires a representation that captures the cause-effect relationships associated with each interaction, but that this should be in the first instance conceptually and computationally simple. With simple representation, computational efficient scanning of pathways for the upstream interactions that control downstream behavior is both tractable and computationally efficient. Several modelling schemes have been proposed as suitable representations for pathways. Ordinary and partial differential equations have proven to be very successful in modeling metabolic pathways (Kell, 2006, Fell, 1992), although they require precise information on concentration and reaction rates, which is largely unknown for most pathways. Accordingly approaches that deal with less or more variable data such as stochastic schemes capture very well the random nature of individual molecular events (McAdams, 1997, Arkin, 1998), but they describe very inefficiently the certainty that accompanies large numbers of proteins. Petri nets have also been considered and whilst the formulation is computationally simple, it is also conceptually complex (Hofe 1998, Kuffner 2000). Stochastic petri nets [Goss, 1998] and hybrid petri nets (Matsuno 2000) have been proposed as extensions. Pi calculus has been used to describe the pathways as a symbolic construction to which quantitative models can be fitted (Pinney et al 2003, Regev et al 2004). Finally, a particularly tractable approach is the use of logic to describe pathways. In this regard the application of Boolean logic as a modelling scheme, is now more recently receiving increasing interest (see Watterson et al 2008). Thus logical graphical models can provide an ideal first base for abstracting a range of formal mathematical models of a pathway. Ultimately these models will require standards for exchange such as SMBL and version control (Hucka 2003). Formal representation of a biologically validated model would next follow. Formal models permit the in silico testing of the ‘what if’ scenarios and that these predictions should go through a cycle of experimental verification. This cycle enables formal models to build on an iterative process of refinement.

E xperiment ati on: sing ular pathw ay appr oach For the reasons of focus and tractability the above pathway biology approach necessarily takes the position of building or constructing a consensus around a single pathway. This has the advantage of defining a sub-system making a more efficient approach for both experimental and computational investigation. However, an assumption is that the current state of literature reflects a sufficient level of understanding about the biology. Thus, while building a graphical representation of a biological pathway from the literature caution should be taken with regard as to whether the literature represents the true underlying biology. Accordingly, it is important to consider how best to biologically validate or experimentally test the constructed pathways. Since the assembled pathways consist of multiple components, gene or



Pathway Biology Approach to Medicine

protein analytic approaches would be expensive and time consuming. For this reason reliable multiplex high-throughput technologies (such as using RNAi or microarrays) would be the method of choice. For example, a microarray approach would be to identify ‘active’ connected regions of the network that show statistically significant changes in expression under different experimental conditions. For this purpose the method of Ideker and colleagues (2002) can be used together with simulation studies for rigorous statistical testing against random networks. Importantly, the results from such statistical and simulation analyses can be informative in revealing both node and edge behaviour and should fit the anticipated biological response. If the results of such analysis have a poor fit to the biology then this might be indicative of a not so good fit for validation purposes. A poor fit might suggest that other key components of the pathway are missing. In this case consideration should be given to further experimental testing. Ideally this would involve a combination of both high throughput driven exploration and hypothesis based mechanistic studies. In the case of a good fit it is likely that there exist many unknown or poorly characterised components of the pathway. In this case, a range of unbiased comprehensive screens such as traditional genetic and more recent molecular based biochemical and functional loss-of-function and gain-of-function screens. Exemplar approaches would include but are not restricted to proteomic based studies such as co-complex purification coupled with mass spectroscopy, yeast two hybrid protein interaction screens, genome-wide RNAi assays and forward genetic approaches. These approaches have been extensively covered in a number of excellent reviews on systems biology. Ultimately these assays should lead on to hypothesis testing of mechanism of action of pathway components. Mechanism based evaluation of pathways can be readily extrapolated to the analysis of clinical samples. For these studies it is important that care is taken in defining precisely the clinical phenotype of the subjects to be studied and the use of robust clinical and laboratory standard operating procedures are essential.

Cl inica l da t a: tract

abi lity

A key constraint in clinical research is in obtaining sufficient number of subjects, especially the control groups and, the amount and availability of sample material outside the medical treatment path of the patients. Thus full consideration including ethical issues has to be given on what and how many samples are available for a particular study. Most importantly it is essential that the clinical phenotype is clearly defined and minimises potential heterogeneity in the patient population. There can also be obvious limitations with regard to obtaining invasive biopsy specimens and the preferred option for both recruitment purposes and the patients would be a non-invasive sampling. A relatively benign noninvasive specimen that can be highly informative is whole blood. Here relatively but readily accessible small samples can be taken and used for systemic measurements of disease condition and treatment response (e.g. Smith et al 2007). For these reasons whole blood sampling is an area receiving increasing interest and is amenable to transcriptomic, proteomic and metabolic screening. In order to ensure the level of security and confidentiality expected for the storage of this sensitive data, the following steps are recommended. The data should be kept on a server protected by security measures at a physical, network and application level. The data should be adequately backed up and archived. Only authorized collaborators should be allowed use of the system and will be subjected to effective authentication as well as auditing. Approval from the local Clinical Data Protection Officer and senior medical officer (following Caldicott Guardian Principles) should be sought to comply with 

Pathway Biology Approach to Medicine

the confidentiality and data protection requirements. Ultimately for the purpose of integrating pathway, clinical records and high throughput data a medical bioinformatic (MBI) system will need to be established, requiring application tools to migrate anonymised data from the clinical databases to pathway database.

Co ncept ua l cha llenge of multip le pathw ay dependencies medicine

in

As a consequence of measuring patient samples using systems biology approach of high through-put technologies multiple cellular and molecular pathways are simultaneously recorded. This raises a major scientific limitation and sets the challenge of how to deal with analysis and understanding of the underlying cross-talk and dependencies in the myriad of potential interrelated networks and pathways. While a clear way forward is yet to be defined we would like to propose a conceptual framework aimed at classifying multiple pathway interrelationships and dependencies. In this regard we consider three types of pathway interdependencies that might help in the future toward a functional classification of clinical data. The types of pathway interrelationships can be labelled as process, sharing and fit: •

•

•

In the process type an output or activity of one pathway produces a resource or input used by another pathway. For instance, the sterol biosynthesis pathway leads to the production of certain oxy-sterols that form ligands for the activation of the Liver X Receptor (LXR) pathway. In the case of sharing, a single resource or pathway is used as inputs by a range of different multiple activities or pathways. For example the Janus Kinase-Signal Transducers and Activators of Transcription (JAK-STAT) signalling pathway is activated by more than 50 cytokines or growth factors. Whereas in the case of a pathway fit, different multiple pathway activities produce a single or common resource. For example a wide range of multiple cytokine, chemokine and pathogen recognition signalling pathways lead to the activation of Nuclear Factor Kappa B (NFKB), a central transcription factor for the regulation of both innate and adaptive immunity.

All of these types of interrelated activities can be coordinated in a hierarchical, non-hierarchical or emerging way and are likely to involve cells, genes, proteins and/or metabolites.

Co nc luding R emarks We hope this report provides a useful starters guide to the application of pathway biology and how it can be extended to clinical research. Ultimately, we anticipate that a comprehensive understanding of pathway structures will also allow us to predict potential disease indications or therapeutic complications or side effects that a treatment could incur. Accordingly pathway biology has future potential to contribute toward a new foundation for the next generation of medicine and clinical practice. Here we envision the use of clinical data and current best evidence coupled with pathway knowledge to make decisions about the care of individual patients.



Pathway Biology Approach to Medicine

A ckn ow ledgment I would like to thank all my colleagues in the Division of Pathway Medicine and our sponsors including the Wellcome Trust, EU FP6 programme, BBSRC and MRC.

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Funahashi, A., Tanimura, N., Morohashi, M., & Kitano, H. (2003). Cell designer: A process diagram editor for gene-regulatory and biochemical networks. BIOSILICO, 1, 159. Glass, K., & Kauffman, S. (1973). The logical analysis of continuous, non-linear biochemical control networks. Journal of Theoretical Biology, 39, 103. Goss, P., & Peccoud, J. (1998). Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri Nets. Proc Natl Acad Sci USA, 95, 6750 Grimes, G.R., Wen, T.Q., Mewissen, M., Baxter, R.M., Moodie, S., Beattie, J.S., & Ghazal, P. (2006). PDQ Wizard: Automated prioritization and characterization of gene and protein lists using biomedical literature. Bioinformatics, 22, 2055-2057. Hofestadt, R. a& Thelen, S. (1998). Quantitative modeling of biochemical networks. Silico Biology, 1(1), 39. Huang, S., (1999). Gene expression profiling, genetic networks and cellular states: an integrating concept for tumorigenisis and drug discovery. Journal of Molecular Medicine, 77, 469. Hucka, M. (2003). The systems biology markup language (SBML): A medium for representation and exchange of biochemical network models. Bioinformatics, 19, 524. Husmeier, D. (2003). Reverse engineering of genetic networks with Bayesian networks. Biochemical Society Transactions, 31(6), 1516. Husmeier, D. (2003). Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks. Bioinformatics, 19, 2271. Ideker, T., Ozier, O., Schwikowski, B., & Siegel, A.F. (2002). Discovering regulatory and signalling circuits in molecular interaction networks. Bioinformatic, 18, S233-240. Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., & Barabasi, A.L. (2000). The large-scale organization of metabolic networks. Nature, 407, 651-4. Joshi-Tope, G., Gillespie, M., Vastrik, I., D’Eustachio, P., Schmidt, E., de Bono, B., Jassal, B., Gopinath, G.R., Wu, G.R., Matthews, L., Lewis, S., Birney, E., & Stein, L. (2005). Reactome: A knowledgebase of biological pathways. Nucl. Acids Res., 33, D428-432. Liang, S., Fuhrman, S., & Somogyi, R. (1998). REVEAL: A general reverse engineering algorithm for inference of genetic network architectures. Pac Symp Biocomput, 3, 18. Kanehisa, M., Goto, S., Hattori, M., Aoki-Kinoshita, K.F., Itoh, M., Kawashima, S., Katayama, T., Araki, M., & Hirakawa, M. (2006). From genomics to chemical genomics: New developments in KEGG. Nucl. Acids Res., 34, D354-357. Kell, D,. (2006). Systems biology, metabolic modelling and metabolomics in drug discovery and development. Drug Discovery Today, 11, 1085. Kirkpatrick, S., Gelatt, C.D., & Vecchi, M.P. (1983). Optimization by simulated annealing. Science, 220, 671-680.



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Kitano, H. (2003). A graphical notation for biochemical networks. Biosilico, 1, 169. Kitano, H., Funahashi, A., Matsuoka, Y., Oda, K. (2005). Using process diagrams for the graphical representation of biological networks. Nat Biotechnol, 23, 961-966. Kohn, K.W. (1999) Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol. Biol. Cell, 10, 2703-2734. Kohn, K.W., Aladjem, M.I., Weinstein, J.N., & Pommier, Y. (2006) Molecular interaction maps of bioregulatory networks: A general rubric for systems biology. Mol. Biol. Cell, 17, 1-13. Laubenbacher, R. & Sigler, B. (2004). A computational algebra approach to the reverse engineering of gene regulatory networks. Journal of Theoretical Biology, 229, 523. Lemer, C., Antezana, E., Couche, F., Fays, F., Santolaria, X., Janky, R.S., Deville, Y., Richelle, J., & Wodak, S.J. (2004). The aMAZE LightBench: A Web interface to a relational database of cellular processes. Nucl. Acids Res., 32, D443-448. Matsuno, H., Doi, A., Nagasaki, M., & Miyano, S. (2000). Hybrid Petri Net representation of gene regulatory network. Pacific Symposium on Biocomputing, 5, 341. Singapore: World Scientific Press. Mendoza, L., Thieffry, D., & Alvarez-Buylla, E. (1999). Genetic control of flower morphogenesis in Arabidopsis thaliana: a logical analysis. Bioinformatics, 15, 593. Moodie, S., Sorokin, A., Goryanin, I., & Ghazal, P. (2006). A graphical notion to describe the logical interactions of biological pathways. Journal of Integrative Bioinformatics, 3. Nikitin, A., Egorov, S., Daraselia, N., & Mazo, I. (2003). Pathway studio--The analysis and navigation of molecular networks. Bioinformatics, 19, 2155-2157. Pagel, P., Kovac, S., Oesterheld, M., Brauner, B., Dunger-Kaltenbach, I., Frishman, G., Montrone, C., Mark, P., Stumpflen, V., Mewes, H.-W., Ruepp, A., & Frishman, D. (2005). The MIPS mammalian protein-protein interaction database. Bioinformatics, 21, 832-834. Pal. R., Ivanov, I., Datta, A., Bittner, M., & Dougherty, E. (2005). Generating Boolean networks with a prescribed attractor structure. Bioinformatics, 21, 4021. Pinney, J., Westhead, D., & McConkey, G. (2003). Petri Net representations in systems biology. Biochem Soc Trans, 31, 1513. Regev, A., & Shapiro, E. (2004). The pi-calculus as an abstraction for biomolecular systems. Modelling in Molecular Biology, Springer. Rual, J.-F., Venkatesan, K., Hao, T., Hirozane-Kishikawa, T., Dricot, A., Li, N., Berriz, G.F., Gibbons, F.D., Dreze, M., Ayivi-Guedehoussou, N., Klitgord, N., Simon, C., Boxem, M., Milstein, S., Rosenberg, J., Goldberg, D.S., Zhang, L.V., Wong, S.L., Franklin, G., Li, S., Albala, J.S., Lim, J., Fraughton, C., Llamosas, E., Cevik, S., Bex, C., Lamesch, P., Sikorski, R.S., Vandenhaute, J., Zoghbi, H.Y., Smolyar, A., Bosak, S., Sequerra, R., Doucette-Stamm, L., Cusick, M.E., Hill, D.E., Roth, F.P., & Vidal, M. (2005). Towards a proteome-scale map of the human protein-protein interaction network. Nature, 437, 1173.



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Salwinski, L., Miller, C.S., Smith, A.J., Pettit, F.K., Bowie, J.U., & Eisenberg, D. (2004). The database of interacting proteins: 2004 update. Nucl. Acids Res., 32, D449-451. [SBGN, 2007] Systems Biology Graphical Notation Level 1 Specification, www.sbgn.org Shmulevich I., Dougherty, E., Kim, S., & Zhang, W. (2002). Probabilistic Boolean networks: A rulebased uncertainty model for gene regulatory networks. Bioinformatics, 18, 261. Shmulevich, I., Dougherty, E., & Zhang, W. (2002). From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proc IEEE, 90(11), 1778. Smith, C.L., Dickingson, P., Forster, T., Khondoker, M., Craigon, M., Ross, A.J., Storm, P., Burgess, S., Lacaze, P., Stenson, B.J., & Ghazal, P. (2007). Quantitative assessment of human whole blood RNA as a potential biomarker for infectious disease. Analyst, 132, 1200-1209. Soon-Hyung Yook, Z.N.O.A.-L.B. (2004). Functional and topological characterization of protein interaction networks. PROTEOMICS, 4, 928-942. Sorokin, A., Paliy, K., Selkov, A., Demin, O., Dronov, S., Ghazal, P., & Goryanin, I. (2006). The pathway editor: A tool for managing complex biological networks. IBM J. Res. Dev. 50, 561-573. Stelzl, U., Worm, U., Lalowski, M., Haenig, C., Brembeck, F.H., Goehler, H., Stroedicke, M., Zenkner, M., Schoenherr, A., & Koeppen, S. (2005). A human protein-protein interaction network: A resource for annotating the proteome. Cell, 122, 957. Watts, D.J., & Strogatz, S.H. (1998). Collective dynamics of `small-world’ networks. Nature, 393, 440. Watterson, S., Marshall, S., & Ghazal, P. (2008). Logic models of pathway biology. Drug Discovery Today, 13, 447-456. Uetz, P., Dong, Y-A., Zeretzke, C., Atzler, C., Baiker, A., Berger, B., Rajagopala, S.V., Roupelieva, M., Rose, D., Fossum, E., & Haas, J. (2006). Herpesviral protein networks and their interaction with the human proteome. Science, 311, 239-242. Werhli, A. & Husmeier, D. (2007). Reconstructing gene regulatory networks with Bayesian networks by combining expression data with multiple sources of prior knowledge. Statistical Application in Genetics and Molecular Biology, 6, 15

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Chapter II

Systems and Control Theory for Medical Systems Biology Peter Wellstead The Hamilton Institute, National University of Maynooth, Ireland Sree Sreenath Case Systems Biology Initiative, Case Western Reserve University, USA Kwang-Hyun Cho Korea Advanced Institute of Science and Technology (KAIST), Korea Olaf Wolkenhauer University of Rostock, Germany

abstract In this chapter the authors describe systems and control theory concepts for systems biology and the corresponding implications for medicine. The context for a systems approach to the life sciences is outlined, followed by a brief history of systems and control theory. The technical aspects of systems and control theory are then described in a way oriented toward their biological and medical application. This description is then used as a reference base against which to indicate specific areas where systems and control theory aspects of systems biology have strong medical implications. Specifically, two systems biology projects are described as examples of where methods from systems and control theory play an important role.

INTR OD UCTI ON In this chapter the authors give their experiences gained working at the interface between the biological/medical sciences and the physical/engineering systems sciences. In doing so we attempt to convey

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Systems and Control Theory for Medical Systems Biology

the contributions that the physical, mathematical and engineering sciences have made, and will continue to make, to innovations in biology and medicine. In this context we stress the role played by systems and control theory in the development of general principles for biological systems, and in particular the understanding of dynamical phenomena in biology and medicine. According to our experiences, systems methods are influencing the biology research sector through a series of evolutionary scientific steps, as follows: • • •

•

Stage 1: High-throughput biochemical instrumentation was (and continues to be) developed to provide rapid measurement and generation of data. Stage 2: To meet the need to process data generated in stage 1, data processing methods are being developed to extract information from very large data records. Stage 3: The information from stage 2 is used to calibrate mathematical models with which to visualise an underlying biological process. This is the current evolutionary state in systems biology. Stage 4: Control and systems theory are applied to the mathematical models of stage 3 to provide understanding of biological behaviour and underlying principles. In summary, the sequence goes from:

measurement → data → information → visualisation → understanding. The current state of the art is that the value of in-silico simulation of biological phenomena is becoming appreciated. Even so, most biological measurement techniques are designed to collect static data, whereas time course data is required to develop mathematical models for visualising system dynamics by in-silico simulation. It is not always appreciated that, as a result of poor data, the calibration and structural correctness of mathematical models is often suspect. Likewise, there is currently little appreciation of the fundamental importance of control and systems theory in understanding biological and physiological phenomena and principles. On the other hand, the role of systems and control theory is clearly established in the medical community through the understanding that it gives to physiological function. Under the historical influence of Claude Bernard’s ideas, as embodied in Cannon’s concept of homeostasis (Bayliss, 1966, Cannon, 1932), feedback control is central to many aspects of current medical understanding, although this is usually intuitive and non-theoretical in nature (Tortora, 2003). Since Cannon’s work in the 1930’s, other researchers have expanded upon the homeostatic feedback principle (Sterling, 2004) in its specific medical and physiological contexts. In the meantime however, systems and control theory has expanded scientifically and progressed to become a mature scientific discipline with fundamental relevance to all areas of scientific endeavour. Throughout this 70-year period of separate development, the medical concepts of control systems and the mathematical tools of control and systems theory have diverged. The aim of this chapter is to reconnect the medical ideas of feedback with mainstream theory by explaining areas where control and systems theory can contribute. We consider this to be vitally important to our scientific futures. For, as indicated above and documented in the recent report Systems Biology: a vision for engineering and medicine (Royal Academy, 2007), the use of systems theory and control concepts will be essential to our understanding of biological systems for medicine.

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Systems and Control Theory for Medical Systems Biology

BRIEF

HIST ORY OF C ONTR OL AND SYSTEMS

THE ORY

Control and systems theory have their origins in the 1700’s with practical devices designed to regulate speed in wind, water and steam energy sources. In the hurly burly of the Industrial Revolution, design changes to improve the performance of feedback regulators rapidly outstripped their designer’s ability to predict their dynamical behaviour. However, as the new invention spread to astronomical instruments, scientists such as Airey and Maxwell became interested. In this context, the appearance of Maxwell’s paper ‘On Governors’ (Maxwell 1867) was a pivotal point in control and systems theory. It gave a mathematical basis for understanding the stability of physical systems and made the mathematical analysis of engineering systems respectable. This process of technical and theoretical development expanded rapidly with industrial growth in the 1800’s. This era is ably described in the historical account (Bennett 1979). The need for analysis and design methods for electronic amplifiers, just as mechanical regulators before, led to the next crucial development in control and systems theory – the systematic stability analysis and design in the frequency domain. The 1930’s framework set by Nyquist (1932), Bode (1945) and Shannon (1948), informed theoretical developments for twenty five years until the needs of aerospace led to an alternative time-domain framework for the theory of signals and systems (Bennett, 1993). The 1950’s saw the beginning of a golden age of theoretical and technical advances in control and systems theory. An age during which research became an international endeavour, with theoretical developments emerged rapidly and from numerous independent sources. It resulted in what we have now: control and systems theory as a mature discipline covering: analysis and design of feedback systems, optimal control theory, multivariable systems theory, modelling, systems identification and much more. The following paragraphs will outline these as they relate to systems biology for medicine.

OUT LINE OF C ONTR OL AND SYSTEMS

THE ORY METH ODS

Control and systems theory, together with methods from communication theory, offers a unified structure within which to mathematically represent, analyse, understand and potentially modify the dynamical behaviour of systems and signals. The principle of homeostasis means that control is accepted in physiology and medicine (Tortora, 2003), also there are books upon basic control and systems theory in medicine (Riggs, 1976). However in the years subsequent to Cannon’s work control and systems theory has developed into a complete theoretical and analytical framework for understanding the behaviour of dynamical systems. In the following we outline the components of this framework.

Mathematical Models for C ontrol and S ystems A nalysis The primary purpose of mathematical models is to allow the dynamical behaviour of systems to be analysed for design, performance prediction and control (Crandall, 1968). For linear systems a classical representation of system dynamics is the transfer function model. Such models, developed from the analysis of frequency response systems, have theoretical foundations in Laplace transform methods and complex variables (Smith, 1966). Transfer function methods are not generally used in systems biology applications because they are designed for linear systems. The nonlinear dynamics encountered

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Systems and Control Theory for Medical Systems Biology

in biochemical reactions is catered for in the alternative form of control and systems model - the state space model (Friedland, 2005). The state space representation is based upon sets of coupled first-order differential equations such as occur naturally in mathematical models of metabolic pathways and cell signalling. Moreover, the state space form accommodates nonlinear dynamical features such as those that appear routinely in biology/physiology. The control and analysis of state space systems is however only fully developed for the case of linear systems. A range of theoretical methods for stability and performance analysis of nonlinear state space equations exists (Freeman and Kokotovic, 1996) and there are methods especially tuned for state space structures found in the life sciences. In the following, and unless stated, we will assume that a state space model form is required or used. (Note that hybrid models that combine continuous dynamics (e.g. reaction kinetics) and logical processes (e.g. in gene regulation), and/or pure time delays (e.g. transport processes) are more complex to analyse.).

Modelling Methods and C omputer B ased S imulation The methods for deriving and developing mathematical models of dynamical systems have been thoroughly developed by the control and systems community, (Wellstead, 1979, MacFarlane, 1970). These physical systems methods, suitably augmented by biochemical reaction methods (Cornish-Bowden, 2004), provide a conceptual basis and practical framework for constructing the differential equation/state space models needed to describe dynamical phenomena in cell biology and physiology. The rapid and easy visualisation of the dynamical behaviour of these models is a basic tool in control and systems analysis and there is a wide range of numerical implementations of dynamical systems simulators for digital computers. A de facto standard for such simulation (and originally developed by control and dynamics experts) is MATLAB (Higham and Higham, 2005). This software has numerous accessories for control and systems analysis and allows the development of specialised toolboxes. One such toolbox is the Systems Biology Toolbox, which is specifically for state space models of signalling and metabolic pathways (Schmidt and Jirstrand, 2006). The ability to easily visualise the behaviour of a complex dynamical system from its mathematical model has had a particular impact in medicine and physiology (Hunter and Borg, 2003). The multiscale methods needed by such areas however require more general modelling software to allow spatial as well as temporal information to model organ and tissue function (Hunter et. al. 2006). In the same spirit, the simulation of metabolic systems and in particular in-silico pharmacokinetics and pharmacodynamics have profited from dynamical modelling methods founded in systems and control theory.

System Identi.cation and Data Analysis Writing down the equations of what describes a metabolic process, signalling pathway, gene regulation system or physiological process is only one aspect of mathematical modelling in systems biology. The more demanding aspects are determining (a) whether the model structure is valid (structure identification) or (b) determining the numerical value of the various model parameters (parameter estimation). These two tasks are part of the area known in control and systems theory as system identification. A good view of basic ideas in systems identification is the classic engineering text (Eykhoff, 1974), while statistical time series approaches are covered in an accessible manner elsewhere (Box and Jenkins, 1970).

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System identification is key to creating good models in systems biology for medicine, since it is commonplace for coefficients of models to be unknown, and in many cases the structure of the pathways is uncertain. Indeed some of the most biologically interesting contributions in systems biology have been where system identification has shown that signalling pathways based on biological deduction were wrong (Swameye, et. al. 2003). Likewise, the use of parameters from the literature is a poor compromise when they can be directly estimated for the experimental situation in hand.

Identi.ability The degree to which a system can be determined from measured data is termed identifiability (Wellstead, 1975) and it is an important concept. Specifically, in some cases it is impossible to uniquely identify a system uniquely from the available measured data. There are two aspects to this. The first relates to the structure of the system, whereby for certain interrelations in the system it is impossible to unambiguously determine particular parameters or distinguish causality. Feedback structures of the kind found in medical physiology are one such form that gives identifiability problems in distinguishing between forward signal transmission and feedback transmission paths. The further aspect concerns whether the system modes are sufficiently excited to allow identification from the measured data. This is of particular relevance to medical systems biology where data is often unsuitable for identification because of limitations on what ‘input’ perturbations are possible. The topic of experiment design is relevant here (Zarrop, 1979).

Random Processes in Control and Systems Theory Of equal importance to the application of systems identification itself is the thorough analysis and validation of the time course data associated with experimental procedures. All measured data is subject to error and the correct treatment of such data from dynamical processes is the aim of random data analysis. A comprehensive and practical reference to these methods is (Bendat and Piersol, 2000). The key issue here is that all measurement processes are subject to distortion (both systematic and random). Likewise the underlying processes that drive the system may themselves be stochastic in nature and require characterisation with the tools of probabilistic data analysis (Papolis and Pillai, 2002).

C ontrol S ystem B asics Feedback Structures Control and systems theory gives us a deep understanding of feedback in its practical and theoretical aspects. From the application of feedback in engineering systems and machines, we have developed a complete theory of feedback in linear dynamical systems. This has been mainly applied to designing and building devices that depend upon closed loop feedback control for their performance. In systems biology, the knowledge won in technological development helps us to understand the role of feedback loops in biological processes. In particular, experience of design of technological control systems allows analogies to be found in living systems for such principles as design for regulation against disturbances (c.f. homeostasis), set-point tracking and feedforward compensation. The better understanding of biological, metabolic and physiological function that this affords allows us to predict consequences of

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Systems and Control Theory for Medical Systems Biology

interventions that disturb physiological and biological loops. This is particularly true where the system has complex crosstalk between interacting channels in which multi-input, multi-output control system analysis (Skogestad and Postletwaite, 1996) can predict the unusual responses that can occur under feedback conditions.

Stability and Transient Response The analysis of time course (transient) behaviour is basic to control and systems theory, and its transfer to the understanding of biological dynamics is of paramount value. There is a wide range of theoretical tools in this area, but the most immediately relevant are drawn from state space analysis. They offer insights into the possible convergence points (e.g. steady state) of systems, stability properties and transient performance. Stability analysis of nonlinear systems is particular relevant to systems biology (Slotine, 1991), since all but the most basic of mathematical models of biological systems are nonlinear with potentially complex dynamical behaviour. Thus stability methods based upon Lyapunov analysis (Bacciotti and Rosier, 2005) and the special structures that occur in life science systems provide insights into behaviour (Angeli and Sontag, 2003).

S ystem Properties In understanding how to control technological systems, control theorists have formalised a number of mathematical properties that are important to the understanding of systems in general. Key among these properties for systems biology in medicine are observability, controllability, sensitivity and robustness. As follows: •

•

•

•

16

Observability. In broad terms, this property relates to the ability to determine states of a system from measurements at the outputs. In systems biology for medicine, the states are concentrations of chemicals in a metabolic, signalling or physiological network. Concentrations that cannot be measured from the available data are said to be unobservable. Controllability. Similarly in broad terms, controllability is the ability of a control mechanism to manipulate all the states of a system from the inputs. This has implications in therapies that aim to adjust biochemical levels by external controls – an uncontrollable state cannot be adjusted in this way. Likewise, in certain signalling pathways it may not be possible from the inputs (e.g. receptor channels) to modify certain chemical concentrations – they are then said to be uncontrollable. Sensitivity. This property is important in understanding the constraints on performance of a dynamical systems. It relates to the sensitivity of the overall dynamical system to variations in different parts of the system. Thus changes in certain parameters (e.g. kinetic coefficients in a pathway model) may have a big influence on the observable system performance – implying a large sensitivity. Others may have only a small impact – implying insensitivity. Robustness. This property is related to sensitivity, in the sense that one purpose of negative feedback is to make a system robust (that is insensitive) to variations in certain parameters or variables. For example, one purpose of homeostatic loops is to make the metabolism robust against external variations – a side result is that it will be sensitive to others as part of a robustness/sensitivity trade off (Dorato, 1998). Robustness is recognised as an important biological principle, albeit with a slightly less formal definition, (Kitano, 2007).

Systems and Control Theory for Medical Systems Biology

T ypes of C ontrol S ystems Related to the properties exhibited by a control system is the purpose that it is intended to serve and the objective or procedure used in its design. Typically, control systems may have the objective that a system variable might be required to follow some external variation within certain limits of accuracy and speed. This would be what is termed classical servo/reference tracking control. Other control systems are set up to maximise (or minimise) some objective function in some optimal way. This is termed optimal control (Bryson and Ho, 1969). When random disturbances predominate then the controller design objective is focussed upon the disturbances. This is termed stochastic control and is treated as branch of optimal control – but more importantly uses Kalman filtering (Kalman and Bucy, 1961). The Kalman/Bucy framework is of importance to systems biology since it provides a state space framework for understanding and analysing random processes. A further controller type that is relevant to systems biology is coordinating control, where the control mechanism must combine the dual function of regulating local behaviour with coordination, (Mesarovic et al., 2004). Beyond this there are many more specialist control systems that are particular to systems forms and application. The book (Goodwin, Graebe and Salgado, 2001) is a modern text that covers almost all of control design methods and types.

EXAMP LES In this section we give two examples of systems and control theory as they occur in medical systems biology research. The examples are both concerned with the investigation of special control structures within a system, and where the existence of the structure is medically informative. In Example 1, we examine interactions between signalling pathways and the implications for positive feedback to trigger critical state transitions. In Example 2 we examine organisational structures in a complex biological process that may have simplifying implications for investigations of biomarkers and molecular targets.

E xample 1: T he D ynamical R ole of C rosstalk B etween W nt and ERK Pathways in T umorigenesis In this example, we consider the use of a mathematical state space model of two cell signalling pathways (Wnt and ERK) to investigate their interaction and its implication for cancer studies. Specifically, this is an example of how interaction (or crosstalk) between systems can be studied using systems and control theory tools – specifically state space modelling, simulation and structural analysis to identify hidden feedback loops. The Wnt pathway conveys a signal from Wnt to β-catenin such that the βcatenin level increases by inhibiting GSK-3β, which normally induces the ubiquitination of β-catenin. The increased β-catenin translocates into the nucleus and induces the expression of various oncogenes by forming a complex with TCF (the abnormal increase of β-catenin commonly occurs for colorectal cancers) (Behrens J. 2005). On the other hand, ERK pathway conveys a signal from growth factors such as EGF, PDGF to ERK through the Raf-1MEKERK cascade. The finally activated ERK (ERKpp) also induces the expression of various proliferation genes (ERK mutants are commonly observed for about 30% of all human cancers).

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Systems and Control Theory for Medical Systems Biology

Figure 1. (A) Crosstalks in the Wnt/ERK pathways and the hidden positive feedback loop formed by these crosstalks. (B) The phase diagrams for a normal status with stimulations over 100min and 500 min durations, respectively. (C) The phase diagrams for an abnormal status with stimulations over 100min and 500 min durations, respectively W nt

(B) ERKpp(nM)

(A)

R af -1

TCF ß-catenin

(C) ERKpp(nM)

X

200 150 100

0 8.5

MEK ERK

250

50

G S K -3ß

ß-catenin

t = 100 t = 500

300

9

9.5

10

10.5

11

11.5

12

12.5

13

13.5

300 250 200 150 100 50 0 10

10.5

11

11.5

12

12.5

13

13.5

14

14.5

The Wnt and ERK signalling pathways are usually considered independent, but there are reports of crosstalk between them. These include the direct activation of ERK pathway by Wnt, the activation of Raf-1 through unknown molecule X which is induced by β-catenin /TCF complex (Yun, MS et. al. 2005, Rottinger, E. 2004), and the inhibition of GSK-3β by ERKpp (Almeida M, 2005, Ding Q, 2005). If these crosstalks are taken together, then a positive feedback loop is revealed embedded in the Wnt/ ERK pathways as illustrated in Figure 1(A). The systems biology question then arises about the role of this hidden positive feedback loop (Y-K. Kwon, K-H. Cho. 2007, D. Kim. Y-K Kwan, et. al. 2007). In a normal status, the signalling molecules become activated by external stimulations to respond to environmental changes and then return to their original inactivated states as the stimulation ceases (Figure 1(B)). However, if there are some mutations and the hidden positive feedback gets enhanced by such mutations (abnormal status), then the system can sustain the activated states even after the external stimulation disappeared (Figure 1(C)). In other words, the hidden positive feedback loop in the Wnt/ERK pathways can induce an irreversible state change that leads to an oncogenic status. The state space mathematical model used to produce Figure 1(B) and (C) is shown in Box 1 (D. Kim, O. Rath, et. al. 2007). The symbols Raf, Wnt, MEK, ERK, catenin, TCF, etc are system states corresponding to the concentrations of the corresponding proteins in the signalling pathways and the mathematical model was implemented and simulated in MATLAB.

E xample 2: Using a C omplex S ystems B iology A pproach to Understand C ellular S ignaling B ehavior in A cute Myelogenous Leukemia (AM L) In this example we illustrate a systems framework developed to search for the coordinating control principles mentioned previously (Mesarovic et al., 2004). In a multilevel, hierarchical system, the task of a coordinator in the upper level is to harmonize the lower-level subsystems by influencing their functions

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Systems and Control Theory for Medical Systems Biology

Box 1. d [ Raf − 1] = Wnt + [ X ] − [ Raf − 1] dt d [ MEK ] = [ Raf − 1] − [ MEK ] dt d [ ERK ] = [ MEK ] − [ ERK ] dt d [GSK − 3 ] = Const − Wnt − [ ERK ] − [GSK − 3 ] dt d [ − catenin] = Const − [GSK − ] − [ − catenin] dt d [ − catenin / TCF ] = [ − catenin] − [ − catenin / TCF ] dt d[ X ] = [ − catenin / TCF ] − [ X ] dt

such that the overall system “goal” is advanced or attained (Sreenath et al., 2007). We demonstrate here a systematic approach to identify a coordinator in a signalling pathway. The identification of a coordinator in a signalling pathway helps in narrowing down molecular targets for further biological study or as biomarkers (for diagnosis). This example examines a conserved pathway, Janus Kinase – Signal Transducer and Activator of Transcription (JAK-STAT), that has been implicated in Acute Myelogenous Leukemia (AML) (Yu & Jove, 2004). The pathway is induced by a small protein, Interleukin-3 (IL3), that effects cell growth and differentiation (Rane & Reddy, 2002). In a healthy cell, IL3 causes transient activation of STAT5 isoform (i.e. STAT5 phosphorylation), whereas in AML, STAT5 is constitutively (continuously) active (Yu & Jove, 2004). Our beginning point is a mathematical model (including numerical values of nominal parameters) described in (Yamada et al., 2003) that has a different receptor complex, but the same downstream mechanism. To better describe the IL3-induced JAK-STAT5 mechanism, the receptor complex was modified to be compatible with the IL3 ligand. The biochemical reactions were transformed into nonlinear differential equations (Sreenath et al., 2007), resulting in a state space model with 49 states, 118 parameters, 2 outputs and IL3 as an input. We estimated 3 receptor complex parameters using semi-quantitative data (Chen et al., 2004) that expresses the relative amount of biochemical in terms of intensity. The biochemical reactions were further modularised using a hybrid method, and represented in the block diagram (Figure 2). A series of in silico experiments were performed to identify a subsystem with the coordinator characteristics (Sreenath et al., 2007). Assuming that each hierarchical system has an overall system objective, a coordinator (at a higher level) should display the following properties: (i) lower level subsystems are functionally independent; (ii) the coordinator can change the lower level subsystems functioning; and (iii) the coordinator can change the lower level subsystem behaviour such that the overall system objective is satisfied.

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Systems and Control Theory for Medical Systems Biology

Figure 2. Block diagram of the modularized JAK-STAT5 system

Figure 3. In silico simulation results. (A) nominal behavior. (B,C) describes a knockdown (elimination) of the indicated biochemical (SHP2 and SOCS respectively)

A

B

C

Results show that eliminating the negative regulators – SHP2 or SOCS – causes a behaviour category different from the nominal behaviour (Figure 3). This implies that SHP2 or SOCS modules are candidate coordinators since they are capable of changing the system behaviour. If SHP2 subsystem is a coordinator, the first coordination condition is not satisfied because of the dependency of SOCS on STAT subsystem. To test if SOCS subsystem is indeed a coordinator, a pathological condition was simulated and the parameters varied within the SOCS subsystem until the system was within its nominal behaviour category (Figure 4). This confirmed the existence of parameters in the SOCS subsystem that promote the overall pathway behaviour to return to normal physiological conditions (Figure 5). Thus, by

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Systems and Control Theory for Medical Systems Biology

Figure 4. In silico simulation results with the parameters of example 2 varied within the SOCS subsystem until the system was within its nominal behaviour category

Figure 5. The SOCS subsystem (module) as a coordinator, with the JAK-STAT5 system represented as a multilevel hierarchical system.

identifying SOCS subsystem as a coordinator in-silico experiments the number of the molecular drug targets is potentially reduced to twelve from 118 parameters – a factor of ten reduction.

C ONC LUSI ON Systems and control theory concepts have been crucial to the development of technological systems from the Industrial Revolution to date. Indeed, modern day technology depends completely upon theoretical methods of systems and control for its function. The practical evidence is that living systems also use

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Systems and Control Theory for Medical Systems Biology

systems and control methods in a structured way to, for example, (a) regulate and organise their performance, (b) achieve certain objectives and (c) resist unwanted external change. Moreover, the systems and control analysis of biological and physiological processes suggests that nature has evolved methods that are remarkably similar to systems and control theory principles used by engineers in technological applications. This in turn means that we can plausibly hope that systems and control theory analysis can be used in biology and to tease out underlying operational principles that can be of use in medicine. The homeostatic principle is the shining of example of such a principle with general application and Example 2 in this chapter presents the essence of another more modern principle with similar potential.

R eferences Academy of Medical Sciences and the Royal Academy of Engineering. (2007). Systems biology: A vision for engineering and medicine. London: Royal Academy of Engineering. Almeida, M., Han, L., Bellido, T., Manolagas, S. C., & Kousteni, S. (2005). Wnt proteins prevent apoptosis of both uncommitted osteoblast progenitors and differentiated osteoblasts by beta-catenin-dependent and -independent signaling cascades involving Src/ERK and phosphatidylinositol 3-kinase/AKT. J Biol Chem, 280, 41342-41351. Angeli, D., & Sontag, E. D. (2003). Monotone control systems. IEEE Trans. Automatic Control, 48, 1684-1698. Bacciotti, A., & Rosier, L. (2005). Liapunov functions and stability in control theory. Berlin: Springer Verlag. Bayliss, L.E. (1966). Living control systems. London: English University Press. Behrens, J. (2005). The role of the Wnt signalling pathway in colorectal tumorigenesis. Biochem Soc Trans. 33, 672-675. Bendat, J. S., & Piersol, A. G. (2000). Random data: Analysis and measurement procedures. New York: John Wiley & Sons. Bennett, S. (1979). A history of control engineering: 1800-1930. London: Peter Peregrinus. Bennett, S. (1993). A history of control engineering: 1930-1955. London: Peter Peregrinus. Bode, H. W. (1945). Network analysis and feedback amplifier design. New York: Van Nostrand. Box, G. E. P., & Jenkins, G. M. (1970). Times series analysis, forecasting and control. New York: Holden Day. Bryson, A., & Ho. YC. (1969). Applied optimal control. London: Taylor Francis Cannon, W.B. (1932). The wisdom of the body. Chicago: W. W. Norton Press. Chen, Y., Yu, W., Bunting, K. D., & Qu, C.-K. (2004). A negative role of SHP2 tyrosine phosphatase in growth factor-dependent hematopoietic cell survival. Oncogene, 23(20), 3659-3669.

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Crandall, S. H., Karnopp, D. C., Kurtz, E. F., & Pridmore Brown, D.C. (1968). Dynamics of mechanical and electromechanical systems. New York: McGraw Hill. Cornish-Bowden, A. (2004). Fundamentals of enzyme kinetics. New York: Portland Press. Ding, Q., Xia, W., Liu, JC., Yang, JY., Lee, DF., Xia, J. et. al. (2005). Erk associates with and primes GSK-3beta for its inactivation resulting in upregulation of beta-catenin. Mol Cell, 19. 159-170. Dorato, P. (1998). Non-fragile controller design: an overview. Proceedings of the American Control Conference, 2829-2831. Eykhoff, P. (1974). System identification. New York: John Wiley & Sons. Freeman, F. A., & Kokotovic, P. V. (1996). Robust nonlinear control design. Berlin: Birkhauser Verlag. Friedland, B. (2003). Control systems design: State space methods. New York: Dover Books. Goodwin, G. C., Graebe, S. F., & Salgado, M. E. (2001). Control system design. New Jersey: Prentice Hall. Higham, D. J., & Higham, N. J. (2005). Matlab Guide. New York: Society for Industrial and Applied Mathematics (SIAM). Hunter, P. J., & Borg, T. K. (2003). Integration from proteins to organs: The physiome project. Nature Reviews Molecular Cell Biology, 4, 237-243 Hunter, P. J., Li, W.W., McCulloch, A. D., & Noble, D. (2006). Multiscale modelling. Computer, 39, 48-54. Kalman, R. E., & Bucy, R. (1961). New results in linear filtering and prediction theory. Trans. ASME J. Basic Engineering, 35, 2-34. Kitano, H. (2007). A robustness-based approach to systems-oriented drug design. Nature Reviews Drug Discovery, advance online publication, 23 February | doi :10.1038/nrd2195. Kim, D., Kwon, Y.-K., & Cho, K-H. (2007). Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways. BioEssays, 29 (1), 85-90. Kim, D., Rath, O., Kolch, W., Cho. K-H. (2007). A hidden oncogenic positive feedback loop caused by crosstalk between Wnt and ERK Pathways. Oncogene, (online publication 22 January 2007; doi: 10.1038/sj.onc.1210230). Kwon, Y.-K., & Cho, K.-H. (2007). Boolean dynamics of biological networks with multiple coupled feedback loops. Biophysical Journal, 92 (8), 2975-2981. MacFarlane, A. G. J. (1970). Dynamical system models. London: Longman. Maxwell, J. C. (1867). On governors. Proceedings of the Royal Society, 16, 270-283. Mesarovic, M. D., Sreenath, S. N., & Keene, J. (2004). Search for organising principles: Understanding in systems biology. IEE Systems Biology, 1(1), 19-27

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Nyquist, H. (1932), Regeneration theory. Bell Systems Technical Journal, 11, 126-147. Papoulis, A., & Pillai, S. U. (2002). Probability, random variables and stochastic processes. New York: McGraw Hill. Rane, S. G., & Reddy, E. P. (2002). JAKs, STATs, and Src kinases in hematopoiesis. Oncogene, 21, 3334-3358 Riggs, D. S. (1976). Control theory and physiological feedback mechanisms. New York: Robert Krieger Publishing. Rottinger, E., Besnardeau, L., & Lepage, T. (2004). A Raf/MEK/ERK signaling pathwayis required for development of the sea urchin embryo micromere lineage through phosphorylation of the transcription factor Ets. Development, 131, 1075-1087. Schmidt, H., & Jirstrand, M. (2006). Systems biology toolbox for MATLAB: A computational platform for research in Systems Biology. Bioinformatics, 22 \(4), 514-515. Shannon, H. (1932). The mathematical theory of communication. Bell System Technical Journal, 27, 379-623. Skogestad, S., & Postlethwaite, I. (1996). Multivariable feedback control. London: John Wiley and Sons. Slotine, J-J., and Li, W. (1991). Applied nonlinear control. London: Prentice Hall. Smith, M. G. (1966). Laplace transform theory. New York: Van Nostrand Reinhold. Sreenath, S. N., Soebiyanto, R. P., Mesarovic, M. D., & Wolkenhauer, O. (2007). Coordination of crosstalk between MAPK-PKC Pathways: An Exploratory Study. IET Systems Biology, 1(1), 33-40. Sterling, P. (2004). Principles of allostasis: Optimal design, predictive regulation, pathophysiology and rational therapeutics. In J. Schulkin (Ed). Allostasis, Homeostasis, and the Cost of Adaptation, (pp. 3245), Cambrige: Cambridge University Press. Swameye, I., Müller, T.G., Timmer, J., Sandra, O., & Klingmüller, U. (2003). Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by data-based modeling. Proc. National Academy of Science, 100, 1028-1033. Tortura, G. J., & Grabowski, S. R. (2003). Principles of anatomy and physiology. New York: John Wiley and Son. Wellstead, P. E., & Edmunds, J. M. (1975). Least squares identification of closed-loop systems. International Journal of Control, 21(4), 689-699. Wellstead, P. E. (1979). Introduction to physical system modelling. Oxford: Academic Press. Yamada, S., Shiono, S., Joo, A., & Yoshimura, A. (2003). Control mechanism of JAK/STAT signal transduction. FEBS Lett., 534, 190-196. Yu, H., & Jove, R. (2004). The STATs of cancer - New molecular targets come of age. Nat. Rev. Cancer, 4, 97-105.

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Yun, MS., Kim, SE., Jeon, SH., Lee, JS., & Choi, KY. (2005). Both ERK and Wnt/beta-catenin pathways are involved in Wnt3a-induced proliferation. J. Cell. Sci., 118, 313–322. Zarrop, M. B. (1979). Optimal experiment design for dynamic system identification. Lecture notes in Control and Inference Science (21). Berlin: Springer.

K ey T erms Closed Loop Feedback Control: This is the process of continuously measuring the output of a system and using a modified version of the measured output at the systems input so as to alter the overall performance of the system. Control Theory: The set of mathematical techniques used to analyse and design control systems. Data Analysis: The analysis of time course data from a system in order to understand the nature of the signal generating mechanisms associated with a system. These are often unwanted noise or errors in the process and are used to modify or correct the mathematical model. Dynamical System: An assembly of components or sequence of reactions whose performance can only be completely described by a study of its behaviour over time. Feedback: The technique of monitoring information from one part of a system and using it to modify a system element at some point prior to the monitoring point. If the monitored information is used to add to the system element it is positive feedback, if it is used to subtract from the system element it is negative feedback. Frequency Domain: The name given to a mathematical space into which mathematical models are transformed for systems and control studies using harmonic analysis of the time course data. This is highly suited for linear systems – in medical systems biology most systems are non-linear. In-silico Simulation: The use of a special computer programme to solve the equations of a mathematical model and produce a set of plots of model parameters over time. Linearity: Is the property of a system where if two inputs sequences Xa and Xb produce responses Ya and Y b, then Xa+Xb will produce the response Ya+Y b . The system is said to be linear – most biological and medical systems do not satisfy this criteria and are said to be non-linear. Mathematical Model: A set of equations, usually ordinary differential equations, the solution of which gives the time course behaviour of a dynamical system. The set of equations for example 1 is an example of a mathematical model. MATLAB: The name of a widely used proprietory software package that is especially suited to the simulation of dynamical system models and their analysis. It is produced by MathWorks Inc. It is adapted from a public domain package of the same name – public domain equivalents are available as Octave and Scilab. Pharmacokinetics: This refers to the dynamical mechanism by which a drug is absorbed, and processed by the body

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Systems and Control Theory for Medical Systems Biology

Pharmacodynamics: This refers to the analysis of the biochemical and physiological effects of drugs and the mechanisms in which they work. Stability Analysis: That part of systems and control theory which is used to study and predict the stability or instability characteristics of a system from a knowledge of the mathematical model. State Space: The name given to the mathematical space into which mathematical models are put for systems and control studies using temporal analysis of the time course data. State space (or time domain) analysis is suitable for linear or non-linear systems analysis. This is therefore highly suited to medical and systems biological analysis. System Identification: The analysis of time course data from a system in order to deduce the nature of the system and the values of parameters that could be used in a mathematical model to reproduce the time course data in simulation. Systems Theory: The set of mathematical techniques used to analyse and understand the (dynamical) behaviour of systems. Transfer Function: The name given to the frequency domain representation of a functional system module with distinct input and output points.

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Chapter III

Mathematical Description of Time Delays in Pathways Cross Talk S. Nikolov Institute of Mechanics and Biomechanics, Bulgaria V. Petrov Institute of Mechanics and Biomechanics, Bulgaria V. Kotev Institute of Mechanics and Biomechanics, Bulgaria G. Georgiev Institute of Mechanics and Biomechanics, Bulgaria

abstract In this chapter we investigate how the inclusion of time delay alters the dynamic properties of (a) delayed protein cross talk model, (b) time delay model of RNA silencing (also known as RNA interference), and (c) time delay in ERK and STAT interaction. The consequences of a time delay on the dynamics of those systems are analysed using Hopf’s theorem and Lyapunov-Andronov theory. Our analytical calculations predict that time delay acts as a key bifurcation parameter. This is confirmed by numerical simulations.

INTR OD UCTI ON The aim of this review is to give an extended analytical consideration of the role of time delay in the behaviour associated with dynamical models: (i) delayed protein cross talk model; (ii) time delay model of RNA silencing and (iii) time delay in ERK and STAT interaction. Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Mathematical Description of Time Delays in Pathways Cross Talk

Some of the results presented here are obtained and published in the papers (Nikolov, Kotev, Georgiev, & Petrov, 2006; Nikolov, Kotev, & Petrov, 2006a; Nikolov, Kotev, & Petrov, 2006b; Nikolov, Vera, Wolkenhauer, Yankulova, & Petrov, 2007; Nikolov & Petrov, 2007; Nikolov, Vera, Kotev, Wolkenhauer, & Petrov, 2008), but new considerations and improvements are also made. The investigations, conducted on time-delay mathematical models, examine how the time-delay influences the processes of protein synthesis, the RNA silencing and the interaction of the ERK and STAT proteins. Using the LyapunovAndronov theory and the Hopf theorem, the bifurcation values of the time delay are discovered, the zones of stability and instability are determined, and from there – the zones of norm and pathology (cancer) for each process. Thus, the greatest advantage of such an approach is revealed, namely – the theoretical forecast (prediction) of various diseases, including cancer.

D ynamical A spects of Protein C ross T alk and T ime D elay

The notion cross talk is introduced in the intracellular kinetics to denote the mutual interaction between signalling pathways (Wolkenhauer, Ullah, Wellstead, & Cho, 2005; Wolkenhauer, Streenath, Wellstead, Ullah, & Cho, 2005). It is realized by corresponding cross talk of the pathways elements, i.e. proteins. So the study of protein cross talk is necessary step in investigating the nature of pathways cross talk. The last is also necessary to analyze more complex networks of pathways. In some cases authors talk just about protein interactions having in view interaction between at least two proteins (Pircher, Petersen, Gustafsson, & Haldosen, 1999). On the other hand, in terms of systems theory, the protein interaction can be defined as feedback between two proteins. That’s why this type of interaction is also called feedback loop. Let us consider a simple hypothetical interaction between two proteins X and Y presented by the following kinetic equations:

dx = k1 y dt

(1.1.1)

dy = − k2 x − k1 y dt

(1.1.2)

where x and y are the concentrations of the proteins X and Y respectively. The kinetic sense of the system (1.1.1)-(2) consists in the following two processes: (i) The protein Y spontaneously degrades in a protein X with a reaction rate constant k1; (ii) The protein X activates the degradation of protein Y with a proportionality coefficient k2. The system (1.1.1)-(2) can be written in the form of following linear oscillator with attenuation:

d2x dx + k1 + k1k2 x = 0 2 dt dt

(1.1.3)

Here the rate constant k1 plays role of a friction coefficient of the oscillator. Let us further suppose that the protein X needs some time τ to activate the degradation of protein Y. That means the rate of degradation

dy (t ) of Y in the moment t, is proportional to the concentration x(t dt

– τ) of X in a previous moment t – τ. Thus instead of (1.1.1)-(2), we should write:

28

Mathematical Description of Time Delays in Pathways Cross Talk

dx = k1 y dt dy = − k2 x(t − ) − k1 y dt

(1.1.4) (1.1.5)

The equations (1.1.4)-(5) are called differential equations with time delay. If the time delay τ is sufficiently small, we can apply appropriate procedure to analyze the role of τ in the qualitative behavior of the system (1.1.4)-(5). For this purpose we develop the function x(t – τ) in Taylor’s expansion:

x(t − ) = x(t ) −

2  d 2 x(t )  dx(t ) +   + ... dt 2  dt 2 

(1.1.6)

and retain only the first, second and third (i.e. up to quadratic one with respect to τ) terms. It is well known that, replacing x(t – τ) with higher order approximation of a Taylor’s series is not better than applying lower order approximation (Elsgoltz, 1957; Driver, 1977). The reason of this paradoxical phenomenon consists in the circumstance that the higher order terms in (1.1.6) are in principle not small. For example, by applying a step-by-step method (Elsgoltz, 1957; Driver, 1977) to solve a time delay system in Taylor’s presentation with higher order terms, a small parameter at the higher derivatives appears. On the contrary, in lower order terms approximation similar parameter does not appear. How detailed the statement of this circumstance is depends on the order of the system. In the present two-order case, Taylor’s series can be applied only up to quadratic approximation. Certainly, linear approximation is also admissible. Further we replace (1.1.4) in the linear approximation of (1.1.6) and write:

x(t − ) = x(t ) − k1 y

(1.1.7)

After substituting (1.1.7) into (1.1.4)-(5), the system becomes:

dx = k1 y dt

(1.1.8)

dy = − k2 x(t ) + k2 y − k1 y dt

(1.1.9)

We consider the last system is approximately equivalent to (1.1.4)-(5) when τ is sufficiently small. In a form of linear oscillator with attenuation this system looks like:

d2x dx + (k1 − k2 ) + k1k2 x = 0 2 dt dt

(1.1.10)

It is seen that the time delay τ in this case “creates” a negative friction in the oscillator. The corresponding phase plot of (1.1.10) could become of type focus if it was a knot before. That means the

29

Mathematical Description of Time Delays in Pathways Cross Talk

attenuation decreases and oscillator behavior approaches to harmonic one. When τ = k1/k2 the resultant friction disappears and the oscillator is harmonic. For τ > k1/k2 the amplitude of the oscillations amplifies with the time. If there are appropriate nonlinear terms in (1.1.1)-(2), (respectively (1.1.10)), the amplitude amplification could be restricted and stable self-oscillations would be observed.

Mathematical Modelling and C oncept “D ynamical D iseases” It is generally accepted that signalling and cell function are both dynamic processes. Analysis of such systems is primarily a matter of finding the number of steady states, their nature (stable/unstable) and of characterising the transitions between them (structural stability analysis). Pathways, understood as biochemical reaction networks, are complex systems. The complexity arises from both the presence of feedback loops in the cell (Wolkenhauer, Streenath, Wellstead, Ullah, & Cho, 2005), a relatively large number of molecules involved, and the nonlinear nature of interactions between molecules (Swameye, Mueller, Timmer, Sandra, & Klingmueller, 2003). The concept “dynamical diseases” is introduced by (Glass & Mackey, 1988) and it is used to characterize an anomalous temporal organization. The indication of a dynamical disease is the change in the dynamics of a given variable. Three types of qualitative changes in the dynamics are possible: 1) variables (which in norm don’t change) under the impact of weak random fluctuations (disturbances) lead to periodical oscillations with a big amplitude. Thus, in the regulation of a given physiological system (which in norm doesn’t possess rhythmical processes) regular oscillations may appear; 2) new periodicities may appear (occur) in a periodical process; 3) rhythmical processes may disappear and be replaced with a constant or aperiodical (chaotic) dynamics. The construction of theoretical (mathematical) models of physiological systems is a powerful tool of understanding the physiological dynamics. Certainly, the modelling should have a concrete application in the experimental and the clinical systems. The basic advantage of the theoretical models of the dynamical diseases is that they allow for the execution of systematic manipulations that are impossible to be carried out in practice. The shortcoming of these models is the existence of a dynamics (behaviour) similar to that of the clinically observed disease, but due to other factors. The cause is hidden in the limited possible number of the types of bifurcations of the stable equilibrium or the oscillating states, whereupon it is possible to achieve a qualitatively similar dynamics in various ways. Nevertheless, the investigations of the dynamical diseases with the help of theoretical models play a significant role. It consists in the development of practical methods in the diagnostics of pathological diseases and a choice of rational therapeutic strategies for their treatment. With the advance in the technologies and the design of the experiments that generate quantitative data sets, there is an increasing demand for mathematical tools to elucidate the dynamic behavior of cells. For example, (i) the influence of time delays, that are a consequence of transport, in particular – processes between the nucleus and the cytoplasm in a cell are particularly relevant to the cyclic changes observed in experiments (Wang, Zhou, Jing, & Chen, 2004; Chen, Wang, Kobayashi, & Aihara, 2004); (ii) the use of S-systems, that are a wider framework to model complex biochemical interactions with significant computational and analytical advantages (Voit, 2000). Oscillations have long been known in metabolic pathways (Heinrich & Schuster, 1996; Heinrich, Neel, & Rapoport, 2002) and are now also considered an important aspect of cell signalling (Nikolov, Yankulova, Nikolova, & Petrov, 2006; Nikolov, Yankulova, Wolkenhauer, & Petrov, 2007). In further detail, dynamical processes in the cell may play determining role in distinguishing norm and pathology of cell functions. This is due to the fact that the corresponding physiological rhythms of

30

Mathematical Description of Time Delays in Pathways Cross Talk

the cell present a set of various dynamical processes depending on multiple parameters. The normal cell is characterised by complex ensemble of rhythms in the different sub-systems, some time distinguishing by more or less expressed aperiodicity. Against this “pseudo-chaotic” back-ground, some abnormal periodicity could appear, what would be an indication of pathology (in our case – carcinoma). A sign of dynamical carcinoma would appear in the form of an unregulated cell division cycle. If we have a theory for controlling cell cycle dynamics, with this expanding knowledge, it would become increasingly apparent how the carcinoma can be medically treated. In recent years, studies of the Cell Division Cycle (CDC) have uncovered many of the genes and proteins that drive and regulate cell division (Elledge, 1996; King., Deshaies, Peters, & Kirschner, 1996; Murray & Kirschner, 1989; Sherr, 1996; Stillman, 1996). Typically, such manipulations could be achieved by introducing mutations into the genes that regulate the cycle. However, these mutations usually result in uncontrolled cell division or complete suppression of cell division, or cause the cell commit fatal errors during the cell cycle. That is why it is necessary to develop methods for gaining more precise control of the CDC by using our understanding of the dynamics of the CDC oscillator. Specifically, we need to model a mechanism that can stop and restart cell division, modulate the frequency of cell division and control the size of dividing cells (possibly breast ones). This control scheme would require only the expression of a protein that binds to and inhibits any one of the CDC proteins. Because similar control scheme would be general and requiring only the expression of a single protein, it would provide a practical means for tuning the characteristics of the cell cycle in vivo.

Physiological and B iochemical A spects of T ime D elay and F eedback Loops: T ime D elay In the analysis of gene regulatory networks one major difficulty can be often encountered (Bratsun, Volfson, Tsimring, & Hasty, 2005 ). It is the vast separation of time scales between what are typically the fast reactions (dimerisation, protein-DNA binding/unbinding) and the slow reactions (transcription, translation, degradation). In this regards, it is important to note that transcriptional and translational processes are not just slow but also are compound multistage reactions involving the sequential assembly of long molecules. Thus, these processes should be connected with a certain characteristic mean delay time. When delays in biochemical reactions are small compared with other significant time scales characterizing the genetic system, one can safely ignore them in simulations. Furthermore, time delays usually do not affect the quasiequilibrium behavior of gene regulatory networks or the mean values of corresponding observables. However, if indeed the time delays are of the order of other processes or longer, and the feedback loops associated with these delays are strong. Taking the delays into account can be crucial for description of transient processes. The fact that delayed-induced stochastic oscillations can occur during transcriptional regulation is supported by recent studies of circadian oscillations in Neurospora, Drosophila, and others. It is widely accepted now that these oscillations are caused by delays in certain elements of gene regulation networks (Schepper, Klinkenberg, Pennartz, & Van Pelt, 1999; Lema, Golombek, & Echave, 2000; Smolen, Baxter, & Byrne, 2001). It is plausible that the role of time delays in circadian rhythms has come to light because the delays in the corresponding reactions are particularly long (several hours) in comparison with other characteristic times of the system. Hence, the shorter delays present in other systems also can have a significant impact on dynamics but they may be more difficult to detect with currently available experimental methods.

31

Mathematical Description of Time Delays in Pathways Cross Talk

The Influence of Feedbacks The feedback can be defined as a capability of the system to adapt its exit in response to its control. Feedbacks are used in biology at the regulation of cell growth by inhibitor factors, produced by the cell itself, and the representation of theoretical models of the pattern structure (Glass & Mackey, 1988; Turing, 1952; Gierer & Meinhardt, 1972; Meinhardt, 1994; Murray, 2002; Miguez, Izus, & Minuzuri, 2006). They can be of two types: positive and negative. Negative feedback (NFB) occursr when a signal is caused by the expression of its inhibitor, serving for the decay or the limitation of the signal (see Figure 1). Positive feedback (PFB) (or autocatalysis) occurs when more inhibitors, or other molecules, which amplify the initial signal and lead to the stabilization of the amplitude, or the increase in the signal’s duration, cause a signal. The wide use of feedbacks and the change in their succession makes them an important factor in cell signals regulation. The time to complete transcription and translation introduces time delay in the following differential equations: .

x1 = k1 f (x2 )− 1 x1 , .

x 2 = k2 x1 −

x

2 2



(1.3.1)

where k1,k 2 are the production rate constants, γ1,γ2 are the degradation rate constants and x1 (t ) = x1 (t − 1 ), 1 > 0; x2 (t ) = x2 (t − 2 ), 2 > 0 are time delays. It is well known that time delay feedback system (1.3.1) may exhibit oscillatory behaviour and negative feedback is important for homeostasis, maintenance of system near a desired state (Thomas & d’Ari, 1990; de Jong, 2002). Usually, NFB is used for limiting the signal’s time length. The simplest kind is, when the signal excites its regulator, which, in its turn, at the reaching of a definite threshold, interrupts the signal, which, from a dynamical point of view, can be related with the appearance of a bifurcation, or stability of the equilibrium state. An example can be given with the control of the cytokine signalisation in the JAK-STAT signal pathway (Starr & Tracy, 1997; Swameye, Mueller, Timmer, Sandra, & Klingmueller, 2003; Timmer,

Figure 1. Negative feedback system. In this case the gene encodes a protein inhibiting its own expression

1

mRNA 2

protein

32

Mathematical Description of Time Delays in Pathways Cross Talk

Mueller, Swameye, Sandra & Klingmueller, 2004), where the regulator is the erythropoietin (EpoR A). JAK are soluble tyrosine kinases, which bind themselves with the cytokine receptors, transducing the signal to the STAT proteins (Sasaki et al., 2001). Beyond a definite EpoR A concentration (threshold), this pathway becomes unstable (which could be explained with the formation of new structures). After a reverse decrease in its concentration, the pathway becomes stable – related with homeostasis. After 1997, the family of discovered cytokine-inducible proteins (such as SOCS, SSI, JAB and CIS) (Freeman, 2000), which impede the determining of the cytokine signalisation, increases. These proteins take part in NFB. The physiological importance of the negative feedback can be revealed through SOCS1, which causes and inhibits an interferon γ signal. When the gene for SOCS1 is exhausted, a lethal outcome is reached. Other transgenetic experiments related with the exhaustion of a given gene show that SOCS is necessary for the control of erythropoiesis. The control of the erythropoietin reply is accomplished by means of NFB. SOCS3 takes part also in the NFB control of metabolic factors, such as: leptin and the hormone growth. Compared to NFB, PFB is less used in the signal kinetics control. It has to do with the lengthening of the signal time duration. Besides for the signal time length control, feedbacks are also applied for spatial regulation control (Hoffman, Levchenko, Scott, & Baltimore, 2002). An example can be given with the expression of the homeotic genes, controlling the development in live organisms. Their specific expression has to be determined within the organism’s development process. This occurs long after the signal is localized, and is expressed as late as in the death. NFB contributes to it’s determining in many cases. This “antiregulation” of the homeotic genes appears, as they activate their own transcription, causing stability of their initially expressed structure. The including of feedbacks in the cellular molecular structure is related with: 1. 2. 3. 4. 5.

PFB and NFB create a left-right symmetry in the vertebrate embryos. PFB can coordinate separate signals. NFB can limit the arrangement of the connections. NFB generates stability. This homeostatic function of NFB has an important role in the cells’ defence from uncontrolled growth and development, leading to cancer formations. PFB can generate instability, very often expressed in tumours. For instance, the RAS-MAP pathway is activated by an EGF receptor (hyperactive in cancer formations), which is induced in it.

In Figure 2, a more complex feedback system is shown. In this case the genes encodes a protein activating synthesis of another protein inhibiting expression of gene: positive and negative feedback.

A ndronov-H opf B ifurcation C alculations in D elayed S ystems: G eneral T heory Time Delayed Systems Delay differential equations (DDEs) are infinite-dimensional systems which find application in many phenomena of physical and biological interest. It is well known that dynamical systems with distributed delay are more general than those with discrete delay. This is because the distributed delay becomes discrete when the delay kernel is a delta function at a certain time. Dynamical systems with distributed time delay have been found in population dynamics and neural networks (Belair & Dufour, 1996; Go-

33

Mathematical Description of Time Delays in Pathways Cross Talk

Figure 2. More complex feedback system. Now, genes encodes a protein activating synthesis of another protein inhibiting expression of gene, i.e. it is an example for positive and negative feedback. gene b

mRNAb

Protein B

gene a

mRNAa

Protein A

palsamy & Leung, 1997). In both biological and artificial neural networks, time delays arise as a result of the finite processing time of information. Usually, fixed time delays in models of delayed feedback systems can sufficiently approximate simple circuits having only a small number of cells. However, due to the spatial nature of the dynamical system resulting from the parallel pathways of a variety of system states, it is desirable to model them using distributed delays. In dynamical systems with delay the rate of change of the present state depends on the past state of the system (Orosz, 2004). Time development of these systems can be described by the following DDE: .

x (t ) = H (xt ,

)

(1.4.1)

where the overdot denotes the differentiation with respect to time t, the state variable is x : R → R n , while the function xt : R → X R n is defined by the shift xt ( ) = x (t + ), ∈ [− , 0]. Here we note that + the length of the delay ∈ R is assumed to be finite. The nonlinear functional H : X R n × R → R n acts on the function space X R n of R → R n functions. For the sake of simplicity, we consider a scalar bifurcation parameter, that is, ∈ R, and assume that H is a near-zero functional in xt for any λ: H (0,

34

) = 0

(1.4.2)

Mathematical Description of Time Delays in Pathways Cross Talk

Hence, DDE (1.4.1) has the trivial solution: x(t) = 0

(1.4.3)

which exists for all the values of the bifurcation parameter λ. Since the function space X R n is infinitedimensional and the dimension of the DDE (1.4.1) phase space also becomes infinite. Using a particular form for the functional H, we obtain the equation: . 0 x (t ) = h  ∫ d −

( ) (x (t + ));

  

(1.4.4)

n× n n n where h, : R × R → R , h (0, ) = 0, and the n × n matrix : [− , 0] → R is a function of the variation θ. The measure γ can be concentrated on some particular values:



m

( ) =  ( )+ ∑ ( 

+

i =1



i

) I



(1.4.5)

where i ∈ (0, ], i = 1, ..., m, m ∈ N , the non-delayed term is formally separated from the delayed terms, and the n × n identity matrix is indicated by I. Substituting measure (1.4.5) into (1.4.4) results in: .  x (t ) = h  

  

(1.4.6)

), ..., x (t − m ); )

(1.4.7)

m

0

(x (t )), ∑ (x (t − )); i

i =1

i

that is: .

x (t ) = f (x (t ), x (t −

1

where f : R n ×... × R n × R → R n and f (0, 0, ..., 0, m delays. If m = 1, then we have the form: .

x (t ) = f (x (t ), x (t −

) = 0. Thus, (1.4.7) is the general form of DDE with

); )

(1.4.8)

Stability and Bifurcations According to the Riesz Representation Theorem, the linearization of functional H with respect to xt is defined by a Stieltjes integral, that is the variational system of (1.4.1) is given as: .

x (t ) =

0

∫d (

−

;

) x (t + )

Note that (1.4.9) can also be obtained from (1.4.4) by considering part of the function h.

(1.4.9)

(x ) = x and taking the linear

35

Mathematical Description of Time Delays in Pathways Cross Talk

Similarly to the case of linear ODEs, one may substitute the trial solution x(t ) = k c t into Eq. (1.4.9) with a constant vector k ∈ C n characteristic exponent ∈ C. It results in the characteristic equation: L( ,



0

) = det 

I−



∫

d

(

,

−



) = 0 



(1.4.10)

which has infinitely many solutions for the characteristic exponent χ. The trivial solution (1.4.3) of the nonlinear DDE (1.4.1) is asymptotically stable (which in Lyapunov sense is stable, too) for the bifurcation parameter λ if all the infinitely many characteristic exponents are situated on the left hand side of the imaginary axis. Andronov-Hopf bifurcation takes place at the critical parameter value λb if there exists a complex conjugate pair of pure imaginary characteristic exponents: 1,2

( b ) = ±i



(1.4.11)

In the parameter space of the DDE, the corresponding stability boundaries are described by the so-called L-curves: R(

) = Re L (i ),

S(

) = Im L (i )

(1.4.12)

that are parameterised by the frequency ∈ R + referring to the imaginary part of the critical characteristic exponents (1.4.11). Since Eq. (1.4.10) has infinitely many solutions for χ, an infinite-dimensional version of the Routh-Hurwitz criterion is needed to decide on which side of the L-curves the steady state is stable or unstable. According to (Kolnanovskii & Nosov, 1986; Stepan, 1989) these kind of criteria can be determined by calculating complex integrals around the characteristic exponents. Thus, in case when not only one but two pairs of pure imaginary characteristic exponents (with two different frequencies) coexist at λb then a co-dimension two double Andronov-Hopf bifurcation occurs. If, a zero exponent and a pair of pure imaginary exponent coexist at λb then a fold bifurcation occurs together with an Andronov-Hopf bifurcation (Sieber & Krauskopf, 2004). These is another condition for the existence of an Andronov-Hopf bifurcation: the critical characteristic exponents χ 1,2 (1.4.11) have to cross the imaginary axis with a non-zero speed due to the variation of the bifurcation parameter λ:

d ( Re  1,2 d 

b

)

 ∂L ( ;  = Re  − ∂  

b

) /  ∂L (  

∂

;

b

)  ≠ 0   



(1.4.13)

where the first equality can be verified by implicit differentiation of the characteristic function (1.4.10). The above conditions (1.4.11) and (1.4.13) can be checked using the variational system (1.4.9). Contrarily, the super- or subcritical nature of the Andronov-Hopf bifurcation , i.e., the stability and estimated amplitudes of the periodic solutions arising about the stable or unstable trivial solution (1.4.3) can be determined only by the investigation of the third degree power series of the original nonlinear DDE (1.4.1).

36

Mathematical Description of Time Delays in Pathways Cross Talk

TIME DE LAY DYNAMICA L MODE LLING OF PHYSI OLOGICA L SYSTEMS N ORM AND PATH OLOGY

IN

D elayed Protein C ross T alk Model Time delay emerges in some cases as a constitutive property of pathways (Timmer, Mueller, Swameye, Sandra, & Klingmueller, 2004). The nature of time delay in biochemical system models is twofold. In some cases the time delay is related to processes that take an intrinsic discrete time to be accomplished (for instance, the synthesis of mRNA), while in other cases it is a consequence of the modelling approach used, in which complex sequences of events, which are not represented in detail, provoke the emergence of an apparent time delay. The processes related to gene expression induce very often time delays in the biochemical systems. Smolen et al. (2001) describes a time delay associated to the translocation of proteins and mRNAs between 50 and 100 minutes. Rateitschak et al. (2007) describes a time delay for gene transcription between 10 and 40 minutes. Finally, in Swameye et al. (2003) a time delay around seven minutes is defined and estimated for nucleocytoplasmic shuttling, which describes the delay associated with a pool of processes not described in detail in the model. Various authors have previously considered biochemical oscillators with time delay (Fall, Marland, Wagner, & Tyson, 2002; Nikolov, Kotev, Georgiev, & Petrov, 2006; Pircher, Petersen, Gustafsson, & Haldosen, 1999; Rateitschak & Wolkenhauer, 2007). Their analyses show that the introduction of a large enough time delay can sometimes change the unique equilibrium of the system and induce periodic solutions (self-oscillation), which arise from the equilibrium through an Andronov-Hopf bifurcation. The aim of this section is to elucidate how the dynamics of the interaction between pathways via cross talk is affected by the time delay associated with gene expression. The role that cooperativity of the end product repression could play in the stability of the system is also analysed.

Case Study In order to study the role of time delay in the cross talk between enzymes and repressors in protein synthesis, we use the model proposed by Jacob and Monod (Jacob & Monod, 1961) for the activation of the operon lactose in E. coli, which is considered a classical case study of gene regulatory networks. Figure 3 shows the structure of the operon and how the presence or absence of lactose induces different responses of the system. In essence, the system acts as a feedback loop where the lac repressor protein, y3, controls the synthesis of the enzyme b-galactosidase, y2, through the repression of the mRNA, y1, production. At the same time y3 is regulated by the effect of b-galactosidase, y2, in the reduction of lactose concentration. In a simple form, the system can be represented by the following mathematical model in time delayed differential equations (Nikolov, Kotev, Georgiev, & Petrov, 2006; Nikolov, Vera, Kotev, Wolkenhauer, & Petrov, 2008): dy1 k1 = − k4 y1 , dt k2 + k3 y3p1 dy dt dy3 = k7 y2 − k8 y3 . dt

2 = k5 y1 (t − ) − k6 y2 ,

(2.1.1)

37

Mathematical Description of Time Delays in Pathways Cross Talk

Figure 3. Scheme of the lactose operon in E. coli proposed by Jacob and Monod (Jacob & Monod, 1961). The system contains three structural genes (Lac Z, Lac Y and Lac A) and a regulatory gene (Lac I). In absence of lactose (a) the regulatory gene induce the production of a repressor, y3, which blocks the activation of the structural genes, and therefore the synthesis of b-galactosidase, y2. However, in presence of lactose (b), the repressor associates to lactose and changes its configuration; afterwards, the repressor is not able to block the activation of the structural genes, which allows the synthesis of mRNA, y1. After a series of structural processes including translocation to the cytosol and conformational changes, y1 induces the synthesis of b-galactosidase and lactose permease. Finally, these translocation and conformational changes provoke a time delay in the transmission of the signal between the nucleus and cytosol (τ).

(a)

(b)

where ki (i = 1,2,..,8) are the kinetic rate constants and p1 measures the cooperativity of the end product repression. There are several mathematical models available in the literature describing the lac operon (Chen, Wang, Kobayashi, & Aihara, 2004; Thomas, 1998; Yildirim & Mackey, 2003; Yildirim, Santillan, Horike, & Mackey, 2004. We have chosen this particular model because of its structural simplicity and reduced number of equations, which allow the use of analytical tools for our study. In the present work,

38

Mathematical Description of Time Delays in Pathways Cross Talk

we consider two representative values for p1 : a) p1 = 1.0 , which means non-cooperative repression (Nikolov, Kotev, Georgiev, & Petrov, 2006) and b) p1 = 2.0 , which represents cooperative repression. The delayed function k5 y1 (t − ) encodes the assumption that the rate of enzyme synthesis is proportional to the mRNA concentration in the nucleus, y1, in the moment (t – τ). Tau, τ, represents the time that takes the translocation of the mRNA to the cytosol and their configurational changes required to start the synthesis of b-galactosidase, y2. Figure 4 contains a scheme of the model discussed with the feedback loop and mechanism clearly indicated. The fixed points of the system represented by Equation 2.1.1 are defined by the following set of algebraic equations, including the rate constants of the model: _ p1 +1

y3

+

kk k k2 _ y3 − 1 5 7 = 0, k3 k3 k4 k6 k8

_

y1 =

k6 k8 _ y3 , k5 k 7

_

y2 =

k8 _ y3 k7

(2.1.2)

The first equation in (2.1.2) has always only one real positive root, which ensures that the system has only one physiologically feasible fixed point. In case of non-cooperativity, the equation describing the stationary values of y3 is simpler:

Figure 4. Simplified scheme of the lactose operon in E. coli. Legend: y1: mRNA; y2: b-galactosidase; y3: lac repressor protein. Dashed arrows represent activation, while dashed lines with a bar represent inhibition. Solid lines represent synthesis (when starting with a circle and curved line, Ө) or degradation (ø). The “clock” symbol represents a time-delay in the process. In absence of lactose, y3 is accumulated repressing the production of mRNA, y1, and ultimately the synthesis of b-galactosidase, y2. When there is a significant concentration of lactose, the formation of the complex lactose-lac repressor reduces the available free y3. In contrast, an increase in the concentration of b-galactosidase reduces the intracellular concentration of lactose, which provokes an increase in the effective amount of y3.

39

Mathematical Description of Time Delays in Pathways Cross Talk

2  _ k  4k k k 1 k y3 =  − 2 +  2  + 1 5 7 2  k3 k k 3 k 4 k6 k8  3 

   

(2.1.3)

Andronov-Hopf Bifurcation of the Time Delay Model In this section, we consider the system when the cooperativity in the end-product repression, p1 , is

  equal to one and all constants of the model are real positive numbers. Let E =  y1 , y2 , y3  denote the _

_

_



_



equilibrium point of the system. We use Andronov-Hopf bifurcation analysis and consider the time delay τ as a bifurcation parameter. The first step is to obtain the characteristic equation for the linearisation of the system near the equilibrium E. Let us consider a small perturbation about the equilibrium level defined as: _

y1 = y1 + x

_

y2 = y2 + y

_

y3 = y3 + z

In the general case, the function

k1 = k2 + k3 y3p1

(2.1.4)

k1 can be written as a MacLaurin series: k 2 + k 3 y3p1

k1 k1 k  k = = 1 1 − 3  + k3  k3   + 1   

k  + 3   

2 2

k  − 3   

3 3

 + ...   

(2.1.5)

_ p1

where = k2 + k3 y 3 and η is a polynomial of z. If we take only linear, square and cubic terms from (2.1.5) and after substitution of (2.1.4) into differential equations (2.1.1) we have:

kk k k2 k k3 dx = − k4 x − 1 23 z + 1 33 z 2 − 1 43 z 3 , dt dy = k5  − x − k 6 y , dt dz = k7 y − k8 z dt

(2.1.6)

_

where = k2 + k3 y3 when p1=1. If we neglect terms of second and third order, the stability matrix leads to the following characteristic equation: 3

+p

2

+ q + r1 = − A −

(2.1.7)

where p = k4 + k6 + k8 , q = k4 k6 + k4 k8 + k6 k8 , r1 = k4 k6 k8 , A =

40

k1k3 k5 k7 2



(2.1.8)

Mathematical Description of Time Delays in Pathways Cross Talk

This characteristic equation (2.1.7), which is a transcendental equation, cannot be solved analytically and has an indefinite number of roots (Elsgolz & Norkin, 1974; Khan & Greenhagh, 1999). In essence, we have two main tools besides a direct numerical investigation: linear stability analysis, which is valid in case of small time delays, and the Hopf bifurcation theorem (Cai, 2005). In the following section we analyse both cases.

Effects of Small Time Delays Using Linear Stability Analysis For a small time delay (i.e., τ ≈ 1 min) the method of linear stability analysis is a very convenient approach to find the bifurcation point of the system. In this case let  − ≈ 1 − ; then the characteristic equation (2.1.7) becomes: 3

+p

2

+ (q − A

)

+ r = 0

(2.1.9)

where r = r1 + A . By applying the Hopf bifurcation theorem and the Routh-Hurwitz criteria, an Andronov-Hopf bifurcation occurs at a value = b where the following conditions are satisfied:

p > 0, q − A R = p (q − A

b b

> 0, r > 0,

)− r = 0



(2.1.10)

Let us define the function h, which represent the characteristic function in case of small time delays: h( ,

)=

3

+p

2

+ (q − A

)

+ r

(2.1.11)

If we evaluate the roots of h at = b, we obtain the following values that represent the eigenvalues of the system in the approximation of small time delay: 1

= − p = − (k4 + k6 + k8 ) < 0,

2,3

= ±ik = ±i q − A



b

(2.1.12)

where i is the imaginary unit. In order to clarify the properties of the system in the Hopf bifurcation ( = b), we analyse the derivative of the eigenvalues around this value of time delay. If we differentiate implicitly h ( ( ), ) we obtain: ∂h ∂h d =− =− / ∂ ∂ d 3

2

−A + 2 p + q − A

(2.1.13)

Then, we evaluate the required derivatives of h at τb. The two roots χ2 and χ3 are complex complementary and therefore have identical real part. Thus, the result for χ2 is identical to the result for χ3. In the particular case of χ2, we obtain:

41

Mathematical Description of Time Delays in Pathways Cross Talk

d

2

d

( b ) = ikA (−3k 2 + q − A b − 2 pki ) L2 + I 2



(2.1.14)

where L = −3k 2 + q − A b , I = 2 pk . The real part of (2.1.14) has the form:

d ( Re  2  d

b

)  = 2 pk 2 A > 0  

L2 + I 2



(2.1.15)

The inequality stated in (2.1.15) is sufficient to ensure that the real part of the eigenvalue χ2(τ) at τ = τb has a positive slope. In this case, the use of the Hopf bifurcation theorem predicts that the system will have a limit cycle for a time delay with the critic value τ = τb when the approximation for small time delays is used.

Effects of Large Time Delays Using Hopf Bifurcation Analysis For larger time delays τ, the linear stability analysis of the previous section is no longer valid and we need to use an alternative approach. If we define = m + in and rewrite (2.1.7) in terms of its real and imaginary parts we obtain:

m3 − 3mn 2 + pm 2 − pn 2 + qm + r1 + A − m cos n = 0, 3m 2 n − n3 + 2 pmn + qn + A − m sin n = 0



(2.1.16)

In order to find the first bifurcation point, we set m = 0 in the equations. Then, the above two equations reduce to the following:

− pn 2 + r1 + A cos n = 0, − n3 + qn + A sin n = 0

(2.1.17)

These two equations in (2.1.17) can be solved numerically, leading to (nb0 , b0 ), the first bifurcation point. The subsequent bifurcation points (nb, τb ) satisfy the following relation: nb

b

= nb0

0 b

+ 2l , l =1,2,...

(2.1.18)

We can guarantee that (2.1.17) has at least one positive root, that is, there is at least one bifurcation point of the system. By squaring the two equations in (2.1.17), adding them, and using properties of trigonometric functions, it follows that:

n 6 + (p 2 − 2q )n 4 + (q 2 − 2 pr1 )n 2 + r12 − A2 = 0

(2.1.19)

Here we note that this is a cubic equation in n 2 that describes the stability of the system. If the condition r12 < A 2 is satisfied, the left-hand side of the equation is positive for large values of n 2 and negative for n = 0 . This means that (2.1.19) has at least one positive real root. Moreover, when we introduce the

42

Mathematical Description of Time Delays in Pathways Cross Talk

variable z = nb2 (2.1.19) reduces to:

g (z ) = z 3 + (p 2 − 2q )z 2 + (q 2 − 2 pr1 )z + r12 − A2 = 0 The derivative of this equation in z has the following value:

g ' (z ) = 3z 2 + 2 (p 2 − 2q )z + q 2 − 2 pr1 ' The interesting point is that g (z ) = b > 0 if nb is the least positive simple root of the equation (2.1.19). This property will be used in the following demonstration. Let us denote the characteristic equation without linear approximation:

H( ,

)=

3

+p

2

+ q + r1 + A −

Again, in order to clarify the properties of the system in the studied fixed point (τ = τb), we analyse the derivative of the eigenvalues around this value of time delay: A − 2 + 2 p + q − A  −

∂H ∂H d =− = / ∂ ∂ d 3

If we evaluate the real part of this equation at the fixed point τ = τb and set dm d

=

b

d  = Re   d 

=

b

=

(2.1.20)

= inb, we obtain:

nb2 3nb4 + 2 (p 2 − 2q )nb2 − 2 pr1 + q 2  L12 + I12

where L1 = −3nb2 + q − A b cos nb b and I1 = 2 pnb + A b sin nb b. The expression between brackets in the previous equation coincides with g ' (z ) = 3z 2 + 2 (p 2 − 2q )z + q 2 − 2 pr1, and then we can guarantee that g ' (z ) = b > 0. This means that this derivative is positive:

dm d

=

b

d  = Re   d 

=

b

=

nb2 g ' (nb2 ) L12 + I12

>0

(2.1.21)

Under these assumptions and according to the Hopf bifurcation theorem (Marsden & McCracken, 1976), we can guarantee that an Andronov-Hopf bifurcation occurs as τ passes through τb (Cai, 2005). The system presents an Andronov-Hopf bifurcation in the case of long time delay. Under reasonably generic assumptions, we can expect to see a small amplitude limit cycle emerging from the fixed point when the value of the time delay changes, which will provoke oscillations of the concentration of proteins and mRNA of the operon with reduced amplitude around a steady-state solution. Only with the information generated until now, it is not possible to decide whether these oscillations will be a sustained or a transient response of the system in a small area near the boundary of stability. Hence, it is necessary to calculate the so-called first Lyapunov value at the boundary of stability region R=0 of the system (2.1.1) to determine: i) the character (stable or unstable) of equilibrium state at R=0; ii) the stability (or instability) of this limit cycle at transition from R<0 to R>0.

43

Mathematical Description of Time Delays in Pathways Cross Talk

Bifurcation Analysis Using First Lyapunov Value Here, we study the advantages of the use of the first Lyapunov value (Andronov, Witt, & Chaikin, 1966; Bautin, 1984, Nikolov, 2004, Nikolov & Petrov, 2004; Shilnikov, Shilnikov, Turaev, & Chua, 2001) for investigating in detail the qualitative properties of the bifurcation behaviour for the system with respect to a time delay. For the purposes of our analysis, we derive an approximation of the model (2.1.1) (for p1 = 1; 2 ) in which y1(t – τ) is expanded as a Taylor’s series of the time delay:

dy1 k1 = − k4 y1 , dt k2 + k3 y3p1 dy2 = k5 y1 (t − dt



) − k6 y2 ≈ k5  y1 −

dy3 = k7 y2 − k8 y3 dt



⋅

y1 +

 y1  − k6 y2 , 2  2 ..



(2.1.22)

where we have retained only the first, second and third terms (i.e. up to quadratic one with respect to τ). Hence, the role of time delay in the qualitative behaviour of system (2.1.1) can be analysed. It is well known that replacing y1(t – τ) with higher order approximations of a Taylor series is not better than applying lower order approximation (Elsgoltz, 1957; Driver, 1977). The reason for this paradoxical phenomenon consists in the circumstance that the higher order terms in the second equation of (2.1.22) are, in principle, not small. For example, by applying a ‘step by step’ method (Elsgoltz, 1957; Driver, 1977) to solve a time delay system in Taylor’s presentation with higher order terms, a small parameter at the higher derivatives appears. On the contrary, in lower order terms approximation a similar parameter does not appear. The detailed statement of this circumstance depends on the order of system. In the present case, Taylor’s series can be applied only up to quadratic approximation. Certainly, linear approximation is also admissible. Following (Bautin, 1984; Nikolov, 2004; Nikolov, 2005), we calculate the so-called first Lyapunov value L1 (see the appendix in (Nikolov & Petrov, 2004) or for a detailed discussion (Andronov, Witt, & Chaikin, 1966; Shilnikov, Shilnikov, Turaev, & Chua, 2001)) at the boundary of the stability region R=0 of the system (2.1.22). In accordance with the Lyapunov-Andronov theory we have: i) the sign of the Lyapunov’s value determines the character (stable or unstable) of the equilibrium state at R = 0; ii) the character of the equilibrium state, at R = 0, qualitatively determines the reconstruction of the phase portrait (including the stability or instability of the limit cycle) at the transition from R < 0 to R > 0 (Andronov, Witt, & Chaikin, 1966; Bautin, 1984). When the system without cooperativity is considered, it is not difficult to obtain that the approximate canonical form of (2.1.22):

dx = −k4 x − c1 z + c2 z 2 − c3 z 3 , dt dy = c4 x − k6 y + c5 z − c6 z 2 + c7 z 3 , dt dz1 = k7 y − k8 z dt

44

(2.1.23)

Mathematical Description of Time Delays in Pathways Cross Talk

where:

c1 = c5 =

k1k3

, c2 =

2

k1k3 k5

k1k32 3

, c6 =

2

, c3 =

k1k32 k5 3

k1k33 4

, c4 = k5 (1 + k4 ),

, c7 =

k1k33 k5 4



(2.1.24)

Hence, the Routh-Hurwitz conditions for stability of the steady state, defined by (2.1.2), are:

p = k4 + k6 + k8 > 0

(2.1.25)

q = k4 k6 + k4 k8 + k6 k8 − c5 k7 > 0

(2.1.26)

r = k4 k6 k8 + c1c4 k7 − c5 k4 k7 > 0

(2.1.27)

R = pq − r = (k6 + k8 )(k42 + k6 k8 + k4 (k6 + k8 ) − c5 k7 )− c1c4 k7 > 0

(2.1.28)

When conditions (2.1.27) or (2.1.28) are not valid, the steady state (2.1.3) becomes unstable. This means that there are several different values for some of the rate constants, k i (i = 1, 2, 3, ..., 8), and time delay, τ, that make the coefficients R and r pass through bifurcation boundaries in the parametric space (p > 0, q > 0, r ), (p > 0, q > 0, R ) or (k1 , k 2 , ..., k8 ) where the steady state (2.1.3) could change its character (stable or unstable): R = pq – r = 0

(2.1.29)

r = 0

(2.1.30)

Following (Bautin, 1984), we call L1 the first Lyapunov value at boundary R = 0 and l1 at the boundary r = 0 . After accomplishing some algebraic operations we calculate the first Lyapunov value at the boundary R = 0 . Thus, we obtain:

L1 (

0 )=

31

4q∆

4 32 2 0

 ∆0   q ( pB1 + B3 ) + (3 p 2 + 8q )B2  − B1 B2      32 

(2.1.31)

where:

B1 = 2 ( ∆ 0 = det

' 31 2

c ), B2 =

c −

' 32 6

11

12

21

22

23

31

32

33

c −

31 6

c , B3 = 3 (

23 2

c −

23 3

c

13 7

)

13



(2.1.32)

45

Mathematical Description of Time Delays in Pathways Cross Talk

Here we note that: 11

= c1 (k4 + k8 ),

31

= (k6 + k8 )(k4 + k8 ),

12

22

= c4 k8 ,

= − (k6 + k8 ) q ,

23

= −c4 q ,

32

21

= − c1c4 + c5 (k6 + k8 ) ,

= c4 k7 , 33

13

= − k4 (k6 + k8 ),

=0



(2.1.33)



(2.1.34)

Consequently, (2.1.32) follows from: ' 31

=

11

22

−

12

21

,

' 32

=

11

32

−

12

31

From (2.1.31) it is easy to see that in this case the first Lyapunov value can be positive or negative, i.e. hard and soft loss stability can take place. Therefore, time delay is a key factor in the bifurcation behaviour of the model (2.1.22). In other words, in the case of safe boundaries, L1 < 0 , a slow drift of the parameters back into the stability region brings a system back into the original response, whereas in the dangerous case, L1 > 0 , this is generally impossible. Obviously, safe and dangerous boundaries are distinguished mainly by the stability or instability of the corresponding equilibrium state, or periodic trajectory, on the boundary (Shilnikov, Shilnikov, Turaev, & Chua, 2001). Here we could note that at the boundary of stability r = 0 (positive feedback loop), two cases occur (Bautin, 1984; Shilnikov, Shilnikov, Turaev, & Chua, 2001): If l1 is different to zero, then in case of a transition from negative values to positive ones the equilibrium state becomes unstable double point, the system has irreversible behaviour and the boundary r = 0 is dangerous. Also, from the sign of the added condition:

∆* = − p 2 q 2 + 4q 3

(2.1.35)

We can have two cases: (i.1) if ∆* < 0 , then the equilibrium state becomes saddle-knot; (i.2) if ∆* > 0 , then the equilibrium state becomes saddle-focus. If the first Lyapunov’s value l1 is zero, then the equilibrium state is stable. In the terms of model (2.1.22), using (2.1.29), we obtain the bifurcation value of time delay, τb: b

=

(k4 k6 + k4 k8 + k6 k8 ) k1k3 k5 k7

2

−

 k4 k6 k8 2  1 1 +  k4 + k6 + k8  k1k3 k5 k7 

(2.1.36)

As a consequence of our analysis, we can predict that a limit cycle will emerge if the time delay is higher than τb, while the cycle limit will vanish if the time delay is smaller. In other words, as a result of the evidence obtained through (2.1.25)-(2.1.28) and (2.1.36) we may conclude that in this case the time delay has a destabilizing role because it changes drastically the properties of the system when pass through the bifurcation point provoking the emergence of a cycle limit. For time delays longer than the bifurcation value τb, the lactose operon would present sustained oscillations with coupled periodic variations on the concentration of both proteins and the mRNA. In contrast, a time delay smaller than τb will provoke only transient oscillations of the species integrating the operon around a stable steady-state.

46

Mathematical Description of Time Delays in Pathways Cross Talk

Numerical Analysis The values chosen for the parameters and used in the numerical analysis were selected according to (Jacob & Monod, 1961; Bliss, Painter, & Marr, 1982; Pircher, Petersen, Gustafsson, & Haldosen, 1999; Fall, Marland, Wagner, & Tyson, 2002; Timmer, Mueller, Swameye, Sandra, & Klingmueller U., 2004). The analytical results stated in previous sections permit us to predict how the properties of the system vary when the parameters in the model are modified. In Figure 5 we show the dependence on k3 and k5 of the critic value of time delay in which the system suffers the transition to a stable limit cycle, τb. The value of τb is quite sensitive to changes in both parameters, especially k3. For example, a change of 50% in the value of k3 multiplies by three the value of the critical time delay, and a change of 100% in k3 increases the value of the critical time delay up to 27 minutes. This means that for very high values on k3, the transition to stable limit cycles will not appear in the system because it requires too long, biologically unfeasible, time delays (much longer than half an hour). In order to compare the predictions with numerical results, the governing equations of the model, represented by (1), were solved numerically using MATLAB (Mathworks, 2007). The use of (2.1.36) permitted us to compute a predicted value for the critic time delay of τb = 4.17 minwhen we fixed the parameters k1 to k8. In Figure 6 we illustrate the dependence of the model behaviour on the value for the time delay (around this predicted critic value τb ). Figure 6a shows a simulation of the dynamics for y1, y2 and y3 when time delay is lower than the critic value τb (τ = 2.5). After several physiologically acceptable fluctuations, the variables describing mRNA, y1, enzyme, y2 and repressor, y3 approach to constant values that describe a steady-state of the system. In other words, in this case the Routh-Hurwitz condition for stability is valid and the system (2.1.1) lies in a stable zone of its parametric space. Notice that in this case R = 0.5168 > 0 . On the other hand, Figure 6b depicts the dynamics for the case of time delays higher than the critic value (τ = 6.5) where R is negative ( R = −0.2397 ). Mathematically, this

Figure 5. Prediction of values of τb (as function of k 3 and k 5 ) using analytical formula (2.1.36)

0 

Taub

0  0  0 

 .

0.

. 0. K5

. 0.



K3

47

Mathematical Description of Time Delays in Pathways Cross Talk

state corresponds to loss of stability. According to the analytical results we can conclude that a stable limit cycle (self-oscillations) occurs. Unfortunately, the information supplied by Figure 6b cannot fully illustrate the self-oscillation behaviour of the dynamical model (2.1.1). Hence, in Figures 7a and 7b we show the self-oscillation solutions for y1 and y3. Although the stable limit cycle occurs, which coincides with the predictions of our qualitative analysis, we can see that the amplitudes of the oscillations for τ = 6.5 min are very small for the different variables (approximately 1% of the total values in the analysed state). These results shown in Figure 7 need additional discussion. The existence of cooperativity in protein-gene interactions results in large changes in activation with small changes in protein concentration (Wolkenhauer, Sreenath, Wellstead, Ullah, & Cho, 2005. On the other hand, the minimum cooperativity required for oscillations becomes small when the length of the feedback loop increases. Since in the case analysed we supposed low cooperativity and a short length feedback loop, the limit cycle has small amplitude (Fall, Marland, Wagner, & Tyson, 2002; Agnati, Tarakanov, & Guidolin, 2005). On the other Figure 6. Stable (a) and unstable (b) solution of the system (1) (p1=1) at τ = 2.5 min and τ = 6.5 min y1

(a)

y1

y3

(b)

y3

Figure 7. Periodic solutions for mRNA (a) and repressor (b) at τ = 6.5. The amplitude of the oscillation is much reduced and it represents only 1% of the values of both variables in the analysed state

y1

y3

(a)

48

(b)

Mathematical Description of Time Delays in Pathways Cross Talk

hand, the case when cooperativity is considered (p1 = 2) is shown in Figure 8. For the same values of the rate constants from k1 to k8 and time delay τ (see (2.1.37)) the stable limit cycle also occurs but now the system (1) has a periodic solution with amplitude much larger than the previous case (amplitude of the oscillation around 100% of the average value in different variables). In Figures 9a and 9b L1(λ0) (calculated on the boundary of stability R = 0 in (2.1.31)) is shown for different values of the bifurcation parameters τ, k5 and k3 (which are respectively, the rate of synthesis of b-galactosidase, y2, and the rate of repression of mRNA, y1, by lac repressor protein, y3). In Figure 9a (k1 = 248, k2 = 0.05, k3 = 1.1, k4 = 0.3, k6 = k7 = 0.2 and k8 = 1.1) both τ and k5 are considered bifurcation parameters. In this case, L1(λ0) is only negative, which ensures soft stability loss. In Figure 9b (k1 = 248, k2 = 0.05, k4 = 0.3, k5 = 0.1, k6 = k7 = 0.2 and k8 = 1.1) k3 and τ are the bifurcation parameters considered. The first Lyapunov value is also negative, and soft stability loss also takes place. This

Figure 8. Periodic (self-oscillation) solutions (a), (b) (c) and phase portrait (d) of the system (2.1.1) (p1=2) at k1 = 250, k2 = 0.05; k3 = 1.1, k4 = 0.3, k5 = 0.4, k6 = 0.62, k7 = 0.2, k8 = 0.65, = 6.5

y2

y1

(a)

(b)

y3

(c)

(d)

49

Mathematical Description of Time Delays in Pathways Cross Talk

behaviour is shown in Figures 9c-g. A stable limit cycle with small amplitude occurs, which is in accordance with the assumption of no cooperativity (p1 = 1). However, the system (2.1.22) has a very long transient regime (Figures 9d-e). Figure 10 demonstrates the dependence of the oscillation magnitude on the cooperativity p1 (considering the same numerical values of rate constants and the time delay than in case represented in Figure 9). Comparing Figure 9d-g and Figures 10a-b, we conclude that for a larger value of cooperativity (p1 = 2) the oscillation magnitudes are also larger and their frequency (during 400 min the system makes 5 spikes) is smaller than the value obtained at p1 = 1.

Figure 9. Analysis of the graphs of L1 versus the bifurcation parameters k5 ∈ [0.001,15], ∈ [8.,8.4897] (a) and k3 ∈ [1,10], ∈ [8.01, 8.05] (b). Stable solutions for k5 = 0.1 and τ = 2, small time-delay (figure 9c), and a sustained oscillation with reduced amplitude at k5 = 0.1 and τ = 8.5 (Figures 9d-g)

(a)

y1 y2 y3

y1 y2 y3

(c)

50

(b)

(d)

Mathematical Description of Time Delays in Pathways Cross Talk

Figure 9. (continued)

y1 y2 y3

y1

(e)

(f)

y2

(g)

Time Delay Model of RNA Silencing Some previous results about numerical investigations of time delay model of RNA silencing were presented in Paper D5.2 of project COSBICS. Also, in the Paper D4.3 of same project a retroviral based expression system for the effective delivery of shRNAs (small hairpin RNAs) which can induce RNAi response in BaF3 cells is established. There, it is proposed design of optimal RNA hairpin construct by employing the web application E-RNAi (Alziman, Horn, & Bourtos, 2004). As a result silencing efficiencies up to 37% of CIS protein levels are achieved. Here, we give the final form of this theoretical investigation. RNA interference (RNAi) is a relatively new mechanism for selectively silencing of genes in a variety of organisms, including plants, fungi and worms (Boese, Scaringe, & Marshall, 2003; Berezhna,

51

Mathematical Description of Time Delays in Pathways Cross Talk

Figure 10. Periodic solution (a) and phase portrait (b) of the system (2.1.28) when: p1 = 2, = 8.5, k1 = 248, k2 = 0.05, k3 = 1.1, k4 = 0.3, k6 = k7 = 0.2 and k8 = 1.1

y1 y2 y3

(a)

(b)

Supekova, Supek, Schultz, & Deniz, 2006; Hannon, 2002). It is rapidly advancing as both a target tool of validation in drug discovery and as a potential therapeutic one. As systematic or therapeutic application RNAi can be triggered by the delivery of double-stranded RNA (dsRNA), small hairpin RNA (shRNA) or micro RNA (miRNA) (Storz, 2002; Hobert, 2004). The specificity of siRNA consists in the fact that together with the corresponding proteins it forms the RNA-induced silencing complex (RISC). The last is capable of recognizing the target mRNA by hibridization and induces endocleolytic cleavage (Figure 11). As it is known, genes provide cells with instructions for making specific proteins that are “encoded” by that gene. By silencing a gene we can refer to stopping or reducing significantly the production of the specified protein encoded by the target gene (Rozema & Lewis, 2003). The cell makes a copy of the gene that encodes for the particular protein in order to initiate the protein production. It is important to note that this copy is not made of DNA, but rather of ribonucleic acid, or RNA. Moreover, it is referred to as “messenger” RNA, or mRNA. It is precisely this mRNA, manufactured in the cell nucleus that travels into the cytoplasm of a cell to the organelles responsible for protein synthesis. There, it directs the production of a protein based on the DNA sequence carried by the mRNA. When this process works uninterrupted and the protein is produced, the gene is said to be expressed. The duration of gene silencing lasted for ~1 week in rapidly dividing cells but longer than 3 weeks in nondividing cells both in vitro and in vivo, supporting the hypothesis that dilution due to cell division is the major factor controlling the duration of luciferase knockdown in rapidly dividing cells. The gene silencing duration by siRNA can be longer than that achieved with other nucleic acid-based gene inhibition strategies, whose knockdown as a rule lasts only in the order of 1-2 days. Modeling in this area (gene expression and RNA silencing) is occurring at a rapid pace (Munroe & Zhu, 2006). In the last decades the different mathematical models of a RNA silencing have been proposed with the goal to understand biological processes that are regulated by the dynamical properties of mRNA (Bergstrom, McKittrick, & Antia, 2003; Bartlett & Davis, 2006; Gafney & Monk, 2006). Generally speaking, the advantages of mathematical modeling are as follows: (i) the development of

52

Mathematical Description of Time Delays in Pathways Cross Talk

Figure 11. Schematic diagram of the basic RNA interference (taken from www.calandopharma.com)

mathematical models leads to a decrease in the number of experiments using expensive biological material, and makes it possible to predict the results of many experiments with a great precision (Edissonov & Nikolov, 2001); (ii) the use of the theory of dynamical systems leads to the creation of base models of the complex biological processes, such as: gene regulation (transcription), gene expression, protein synthesis, interaction between various molecules, etc., and allows investigation of new mechanisms of the RNA interference in qualitative ways; (iii) the results of the modeling can be presented visually and used by biologists, biochemists and immunologists in clinical practice and therapy. To our knowledge, there are only a few published mathematical models of studies regarding the kinetics of the intracellular RNAi process (Bergstrom, McKittrick, & Antia, 2003; Arciero, Jackson, & Kirschner, 2004; Raab & Stephanopoulos, 2004; Groenenboom, Maree, Hogeweg, 2005; Bartlett & Davis, 2006). Of these models, none has combined the delivery process and the interaction with the RNAi machinery in mammalian cells. For example, in (Groenenboom, Maree, Hogeweg, 2005), Groenenboom and co-authors proposed a mathematical model that contained several extensions to the core RNAi pathway, providing for siRNA degradation by Dicer (RNase III family of endonucleases) as well as primed amplification.

Models A Basic Model of RNA Silencing In (Bergstrom, McKittrick, & Antia, 2003), a mathematical description of a conceptual model of RNA silencing process is presented. In Figure 12 a schematic outline of the basic elements comprising this model is provided. We can model the steps denoted in Figure 12 by using the following autonomous system of ordinary differential equations solved with respect to the derivatives:

53

Mathematical Description of Time Delays in Pathways Cross Talk

Figure 12. Schematic diagram of the basic RNA-silencing model according to (Bergstrom, McKittrick, & Antia, 2003)

Degradation

Synthesis

Complex

dsRNA Cleavage and Association

mRNA RISC

dD = − a.D + g .C , dt dR = an.D − d R .R − b.RM , dt dC = − (g + dC ).C + b.RM , dt dM = h − d M M − b.RM dt

(2.2.1)

In this dynamical system, the state variables D,R,C,M represent the concentrations of the dsRNA, RISC, RISC-mRNA complex, and mRNA at time t. Here, we present an initial analysis of the system (2.2.1), which differs from the results presented in Bergstrom, McKittrick, and Amtia (2003). The nonzero steady state values of D,R,C,M in analytical form are: D=

_ ( g + dC )d R d d g h C ,R = C ,C = − M R ,M = a dR g+dC b b

where

(2.2.2)

= [g (n − 1) − d c ]. For parameter values:

a = 10; b = 0.1; h = 2; g = 0.1; d M = 0.5; d R = 0.1; d C = 0.05; n = 5

(2.2.3)

The steady state values (2.2.3) are positive and have physical sense. Then their stability can be analysed by linearizing the system (2.2.1) around the steady state (2.2.2) and computing the corresponding Routh-Hurwitz coefficients. In this case they all are positive and have the form:

54

Mathematical Description of Time Delays in Pathways Cross Talk

p = a + d R + bM + g + d C + bR + d M

(2.2.4)

q = a (d R + bM + g + dC + d M + bR ) + (d R + bM )( g + d C ) + + (d R + bM )(d M + bR ) − b 2 MR + ( g + d C )(d M + bR )

(2.2.5)

r = a (d R + bM )( g + d C ) − abgnM + a (d R + bM )(d M + bR ) − − ab 2 MR + a (d M + bR )( g + dC ) + bRM ( g + dC ) + bRM ( g + dC )

(2.2.6)

s = a ( g + dC )  d R (d M + bR )  − abgnd M M

(2.2.7)

l = pqr − sp 2 − r 2

(2.2.8)

It can be shown that when the steady state values C , D, M , R are positive, then the Routh-Hurwitz coefficients are positive, too. Thus, all physically meaningful steady state values are stable (in accordance with the corresponding Routh-Hurwitz criterion of stability) (Bautin, 1984), and the model (2.2.1) can be considered as realistic at least in qualitative sense.

Model with Time Delay In this section, we investigate the following system:

dD = − a.D + g .C (t − ) , dt dR = an.D − d R .R − b.RM , dt dC = b.RM − (g + d C ).C (t − dt dM = h − d M M − b.RM . dt

),

(2.2.9)

where the delay function C(t – τ) expresses the assumption that the net rate of degradation of dsRNA by Dicer and background process, and the net rate of loss of dsRNA are proportional to the triggers process of binding of mRNA to form the RISC-mRNA complex in the moment (t – τ). This is in view of the consideration that the regeneration (or degradation) of the RISC-mRNA complex needs a finite time τ. Of course, the finite time τ of regeneration can be different from this of degeneration. Because, here, in order to make the analytical investigation of system (2.2.9) easier, we shall assume that_ the two _ _ _ h ) times are equal. Hence, the system (2.2.9) has also two steady states- the trivial ( D = C = R = 0, M = dM and see (2.2.2). Further, we investigate the bifurcation structure, particularly the Andronov-Hopf bifurcation for the system (2.2.9), using time delay as the bifurcation parameter. Firstly, we obtain the characteristic equa_ _ _ _ _  tion for the linearization of the system (2.2.9) near the equilibrium E  D > 0, R > 0, C > 0, M > 0  (i.e.   all are positive and the silencing reaction controls the level of mRNA below its normal level). Next, we _ _ _ _ consider a small perturbation about the equilibrium level, i.e., D = D + x, R = R + y, C = C + z , M = M + w.

55

Mathematical Description of Time Delays in Pathways Cross Talk

Substituting these into the differential equations (2.2.9) we have:

dx = − ax + g  − z , dt dy = anx − a1 y − a2 w − byw, dt dz = a3 y − a4  − z + a2 w + byw, dt dw = − a3 y − a5 w − byw dt

(2.2.10)

where _

_

_

_

a2 = b R, a3 = b M , a4 = g + d C , a5 = d M + b R

a1 = d R + b M ,

(2.2.11)

Hence, we obtain the stability matrix in the form:  −a 0   an − a1 0 a3  0 − a3 

g−

0 − a2

0 − a4  −

a2 − a5

0

      

(2.2.12)

The stability matrix (2.2.12) leads to the following characteristic equation: 4

+ K1

3

+ K2

2

+ K3 = −

(T

1

3

+ T2

2

+ T3 + T4 )

(2.2.13)

where K1 = a + a1 + a5 , K 2 = a (a1 + a5 ) + a1a5 − a2 a3 , K 3 = a (a1a5 − a2 a3 ), T1 = − a4 , T2 = − K1a4 , T3 = −  a (a1a4 − nga3 + a4 a5 ) + a4 (a1a5 − a2 a3 ) , T4 = − a  a4 (a1a5 − a2 a3 ) + gna3 (a2 − a5 )

(2.2.14)

Generally speaking, the transcendental equation (2.2.13) cannot be solved analytically and has an indefinite number of roots. In essence, we have two main tools besides direct numerical investigation; firstly, the linear stability analysis, especially in the case of small time delay (i.e. t < 1 ), and secondly, the Hopf bifurcation theorem for larger time delay.

Andronov-Hopf Bifurcation of the Time Delay Model: Linear Stability Analysis For a small delay τ(τ < 1), the method of linear stability analysis is much convenient to find the bifurcation point. Thus, let  − ≈ 1 − , then the eigenvalue equation becomes:

56

Mathematical Description of Time Delays in Pathways Cross Talk

4

3

+p

2

+q

+ r + s = 0

(2.2.15)

By the Hopf bifurcation theorem and the Routh-Hurwitz criteria, an Andronov-Hopf bifurcation occurs at a value τ = τb where: p=

a4 + (1 − a4 1 − a4

s=−

T4 1 − a4

b

)K1 > 0,

b

)=

K 2 + K1a4 − K 4 1 − a4 b

b

> 0, r =

K 3 − T3 + T4 1 − a4 b

> 0, l = pqr − sp 2 − r 2 = 0

4

+p

3

+q

b

> 0,



(2.2.16)

+ r + s

(2.2.17)

b

where the condition a4 h( ,

q=

≠ 1 is valid. Let:

b 2

Evaluating h at τ = τb yields:

h( ,

b

)=

where k 2 = 1,2

4

+p

3

+q

2

+ k 2 p + k 2 (q − k 2 )

(2.2.18)

r . The eigenvalues of (2.2.15) at τb are: p

r p

= ±ik = ±

(2.2.19)

sp p and the type of the other pair roots depend on the sign of the equality ∆1 = − . Here we note that i r 4 is imaginary unit. If (i) ∆1 > 0 then: 3,4

=−

p ± ∆ 2i 2

2 where ∆ 2 =

3,4

=−

(2.2.20)

sp p 2 − (∆ 2 > 0 ); (ii) ∆1 < 0 then: r 4

p ± ∆2 2

where now ∆ 2 = −∆1 . Differentiating implicitly h (

(2.2.21)

( ), ) yields:

d p' 3 + q' 2 + r ' + s' ∂h ∂h =− =− 3 / ∂ ∂ d 4 + 3 p 2 + 2q + k 2 p

(2.2.22)

where: a (K − T ) + T  a4  a42 K1 + a4 K 2 + T3 a4T4 ' p = , r ' = 4 3 3 2 4 , s' = −  , q = 2 (1 − a4 ) (1 − a4 (1 − a4 )  1 − a4  2

'

) 2

(2.2.23)

57

Mathematical Description of Time Delays in Pathways Cross Talk

Evaluating the required derivatives of h at τb, we obtain:

d

1

d

( b ) = −  s

'

(

)

− q ' k 2 + (− p ' k 2 + r ' )ki  −2 pk 2 − 2k (q − 2 k2 ) i 2

L +I

2



(2.2.24)



(2.2.25)

or:

d

1

d

( b ) = 2k

2

N + 2k  pk 2 (r ' − p ' k 2 )+ (q − 2k 2 )(s ' − q ' k 2 ) i L2 + I 2

where L = −2 pk 2 , I = 2k (q − 2k 2 )i and N = p (s ' − q ' k 2 )+ (q − 2k 2 )(p ' k 2 − r ' ). The real part of (2.2.25) has the form:

d ( Re  1  d

b

) =  

2k 2 N L2 + I 2

(2.2.26)

The real part (see (2.2.26)) is always positive if N > 0, i.e., if the following conditions are valid:

s' > q'k 2 , q > 2k 2 , p ' k 2 > r ' or

q < 2k 2 , p ' k 2 < r '

(2.2.27)

So inequalities (2.2.27) are sufficient to have positive slope of the real part of the eigenvalue χ1(τ). This fact (according to the Hopf bifurcation theorem (Marsden & McCracken, 1976)) guarantees the bifurcation to a limit cycle for τ = τb.

Hopf Bifurcation Analysis It is well known that for a larger time delay τ, the linear stability analysis of the previous section is no longer effective and we need to use another approach (Marsden & McCracken, 1976; Galach, 2003; Cai, 2005; Kavasseri, 2005). The stability of (2.2.2) depends on the sign of the real parts of the roots of Eq. (2.2.15). We let χ = m + in (m,n ∈ R) and rewrite Eq. (2.2.15) in terms of its real and imaginary parts as:

m 4 + n 4 − 6m 2 n 2 + K1 (m3 − 3mn 2 )+ K 2 (m 2 − n 2 )+ K 3 m =

{

=  − m T1 (m3 − 3mn 2 )cos n + (3m 2 n − n3 )sin n  + + T2 (m 2 − n 2 )cos n + 2mn sin n  + T3 [m cos n + n sin n ]+T4 cos n },

4mn (m 2 − n 2 )+ K1 (3m 2 n − n3 )+ K 2 (2mn ) + K 3 n =

{

=  − m T1 (3mn 2 − m3 )sin n + (3m 2 n − n3 )cos n  + + T2 (n 2 − m 2 )sin n + 2mn cos n  + T3 [n cos n − m sin n ]−T4 sin n

58

}

(2.2.28)

Mathematical Description of Time Delays in Pathways Cross Talk

To find the first bifurcation point, we set m = 0. Then the above two equations reduce to: n 4 − K 2 n 2 = (−T2 n 2 + T4 )cos n + (−T1n3 + T3 n )sin n ,

− K1n3 + K 3 n = (−T1n3 + T3 n )cos n + (T2 n 2 − T4 )sin n

(2.2.29)

These two equations into (2.2.29) can be solved numerically. If the first bifurcation point is (nb , then the other bifurcation points (nb , b ) satisfy: 0

nb

b

= nb0

0 b

v = 1, 2, ...

+ 2v ,

0 b

),

(2.2.30)

By squaring the two equations into (2.2.29) and then adding them, it follows that:

n8 + (K12 − 2 K 2 − T12 )n 6 + (K 22 − 2 K1 K 3 + 2T1T3 − T22 )n 4 + (K 32 − T32 + 2T2T4 )n 2 − T42 = 0

(2.2.31)

Here we note that this is a quartic equation about n2 and the left side is positive for large values of 2 n2 and negative for n = 0 because −T4 is always negative, i.e., (2.2.31) has at least one positive real root. Moreover, to apply the Hopf bifurcation theorem, according (Khan & Greenhagh, 1999), the following theorem in this situation applies. Theorem 1. Suppose that nb is the last positive simple root of Eq. (2.2.31). Then in ( b ) = inb is a simple root of Eq.(2.2.13) and m ( ) + in ( ) is differentiable with respect to τ in a neighbourhood of τ = τb. To establish Andronov-Hopf bifurcation at τ = τb, we need to show that:

dm d

=

b

≠0

Hence, if we denote H ( ,

)=

4

d ∂H ∂H / =− = d ∂ ∂ =

− − 3

4

+ 3K1

2

+ 2 K 2 + K3 + 

−

3

+ K1

(T (T

1 1

3

+ K2

+ T2

2

+ T2

2

3

2

+ K3 − −

+ T3 + T4 )

=

=

b

d  = Re   d 

{

=

b

1

+ T3 + T4 )−  −

Evaluating the real part of this equation at τ = τb and setting

dm dt

(T

3

+ T2

(3T

1

2

2

+ T3 + T4 ), then:

+ 2T2 + T3 ) (2.2.33)

= inb yield:

n 4n + 3n (K − 2 K 2 − T12 )+ 2nb2 (K 22 − 2 K1 K 3 + 2T1T3 − T22 )+ K 32 − T32 + 2T2T4 2 b

6 b

4 b

2 1

2 1

(2.2.32)

}

2 1

L +I

59

Mathematical Description of Time Delays in Pathways Cross Talk

where:

L1 = K 3 − 3K1nb2 +

b

(n

2 b

− K 2 )nb2 + (3T1nb2 − T3 )cos nb

b

− 2T2 nb sin nb

b

and

I1 = −2 K 2 nb + 4nb3 − Let

g(

=

=

b

3

=4

3 b

− K1nb3 )+ 2T2 nb cos nb

+ (K12 − 2 K 2 − T12 )

4

Then for g

)

(K n

b

+ (3T1nb2 − T3 )sin nb

b

= nb2, then (2.2.31) reduces to:

)=

g' (

b

'

dg d

3

+ (K 22 − 2 K1 K 3 + 2T1T3 − T22 )

2

+ (K 32 − T32 + 2T2T4 ) − T42 = 0

( ) we have: = =

b

+ 3 (K12 − 2 K 2 − T12 )

2

+ 2 (K 22 − 2 K1 K 3 + 2T1T3 − T22 ) + K 32 − T32 + 2T2T4

If nb is the least positive simple root of the Eq. (2.2.31) then:

dg d

= nb2

>0

(2.2.34)

Hence: dm d

=

b

d  = Re   d 

= =

b

nb2 g ' (nb2 ) L12 + I12

>0

(2.2.35)

According to the Hopf bifurcation theorem (Marsden & McCracken, 1976) we define the following main result in this section. Theorem 2. If nb is the least positive root of Eq.(2.2.31), then an Andronov-Hopf bifurcation occurs as τ passes through τb. Here we note that a similar phenomenon appeared in the epidemic model with a time delay in vaccination for nonsexually transmitted diseases (Marsden & McCracken, 1976).

N umerical A nalysis of the T ime D elay Model In this section, we analyze numerically the time delay model constituted by Eq. (2.2.9) for the concentrations of the double-stranded RNA (dsRNA)-D(t), the RNA-induced silencing complex (RISC)-R(t), RISC-mRNA complex-C(t), and mRNA at time t, respectively. The corresponding numerical values of the model parameters are those in (2.2.3). However, we do not know the exact time point at which the RISC-mRNA complex begins to regenerate (or degrade) and assume that it takes a little bit longer;

60

Mathematical Description of Time Delays in Pathways Cross Talk

hence we set τ = 10 or 13 hours. The governing equations of the model, represented by Eq.(2.2.9), were solved numerically using MATLAB (Mathworks, 2007). The following Figures 13 and 14 demonstrate the dependence of the model behavior on the parameter τ. We fix the model parameters (see (2.2.3)) and vary the time delay τ, which from the point of view of qualitative theory plays the role of a bifurcation parameter. In Figure 13, the stable solutions for dsRNA, RISC, RISC-mRNA complex and mRNA are shown for τ = 10. It is evident that after several physiologically acceptable fluctuations, the concentrations of the dsRNA, RISC, RISC-mRNA complex and the mRNA approach constant values (equilibrium states). In other words, in this case the system (2.2.9) lies in a stable zone of its parametric space. In Figure 14 the case when τ = 13 is shown. It is seen that for the same values of the rate constants, after the Andronov-Hopf bifurcation, the stable limit cycle with period one occurs and the system (2.2.9) has periodic solutions. Thus, it means that time delay amplifies the instability of the steady state. In other words, as a result of the evidence obtained in Figures 13 and 14, we may conclude that the time delay has destabilization role in the RNA silencing process.

Figure 13. Stable solutions of the system (2.2.9) at τ = 10. The time is in hours

61

Mathematical Description of Time Delays in Pathways Cross Talk

Figure 14. Unstable periodic solutions of the system (9) at τ = 13 after introduction of large (high) dose of dsRNA

Figure 15 depicts the case when the initial dose of dsRNA is small. Many experimental studies as (Parrish, Fleenor, Xu, Mello, & Fire, 2000; Lipardi, Wei, & Paterson, 2001; Giordano, Rendina, Peluso, & Furia, 2002) suggest that larger initial doses of dsRNA engender larger silencing reactions or induce silencing more effectively. For example, in Ref. 81, the authors suggest that effective gene silencing by RNAi depends on a number of important parameters, including the dynamics of gene expression and the RNA dose. Their experiments demonstrate that different levels of silencing can be attained by modulating the dose level of RNA and the time of transfection and illustrate the importance of a dynamic analysis in designing robust silencing protocols. Thus, we expect dosage dependence to be useful in avoiding self-directed reactions. Comparing Figure 14 and Figure 15, we conclude that the time for formation of stable limit cycle in case with a small dose is larger than this with a high dose. But, on the other hand the amplitude of oscillations of dsRNA (for small initial dsRNA concentration) is longer. Note that frequency is also higher. Because greater quantities of dsRNA typically are a more reliable indicator of the presence of non-self, dosage reduces the impact of mistaken reactions to selfderived genetic material.

62

Mathematical Description of Time Delays in Pathways Cross Talk

Figure 15. Unstable periodic solutions of the system (9) at τ = 13 after introduction of a small dose of dsRNA. The time is in hours

Time Delay in ERK and STAT Interaction From the results described in the work (Pircher, Petersen, Gustafsson, & Haldosen, 1999), a model for interaction between ERK and STAT5a in CHOA cells can be derived. As it is proved in (Pircher, Petersen, Gustafsson, & Haldosen, 1999), in unstimulated cells STAT5a is complexed with inactive ERK that binds to STAT5a via its C-terminal substrate recognition domain to an unknown region on STAT5a. Then via its active site it binds to the C-terminal ERK recognition sequence in STAT5a. On the other hand, upon GH stimulation, MEK activates ERK through phosphorilation of specific threonine and tyrosine residues in ER K. The active ERK phosphorilates serine 780 in STAT5a, resulting in decreased affinity between the two proteins and dissociation of the complex. From the biochemical diagram in (Pircher, Petersen, Gustafsson, & Haldosen, 1999), we can write the following system of ordinary differential equations for the kinetics of STAT5a/S phosphorylation and ERK activation,

63

Mathematical Description of Time Delays in Pathways Cross Talk

described by concentration variables e1,e2,s1,s2 denoting concentrations of ERK-inactive, ERK-active, STAT- and STAT-phosphorylated respectively. It has the form: de 1 = − k0 e1s1 + k2 e2 − I , dt de 2 = k0 e1 (t − ) s1 (t − ) − k2 e2 + I , dt ds 1 = − k1e1 s1 + k3 s2 + A, dt ds 2 = k1e1 (t − ) s1 (t − ) − k3 s2 − A dt

(2.3.1)

where k1 is proportional to the frequency of collisions of ERK and STAT protein molecules and present rate constant of reactions of associations; k2 and k3 are constants of exponential growths and disintegrations; I > 0 and A > 0 are inhibitor and activator sources respectively, τ is time delay of ERK and STAT interaction (i.e. ERK activation and STAT phosphorylation). The source I inhibits the inactivation of active ERK, and A activates the dephosphorylation of phosphorylated STAT5a. The terms I and A can be also considered as some effective (apparent) inhibitor and activator, under condition that they present really some in-flux and out-flux of the active ERK and phosphorylated STAT5a respectively. Generally said, by introducing I and A we take into account the natural circumstance that ERK and STAT interaction is not isolated but open process in the intracellular space. We can consider I and A as algebraic values having different signs (plus or minus) and determining one or another type of behavior of the system (2.3.1). In this way (2.3.1) can be used as dynamical model of ERK and STAT interaction. A more concrete interpretation of the inhibitor I and activator A can be given in connection with the role of the SOCS proteins in linking JAK/STAT and MEK/ERK pathways. Biological responses elicited by the JAK/STAT pathway are modulated by inhibition of JAK (and respective attenuation of STAT) by a member of the Suppressors of Cytokine Signalling (SOCS) proteins. On the other hand over-expression of some SOCS family members induces activation of ERK, which can phosphorylate STATs. Further we apply the linear time delay approximation explained in one from the previous sections. As a result the relations:

e1 + e2 = e0 − k0 e1s1

(2.3.2)

s1 + s2 = s0 − k1 e1s1 (here it follows s1 – s1 > 0)

(2.3.3)

can be obtained. By replacing them in the second and fourth equation of (2.3.1-2), the last is reduced to the following two-dimensional system of ordinary differential equations (without time delays):

de1 = − k0 (1 + k2 )e1s1 − k2 e1 + k2 e0 − I dt

(2.3.4)

ds1 = − k1 (1 + k3 )e1s1 − k3 s1 + k3 s0 + A dt

(2.3.5)

64

Mathematical Description of Time Delays in Pathways Cross Talk

The system (2.3.4-5) (together with the formulas (2.3.2-3)) is considered to be equivalent to the time delay system (2.3.1) when τ is sufficiently small. Certainly, the behavior of the variables e1 and s1 (inactive ERK and non-phosphorylated STAT respectively) is leading one with respect to that of e2 (active ERK) and s2 (phosphorylated STAT). Thus we can qualify the system (2.3.4-5) as a driver of ERK and STAT cross talk and the variables e1 and s1 can be called driving variables. This is the first conclusion from the qualitative analysis of the time delay system (2.3.1) in linear approximation. The steady state value of e1 is e10 = e0 −

k (1 + k2 ) I k0 k3 (1 + k2 ) A − ( s0 − s10 ) − 0 k2 k1k2 (1 + k3 ) k1k2 (1 + k3 )

(2.3.6)

0

where s1 is determined as a positive root of quadratic equation we obtain after substituting (2.3.6) in the steady state equations of (2.3.4-5), i.e. the right hand sides of (2.3.4-5) equated to zero. To study the nature (stable or not) of the steady state we introduce in (2.3.4-5) the substitutions: e1 = e10 + x , s1 = s10 + y

(2.3.7)

where x and y are variations (small disturbances, perturbations). After corresponding linearization the variation system for x and y takes the form: dx = −  k2 + k0 s10 (1 + k2 )  x − k0 (1 + k2 )e10 y − k0 (1 + k2 ) xy, dt dy = − k1 (1 + k3 ) s10 x −  k3 + k1e10 (1 + k3 )  y − k1 (1 + k3 ) xy dt

(2.3.8)

The Routh-Hurwitz conditions for stability of the steady state (2.3.6-7) are: k2 + k3 + k0 s10 (1 + k2 ) + k1e10 (1 + k3 ) > 0

(2.3.9)

k2 k3 + k1k2 e10 (1 + k3 ) + k0 k3 s10 (1 + k2 ) > 0

(2.3.10)

It is evident from (2.3.9-10) that in the presence of time delay τ the inequalities are stronger than in the absence of τ. That means the time delay amplifies the stability of the steady state of the driver system (2.3.4-5) as well as of the whole time delay model (2.3.1) of ERK and STAT cross talk, at the condition of sufficiently small τ, i.e. in linear approximation.

Co nc lusi on In this chapter we present some results obtained from us in (Nikolov, Kotev, Georgiev, & Petrov, 2006; Nikolov, Kotev, & Petrov, 2006a; Nikolov, Kotev, & Petrov, 2006b; Nikolov, Vera, Wolkenhauer, Yankulova, & Petrov, 2007; Nikolov & Petrov, 2007; Nikolov, Vera, Kotev, Wolkenhauer, & Petrov, 2008). The main conclusions from section 2.1, where we investigate whether the inclusion of time delays alters the

65

Mathematical Description of Time Delays in Pathways Cross Talk

dynamical properties of the Jacob-Monod model (which describes the control of the b-galactosidase synthesis by the lac repressor protein in E.coli), are: •

•

•

The basic view that the time delay τ is a key factor in the dynamical behaviour of the system has been confirmed by the analytical calculations and numerical simulations. From the qualitative theory of DDE and ODE viewpoint, time delay appears as a bifurcation parameter on whose values depend the altered (stable or unstable) behaviour of the model. When no delay is considered in the synthesis of b-galactosidase, only a soft loss of stability take place, and changes of time delay through the critic value τb has reversible behaviour. This means that at the transition of R through the boundary R = 0 from positive values to negative ones a stable limit cycle emerges, i.e., selfoscillations of the system appear. Inversely, at the transition of R from negative values to positive ones the stable limit cycle disappears, i.e., the self-oscillations cease. However, when a time delay is considered the properties of the system changes drastically, and hard loss of stability emerges. For time delays longer than τb, the lactose operon would present sustained oscillations with coupled periodic variations on the concentration of both proteins and the mRNA. In contrast, a time delay smaller than τb will provoke only transient oscillations of the species integrating the operon around a stable steady-state. We can say that in this situation time delay has a destabilizing role. When simple (non-cooperative) inhibition of mRNA production by the lac repressor protein is considered (p1=1.0), oscillations in values of concentrations for proteins and mRNA appear but the amplitude of such oscillations is much reduced (around 1% of the average concentration in the cases shown in Figures 7 and 9). If the system is not able to distinguish these fine-tuning oscillations, the lac operon would act as if an effective quasi steady-state exists. From a biological perspective, it could be reasonable to think that the system presents at least local robustness with respect the concentration of lactose (which is a primary carbon source of the system), and then this reduced amplitude oscillations would not provoke a differentiated response of the system during the different phases of the oscillation. In contrast, when cooperativity in the repression of mRNA synthesis is considered (p1=2.0), the oscillations also occurs but the magnitude of this oscillations in the concentration of proteins and mRNA is actually significant. In some cases (Figures 8 and 10) the cooperativity provokes oscillations with changes all-nothing for the concentration of the proteins during the period of the oscillations. Therefore, the oscillations induced for time delays higher than the critic value τb in a system with cooperavity could provoke clearly differentiated responses of the system during the period of the oscillations. The conclusion of our analysis is that in the case of the lac operon analysed, not only time delay in galactosidase synthesis but also cooperativity in the end product repression is necessary to induce a regime of effective sustained oscillations. From a physiological viewpoint, the hard (irreversible) loss of stability might be related to the emergence of new configurations in the regulatory gene circuit that could lead the system into a pathologic state. Similar behaviour has been already detected and discussed in other biological systems with different nature such as cardiac pulsations and ocular system (Petrov & Nikolov, 1998; Petrov & Nikolov, 1999), but this conclusion that we point here for hard stability loss is suggested here by the first time for protein synthesis systems.

The main conclusions from investigations in section 2.2 of time delay model of RNA silencing are as follows.

66

Mathematical Description of Time Delays in Pathways Cross Talk

Besides the stability, the original model (2.2.1) captures the following features of RNA-silencing dynamics from empirical studies (As it is argued in paper (Bergstrom, McKittrick, Antia, 2003)): • • •

The model detects and degradates the initial dose of dsRNA by essential initial drop in dsRNA concentration. It demonstrates a rapid generation of sequence-specific siRNA by rapid rise of RISC in the early stages of reaction. It shows an amplification of the response, producing “secondary” dsRNA and siRNA molecules by the increase in dsRNA concentration.

In other words, if the system possesses a stable equilibrium state, then this corresponds to a normal silencing process. On the other hand, the existence of unstable equilibrium states, stable limit cycles (self-oscillations) or chaotic attractors in this case corresponds to a pathology, i.e. an abnormal RNA silencing process. To our knowledge, in the literature up until now, time delay models describing gene silencing have not been suggested or investigated. Therefore, this investigation of ours is a new outlook on the problems and the factors influencing silencing. From the accomplished analytical and numerical calculations it becomes clear that time delay τ is a key factor in the behavior of model (2.2.9). In this case it has a destabilizing role on the silencing process. In terms of dynamical systems τ plays the role of a bifurcation parameter. If τ (i.e. the time necessary for the regeneration (or degradation) of the RISC-mRNA complex)) is greater than a certain (bifurcation) value in model (2.2.9), through Andronrov-Hopf bifurcation appears a self-oscillation related with an abnormal silencing mechanism. A possible cause is that the longer time brings about a production of a longer dsRNA, different from the one necessary for silencing. The appearance of periodical solutions in the time delay model (2.2.9) makes its behavior much richer compared to the original model proposed by Bergstrom and co-workers in (Bergstrom, McKittrick, Antia, 2003). This allows for investigating more properties and regimes of the silencing mechanism. From the simulations made in Figure 15 it is seen that at smaller initial doses of dsRNA the time for establishing of the stable limit cycle is longer, i.e. we have a longer transition period. On the other hand, however, the appearing self-oscillations are with a greater amplitude and frequency than those at a bigger initial dose of dsRNA. In particular, only the amplitude of D (dsRNA) is altered. It is held in the literature (Bergstrom, McKittrick, & Antia, 2003; Raab & Stephanopoulos, 2004; Groenenboom, Maree, Hogeweg, 2005; Bartlett & Davis, 2006), that bigger initial doses of dsRNA cause stronger silencing reactions or make silencing more effective. Moreover, it may be expected that the dependence on dosing is useful for avoiding self-directed reactions. In conclusion it may be noted that in practice time delay for generation can be different from this for degeneration. This in its turn makes the analytical investigation harder. For that reason it is assumed here that the two times are equal. From the numerical simulations (which are not shown) it became clear that the two times are very similar. For some of our conclusions an empirical verification is needed. The last section 2.3 of this chapter presents original elaboration of the ERK and STAT interaction model in the form of time delay of ERK activation and STAT phosphorylation has essential dynamical role. The basic view is that time delay τ in the RNA silencing is a key factor in the dynamical behaviour of model (2.3.1) confirmed by appropriate analytical calculations. From the qualitative theory of DDE viewpoint, time delay in this case has stabilization role.

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K ey T erms Andronov-Hopf Bifurcation: From a mathematical point of view, the onset of sustained oscillations generally correspond to the passage through an Andronov-Hopf bifurcation point. Obviously, for a critical value of a control parameter (named bifurcation), the system displays damped oscillations and eventually reaches the steady state- stable focus. Beyond the bifurcation point, a stable solution

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arises in the form of a small-amplitude limit cycle surrounding the unstable steady state [Golbeter, A., Nature, 420:238-245, 2002]. This bifurcation is very typical for biological systems. Chaotic Dynamics: Chaotic motions are based on homoclinic (heteroclinic) structures which instability accompanied by local divergence and global contraction. Meanwhile, the transition from stability to instability requires the vanishing of stable equilibrium states and of stable periodic motions or sufficiently large increase in the periodic ones. DDEs: Delay differential equations. Those equations contain in addition derivatives which depend on the solution at previous times. Also they are infinite-dimensional systems which find application in control systems, biology, chemical kinetics, and other areas. ERK: Extracelullar Signal-Regulated Kinase. Cell signalling protein activated STAT through serine phosporilation. NFB: Negative feedback. In this case a signal is caused by the expression of its inhibitor. PFB: Positive feedback (or autocatalysis). Now, more inhibitors, or other molecules amplify the initial signal and lead to the stabilization of the amplitude, or the increase in the signal’s duration. RNA Silencing: Or also known as RNA interference similar to immune system guards against exploitive parasitic elements by (i) identifying non-self-elements; (ii) generating target-specific responses against these foreign elements, and (iii) rapidly amplifying these responses to clear or otherwise inactive the threat. STAT: Signal Transducer and Activator of Transcription is a family of latent cytoplasmic proteins that are activated to participate in gene control when cells encounter various extracellular polypeptides. Time Delay: Past memory (history).

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Chapter IV

Deterministic Modeling in Medicine Elisabeth Maschke-Dutz Max Planck Institute for Molecular Genetics, Germany

abstract In this chapter basic mathematical methods for the deterministic kinetic modeling of biochemical systems are described. Mathematical analysis methods, the respective algorithms, and appropriate tools and resources, as well as established standards for data exchange, model representations and definitions are presented. The methods comprise time-course simulations, steady state search, parameter scanning, and metabolic control analysis among others. An application is demonstrated using a test case model that describes parts of the extrinsic apoptosis pathway and a small example network demonstrates an implementation of metabolic control analysis.

INTR OD UCTI ON We can observe the molecular background of complex disease processes with systems biology. Today, drug development plays a central role in the interdisciplinary area of systems biology. Scientists from various disciplines, such as biology, bioinformatics, medical research, chemistry, physics, computer science and mathematics, work together to analyze complex disease processes by studying molecular interaction networks. The aim is to understand and analyze the complex behavior of human diseases. Through this collaborative research we can obtain specific methods and results that can lead to new predictions and assumptions about the observed diseases and processes. Metabolic pathways like the citric acid cycle and glycolysis, for example, are important processes that may be used to analyze the complex mechanism in living biological systems. The modeling of these pathways provides appropriate structures for observing the behavior of metabolic diseases, i.e. diabetes. Gene regulatory networks describe protein-DNA interactions or indirectly as the interaction Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Deterministic Modeling in Medicine

between DNA and DNA. Here, we can also examine the regulation of the activity of single genes and the behavior of single molecules, as well as observe the interaction and regulation between different genes and proteins in complex structures. The normal function of single genes is affected in several diseases. A lot of information is available about the functionality of single genes in different diseases and also the roles of mutations in these genes are comprehensively described (Weinberg 1994). Many project studies about this topic are currently underway, and we expect more interesting results in the future (Futreal et al. 2004). Multiprotein complexes are the result of numerous protein-protein interactions. These interactions are essential for physiological processes. In biological networks, diffusion and the molecular transport across cell membranes are also important physiological processes. In different compartments of the cell the function of a protein can change, because the functionality of a protein depends also on the existing targets in the appropriate compartments. For example the p53 protein acts in the nucleus as a transcription factor of apoptosis. The protein Mdm2 in turn can bind to p53 and initiates its ubiquitination and subsequent degradation in the cytoplasm. In the cytoplasm p53 can not act as a transcription factor and instead the degradation of p53 is initialized in this compartment. Signaling pathways play an important role in many diseases. For example the cell signaling mechanism regulates cell proliferation and cell differentiation. The main structures that are responsible for the progression of cancer are interferences in signaling pathways (Cui et al. 2007). The reasons for these inferences in turn are founded in mutated proteins. Using mathematical models we can describe complex cellular processes. This chapter gives an overview of the possibilities available to analyze these molecular, cellular and physiological processes with mathematical modeling, and outlines how we can integrate experimental data. We demonstrate the utilization of the mathematical model analysis in two examples. Time-course simulation and parameter scanning are applied to a model for the extrinsic apoptosis pathways and metabolic control analysis is applied to a small sample network.

MATHEMATICA L MODE LING We can describe biological systems with Boolean models, stochastic models and deterministic models. Boolean networks are based on the Boolean logic (Kaufmann 1993) and can be used to describe gene regulatory interactions. There are two Boolean states: expressed and not expressed. The expression level of a gene is represented in one of the two binary states, ‘0’ and ‘1’. In 1977 Gillespie introduced the exact stochastic simulation algorithms called direct method and first reaction method (Gillespie 1977). The stochastic modeling process deals with discrete variables that are numbers of molecules. Up to now, the stochastic modeling methods are improved and extended (Gibson & Bruck 2000).This chapter will point out the deterministic, kinetic modeling of biochemical reaction networks. This kind of modeling uses continuous variables and allows the representation of the structure and behavior of the modeling system in a very detailed and arbitrarily complex way. The knowledge of complex diseases according to their molecular background, and the use of drugs and predictions resulting from the interpretation of experimental data, provides information about the constitution of the mathematical model. We can include this information into the model structure in analogous mathematical terms and equations. The introduced deterministic approach is based on a system of ordinary differential equations (ODE system).

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Many useful analysis methods exist. The presented methods analyze model behavior in different states and under different conditions.

T opology and S toichiometry In this paragraph we describe the techniques used to build reactions between the specific components of the model. A simple stoichiometric equation has the form:

n1 A + n2 B ⇒ n3C

(1)

In this equation A and B are called the reactants and C is called the product of the reaction. The ni with i=1,2,3 are the stoichiometric coefficients. A reaction can either be reversible A ⇔ B or irreversible A ⇒ B. In the reversible form equation (1) is denoted by:

n1 A + n2 B ⇔ n3C

(2)

All stoichiometric coefficients in the mathematical model can be represented in a so called stoichiometric matrix. We can represent the reactions vj j=1,..,m and the functions of the concentrations Si i= 1,..,n of the participating substances in vector form. The stoichiometric matrix has this form:

 n11  n1m  S1        N=   nn1  nnm  S n v  v 1

m

(3)

Note: there is no unique mapping from a stoichiometric matrix to a reaction system. More than one system can be consistent with a single stoichiometrie.

B alance E quation The rate equation of a reaction is also called kinetic law and is the mathematical formula for the velocity of the reaction. Depending on a local point p, the time t and Si i=1,..,n as a function, that describes the concentration of a substance, the rate equation v has the formula: v ( p, t ) = v S ( p, t ), t 

(4)

S is the vector of the function Si i=1,..,n and v describes the vector of the reaction rates. The velocity vj j=1,..,m also denotes the flux of the reaction. In the following paragraph, we introduce different well known mathematical formulations of kinetic laws. The change in concentration of a single substance can be described by the balance equation. For the function Si i=1,..,n the balance equation reads: m ∂Si = ∑ nij v j ∂t j =1

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(5)

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where vj j=1,..,m are the reaction rates and nij i=1,..,n and j=1,..,m are the stoichiometric coefficients. The according matrix notation is:

∂S = Nv ∂t

(6)

If the system only depends on time, we call the system autonomous, in this case equation (4) shows the formula: v(t) = v(S(t))

(7)

Equation (5) can then be formulated by: dS (t ) dt

= Nv (S (t )) = f (S (t ))

(8)

Here f(S(t)) is a vector of functions f i i=1,..,n that depend on the time-dependent concentrations Si i=1,..,n. In this way, a system of ordinary differential equations which represent the deterministic mathematical model of the according network is built. It is called an ODE system.

R eaction K inetics The rate equation of a reaction is described in detail with mathematical terms using kinetic laws. The calculation rule of the reaction velocities depends on real-value kinetic parameters and the concentration of several components. These components can be the reactants themselves and also the products of the reactions. The concentration of other components in the model can also be part of the calculation rule. These components are called the modifiers of the reactions and their concentration can also control the fluxes , however, there is no mass flow of these components in the reaction. An example for a modifier in a reaction can be an enzyme that catalyzes a reaction, but is neither a reactant nor a product of the reaction. In a general formulation, the kinetic law can be written thus: v = v(k,R,P,M)

(9)

In this equation k = (k1,...,kl ) are the real-value kinetic parameters, R = (R1,...,Rr ) and P = (P1,...,Ps ) are the concentrations of the reactants and products, respectively. In respect to this context, the complexity and the variety of the reaction inhibitions and activations can be involved in the calculation rule by the modifiers M = (M1,...,Mt ) and so the calculation rule of the kinetic reaction could also be a very sizable formula. Well known kinetic laws are for example the Law of Mass Action or the Michaelis Menten kinetics. In the 19th century Cato Maximilian Guldberg and Peter Waage introduced the Law of Mass Action (Guldberg and Waage 1879). This law defines a rate equation for elementary reactions and also presents an equilibrium constant that is derived by using kinetic data and the proposed rate equation.

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For the simple reaction: A + B ⇔ AB

(10)

According to the Law of Mass Action, the two kinetic constants k1 and k–1 are established and equation (10) can be written as:

A+ B

k1  → AB ← k−1

(11)

Now the reaction rate is defined by: v = v1 − v−1 = k1 * [A]* [B ]− k−1 * [AB ]

(12)

The equilibrium constant of this reaction is defined by:

keq =

[AB ] k1 = k−1 [A][B ]

(13)

Note: the directionality of equation (11) defines the association equilibrium constant in equation (13). We can define the dissociation equilibrium constant from the reciprocal value of the association equilibrium constant. The changes in the concentrations by the reaction rate defined in (12) are characterized by the following ODEs: d [A] d [B ] = = −v1 + v−1 = −v dt dt

and

d [AB ] dt

= v1 − v−1 = v

(14)

Using the information given by the Mass Action Law, we can describe the decay of a reactant: A ⇒

(15)

with the reaction rate: v = k*[A]

(16)

Brown (1902) was the first to propose the control an enzyme has on a reaction. The considered reaction is an irreversible reaction and has one reactant and one product. No other effectors take part in this reaction. In the according reaction scheme the enzyme E is included, S denotes the reactant and P denotes the product: k1  → k2 →E + P E+S ES  ← k−1

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(17)

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The formation of the enzyme-reactant complex is reversible but the release of the product from this complex is an irreversible reaction. Now the changes in the concentrations of the components over time are: d [ES ] dt d [S ] dt

=−

d [E ] dt

= k1 * [E ]* [S ]− (k−1 + k2 )* [ES ] ,

d [P ] dt

= k2 * [ES ] ,

= − k1 * [E ]* [S ]+ k−1 * [ES ]

(18)

A rate law for enzymatic reactions, based on this principle but using more complex reaction structures is given by the Michaelis-Menten kinetics (Michaelis and Menten 1913). This and various other enzyme kinetic rate laws are described in Klipp et al. (2005). In particular various forms of interactions: for example, different types of inhibition can be included in these calculation rules.

MODE LING OF AP OPT OSIS Apoptosis, the programmed death of a cell, has different causes. During embryonic development, apoptosis can be initiated from immune system reactions or DNA damage, for example. Apoptosis plays an important role in cancer disease. Abnormal cells divide and grow without control and these cells lose the ability to regulate apoptosis. The (signaling) pathway of apoptosis in general is well known (Hanahan and Weinberg, 2000; MacFarlane and Williams, 2004) and allows us to analyze the characteristics of apoptotic mechanism in mathematical models. There are two principal pathways of apoptosis. The intrinsic (Bcl-2 inhabitable or mitochondrial) pathway of apoptosis is induced by various forms of intercellular stress, developmental cues or external stimuli and the extrinsic or Caspase 8/10 dependent pathway of apoptosis is initiated by the engagement of death receptors. A very detailed description of cancer relevant pathways including the extrinsic and intrinsic apoptosis pathways, with all the important processes is described in Weinberg (2006). To illustrate the possibilities and structures of this kind of modeling in a medical context, two previously published apoptosis models are briefly described in the following sections.

A n E xtrinsic A poptosis Model The first model is published and characterized in Eissing et al. (2004). This model is also used in this chapter to explain and demonstrate graphically the results of mathematical calculations and analysis methods. A part of the extrinsic apoptosis pathway in a caspase activation model for receptor-induced apoptosis is shown. In this model the functionalities of Caspase 8 and Caspase 3 are integrated. Caspases belong to the enzyme family of the proteases. They are very important enzymes in apoptosis and they cleave other proteins. Two different types of caspases exist. Caspase 8 is an initiator (apical) caspase. These caspases are activated to trigger apoptosis and they activate (cleave) inactive pro-caspases of effector caspases. The effector caspases in turn cleave other proteins. This process finally results in cell death. Caspase 8 activates the inactive pro-form of the effector Caspase 3. BAR, a bifunctional apopto-

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sis regulator, binds itself to activated caspase proteins and plays an important role in the regulation of apoptotic mechanism. When an activated caspase protein binds to the regulator, the caspase protein can not perform its function and does not induce and support the apoptotic process. The Caspase 8 – BAR complex (C8a-BAR) represents this compound. The family of the IAP (inhibitor of apoptosis proteins) has the functionality to inhibit and to avoid cell death. In the considered model the IAP protein binds activated Caspase 3 to an IAP-Caspase 3 complex (C3a-IAP). Activated Caspase 3 creates a positive feedback loop in the activation of Caspase 8, and Caspase 8 in turn, provides a positive feedback in the activation of Caspase 3. Another positive feedback loop of activated Caspase 3 acts upon the degradation of IAP. The activation of Caspase 3 finally results in the controlled cell death. Figure 1 illustrates and displays the components of the model and the reactions.

A n Intrinsic A poptosis Model The rapid kinetics of effector caspase activation in the intrinsic apoptosis pathway and the role of the formation of the apoptosome, the activations of effector Caspases 3, initiator Caspase 9 and the behaviour of XIAP are the main studies of the model published and presented in Rehm et al. (2006). The release of cytochrome c triggers the formation of a multi-protein complex, the aptosome, that also comprises the apoptotic protease-activation factor 1 (Apaf-1) and Procaspase 9. Thus, Procaspase 9 passes into the activated Caspase 9 and activates effector Caspase 3. Positive feedback loops of both the activated Caspase 3 and the activated Caspase 9 in the activation of Caspase 3 and the activation of Caspase 9, are part of the modelled signalling network. The X-linked-inhibitor-of-apoptosis-protein (XIAP), a member

Figure 1. Caspase activation model for receptor-induced apoptosis. The reactions and components of extrinsic apoptosis are graphically shown. Red, dashed arrows indicate a modifier influence and not a mass flow. This model is published and presented in Eissing et al. (2004)

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of IAP family proteins, acts as an inhibitor of Caspase 3 and Caspase 9. Smac counteracts XIAP and displaces the caspases from their XIAP interaction sides. Bir1-2 and Bir3-RING fragments result from the Caspase 3 dependent cleavage of XIAP. The bindings of Caspase 9 to Bir3-RING and Caspase 3 to Bir1-2 are also part of the model. A special mathematical feature of this model is the Smac release and the cytochrome c initiated apoptosome formation through time and half-time dependent kinetics, which are reflected by the accordingly defined analytic functions. The computational model of this process is based on 53 reactions and the main aim of this model is to verify effector caspase activation and the control of this activation by XIAP. In addition to the results and predictions that are made in the analysis of these models, there is one aspect that we observe in the results of both models. If enough activated caspase 3 is in the system apoptosis is initialized and the cell starts to die. Both models show this switch or breakpoint, the so called point of no return.

A LG ORITHMS

AND MODE L ANA LYSIS METH ODS

T ime-C ourse S imulation Quantitative time-course simulation describes the changes over time in the concentrations of the model components. In addition to the time-course concentration time-course fluxes can also be calculated. Both courses give a good general overview, the time-course concentration indicates the quantitative behavior of the substances in the network, and the reaction rates clarify the flux through the according network system. The calculations can be performed by using appropriate numerical solvers for ODE systems. LSODA (Hindmarch 1983, Petzold 1983) a variant of the LSODE package (Hindmarch 1980) can be used. The algorithm switches automatically between stiff and non-stiff methods and offers a good opportunity for solving systems with different problem definitions. The algorithm is available in different programming languages, in easy to use software packages. For example, SciPy the Scientific Tools for Python (Jones et al. 2001 -) offers an implementation of this algorithm. An alternative choice is Limex (Deuflhard and Nowak 1987), a solver that uses an extrapolation method to solve linearly-implicit differential-algebraic systems (DAEs). An implicit one step method is combined with stepped extrapolation, offering adaptive control of step size and order. This algorithm is written in the programming language Fortran and the source code is available at the CodeLib library of the the Zuse Institute Berlin via the URL http://www.zib.de/Numerik/numsoft/CodeLib/ivpode.en.html. The possibility to transform the source code to another programming language or to embed the source code in another programming language is offered. Several graphical tools provide interfaces for the currently used programming languages and they can easily provide a graphical representation of the simulated time-course output. For example, the powerful graphical tool Gnuplot is freely available at http://www. gnuplot.info/ and runs on commonly used computer platforms. A Gnuplot application interface for the programming language C++ is available at http://www.suiri.tsukuba.ac.jp/~asanuma/gnuplot++/ and a Python package that interfaces with Gnuplot (Gnuplot.py) also exists and is available at http://gnuplotpy.sourceforge.net/. Time-course simulations can also be performed with modeling tools, outlined in this chapter under the sub-title Modeling Tools and Model Repositories.

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E xample of T ime-C ourse S imulations The apoptosis model published in Eissing et al. (2004) exemplifies this method. Figure 2 shows a graphical representation of the calculated time-course results. The time-course calculations and the graphical output results are generated by the tool PyBioS (Wierling et al. 2007, Klipp et al. 2005), a Web-based modeling and simulation system. The curves represent the changes in concentration for the duration of the model components. The abbreviation C3 refers to Caspase 3, C3a refers to the activated Caspase 3, C8 to Caspase 8 and C8a to Caspase 8 in the activated form. It is quite obvious that there is a switch from the life state to the death state of the cell. Figure 2 illustrates the behavior of the Caspase 3 – IAP - complex. Initially, the inhibitor protein IAP binds the activated Caspase3 and avoids the initialization of the apoptosis process. After some time there is a peak in the curve that indicates the point of no return and subsequently the concentration of this complex doesn’t change with time. When the concentration of the activated Caspase 3 has reached a significant level, the apoptosis inhibitor protein IAP has no chance to stop the apoptotic process.

Parameter S canning Parameter Scanning gives us information about the influence of the kinetic parameters defined in the kinetic rules on systems behavior. Under the assumption that the system reaches a stable steady state we can perform this sensitivity analysis. The system reaches a steady state or stationary state, when the quantitative values like the concentration and the fluxes no longer change with time. This characteristic is equivalent to reaching the root of the ODE system and fulfilled by the balance equation (5):

dSi =0 dt

i=1,... ,n

(19)

In a nonlinear system this equation can have several solutions. An important precondition to make predictions about a systems behavior in the steady state is the stability of the steady state. In this case, stability means that the system stays in this state and each system that starts in a neighborhood arbitrary close to this state, also results in this steady state. A detailed theory about the stability of a steady state is described in Walter (1998) and also in Klipp et al. (2005). Through linearization of the autonomous system, we can perform a linear stability analysis to gain information about the stability of the system. Thus the steady state S 0 = (S10 , , S n0 ) can be called stable if all eigenvalues of the Jacobian matrix of the system of functions in equation (8) are negative at this point. The Jacobian matrix of this function in the state S0 is defined by:

M

82

 ∂f1 (S 0 ) ∂f1 (S 0 ) ∂f1 (S 0 )     ∂S 2 ∂S n   ∂S1   0 0 ∂f 2 (S 0 )  ∂f 2 (S ) ∂f 2 (S )  0  ∂S 2 ∂S n  f (S )=  ∂S1    : : : :   0 0 0 ∂f n (S )  ∂f n (S ) ∂f n (S )    ∂S 2 ∂S n   ∂S1

(20)

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Figure 2. Time-course simulation of different components of the apoptosis model in (Eissing et al. 2004). The switch between the life state and the death state of the cell is explicitly visible

The roots of the ODE system (19) can be calculated using the MINPACK subroutine HYBRID1, available at Netlib Library, a collection of mathematical software, papers, and databases. For more details see http://www.netlib.org/. This numerical algorithm is a modification of the method described in Powell (1970). The Jacobian matrix can be determined by the forward difference formulas:

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∂f j (S 0 ) ∂Si

=

f j (S 0 (i ))− f j (S 0 )

i =1,..,n , j=1,..,n

(21)

with a sufficiently small real value ε > 0. The vector S 0 (i ) in this equation is defined through:  S10    0 S (i ):=  Si0 +     S0  n

       

(22)

We can compute the eigenvalues of the system by using an appropriate routine from the LAPACK package included in the Netlib Library. If the Jacobian matrix (20) of the system is singular, the numerical root finding method cannot find a unique solution and fails. In this case we can determine the steady state of the system with a time-course simulation. We perform time-course simulation until the changes in the values of the concentrations in S (t ) = (S1 (t ), , S n (t )) are under a given threshold and stay under this threshold. For two vectors of the concentration values S1 and S2 this condition can be proved by: || S1 − S 2 ||2 <

(23)

In this equation || . ||2 denotes the Euclidian vector norm and ε is a sufficiently small positive real value. In the case of a stable steady state, a determined kinetic parameter scans a predefined interval and the according values of the regarded components of the model in the steady state are calculated. This enables us to analyze the influence of the scanning kinetic parameter against the behavior of the model. Controlled quantities are in general the concentration of the substances and the values of the reaction rates. Furthermore, we can analyze the sensitivity of the concentration of a model component against a single reaction, and analyze the influence of an enzyme on a reaction rate. In this manner we can apply several analysis approaches.

E xample of a Parameter S can In this paragraph we apply a parameter scan to analyze the behavior of the apoptosis model described in Eissing et al. (2004). The activation of the effector Caspase 3 plays an important role in this extrinsic apoptosis pathway. The parameter k1 controls this activation in the reaction model. The according kinetic reaction is: v1 = k1 *[Caspase8a]*[Caspase3]

(24)

The concentration of activated Caspase 8 serves as a modifier and Caspase 3 serves as a reactant in this reaction. 84

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Figure 3 illustrates the surprisingly fast influence of this reaction on the components of the model. A minor amount of the parameter k1 in the range of 10 -5 is enough to start apoptosis. We implemented parameter scanning and the according graphical results with PyBioS. The green horizontal bar at the top of the figures denotes that the found steady states are stable. In the shortcuts of the implemented mode C3 represents Caspase 3, C3a represents the activated form of Caspase 3, abbreviation C8 stands for Caspase 8 and C8a for the activated form of Caspase 8.

Metabolic C ontrol A nalysis Metabolic Control Analysis (MCA) defines a quantitative framework for characterizing the interactions between particular reactions, kinetic constants and values of fluxes and concentrations. The local and global behavior of the network system under the influence of small (infinitesimal) changes is described. Controlled variables could be the rate laws or the concentrations of substances. Controlling parameters can be kinetic constants or the concentration of an enzyme, for example. More detailed comprehensive theories of stationary control states are presented in numerous instances e. g. (Fell 1992; Schuster & Heinrich 1992; Cornish-Bowden 1995). There are two local control coefficients that can always be calculated, because there is no need for a steady state. The local control coefficients are the elasticity coefficients. These coefficients can be v calculated at a certain time point or at a steady-state. The ε-elasticity = S describes the sensitivity of the rate vk of a reaction to the change of the concentration Si. The π-elasticity = vp describes the sensitivity of the rate vk against a small change in a kinetic parameter pl : v

:=

S

Si ∂vk vk ∂Si i=1,..,n; k=1,..,m.

v p

:=

pl ∂vk vk ∂pl l=1,..,r; k=1,..,m.

(25)

Under the assumption that the system reaches a stable steady state we can also calculate global control and response coefficients. The control coefficients show the influence of a small disturbance in the rate of the steady state fluxes or the steady state concentrations. These control coefficients are the flux-control coefficient Ckj for the control of the rate vk over the steady state flux Jj and the concentration-control coefficient Cki that describes the impact of the rate vk on the steady state concentration Si :

C

j

:= k

vk ∂J j J j ∂vk j=1,..,m; k=1,..,m.

C

i k

:=

vk ∂Si Si ∂vk i=1,..,n; k=1,..,m.

(26)

The response coefficients show the resonance of the steady state fluxes and the steady state concentrations against small changes in a certain parameter. These coefficients do not only clarify direct influence of controlled quantities but also show indirect influences. This is useful to understand system coherences which are not obviously visible. Rmj shows the response of the steady-state flux to a small change in the parameter pm and Rmi expresses the response of the steady-state concentration Si to a small modification in the parameter pm:

R

j l

:=

pl ∂J j J j ∂pl j=1,..,m; l=1,..,r.

pl ∂Si i=1,..,n; l=1,..,r. i ∂pl

R := S i l

(27)

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Figure 3. The influence of Caspase 3 activation is represented in this model by the kinetic constant k1. The graphics illustrate the strong influence of this activation on all components of the model. Above: The described influence on the concentration of Caspase 3, cleaved Caspase 3, IAP and the activated Caspase3-IAP complex. Below: The steady state behavior of the concentration of Caspase 8, activated Caspase 8, BAR and the activated Caspase8-BAR complex, depending on changes in the parameter k1.

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In the definitions (25), (26) and (27) all coefficients are normalized. For an elaborate derivation and description of the calculation rules for the coefficients see (Hofmeyr 2001). v v The calculation of the non-normalized local coefficients S = Sik and p = pkm can be performed by the forward difference formulas:

( )

vk Si

=

∂vk vk (S (i ))− vk (S ) = ∂Si

vk pm

=

( )

∂vk vk (p (m ))− vk (p ) = ∂pm

(28)

In the equations we use a sufficiently small ε > 0. S (i ) and pε (m) are defined through:

 S1    S (i ) =  Si +     S  n

  p1       p (m ) =  pm +        p r  and 

       

(29)

The decomposition of the stoichiometric matrix N defined in (3) to reduced row echelon form (Strang 1980) by Gauss elimination: N = LNR

(30)

provides the reduced stoichiometric matrix NR with r linear independent rows and the link matrix L. If rank(N) =n (r=n), then L is the identity matrix I and N = NR. The Jacobian matrix M of NR and so the S Jaciobian matrix of the independent components of the system can be determined by M = N R L. We can calculate the none-normalized control coefficients arranged in matrices with: CS = −LM −1N R

CJ =

S

CS + I

(31)

The matrix representation of the response coefficients are determined through R S = CS εp

R J = CJ εp

(32)

We can normalize the coefficients through the multiplication with the according normalization factors. They are included in the equations (25), (26) and (27). In complex model structures it could be helpful to analyze the dependencies and influences of the components of the system with these methods. A necessary precondition is a stable steady state. Calculating these coefficients for a given model is straight forward. First we determine the ε-matrices with the forward differences formulas. Then the other coefficients can be calculated using common matrix operations. The standard linear algebra algorithms are implemented in several software packages and for example available at the Netlib library as components of the LAPACK package. Some modeling tools also provide this analysis method, as described in the section Modeling Tools and Model Repositories.

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E xample for Metabolic C ontrol A nalysis The following reactions and kinetics demonstrate a simple network example:

v0 : ES ⇒ E + S1 v1 : S1 ⇒ S 2 v2 : S 2 + E ⇒ ES

v0 = k0 * ES k * S1 v1 = 1 k3 + S1

(33)

v2 = k2 * S2

Figure 4 shows colored box plots of the normalized concentration control coefficients and the normalized ε-elasticity coefficients, in matrix form. Even though the example model is very small and consists of only three reactions, the according matrix plots show more than ten values per coefficient matrix. The example demonstrates, that metabolic control analysis describes complex relations according to certain values. The control coefficients box plot describes an indirect negative influence of v0 on the steady state concentration of S2 and the influence of v1 upon the concentration of S1 is significantly less than the influence of v2 on S2.

E xperimental D ata and D rug D evelopment Experimental data is already available for various diseases in different states. Data that includes medical drug treatment also provides information that could be used for modeling. In Lamb et al. (2006) the authors describe the connection between diseases, genetic perturbations and the influence of drugs. In Karaman et al. (2008) we find an interaction map for kinase inhibitors in a quantitative analysis. There are several options for including the knowledge provided from literature and experimental data in according model structures. Because the information about the considered studies is often very specific, the applied methods depend on different conditions and are individual. Here, we describe general possibilities and instructions.

Figure 4. A simple example network illustrates the implementation of metabolic control analysis. This figure illustrates the reaction network, the normalized concentration control coefficients and normalized ε-elasticity coefficients in colored box plots

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One possibility to include experimental data in a model is to initialize the start values of the according ODE system with corresponding values. These values can be obtained directly from the experimental data or they can be determined by mathematical equations. The corresponding equations result from an existing functional situation in the model. Another possibility for including information from experimental data, is to integrate this knowledge into the kinetic laws. The given information can be used to determine the kinetic parameters directly, or to fit the kinetic data using specifically adapted algorithms. There are also several methods for integrating the influence of drugs in kinetic law formulae. For instance, we can determine the value of a kinetic constant using knowledge about the dose rate and the concrete function of the impact of a drug. A lot of comprehensive, active research already exits in this area.

AVAI LAB LE T OOLS AND DATA Several user-friendly software tools are available. These tools offer the possibility to perform time-course simulations and different analysis methods. An established data exchange format allows for flexible usage, and model repositories provide particular models for different problems. These possibilities allow us to look at the given problem from different perspectives. Many databases are available in this research area. They provide both essential and specialist resources which can be used for modeling.

Modeling T ools and Model R epositories This section introduces the useful tools available for developing and analyzing biological and biomedical models. Systems biology standards and two model repositories are presented. A short overview and the according URLs are listed in Table 1. Mathematica, a mathematical software system, provides a large amount of computational methods and necessary tools for these kind of kinetic modeling, simulation and analysis methods. The software is developed by Wolfram Research. Another mathematical commercial software package that is capable of the computations and representations is Matlab, developed by MathWorks. This software package is often used in scientific research, provides good documentation and is suitable to use for the calculations and graphical representations. For more details about using Mathematica and Matlab in this context see Klipp et al. (2005). COPASI (Hoops et al. 2006) a complex pathway simulator tool is also available as Freeware. This tool is user-friendly and offers the possibility to build models, run simulations and apply various analysis methods. MCA, steady state calculations, linear stability analysis, parameter scanning and parameter estimation using experimental data are the main features of this modeling tool. A graphical representation of the results is easy to follow and can be configured in various ways. The import and export of models in SBML, the Systems biology Markup Language, is also available. The E-Cell System (Tomita et al. 1999, Takahashi et al. 2003) is a software platform that provides modeling, simulations and analysis methods of cell simulations at the molecular level. A graphical userinterface clearly arranges the various functions of the object-oriented tool. Further information about this tool, its functions and underlying theory is available on the E-Cell System Web site. Cell-Designer (Funahashi et al. 2003) is a tool for modeling biochemical networks. The tool provides a diagram editor and also supports time-course simulations and parameter scanning. Systems Biology

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Table 1. This table lists the Web sites of modeling tools, systems biology standards and model repositories Modeling Tools PyBios

http://pybios.molgen.mpg.de/Pybios

Mathematica

http://www.wolfram.com/

Matlab

http://www.mathworks.com/

Copasi

http://www.copasi.org

E-Cell

http://www.e-cell.org

Cell-Designer

http://www.systems-biology.org/cd/

JDesigner

http://jdesigner.org/

Jarnac

http://www.sys-bio.org/software/jarnac.htm

Systems biology Standards and Workbench SBML, Systems Biology Markup Language

http://sbml.org/

SBGN, Systems Biology Graphical Notation

http://sbgn.org/

SBW, Systems Biology Workbench

http://sbw.sourceforge.net/

Model Repositories BioModels database

http://www.ebi.ac.uk/biomodels/

JWS Online repository

http://jjj.biochem.sun.ac.za/index.html

Markup Language, SBML the standard for representing models of biochemical and gene-regulatory networks is also supported. Parts of the new notation SBGN, Systems Biology Graphical Notation are implemented in the new release CellDesigner 4.0 beta. SBGN is developed as a standard for graphical representations of computational models in systems biology. The Systems Biology Workbench SBW (Hucka et al. 2002) includes several software packages for modeling, analysis and visualization in systems biology. The applications communicate via a simple network protocol. A detailed description of the software package can be found in Sauro et al. (2003). JDesigner is a graphical network designer for biochemical networks and part of the SBW. Simulations can be performed in JDesigner by Jaranc, a tool that offers a simulation service within the SBW. JDesigner and Jarnac are described in more detail in Hucka et al. (2002). PyBioS supports modeling, time-course simulations, various analysis methods and the dynamic population of models by using information provided by databases interfaces to pathway databases. PyBioS is a Web-based environment and provides a model repository. The export and import of models is enabled via an SBML interface. Figure 5 gives an overview of the appearance and functions of PyBioS.

D ata R esources and D atabases A large amount of data resources and various databases are accessible via the Internet. Table 2 comprises the information about some databases which provide information and data that we can use for modeling. Most of the databases are described in Wierling et al.(2007).

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Figure 5. The Web-based PyBioS simulation environment. The model repository (A) offers models to be selected. The search interface (B) enables the automatic population, with access to several databases. The graphic shows some hits that are actually found. Graphically represented time-course simulations can be found in (C). The result of metabolic control analysis is represented in colored box plots (D) and a network graph (E) visualizes the network structures of the corresponding reactions.

C ONC LUSI ON Within biomedical science, mathematical modeling is becoming more and more important. With the help of several mathematical means, the modeling ability can be extended to encompass biomedical systems and to analyze system behavior and structures in an arbitrarily detailed manner. From single genes to proteins and protein complexes that can act, for instance, as transcription factors the expression of other genes can subsequently be inhibited or activated and with this positive or negative feedback loops can be established. Based on such information of intra- and extracellular biological network structures, we can create models of varying complexity. The deterministic, kinetic modeling introduced here supports the essential and useful possibilities available for understanding and analyzing the functionality of diseases in living systems. The integra-

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Table 2. Useful databases freely available on the WWW Pathway databases KEGG , the Kyoto Encyclopedia http://www.genome.jp/kegg/ of Genes and Genomes Reactome, a compendium of biological pathways

http://www.reactome.org

HumanCyc, HumanGenes and Metabolism

http://humancyc.org/

Pathway Interaction Database

http://pid.nci.nih.gov/

BioCarta, pathway database

http://www.biocarta.com/

NetPath, signal transduction pathways

http://www.netpath.org/

The Cancer Cell Map

http://cancer.cellmap.org/cellmap/home.do

IntAct, protein interaction data

http://www.ebi.ac.uk/intact/site/index.jsf

MINT, protein interactions

http://mint.bio.uniroma2.it/mint/Welcome.do

HPRD, human protein reference database

http://www.hprd.org

BioGRID, set of physical and genetic interactions

http://www.thebiogrid.org/

Spike, biological signaling networks

http://www.cs.tau.ac.il/~spike/

Genetic Inheritance OMIM, human genes and genetic disorders

http://www.ncbi.nlm.nih.gov/sites/entrez?db=omim

Expression data GEO, Gene Expression Omnibus http://www.ncbi.nlm.nih.gov/projects/geo/ Array Express, micro array data

http://www.ebi.ac.uk/microarray-as/aer/

Kinetic data BRENDA, Enzyme information system

http://www.brenda-enzymes.info/

SABIO-RK, reaction kinetics database

http://sabio.villa-bosch.de/SABIORK/

tion of drug interactions can help us to identify important influences and adverse effects on the according biomedical processes. The presented analysis methods are useful instruments for studying the relationships and interactions between the components in the observed processes. We can also ascertain the influence of individual model components on global model behavior. In this way, we can identify important, previously unrecognized coherences. Furthermore, the cooperation of exact and applied science in the biomedical research area, provided by mathematical modeling will continue to develop new methods for understanding the complex interaction mechanisms of various diseases.

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A ckn ow ledgment The author thanks Christoph Wierling and Hendrik Hache for proof-reading of this chapter and their constructive feedback and Andriani Daskalaki for her good ideas and assistance. The author address special thanks to Jane Conway for her excellent proof-reading. This work was supported by the EU grants AnEUploidy and EMI-CD within the Framework 6 funding, and the Max Planck Society.

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Hindmarch, A. C. (1983). Odepack, a systematized collection of ode solvers. In R. Stepleman et al. (eds.), IMACS Transactions on Scientific Computation, 1, 55-64. Hofmeyr, J. H. S. (2001). Metabolic control analysis in a nutshell. In Yi, T. M., Hucka, M., Morohashi, M., Kitano, H. (eds.), Proceedings of the 2nd International Conference on Systems Biology, (pp. 291300). Madison, WI: Omnipress. Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., et al. (2006). COPASI – a COmplex PAthway SImulator. Bioinformatics, 22, 3067-3074. Hucka, M., Finney, A., Sauro, H. M., Bolouri, H., Doyle, J., & Kintano, H. (2002). The ERATO systems biology workbench: Enabling interaction and exchange between software tools for computational biology. Procedings of the Pacific Symposium on Biocomputing, 7, 450-461. Jones, E., Oliphant, T., Peterson, P., & others. (2001). SciPy: Open source scientific tools for Python. http://www.scipy.org Karaman, M. W., Herrgard, S., Treiber, D. K., Gallant, P., Atteridge, C. E., Campbell, B. T., et al. (2008). A quantitative analysis of kinase inhibitor selectivity. Nature Biotechnology, 26, 127-132. Kaufmann, S. A. (1993). The origins of order: Self-organization and selection in evolution. New York: Oxford University Press. Klipp, E., Herwig, R., Kowald, A., Wierling, C., & Lehrach, H. (2005). Systems biology in practice: Concepts, implementation and application. WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Lamb, J., Crawford, E. D., Peck, D., Modell, J. W., Blat, I. C., Wrobel, M. J., et al. (2006). The connectivity map: Using gene-expression signatures to connect small molecules, genes and disease. Science 313, 1929-1935. Le Novére N., Bornstein, B., Broicher, A., Courtot, M., Donizelli, M., Dharuri, H. et al. (2006). BioModels database: A free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Research, 34, 689-691. MacFarlane, M., & Williams, A. C. (2004). Apoptosis and disease: A life or death decision. EMBO Rep, 5, 674-678. Michaelis, L., & Menten, M. L. (1913). Kinetic der Invertinwirkung. Biochem. Z., 49, 333-369. Petzold, L. (1983). Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. Siam J. Sci. Stat. Comput., 4, 136-148. Powell, M. J. D. (1970). A hybrid method for nonlinear equations. In P. Rabinowitz. Gorden & Breach, (eds.), Numerical methods for nonlinear algebraic equations (pp. 84-114). Rehm, M., Huber, H. J. , Dussmann, H., Prehn, J. H. M. (2006). Systems analysis of effector caspase activation and its control by X-linked inhibitor of apoptosis protein. The EMBO Journal, 25, 4338–4349. Sauro, H. M., Hucka, M., Finney, A., Wellhock, C., Bolouri, H., Doyle, J., et al. (2003). Next generation simulation tools: The systems biology workbench and bioSPICE integration. Omics, 7, 355-372.

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Schuster, S., & Heinrich, R. (1992). The definitions of metabolic control analysis revisited. BioSystems, 27, 1-15. Strang, G. (1980). Linear algebra and its applications, 2nd Edition. New York: Academic Press. Takahashi, K., Ishikawa, N., Sadamoto, Y., Sasamoto, H., Otha, S., Shiozawa, A., et al. (2003). E-Cell 2: Multi-platform E-Cell simulation system. Bioinformatics, 19, 1727-1729. Tomita, M., Hashimoto, K., Takahashi, K., Shimizu, T. S., Matsuzaki, Y., Miyoshi F., et al. (1999). E-CELL: Software environment for whole-cell simulations. Bioinformatics, 15, 72-84. Walter, W. (1998). Ordinary Differential Equations. New York: Springer Verlag. Weinberg, R. A. (1994). Oncogenes and tumor suppressor genes. CA: A Cancer Journal for Clinicians, 44, 160-170. Weinberg, R. A. (2006). The biology of cancer. Garland Science, Taylor & Francis Group, LLC. Wierling, C., Herwig, R., & Lehrrach, H. (2007). Resources, standards and tools for systems biology. Briefings in functional genomics and proteosomics, 6, 240-251.

K ey T erms Bcl2: Is the prototype for a protein family of mammalian genes and the proteins coded by these genes. The name is derived from B-cell lymphoma 2. C++: The programming language C++ was developed in 1979 by Bjane Stroustrup. It supports object-oriented programming and is an enhancement to the programming language C. DAE: A differential-algebraic equation (DAE) is a special kind of differential equation and expressed by means of differential algebra. This equation does not necessarily include all dependent variables, and their derivates must not be expressed explicitly. Deterministic: An algorithm is called deterministic when the same results are always obtained under identical conditions. In this respect, deterministic mathematical modeling describes systems without any random possibility function. Identical starting conditions always provide the same output. Eigenvalues: In linear algebra the equation Av = v defines the eigenvalues λ and the corresponding eigenvectors v of a linear transformation represented by a quadratic matrix A. λ is a complex value and v is a complex valued vector. The eigenvalues describe essential characteristics of the linear map. Enzyme: Protein molecules that catalyze chemical reactions. They play an important role in most metabolic processes and are responsible for activation and control of biochemical reactions in living systems. Euclidean Norm: The Euclidean space denotes an n-dimensional space that can be characterized through Euclidean geometry. An n-dimensional vector describes a point in this space. The Euclidean norm defines the length of a vector and the distance function between two vectors is called an Euclidean metric.

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Experimental Data: Gene expression profiles derived from micro array based experiments with different study foci, i.e. prostate cancer, compound testing or diabetes. Fortran: The name of a programming language derived from FORmula TRANSlation. Fortran was developed in the 1950s and was especially used for numerical programming. The programming language directly supports numerical operations and because of this, optimized compiler calculations can be performed. Up to now, various numerical programming libraries are available and used in mathematical, physical and chemical science. Kinetics: In this chapter the term kinetic is used in a chemical sense and describes the principles of reaction velocities. Linearization: In mathematics, linearization describes the linear approximation of a function at a given point. Object-Oriented: Object-oriented programming uses abstract objects and their interactions to describe the contents and the functionalities of the program, according to its design. ODE: An ordinary differential equation is an equation that contains a function and the derivates of this function. It differs from partial differential equations in that, in an ordinary differential equation, the included function depends on only one variable. Protein Complex: A group of two or more chemically bound proteins formed by stable proteinprotein interactions. Python: The high-level programming script language Python supports functional, object-oriented and imperative programming paradigms. Stoichiometry: The quantitative relationship between the reactant and the product in a chemical reaction is described by the stoichiometry. It can be used to calculate the quantitative amount of the product or the educt of a reaction, where one of both measurable quantities is known. Topology: The topology defines the properties of spaces and maps. Dependent on the described space arbitrary complex structures used.

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Chapter V

Synthetic Biology as a Proof of Systems Biology Andrew Kuznetsov Freiburg University, Germany

abstract Biologists have used a reductionist approach to investigate the essence of life. In the last years, scientific disciplines have merged with the aim of studying life on a global scale in terms of molecules and their interactions. Based on high-throughput measurements, Systems Biology adopts mathematical modeling and computational simulation to reconstruct natural biological systems. Synthetic Biology seeks to engineer artificial biological systems starting from standard molecular compounds coding in DNA. Can Systems and Synthetic Biology be combined with the idea of creating a new science—‘SYS Biology’ that will not demarcate natural and artificial realities? What will this approach bring to medicine?

“We live in a society exquisitely dependent on science and technology, in which hardly anyone knows anything about science and technology.” - Carl Sagan

Intr od ucti on Sometimes, we are like the three blind Indian philosophers who tried to guess what kind of animal the elephant was by touching various parts of it. One blind man while touching the side of elephant announced the animal was like a wall. The second philosopher hugged its leg and declared that the animal was like a tree and the third blind man, while holding on to its tail said the animal was a snake. All three were correct, but all three had a distorted perspective of an elephant. This allegory captures a weakness of the analytical reductionist approach to biological science and illustrates a paradigm that the whole is greater Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Synthetic Biology as a Proof of Systems Biology

than the sum of its parts. A system, holistic approach to Biology means the synthesis of knowledge from various sources and by different methods of data extraction. This approach starts with data collection and modeling to understand how components of the system interact, continues with experimentation and then returns to modeling to refine our understanding of interactions and to identify new questions to be addressed. This system of thinking emphasizes relationships rather than isolated entities. The idea of a system-level understanding of Biology is not new. In 1943, Erwin Schrödinger published the book ‘What is Life’, a seminal work on scientific thought that examined the relationship between the laws of Physics and the mechanisms of life. In particular, it provoked the development of Molecular Biology and led to the research we know as Systems Biology. Norbert Wiener (1948) and Ludwig von Bertalanffy (1969) described a systems approach to living organisms i.e. the holistic view that ‘mysterious’ properties of life arise at the system level from dynamical interactions and diversity of system components. Breakthroughs in Molecular Biology during the last decades have enabled an analysis of dynamical interactions inside living cells and between them. Systems Biology appeared as a result of the Human Genome Project as well as from a growing understanding of how genes and their proteins give rise to biological forms and functions. Recent studies have involved high-throughput experiments in Genomics, Transcriptomics, Proteomics and Metabolomics. These ‘-omics’ should be fused together to reach an understanding of Biology at a top system-level (Kitano, 2002a). The new field has attracted biologists, engineers, mathematicians, physicists and chemists who are tackling complex biological problems. The Internet allows researchers to distribute massive amounts of data. In particular, the theory of dynamical systems, agent-based approach and systems engineering methods provide the opportunity to study the collective behavior of biological entities. The challenge is to connect genetic circuits with physiological behavior. Following Systems Biology, the goal of Synthetic Biology is both to improve our quantitative understanding of natural phenomenon and to establish an engineering discipline to design artificial biological systems. It will strongly depend on what possibilities there will be in the multi-scale modeling of whole organisms. Biological models often have numerous unknown parameters such as kinetic constants, decay rates and drift terms. A big problem for Systems/Synthetic Biology (‘SYS Biology’ for short) is that these parameters are often very difficult to measure. However, Systems Biology researchers believe that methods of dynamic analysis, modeling and simulation can provide a deeper understanding of life (Kitano, 2002b). Synthetic Biology, with the goal of synthesizing life from scratch, gives us other modern hype-and-hope, namely the ‘understanding by building’. Regarding complex dynamical systems, Richard Feynman wrote: “What I cannot create I do not understand.” By creating artificial life, we are beginning to answer Schrödinger’s question: “What is Life?” This will give us new opportunities to distinguish the health and pathology for treating for example, schizophrenia, cancer and diabetes.

Co nnecti on between

gen otype and phen otype

A current front of ‘-omics’ research has moved from metabolic pathway analysis to the reconstruction of regulatory networks, identification of protein/DNA, protein/RNA and protein/protein interactions, simulations of signal transduction reactions, validation of experimental data available from highthroughput measurements and to studies on the correlation between gene expressions and phenotype. The relation between genotype and phenotype is a central question. Do selective forces which act on the phenotype affect individual genes? Or, is there an epigenetic influence arising from the complex interac-

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tion between many gene products? (Wagner, 1996) The latest finding demonstrated that the metabolic pathway assignment is useful in verifying genomic annotations. But, there are many gaps in genetic and epigenetic events, e.g. the effects of posttranscriptional and posttranslational regulation. What is missing is a relation between high-level functional states and genetic networks. The global organization and its effects are mostly ignored. Life has been a great secret so far! How can an adapting and developing dynamics emerge from information hidden in the genome? Still in the case of very simple circuits that are carefully designed, the phenotype can often not be predicted. Goldstein (1999) defined emergence as “the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems.” An emergent structure is more than a sum of its parts because the interactions between these parts play a significant role. Life is an example of emergent properties by combinations of individual atoms that form molecules such as DNA, RNA, proteins, carbohydrates and lipids, which in turn create organelles, cells, tissues, organs, organisms and communities. An understanding of such emergent events requires system-level perspectives. In fact, a transition from molecules to physiology occurred in Biology and it is generally believed that multi-scale and nonlinear feedback mechanisms can be understood through mathematical and computational models. A problem is that the theory of dynamical systems used in Physics and Chemistry might be not enough for biological entities. Living cells are super complex agents containing a vast amount of information that cannot be reduced to simple rules or sophisticated mathematical functions.

D at a acq uisiti on and system- le ve l underst anding Because biological systems are not just an assembly of genes and proteins, their properties cannot be fully understood by drawing a plain connection graph. Modeling results contain many false outputs that need to be verified by wet lab experiments. Historically, Biology has dealt with vast experimental data as well as spatial and temporal phenomena that are more complex than in other natural sciences. These large data sets often bring more confusion than understanding— “… our ability to generate data now outstrips our ability to analyze it” (Patterson, 2003). On the other hand, Proteomics is substrate limited and currently available experimental data on gene expression are usually not sufficient to reconstruct the structure of pathways and regulatory networks. Furthermore, the system approach is based on information in public databases that are often incomplete, not standardized and properly annotated and the quality of the data is often uncertain. A Systems Biology community needs information standards. Systems Biology Markup Language (SBML) is an XML-based language for representing models of biochemical reaction networks which has evolved since 2000. Today, SBML is supported by over 100 software packages, such as Cell Designer, Systems Biology Workbench (SBW), including JDesigner/Jarnac and SBML toolbox for MATLAB users (Keating et al, 2006). SBML website provides information and the tools needed to understand Systems Biology (http://sbml.org/index.psp). One of difficult problems that scientists deal with is how to transform a natural phenomenon into a set of equations. It is usually impossible to describe a phenomenon totally, so one looks for a set of equations which describes the system approximately. In general, after we have built a set of equations, we compare the data generated by equations with real data collected by measurement. If the two sets of data ‘close’, then the equations will result in a good description of the real-world system. If not, then the underlying equations have to be modified. The set of equations is called a model for the system. The problem of stating clear assumptions and describing parameters and variables on which the model will

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be based is not a trivial task. One could build a so-called white box model based on first principles, but in many cases such models would be complex and it would be impossible to obtain the nature of biological systems. A more common approach is therefore to start from measurements of the behavior of system and then to determine a mathematical model of data without going into details. This approach is called system identification. There are two types of models: the grey box model and the black box model. In the grey box model, the structure is typically chosen by the user. The model contains unknown parameters which can be estimated using algorithms of system identification to agree with experimental data. In the black box model, no prior model is available. Most system identification algorithms are of this type. The idea is to fit linear and nonlinear models to data. This data-driven approach helps to describe systems with a complex dynamics and structural uncertainty that are not easily modeled from first principles. A complexity of models is associated with the number of parameters in the model and the polynomials of higher degrees. Modern computers often appear to have an infinite capacity for calculation. However, to solve certain simple problems computing devices show their limits. Natural biological systems are a product of more than 3500 million years of evolution and molecular computation; they are not optimized to be modeled easily. Furthermore, several genome projects have shown that most genes have not yet been characterized, especially in multicellular organisms. Hopefully, network structures of a large set of gene interactions and biochemical pathways are well known and a behavior of those systems can be understood through metabolic, sensitivity and dynamic analysis methods including the phase portrait and bifurcation analysis.

Itera ti ve refinement : management bi ologica l kn ow ledge

of kn own and unkn own

Because SYS Biology—reverse and direct engineering of genetic networks—is extremely complex; the most reasonable way to study and manage this complexity is the iterative refinement which combines experimental and computational methods. A source of knowledge for Systems Biology is the high-throughput experimental methods such as microarray and mass spectrometry. An extraction of patterns and correlations from the vast measurements and large databases is difficult e.g. techniques to test multiple hypotheses include the cluster analysis, data mining and machine learning (Kell, 2005; Bosl, 2007). There are several approaches to the reverse engineering of genetic regulatory networks from gene expression data. The traditional one is a mathematical description of the biochemical processes in terms of differential equations however, it is restricted by small systems. The other one is cluster analysis from the theory of experiment. Although, clustering provides a simple way to extract qualitative information about genes co-expression from large data sets, it does not lead to a distinction between individual genes. A compromise between these two extremes is Bayesian networks. The Bayesian learning paradigm is suitable for representing conditional relations between multiple interacting quantities; their probabilistic nature is capable of handling a noise inherent in biological processes and microarray experiments. However, an inference problem is hard if the interactions between hundreds of genes learned from small data sets. Quantitative studies of complex biological networks are not easy to perceive (Friedman et al, 2000; Husmeier, 2003; Bansal et al, 2007).

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Modeling via D ifferential E quations In some cases, interactions among system components can be described by classical ordinary differential equations (ODE). When spatial effects (e.g. diffusion) play a significant role in a system, partial differential equations (PDE) can be applied. This approach has been used to explain the existence of morphogens by Alan Turing (1952). Both ODE and PDE models are deterministic, i.e. given the same initial conditions for each model, repeated simulations will produce the same results. Both models can be analyzed by parametric sensitivity analysis and bifurcation analysis. Parametric sensitivity analysis can be carried out to characterize quantitative changes of model dynamics in response to perturbations of model parameters (Varma et al, 1999). Bifurcation analysis is used to determine how qualitative properties of a system depend on its parameters, in particular, to find the steady-state solutions of a system and their stability (Guckenheimer, Holmes, 2002). The differential equations may be not adequate if the number of molecules is low because there will be fluctuations in the cellular processes. When molecular noise affects a cellular function, it has to be captured by mathematical analysis. This can be carried out by chemical master equations (CME). CME model can be solved by using the Gillespie’s fist reaction method (Gillespie, 1976). This algorithm chooses the fastest individual reaction and then transitions to the next state. Gibson modified Gillespie’s method to execute only the logarithm of a number of reactions by simulation (Gibson, Bruck, 2000). “One can now use a Gibson-modified Gillespie algorithm to execute 1010 reaction events per day on 800-MHz Pentium III Processor.” A hypothetical simulation of E. coli will need 1014-1016 reaction events per cell and seems quite tractable (Endy, Brent, 2001). Similar to the spatial extension of ODE to PDE, the same spatial effects can be included into stochastic models. Examples of deterministic/stochastic and non-spatial/spatial simulators given by Lok and Brent (2005) are summarized in Table 1.

D ata-D riven Modeling A pproaches Data-driven modeling approaches such as clustering (data organization), principal components (data compression) and partial least squares (data prediction) help users to analyze large amounts of data by specific data representation. Because cellular events are dynamic, time courses are the most typical. However, time-course plots are limiting for applications that track many variables together. An alternative view of the same data is to consider each variable on its own axis as a dimension. In this case, the state of a system will be described as a vector. In addition, it is possible to identify a small number of more important dimensions by reorganizing the data space. The goal of data-driven modeling is to extract the more informative dimensions from a whole data space. The aim of clustering is to define a distance between either the vectors themselves (Euclidean distance) or the parameters that are derived from the vectors (Pearson distance) in a way that reveals potential biological sense. Principal components analysis reduces the dimensionality by finding new axes, called principal components, as a result of the linear combination of axes that are the most tightly connected with one another. This method allows the user to view the data in 3D or 2D space and record the most important biological information. Partial least squares analysis allows user to pose hypotheses and predictions. Rather than performing the regression in the original data space, this approach reduces the dimension to a principal component space and finds the regression between independent and dependent principal components (Janes, Yaffe, 2006).

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Table 1. Molecular dynamics and simulation of biochemical networks Deterministic

Stochastic

Non-spatial

ODE Gepasi1

Gillespie’s first reaction algorithm Stochastirator3

Spatial

PDE Virtual Cell2 • exact • approximate • hybrid approach special-purpose hardware – Field Programmable Gate Arrays (FPGAs)

reaction events occur during collision MCell4 ray-tracing algorithms ChemCell5 Moleculizer6 for protein complexes; the program automatically generates the network of reactions BioNetGen7 signaling pathways

- http://www.gepasi.org/ - http://www.nrcam.uchc.edu/login/login.html 3 - http://opnsrcbio.molsci.org/stochastirator/stoch-main.html 4 - http://www.mcell.cnl.salk.edu/ 5 - http://www.cs.sandia.gov/~sjplimp/cell.html 6 - http://www.molsci.org/~lok/moleculizer/ 7 - http://cellsignaling.lanl.gov/bionetgen 1 2

A gent-B ased A pproach: D ata Mining and S imulation in a S ingle Platform According to science, the world is a stratified structure with many levels. Entities on each level interact with other entities at the same level and generate new selective qualities for a next higher level. Because these adaptive interactions are too complex to be captured by analytical methods, computer simulation is used. The basic idea of such simulation is to specify the rules of behavior of individual entities as well as the rules of their interactions. Simulated entities are called agents, the simulation of their behavior is known as agent-based simulation. Properties of individual agents describing their behavior and interactions are specified as elementary properties, and properties emerging on the higher, collective level are defined as emergent properties. In this respect, an agent is like a computing system with a well defined interface capable of adaptive problem-solving actions without user intervention. Agent-oriented engineering has much in common with object-oriented programming and was used to develop software for assistants for bioinformaticians and as problem solvers for biologists. Agents have been exploited in Systems Biology for the management of primary databases, genome analysis and annotation, for identification of spots on a microarray and 2D gels, in mass spectrometry and in biological systems simulation such as the molecular self-organization (Troisi et al, 2005), bacterial chemotaxis (Emonet et al, 2005) and T-cell recognition (Casal et al, 2005). An agent paradigm of distributed computing can be considered as a generalization of cellular automata; each agent acts like a finite state machine. Agent-to-agent interactions and messages passing between agents are essential for collective behavior. The agent-based simulation increases the biological intuition and is more suitable than other modeling methods because the ‘cell as agent’ is a natural metaphor for biologists. “A biological process can be described by a graphical semi-formal model, validated by a formal model, simulated by a multi-agent system and finally tested with experimental results” (Merelli et al, 2007).

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S ynthetic B iology

B iology is an engineering

appr oach t o S ystems

The term Synthetic Biology was originally used to describe efforts merging different disciplines in order to reach a holistic understanding of life. This term also has been applied to the combination of science and technology in their attempt to design novel biological functions. In 1978, Waclaw Szybalski wrote that “The work on restriction nucleases … has led us into the new era of synthetic biology.” Along this line, a straightforward tactic to test our understanding of a natural system is to make a version of the system; the similarity between observation and expectation is the highlight of a ‘constructive paradigm’. The potential of gene synthesis was demonstrated in 1964 by the team of Gobind Korana as a part of their work on the elucidation of genetic code. Synthetic Biology means an expansion of biotechnology to an engineering formalism, with “the ultimate goal of designing and building engineered biological systems that process information, manipulate chemicals, fabricate materials and structures, produce energy, provide food, maintain and enhance human health and our environment.” An important aspect of Synthetic Biology, which distinguishes it from conventional genetic engineering, is a strong emphasis on foundational technologies that make the engineering of Biology easier and more reliable (Endy, 2005). Such examples are the common systems engineering doctrines, which has been accepted by biologists, including step-by-step modeling and experimentation trials, sharing models, but not raw data, and microarray-based DNA synthesis (Tian et al, 2004; Stähler et al, 2006). Synthetic Biology has two branches. The first one, ‘reconstruction of life’, is a dissection of biological systems into minimal modules. This approach includes experiments to obtain information on isolated parts, the simulation of systems from these parts and future experimental verification. The second one is the ‘construction of life’. In this case, the goal is to build systems inspired by biological knowledge. The general idea here is to combine modular, robust and reusable artificial components to reach even more interesting properties about life that are yet unknown. Because natural biological systems are extremely complex, it makes sense to ‘rewrite’ them according to our view and deal with the artificial systems. This notion draws its inspiration from refactoring, a process used to improve the computer software. DNA synthesis, as expected, will replace a traditional recombinant technology and will allow ‘DNA programming’, for instance, the large-scale genome synthesis, change of codons to improve gene expression, and the incorporation of novel amino acids into polypeptides. The construction of synthetic metabolic pathways would prevent a complexity of life created by evolution. Through the synthesis, we could escape ‘cross talks’ and reduce the entanglement of signaling pathways. More remarkable is that Synthetic Biology has naturally accepted the agent and amorphous computing paradigms (Abelson et al, 2000). “It is a way of thinking about existing biological machines and of constructing new ones” (Baker et al, 2006). The latest success in the modification of cellular processes and improvements in DNA synthesis technology led to the recognition of living cells as a ‘programmable matter’. Through genetic engineering and principles of abstraction, composition and specification, it is now possible to program bacterial cells with sensors, logics and actuators like computers or robots (Voigt, 2006). Information propagates in cells through synthetic transcriptional cascades. The artificial cell-to-cell communication was programmed to reach a coordinated bacterial behavior and pattern formation that allowed observing how global behavior emerges from local interactions between cells. There are attempts to exploit synthetic gene networks representing analog and digital logic circuitry

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that regulate gene expression, differentiation and cell communication in higher organisms (Andrianantoandro et al, 2006).

S ynthetic bi ologist’s genetic circ uits

t oolkit : the plug-and-p lay design

of

A design of de novo genetic circuits starts by the identification of suitable genetic elements (building blocks) including promoter regions, ribosome binding sites, structural genes, attenuators of transcription and so on. There are active efforts to collect genetic elements as Biobricks—pieces of DNA flanked by idempotent restriction sites. A registry of Standard Biological Parts (http://parts.mit.edu/) includes the catalog of standard DNA components that can be distributed and shared among students. One idea behind the registry is that these genetic parts can be recombined to produce many types of devices in an abstract hierarchical manner. At the next level, devices with a matching interface can be assembled into more complex systems. This aim could be achieved by the idempotent vector that recreates exactly the same restriction site and contains DNA parts with the desired functions. The strategy includes genetic transformation by the designed genetic construct and observation of the actual result compared with the desired output. Well characterized Biobricks will not only serve as building blocks but will provide kinetic parameters for simulation. In the future, as DNA synthesis becomes less expensive, the registry will be replaced by specifications of in silico building blocks—‘LEGO set of life’ for the computer added design (CAD). Many kinds of circuits like transcriptional cascades with feedback and feedforward motifs may be constructed by combinations of existing genetic parts. These networks, for example, can serve as memory elements, perform digital computation, send and receive chemical signals, attenuate gene expression noise, or generate oscillations and single pulses (Guido et al, 2006; Heinemann, Panke, 2006). However, many questions remain (Drubin et al, 2007). How would higher levels of complexity for synthetic biological systems be designed? What kind of standards do we need? Who will contribute subsystems? Modern cloning technique was not restricted by the MIT Biobricks assembly method (Knight, 2003). Typically, PCR with extended primers keeps any flanking restriction site for the cloning DNA which can be inserted into a desirable vector. There are many other cloning strategies each with advantages and disadvantages e.g. the NOMAD technology (Rebatchouk et al, 1996), Gateway recombination cloning system (Brasch et al, 2004), and Topo cloning (Invitrogen). Many commercial firms like Invitrogen and Stratagene have advanced their own schemes for cloning including equipments and competent cells for easy transformation. A real problem for cloning techniques is the small capacity of cloning vectors which is about 10-12 kb for E. coli system. Using an artificial chromosome may be necessary in order to exceed this limit. In addition to Biobricks registry, there is significant interest in filling the databases for aptamers and protein domains. Perhaps Synthetic Biology will not be restricted by one catalogue of known biological parts but will include the tools needed to supplement custom-made parts and to utilize natural sequences from NCBI (http://www.ncbi.nlm.nih.gov/). When a circuit is built, it can be evaluated by quantitative analyses including assays for the reporter gene expression, cell growth, light microscopy, flow cytometry and microfluidics. Single cell measurement has been used to study binding constants, degradation rates, noises in gene expression and variations of chemotaxis activity. Such observations help to explain how a biological system acts and provide the basis for modeling. Differences between predicted and measured behavior can give details why a

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synthetic system does not work as anticipated. In some cases, engineered cells have to be characterized under specific conditions for a long time scale. Such tasks will benefit from microfluidics focusing on miniaturization of cell environment in order to make possible the single cell assessment. Technologies that allow the study of cells in microfabricated devices and perform parallel ‘postgenomic’ data collection will be especially useful in Synthetic Biology. Standardization of measurements will ultimately enable CAD applications (Marguet et al, 2007).

Evolu ti on as a techn ology f or S ynthetic life’

B iology : an ‘ersa tz

A manufacture of biological parts and devices can be achieved through either rational design or laboratory evolution. Usually preliminary design includes the modeling, testing, and modification of basic circuit components such as promoters and ribosomal binding sites. The rational design requires prior information about the parts, which is sometimes unavailable. Opposite of the laboratory evolution is the method of debugging synthetic biological systems (Yokobayashi et al, 2002). The process launches with the generation of a huge library of diverse DNA molecules by error-prone PCR and DNA shuffling or combinatorial synthesis. The library is then subjected to a selection that provides a connection between genotype and phenotype in order to reach the preferred function. Laboratory evolution requires highthroughput measurements covering a large search space. It should be mentioned that the fitness function is not evident in many applications and the selection pressure can be applied only in simple cases as for antibiotic resistance. An evolution of complex behavior may not be straightforward. It is not clear at the moment how such laboratory evolution can easily be tailored to screen for a content dependent design of complex genetic networks. There are questions that should be addressed about the evolutionary stability of artificial networks. Both methods could be considered as different modes to optimization and should be used in combination; an example of the ‘intermediate’ method is the modular recombination or compositional evolution (Hiraga, Arnold, 2003). The next step in Synthetic Biology research would be a ‘computational evolution’ where a set of parts can evolve in silico into networks that demonstrate desired behaviors. Whether such molecular evolution is tractable for digital computers is an open question. As an alternative, the cellular computation could be designed to take advantage of the vast parallelism of cell agents. In the context of cellular computing, a heterogeneous population of cells is able to investigate a very large search space (Kuznetsov et al, 2006; Tan et al, 2007). Basically, Systems Biology might contribute in producing artificial cells demonstrating behaviors which we associate with life (Barrett et al, 2006). In modern terms, DNA can be considered as software and the rest of the cell as hardware. Technically, it will soon be possible to synthesize a whole bacterial genome de novo and introduce it into a ‘lipid sack’ to generate a protocell. This life-like biological agent will encapsulate macromolecules, capture energy, maintain ion gradients and divide (Forster, Church, 2007). However, the modern approach to artificial life is more pragmatic with the intention of cleaning genomes. Recent achievements in Comparative Genomics have revealed the essential genes that maintain the replication, transcription, translation, reparation, protein processing and metabolism. It is possible to cut out mobile elements and unknown genes with insufficient functions to make the genome easier to customize. Progress has been made towards the identification of non-essential genes in the genome of Escherichia coli. Kang et al (2004) removed by knockout redundant genes to be close

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to a core genome. It was observed that E. coli strains with a reduced genome were genetically more stable, increased protein synthesis and even improved electroporation efficiency. A resulting bacterium with the minimal genome may serve as a vessel for synthetic genetic networks. Mesoplasma florum L1 with very attractive cultivation properties has the genome size of 793 kb comprising only 517 genes. The genomic sequence has become available and molecular biology methods are developed. A similar approach is being followed with Mycoplasma genitalium G-37 (580 kb, 482 genes), for which comprehensive data are available (Glass et al, 2006). These findings show that a redesign of an entire synthetic microorganism is not far off in the future.

Minima l synthetic

organism

as therape

utic nan ob ot

Artificial bacterial robots are expected to appear in the coming years. “Applied to medicine, nanorobots would be programmed for specific biological task and injected into the blood … to work at the cellular level … attacking cancer cells” (Patel et al, 2006). To effectively fight cancer, therapeutic nanobots should recognize malignant cells and destroy them. Anticancer agents should avoid immunological surveillance; demonstrate decentralized and distributed swarm intelligence and emergent cooperative behavior. It means that they will have to obtain sensors, computational resources to make decisions and actuators to act on target tumor cells. Nearly 150 years ago, live bacteria were used in the treatment of cancer. Today there is revived interest in using bacteria as anti-tumor agents. Bifidobacterium, Clostridium and Salmonella have been shown to preferentially reproduce within solid tumors and have been used to transport DNA encoded toxins, prodrug-activating enzymes, cytokines and angiogenesis inhibitors (Pawelek et al, 2003). Bacteria can feel their environment and distinguish between cell types. The sensors, logics and actuators could be embodied in genetic circuits of bacteria to perform coordinated tasks for therapy. Anderson et al. (2006) engineered the non-pathogenic bacteria E. coli able to invade mammalian cells selectively at high cell density or anaerobic conditions (Figure 1). Previous microarray analysis identified several genes in E. coli,

Figure 1. Condition dependent invasion. At a low cell density or normal aerobic growth conditions, the engineered bacteria are noninvasive. Above a critical cell density or in a hypoxic environment, sensors are activated resulting in the synthesis of invasin from Y. pseudotuberculosis that leads to the invasion of HeLa cells (Anderson et al, 2006)

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whose expression is strongly induced after the shift from aerobic to anaerobic growth. The formate dehydrogenase ( fdhF) is one of the most strongly induced genes. Therefore, fdhF promoter was chosen to activate the invasion after the transition to an anaerobic environment. The inv gene encoding invasin from Yersinia pseudotuberculosis was cloned in E. coli under fdhF promoter (Figure 2a). Typically, the invasin binds to β1-integrins presented on the surface of eukaryotic cells and induces bacterial uptake by mammalian cells. If fdhF promoter is active, then invasin is expressed in E. coli initiating adhesion and invasion (Figure 2b). The inv gene provoked invasion of the cervical carcinoma, hepatocarcinoma and osteosarcoma. The engineered bacteria invaded tumor cells either under anaerobic conditions or when their density was high (mechanism is not shown). Modification of gene circuits by the coupling of hypoxia-sensing and quorum-sensing into AND gate may improve the specificity of bacterial invasion of tumor cells. The authors wrote that “Genetic logic circuits or response regulatory networks could integrate multiple inputs to achieve more accurate environmental sensing.” In general, cancer research has focused on the identification of molecular differences between malignant and healthy cells. Although, there have been attempts to summarize experimental results through mathematical models, the gaps between in vitro cell lines, animal tumor models, and human in vivo tumors are still very large. The picture is very complex and will continue to be so; about 300 genes have been identified in tumorgenesis. Molecules from many parallel signal transduction pathways are involved. Their activities appear to be controlled by multiple factors (Khalil, Hill, 2005; Hornberg et al, 2006). However, there is great hope that the measured in vivo data can be used for ‘personalized medicine’. Vectors on the basis of retroviruses, adenoviruses and lentiviruses have been attempted to deliver genes into human cells. Still numerous problems exist such as ensuring those viruses will infect the correct target cells. Under a new light of collective artificial intelligence and bacterial programming, it seems that the viruses are too primitive to be applied as smart therapeutic agents to perform a swarm algorithm. They simply do not have enough computing power to make ‘intelligent decisions’ about cell type invasion. However, the experiences of viruses in Molecular Biology can be extremely useful in the construction of a ‘bug’ with diagnostic and therapeutic modules in one device. A genome synthesis will make it possible to fabricate this minimal cell. This way of managing a cancer system Figure 2. Design and results of anaerobic invasion. (a) fdhF promoter was fused with inv gene. (b) Bacteria, recovered from cells after invasion with no plasmid (wt) and with the FdhInv gene, grown with no induction in white and anaerobic induction in black. Assays in which no bacteria were recovered are indicated by an asterisk (Anderson et al, 2006)

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phenomenon has one advantage. Synthetic genomes will be supplied with manuals and documentation. ‘Cell chassis’ will create a context for installing new genetic modules and become an ideal therapeutic nanobot. These autonomous agents will perform logic operations to make a collective verdict. “The complex biological system engineered to perform a task should be the cell, and in fact not just one cell, but a population of cells” (Weiss, 2007).

Co nstr ucti on of multice llular systems, organisms (GM O)

genetica

lly modified

A human body is a complex multi-agent system of 1014 highly specialized cells organized in tissues and organs. Individual cells take their origin from a single fertilized egg. This process of differentiation and morphogenesis is organized by an accompaniment of chemical gradients, cellular receptors, differential gene expression and cell migration (Gilbert, 2000). Typically, coordinated cell behavior Figure 3. E. coli receiver cell can shine in green only at an intermediate distance from the sender cell Circuit operation for a sender and three receivers, exposed to high, medium, and low AHL concentrations, showing the relevant protein activities in cells at different distances from the sender as mediated through transcriptional regulation (orange, constitutively expressed response proteins; blue/green, expression of regulated proteins; green and red arrows, transcriptional induction and repression respectively). High levels of LacI or LacIM1 are required to repress GFP (Basu et al, 2005)

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involves cell-to-cell communication and intracellular signal processing. Synthetic Biology has been used to exploit and improve by design the pattern formation mechanisms found in Nature. To address this question, Basu et al (2005) created artificial patterns from bacterial cells. Authors demonstrated “a synthetic multicellular system in which genetically engineered ‘receiver’ cells are programmed to form ring-like patterns of differentiation based on chemical gradients of an acyl-homoserine lactone (AHL) signal that is synthesized by ‘sender’ cells” (Figures 3, 4). An AHL communication signal from sender cells is initiated by expression of the LuxI enzyme. “LuxI catalyses the synthesis of AHL which diffuses through the cell membrane and forms a chemical gradient around the senders. AHL diffuses into nearby receiver cells and binds to LuxR, an AHL-dependent transcriptional regulator which activates the expression of lambda repressor (CI) and Lac repressor (LacIM1, a product of a codon-modified lacI). Receiver cells in close proximity to the senders receive high concentrations of AHL resulting in high cytoplasmic levels of CI and LacIM1 and repression of the green fluorescent protein (GFP). Receivers that are far from the senders have low AHL concentrations, and accordingly LacIM1 and CI are expressed only at basal levels. This enables the expression of a wildtype LacI, again resulting in GFP repression. At intermediate distances from the senders, intermediate AHL concentrations result in moderate levels of CI and LacIM1. However, because the repression efficiency of CI is significantly higher than that of LacIM1, CI effectively shuts off LacI expression while the LacIM1 concentration is below the threshold required to repress GFP production. This difference between the CI and LacIM1 repression efficiencies, in combination with a feed-forward loop that begins with LuxR and culminates in GFP, affords the circuit the desired non-monotonic response to AHL dosages” (Basu et al, 2005). The authors have shown how a population of bacterial cells can sense a chemical gradient and form three distinct regions. The space design parameters were determined by modeling and experimentation. Ron Wiess expects it will be possible to extend the artificial rules of pattern formation within bacteria to

Figure 4. Formation of various patterns. (a) Simulation with two senders that results in the formation of an ellipse. (b–d) Experiments showing various GFP patterns formed as a result of the placement and initial concentrations of sender cells: b, ellipse, two sender disks; c, heart, three sender disks; and d, clover, four sender disks (Basu et al, 2005)

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coordinate a collective behavior of eukaryotic cells. “The integration of such systems into higher-level organisms … will have practical applications in three-dimensional tissue engineering, biosensing and biomaterial fabrication.” The cell behavior during development of multicellular organisms correlates with the spatiotemporal pattern of gene expression. Synthetic gene networks, artificial cell-to-cell communication, and spatiotemporal dynamics of yeast and mouse embryonic stem cells are under active investigation with the ultimate goal of organ engineering (Weiss, 2007). The most interesting objectives are not just genetic circuits but circuits embedded into host cells. Natural genetic circuits are not optimized for the operation within a foreign cellular context. In fact, the same genetic circuit can have various behaviors in different strains. Theoretically, genetic circuits should be disconnected from the cellular context. This is exactly the same old problem that Genetic Engineering had with GMOs. Transgenesis has been used for decades to study molecular mechanisms of basic cellular processes as well as to create organisms that produce therapeutic proteins. But these efforts were mostly unsuccessful because of the extreme complexity of biological systems. The uncertainty and context dependence of installed genetic programs as well as mutations and long-term instability are well known obstacles to Genetic Engineering (Kuznetsov, 1995; Cases, de Lorenzo, 2005). It is now apparent: “genetic circuits function best if the number of interactions between the circuits and the host cell are minimized.” For Synthetic Biology, this minimization means engineering a simple organism with a minimal set of genes by synthesizing its genome. But the critical question of whether a synthetic minimal genome would be a comfortable niche for selfish genetic elements presented in the natural environment is open. To avoid this problem, the development of a completely artificial genetic code as well as the search for alternative energy sources and unusual substrates totally separating the therapeutic agents—an ‘orthogonal life’ would be a wiser decision.

Co nc lusi on At the same time that high-throughput technologies have accelerated Genome Analysis and Proteomics, the Functional Genomics have remained a bottleneck since it has been based on the slow cloning of recombinant DNA. Paradoxically, a complexity of Biology was the basis for the development of Systems and Synthetic Biology. One important goal of SYS Biology is to understand life processes in detail in order to predict their behavior. If we wish to create a biological system that behaves in a predictable way, how could that system be organized? If we want to get a bacterium producing artemisinic acid to combat malaria, how should the metabolic network of the bacterium be rewritten? Or, if our dream is to produce a smart drug against HIV, what is the best swarm algorithm in vivo? SYS Biology is becoming a top field with a great potential to revolutionize Biotechnology. Nevertheless, Systems and Synthetic Biology are in they initial stages and attempting to define themselves and we are at the singular point in our understanding of what these new technologies will contribute to Biology and Medicine. In addition to numerous scientific challenges, there are also questions regarding strict safety and health regulations. Attention has only been given to ‘dual-use’ technologies. Recent efforts have focused on the relations of scientists and the media. Eethical issues have just started to be explored. Many questions have arisen (Rai, Boyle, 2007), e.g. what is the best financial mechanism to support this research? what is more suitable, open source or copyright? is academic freedom important? Similarly, the basic philosophical ideas of ‘constructive biology’ have been formulated (Zoloth, 2005): 1) Genes are selfish. 2) Dignity is the intactness of being. 3) Nature is fixed. 4) Nature is normative. 5) Suffering is what

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defines the human condition. 6) Slopes are slippery. 7) Dual-use is inevitable. 8) Mistakes are inevitable. 9) We will be like gods. 10) The marketplace will distort science. 11) An unfair world (inequity). 12) A ‘synthetic’ world, i.e. could we call it carefree Biology? The paradigm shift to a systems/synthetic science and technology can only be done through the collaboration of different disciplines: Mathematics, Information Science, Physics, Chemistry, Biology, Medicine, Micro- and Nano-Engineering. The Genetics, Nanotechnology, Robotics and their fusion (GNR) are considered the key technologies for the 21st century. Radical discoveries and novel applications, such as the alteration of biomolecules and programming molecular interactions leading to an assembly into sophisticated artificial systems are expected from this new union.

A ckn ow ledgment The author is very grateful to Systems Biology and Synthetic Biology scientific communities for materials that have been taken from the open sources like PubMed, SBML portal, OpenWetWare and Wikipedia. Thanks also to Bert Schnell for his help with the manuscript and for which he declares no financial interest.

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Hornberg, J.J., Bruggeman, F.J., Westerhoff, H.V., & Lankelma, J. (2006). Cancer: A Systems Biology disease. Biosystems, 83(2-3), 81-90. Husmeier, D. (2003). Reverse engineering of genetic networks with Bayesian networks. Biochemical Society Transactions, 31(6), 1516-1518. Janes, K.A., & Yaffe, M.B. (2006). Data-driven modelling of signal-transduction networks. Nature Reviews Molecular Cell Biology, 11, 820-828. Kang, Y., Durfee, T., Glasner, J.D., Qiu, Y., Frisch, D., Winterberg, K.M., & Blattner, F.R. (2004). Systematic mutagenesis of the Escherichia coli genome. Journal of Bacteriology, 186, 15, 4921-4930. Keating, S.M., Bornstein, B.J., Finney, A., & Hucka, M. (2006). SBML Toolbox: An SBML toolbox for MATLAB users. Bioinformatics, 22(10), 1275-1277. Kell, D. (2005). Metabolomics, machine learning and modelling: towards an understanding of the language of cells. Biochemical Society Transactions, 33(3), 520-524. Khalil, I.G., & Hill, C. (2005). Systems biology for cancer. Current Opinion in Oncology, 17(1), 4448. Kitano, H. (2002a). Systems Biology: A brief overview. Science, 295, 1662-1664. Kitano, H. (2002b). Computational Systems Biology. Nature, 420, 206-210. Knight, T. (2003). Idempotent vector design for standard assembly of biobricks. MIT Artificial Intelligence Laboratory, MIT Synthetic Biology Working Group. Retrieved from http://dspace.mit.edu/ bitstream/1721.1/21168/1/biobricks.pdf Kuznetsov, A., Schmitz, M., & Mueller, K. (2006, July 26-28). On Bio-Design of Argo-Machine. Presented at 7th German Workshop on Artificial Life (GWAL-7 (pp. 125-133). Jena, Germany. Kuznetsov, A.V. (1995). Transgenic animals: The methods of construction. Russian Biotechnology, 3-4, 3-6. Lok, L., & Brent, R. (2005). Automatic generation of cellular reaction networks with Moleculizer 1.0. Nature Biotechnology, 23(1), 131-136. Marguet, P., Balagadde, F., Tan, C., & You, L. (2007). Biology by design: Reduction and synthesis of cellular components and behaviour. Journal of Royal Society Interface, 4(15), 607-623. Merelli, E., Armano, G., Cannata, N., Corradini, F., d’Inverno, M., Doms, A., Lord, P., Martin, A., Milanesi, L., Moller, S., Schroeder, M., & Luck, M. (2007). Agents in bioinformatics, computational and systems biology. Briefings in Bioinformatics, 8(1), 45-59. Patel, G.M., Patel, G.C., Patel, R.B., Patel, J.K., & Patel, M. (2006). Nanorobot: a versatile tool in nanomedicine. Journal of Drug Targeting, 14(2), 63-67. Patterson, S.D. (2003). Data analysis—the Achilles heel of proteomics. Nature Biotechnology, 21(3), 221-222.

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Pawelek, J.M., Low, K.B., & Bermudes, D. (2003). Bacteria as tumour-targeting vectors. The Lancet Oncology, 4, 548-556. Rai, A., & Boyle, J. (2007). Synthetic Biology: Caught between Property Rights, the Public Domain, and the Commons. PLoS Biology, 5(3) e58, 389-393. Rebatchouk, D., Daraselia, N., & Narita, J.O. (1996). NOMAD: a versatile strategy for in vitro DNA manipulation applied to promoter analysis and vector design. Proceedings of the National Academy of Sciences of the United States of America, 93(20), 10891-10896. Schrödinger, E. (1944). What is Life? Available as a Canto Edition from Cambridge University Press. 1992. Stähler, P., Beier, M., Gao, X., & Hoheisel, J.D. (2006). Another side of genomics: Synthetic biology as a means for the exploitation of whole-genome sequence information. Journal of Biotechnology, 124(1), 206-212. Tan, C., Song, H., Niemi, J., & You, L. (2007). A synthetic biology challenge: making cells compute. Molecular Biosystems, 3(5), 343-353. Tian, J., Gong, H., Sheng, N., Zhou, X., Gulari, E., Gao, X., & Church, G. (2004). Accurate multiplex gene synthesis from programmable DNA microchips. Nature, 432, 1050-1054. Troisi, A., Wong, V., & Ratner, M.A. (2005). An agent-based approach for modeling molecular self-organization. Proceedings of the National Academy of Sciences of the United States of America, 102(2), 255-260. Turing, A. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London, 237(641), 37-72. Varma. A., Morbidelli, M., & Wu, H. (1999). Parametric sensitivity in chemical systems. Cambridge, New York: Cambridge University Press. Voigt, C.A. (2006). Genetic parts to program bacteria. Current Opinion in Biotechnology, 17(5), 548557. Wagner, A. (1996). Can nonlinear epigenetic interactions obscure causal relations between genotype and phenotype? Nonlinearity, 9, 607-629. Weiss, R. (2007, January 11-13). Developments in synthetic biology. In the lecture presented at Systems Biology, Bioinformatics and Synthetic Biology Workshop (BioSysBio 2007), Manchester, UK. Wiener, N. (1948). Cybernetics or control and communication in the animal and the machine. Cambridge, MA: MIT Press. Yokobayashi, Y., Weiss, R., & Arnold, F.H. (2002). Directed evolution of a genetic circuit. Proceedings of the National Academy of Sciences of the United States of America, 99(26), 16587-16591. Zoloth, L. (2006, May 20-22). Ethical challenges in Synthetic Biology. The lecture presented at Second International Conference on Synthetic Biology (Synthetic Biology 2.0). University of California, Berkeley, CA.

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K ey T erms Agent: A computing system with a well defined interface capable of adaptive problem-solving actions without user intervention. Amorphous Computing: The action of generating a coherent behavior from a group of unreliable agents such as living cells. Competent Cell: A cell that can accept foreign DNA. Emergence: Refers to new unexpected behaviors and patterns that arise out of a multiplicity of relatively simple interactions. An emergent behavior can appear when a number of simple entities (agents) operate in an environment while forming more complex behaviors as a community. Minimal (or core) Genome: The minimum set of genes necessary for a cell to propagate under specific environmental conditions. Nanorobot (or nanobot): Can be defined as the artificially fabricated object able to freely move in a human body and interact with specific cells at the molecular level itself e.g. seeking out cancer cells and destroying them. Orthogonal Life: A term stressing the complete isolation of artificial life-like creatures from natural processes by using the alternative genetic code and the reliable interface. Chen’s rules should be taken in an account: 1) nanomachines should only be specialized, not general purpose, 2) nanomachines should not be self-replicating, 3) nanomachines should not be made to use an abundant natural compound as fuel, 4) nanomachines should be tagged so they can be tracked. Refactoring: Any modification of a computer program which improves its readability or simplifies its structure without changing its results. Synthetic Biology: An engineering discipline concerning synthesis of novel biological systems that are not found in nature. It has involved a paradigm enabling scientists to create ‘life from scratch’ that will help to understand principles of Biology. Synthetic Biology holds promise for programming bacteria to seek and destroy tumors. However, the complexity of Biology and emergent effects have provoked many technical and ethical challenges. SYS Biology: A speculative merge of Systems Biology and Synthetic Biology that can be defined as an approach to the biological reality, where natural and artificial processes should be described in terms of their components and their interactions in a framework of mathematical models towards a reconstruction of biological systems. Systems Biology: The study of an organism, viewed as an interacting network of genes, proteins, and biochemical reactions which give rise to life. Instead of analyzing individual aspects of the organism, systems biologists focus on all the components and the interactions among them. Systems Biology is the discipline that specifically addresses the fundamental properties of biological complexity. Transgenensis: The introduction of foreign genes into a living organism that confers upon the organism a new property that will be transmitted to a progeny.

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Section II

Advanced Computational Methods for Systems Biology

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Chapter VI

Computational Models for the Analysis of Modern Biological Data Tuan D. Pham James Cook University, Australia

abstract Computational models have been playing a significant role for the computer-based analysis of biological and biomedical data. Given the recent availability of genomic sequences and microarray gene expression, and proteomic data, there is an increasing demand for developing and applying advanced computational techniques for exploring these types of data such as: functional interpretation of gene expression data, deciphering of how genes, and proteins work together in pathways and networks, extracting and analysing phenotypic features of mitotic cells for high throughput screening of novel anti-mitotic drugs. Successful applications of advanced computational algorithms to solving modern life-science problems will make significant impacts on several important and promising issues related to genomic medicine, molecular imaging, and the scientific knowledge of the genetic basis of diseases. This chapter reviews the fusion of engineering, computer science, and information sciences with biology and medicine to address some latest technical developments in the computational analyses of modern biological data: microarray gene expression data, mass spectrometry data, and bioimaging.

Micr oarra y G ene E xpressi on D at a Microarrays are a relatively new biotechnology that provides novel insights into gene expression and gene regulation (Brazma and Vilo, 2000; Whitchurch, 2002; Zhang at al, 2002; Pham et al, 2006a). Microarray technology has been applied in diverse areas ranging from genetics and drug discovery to disciplines such as virology, microbiology, immunology, endocrinology, and neurobiology. Microarraybased methods are the most widely used technology for large-scale analysis of gene expression because Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Computational Models for the Analysis of Modern Biological Data

they allow simultaneous study of mRNA abundance for thousands of genes in a single experiment (Kellum and Liu, 2003). The generation of DNA microarray image spots involves the hybridization of two probes labelled with a fluorescent red dye or a fluorescent green dye. The relative image intensity values of the red dye and the green dye on a particular spot of the arrays indicate the expression ratio for the corresponding gene of the two samples from which the mRNAs have been extracted. Thus, robust image processing of microarray spots plays an important role in microarray technology (Nagarajan, 2003; Liew at al, 2003; Lukac et al, 2004). DNA microarray data consists of a large number of genes and a relatively small number of experimental samples. The number of genes on an array is in the order of thousands, and because this far exceeds the number of samples, dimension reduction is needed to allow efficient analysis of data classification techniques. Many statistical and machine-learning techniques based different computational methodologies have been applied for cancer classification in microarray experiments. These techniques include linear discriminant analysis, k-nearest neighbor algorithms, Bayes classifiers, decision trees, neural networks, and support vector machines (Dudoit and Fridlyand, 2003; Golub et al, 1999; Guyon et al, 2002). Nevertheless, common tasks of most classifiers are to perform feature selection and decision logic. Based on the motivation that conventional statistical methods for pattern classification break down when there are more variables (genes) than there are samples, Nguyen and Rocke (2002) proposed a partial least-squares method for classifying human tumor samples using microarray gene expression data. Zhou et al. (2004) proposed a Bayesian approach for selecting the strongest genes based on microarray gene expression data and the logistic regression model for classifying and predicting cancer genes. Yeung et al. (2005) reported that conventional methods for gene selection and classification do not take into account model uncertainty and use a single set of selected genes for prediction, and introduced a Bayesian model averaging method, which considers the uncertainty by averaging over multiple sets of overlapping relevant genes. Furey et al. (2000) applied support vector machines for the classification of cancer tissue samples or cell types using microarrays. Lee et al. (2003) proposed a Bayesian model for gene selection for cancer classification using microarray data. Statnikov et al. (2005) carried out a comprehensive evaluation of classification methods for cancer diagnosis based on microarray gene expression data. Recently Pham et al. (2006b) carried out cancer classification by transforming microarray data into spectral vectors. The same authors used the spectral difference or spectral distortion between the pair of spectra for pattern comparison, which appears to be a potential approach for the cancer classification using microarray gene expression data.

Mass spectr

ometr y da t a

Current best practice for reducing human mortality rates caused by complex diseases is to detect their symptoms at early stages. By early recognition of symptoms, one can get the most effective clinical treatment for the best outcome. Recent advances in biotechnology open doors to fascinating opportunities for the better understanding of the biology of many complex human diseases at molecular levels. These advances will hopefully lead to the early detection and treatment of such diseases (Petricoin and Liotta, 2003; Wulfkuhle et al, 2003).

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Besides the availability of genomic data, life-science researchers study proteomics in order to gain insight into the functions of cells by learning how proteins are expressed, processed, recycled, and their localization in cells. Proteomics is defined as the study of proteome which refers to the entire set of expressed protein in a cell. Major research areas of proteomics include structural, functional, and interaction studies (Holmes et al, 2005). Structural proteomics uses X-ray crystallography, nuclear magnetic resonance, or even both to study the final three dimensional shape of proteins. Functional proteomics involves the use of mass spectrometry (MS) to study the regulation, timing, and location of protein expression. Interaction studies seek to understand how protein pair between themselves and other cellular components interacts to constitute to more complex models of the molecular machines. In particular, protein expression profiles or expression proteomics can be used for large-scale protein characterization or differential expression analysis that has many applications such as disease classification and prediction, new drug treatment and development, virulence factors, and polymorphisms for genetic mapping, and species determinants (Adam et al, 2001; Griffin et al, 2002; Aebersold and Mann, 2003; Weir et al, 2003). In comparison with transcriptional profiling in functional genomics, proteomics has some obvious advantages in that it provides a more direct approach to studying cellular functions because most gene functions are characterized by proteins (Xiong, 2006). The identities of expressed proteins in a proteome can be determined by protein separation, identification, and quantification. One of many approaches for separating proteins involves two-dimensional gel electrophoresis followed by gel image processing. Once proteins are separated, protein differential expression can be characterized using mass spectrometry, which is a high-resolution technique for determining molecular masses and provides rapid and accurate measurement of protein profiling in complex biological and chemical mixture. Protein profiling of plasma and serum can be prepared with a matrix-assisted laser desorption ionization (MALDI) ion source or the surface-enhanced laser desorption ionization (SELDI) ion source coupled to a time-of-flight (TOF) mass analyzer with a chevron micochannel plate detector. Detailed descriptions on mass spectrometry and its advanced developments can be found in the review by Shin and Markey (2006). In regards to recent applications of proteomic technology, proteomic patterns have recently been utilized for early detection of cancer progressions (Sauter et al, 2002; Petricoin et al, 2002; Conrads et al, 2003). Furthermore, methods for classification of normal and cancerous states using mass spectrometry data have been recently developed. Petricoin et al. (2002) applied cluster analysis and genetic algorithms to detect early stage ovarian cancer using proteomic spectra. Ball et al. (2002) applied integrated approach based on neural networks to study SELDI-MS data for classification of human tumors and identification of biomarkers. Lilien et al. (2003) applied principal component analysis and a linear discriminant function to classify ovarian and prostate cancers. Sorace and Zhan (2003) used mass spectrometry serum profiles to detect early ovarian cancer. Wu et al. (2003) compared the performance of several methods for the classification of mass spectrometry data. Tibshirani et al. (2004) proposed a probabilistic approach for sample classification from protein mass spectrometry data. Morris et al. (2005) applied wavelet transforms and peak detection for feature extraction of MS data. Yu et al. (2005) developed a method for dimensionality reduction for high-throughput MS data. Levner (2005) used feature selection methods and then applied the nearest centroid technique to classify MS-based ovarian and prostate cancer datasets. Zhou et al (2006) applied genetic algorithms for protein biomarker discovery for risk stratification of cardiovascular events. Pham et al. (2006c) have applied the linear predictive coding method for the

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prediction of the risk of major adverse cardiac events using mass spectral data. The motivation of this research was initiated from the original work presented in Brennan et al. (2003), who studied 604 patients who presented in emergency room with chest pain. The blood samples were collected at the presentation of the emergency room and the protein level of MPO (myloperoxidase) and other known cardiovascular biomarkers were measured. The patient’s outcome (any cardiovascular event) was monitored for 6 months. The study showed the MPO to be a new biomarker for the prediction of MACE (major adverse cardiac events) risk in 30 days after the presentation of chest pain in emergency room with accuracy about 60%. Recently, the FDA (U.S. Food and Drug Administration) approved the CardioMPO kit for measurement of MPO level (http://www.fda.gov/cdrh/reviews/K050029.pdf). In particular, Pham et al. (2006b) computed the prediction coefficients as a spectral feature of the MS data and used the minimum distortion rule to classify control and disease samples. The experimental results appeared to be promising and feasible for protein peak-detection strategy. Given the promising integration of several machine-learning methods and mass spectrometry data in high-throughput proteomics (Shin and Markey, 2006), this new biotechnology still encounters several challenges in order to become a mature platform for clinical diagnostics and protein-based biomarker profiling. Some of major challenges include noise filtering of MS data, selection of computational methods for MS-based classification, feature extraction and feature reduction of MS datasets (Anderle et al, 2004; Salmi et al, 2006).

B io-imaging da t a By the use of fluorescence-based reagents, high content screening (HCS) studies cell functions by extracting the temporal and spatial information about target activities within cells (Giuliano et al., 1997). Particularly due to the huge volumes of acquired images, the automation of HCS systems has become necessary to help life-science researchers understand the complex process of cell division or mitosis at a rapid speed (Debeir et al., 2005; Fox, 2003). Its power comes from the sensitivity and resolution of automated light microscopy with multi-well plates, combined with the availability of fluorescent probes that are attached to specific subcellular components, such as chromosomes and microtubules, for visualization of cell division or mitosis using standard epi-fluorescence microscopy techniques (Yarrow et al., 2003). By employing a carefully selected reporter probes and filters, fluorescence microscopy allows specific imaging of phenotypes of essentially any cell component (Murphy, 2001). With these probes we can determine both the amount of a cell component, and most critically, its distribution within the cell relative to other components. Typically, 3-4 different components are localized in the same cell using probes that excite at different wavelengths. Any change in cell physiology would cause a redistribution of one or more cellular components, and this redistribution provides a certain cytological marker that allows for scoring of the physiological change. In time-lapse microcopy images are usually captured in a time interval of more than 10 minutes. During this period dividing nuclei may move far away from each other and daughter cell nuclei may not overlap with their parents. An essential task for high content screening is to measure cell cycle progression (inter phase, prophase, metaphase, and telophase) in individual cells as a function of time. Cell cycle progress can be identified by measuring nuclear changes. Thus, automated time-lapse fluorescence microscopy imaging provides an important method for the observation and study of cellular nuclei in a dynamic fashion (Hiraoka and Haraguchi, 1996; Kanda et al., 1998). Stages of an automated cellular

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imaging analysis consist of segmentation, feature extraction, classification, and tracking of individual cells in a dynamic cellular population; and the classification of cell phases is considered the most difficult task of such analysis (Chen et at., 2006). Given the advanced fluorescent imaging technology, there still remain technical challenges in processing and analyzing large volumes of images generated by time-lapse microscopy. The increasing quantity and complexity of image data from dynamic microscopy renders manual analysis unreasonably time-consuming. Therefore, automatic techniques for analyzing cell-cycle progress are of considerable interest in the drug discovery process. Steps for automatic analysis of cell images include image segmentation, feature extraction and classification; whereas the solution for image segmentation plays an important role in providing accurate information for feature extraction and object classification. Wählby et al. (2004) combined intensity, edge and shape information for 2D and 3D segmentation of cell nuclei in tissue section. Pham et al. (2006c) have developed several classification models for identifying individual cell phase changes during a period of time. The same authors extracted the information of image spatial-continuity as a novel feature using the concept of geostatistics (Isaaks and Srivastava, 1989) and the theory of linear predictive coding (LPC) (Makhoul, 1975); and also presented another scheme for extracting two-dimensional image feature known as the spatial linear predictive coding (SLPC) coefficients. Classification of cell phases was then carried out by the vector quantization based templates for pattern matching.

R eferences Aebersold, R., & Mann, M. (2003). Mass spectrometry-based proteomics. Nature, 422, 198-207. Anderle, M., Roy, S., Lin, H., Becker, C., Joho, K. (2004). Quantifying reproducibility for differential proteomics: noise analysis for protein liquid chromatography-mass spectrometry of human serum. Bioinformatics, 20, 3575-3582. Adam, B.L., Vlahou, A., Semmes, O.J., Wright Jr., G.L. (2001). Proteomic approaches to biomarker discovery in prostate and bladder cancers. Proteomics, 1, 1264-1270. Ball, G., Mian, S., Holding, F., Allibone, R.O., Lowe, J., Ali, S., Li, G., McCardle, S., Ellis, I.O., Creaser, C., & Rees, R.C. (2002). An integrated approach utilizing artificial neural networks and SELDI mass spectrometry for the classification of human tumours and rapid identification of potential biomarkers. Bioinformatics, 18, 395-404. Brazma, A., & Vilo J. (2000). Gene expression data analysis. FEBS Letters, 480, 17-24. Brennan, M-L., Penn, M.S., Van Lente, V., Nambi, M.H., Shishehbor, R.J., Aviles, M., Goormastic, M.L., Pepoy, E.S., McErlean, E.J., Topol, S.E., Nissen, S.L., Hazen (2003). Prognostic value of myeloperoxidase in patients with chest pain. The New England Journal of Medicine, 13, 1595-1604. Chen, X., Zhou, X., & Wong, S.T.C. (2006). Automated segmentation, classification, and tracking cancer cell nuclei in time-lapse microscopy. IEEE Trans. Biomedical Engineering, 53, 762-766. Conrads, T.P., Zhou, M., Petricoin III, E.F., Liotta L., Veenstra, T.D. (2003). Cancer diagnosis using proteomic patterns. Expert Rev. Mol. Diagn., 3, 411-420.

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Debeir, O., Ham, P.V., Kiss, R., & Decaestecker, C. (2005) Tracking of migrating cellsunder phase-contrast video microscopy with combined mean-shift processes. IEEE Trans. Medical Imaging, 24, 697-711. Dudoit, S., & Fridlyand, J. (2003). Classification in microarray experiments. Statistical Analysis of Gene Expression Microarray Data, 3, 93-158, T. Speed, (ed.)Boca Raton, FL: Chapman & Hall,. Fox, S. (2003). Accommodating cells in HTS. Drug Discovery World, 5, 21-30. Furey, T.S., Cristianini, N., Duffy, N., Bednarski, D.W., Schummer, M., & Haussler, D. (2000). Support vector machine classification and validation of cancer tissue samples using microarray expression data. Bioinformatics, 16, 906-914. Golub, T.R., Slonim, D.K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J.P., Coller, H., Loh Jr. M.L., Downing, M.A., Caligiuri, C.D., BloomÞeld, E., & Lander, S. (1999). Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science, 286, 531-537. Griffin, T., Goodlett, T., & Aebersold, R. (2002). Advances in proteomic analysis by mass spectrometry. Curr. Opin. Biotechnol., 12, 607-612. Giuliano et al. (1997). High-content screening: A new approach to easing key bottlenecks in the drug discovery process. J. Biomolecular Screening, 2, 249-259. Guyon, I., Weston, J., Barnhill, S., & Vapnik, V. (2002). Gene selection for cancer classification using support vector machines. Machine Learning, 46, 389-422. Hiraoka, Y., & Haraguchi, T. (1996). Fluoresence imaging of mammalian living cells. Chromosome Res, 4, 173-176. Holmes, M.R., Ramkissoon, K.R., Giddings, M.C. (2005). Proteomics and protein identification. In Baxevanis AD, Ouellette BFF, (eds.), Bioinformatics: A practical guide to the analysis of genes and proteins (pp. 445-472). New Jersey: John Wiley & Sons. Isaaks, E.H., & Srivastava, R.M. (1989). An introduction to applied geostatistics. New York: Oxford University Press. Kanda, T., Sullivan, K.F., & Wahl, G.M. (1998). Histone-GFP fusion protein enables sensitive analysis of chromosome dynamics in living mammalian cells. Current Biology, 8, 377-385. Kellam P., & Liu, X. (2003). Experimental use of DNA arrays. Orengo, C.A., Jones, D.T., & Thornton, J.M. (eds.). Bioinformatics: Genes, Proteins & Structures, Bios. Oxford. Lee, K.E., Sha, N., Dougherty, E.R., Vannucci, M., & Mallick, B.K. (2003). Gene selection: A Bayesian variable selection approach. Bioinformatics, 19, 90-97. Levner, I. (2005). Feature selection and nearest centroid classification for protein mass spectrometry. BMC Bioinformatics, 6(68). Liew, AW-C, Yan, H., & Yang, M. (2003). Robust adaptive spot segmentation of DNA microarray images. Pattern Recognition, 36, 1251-1254. Lilien, R.H., Farid, H., & Donald, B.R. (2003). Probabilistic disease classification of expression-dependent proteomic data from mass spectrometry of human serum. J. Computational Biology, 10, 925-946.

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Lukac, R., Plataniotis, K.N., Smolka B., & Venetsanopoulos, A.N. (2004). A multichannel order-statistic technique for cDNA microarray image processing. IEEE Trans. Nanobioscience, 3,272-285. Makhoul, J. (1975). Linear prediction: a tutorial review. Proceedings of the IEEE, 63, 561-580. Morris, J.S., Coombes, K.R., Koomen, J., Baggerly, K.A., Kobayashi, R. (2005). Feature extraction and quantification for mass spectrometry in biomedical applications using the mean spectrum. Bioinformatics, 21, 1764-1775. Murphy, D.B. (2001). Fundamentals of light microscopy and electronic imaging. Wiley-Liss. Nagarajan, R. (2003). Intensity-based segmentation of microarrays images. IEEE Trans. Medical Imaging, 22, 882-889. Nguyen, D.V., & Rocke, D.M. (2002). Tumor classification by partial least squares using microarray gene expression data. Bioinformatics, 18, 39-50. Petricoin, E.F., et al. (2002). Use of proteomic patterns in serum to identify ovarian cancer. Lancet, 359, 572-577. Petricoin, E.F., & Liotta, L.A. (2003). Mass spectrometry-based diagnostics: The upcoming revolution in disease detection. Clinical Chemistry, 49, 533-534. Pham, T.D., Wells, C., & Crane, D.I. (2006a). Analysis of microarray gene expression data. Current Bioinformatics, 1(1), 37-53. Pham, T.D., Beck, D., & Yan, H. (2006b). Spectral pattern comparison methods for cancer classification based on microarray gene expression data. IEEE Trans. Circuits and Systems I: Fundamental Theory and Applications, special issue on Advances on Life Science Systems, 53(11), 2425-2430. Pham, T.D., Tran, D.T., Zhou, X., & Wong, S.T.C. (2006c). Integrated algorithms for image analysis and identification of nuclear division for high-content cell-cycle screening. Int. J. Computational Intelligence and Applications, 6, 21-43. Salmi, J., Moulder, R., Filen, J-J., Nevalainen, O.S., Nyman, T.A., Lahesmaa, R., & Aittokallio, T. (2006). Quality classification of tandem mass spectrometry data. Bioinformatics, 22, 400-406. Shin, H., Markey, M.K. (2006). A machine learning perspective on the development of clinical decision support systems utilizing mass spectra of blood samples. J. Biomedical Informatics, 39, 227-248. Sorace, J.M., & Zhan M. (2003). A data review and re-assessment of ovarian cencer serum proteomic profiling. BMC Bioinformatics, 4(24). Statnikov, A., Aliferis, C.F., Tsamardinos, I., Hardin, D., & Levy S. (2005). A comprehensive evaluation of multicategory classification methods for microarray gene expression cancer diagnosis. Bioinforamtics, 21, 631-643. Tibshirani, R., Hastie, T., Narasimhan, B., Soltys, S., Shi, G., Koong, A., Le, Q-T. (2004). Sample classification from protein mass spectrometry, by peak probability contrasts. Bioinformatics, 20, 3034-3044. Verma, D., & Meila, M. (2003). A comparison of spectral clustering algorithms. Technical Report, UWCSE-03-05-01. University of Washington.

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Wählby, C., Sintor, I.-M., Erlandsson, F., Borgefors, G., & Bengtsson, E. (2004). Combining intensity, edge and shape information for 2D and 3D segmentation of cell nuclei in tissue sections. Journal of Microscopy, 215, 67–76. Weir, M.P., Blackstock, W.P., Twyman, M. (2003). Proteomics, Bioinformatics: Genes, Proteins & Computers. C.A. Orengo, D.T. Jones, J.M. Thornton, (eds.). BIOS Scientific Publishers, 245-257. Whitchurch, A.K. (2002). Gene expression microarrays. IEEE Potentials, 21, 30-34. Wu, B., Abbott, T., Fishman, D., McMurray, W., Mor, G., Stone, K., Ward, D., Williams, K., & Zhao, H. (2003). Comparison of statistical methods for classification of ovarian cancer using mass spectrometry data. Bioinformatics, 19, 1636-1643. Wulfkuhle, J.D., Liotta, L.A., & Petricoin, E.F. (2003). Proteomic applications for the early detection of cancer. Nature, 3, 267-275. Xiong, J. (2006). Essential Bioinformatics. New York: Cambridge University Press. Yarrow, J.C., Feng, Y., Perlman, Z.E., Kirchhausen, T., & Mitchison, T.J. (2003). Phenotypic screening of small molecule libraries by high throughput cell imaging. Comb Chem High Throughput Screen, 6, 279-286. Yeung, K.Y., Bumgarner, R.E., & Raftery, A.E. (2005). Bayesian model averaging: Development of an improved multi-class, gene selection and classification tool for microarray data. Bioinformatics, 21, 2394-2402. Yu, J.S., Ongarello, S., Fiedler, R., Chen, X.W., Toffolo, G., Cobelli, C., & Trajanoski, Z. (2005). Ovarian cancer identification based on dimensionality reduction for high-throughput mass spectrometry data. Bioinformatics, 21, 2200-2209. Zhang, X.Y., Chen, F., Zhang, Y.T., Agner, S.G., Akay, M., Lu, Z.H., Waye, M.M.Y., & Tsui, S.K.W. (2002). Signal processing techniques in genomic engineering. Proceedings of the IEEE, 90, 1822-1833. Zhou, X., Liu, K-Y., & Wong, S.T.C. (2004). Cancer classification and prediction using logistic regression with Bayesian gene selection. J. Biomedical Informatics, 37, 249-259. Zhou, X., Wang, H., Wang, J., Hoehn, G., Azok, J., Brennan, M.L., Hazen, S.L., Li, K., & Wong, S.T.C. (2006). Biomarker discovery for risk stratification of cardiovascular events using an improved genetic algorithm. Proc. IEEE/NLM Int. Symposium on Life Science and Multimodality, 42-44.

K ey terms Artificial Neural Networks: Machine learning methods consisting of interconnecting artificial neurons that simulate the properties of biological neural networks. Biomarker Discovery: Discovery of molecular parameters associated with the presence and severity of specific disease states.

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Cluster Analysis: Methods for grouping objects of similar kind into respective categories. Decision Trees: Predictive models that map the observations about an event to infer about its target value. Discriminant Analysis: Statistical analysis to discriminate between two or more groups of samples. Feature Extraction: Extraction of representative properties of an object for the purpose of classification. Feature Reduction: Compression of the feature space of an object. Genetic Algorithms: Biologically inspired optimization methods. Geostatistics: Applied statistics of spatially correlated data High Content Screening: A high throughput platform for understanding the functions of genes, RNA, proteins, and other cellular constituents at the level of the living cell. k-Nearest Neighbor Algorithms: Methods for classifying objects based on closest training samples in the feature space. Linear Predictive Coding: An encoding method that allows the prediction of the value of the signal at each sample as a linear combination of the past values of the signal. Mass Spectrometry Data: A dataset that consists of relative intensities a chromatographic retention time and the ratios of molecular mass over charge. The mass spectrum for a sample is a function of the molecules and used to test for presence or absence of one or more molecules which may relate to a diseased state or a cell type. Microarray Gene Expression Data: Modern biotechnological data generated for studying the interaction of large numbers of genes and how a cell’s regulatory networks control genes simultaneously. Naive Bayes Classifier: A classification technique that is based on the so-called Bayesian theorem. Proteomics: The study of the structure and function of proteins, Spectral Distortion: A measure of mismatch between two signals based on their spectral properties. Support Vector Machines: machine learning algorithms that map input vectors to a higher dimensional space where a maximal separating hyperplane is constructed. Time-Lapse Microcopy Imaging: Microscopy imaging that captures images of dynamic events at predetermined time intervals. Vector Quantization: A technique that compresses k dimensional vectors to a finite set of n dimensional vectors, where n is smaller than k. Wavelet Transform: The representation of a signal in terms of scaled and translated copies of a finite length or fast decaying oscillating waveform.

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Chapter VII

Computer Aided Knowledge Discovery in Biomedicine Vanathi Gopalakrishnan University of Pittsburgh, USA

abstract This chapter provides a perspective on 3 important collaborative areas in systems biology research. These areas represent biological problems of clinical significance. The first area deals with macromolecular crystallization, which is a crucial step in protein structure determination. The second area deals with proteomic biomarker discovery from high-throughput mass spectral technologies; while the third area is protein structure prediction and complex fold recognition from sequence and prior knowledge of structure properties. For each area, successful case studies are revisited from the perspective of computer-aided knowledge discovery using machine learning and statistical methods. Information about protein sequence, structure, and function is slowly accumulating in standardized forms within databases. Methods are needed to maximize the use of this prior information for prediction and analysis purposes. This chapter provides insights into such methods by which available information in existing databases can be processed and combined with systems biology expertise to expedite biomedical discoveries.

INTR OD UCTI ON The mission of this chapter is to introduce concepts and terms that form the core of methods devised for important problems in bioinformatics and systems biology applications. Successful case studies are presented that utilize prior knowledge to aid in novel biomedical discoveries. Machine learning techniques are applied to various important biological problems, namely macromolecular crystallization, biomarker discovery from proteomic mass spectra and protein structure prediction via fold recognition. A common theme is the utilization of protein sequence properties and known task-specific information that serve as prior knowledge for guiding knowledge discovery. Much of the task-specific information Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

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is obtained through direct interactions between the bioinformatician and the domain expert in biomedical science. Systematization of the processes by which biomedical discoveries are made can uncover useful information that can help the bench scientist prioritize and focus efforts. A major goal of this chapter is to describe efforts made toward such systematization in some critical research areas. Recent novel machine learning algorithms have demonstrated some success in identifying and characterizing “interesting relationships” among domain concepts resulting in discovery of explanations for well-known observed scientific phenomena. The domain expert plays a very important role in studying output generated by computer programs and providing input to bioinformaticians on how to focus their subsequent efforts. Thus, communication between multi-disciplines is crucial to successful computer-aided biomedical discovery. For example, modeling protein sequence-structure relationships is a challenging bioinformatics task. Prior knowledge about protein fold can be used to better model protein families containing remote homologs that have very few sequence characters in common between members of the same family. Such knowledge is obtained typically from study of the literature combined with communication with a domain expert.

BACKGR

OUND

Knowledge discovery in biomedicine in the current world is very often the result of computational analyses combined with interpretation by domain experts. Langley (1998) states that artificial intelligence researchers have tried to develop intelligent artifacts that replicate the act of discovery. There are distinct steps in the scientific discovery process discussed therein (Langley, 1998) during which developers or users can influence the behavior of a computational discovery system. Furthermore, Langley (1998) suggests that such intervention is the preferred approach for using discovery software. In this chapter, we present an approach to data modeling and discovery that is consistent with this viewpoint. Jurisica and Wigle (2006) define knowledge discovery (KD) as the process of extracting novel, useful, understandable and usable information from large data sets. The authors review knowledge discovery in proteomics and present examples of such algorithms in the literature that aid protein crystallization. The case studies presented in this chapter reflect state-of-the-art challenges in proteomics along with computer-aided solutions. Quantitative and qualitative discoveries are described along with the methods by which they are arrived at. The KD process in complex real-world domains requires multi-disciplinary methods involving both artificial intelligence and statistics applied to databases (Jurisica & Wigle, 2006). Proteomics can be defined simply as the study of protein composition in a protein complex, organelle, cell or entire organism (Russell, Old, Resing, & Hunter, 2004). Current high-throughput proteomic technologies require robotics and computational techniques to decipher signals within multitudes of data. It is becoming clear that the high dimensionality poses a serious challenge to existing artificial intelligence tools for knowledge discovery and reasoning (Jurisica & Wigle, 2006). The unavailability of large numbers of samples combined with the high dimensionality of the feature space limits the usefulness of models obtained from such data. Moreover, uncertain and missing values in the data combined with evolving knowledge of the underlying mechanisms requires an intelligent information system to be flexible and scalable (Jurisica & Wigle, 2006).

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KN OW LEDGE DISC OVERY IN BI OMEDICA L APP LICATI ONS We believe that systematization of belief systems is useful for knowledge discovery in biomedical applications. This involves collaborative input to create useful representations of prior knowledge of the domain and task, in order to facilitate knowledge discovery. To support this, we present case studies for three problem areas in computational systems biology: (1) Protein Crystallization Screen Design; (2) Proteomic Biomarker Discovery from Mass Spectra and (3) Protein sequence-to-structure prediction.

Protein C rystallization S creen D esign Proteins are macromolecules along with nucleic acids, protein and DNA complexes. Protein crystallization is the major bottleneck in structure determination of proteins because of the large number of variables that affect the formation of a protein crystal suitable for X-ray diffraction. The relationships between these variables and the propensity of a macromolecule to crystallize are still not fully understood. Hence, macromolecule crystallization is largely considered an art rather than a science (Ducruix & Giege, 1992). Past experience has been utilized to guide experimenters toward initial conditions that favor crystal growth (for example, agents proposed by Jancarik and Kim (Jancarik & Kim, 1991); and the Hampton Research Crystal Screen). The idiosyncratic nature of individual proteins requires optimization of conditions obtained from the first screening step. Conceptually, protein crystal growth can be divided into two phases: (a) screening a subset of possible experimental conditions to determine promising areas to search further and (b) optimization of the initial search conditions to yield crystals of good quality (resolution limit of diffraction < 3.5 Å). The Biological Macromolecular Crystallization Database (BMCD) is a repository for experimental data from successful crystallization studies (Gilliland, Tung, & Ladner, 2002). These positive examples of successful crystallization plans have been subjected to various statistical and machine learning analyses staring with inductive learning to extract useful associations between crystallization conditions and obtaining good quality crystals (Hennessy, Gopalakrishnan, Buchanan, Rosenberg, & Subramanian, 1994). Even though the BMCD is a useful resource, the lack of information about failed experimental setups for each protein that had been successfully crystallized hinders the predictive ability of models gleaned from this data. Even though protein crystallization is generally regarded as an art, there exists prior knowledge about the process by which protein crystals nucleate, grow and stop growing. Figure 1 depicts a hanging drop vapor diffusion experiment as part of a typical 6 x 4 setup tray. This method is commonly utilized for protein crystallization, with a droplet of purified protein in solution hanging from the cover slip over well containing mother liquor which is a cocktail of buffer, precipitant and possibly salts at various concentrations. The drop solution contains the protein along with the same cocktail reagents of the mother liquor except at lower concentrations. A protein crystal is formed when water evaporates from the drop at a slow rate in an attempt to reach system equilibrium. Initially, the precipitant concentration in the drop is at lower concentration insufficient for crystallization. As the water evaporates from the drop, precipitant concentration increases driving the protein from a liquid to a solid state. A phase diagram plot of protein concentration versus precipitant concentration in the hanging drop reveals three regions - undersaturation, saturation and supersaturation. It has been observed that proteins nucleate at a supersaturation close to the boundary between saturation and supersaturation regions; whereas growth of the crystal takes place only within the saturated region. Hence, a model that takes

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this prior knowledge into account can help novice crystallographers better understand how to get the protein in the liquid phase into an appropriate solid phase to obtain good crystals of diffractible quality. If the precipitant was too concentrated in the drop solution, it is likely that only a solid amorphous precipitate would result, since the solid phase would occur in a region of supersaturation far from the boundary between saturation and supersaturation regions. This empirical observation however is still a useful partial result in honing onto appropriate initial crystallization conditions. Gopalakrishnan et al. (2002) present a simple simulator of protein crystallization. Novice crystallographers can utilize commonly used laboratory reagents virtually to set up experiments for different hypothetical proteins. The simulator allows the user to observe experiments from time to time by requesting this as another input. Subjective testing showed that the underlying simple model was a reasonable approximation of the overall behavior of the system by which protein crystals nucleate, grow and stop growing(Gopalakrishnan, Buchanan, & Rosenberg, 2000; Gopalakrishnan, Buchanan, & Rosenberg, 2002). However the simulation though numerical in nature is meant to only convey qualitative behavior patterns. The quantitative outputs are not to be taken as what one would observe in the laboratory. Further refinement of the input functions and their parameters based on actual experimental information would be necessary to utilize the quantitative outputs (such as the resolution limit of diffraction of a crystal obtained over a particular time interval of simulation).

Figure 1. Illustration of a typical crystallization tray. Each well has a mother liquor solution containing buffer and precipitant at a higher concentration than in the hanging drop. The drop contains protein at a particular concentration initially in the liquid phase. Vapor diffusion drives the protein in the drop into a solid phase (such as amorphous precipitate or crystal). The rate of vapor diffusion determines the outcome of an experiment (such as whether or not a solid phase appears, and the quality of crystal if applicable).

A T ra y

A well (a n experiment)

B u ffe r = 0 .1 M Tris -H C l p H 8 .5 P re cipita nt = 30 % w /v P E G 4 0 0 0 S a lt = 0 .2 M M g C l 2

S evera l E xperiments in P a rallel

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A systematization of macromolecular classes is presented in Hennessy et al. (2000) and utilized toward objective screen design using statistical techniques (Hennessy, Buchanan, Subramanian, Wilcosz, & Rosenberg, 2000). Further systematization of belief systems in crystallization is attempted through the development and characterization of various chemical hierarchies and relationships within the domain (Gopalakrishnan, Livingston, Hennessy, Buchanan, & Rosenberg, 2004). Such representations are utilized within a novel autonomous discovery system for uncovering relationships among parameters influencing macromolecular crystallization. This system called Heuristic Autonomous Model Builder (HAMB) (Livingston, Rosenberg, & Buchanan, 2003) is a task-based agenda system built on top of a rule-based machine learning algorithm, Rule Learner (RL) (Clearwater & Provost, 1990). HAMB utilizes prior knowledge to annotate rule sets that are generated by RL - these represent models of the data from the BMCD. The annotations are obtained through interactions with the domain expert to characterize “interestingness” of features and relationships within the domain. Thus, HAMB is able to autonomously prioritize learning tasks for RL, and provide appropriate data and target classes based on interestingness categories. Though “interestingness” again is captured numerically, the categorization overall is qualitative. HAMB’s analysis of augmented BMCD data results in some novel suggestions such as: (a) different crystallization methods should be used for specific types of macromolecules; and (b) different ionic strengths may be required when crystallizing enzymes, ‘heme’-containing proteins and small proteins (Gopalakrishnan et al., 2004). An important variable that influences protein crystallization is the pH of the experimental setup, and hence values of this variable is more abundantly reported in the protein data bank (PDB) (Berman et al., 2002). The entries in the PDB were analyzed by Dougall (2007) in an effort to understand the relationships between protein sequence properties and the reported pH of crystallization (Dougall, 2007). Since the pH is more abundantly reported than other variables of protein crystallization, Dougall (2007) was able to parse the PDB to create substantial training and test datasets (3000 to 5360 examples from different versions of the database) for statistical and machine learning analyses. This analysis verified that there is indeed no correlation between the pH at which a protein crystallizes; and its isoelectric point (pI) where the net charge is zero agreeing with previous work (Kantardjieff & Rupp, 2004). Furthermore, upon examination of net charge per kDa (kilodalton), which is the specific charge of the protein and can be estimated from the sequence; it was found that most of proteins in the training set crystallized at a pH that resulted in low specific charge. This trend was also observed in the test datasets. This discovery that most globular proteins in a nonredundant set of the PDB crystallize at a pH that results in a low specific charge seems to be consistent with well-known facts relating to structural stability of proteins.

Proteomic B iomarker D iscovery from Mass S pectra Biomarkers are biological molecules that are indicators of physiologic state and also of change during a disease process (Srinivas, Srivastava, Hanash, & Wright, 2001). Biomarkers can be utilized to provide early detection of disease and monitor its progression. Proteomic technologies allow us to detect abundances of various proteins present in clinical samples, thereby providing us with a map of protein-related changes caused by disease. Proteomics is the study of the entire set of proteins in a cell, and proteomic biomarker panels that represent states of protein abundances or representations within the cell are useful indicators of patient health within the clinical context. Screening using a panel of biomarkers can enhance the positive predictive value of a test while minimizing false positives or false negatives. Protein markers can be used in detection, diagnosis, monitoring of therapy, and ultimately, prevention and risk

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Figure 2. Generic mass spectrometry (MS)-based proteomics experiment. Figure redrawn from review in Nature by Aebersold and Mann, 2003. (1) Sample fractionation

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assessment (Srinivas, Verma, Zhao, & Srivastava, 2002). Commonly used technologies for proteomic screening are based on mass spectral (MS) analyses of clinical samples and complex mixtures of proteins obtained through chromatographic separation. MS measurements are carried out in the gas phase on ionized analytes. By definition, a mass spectrometer consists of an ion source, a mass analyzer that measures the mass-to-charge ratio (m/z) of the ionized analytes, and a detector that registers the number of ions at each m/z value (Aebersold & Mann, 2003). The two most common techniques used to volatize and ionize proteins or peptides for MS analysis are electrospay ionization (ESI) (Fenn, Mann, Meng, Wong, & Whitehouse, 1989) and matrix-assisted laser desorption/ionization (MALDI) (Karas & Hillenkamp, 1988). ESI desolvates and ionizes the analytes out of a solution and can be coupled with liquid-based separation tools such as liquid -chromatography (LC). MALDI sublimates and ionizes samples out of a dry, crystalline matrix via laser pulses and is normally used to analyze relatively simple peptide mixtures. A recent related technology is called surface-enhanced laser desorption/ionization (SELDI), where protein chip arrays are used to provide a variety of surface chemistries for researchers to optimize protein/peptide segregation, capture and analysis. The chemistries on these chips include classical chromatographic surfaces such as hydrophobic for reversed-phase capture, cation-and anion exchange surfaces, and immobilized metal affinity capture (IMAC) for capturing metal-binding (e.g., phosphorylated) proteins. Bound proteins are liberated by ionization (Jr et al., 1999). Figure 2 is adapted from Aebersold and Mann’s review in Nature (Aebersold & Mann, 2003), and shows a generic MS-based proteomics experiment. The five stages of a typical proteomics experiment are depicted, wherein proteins to be analyzed are first extracted from cells (stage 1) and then digested into peptides (stage 2) in order to enhance sensitivity of detection by mass alone. In stage 3, peptides elute from high-pressure liquid chromatography (HPLC) column ordered by hydrophobicity, making the mixture simpler for analysis. In stage 4, a mass spectrometer samples this mixture every few seconds,

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producing a mass spectrum of peptides eluting at each time point. In stage 5, peptides of selected masses are fragmented into sub-peptides; and a series of tandem mass spectrometric or MS/MS experiments ensue, producing MS/MS spectrums. Peptides are identified based on their MS and MS/MS spectra. Four basic types of mass analyzers are used in current proteome research (Aebersold & Mann, 2003) namely - the ion trap, time-of-flight (TOF), quadrupole and Fourier transform ion cyclotron (FT-MS) analyzers. Each can be used alone or in tandem in order to exploit the strengths of the approaches. MALDI is usually coupled to TOF analyzers that measure the mass of intact peptides, whereas ESI has mostly been coupled to ion traps and triple quadrupole instruments and used to generate fragmentation or collision-induced dissociation (CID) spectra of selected precursor ions (Aebersold & Goodlett, 2001). Due to its simplicity, excellent mass accuracy, high resolution and sensitivity, MALDI-TOF is a generally used technique to identify proteins by peptide-mass mapping or fingerprinting. Recently introduced MALDI-TOF/TOF-MS/MS instruments can also be used to generate CID spectra. Identification and quantification of the components of a complex protein sample is a multi-step operation. While instruments and methods are needed for separating, identifying and quantifying the polypeptides, tools are also required to integrate and analyze all of the produced data. Proteomics studies necessarily result in large amounts of data. Analysis of complete proteomes for biomarkers is therefore time-consuming and poses computational challenges, as the problem can be likened to search of a “needle in a haystack”. Quality of the high-throughput proteomic data, like that of high-throughput genomics data, can also be highly suspect. Biomarker discovery from clinical proteomic mass spectra requires computational techniques to select features that are relevant with respect to disease classification. The problem is particularly difficult due to the small number of available clinical samples, and the large number of features or analytes (m/z values) whose abundances are traced via mass spectral technologies such as MALDI and SELDI-TOF. In the machine learning and data-mining field, this problem is basically one of feature selection. Feature selection methods are divided into three typical groups: Filter, Wrapper and Embedded methods (Hauskrecht, Pelikan, Valko, & Lyons-Weiler, 2007). Filter methods rank each feature according to some univariate metric, and utilize only the highest ranked features. Wrapper algorithms (Kohavi & John, 1997) search for the best subset of features using all available features and a classification algorithm. Embedded methods incorporate feature selection as part of the model building process, for example the CART method (Breiman, Friedman, Olshen, & Stone, 1984). Gopalakrishnan et. al. (2006) describe the process by which biomarkers are discovered and validated for Amyotrophic Lateral Sclerosis (ALS), a rare but rapidly neurodegenerative disease for which there is currently no cure (Gopalakrishnan, Ganchev, Ranganathan, & Bowser, 2006). Proteomic mass spectral analyses of cerebrospinal fluid samples (CSF) from control and patient cohorts is performed using SELDI-TOF (Ranganathan et al., 2005). Statistical techniques and a wrapper-based rule learning (RL-Wrap) approach are applied to select putative biomarker panels that enable early detection of ALS. Three biomarkers are identified using peptide mass fingerprinting and tandem MS/MS, that are either decreased (transthyretin, cystatin C) or increased (carboxy-terminal fragment of neuroendocrine protein 7B2) in ALS CSF (Ranganathan et al., 2005). The latter was discovered only by the use of the rule learner. More details on the biomarker discovery and validation processes follow. Ranganathan et al. (2005) utilize Ciphergen ProteinChips (Ciphergen Biosystems, Inc. Palo Alto, CA, USA) to collect mass spectra from CSF samples. The SAX2 and IMAC binding surfaces yielded quality spectra with reasonable reproducibility. Total number of subjects used for mass spectrometry analyses was 23 ALS and 31 controls. Of these, 15 ALS and 21 controls formed the initial training group for pre-

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liminary data analyses, keeping 8 ALS and 10 controls blinded as a test set. For subsequent analyses, all the data was pooled and test sets were generated at random keeping a fairly even distribution of disease to control cases. Total ion current of all profiles was used to normalize each of the spectrograms. The Ciphergen 3.1 Biomarker Wizard application auto detected mass peaks by clustering. This output was analyzed using non-parametric Mann-Whitney analysis to yield 30 mass ion peaks with statistically significant (p < 0.01) differences between control and ALS subjects. Apart from the univariate analysis, non-linear modeling was performed using an inductive rule-learning algorithm, RL (Clearwater & Provost, 1990). This evolved from Meta-DENDRAL (Feigenbaum & Buchanan, 1993) which was used for predicting mass spectra of complex organic molecules. RL primarily searches a space of possible rules (IF-THEN statements) by successive specialization, guided by data in the training set and by prior knowledge. It learns a disjunctive set of weighted conjunctive rules. One of the distinguishing features of RL is its knowledge-based approach to learning. Prior knowledge can be used to guide the process by which its rule-based models are constructed. This may include the legal semantics and syntax for the rules plus additional bias about plausible and implausible relationships that are well agreed upon by the domain experts. RL models are easily understood by domain experts. This has been crucial to the successful application of RL to knowledge discovery in the various biomedical domains discussed herein. For this study, both raw and normalized spectral data were analysed. Due to the large space of features, a wrapper algorithm was developed which selected features and ran RL for each subset, until all features had been seen at least once by RL. Then, the rule-based models obtained from each subset are parsed to pool together only those features that appeared in the models. Then, RL was again applied to this final subset of features using the training data as input. The final model is then used to predict the class labels for the test data. A three-fold or five-fold cross-validation is utilized to tune the RL input parameters during the training. These parameters are then utilized for obtaining the final set of rules. To apply the rules to predict test data, the inference engine applies evidence gathering using ‘weighted voting’. Each rule in the model has a certain weight associated with it that reflects its degree of certainty as gathered from the training data. The degree of certainty is based on the proportion of correct class labels assigned by that rule to the total number of matches to the rules antecedents. A sample rule produced from RL applied to proteomic mass spectra (Gopalakrishnan et al., 2006) is shown below: ((zn3010.6341 in 0.302..0.481)) ==> (GROUP = ALS) CF=0.873, TP=10, FP=0,Pos=18,Neg=22 This rule states that if the normalized abundance of m/z value (or mass value) 3010.6341 produced from a Zn-IMAC SELDI chip is in the range of 0.302 to 0.481, the sample is classified as ALS with a certainty factor of 0.873. There are several functions available within RL for calculating the certainty factor for each rule. The number of true positives covered by that rule is 10 out a total of 18 positive examples. The total number of controls and ALS cases analyzed in this particular RL run is 40. Several models were obtained from the RL analyses. One best model was chosen that performed very well on a randomly chosen test set containing 7 ALS and 5 Control cases. The twelve features in this model were chosen for further experimental analyses – namely, peptide mass fingerprinting and tandem MS/ MS analyses. One novel peptide biomarker was identified directly via tandem MS/MS sequencing that

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yielded a 100% sequence match with the carboxy-terminal fragment of neuroendocrine protein 7B2. This finding presents a clue to the metabolic pathways of ALS and is both interesting and significant from a biomedical standpoint. Understanding and systematization of this process by which biomarkers are discovered from proteomic mass spectra will facilitate biomedical knowledge discovery as illustrated in the above case study. This would include obtaining and encoding prior knowledge of task-specific and domain-specific information. For example, knowledge about the type of clinical sample (e.g., blood, urine, CSF, tears, saliva) and known abundances of proteins found in that source would enable better feature selection for disease-specific biomarker discovery. Other types of prior knowledge would include: (a) relationships between proteins found in pathways and (b) the encoding of specific domain knowledge such as bond fragmentation patterns in MS data. Machine learning algorithms that can utilize such prior knowledge to help constrain the hypothesis space will be immensely useful in such tasks.

Protein S equence to S tructure Prediction and C omplex F old R ecognition Protein sequence to structure prediction is a fundamental problem in bioinformatics. Protein structure is described hierarchically starting with primary sequence represented by the polypeptide chain of amino acids, followed by secondary structure classified mainly into helix, sheet and coil. Tertiary structure represents the entire three-dimensional structure of a protein described by the location and spacing between atoms of one polypeptide chain. Quaternary structure refers to the three dimensional structure of more than one polypeptide chain, for example the hemoglobin macromolecule contains four polypeptide chains. Protein sequence databases such as the Swiss-Prot are much more populated than the structure database (PDB) due to the various difficulties associated with protein structure determination as discussed earlier. Hence, prediction of protein structure from sequence information is commonly performed as an attempt to model aspects of actual structure. It is believed that such models might provide clues to protein function. Protein secondary structure prediction has been extensively studied (Cuff and Barton, 1999; Rost, 2001). Since protein secondary structure refers to repetitive structural components based only on the backbone of a polypeptide chain without consideration of the individual amino acid side-chains and their interactions, there is an inherent information loss. Secondary structure prediction algorithms typically assign a prediction per residue along the sequence. Invariably, this results in loss of predictive accuracy per residue at the global sequence level of the polypeptide chain. The most difficult predictions are at the boundaries of helices, sheets and coils. Recent improvements have been made to structure prediction algorithms by incorporating evolutionary information, and also by combining the results of multiple independent prediction methods into a consensus prediction (Rost, 2001). Liu et al. (2004) compare probabilistic score combination methods for secondary structure prediction. Herein, the combination problem for protein sequences is formulated to take into account both short and long-range interactions so as to be able to consider the protein sequence as a whole as opposed to window-based methods which may not be able to capture constraints and dependencies of long-range interactions (Liu, Carbonell, Klein-Seetharaman, & Gopalakrishnan, 2004). Traditional window-based combination methods are compared with graphical models such as Hidden Markov Models (HMMs), Maximum Entropy Markov Models (MEMMs) (McCallum, Freitag, & Pereira, 2000) and chain-structured Conditional Random Fields (CRFs) (Lafferty, McCallum, & Pereira, 2001). Using the CB513 dataset by Cuff and Barton (1999) that contains 513 non-homologous proteins that have an SD score of

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Figure 3. (A) Representative structure for the parallel beta-helix fold from the PDB; (B) prior knowledge example: one rung of the repetitive beta-helix fold containing the conserved B2-T2-B3 segment (figure adapted from(Cowen, Bradley, Menke, King, & Berger, 2002) and (C) representative triple-beta spiral structure from the PDB.

less than five, a gold standard protein secondary structure assignment is made using the DSSP definition (Kabsch & Sander, 1983). This definition is based on hydrogen bonding patterns and geometrical constraints. DSSP assign one of eight labels to each amino acid – these labels are reduced to a standard set of three based on discussion by Cuff and Barton (1999): H and G to Helix (H), E and B to Sheets (E) and all others to Coil (C). The state-of-art performance achieved by window-based methods is by using PSI-BLAST profiles (Jones, 1999). Liu et al. (2004) tried four graphical models and discovered that CRFs perform the best. Overall, the graphical models for score combination yielded better accuracies for secondary structure prediction on this dataset compared to window-based methods. Standard prediction accuracy measures were utilized such as Q3 score for overall per-residue accuracy, Matthew’s correlation coefficients per structure type (CH, CC, CE) and segment of overlap (SOV) (Rost, Sander, & Schneider, 1994; Zemla, Venclovas, Fidelis, & Rost, 1999). Having discovered that CRFs performed very well for modeling protein secondary structure prediction particularly beta sheets that involve long-range interactions, Liu et al. (2006) proposed a variant named Segmentation Conditional Random Fields for modeling complex protein folds. Protein fold refers to frequent arrangement pattern of several secondary structure elements, such as the β−α−β structural motif. In contrast to traditional graphical models such as the Hidden Markov Model (HMM), SCRFs follow a discriminative approach allowing any set of features to be included. Globally optimal solutions are obtained for the model parameters using a convex optimization function. Potential long-range interactions are modeled within a special kind of graph, called the protein structural graph (Liu, Carbonell, Weigele, & Gopalakrishnan, 2006). This graph has an additional set of edges between nodes that represent segments of a protein sequence, classified into secondary structure elements that are within and outside the fold of interest. Given a protein sequence and a structural graph representing the repetitive elements of that fold, the SCRF models the conditional probability of a segmentation of the protein sequence given that graph. The parameters of the model are estimated from the training data, based on features extracted from sequences belonging to the fold family. The right-handed parallel beta helix fold (Figure 3 A&B) is mod-

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eled successfully using SCRFs. Only 14 structures with this fold have been resolved. These belong to nine beta-helix families of closely related proteins in the SCOP database (Murzin, Brenner, Hubbard, & Chothia, 1995). Cross-family validation shows that the SCRF model performs comparably to that of the heuristic BetaWrap algorithm (Bradley, Cowen, Menke, King, & Berger, 2001) developed for modeling the parallel beta helix fold. The generality of the SCRF model makes it useful for protein fold recognition. Potential members of the beta-helix fold family are identified from the UniProt reference databases (Leinonen et al., 2004). A few of these predictions were subsequently confirmed as beta-helices from recently crystallized proteins whose structures were resolved by X-ray crystallography (Liu, 2006). Quaternary structural folds consist of multiple protein chains that form chemical bonds among side chains to reach a structurally stable domain. The complexity associated with modeling the quaternary fold is handled in Liu et al. (2007) using a segmentation conditional graphical model (SCGM) along with efficient inference and learning algorithms for training and testing. This complexity arises because the labels of all chains have to be considered jointly since every chain contributes to the stability of the overall structure (Liu, Carbonell, Gopalakrishnan, & Weigele, 2007). While the SCGM model provides a flexible and scalable framework for utilizing structural properties of a protein fold, the choice of feature functions that represent segment-based features is key to accurate prediction. Two types of features are discussed in Liu et al. (2007). The node feature covers properties of an individual segment, such as “average hydophobicity” or, “length of the segment”. The pairwise feature captures dependencies between segments whose corresponding subsequences form chemical bonds in the three-dimensional structures (Liu et al., 2007). Liu et al. (2007) model two complex protein folds, the triple-β-spiral (van Raaij, Mitraki, Lavigne, & Cusack, 1999) and the double-barrel trimer.(Benson, Bamford, Bamford, & Burnett, 2004). The protein structure graph for the triple-β-spiral (TBS) is constructed based on observed characteristics of members of that fold family whose structures had been resolved and deposited in the PDB. Weigele et al. (2003) study members of the TBS fold family (Figure 3C) and make several observations about the structural characteristics (Weigele, Scanlon, & King, 2003). Such constraints constitute an example of prior biological knowledge constraining the model space (Liu et al., 2007). In this subsection the problem of complex fold recognition is studied and novel methods that utilize probabilistic graphical modeling are discussed. The methods are variants of conditional graphical models and can use prior information available about structural folds in order to model complex folds such as the Triple Beta Spiral. The prior information encoded is based on known partial sequencestructure information and sequence alignment of the protein families. The methods are significant in that they comprise general models for the particular complex fold being recognized and perform well even though the members of the fold family have very little sequence homology, and there exists only a sparse representation of resolved structures for the fold in the PDB.

F UT URE TRENDS Systems biology applications are of great importance to the future of biomedicine. The case studies described in this chapter represent significant research areas that challenge computational biology. Systematization of prior knowledge will enable efficient solutions to these challenges. Ontologies are beginning to gain popularity in sub-domains of bioinformatics. Enriching the information space provided by such ontologies will enable rapid retrieval for analysis purposes. Integration of ‘omic’ data with

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clinical and health records is an essential aspect of biomedical knowledge discovery. Furthermore, the discovery of more protein sequence-structure-function relationships that are core to systems biology will enhance the quality of bioinformatic databases.

C ONC LUSI ON This chapter presents a perspective on successful use of intelligent computational aids for knowledge discovery in three collaborative areas of biomedicine. The case studies represent different applications of machine learning techniques to various important biological problems, namely macromolecular crystallization, biomarker discovery from proteomic mass spectra and protein structure prediction via fold recognition. A common theme is the utilization of protein sequence information to derive proteinspecific properties that can serve as prior knowledge for guiding knowledge discovery. The learning algorithms are unique in that they can represent prior knowledge and use this to constrain the search space of possible models that can fit the data. Rule-based machine learning systems can facilitate biomedical knowledge discovery since these models are easily understood. Graphical models enable effective representation of prior knowledge that captures structure within the data.

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Rost, B., Sander, C., & Schneider, R. (1994). Redefining the goals of protein secondary structure prediction. J Mol Biol, 235(1), 13-26. Russell, S. A., Old, W., Resing, K. A., & Hunter, L. (2004). Proteomic informatics. Int Rev Neurobiol, 61, 127-157. Srinivas, P. R., Srivastava, S., Hanash, S., & Wright, G. L., Jr. (2001). Proteomics in early detection of cancer. Clin Chem, 47(10), 1901-1911. Srinivas, P. R., Verma, M., Zhao, Y., & Srivastava, S. (2002). Proteomics for cancer biomarker discovery. Clin Chem, 48(8), 1160-1169. van Raaij, M. J., Mitraki, A., Lavigne, G., & Cusack, S. (1999). A triple beta-spiral in the adenovirus fibre shaft reveals a new structural motif for a fibrous protein. Nature, 401(6756), 935-938. Weigele, P. R., Scanlon, E., & King, J. (2003). Homotrimeric, beta-stranded viral adhesins and tail proteins. J Bacteriol, 185(14), 4022-4030. Zemla, A., Venclovas, C., Fidelis, K., & Rost, B. (1999). A modified definition of Sov, a segment-based measure for protein secondary structure prediction assessment. Proteins, 34(2), 220-223.

KEY TERMS Clustering: The unsupervised grouping of data items in the absence of class labels. Conditional Random Fields (CRFs): These are undirected discriminative graphical models that directly compute the conditional likelihood of a hidden state sequence (y) given the observation sequence (x). This P(y|x) is proportional to the product of the potential functions over all the cliques in the graph. CRFs define the clique potential as an exponential function and guarantee finding of the global optimum since the optimization function is convex (Lafferty et al., 2001). Forward and backward probability calculations are derived similar to HMMs. Unlike HMMs, no assumptions are made about independence of the observed features. The feature definition can also be arbitrary, including overlapping features and long-range interactions (Liu et al., 2006). Feature Extraction: The process of extracting and building features from raw data such as the amino acid sequence of a protein. Feature functions are utilized to extract and process informative features that are useful for prediction. Hidden Markov Models (HMMs): These are directed chain-structured probabilistic graphical models that are generative in nature. They assume that the data are generated by a particular model and compute the joint distribution, P(x, y) of the observation sequence x, and the hidden state sequence y. Inductive Rule Learning: The development of IF-proposition-THEN-concept rule-based models from feature vectors, which are (attribute, value) pairs that describe the training examples. The rulebased models are expected to generalize to classify test examples accurately.

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Metabolomics: The study of small molecule metabolites and their expression within a system or organism. Supervised Machine Learning: The use of class labels as prior knowledge to learn discriminative models from training examples consisting of feature vectors descriptive of the target class. X-Ray Crystallography: The most general method for experimental determination of protein and other macromolecule three-dimensional structure. A good quality crystal is obtained first from a purified sample and then subjected to X-ray diffraction.

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Genomics and Bioinformatics for Systems Biology

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Chapter VIII

Function and Homology of Proteins Similar in Sequence: Phylogenetic Pro.ling

Thomas Meinel Max Planck Institute for Molecular Genetics, Germany

abstract The function of proteins is a main subject of research in systems biology. Inference of function is now, more than ever, required by the upcoming of novel protein sequences in consequence of the discovery of new proteomes. The calculation of sequence similarity is an easily feasible way to compute protein comparisons. The comparison of complete proteomes touches one of the earliest topics in bioinformatics; the biologically meaningful organization of proteins in protein families. Several approaches that interpret function or evolutionary aspects of proteins from sequence similarity are reviewed, which in particular reflects the arsenal of techniques introduced until now. Phylogenetic profiling, a method that compares a set of genes or proteins by their presence or absence across a given set of organisms, is also presented in this chapter. Proteins in a functional context, for example, a pathway or a protein complex, are represented by identical or similar phylogenetic profiles. The detection of functional contexts by phylogenetic profiling is also playing a prospective role as an analytic tool in systems biology. Already established tools for phylogenetic profiling as well as particular biological examples based on the SYSTERS protein family data set are presented.

INTR OD UCTI ON Protein sequence similarity is a feature that plays a central role in comparative proteomics for the inference of protein function or analysis of protein evolution. To study the complexity of functional cellular units like proteins, basic research can often only be conducted on animal models with the completely available experimental design. These studies are expected to play a significant role in medical research. Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Function and Homology of Proteins Similar In Sequence

Results are considered to be comparable with results from clinical diagnostics. It must be confirmed that results are transferable to human proteins if such experiments are not possible. Therefore, the determination of proteins with identical function in animal models and in human is essential. Evolution of life can be characterized by the development of species as well as by the divergence of protein sequences, and it is notable that also the development of protein function is an evolutionary process. Several more or less independent biological research fields are introduced to elucidate the backgrounds of a particular evolution event - often only under constraints of the temporary availability of appropriate methods. The development of techniques for a rapid and voluminous sequencing of DNA continues to lead to complete gene sets, genomes, for an increasing list of organisms. Computational techniques calculate the translation of genomic information to proteins including processes like alternative splicing or translation start site variation. The generation of all electronically inferred proteomes is based on such specific algorithms. In parallel to the development of those tools, new evolutionary events were detected and investigated. Some of them are evolutionary events like gene duplication, gene fusion or fission, protein domain rearrangements, horizontal gene transfer, multiple copy number of genes. In its first part, this book chapter emphasizes the reasons for distinguishing between sequence similarity and homology and function of proteins. Sequence similarity is a parameter that can be computed from a simple biophysical trait of a protein, the sequence, i.e., the primary protein structure. However, it is more complex to determine protein homology, even if it is plausible that proteins with common evolutionary history are similar in sequence. The other way around, in the context of bioinformatics, inference of homology is the interpretation of an observation - namely sequence similarity. The goal here is to determine similar proteins in recent organisms as descendants from a gene with common ancestry and thereby as homologs. The matter of inference of protein function can be discussed in the same way: Similar proteins possess with high probability a common ancestry and therefore similar function. But proteins can adopt function or are specialized during their evolutionary history. Proteins of similar function not necessarily possess similar sequence, therefore. Consequently, it is necessary to know existing protein sequence comparison methods and underlying methods for the partitioning of proteins into protein families. In fact, a scientist works with more or less closely related members of protein families when using an expression like ‘two homologous genes’. Methodological backgrounds of established data sets are therefore briefly reviewed by this book chapter. It is observed that proteins in a common functional context are evolutionary conserved in most of the organisms that own such a functional context. A phylogenetic profile is a pattern of presence or absence of a gene or protein across a given set of organisms. Phylogenetic profiling is a method that compares proteins by their phylogenetic profiles. Because proteins are different in organisms, a grouping of proteins is essential for the generation of a phylogenetic profile. Phylogenetic profiling is therefore depending on the method for partitioning of the protein space into protein families. This book chapter in its second part reviews the backgrounds of established phylogenetic profiling tools, restrictions to subsets of organisms on super-kingdom level, general limitations for the detection of functional contexts, and provides particular biological examples of phylogenetic profiles. Phylogenetic profiling as a method to infer unknown protein contexts or to elucidate contexts of proteins unknown in function becomes prospectively relevant in systems biology, and more so with the increasing number of complete eukaryotic proteomes. Function of proteins is a central issue of this review, as subject of detection for unknown proteins using sequence similarity and as subject of inference of functional contexts in phylogenetic profiling.

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F UNCTI ON OF PR OTEINS Predicting and analyzing the function of novel proteins presents one of the main challenges in computational biology, more than ever since the number of proteins continuously explodes with the increasing number of completely sequenced organisms. Functionality models revealed from the analysis of particular chemical parameters, e.g., enzyme kinetics, and led to sketches of selective pathway maps. Nowadays, this knowledge provides the basis for comparative methods of protein function detection, as one of the main research topics in the field of systems biology.

A nnotating F unction of Proteins Only three percent of proteins in databases that are annotated with substantive information and annotations other than ‘unknown’ or ‘hypothetical’ are supported by experiments (Brown & Sjölander, 2006). For most of protein sequences, the annotation according function is acquired electronically from other similar sequences. This crucial point is well known and leads to a pretended reliability of sequence annotation for proteins (Valencia, 2005). Systematic errors in databases can hereby be propagated and are, if seldom detected, not necessarily corrected. Some approaches take this into account and claim for categorization only using physical parameters like structural properties or similarity of sequence. They do not take responsibility for functional classification. The SYSTERS protein family approach (Krause, Stoye, & Vingron, 2005), e.g., relies only on sequence similarity, the respective data set references annotations of protein sequence entries by extracting most common keywords. It is more advantageous to deduce protein function from structural or phylogenomic properties (Krishnamurthy, Brown, Kirshner, & Sjölander, 2006; Brown & Sjölander, 2006. Relying on phylogenomic trees includes the evolutionary aspect more than using purely sequence parameters. For instance, genome duplications or domain shuffling are hereby better regarded, spatial specialization or neofunctionalization of paralogous genes can be better detected. Excluding the so called in-paralogs, groups of orthologs can be more precisely classified by phylogenomics, but this is always difficult because evolutionary distances can extremely vary for particular orthologous groups (Luz & Vingron, 2006). Even if the three-dimensional protein structure stays conserved, a single exchange of amino acid residues at substrate-specific reaction centers can critically lead to a change in function. But it is very difficult to define general rules for the inference of a genomic-scale orthology data set. A performance assessment of orthology detection (Chen, Mackey, Vermunt, & Roos, 2007) used statistical techniques for a pairwise comparison of several methods, some of them are explained in the data sets section. Shift of function in protein subfamilies presents a special aspect in function prediction (Brown, Krishnamurthy, & Sjölander, 2007). Such conversions of protein function are analyzed and collected in the FunShift database (Abhiman & Sonnhammer, 2005a; 2005b). Subfamilies that are derived from Pfam families are analyzed (Mistry, Bateman, & Finn, 2007). They can possess conservation shifting sites, i.e., different amino acid residues at conserved sites with probable functional evidence, as well as rate shifting sites, i.e., sites of different evolutionary rates in two subfamilies.

Categorization According Predefined Functional Classes Enzymes or pathways include per se information on identified function. Experimental results comprised in enzyme data collections like IntEnz (Fleischmann et al., 2004) or Brenda (Barthelmes, Ebeling,

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Chang, Schomburg, & Schomburg, 2007) have been developed. Functional enzymes in a pathway context are manually curated and analyzed in the KEGG database (Kanehisa et al., 2008) or Reactome (Vastrik et al., 2007). The GO annotation is a collection of structural or functional terms intended by the Gene Ontology Consortium (Ashburner et al., 2000). It attempts to annotate each gene or protein with GO terms, i.e., characterizing descriptions, and GO identifiers for standardization. Three categories (biological process, molecular function, cellular component) facilitate the structure, GO terms are organized in sublevels. Special attempts, GO tools and non-consortium tools, are available for searching and browsing, annotation, microarray analysis support and verify annotations through statistical support.

Ubiquitary and Organism Group-Specific Protein Function Housekeeping and information transduction genes are essential for a living organism and exist therefore as ubiquitary proteins in almost all organisms. Using those functional genes reveals advantageous phylogenetic or orthology analyses. Attempts that focus on the inference of the tree of life are frequently compared by the phylogeny of the ubiquitary 16S rRNAs that serves for a reference tree. In contrast, loss of essential genes that participate in pathways of the host organism is observed in parasitic or symbiotic organisms. There exist also many highly specialized proteins uniquely in small groups of organisms. They contribute, beyond gene regulation phenomena, to the individuality of those species.

SEQ UENCE SIMILARITY

AND H OMOLOGY

A sequence comparison procedure analyzes the primary protein structure of two proteins, the sequence. This is an observation and can be interpreted in an evolutionary sense as homology. In this section, the basics for sequence similarity and homology are described.

S imilarity of S equences The basis of most protein categorization approaches is a sequence comparison, well-known are routines like BLAST (Altschul et al., 1997) or the Smith-Waterman algorithm (Smith & Waterman, 1981). These widespread tools are known as applications that support fast access to biological data resources and prove their strengths in, for instance, the general task to confirm if a newly detected protein as similar to an already known protein. They are working with differences on the levels of technical background, algorithm assumption and time efficiency, but they generally consider local sequence similarity. Therefore, conserved protein substructures, mostly found as protein domains, govern a sequence comparison. The most frequently used comparison parameter is the expectation value, e-value, for the probability that two protein sequences are not randomly found in a sequence database. The e-value depends on the sequence length as well as the database size. Thus, querying two sequences obtained from two organisms against the proteome of the respective other organism, e-values differ from each other if, even identical, sequences are queried against proteomes of different sizes. This leads to the insight that an e-value is not only a parameter exclusively for relative considerations but also has to be determined in reciprocal directions.

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Orthology, Paralogy Orthology and paralogy are key concepts of evolutionary genomics and are therefore discussed in depth (Koonin, 2005; Fitch, 2000; Sonnhammer & Koonin, 2002). Homology includes the terms orthology and paralogy. Two independent evolutionary processes towards two recent genes revealed, when diverged after a last speciation event, as two physically distinguishable protein sequences in both organisms, as homologs. Underlying processes are mutations, insertions, deletions, or events in higher dimensions like domain shuffling or changes in the gene order. These events, always infecting the information level - the DNA -, reveal in substantial changes of the result of translation, the protein (with the exception of synonymous mutations according to the ambiguity of the genetic code). Out of all proteins in both proteomes under consideration, it is therefore mostly probable and plausible that a close evolutionary relationship of proteins is reflected by higher sequence similarity compared to all other proteins in the proteome. Orthologs are per definition genes in two different species that have vertically descended from a single gene in the last common ancestor. Orthologs are considered to be detectable by sequence similarity. The best pairwise hit, as result of the similarity search of two proteomes against the other, is the central criterion in the InParanoid method (Remm, Storm, & Sonnhammer, 2001): Two so-called main orthologs, a term originally defined in the field of evolution, form the seed for an orthologous group, and other closely similar sequences of both organisms are successively added to the seed. Hence, the central step for this fully automatic approach is the all-against-all sequence comparison that can only indicate the underlying evolutionary process and can be used for such an interpretation. The analysis of homology is more complex because the number of paralogs, which resulted from a split and remained as similar proteins in a single organism, is often very large: Paralogs occur as results of genome duplications. Alternative splicing isoforms can technically not easily separated from duplication products by similarity measurements. All paralogous genes together are orthologs from the point of view of a closely similar gene in a second organism. The time points of both incidences, of speciation and of divergence start, are important and have to be distinguished: out-paralogs predate a species split, in-paralogs arose after a split into two species. The latter are, by definition and in the prevailing terminology, properly paralogs. Out-paralogs should be more precisely distinguished in the group of all orthologs. The nature of those definitions rules some basic computational approaches and the underlying methods. All-against-all comparisons by sequence similarity searches are the initial step in most of the methods described in this section. For analyses of hundreds of proteomes, any methodology is limited by the complexity of homology.

B est H its, S um of H its One widely used method for determining pairwise orthologs is the calculation of the reciprocal best hit. This one-to-one combination of sequences of two organisms can be expanded to a proteome-wide comparison. Much more frequent is the occurrence of multiple best hits. One-to-many or many-to-many sets are built by sum-of-hits approaches. In this case, high-scoring sequence pairs with distance measures smaller than the arbitrary distance threshold participate additionally to the core set of orthologs. A difficulty occurs if the reciprocal best hit concept is applied and more than two organisms are considered. Then, for three organisms {A; B; C}, for instance, the pairwise comparisons {A-B; A-C;

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B-C} are to be calculated. Frequently, pairwise best reciprocal hits appear to sequence pairs as {a1-b1; a1-c1; b1-c2}. In this case, the individuals of A and B point at different sequences of proteome C (c1 and c2). It is obvious that this problem is increased with the number of proteomes. The categorization of proteins can be successful in the sum-of-hits manner, regarding the implications of orthology and paralogy. Methods that facilitate this goal are the focus of the next section.

SEQ UENCE SIMILARITY OF PR OTEIN FAMI LIES

IS A CAPAB LE PARAMETER

F OR THE INFERENCE

The common evolutionary background of proteins can, under the constraints discussed, be successfully determined by computational calculations that utilize sequence similarity. The presentation of methods that perform all-against-all comparisons of full-length proteins (mainly measuring local similarities) with the strategy of finding reciprocal best hits is the focus of this section. The publication by Krause (2006) reviews the history of protein family forming as well as backgrounds and descriptions of established approaches and data sets.

D ata Origin Types of data sets are either focused on the complete protein space, i.e., the set of known and available proteins, or a data set consists of a closed protein space, for instance by restriction to taxonomic groups like bacteria, eukaryotes, plants, animals. In each case, however, all available data reflect only a snapshot of the available knowledge of proteins. In public protein sequence databases, several tenthousands of organisms are represented by at least one protein sequence. Currently round about 600 complete proteomes, with sizes between 500 and 25,000 proteins, are known. The number is steadily increasing. Also refined methods that determine proteins from genomic information via new alternative splicing isoforms or alternative start site transcripts enhance the space of (putative) homologous proteins in sequence databases. To categorize sequences from a global organism set regards the evolutionary aspect more than a sequence set that is reduced regarding only a subgroup of organisms. However, a reduction of the sequence space is often necessary.

Preprocessing of D ata Taking into account the high variability and the large amount of proteins is one of the challenging tasks in optimizing algorithms, the available technical background, software, or computing time. An answer for limited capacity can be the reduction of the sequence space. This is frequently the reason for a pre-selection by a similarity criterion, e.g., 97, 80, or 50 percent. Universal protein sequence databases like UniProt (The UniProt Consortium, 2008) serve for sequence subsets and can be utilized for such restrictions, UniRef50 is a set with a similarity level of 50 percent. To achieve the complete sequence space, an replenishing step is required that follows the protein family inference processing.

Measures of S equence S imilarity and D istance Most frequently used distance measures are calculated from similarity scores. These distance measures and subsequently calculated e-values, which serve as essential decision parameters, are required in the 148

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categorization phase. They are calculated by prominent alignment-dependent approaches like BLAST or the Smith-Waterman algorithm. A similarity score sub-summarizes the validation result of a comparison in each single letter position within two character strings of protein sequences. Hereby, a pre-calculation of average ratios is used which examined the mutation from each single amino acid towards another. Such a mutation probability matrix, known as a scoring matrix, implicates models of evolution (Dayhoff, Schwartz, & Orcutt, 1978; Henikoff & Henikoff, 1992). The basis for computing similarity scores are pairwise alignments including gaps that indicate deletions or inventions and gap penalties that have influence on the scoring. The character string comparison is performed on a pairwise protein sequence alignment. Such a significance test on often not clearly similar sequences utilizes local alignments, and e-values are calculated from local similarity scores. The BLAST algorithm is a heuristic search method and is used for approximate local sequence similarity. Newer concepts also consider alignment-free distant measures (Kelil, Wang, Brzezinski, & Fleury, 2007).

C ategorization Methods aimed at the partitioning of data to subsets wherein common traits are shared are clusterings. Variations of clusterings are adapted for special tasks. A concept of a categorization is smart if it relies solely on information within the data. Clusterings satisfy this requirement. Single linkage clustering is a common, computationally cheap and well-studied categorization method in sequence comparison analyses that use distances. Hierarchical clusterings, as one application option, organize sub-clusters and further sub-levels in a tree structure. Applying a hierarchical clustering on protein sequences, the result is a protein sequence tree. Herein, edge lengths correspond to the distance measure. The choice of a suitable threshold to separate biologically meaningful sub-clusters is the crucial point of hierarchical clusterings. Sophisticated attempts with dynamical distance measure cutoffs, more widely than fixed cutoffs, are introduced to separate clusters of coherent proteins. Other methods of protein sequence partitioning utilize techniques like Markov clustering (confer next section) or spectral clustering (Paccanaro, Casbon, & Saqi, 2006). Automated phylogenetic trees based on a particular similarity measure and followed by subsequent partitioning (Kelil, Wang et al. 2007) are reported to serve for a successful categorization as well as layout based heuristics for weighted cluster editing (Wittkop, Baumbach, Lobo, & Rahmann, 2007).

SEQ UENCE -BASED

PR OTEIN FAMI LY DATA SETS

Pre-selection of data and applied methods that are aimed at to infer protein families from sequence information stand in a close connection to the resulting data set. In this book chapter, some approaches that claim for the inference or detection of orthology are included under the umbrella term protein family. Established protein family inferring approaches and underlying methods that utilize whole sequence information are explained in this section.

SYSTERS SYSTERS (systematic re-search) is initially introduced as a set-theoretical approach. In the current version, a hierarchical clustering (Krause, Stoye, & Vingron, 2005) utilizes the whole protein space 149

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from publicly accessible protein sequence resources. Starting with an all-against-all Smith-Waterman comparison on the basis of a pre-calculated non-redundant protein sequence set (80 percent criterion), a single linkage tree of the non-redundant set is constructed from pairwise sequence distances. The internal structure of the tree, i.e., the data itself, separate SYSTERS superfamilies using a specific characteristic, the subtree size, to determine dynamical e-value cutoffs. In a second step a graph-based approach, the minimal cut algorithm, subdivides superfamily graphs into clusters. These so called SYSTERS protein families are formed fully automatically and are the working entities of the SYSTERS data set. Sequences closely related to sequences of the non-redundant set are added to respective families. Hence, they are completing the redundant protein sequence set as it was achieved from the data resources. SYSTERS restrictively stands for the clustering of similar sequences and references terms of homology or function from annotations of the single sequence entries. However, additional information - posterior calculated phylogenetic trees and multiple alignments - is achievable in the web server (Meinel, Krause, Luz, Vingron, & Staub, 2005) and supports the clustering of sequences towards SYSTERS protein families.

C OG : C lusters of Orthologs Completely sequenced archaeal and bacterial proteomes were compared by an all-against-all BLAST search (Tatusov, Koonin, & Lipman, 1997). The formation of a cluster of orthologous groups, COGs, initially succeeds for closely similar genes of three organisms, a triangle represents the similarity measures of the pairwise best hits as edges. If this triangle is detected to comprise a common edge to further triangles, these mutually consistent genome-specific best hits were merged to that COG. The core domain architecture of a protein drives the construction of a COG using position-specific scoring matrices for individual domains. Multi-domain proteins that artificially bridge a COG were manually split into individual domains and support the assignment of COGs in accordance with their distinct evolutionary affinities. Examinations and visual inspections follow the intermediate classification. In a later update version of the COG database, few eukaryotic genomes were added to the data set, now called as KOG (Tatusov et al., 2003), by a special software, the COGNITOR program.

T ribeMC L: T ribes, E nsembl F amilies The TribeMCL algorithm compares protein sequences in an all-against-all manner using BLAST, and pairwise asymmetric results are cutoff-restricted. Expectation values enter into a so called MarkovMatrix that can be represented as connection graph (Enright, Van Dongen, & Ouzounis, 2002). The Markov Clustering (MCL) procedure simulates a random walk through this graph by iterative rounds by alternating decision parameters until the result is robust. This bootstrapping-like procedure allows protein families hidden in the graph to become visible by gradually stripping the graph down to its basic components. For the Tribes database (Enright, Kunin, & Ouzounis, 2003), protein sequences of 83 complete genomes of all three super-kingdoms of life entered into the procedure; for the Ensembl database, TribeMCL is used to infer Ensembl families only for currently more than 25 eukaryotic organisms into the Ensembl database (Flicek et al., 2008), wherein some of them are still incomplete as draft genomes. Ensembl provides an alternative orthology and paralogy prediction method in contrast to Ensembl Families. Advanced sequence-based and phylogeny-based approaches are combined in Ensembl Orthologies. The method can be conferred by http://www.ensembl.org/info/about/docs/compara/homology_method.html.

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InParanoid Proteins of currently 35 eukaryotic organisms are taken into the calculation of similarity scores, for the detection of two so-called main orthologs as well as of adequate in-paralogs. The main orthologs are the seed sequences of an orthologous group and is passed by a best hit similarity score. Closest related sequences of each of the two organisms, in-paralogs, are successively added to the seed if the similarity to their organism-specific correspondent is within the score. Out-paralogs are more distant from the main orthologs and form an own group. Each group is restricted to a pair of organisms, and orthologs from other organisms will not be respected in the group (Remm, Storm, & Sonnhammer, 2001; O’Brien, Remm, & Sonnhammer, 2005). Results are available in the InParaniod database (Berglund, Sjölund, Ostlund, & Sonnhammer, 2008). For extension of this approach on multiple proteomes and circumvent the restriction by pairwise considerations, a subsequent clustering using the InParanoid output was introduced. The algorithm called MultiParanoid (Alexeyenko, Tamas, Liu, & Sonnhammer, 2006) merges multiple pairwise ortholog groups into ortholog groups of multiple proteomes.

OrthoMC L OrthoMCL is a graph clustering algorithm that identifies homologous proteins based on sequence similarity (Li, Stoeckert, & Roos, 2003; Chen, Mackey, Stoeckert, & Roos, 2006). Species are compared in order to detect putative orthologs by the reciprocal best hit. In-paralogs are identified within the same genome that are more similar to each other compared to any sequence from other genomes. OrthoMCL, as a fully automated method, combines the homology definitions of the InParanoid approach with the technique of the Markov clustering (that is also used for TribeMCL) to resolve the many-to-many orthologous relationships inherent in comparisons across multiple genomes.

P-POD The Princeton Protein Orthology Database, P-POD (Heinicke et al., 2007), results from the idea to compare automatically derived orthology with knowledge from literature. OrthoMCL is the underlying automatic algorithm. P-POD claims to be a comparative genomics analysis tool that combines phylogenetic relationships and information from curated literature or other resources oriented in issues like diseases. It appeals particularly to experimentally working biologists who are achieving information from or about genes in well-studied model organisms.

OTHER

ATTEMPTS

THAT DETECT

PR OTEIN FAMI LIES

Protein domains as well as phylogenies, that are based on multiple sequence alignments are used to categorize proteins into protein families beyond pure whole sequence-oriented methods.

Pfam Protein domains are conserved functional substructures and therefore possess an evolutionary background. The Pfam database (Finn et al., 2006)) comprehends round about 8,000 manually curated

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protein families. They are generated using Hidden Markov Models (HMMs; a statistically supported method) for protein domains. Therefore, Pfam families are domain driven. To respect evolutionary relationships, Pfam families are organized in so called clans, respecting the fact that artificially high thresholds frequently separate two related families or divergent members of families which cannot be regarded in a HMM.

PhIG s The Phylogenetically Inferred Groups (PhIGs) database introduces known evolutionary relationships in addition to protein sequence distances from a BLAST all-against-all comparison to an iterative hierarchical clustering (Dehal & Boore, 2006). In contrast to the prior presented attempts, multiple sequence alignments of proteins are used to derive orthology from sequence information. A complete phylogenetic gene tree is created using widely accepted analytic methods of molecular evolution.

T reeF am For the TreeFam database (Li et al., 2006; Ruan et al., 2008), orthology of genes is declined from phylogenetic trees of all animal gene families considering that the analysis of phylogenetic trees is an established and very accurate way of determining orthology. 25 animal genomes are regarded in phylogenetic trees. The TreeFam database provides in its major part, TreeFam-B, phylogenetic trees that are automatically generated using clusters of PhIGs as seed. A second part consists of manually curated trees (TreeFam-A; which comprises less than 10 % of all trees).

TAX ON OMY AND THE N UMBER OF C OMPLETE LY SEQ UENCED ORGANISMS The overwhelming number of bioinformatics approaches relies on a taxonomy that is provided by the NCBI (Wheeler et al., 2004). NCBI collects expert knowledge and provides references for the included organisms. The data set is maintained daily. The NCBI taxonomy serves for universally used digital taxonomic identifiers, the TaxIDs. Lineages to each organism are provided as well as the universal taxonomic tree including internal nodes like super-kingdom, class, order, family and species or sublevels like subspecies as leaves. In phylogenetic analyses, species as well as subspecies as well as strains are often considered as operational taxonomic units, a synonym to the notation organisms. In addition to TaxIDs, a second taxonomic nomenclature is provided by the taxonomic division of the ExPASy server (ExPASy Proteomics Server, 2008) and is used in the UniProt and Swiss-Prot databases. It is characterized by the usage of mnemonics that abbreviate organism names most frequently by five letters. Respective organisms are a subset of the NCBI taxonomy, corresponding organisms are linked via standard NCBI TaxIDs. In practice, Swiss-Prot combines those mnemonics with gene names in protein sequence identifiers (e.g., SYFA_HUMAN, human phenylalanyl tRNA-synthetase alpha chain). Currently, round about 25 eukaryotic genomes are completely analyzed. Due to the easier sequencing according to smaller genome sizes and the importance under biotechnological or disease aspects, the number of bacterial and archaeal genomes is much larger, above 550 and round about 50, respectively.

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Completed and ongoing genome projects are recorded in the GOLD database (Liolios, Mavromatis, Tavernarakis, & Kyrpides, 2008).

PHY LOGENETIC

PR OFI LING

Phylogenetic Profiles Combine Gene Presence Information with Taxonomic Information; Phylogenetic Profiling A phylogenetic profile is a presence or absence pattern of a discrete gene or protein across a given set of organisms. The array of organisms can be organized with respect to their taxonomy. Then, phylogenetic profiles (or phyletic patterns, synonymously) visualize the presence of a gene or protein in a systematic and easily readable way. Proteins of organisms, that are represented in the phylogenetic profile, are usually not identical by sequence. Therefore, a phylogenetic profile has generally to be associated to an instance that categorizes proteins, e.g., to protein families as presented in a prior section. Hence, the population of a phylogenetic profile depends on the protein family inferring method. It is remarkable that a phylogenetic profile generally represents a protein family that contains at least one member protein of each of organisms represented. A phylogenetic profile serves for a taxonomic overview about a protein family. Vice versa, a protein family can be identified by a phylogenetic profile. Phylogenetic profiling achieves a comparison of several phylogenetic profiles. Similar or identical profiles possess a special importance with biological background.

C onservation of Proteins in a F unctional C ontext Leads to a C onservation of Phylogenetic Profiles If a functional context of proteins is evolutionary conserved and is occurring in a set of organisms, affiliated proteins possess also a common evolutionary history. Each of the essential proteins must survive against any evolutionary pressure. Then, this group of organisms contributes co-inherited members to respective protein families and therefore to identical presence indications in each single phylogenetic profile. Hence, the idea was emphasized that similar phylogenetic profiles could be used to predict functional relationships between proteins of unknown function (Pellegrini, Marcotte, Thompson, Eisenberg, & Yeates, 1999). A functional context concerns proteins that are in a physical contact (e.g., interactions among proteins or domains of proteins) or enzymes in a shared pathway. However, similar or identical profiles do not necessarily indicate common functional context. Ubiquitary families of essential proteins, that are merely present in two organisms are not necessarily functionally related or co-evolved, but are represented by phylogenetic profiles with presence indications for all organisms. Analogously, there might also exist organism-specific protein families that are not involved in a common functional background but are characterized by similar phylogenetic profiles. It could be shown (Jothi, Przytycka, & Aravind, 2007) that the correlation is weak between profile similarity measured by mutual information and membership in a KEGG pathway measured by scoring similarities albeit only informative organisms were careful filtered out for the analysis. A hierarchical

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clustering of phylogenetic patterns of COGs (Glazko & Mushegian, 2004) analyzed the pattern distance, graphs producing methods, the partitioning into subgraphs, and the estimation of error rates for the prediction of functional linkage. Several measures for phylogenetic patters were introduced (Wu, Kasif, & DeLisi, 2003), the simplest is the Hamming distance that counts the differences of each position in a profile. Other measures successfully applied are the Pearson correlation coefficient and mutual information. This assessment revealed that similar as well as complementary profiles possess similarities to common KEGG pathways. The calculation of the overlap of gene pairs to Gene Ontologies was used to benchmark methods and metrices that compare phylogenetic profiles (Cokus, Mizutani, & Pellegrini, 2007). The organism set of the most phylogenetic profiling approaches is dominated by the bacterial and the archaeal super-kingdom. More interesting in the context of clinical studies is the inclusion of eukaryotic organisms. The Ensembl database serves for sequence and protein family information of several eukaryotes. PhyloPat (Hulsen, de Vlieg, & Groenen, 2006) is initiated to summarize all Ensembl orthologs into phylogenetic patterns. However, assessments on phylogenetic profiles excluding prokaryotic proteins revealed poor results (Snitkin, Gustafson, Mellor, Wu, & DeLisi, 2006; Jothi, Przytycka, & Aravind, 2007). Convergence events, non-orthologous gene displacements, can lead to a complementary profile combination. This means that all presence states in the first profile are absence state in the second and vice versa. However, two complementary profiles with proteins of identical functional background do not necessarily indicate convergence. If the family inferring approach separates two divergent groups of proteins with common history into two protein families like in the SYSTERS data set, both respective phylogenetic profiles are complementary, too.

Phylogenetic Profiles on the Basis of the SYSTERS Data Set Phylogenetic profiling basing on the SYSTERS data set is introduced in regard to several boundaries. E.g., at least three completely sequenced organisms must contribute proteins to a protein family and therefore to the set of phylogenetic profiles. The SYSTERS subset with protein families of that quality is called PhyloMatrix (Meinel, Krause, Luz, Vingron, & Staub, 2005). 106 organisms of all three super-kingdoms are included to the profile set, the current release from 2003 consists of 78 bacterial, 12 eukaryotic, and 16 archaeal proteomes (organisms in taxonomic order are available upon web request). 7,563 unique phylogenetic profiles represent 19,374 SYSTERS protein families, 1,933 families are characterized by a single profile that comprises the three organisms human, mouse, and pufferfish. This might plausibilize the correlation of unspecific profiles in eukaryotic phylogenetic profiling as assessed by several authors. A specificity of the PhyloMatrix profile set is, according to the original SYSTERS clustering procedure, the partitioning of obviously orthologous sequences into separate protein families that are not quenched together by a post-processed manual curation. Therefore, phylogenetic profiling in SYSTERS can additionally be used for evolutionary studies of divergence phenomena. A special group of ubiquitary proteins with a central role in the information transduction chain shall demonstrate this SYSTERS specificity as well as serve for an example for phylogenetic profiling basing on PhyloMatrix. It is also traceable in the SYSTERS web interface. Figure 1(a) presents an example that illustrates the classical profiling approach - two proteins in a functional context comprise a similar phylogenetic profile - and the specificity of the SYSTERS clustering

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Figure 1. (a) Phylogenetic profiles (o/-; presence/absence) of three SYSTERS protein families in superfamily 115499 (profiles A to C) and four families in SYSTERS superfamily 113736 (profiles D to G). All seven families comprise phenylalanyl tRNA-synthetases. A functional context, here given by two protein subunits, is observed for protein families in profile combinations A-D and B-E. Confer the PhyloMatrix web service for details. (b) Protein domain composition (colored; Pfam code) in α-subunits, β-subunits and compartment-specific isoforms of phenylalanyl tRNA-synthetases, clustered in two SYSTERS superfamilies (SF) and seven SYSTERS protein families (PF), confer Figure 1. Eukaryotic isoforms are distinguished according to the respective cellular compartmentalization. SYSTERS superfamily 115499 SYSTERS protein family 141095 - Phenylalanyl-tRNA synthetase alpha subunit A ------------------------------------------------------------------oo---------- oooooooooo-o oooooooooooooooo SYSTERS protein family 141096 - Phenylalanyl-tRNA synthetase alpha subunit B oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo--oooooooooo ------------ ---------------SYSTERS protein family 141094 - mitochondrial Phenylalanyl-tRNA synthetase C ------------------------------------------------------------------------------ ooooooooo--o ----------------

|<-Bacteria------------------------------------------------------------------->|<-Eukaryota>|<-Archaea----->|

SYSTERS superfamily 113736 SYSTERS protein family 139353 - Phenylalanyl-tRNA synthetase beta subunit D ------------------------------------------------------------------oo---------- oooooooooo-o oooooooooooooooo SYSTERS protein family 139351 - Phenylalanyl-tRNA synthetase beta subunit E oooooooo-ooooooooooooooooooooooooooooooooooooooooooooooooooooooooo--oooooooooo ----o------- ---------------SYSTERS protein family 139354 - hypothetical protein F ------------------------------------------------------------------------------ ooo-ooo----- ---------------SYSTERS protein family 139352 - Phenylalanyl-tRNA synthetase beta subunit G ---------------------------------------ooooooooooooooooo---------------------- ------------ ----------------

(a)

(b)

to separate more divergent groups of proteins from each other. Aminoacyl tRNA-synthetases, aaRSs, link highly specifically amino acids to the cognate tRNAs as key components in the protein translation machinery. Sequence similarities and distances for protein sequences of aaRSs are well-studied in prokaryotes (Woese, Olsen, Ibba, & Söll, 2000). Phenylalanyl tRNA-synthetases, PheRSs, comprise, in bacteria as well as in archaea, both alpha and beta subunits. These two groups of interacting proteins

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are clustered separately from each other in two SYSTERS superfamilies; respective profile pairs are similar: A-D and B-E. However, each superfamily is split in, at least, two main protein families. Figure 1(b) illustrates slightly different protein domain compositions observable in both bacterial subunits. The generalized sketch for the respective SYSTERS protein families 141096 (alpha subunits) and 139351 (beta subunits) reveals one or two additional domains in comparison to archaeal and eukaryotic proteins (Wolf, Aravind, Grishin, & Koonin, 1999). This difference forces the separation of the sequences into the two SYSTERS protein families PF 141095 and PF 139353 indicated by complementary phylogenetic profiles presented in Figure 1(a) by the profile pairs A-B and D-E. Here, the evolutionary history can be verified as divergence. In addition, the endosymbiotic history seems to be reflected by a third family albeit the annotation in the respective entries is poor (confer the SYSTERS web server for more information). While cytosolic proteins in eukaryotes are combined with archaeal proteins, mitochondrial proteins are clustered additionally in their own family PF 141094. Figure 1(b) discloses that two functions, one of a single domain of the bacterial alpha subunit and one of a single domain in the beta subunit, are comprised towards a single mitochondrial protein consisting of two concatenated domains with an obviously preceding history. The given example of phenylalanyl tRNA-synthetases very insistently demonstrates those influences of several evolutionary events that can be observed by phylogenetic profiles: The early separation towards archaea and bacteria is reflected by complementary pattern pairs, the endosymbiosis event by co-occurrence of two alpha-like subunits in eukaryotes, and the similarity (or identity) of profiles base on the functional context of alpha and beta subunits. Aminoacyl tRNA-synthetases, aaRSs, are equally key components of the information transduction chain generally ubiquitary proteins. In Figure 2, phylogenetic profiles demonstrate this for at least fourteen aaRSs by the presence in all organisms, some of them are comprised in a single protein family. At least two protein families exist for each of the six other aminoacyl tRNA-synthetases separating archaeal from bacterial proteins. Eukaryotic proteins are exclusively clustered together with archaeal proteins - GlyRSs and, as explained previously, both PheRS subunits -, or exclusively clustered together with bacterial proteins, LysRSs. This is supported by (nearly perfect) complementary phylogenetic profiles. A separate mitochondrial protein family is known at least for PheRSs. According to the endosymbiont theory, whereby mitochondrial proteins are recruited from an invasive bacterium, mitochondrial aaRSs in eukaryotes are more similar to bacterial than to archaeal proteins. This is visible in profiles for LysRSs, but also for ProRSs, TrpRSs and TyrRSs. Eukaryotes possess additionally archaea-like, cytosolic proteins for the latter three aminoacyl tRNA-synthetases. In the protein family pairs of aaRSs complementary patterns base on divergence even if an affiliation to common SYSTERS superfamilies is not always given (data available in the web server). For both GlyRS families, for instance, the common structural superclass is evident (data not shown). Locally complementary profiles are found for GlyRSs, LysRSs, and ProRSs within the bacterial super-kingdom, for LysRSs and SerRSs within the archaeal super-kingdom. Proteins can be specific for a group of organisms. Horizontal gene transfer can frequently be observed in the bacterial super-kingdom and is detectable by phylogenetic profiles. Spirochaetes, a separate bacterial taxonomic class, are known for an individual behavior in profiles. Also the two single bacterial presence indicators in the given example, profile A and D in Figure 1(a), belong to this effect. Horizontal gene transfer leads to single presence states outside of an organism group in the profile of an organism-specific protein family.

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Figure 2. Significant phylogenetic profiles for all twenty aminoacyl tRNA-synthetases (o/-, presence/ absence): ubiquitary SYSTERS protein families for Ala, Cys, His, {Ile, Leu, Val}, Met, Arg, Ser, Thr, {Asp, Asn, Glu, Gln} specificity, and organism-specific SYSTERS protein families for Phe, Gly, Lys, Pro, Trp, Tyr specificity. IUPAC-IUB three-letter codes for amino acids stands for the aminoacyl specificity of respective tRNA-synthetases. A facultative minor letter indicates subunits of a protein complex, a, alpha; b, beta; e, epsilon; m, mitochondrial. Curly brackets indicate that groups of aminoacyl tRNAsynthetases are unified in a single SYSTERS Protein Family (e.g., PF 139203 for Ile, Leu, Val) due to high sequence similarities. |<-Bacteria------------------------------------------------------------------>|<-Eukaryota>|<-Archaea----->| oooooooo-ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooo-o oooooooooooooooo PF 143119 Ala oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooo-o ooooooo-ooo-oo-o PF 143743 Cys ------------------------------------------------------------------oo---------- oooooooooo-o oooooooooooooooo PF 141095 Phe-a oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo--oooooooooo ------------ ---------------- PF 141096 Phe-a ------------------------------------------------------------------------------ ooooooooo--o ---------------- PF 141094 Phe-m ------------------------------------------------------------------oo---------- oooooooooo-o oooooooooooooooo PF 139353 Phe-b oooooooo-ooooooooooooooooooooooooooooooooooooooooooooooooooooooooo--oooooooooo ----o------- ---------------- PF 139351 Phe-b oooooo--------------------------------------------oooo--oooooooo-oooo---o----- oooooooooo-o oooooooooooooooo PF 141159 Gly ------oooooooooooooooooooooooooooooooooooooooooooo----oo--------o----ooo-ooooo ----o------o ---------------- PF 152193 Gly oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooo-o oooooooooooooooo PF 138672 His oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooo-o oooooooooooooooo PF 139203 {Ile,Leu,Val} ----o-------------------------------------------------------------oo---------- ------------ o---oooooooooooo PF 149724 Lys ooooooooooooooooooooooooo--ooo--oooooooooooooooooooooooooooooooooo--oooooooooo oooooooooo-o -ooo-oo--------- PF 138269 Lys ------------------------ooo--ooo---------------------------------------------- ------------ ---------------- PF 149725 Lys ooooo-oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooo-o oooooooooooooooo PF 137021 Met o-----oooooooooooooooooo-----------ooo-----------o-------o-ooooo--o-o---o----- oooooooooo-o oooooooooooooooo PF 138344 Pro -oooooooooooooooooooooooooooooooooooooooooooooooo-ooooooooo-----oo-o-ooo-ooooo ooooooooo--- ---------------- PF 127052 Pro oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooo-o oooooooooooooooo PF 150167 Arg oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooo ooooooo-ooo-oo-o PF 146233 Ser ----------------------------o------------------------------------------------- ------------ -------o---o--o- PF 129876 Ser oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooo-o oooooooooooooooo PF 143907 Thr ------------------------------------------------------------------------------ oooooooooo-o oooooooooooooooo PF 143128 Trp oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oo-oooooo--o ---------------- PF 143124 Trp ------------------------------------------------------------------------------ oooooooooo-o oooooooooooooooo PF 137023 Tyr oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ooooooooo--o ---------------- PF 139117 Tyr

oooooooooooooooooooooooooo-ooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooo-o oooooooooooooooo PF 138346 {Asp,Asn} ------------------------------------------------------------------------------ ------------ oooooooooooooooo PF 142105 Gln-e oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ooooooooo--o ---------------- PF 138345 {Glu,Gln} ooooooooooooo--ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ooooooooo--o oooooooooooo--oo PF 140465 {Asp-a,Asn-a, Gln-a,Glu-a} oooooo---------o--------oo-oooooooooooooooooooooooooooooo-oooooooooooooooooooo oo-oooooo--o ooo-oooo---o--oo PF 142104 {Asp-b,Asn-b, Gln-b,Glu-b} |<-Bacteria------------------------------------------------------------------>|<-Eukaryota>|<-Archaea----->|

Analyses Using Phylogenetic Profiles Co-inheritance was predicted by functional annotations using pairs of phylogenetic profiles as well as genome-wide proteins network linkages in baker’s yeast or the bacterium Escherichia coli (Date & Marcotte, 2003; Wu, Hu, & DeLisi, 2006; Zheng, Roberts, & Kasif, 2002). The modularity in the evolution of functional modules, sets of orthologous groups expressed in blocks of phylogenetic patterns, was analyzed and quantified (Snel & Huynen, 2004). It was shown that the interspecies flexibility depends on functional differentiation within orthologous groups. In other words, it cannot be expected that the

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functional basis of a phylogenetic pattern is perfectly respected by all members of a protein family as well as the organism composition of the pattern is perfect. In the study of Snel and Huynen (2004), several data types of origin were acquired: metabolic pathways, protein complexes, transcriptional modules. This gives an impression of the universality of using phylogenetic profiling. Other reference sets use homologous proteins with reference proteins (Pellegrini, Marcotte, Thompson, Eisenberg, & Yeates, 1999; Marcotte, Pellegrini, Thompson, Yeates, & Eisenberg, 1999), in-detail-studies within a protein group of interest like tRNA-synthetases (Dohm, Vingron, & Staub, 2006), clusters of orthologs (Tatusov, Koonin, & Lipman, 1997), Pfam protein domains (Ye & Godzik, 2004; Pagel, Wong, & Frishman, 2004; Yang, Doolittle, & Bourne, 2005), proteins associated to distinct pathways (Dandekar, Schuster, Snel, Huynen, & Bork, 1999) or analyze keywords (Liberles, Thoren, von Heijne, & Eloffson, 2002). Phylogenetic profiles were helpful for the subcellular localization of protein groups (Marcotte, Xenarios, van Der Bliek, & Eisenberg, 2000). Very effective is the simultaneous visualization for phylogenetic profiles and networks restricted to respective compounds (Doerks, von Mering, & Bork, 2004).

Phylogenetic Profiling Approaches Most of prominent phylogenetic profiling approaches are established in the world wide web. URLs of exemplary internet services are provided: •

•

•

• •

• •

•

158

The COG data set (http://www.ncbi.nlm.nih.gov/COG/) can be directly accessed by browsing phylogenetic profiles. COGs are the basis for many studies on phylogenetic profiles referenced in this review. PhyloMatrix (http://systers.molgen.mpg.de/PhyloMatrix/): SYSTERS is a fundamental data resource for protein families. The underlying method is an automated approach that strictly bases on sequence similarity. In the PhyloMatrix web service, various query options provide access to phylogenetic profiles of SYSTERS protein families as well as an outlink from each protein family serves for access to the PhyloMatrix tool. PhyloPat (http://www.cmbi.ru.nl/phylopat/) is based on Ensembl families and comprises more than 25 genomes. This service possesses a high-quality web functionality and allows for access by profiles to respective gene families. OrthoMCL (http://www.orthomcl.org) provides phyletic patterns for orthologous groups of protein sequences from multiple eukaryotic genomes. The STRING database (http://string.embl.de) provides simultaneously information about the taxonomic distribution for proteins and respective networks of gene neighborhood, (von Mering et al., 2007). ProLinks (http://dip.doe-mbi.ucla.edu/pronav/) is integrated in the Database of Interacting Proteins and contains a phylogenetic pattern search option with text display output (Bowers et al., 2004). PLEX (http://bioinformatics.icmb.utexas.edu/plex/), the Protein Link EXplorer (Date & Marcotte, 2005), provides phylogenetic profiles accompanied by quantitative estimates of linkage confidence. PhylProM (http://www.sbc.su.se/~anna/PhylProM/index.html) is one of the first services that introduced keyword-based phylogenetic profiling (Liberles, Thoren, von Heijne, & Eloffson, 2002).

Function and Homology of Proteins Similar In Sequence

DISC USSI ON This book chapter reviews the sequence-based origin of information for methods that determine functional properties and evolution of proteins. Evolutionary events can be observed in three dimensions: divergence of sequences, speciation, and divergence of protein function. The arrows in Figure 3 illustrate the evolution of these three dimensions. Techniques for determining sequence similarity are considered as well as subsequent clustering procedures including several attempts of categorization towards orthology or similarity. Here, sequence-based or appropriate phylogeny-inferring methods are utilized for the respective approaches. As illustrated in Figure 3, the sequence-information-based term ‘protein family’ or, alternatively, the evolutionary term ‘ortholog’ can be deemed to be the link between sequence grouping information and taxonomic information. Many computational attempts combine the

Figure 3. There are three dimensions of evolution covered by computational molecular biology: divergence of sequences, speciation towards organisms, and invention or divergence of function. A protein sequences distance, which is a measure for the divergence of two sequences, is suggested by the interspace of two dots; protein sequences as grayish dots; two different methodological approaches, dotted or solid circles, are assumed. Speciation is visualized as a symbolic taxonomic tree with organisms as leaves, dark squares. Family proteins (or orthologs; corresponding to the inferring method) combine information about clustering and species but not regarding function. To comprise proteins in enzymes, respectively pathways, is a categorization of protein function across organisms without sequence information. In paralogs, function can be slightly shifted for sequences within a single organism and with common evolutionary history. Phylogenetic profiling (PP) can be applied on both family proteins or enzymes.

P ro te in S e q u e n c es

O rg a n is m s PP

pa

e or nzy pa me th w s ay s PP

fam ily p roteins or o rthologs

ra lo g s

P ro te in F u n c tion

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term ‘function’ with the result from inference of orthology. However, function more often possesses own evolutionary aspects: there can exist functional shifts caused by mutations, or function differences between isoforms. Therefore, protein function cannot be directly determined from orthology, it can be, at most, deduced from it. Each protein family definition depends on the methodology of protein comparisons and categorization. One aspect that rules the partitioning of proteins is the extremely different speed of evolution for different proteins. Induced problems often can only be attempted by manual curation. In approaches that are induced to detect homology function, a motivation for manual curation can preferentially occur. The SYSTERS method clusters similar proteins without possible limitation by manual curation. In contrast to this, it is remarkable that some approaches rely often only on sequence similarity while claiming to infer orthology. Therefore, similarly like in already established in phylogeny-based approaches, it is an advantage to cumulate information and include phylogeny methods to a purely family-forming approach than to claim for orthology. At this point, it is suggested to generally add assured information on function to the knowledge about sequence similarity. A concept of ‘functional orthology’ would reduce the number of respective ortholog candidates, as for instance existing in alternative splicing isoforms, and give a more exact picture of comparable proteins in different organisms. Orthologous connections between organisms also would hereby raise from the current information level, the gene level, to the transcript/protein level towards the operational biological unit that currently is not the case. This would also support the portability of information on function from animal models to other organisms like human and could be achieved by including additional experimental evidence to cluster information, for instance by data from microarray-based experiments. Phylogenetic profiles in general provide visualized information about the taxonomic distribution of a single protein family. As illustrated in Figure 3, phylogenetic profiling works in parallel to a clustering of sequences with origin from different organisms and combines several protein families. It can be used to indicate functional contexts by pattern similarity because it works independent from the knowledge on function or functional contexts of respective protein families. A refinement of phylogenetic profiling can be achieved either with extension of the organism number in the profile or with a refined definition of the biological entity. In comparison to the current number of prokaryotic organisms, currently a few hundred, the number of eukaryotic proteomes (twenty to thirty) are very sparse for phylogenetic profiling. Specific bacterial protein contexts are well to observe within the broad bacterial sub-pattern, for instance flagellar proteins. Many prokaryotes of the bacterial superkingdom are pathogens and therefore of interest for research on pathogenic-induced diseases. Here, phylogenetic profiling can help to understand protein functionality within the bacterial super-kingdom. Parasites, a special group of prokaryotes, are observable by special presence or absence indications in phylogenetic profiles and related protein families are directly detectable. Eukaryotic proteomes support significantly the endosymbiont hypothesis for mitochondria in combination with respective complete prokaryotic sub-patterns. Many eukaryotic protein families show unresolved all-presence indications in phylogenetic profiles. The currently sparse resolution within the eukaryotic sub-pattern would be increased with an exhaustive increase in research on proteomes of eukaryotes. Currently more than 25 Ensembl organisms are available in the PhyloPat approach. Here, however, phylogenetic profiling of eukaryotes is not supported with prokaryotic sequence information of evolutionary relevance. The information content of the biological entity, i.e., the protein family or cluster of orthologous genes, varies with the underlying methodological approach. Modulating or extending the approach,

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the definition of a biological entity can be refined towards increased information content in terms of function or evolution. Any biological entity can be the instance that is assigned with a phylogenetic profile, whereas a change of the definition background not necessarily induces changes in the profile. Phylogenetic profiling using SYSTERS protein families, for instance, extends the original functional context approach wherein a particular pattern represented a singular gene (family): The evolutionary complexity can be resolved in a SYSTERS superfamily by differentiation into separate SYSTERS protein. Here, additional divergence information can be detected. In general, there exists a competition regarding divergence and convergence within complementary profiles. A general observation in SYSTERS is that the detection of divergence is more frequent than the detection of convergence. However, in the case when many similar sequences of a particular organism occur in a single protein family, additional discrimination between orthology and paralogy or the usage of the functional orthology concept would increase the accuracy of this method. Phylogenetic profiles are generated for many established data sets or are initiated for separate purposes of assessments. Most of them are BLAST-based attempts, many validations are using the COG data set. Phylogenetic profiling on other prominent protein classification systems, in particular phylogeny-based attempts, consequently would refine insights into the efforts that the phylogenetic profiling method gives. Phylogenetic profiling currently only combines two scientific fields, taxonomy with function or taxonomy with sequence information. In the latter case, function verified by experiments as the third evolutionary field should be introduced to improve the tagging or even solidify the inference of functional contexts. A restriction to experimental confirmed function information, for instance by the functional orthologs concept, would give a higher information quality, not only for the protein family but also for phylogenetic profiling. Phylogenetic profiling offers the opportunity to gain insight into large-scale data by an intuitive, easily readable and fast visualization.

ACKN OW LEDGMENT TM hereby wants to thank Antje Krause for a fundamental introduction into the field of computational molecular biology in its particular view on protein families. Valuable hints for the concept of this review are adopted from her thesis.

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K ey terms BLAST: Basic Local Alignment Search Tool. A heuristic algorithm for searching of similar words or sequences in databases. Distance Measure: Measure to compare protein sequences by their amino acid composition. Subsumming validations of two character states (amino acids on an identical position) in a similarity measure leads to the similarity score. The distance is the difference of the relative similarity to 1. E-Value: Parameter that describes the probability that a protein or nucleotide sequence is not randomly found in a sequence database. Local Sequence Similarity: Similarity of two sequences is often found only on a local sequence level by a sequence comparison algorithm (e.g., BLAST). Identical partial subsequences are found in protein domains, for instance, and induce local sequence similarity. Multiple Sequence Alignment: Three ore more sequences are displayed in a picture with comparable characters in a column (for proteins: amino acid residues). Pairwise Sequence Alignment: Two sequences are displayed in two rows with comparable characters, amino acid residues for protein sequences, in columns. Phylogenetic Profile: Presence/absence indication for a family of genes or proteins across a given set of organisms. A phylogenetic profile represents a gene or protein family by serving for a taxonomic overview. Phylogenetic Profiling: Comparison of two or more phylogenetic profiles. Protein families of functional contexts possess similar phylogenetic profiles. Similarity Of Sequences: Two protein sequences can be compared in each amino acids position. Identical residues or similar biophysical behavior of compared amino acids determines sequence similarity. Necessary is an alignment of at least two protein sequences. Similarity Score: Measure of exchange of each of all twenty amino acids towards each of the remaining nineteen others with organization in a scoring matrix.

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Chapter IX

Computational Methods for the Prediction of GPCRs Coupling Selectivity Nikolaos G. Sgourakis Rensselaer Polytechnic Institute, USA Pantelis G. Bagos University of Central Greece, and University of Athens, Greece Stavros J. Hamodrakas University of Athens, Greece

abstract GPCRs comprise a wide and diverse class of eukaryotic transmembrane proteins with well-established pharmacological significance. As a consequence of recent genome projects, there is a wealth of information at the sequence level that lacks any functional annotation. These receptors, often quoted as orphan GPCRs, could potentially lead to novel drug targets. However, typical experiments that aim at elucidating their function are hampered by the lack of knowledge on their selective coupling partners at the interior of the cell, the G-proteins. Up-to-date, computational efforts to predict properties of GPCRs have been focused mainly on the ligand-binding specificity, while the aspect of coupling has been less studied. Here, we present the main motivations, drawbacks, and results from the application of bioinformatics techniques to predict the coupling specificity of GPCRs to G-proteins, and discuss the application of the most successful methods in both experimental works that focus on a single receptor and large-scale genome annotation studies.

Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Computational Methods for the Prediction of GPCRs Coupling Selectivity

INTR OD UCTI ON / BACKGR

OUND

G-protein coupled receptors (GPCRs) comprise a very important family of eukaryotic cell-surface membrane proteins. They are characterized by the structural hallmark of seven transmembrane helices, as exemplified by the crystal structure of rhodopsin (Palczewski et al. 2000), that has been extensively used as a homology modeling template for many receptor sequences (Nikiforovich et al. 2001; Becker et al. 2003). GPCRs play a pivotal role in signal transduction of eukaryotic cells, acting as the major sensors at the boundary between a cell and the outside world. Depending on their ligand-binding specificity, GPCRs can be activated by a broad range of external stimuli, from ions and small molecules to larger peptides and proteins, including light (Gether 2000). To perform these functions, GPCRs have evolved to a diversity of sequences that are traditionally classified in six major families, based mainly on shared homology (Horn et al. 2003). GPCRs have known representatives in most eukaryotic organisms, including yeast and plants, such as the recently discovered Arabidopsis thaliana seven-transmembrane (7TM) domain receptor GCR1 (Jones and Assmann 2004). As signified by their name, upon binding to a ligand, GPCRs exert their role through the specific interaction with a more limited repertoire of intracellular proteins that hydrolyze GTP, namely the G-proteins (Neer and Clapham 1988). G-proteins are heterotrimeric complexes composed of three subunits Gα, Gβ and Gγ. They are classified into four main families, according to the type of their αsubunit, which also possesses Ras-like GTPase activity (Benjamin et al. 1995). These include Gs and Gi/o, which stimulate and inhibit adenylate cyclase, respectively (Johnston and Watts 2003), Gq/11, that activates phospholipase C (Exton 1993) and the less characterized G12/13 family that activates the Na+/H+ exchange pathway (Kurose 2003). At least 16 different subtypes of Gα subunits have been identified and classified in these four families (Downes and Gautam 1999; Kristiansen 2004). Interaction of the G-protein trimer with the activated receptor triggers the exchange of the bound GDP with GTP, and subsequently the dissociation of the complex to Gα and Gβγ moieties, that activate downstream effector molecules. Hydrolysis of GTP to GDP by the α subunit renders the complex to its original, inactive state (Neer 1995). As a result, depending on the selectivity of the GPCR - G-protein interaction, a specific downstream pathway may be activated. Despite extensive experimental and computational studies, the structural basis of this specificity is not well characterized, while the mechanisms that determine the function of the activated GPCR/G-protein complex are yet to be uncovered (Muramatsu and Suwa 2006). Furthermore, the diversity of GPCR-G-protein interactions is enriched by several receptors that may alternatively interact with more than one family of G-proteins, known as promiscuous GPCRs. For instance, the human thyrotropin receptor can couple to all four G-protein families (Laugwitz et al. 1996). In general, promiscuity seems to be a rule rather than an exception for interactions between GPCRs and G-proteins (Wess 1998; Oliveira et al. 1999; Horn et al. 2000). Several lines of evidence indicate the importance of the GPCR intracellular regions, as well as the intracellular boundaries of the transmembrane helices (Gether 2000). It is also established that the regions of interaction on the G-protein are mainly the N-terminus of the Gα and the N- and C-termini of Gγ subunit. However, up to date, these findings have not been incorporated to a high-resolution, systematic model of GPCR – G-protein interactions, while the nature of the underlying mechanism is believed to be specific to the interacting partners (Wess 1998). Due to their function as input nodes in the signaling pathways of eukaryotic cells, GPCRs play a very important role in health and disease (Muller 2000). GPCRs are involved in a variety of pathological conditions including cystic fibrosis, cancer and HIV-mediated infection of host cells. The ability

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Computational Methods for the Prediction of GPCRs Coupling Selectivity

to rationally modulate the cell’s signaling pathways through these ‘target’ molecules has introduced a new era in pharmacology. In fact, the significance of G-Protein coupled receptors (GPCRs) as major pharmacological targets can be compared with no other single family of proteins. This is further illustrated by the fact that more than 50% of all known drugs act on GPCRs, a family that is represented by less than 1% of open reading frames (ORFs) identified in the human genome. Taking into account the growing number of novel GPCRs, that could be used as potential drug candidates (Chalmers and Behan 2002; Dechering 2005), the variety of signaling pathways that start or can be regulated by GPCRs and the rate of expansion of biological sequence databases, the wealth of pharmacological targets available within this versatile family of proteins is evident. Furthermore, recent genomics initiatives have resulted in a plethora of newly discovered GPCR sequences. These receptors are often characterized as orphan GPCRs (oGPCRS), in the sense that they lack any annotation regarding their function. Most importantly, the endogenous ligands of oGPCRs are yet to be identified. The lack of knowledge on the ligand repertoire that can activate these receptors limits their utility as drug candidates for traditional ligand-based assays. One approach to overcome this limitation involves the use of constitutively active GPCRs (reviewed in (Chalmers and Behan 2002)), that stimulate cellular signaling in the absence of a bound ligand. Constitutively Active Receptor Technology (CART) is based on the ability to genetically engineer receptors by modifying the conformation of a ‘latch’ region of the core seven-transmembrane domain. However, high-throughput screening involves detection of a cellular response, such as cAMP production in the case of receptors that couple to Gi/o or Gs and calcium flux or inositol phosphate production for Gq/11-coupled receptors. Therefore, the knowledge of the interacting G-protein is essential in designing these assays. Prediction methods, based on the available genomic information, offer an attractive alternative in deciphering the coupling specificity experimentally, a procedure that consumes time and laboratory resources. Although several computational methods have been developed to provide information on the ligandbinding properties of GPCRs (reviewed in (Lu et al. 2006)), as well as on their phylogeny (Papasaikas et al. 2003; Shigeta et al. 2003; Papasaikas et al. 2004), the aspect of selective coupling to the G-proteins has been less studied. In particular, the application of standard bioinformatics tools to develop prediction methods of the immediate interacting partners of GPCRs was hampered for many years by the lack of a systematic database of interactions, and more importantly by the lack of experimental data on the mechanism of selective binding, activation and signal transduction through their G-protein partners. Recently, the range of G-proteins and their interaction with GPCRs has been extensively annotated in the G-protein Database (Elefsinioti et al. 2004). Such knowledge is essential in designing experiments for screening orphan receptors against libraries of potential ligands by providing the missing link between GPCRs and cellular responses. In this review we focus to briefly describe the main motivations, drawbacks and results from the application of computational methods for the prediction of GPCRs coupling selectivity.

C OMPUTATI ONA L METH ODS F OR C OUPLING PREDICTI

ON

Several methods have been developed for the prediction of GPCR’s coupling selectivity to G-proteins and their properties are summarized in Table 1. Their training philosophy, performance and caveats are discussed herein in further detail. An attractive feature of some of these methods is their availability online through web-based servers, for non-commercial users. Such methods can be widely used as

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Computational Methods for the Prediction of GPCRs Coupling Selectivity

online prediction tools by both experimentalists, targeted at the characterization and study of specific receptors or bioinformaticians, for large scale genome annotation projects and the development of new, more efficient computational tools.

Pattern and N aïve B ayes Models-B ased Methods The increasing biochemical evidence that GPCR–G-protein recognition takes place within the intracellular loops of the receptor (Wess 1998; Wong 2003) motivated the application of pattern discovery techniques aimed at identifying the functionally important segments of residues for the interaction with G-proteins, and using these patterns to classify GPCRs according to their coupling specificity (Möller et al. 2001). This was the first extensive pattern discovery study applied for the prediction of GPCRs’ coupling selectivity. The authors used a non-redundant dataset of 103 human GPCRs with experimentally determined coupling selectivity (Alexander 2000). However, this approach was limited by the low degree of accuracy of regular expressions as classifiers of biological sequences, as well as the need for prediction of the transmembrane segments of GPCRs in a preceding step, as discussed later. In specific, the use of regular expressions limits the extent of sequence variability that can be incorporated to the prediction model. Furthermore, this choice of model leads to a redundancy of patterns that describe the same coupling group, as exemplified in figure 1 of reference (Sgourakis et al. 2005). Thus, the common experimental observation of different coupling to G-proteins for receptors from the same subfamily cannot be reproduced by such a prediction scheme. This also adheres to the low sensitivity of the method (30-40% as reported by the authors). In general, it appears that the coupling of GPCRs to G-proteins is a late event in molecular evolution that has been achieved by the mutation of key residues of the receptor’s intracellular domains to fine-tune interaction with certain families of G-proteins, while excluding others (Wess 1998; Sgourakis et al. 2005). This is the basis of the coupling prediction problem, and the reason that traditional sequence alignment methods produce predictions with little accuracy that cannot be generalized to the entire repertoire of receptors (Horn et al. 2000). More advanced statistical recursion methods such as Naïve Bayes models (Cao et al. 2003) were also applied for the same task. The authors used a training dataset of 91 receptors (Alexander 2001). This approach introduced a new method in GPCR coupling prediction that however did not lead to a significant increase in accuracy (72%, validated in an independent dataset of 55 GPCRs). Furthermore, their method seemed to over-predict interactions for most GPCRs in their dataset, by assigning multiple interacting partners (i.e. the number of promiscuous receptors was more that the experimentally observed). The authors justified this observation by arguing that promiscuous coupling is a common attribute of GPCRs (Oliveira et al. 1999), although not always experimentally determined. However, this raises issues regarding the specificity of their model.

Profile Hidden Markov Models–Based Methods Profile Hidden Markov Models (pHMMs) (reviewed in (Eddy 1998)) have been widely used as a statistical recursion tool for the classification of biological sequences (Krogh et al. 1994). The first application of Hidden Markov Models as predictors of GPCR’s coupling specificity was carried out by Goldstein’s group (Qian et al. 2003). This was also the first information-intensive computational approach to classify GPCRs according to their coupling specificity. The authors used the intracellular domains of GPCRs with known coupling specificity to train tree-based Hidden Markov Models (Mitchison and Durbin 1995) that

170

94% 93%

103 GPCRs

91 GPCRs

102 GPCRs

132 GPCRs

282 GPCRs**

188 GPCRs

282 GPCRs**

153 GPCRs

“Vilo et al.”

“Cao et al.”

“Sreekumar et al.”

GRIFFIN

PREDCOUPLE

PREDCOUPLE2

“Guo et al.”

“Ono et al.”

yes

yes yes

no

Gi/o, Gs, Gq/11 Gi/o, Gs, Gq/11, G12/13 Gi/o, Gs, Gq/11 Gi/o, Gs, Gq/11

no

Gi/o, Gs, Gq/11

no

Gi/o, Gs, Gq/11 no

no

Gi/o, Gs, Gq/11

Gi/o, Gs, Gq/11

no

Promiscuous

Gi/o, Gs, Gq/11

G-protein classes

None required  Biological functions

ACC and SVMs pHMMS, NLP and Decission Trees

None required

None required

Refined pHMMs / QFAST algorithm Refined pHMMs and ANNs

Ligand Properties

Transmembrane topology

knowledgerestricted pHMMs SVMs and pHMMs

Transmembrane topology

Transmembrane topology

Transmembrane topology

Additional inputs

Naïve Bayes Models

Regular expressions

tree-based HMMs

Method

** Several non-human receptors were included

* A significant drop in accuracy is expected for this method for full-length GPCR sequences

92%

90%

85%

>95%*

72%*

N/R

83%*

95 GPCRs

“Qian et al.”

Accuracy

Trainning set

Tool

not available

program download

web server

web server

web server

personal communication

personal communication

web server

personal communication

Availablity

 -

-

http://bioinformatics. biol.uoa.gr

http://bioinformatics. biol.uoa.gr

http://griffin.cbrc.jp/

[email protected]

jack.cao@astrazeneca. com

http://ep.ebi.ac.uk/ GPCR/

richard.goldstein@ nimr.mrc.ac.uk

URL / email

Computational Methods for the Prediction of GPCRs Coupling Selectivity

Table 1. Prediction methods of GPCRs coupling selectivity. The training dataset, applied technique and performance of each method are presented, in addition to its online availability. Out of 9 published methods, 4 can predict efficiently promiscuous coupling, 3 are available through an online server for non-commercial users and only 1 can predict coupling to G-proteins of the G12/13 family. N/R: Not reported.

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Computational Methods for the Prediction of GPCRs Coupling Selectivity

could act as classifiers when aligned against a GPCR sequence of unknown selectivity. Their method was found to perform quite well, given the small size of the training dataset (95 receptor sequences). In a following study, Sreekumar and coworkers used all the intracellular domains of GPCRs with known coupling selectivity concatenated in a single sequence to train their models (Sreekumar et al. 2004). For this reason, these profiles were described as knowledge-restricted HMMs. This strategy leaded to a high degree of correct classification rate (~95%), when tested against receptors with known location of the transmembrane segments. However their approach, and also the previously mentioned methods, was limited by the requirement of known transmembrane topology of the receptor under query. Despite the high-efficiency in predicting the coupling specificity of GPCRs with known transmembrane topology, this limitation rendered these methods practically inapplicable in the case of oGPCRs, where no information other than the sequence is available. At this point we should notice the relative low accuracy of transmembrane segment prediction algorithms, despite the development of methods targeted specifically at GPCRs (Rayan et al. 2000). Even the most accurate methods predict the correct topology with a rate that does not exceed 75% on a residue level (Viklund and Elofsson 2004). In a previous bioinformatics work (Sgourakis et al. 2005), we have addressed the problem of GPCR coupling specificity despite the lack of transmembrane topology information with a high degree of efficiency. This was made possible through the implementation of a selection process to generate refined Hidden Markov Models of high discriminative power that model the intracellular domains of receptors that couple to the three main families of G-proteins. Results from individual profiles that corresponded to different intracellular domains were combined by the QFAST algorithm (Bailey and Gribskov 1998), to produce the final score for each coupling group, while ROC-curve analysis was used to optimize the cutoff that is applied to produce a final prediction. This strategy allowed for the first time the prediction of interaction for promiscuous receptors, although with a rather small accuracy that did not exceed 30%. Another novelty of our approach was the inclusion of the membrane-proximal segments of the transmembrane domains extending from the intracellular face of the membrane to train the highly refined, discriminative models. This was motivated by the fact that the location of the membrane boundaries is not precisely determined, even in high-resolution crystal structures. Furthermore, according to the general model of receptor activation, the intracellular face of a receptor “opens up” during the binding of the ligand, rendering residues at the interior of the receptor towards the membrane accessible to interaction with the G-protein (Gether 2000). In addition, this method offers the advantage of high specificity against non-GPCR sequences through the implementation of GPCR-specific profiles from the PFAM database (Sonnhammer et al. 1998; Bateman et al. 2004). Therefore, for the first time we provided a high-throughput genome annotation pipeline that could be used independently of transmembrane prediction schemes to guide experiments that aim to decipher the role of oGPCRs.

Methods that C ombine a Variety of T echniques In a following study (Sgourakis et al. 2005), we expanded the range of GPCRs recognized by our models, by including the less characterized group of G12/13-coupled receptors in addition to the Gi/o, Gq/11 and Gs families. A very important aspect of GPCR signaling (as reviewed in (Riobo and Manning 2005)), G12/13 coupling was ignored by previous methods and, to the best of our knowledge, by all methods published to date due to the lack of experimentally determined interaction data (Moller et al. 2001; Cao et al. 2003; Yabuki et al. 2005; Guo et al. 2006). To overcome this limitation, we performed

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Computational Methods for the Prediction of GPCRs Coupling Selectivity

an extensive literature search and were able to construct an extensive, non-redundant dataset of 188 GPCR sequences, annotated according to their coupling specificity that includes 35 sequences of receptors that couple to G12/13. A very important feature of this method is the incorporation of sequences belonging to promiscuous receptors (65 in total) that were also retrieved from the literature. By using an intuitive method to train our models, and the aforementioned optimization procedure, we were able to construct a refined library of pHMMs that could efficiently model promiscuous coupling (with an accuracy of 85%, exceeding all published methods), as well as interactions with G12/13 proteins (with an accuracy of 95%), as evaluated in a five-fold cross-validation procedure. In addition, we introduced an Artificial Neural Network algorithm to combine the results of independent models in producing the final prediction of the method. This methodology was later adapted for the identification of promoters in large-scale genomic data from prokaryotic genomes (Mann et al. 2007). Furthermore, the specificity of this improved method against non-GPCR sequences was enhanced by the use of the results from querying an unknown sequence against all refined models in our database, combined with the QFAST algorithm. This addition to the already implemented highly specific GPRC profiles from the PFAM database (Bateman et al. 2004), was proven to a very efficient filter in screening non-GPCR sequences, by effectively identifying all non-GPCRs in two independent datasets consisting of 1113 globular and 1356 transmembrane non-GPCR sequences (adopted from (Papasaikas et al. 2003)). Support Vector Machines have also been applied to the same task, in numerous studies (Yabuki et al. 2005; Guo et al. 2006). In the first published method, Yabuki and coworkers used a hierarchical approach to train a method that besides the receptor’s sequence also uses properties of the ligand as inputs, to produce a prediction on its coupling sensitivity. They rationalize the use of ligand information by considering the activated receptor as an entity that is composed of the ligand, the GPCR and the Gprotein. Indeed, several lines of evidence indicate that the same receptor can signal through a variety of pathways, depending on its bound agonist, a phenomenon known as agonist trafficking (Hermans 2003). Their method, that is available for online use through a web-based server, uses both profile Hidden Markov Models and Support Vector Machines (SVMs) (reviewed in (Yang 2004)). The pHMMs are used in a first step to separate class A, that includes the majority of known receptors, from all the others. Thus, pHMMs generated for the opsins and olfactory receptors subfamilies and the class B, class C, frizzled and smoothened, families are used to classify GPCRs not belonging to class A. The authors claim that the coupling specificity for these receptors is ubiquitously determined by their family type, although there are several reported examples in the literature where this is not the case (Wess 1998). In a next step, a series of SVM classifiers is used to predict coupling of the remaining GPCRs into the three main coupling groups. Several parameters are used as inputs to the SVM at this step, including scores from pHMMs that were trained from GPCRs that bind peptide or amide ligands. The final, integrated system produces predictions with an accuracy of >85%, as evaluated in 4-fold cross validation procedure. However, the observables used as inputs to the method are derived from the sequence of the intracellular loops, and also from the aminoacid composition of very specific positions with respect to the sequence of bovine rhodopsin, that is used as an alignment template. Therefore, the entire prediction is expected to be very sensitive to the performance of the alignment algorithm, which will produce the position of the transmembrane segments. Given the variability in the output of such algorithms that is not guaranteed to have seven transmembrane segments, we can assess the amount of error that resides in this strategy: Qian and coworkers repot that of a total of 470 GPCR sequences submitted to the TMHMM server (Krogh et al. 2001) for prediction of transmembrane topology only

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Computational Methods for the Prediction of GPCRs Coupling Selectivity

417 were predicted as having seven transmembrane segments (Qian et al. 2003). However, the method of Yabuki and coworkers predicts seven transmembrane segments even for sequences not belonging to GPCRs. We can thus conclude that this method is not suitable for application in large-scale genomic data for high-throughput genome annotation purposes. Recently, a second method that uses SVMs was published (Guo et al. 2006). The main motivation of this method is to avoid the use of membrane topology information both at the prediction and training steps. It uses the Autocross Covariance Transform method (Wold et al. 1993) to generate the input vectors for the SVM classifier, based on the physicochemical properties of the entire GPCR sequence as described by the projections on the first three eigenvectors of a 29-dimensional space that includes features such as bulk, hydrophobicity and electrostatics (Hellberg et al. 1987). The authors adopted a dataset from a previously published work from our group (Sgourakis et al. 2005) to train their method. In addition, to enhance the specificity of their method against non-GPCR sequences, they used a dataset of 1090 non-GPCR transmembrane proteins, adopted from an earlier work on GPCR classification (Guo et al. 2006). Given the low degree of sequence similarity between the intracellular domains of different receptors, and the heuristic nature of most alignment algorithms, the advantage of this strategy is that it does not rely on the accuracy of sequence profiles. Furthermore, the construction of GPCR-specific models results in a high degree of accuracy (>95%) in discriminating GPCRs from non-GPCR sequences. Thus, this method can also be used as a stand-alone tool. The authors report an accuracy of 91.3% for non-promiscuous GPCRs, as evaluated in a jackknife test with a non-redundant training dataset, and an accuracy of 80% for promiscuous receptors. In general, this approach yields reliable predictions from GPCR sequence alone, for all GPCR coupling types, including promiscuous receptors, without the requirement of any transmembrane topology information or filtering of non-GPCR sequences in a preceding step. However, it does not provide predictions for G12/13–coupled receptors, since, as the authors claim, a dataset could not be established due to the deficiency of data. On the contrary, as shown in our preceding study (Sgourakis et al. 2005), this problem can be solved through a careful and extensive retrieval set of data from the literature. In fact, we freely provide the required dataset in our web-based server: (http://bioinformatics.biol.uoa.gr/PRED-COUPLE2/training).

T ext Mining Methods In another study (Ono and Hishigaki 2006), the information included as input for the prediction is mined from the literature using Natural Language Processing (NLP) techniques. In this approach, text mining was used to extract features of biological functions as keywords from various databases. The authors claim a correct classification rate of 92.2%, when tested against a dataset of 152 GPCRs with known coupling specificity. However, this method is also depended on the availability of the known biological functions used as input to the predictor. In case of a novel sequenced orphan GPCR, such knowledge is missing and thus the method could not be benefited by the inclusion of the biological function. Following a similar rationale, the method cannot be applied for searching whole genomes in order to characterize orphan GPCRs. When the biological functions are not included in the prediction, the methods accuracy drops significantly below 90%, and thus is comparable to earlier methods.

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INSIGHTS

FR OM THE APP LICATI ON OF C OMPUTATI ONA L T OOLS

The utility of these methods was confirmed by their use in combination with experimental data to decipher the coupling specificity of important receptors. In a recent study that focused on the differential activation of the Cockroach species Periplaneta Americana Adipokinetic Hormone Receptor (AKHR), the effects of two different types of hormones were studied (Wicher et al. 2006). In order to have a starting point for characterizing the pathways activated by this receptor, the authors used both GRIFFIN (Yabuki et al. 2005) and PRED-COUPLE (Sgourakis et al. 2005) to obtain a prediction of the coupling specificity of AKHRs. Both tools predicted coupling with Gs, however our method also predicted a further coupling specificity for Gq. The experiments carried out by Wicher and coworkers confirmed coupling with Gq in addition to Gs, through the depletion of ion currents, as a result of Gq-mediated inhibition of K+ channels. Furthermore, they were able to detect differences in the coupling specificity of the receptor, based on the type of bound hormone: both hormones induce coupling to Gq with the same efficiency, while AKH I has a higher potential to induce coupling to Gs. This example indicates the high accuracy level of current prediction tools, since AKHR was not included in the training datasets of either GRIFFIN or PRED-COUPLE. Computational prediction tools have also been very useful in characterizing the function of light receptors in photoreceptive retinal ganglion cells (pRGCs). These receptors belong to the Melanopsin gene family Opn4 and comprise alternate light sensors that are responsible for the perception of environmental brightness (Peirson and Foster 2006). Their function is independent of the typical Vitamin A–based photopigments, such as rhodopsin. Melanopsins are believed to resemble intervertebrate photopigments, however, the signaling pathways in vertebrate cells are not known. Peirson and Foster applied the prediction methods developed by our group to obtain an estimate of the variability in coupling specificity within the Melanopsin gene family (figure 2 in (Peirson and Foster 2006)). First, they confirm the validity of our method through a variety of correct predictions. Furthermore, for the melanopsins, this analysis predicts an extensive range of interactions with the G-protein families. Although not proven to be true in vivo, this is a striking difference of the Melanopsin receptors from the visual pigment opsins that is supported by several lines of experimental evidence (Newman et al. 2003; Melyan et al. 2005). The sequence variability in the third intracellular loop of the Melanopsin GPCRs was proposed to be the basis of this variability. In a recently published study (Muramatsu and Suwa 2006), Muramatsu and coworkers provided insight into the structural basis for GPCR-G-protein coupling selectivity, focusing on class A receptors from the GPCRDB 7.0 database (Horn et al. 2003), through the identification of key residues located mainly in the intracellular loops of the receptors. To perform this task, they used the solved crystal structure of rhodopsin (Palczewski et al. 2000) as a reference frame for the mapping of multiple sequence alignments of selected loop sequences. A Hidden Markov Model–based alignment procedure was used, and states in the model were assigned according to the position of transmembrane helices of rhodopsin. Based on the statistics of the occurrence of different residues at various positions in the alignment, the authors were able to infer a set of rules that correlate clusters of residues with the coupling specificity of GPCRs. Furthermore, they were able to identify mutation data from the literature in support of their observations. This study confirms the importance of the membrane-proximal boundaries of the transmembrane helices in establishing the coupling selectivity of GPCRs. Another interesting observation was that residues responsible for coupling to Gi/o and Gq/11 can be also found at the transmembrane and extracellular domains of GPCRs. Mutation studies on selected receptors corroborate this finding.

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Allosteric changes transmitted across the plasma membrane to the G-protein binding interface upon ligand binding could account for these observations. Also, this analysis suggests, that a few residues along the sequences of receptors that couple to Gq/11 are responsible for their selectivity, a fact that perhaps explains the lower accuracy of some prediction methods for this class of receptors (Cao et al. 2003; Guo et al. 2006). However, these results are very sensitive to the choice of the alignment template of rhodopsin, a structure that may not cover the entire spectrum of class-A receptors. In the absence of a solved structure of the activated complex of GPCR with bound G-protein, more mutation data are needed to confirm these findings.

F UT URE TRENDS

/ C ONC LUSI ON

The field of GPCR computational biology has shown many advances in the post-genomic era; however the mechanism of selective binding to G-proteins is yet to be uncovered, mainly due to the lack of high-resolution structural data. The structure of complexes of GPCRs with different G-proteins and in different activation states would undoubtedly provide insight into the series of molecular events required for G-protein activation, and explain the basis of the coupling selectivity of GPCRs, at the atomic level. Prediction methods could provide important information in designing experiments, and facilitate the structure generation process by suggesting the “active interface” between GPCRs and G-proteins. Immediate advances in the field of computational prediction of the coupling selectivity of GPCRs could result from the application of consensus methods that utilize a variety of machine learning techniques, a strategy that has been proven successful for a variety of problems in bioinformatics (Cuff et al. 1998; Arai et al. 2004; Bagos et al. 2005; Tjalsma and van Dijl 2005; Hamodrakas et al. 2007). Finally, the incorporation of high-throughput coupling data from biochemical experiments would iteratively improve the efficiency of prediction algorithms and provide additional clues to the structural basis of GPCRs coupling specificity to G-proteins.

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Sonnhammer, E. L., Eddy, S. R., Birney, E., Bateman, A., & Durbin, R. (1998). Pfam, multiple sequence alignments and HMM-profiles of protein domains. Nucleic Acids Res, 26(1), 320-2. Sreekumar, K. R., Huang, Y., Pausch, M. H., & Gulukota, K. (2004). Predicting GPCR-G-protein coupling using hidden Markov models. Bioinformatics, 20(18), 3490-9. Tjalsma, H. & van Dijl, J. M. (2005). Proteomics-based consensus prediction of protein retention in a bacterial membrane. Proteomics, 5(17), 4472-82. Viklund, H. & Elofsson, A. (2004). Best alpha-helical transmembrane protein topology predictions are achieved using hidden Markov models and evolutionary information. Protein Sci, 13(7), 1908-17. Wess, J. (1998). Molecular basis of receptor/G-protein-coupling selectivity. Pharmacol Ther, 80(3), 231-64. Wicher, D., Agricola, H. J., Sohler, S., Gundel, M., Heinemann, S. H., Wollweber, L., Stengl, M., & Derst, C. (2006). Differential receptor activation by cockroach adipokinetic hormones produces differential effects on ion currents, neuronal activity, and locomotion. J Neurophysiol, 95(4), 2314-25. Wold, S., Jonsson, J., Sjostrom, M., Sandberg, M., & Rannar, S. (1993). DNA and peptide sequences and chemical processes multivariately modeled by principal component analysis and partial least-squares projections to latent structures. Analytica Chimica Acta, 277(2), 239-253. Wong, S. K. (2003). G protein selectivity is regulated by multiple intracellular regions of GPCRs. Neurosignals, 12(1), 1-12. Yabuki, Y., Muramatsu, T., Hirokawa, T., Mukai, H., & Suwa, M. (2005). GRIFFIN, A system for predicting GPCR-G-protein coupling selectivity using a support vector machine and a hidden Markov model. Nucleic Acids Res, 33(Web Server issue), W148-53. Yang, Z. R. (2004). Biological applications of support vector machines. Brief Bioinform, 5(4), 328-38.

key T erms Coupling Selectivity: G protein trimers are named after their α-subunits, which on the basis of their amino acid similarity and, most importantly by their cellular function, are grouped into four families. These include, Gαs and Gαi/o, which stimulate and inhibit respectively adenylate cyclase, Gαq/11 which stimulates phospholipase C, and the less characterized Gα12/13 family that activates the Na+/ H+ exchanger pathway. The specificity of the interaction of a given GPCR with the pool of available intracellular G-proteins is termed coupling selectivity or specificity. The ability of certain GPCRs to interact with more that one types of G-proteins (i.e. Gαs and Gαi/o) is known as promiscuous coupling selectivity. GPCRs coupled to members of the Gα12/13 family are all exhibiting promiscuous coupling preferences. Genome Annotation: The functional characterization (by means of biochemical experiments or computational prediction algorithms) of novel genes in newly sequenced and assembled genomes.

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G-Protein Coupled Receptors (GPCRs): Also known as seven transmembrane (heptahelical) receptors, due to their characteristic membrane topology (seven transmembrane helices, extracellular N-terminus and intracellular C-terminus). They are transmembrane proteins acting as the sensory component of cellular signalling pathways. GPCRs, are a key class of eukaryotic membrane receptors and roughly 50% of all small molecule therapeutics target GPCRs. Vision, smell and some of taste uses GPCRs. Ligands for GPCRs cover a wide range of organic chemical space, including proteins, peptides, sugars, amines and amino-acids, nucleotides, lipids and more. They transduce signals from extracellular space into the cell, through their interaction with G proteins, which act as switches forming hetero-trimers composed of different subunits (α,β,γ). Two GPCRs’ crystal structures are currently available, the structure of Rhodopsin and the recently solved three-dimensional structure of beta-2 Adrenergic Receptor. G-Proteins: The term is used to describe GTP-binding proteins. There are two classes of G-proteins, the small cytoplasmic G-proteins (Gh) and the hetero-trimeric G-proteins composed of different subunits (α,β,γ) that mediate the signal of heptahelical receptors (GPCRs). Agonist binding to GPCRs leads to association of the hetero-trimeric G protein with the receptor, GDP-GTP exchange in the G protein α subunit followed by dissociation of the G protein into α-GTP and βγ complexes. The dissociated subunits can activate or inhibit several effectors such as adenylyl cyclase, PLCβ, tyrosine kinases, phosphodiesterases, phosphoinositide 3-kinase, GPCR kinases, ion channels, and molecules of the mitogen-activated protein kinase pathway, resulting in a variety of cellular functions. However, there is evidence that some GPCRs transduce their signal through in a way that is not G protein-dependent, and also that hetero-trimeric G proteins are involved in mediating the action of single-spanning membrane receptors. Hidden Markov Models (used herein): Probabilistic models widely used for describing features of a protein sequence. Hidden Markov Models introduce a “regular grammar” that characterizes a set of biological sequences. These are generative models, which renders them highly applicable in biological sequence analysis. In general, a HMM is composed of a set of states that form a first order Markovian process, connected by means of the transition probabilities. Each state, has a unique probability distribution for generating (emitting) the symbols of the finite alphabet (nucleotides or amino-acids). The most widely used variant of Hidden Markov Model (HMM) is the profile HMM which models in a probabilistic manner the matches, inserts and deletions occurring in every column of a multiple sequence alignment. However, other variations are also common (i.e. the circular HMM). Orphan Receptors: GPCRs for which no information on their ligand or coupling specificity is available. These are usually identified as a result of genome sequencing projects and large efforts are undertaken to functionally characterize them.

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Chapter X

Bacterial β-Barrel Outer Membrane Proteins:

A Common Structural Theme Implicated in a Wide Variety of Functional Roles Pantelis G. Bagos University of Central Greece, and University of Athens, Greece Stavros J. Hamodrakas University of Athens, Greece

abstract β-barrel outer membrane proteins constitute the second and less well-studied class of transmembrane proteins. They are present exclusively in the outer membrane of Gram-negative bacteria and presumably in the outer membrane of mitochondria and chloroplasts. During the last few years, remarkable advances have been made towards an understanding of their functional and structural features. It is now wellknown that β-barrels are performing a large variety of biologically important functions for the bacterial cell. Such functions include acting as specific or non-specific channels, receptors for various compounds, enzymes, translocation channels, structural proteins, and adhesion proteins. All these functional roles are of great importance for the survival of the bacterial cell under various environmental conditions or for the pathogenic properties expressed by these organisms. This chapter reviews the currently available literature regarding the structure and function of bacterial outer membrane proteins. We emphasize the functional diversity expressed by a common structural motif such as the β-barrel, and we provide evidence from the current literature for dozens of newly discovered families of transmembrane β-barrels.

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Bacterial β-Barrel Outer Membrane Proteins

INTR OD UCTI ON Integral membrane proteins are divided into two distinct structural classes, the α-helical membrane proteins and the β-barrel membrane proteins. α-helical membrane proteins class is the more abundant and well studied, since such proteins are located mostly in the cell membranes of both prokaryotic and eukaryotic organisms, performing a variety of biologically important functions. Proteins of this class have their membrane spanning regions forming α-helices consisting mainly of hydrophobic residues (von Heijne 1999). These proteins have been studied extensively in a computational manner during the last few years and a variety of prediction algorithms have been proposed (Möller, Croning et al. 2001). Members of the latter class (β-barrel membrane proteins) are located in the outer membrane of Gram-negative bacteria, and presumably in the outer membrane of chloroplasts and mitochondria, a fact explained by the theory of endosymbiosis. The members of this class are having their membrane spanning segments formed by antiparallel amphipathic β-strands, creating a channel in a form of barrel that spans the outer membrane (Schulz 2002). A continuously increasing number of β-barrel proteins located in the bacterial outer membrane are characterized, and a number of structures have been solved at atomic resolution (Schulz 2002). These proteins have been shown to perform a wide variety of functions such as active ion transport, passive nutrient uptake, membrane anchoring, adhesion, and catalytic activity. Considering the fact that a large number of pathogens are actually bacteria belonging to the Gram-negative bacteria class and the important biological functions in which outer membrane proteins are involved in, it is not a surprise that these proteins attract an increased medical interest. In the following sections we will fist try to describe briefly the structural features observed so far in the β-barrel outer membrane proteins with known three dimensional structure. Then, we will discuss the available computational methods used for the prediction of the transmembrane strands of β-barrel outer membrane proteins as well as for the discrimination of such proteins from water-soluble and alpha-helical membrane proteins. Afterwards, we will discuss in detail the functional roles in which β-barrel outer membrane proteins are implicated into. Emphasis will be given in newly characterized families of β-barrel outer membrane proteins that are involved in a series of crucial for the survival of the bacterial cell functions and in the implications for the pathogenicity of these organisms.

STR UCT URA L FEAT URES OF β-BARRE

LS

The β-barrel is a protein fold occurring in soluble proteins as well in transmembrane ones. A β-barrel may be considered as a β-sheet that twists and coils to form a closed barrel-shaped structure, which is stabilized by the hydrogen bonds formed by the sheet edges (first and last strands). The observed so far transmembrane β-barrels preferentially lay their axis along the membrane normal and are exclusively composed of meandering all-next-neighbor antiparallel β-strands, suggesting a repeating β-hairpin structural motif. It has been shown that any type of β-barrel can accurately be described solely by two parameters, namely the number of β-strands n and the shear number S. S is a measure of the stagger of the strands in the sheet. Theoretical analysis combined with available three dimensional structures proved that these two parameters determine all other features of the β-barrel (Murzin, Lesk et al. 1994; Murzin, Lesk et al. 1994). Currently, available high-resolution structures of transmembrane β-barrel proteins include β-barrels of varying features, with 8 ≤ n ≤ 22 and 8 ≤ S ≤ 24 (Table 1). Furthermore,

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Bacterial β-Barrel Outer Membrane Proteins

it is worth mentioning that all transmembrane β-barrels observed so far consist of an even number of strands. Remarkable advances have recently been made towards the understanding of bacterial β-barrel forming transmembrane protein structure and function. Their functional roles and the biological processes they are involved in are diverse and may differ between organisms. X-ray crystallography has revealed a number of unique 3-dimensional protein structures representatives of large functionally related families. Long mobile loops resistant to proteolysis (OmpA) or rigid extensions of the barrel-forming β-strands (OmpX) in the extracellular space, are known to provide molecular recognition sites. Porins of various families are known to mediate the passive transport of small molecules under different environmental conditions (OmpF, PhoE, OmpW, OmpG, OprP) or active translocation of larger molecules (TonB-dependent receptors, FhuA, FepA, FecA, FptA, FpvA). Known examples of proteins promoting virulence through adhesion to host cells are the Neisserial OpcA and NspA. In the type V secretion pathway (autotransporters, NalP), a C-terminal β-barrel domain is necessary to form the pore in the outer membrane, in order to allow the translocation of the secreted mature protein, which is called the passenger domain. Other outer membrane proteins with known 3-dimensional structures constitute examples of active transport of long-chain fatty acids (FadL), and specific receptors for nucleosides (TsX), whereas specific porins are mediating the intake of various carbohydrates (maltose-Maltoporin, sucrose-Sucroporin). Furthermore, β-barrel transmembrane proteins have been reported to exhibit key enzymatic activities, either as extracellular proteases (OmpT), phospholipases (OmpLA) or enzymes implicated in the acylation of lipid A (PagP, PagL). Several of these proteins have been shown to function as monomers, but there are known cases where oligomerisation is required for their proper function. In Table 1, we list some representative members of the available β-barrel outer membrane proteins whose structure has been determined at atomic resolution, along with a brief description of their structural and functional properties. Among the available three-dimensional structures, some could be considered as unusual cases of transmembrane β-barrel forming proteins. In these proteins, the transmembrane β-barrels are formed by more than one aminoacid chains. In the type I secretion pathway (Sec-independent), outer membrane proteins (TolC, VceC) are functioning in conjunction with cytoplasmic membrane transporters to promote the export of various solutes such as metals, drugs, secreted proteins, across the two envelopes of the Gram-negative bacterial cell envelope. A protein belonging to this class is Escherichia coli TolC (Koronakis, Sharff et al. 2000). TolC is a mixed β-barrel and α-helical protein, which spans both the outer membrane and the periplasmic space of gram-negative bacteria. Three TolC protomers assemble to form a continuous, solvent accessible conduit, a channel-tunnel over 140 Å long. Each monomer of the trimer contributes 4 β-strands to the 12-strand β-barrel. Another protein belonging to this class is the subtle case of α-haemolysin from Staphylococcus aureus and other microbial toxins such as aerolysin and the anthrax-protective antigen. Regarding the case of α-haemolysin it has been shown (Song, Hobaugh et al. 1996) that is active as a transmembrane heptamer, where the transmembrane domain is a 14-strand antiparallel β-barrel, in which two strands are contributed by each monomer. This endotoxin causes disease by forming pores on the infected cell membrane leading to cell lysis or to the destruction of small molecule concentration gradients. Recently, the structure of a Mycobacterial (Gram-positive) outer membrane channel (MspA) has been determined at atomic resolution (Faller, Niederweis et al. 2004). The Mycobacterial outer membranes are the thickest biological membranes known to date, and present a decreased fluidity toward the periplasmic side of the membrane as opposed to the outer membrane of Gram-negative bacteria (Liu, Rosenberg et al. 1995). More recently, the structure of the HiA

184

Bacterial β-Barrel Outer Membrane Proteins

Table 1. A list of representative outer membrane proteins with structures determined at atomic resolution. Note that, although some proteins seem to be related based on their structural features (i.e. OmpX and NspA) they exhibit no significant sequence similarity and thus are listed separately. Other families (general porins, TonB-dependent Receptors) are over-represented in PDB with members showing weak or modest sequence similarity (i.e. OmpF with Omp32, OmpC and OmpK36) and thus we list only one representative. Each protein in the table is a representative of a single PFAM family. Note though, that PFAM-B codes (marked with an asterisk) are subject to change from version to version. Protein name

function

Number of βstrands

PDB code (Berman, Battistuz et al. 2002)

PFAM code (Finn, Mistry et al. 2006)

Organism

OmpA

Structural protein

8

1QJP

PF01389

Escherichia coli

OmpX

Adhesion

8

1QJ8

PF06316

Escherichia coli

NspA

Adhesion

8

1P4T

PF02462

Neisseria Meningitidis

PagP

Enzyme

8

1MM4

PF07017

Escherichia coli

PagL

Enzyme

8

2ERV

PB038312 *

Pseudomonas aeruginosa

OmpW

General Porin

8

2F1T

PF03922

Escherichia coli

OmpT

Enzyme

10

1I78

PF01278

Escherichia coli

OpcA

Adhesion

10

1K24

PF07239

Neisseria Meningitidis

OmpLA

Enzyme

12

1QD5

PF02253

Escherichia coli

NalP

Autotransporter

12

1UYN

PF03797

Neisseria Meningitidis

Tsx

Transporter

12

1TLY

PF03502

Escherichia coli

OmpG

General Porin

14

2F1C

PB051875 *

Escherichia coli

FadL

Transporter

14

1T1L

PF03349

Escherichia coli

OprP

General Porin

16

2O4V

PF07396

Pseudomonas aeruginosa

OmpF

General Porin

16

2OMF

PF00267

Escherichia coli

Porin

General Porin

16

2POR

PB028487 *

Rhodobacter capsulatus

Maltoporin

Specific Porin

18

2MPR

PF02264

Salmonella typhimurium

FepA

TonB-dependent Receptor

22

1FEP

PF00593

Escherichia coli

autotransporter of Haemophilus influenzae has been solved revealing a β-barrel with 12 transmembrane β-strands, comprised by four strands from each subunit (Meng, Surana et al. 2006). The central channel has a pore of 1.8 nm in diameter that is traversed by three N-terminal alpha-helices, one from each subunit. This structure is considered to be representative of the Autotransporter-2 family. The analysis of observed three-dimensional structures of β-barrel outer membrane proteins has provided us with a set of rules describing the structural features of this class of proteins. These are: 1.

2.

The transmembrane β-strands are mainly amphipathic showing an alternation of hydrophobic and (mostly) polar residues. The hydrophobic residues interact with the hydrophobic lipid chains, whereas the polar residues are facing toward the barrel interior, and hence interact with the aqueous environment of the pore. The aromatic residues have a greater tendency to be located in the interfaces with the polar heads of the lipids, forming the so-called aromatic belts around the perimeter of the barrel.

185

Bacterial β-Barrel Outer Membrane Proteins

3.

4.

5.

6.

7.

Both the N-terminal and the C-terminal of the proteins are located in the periplasmic space (inside with respect to the outer membrane). In some cases, the N-, and C-terminal tails of the protein, may be formed by more than 100 residues-long stretches. The segments connecting the transmembrane β-strands that are located in the periplasmic space (inside loops) are generally shorter, from those of the extracellular space (outside loops). The periplasmic loops are having a length no longer than twelve residues, whereas the extracellular loops may be significantly longer, with lengths exceeding thirty residues, occasionally. This observation is possible due to the meander arrangement observed in currently available structures. The length of the transmembrane strands varies according to the inclination of the strand with respect to the lipid bilayer, and ranges between six and twenty-two residues. However, in some cases only a small portion of the strand is embedded in the lipid bilayer, and the rest of it protrudes far away from the membrane, to the extra-cellular space, forming flexible hairpins. β-barrel outer membrane proteins show great sequence variability in their amino acid sequences. This, in general, is larger than that of the globular proteins, and it is even larger when referring to the extracellular loops, which are often used as antigenic epitopes. Adjacent strands are connected by a network of hydrogen bonds, stabilizing the barrel.

Computational prediction and discrimination of transmembrane β-barrel proteins is in principle harder than the prediction of α-helical transmembrane segments. Despite the fact that transmembrane β-strands in available high-resolution structures are placed with relatively large angles with respect to the normal to the lipid bilayer, they are significantly shorter than transmembrane α-helices due to their extended conformation, their lengths being typically between six and twenty-two residues. A β-strand of between seven and nine residues might be sufficiently long to span the hydrophobic core of the membrane. Additionally, transmembrane β-strands face different environments (the hydrophobic exterior of the β-barrel opposed to the aqueous pore interior), often resulting in alternating hydrophobic-hydrophilic residues. This alternation is not always exact, since residues on the outer surface of the barrel (facing the apolar lipidic environement) tend to be hydrophobic, whereas residues pointing to the barrel interior are not always polar. Even though hydrophobicity peaks in a classical hydropathy plot are well correlated with the location of transmembrane β-strands (Zhai and Saier 2002) their average hydrophobicity is significantly lower than those of transmembrane α-helical segments. This fact should be related with the underlying translocation mechanism, since in the opposite case outer membrane proteins might be trapped in the inner membrane during the translocation process. Additionally, oligomerisation of β-barrel domains inside the lipid bilayer weakens the necessity for a hydrophobic barrel exterior, since polar side-chains may provide favourable interactions in the interaction interface. Summarising the above factors, the sequence signal to be detected is rather weak. Furthermore, common structural features with globular water-soluble proteins with a β-barrel in their three dimensional structures might result in a big number of undesired false positives. Nevertheless, if a protein sequence of such a protein is carefully examined, several structural characteristics, for example the predomination of aromatic residues at the interfacial positions, might accurately reveal the location of transmembrane β-strands (for excellent reviews see (Schulz 2002; Schulz 2003; Wimley 2003)).

186

Bacterial β-Barrel Outer Membrane Proteins

C OMPUTATI ONA L PREDICTI

ON METH ODS

During the last few years, several prediction algorithms have been developed aiming specifically at the outer membrane proteins. The prediction algorithms all utilize the rules that we mentioned in the previous paragraphs. However, there is a large variation on the algorithmic techniques used for this purpose. Furthermore, there are two major classes of prediction methods, the methods aiming at predicting the location of the transmembrane β-strands and the methods aiming at discriminating β-barrel outer membrane proteins from other classes of proteins such as globular and alpha-helical membrane ones. From a historical perspective, the prediction algorithms are divided in three categories. The first consists of methods that were using hydrophobicity plots and the alteration of hydrophobic and polar residues. Such methods with various modifications were proposed by Vogel an Jahning (Vogel and Jahnig 1986), Schirmer and Cowan (Schirmer and Cowan 1993), Gromiha and Ponnuswamy (Gromiha and Ponnuswamy 1993) and Zhai and Saier (Zhai and Saier 2002). Another important class of methods consists of predictors that use statistical properties of the amino-acids occurring in the β-barrel outer membrane proteins. Such algorithms are the rule-based algorithm of Gromiha and coworkers (Gromiha, Majumdar et al. 1997), methods using the Gibbs sampler (Neuwald, Liu et al. 1995; Mannella, Neuwald et al. 1996), the window-based method of Wimley (Wimley 2002) and various methods using the amino-acid and dipeptide composition of the proteins (Liu, Zhu et al. 2003; Bagos, Liakopoulos et al. 2004; Gromiha, Ahmad et al. 2005; Gromiha and Suwa 2005). More advanced such methods are the BOMP program that uses a combination of regular expression patterns, the β-barrel score of Wimley, and Principal Component Analysis (Berven, Flikka et al. 2004), and the TMB-Hunt (Garrow, Agnew et al. 2005) program that uses evolutionary information and a K-NN classifier. However, various machine learning methods such Hidden Markov Models (HMMs) and Neural Networks (NNs) have been shown to achieve higher accuracy especially for locating the transmembrane strands. The first application of a NN for predicting the location of transmembrane strands was performed by Diederichs and coworkers (Diederichs, Freigang et al. 1998), followed by the development of the B2TMPRED (Jacoboni, Martelli et al. 2001) and TMBETA-NET methods (Gromiha, Ahmad et al. 2004), whereas the TBBPred method (Natt, Kaur et al. 2004) uses a combination of NNs and Support Vector Machines. The highest scoring algorithms however have been shown to be the Hidden Markov Models (HMMs). The first such method was the HMM-2BTMR (Martelli, Fariselli et al. 2002), followed by the method of Liu and coworkers (Liu, Zhu et al. 2003), the PRED-TMBB method (Bagos, Liakopoulos et al. 2004; Bagos, Liakopoulos et al. 2004) and the Prof-TMB method (Bigelow, Petrey et al. 2004; Bigelow and Rost 2006). Finally we have to mention the consensus algorithms that combine the results of various individual predictors. Such an algorithm is ConBBPRED (Bagos, Liakopoulos et al. 2005) that specifically aims to locate the transmembrane strands and the TMB-Hunt2 (Garrow and Westhead 2007) and PSORT-B (Gardy, Spencer et al. 2003) algorithms that are oriented towards a better accuracy in discrimination of β-barrels. However, not all algorithms cited here are available to the scientific community. In Table 2, we list the available prediction servers along with a short description.

F UNCTI ONA L DI VERSITY

OF β-BARRE

LS

Besides the relative few observed 3-dimensional structures of β-barrel membrane proteins, there is additionally a plentiful of examples of proteins representatives of large families, whose structure has not 187

Bacterial β-Barrel Outer Membrane Proteins

Table 2. The currently available methods for predicting the transmembrane strands of beta-barrel outer membrane proteins as well as discriminating them form globular ones. For explanation of the methods see at the text and in a recent evaluation (Bagos, Liakopoulos et al. 2005). Method

Reference

TM Strands

TM Strands + Orientation

Discrimination

URL

B2TMPRED

(Jacoboni, Martelli et al. 2001)

x

-

-

http,//gpcr.biocomp.unibo.it/cgi/predictors/ outer/pred_outercgi.cgi

BOMP

(Berven, Flikka et al. 2004)

-

-

x

http,//www.bioinfo.no/tools/bomp

ConBBPRED

(Bagos, Liakopoulos et al. 2005)

x

x

-

http,//bioinformatics.biol.uoa.gr/ ConBBPRED/

HMM-B2TMR

(Martelli, Fariselli et al. 2002)

x

x

-

http,//gpcr.biocomp.unibo.it/biodec/

MCMBB

(Bagos, Liakopoulos et al. 2004)

-

-

x

http,//bioinformatics.biol.uoa.gr/mcmbb

OM_Topo_predict

(Diederichs, Freigang et al. 1998)

x

x

-

http,//strucbio.biologie.uni-konstanz. de/~kay/om_topo_predict2.html

PRED-TMBB

(Bagos, Liakopoulos et al. 2004; Bagos, Liakopoulos et al. 2004)

x

x

x

http,//bioinformatics.biol.uoa.gr/PREDTMBB/

ProfTMB

(Bigelow, Petrey et al. 2004)

x

x

x

http,//cubic.bioc.columbia.edu/services/ proftmb/

PSORT-B

(Gardy, Spencer et al. 2003))

-

-

x

http,//www.psort.org

TMB-Hunt

(Garrow, Agnew et al. 2005)

-

-

x

http,//www.bioinformatics.leeds.ac.uk/ betaBarrel/

TMB-Hunt2

(Garrow and Westhead 2007)

x

x

x

http,//www.bioinformatics.leeds.ac.uk/TMBWeb/TMB-Hunt2

TBBpred

(Natt, Kaur et al. 2004)

x

-

x

http,//www.imtech.res.in/raghava/tbbpred/

TMBETA-NET

(Gromiha, Ahmad et al. 2004)

x

-

x

http,//psfs.cbrc.jp/tmbeta-net/

been determined yet but there is enough experimental evidence to suggest their localization to the outer membrane forming β-barrels. The experimental techniques used, range from subcellular fractionation to determine the localization to the outer membrane, liposome swelling activity to determine channel properties, circular dichroism to determine the secondary structure content, low-resolution electron microscopy and antibodies experiments, deletion constructs and protease protection activities to locate surface exposed loops. During the last few years dozens of such families have been characterized experimentally even though the protein databases have not incorporated yet the available information concerning the functional annotation. In the following sections we describe the currently available information reported in the literature concerning the functional diversity of β-barrel transmembrane proteins. We classify the functional roles of such proteins as general porins, specific porins, structural proteins, translocation channels, and various uncharacterized or unclassified proteins. Although the classification is based on functional properties, the sequence and structure characteristics of such proteins are also diverse even within each class.

188

Bacterial β-Barrel Outer Membrane Proteins

G eneral Porins A large portion of such proteins constitutes various non-specific porins, having however no detectable sequence similarity to the already well-known families. In Chlamydia, MomP constitutes the largest portion of the OM mass, and it is speculated that this protein possesses 16 transmembrane strands (Hughes, Shaw et al. 2001; Rodriguez-Maranon, Bush et al. 2002; Findlay, McClafferty et al. 2005; Yen, Pal et al. 2005), whereas PorB (Kubo and Stephens 2000; Kawa and Stephens 2002; Kawa, Schachter et al. 2004) shows also pore-forming activity although with different properties compared to MomP. In Campylobacter, MomP besides acting as a porin, it is involved in the structural organization of the outer membrane, and acts as an adhesin (Moser, Schroeder et al. 1997; De, Jullien et al. 2000; Zhang, Meitzler et al. 2000; Bolla, Saint et al. 2004), whereas Omp50 shows a pore forming activity with cationselective channel properties (Bolla, De et al. 2000; Dedieu, Pages et al. 2004). In Borellia, omp66 and its homologues are large MW (66-kDa) outer membrane proteins that exhibit porin activity. The average single-channel conductance predicts a rather large pore diameter of 2.6 nm and prediction methods suggest a large number (perhaps larger than 22) of transmembrane strands (Skare, Mirzabekov et al. 1997; Bunikis, Luke et al. 1998; Exner, Wu et al. 2000). In Fusobacterium, FomA is a trimeric porin, which exhibits channel properties similar to that of the other general porins. Results obtained from limited proteolysis of purified FomA protein, indicate that the N-terminal part of the FomA protein is not an integral part of the β-barrel, but forms instead a periplasmic domain (Kleivdal, Puntervoll et al. 2001; Puntervoll, Ruud et al. 2002). In Leptospira, OmpL1 and its homologues, are heat modifiable porins that form trimeric structures. OmpL1 has been reconstituted in planar lipid bilayers showing an average single channel conductance similar to those of the major porin activity of native leptospiral membranes. OmpL1, is expressed during infection and thus it has a role in the induction and persistence of leptospiral interstitial nephritis. Sequence analysis suggests that the protein has 10-12 transmembrane strands (Shang, Exner et al. 1995; Barnett, Barnett et al. 1999; Haake, Mazel et al. 1999). The 37-kDa outer membrane porin OmpH of the deep-sea marine bacterium Photobacterium profundum strain SS9 is been synthesized in response to elevated hydrostatic pressure and it seems that is responsive to changes in the pressure regime of the deep-sea bacterium The results from reconstitution of OmpH in liposome bilayers as well as mutational studies are consistent with the hypothesis that OmpH functions as a relatively large, nonspecific diffusion channel. Prediction methods suggest that OmpH possesses a 16-stranded transmembrane β-barrel, similar to other general porins (Bartlett, Chi et al. 1993; Bartlett and Chi 1994; Macdonald, Martinac et al. 2003).

Specific Porins Another important class of outer membrane proteins includes the specific channels, either those that are responsible for resistance to various antibiotics, or those needed for intake of metabolites. In the first case we encounter the CarO OMP which is responsible for carbapenem and imipenem resistance in the Moraxellaceae family of gamma-proteobacteria (Mussi, Limansky et al. 2005) and the distantly related family of 33-36 kDa OMPs members of which are implicated in the resistance against Imipenem (Clark 1996; Limansky, Mussi et al. 2002; Siroy, Molle et al. 2005; Siroy, Cosette et al. 2006). Other examples are members of the Pseudomonas OprH family, which are small outer membrane proteins (21-kDa), when overexpressed under Mg2+ starvation conditions cause resistance to polymyxin B, gentamicin, and EDTA. There is experimental evidence (Circular Dichroism, PCR-based site-directed deletion and

189

Bacterial β-Barrel Outer Membrane Proteins

epitope insertion mutagenesis) suggesting a β-barrel structure consisting of 8 transmembrane strands (Bell, Bains et al. 1991; Rehm and Hancock 1996). We also have to mention the bacterial copper resistance proteins. Copper is essential as it serves as cofactor for a variety of enzymes. However, excess of copper is toxic and leads to radical formation and oxidation of biomolecules. CopB serves to extrude copper when it approaches toxic levels. The protein CopB is located in the outer membrane, and seems to form a β-barrel with 10-12 transmembrane strands. The N-terminal, domain (~100 residues) is predicted to be periplasmic, suggesting a structural resemblance with TonB dependent Receptors however, no sequence homology is apparent (Cha and Cooksey 1991; Lim and Cooksey 1993; Bissig, Voegelin et al. 2001). In Pseudomonas, OprD facilitates the diffusion of basic amino acids as well as the structurally analogous β-lactam antibiotics such as imipenem. Mutational inactivation of the OprD gene is associated with carbapenem resistance in Pseudomonas aeruginosa, whereas the C-terminal portion of OprD, and in particular, the hypothetical loop L7, was responsible for the unusual meropenem hyper-susceptibility. Various members of the family have shown different specificities in the uptake of metabolites including glycine-glutamate, histidine, proline, tyrosine, cis-aconitate and pyroglutamate (Yoshihara, Yoneyama et al. 1998; Ochs, Lu et al. 1999; Epp, Kohler et al. 2001; Hancock and Brinkman 2002; Pirnay, De Vos et al. 2002; Tamber, Ochs et al. 2006). The Pseudomonas aeruginosa porin B (OprB), is another substrate-selective channel for a variety of different sugars (Wylie and Worobec 1994). This protein may facilitate diffusion of a variety of diverse compounds, but is probably restricted to carbohydrates and does facilitate glucose fusion across the outer membrane (Wylie and Worobec 1995). The high-affinity glucose transport system is primarily specific for glucose and well conserved although the outer membrane components may differ in channel architecture and specificity for other carbohydrates (Adewoye, Tschetter et al. 1998; Adewoye and Worobec 1999). Similarly to other porins, these proteins are predicted to have 16 transmembrane strands. Homologues are also found Pseudomonas chlororaphis, Burkholderia cepacia, Pseudomonas fluorescens, Acinetobacter calcoaceticus and Xanthomonas campestris. KdgM is an oligogalacturonate-specific porin protein found in Erwinia chrysanthemi (Blot, Berrier et al. 2002). This phytopathogenic Gram-negative bacterium, secretes pectinases, which are able to degrade the pectic polymers of plant cell walls, and uses the degradation products as a carbon source for growth. KdgM is a major outer membrane protein, whose synthesis is induced in the presence of the pectic derivatives. KdgM behaves like a voltage-dependent porin that is slightly selective for anions and that exhibits fast block in the presence of trigalacturonate (Condemine, Berrier et al. 2005). KdgM seems to be monomeric, and topological models suggest that possesses a 14-stranded β-barrel, with six rather short extracellular loops and a larger one that restricts the size of the pore (Pellinen, Ahlfors et al. 2003). CymA of Klebsiella oxytoca, is another specific porin essential for growth on cyclodextrins. However, it can also complement the deficiency of a LamB mutant of Escherichia coli for growth on linear maltodextrins, indicating that both cyclic and linear oligosaccharides are accepted as substrates. CymAinduced membrane conductance decreased considerably upon addition of alpha-cyclodextrin, whereas the affinity was lower for β-cyclodextrin and even lower for gamma-cyclodextrin. Unlike most bacterial porins, CymA does not form trimeric complexes in lipid membranes and shows no tendency to trimerize in solution. However, it seems to form homotetramers with a central pore, and therefore lacks the typical trimeric structure of most porins (Pajatsch, Andersen et al. 1999; Orlik, Andersen et al. 2003) In E. coli, RafY is part of an operon that includes also a permease and the enzymes required for raffinose utilization. RafY forms an ion-permeable channel with a single-channel, which is approximately twice of that of the general diffusion pores OmpF and OmpC. Since RafY is able to accomodate the

190

Bacterial β-Barrel Outer Membrane Proteins

diffusion of other oligo-sacharides, it seems that it is a general diffusion pore with a diameter, larger than that of the general diffusion porins, allowing the diffusion of high-molecular-mass carbohydrates through the outer membrane (Ulmke, Lengeler et al. 1997; Andersen, Krones et al. 1998). Lastly, we have to mention FmdC, which is a porin involved in the transport of short-chain amides and urea through the outer membrane of Methylophilus methylotrophus under conditions where these nitrogen sources are present at very low concentration. Its synthesis is inducible by short chain amides and urea, and the protein is thought to transport these molecules across the outer membrane (Mills, Wyborn et al. 1997).

S tructural Proteins There are also several structural proteins conferring to the stability of the outer membrane through the interaction with peptidoglycans, having though no sequence similarity to the OmpA family of proteins in their transmembrane domain (Porphyromonas and Acinetobacter MomPs, Pseudomonas OprF). MomP of Porphyromonas gingivalis resembles the members of the OmpA family in their C-terminal domain that protrudes to the periplasmic space. The N-terminal membrane anchoring domain though, does not show any significant sequence similarity. Two-dimensional, diagonal electrophoresis and chemical cross-linking experiments with or without a reducing agent clearly showed that this protein mainly forms stable heterotrimers via intermolecular disulfide bonds. It has been suggested that they play an important role in outer membrane integrity, and similarly to members of the OmpA family, are likely to function as a stabilizer of the cell wall rather than as a major porin in this organism (Ross, Czajkowski et al. 2004; Nagano, Read et al. 2005) In Acinetobacter radioresistens KA53 the OmpA (MomP) was shown to constitute most of the emulsifying activity. The transmembrane β-barrel is likely to possess 8 membrane spanning β-strands, whereas the C-terminal domain is probably acting in interactions with the peptidoglycan layer (OforiDarko, Zavros et al. 2000; Toren, Orr et al. 2002; Gribun, Nitzan et al. 2003; Pessione, Giuffrida et al. 2003; Vashist and Rajeswari 2006; Akimana and Lafontaine 2007). A third, structurally similar, family of proteins includes homologues of the OprF of P. aeruginosa. It has been shown that members of this family (similar to members of the OmpA family), are showing a modular architecture, composed of two distinct structural domains. A N -terminal β-barrel domain formed by 8 β-strands with short turns at the periplasmic ends, and long flexible loops at the external ends, that anchors the protein to the outer membrane, and a C-terminal domain that protrudes into the periplasmic space interacting with peptidoglycans. There is also evidence for a pore-forming activity of the β-barrel domain, possibly larger than that of the OmpA of E. coli (Brinkman, Bains et al. 2000; El Hamel, Freulet et al. 2000; Saint, El Hamel et al. 2000). In Geobacter sulfurreducens, OmpJ is the most abundant protein isolated from the outer membrane. Deletion of the ompJ gene results in a strain that grew in fumarate, but could not grow with metals, such as soluble or insoluble Fe(III) and insoluble Mn(IV) oxide. The presumed effect of OmpJ in extracellular electron transfer is indirect, as OmpJ is required to keep the integrity of the periplasmic space necessary for proper folding and functioning of periplasmic and outer membrane electron transport components (Afkar, Reguera et al. 2005). Prediction methods indicate that OmpJ possess 20 transmembrane β-strands and homologues are found only in bacteria members of the Geobacteraceae family. In cyanobacteria, the tandemly lying genes somA and somB that were initially identified in Synechococcus PCC 6301 encode two functionally characterized outer membrane porins, that are predicted to form probably a 16-stranded β-barrel. Homologues that were also identified in other cyanobacteria,

191

Bacterial β-Barrel Outer Membrane Proteins

share an N-terminal motif, with similarity to S-layer homology (SLH) domains, that probably form periplasmic extensions connecting the outer membrane to the peptidoglycan layer. The C-terminal part, forms a β-barrel and it has been shown to form pores in lipid bilayers with single-channel conductances (Umeda, Aiba et al. 1996; Hansel, Pattus et al. 1998; Hansel and Tadros 1998).

S ecretion and Protein T ranslocation C hannels Secretins form large pores in the outer membrane, participating in protein secretion during the type II, and type III terminal branch of the General Secretion Pathway (GSP) of Gram-negative bacteria (Koster, Bitter et al. 2000; Thanassi 2002). The type II secretion pathway is dependent on the Sec system, since the secreted proteins must carry a signal peptide sufficient for the translocation through the inner membrane, and responsible for the secretion of toxins and exoenzymes. Type III secretion pathway is Sec-independent and allows the translocation of effector proteins from bacteria to the eukaryotic target cells. Members of the family, include PilQ of N. meningitidis, PulD of K. oxytoca, GspD of E. coli, the pIV protein playing a role in the assembly of the filamentus bacteriophage, and other proteins of Gram-negative bacteria. Electron microscopy, suggests that secretins form large channels in the outer membrane with an internal diameter of approximately 7 nm. The structure of PilQ, has been determined to 12 Å resolution, suggesting a 12-meric structure (Collins, Frye et al. 2004). It is believed that the C-terminal part of secretins forms the transmembrane β-barrel domain; however there is a lack of a high-resolution three-dimensional model, and thus the true folding state of the channel is ambiguous. There is also evidence that secretins, play an active role in the assembly of the pili, besides acting solely as channels. Ushers are another family of integral outer membrane proteins participating in the chaperone/usher secretion pathway, a terminal branch of the General Secretion Pathway (GSP) dedicated to the biogenesis of adhesive surface structures associated with pathogenesis (Thanassi 2002). As the name of the pathway implies, the Ushers work in conjuction with a periplasmic chaperone in order to assemble and secrete more than 30 different surface molecules in a broad range of gram-negative bacteria. The most studied example of the chaperone/usher pathway is the assembly and biogenesis of the type 1 and P pili, expressed by the uropathogenic E. coli. The members of the Usher family (PapC, FasD, FaeD, FimD etc), display properties of the β-barrel proteins, and are predicted to form channels consisting of 24-32 β-strands. Recently, it has been proposed that the Ushers form twin dimeric pores in the outer membrane, and the C-terminal parts of the sequences are responsible for the dimerisation (Henderson, So et al. 2004). In addition, the N-terminal 100-120 aminoacids are believed to be involved in the recognition of the periplasmic chaperone (Ng, Akman et al. 2004). The Neisserial Omp85 and their homologues in other species constitute a family of proteins involved in protein translocation through the outer membrane. Transmembrane β-barrels are synthesized in the cytoplasm and transferred through the inner membrane using the Sec system. In the periplasmic space, chaperones such as SurA and Skp, are binding the OMP and target it to the outer membrane (Bos and Tommassen 2004). It is believed that the highly conserved Omp85 acts in vivo, in a way that facilitates the correct folding and the insertion of other β-barrels in the outer membrane (Gentle, Gabriel et al. 2004; Voulhoux and Tommassen 2004). Homologues of Omp85 (which is sometimes referred as Bacterial Surface Antigen D15) are also found in mitochondria (Sam50/Tob55) and chloroplasts (OEP75) (Paschen, Waizenegger et al. 2003). The transmembrane domain (probably having 14 β-strands), is located in the C-terminus, whereas in the N-terminus, Omp85 possesses 5 conserved POTRA (Polypeptide Transport)

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domains. These domains are believed to interact with the transferred β-barrel, and the final insertion into the OM is performed with lateral diffusion (Moslavac, Mirus et al. 2005). Another distantly related family of proteins constitutes the transporters of the two-partner secretion system. The two-partner secretion (TPS) system (which along with autotransporters comprises the type V secretion pathway in bacteria) is composed of two separate proteins, with TpsA being the secreted protein and TpsB its specific transporter (Newman and Stathopoulos 2004). The secreted proteins are exported in a Sec-dependent manner across the inner membrane, after which they cross the outer membrane with the help of their cognate transporters. Translocation appears to be folding-sensitive, indicating that TpsA proteins cross the periplasm and the outer membrane in non-native conformations and fold progressively at the cell surface. A major difference of the TPS pathways compared to the AT arises from the manner by which specificity is established between the secreted protein and its transporter. The TPS pathway has solved the question of specific recognition between the TpsA proteins and their transporters by the addition to the TpsA proteins of an N-proximal module, the conserved TPS domain, which represents a hallmark of the TPS pathway. The exoproteins of the TPS system have been reported to be adhesins, haem-binding proteins, antigenic factors and haemolysins/cytolysins (Jacob-Dubuisson, Fernandez et al. 2004). The structure of the TPS domain has been solved and it is seen to fold as a β-helix, but currently there is no available structure for the transmembrane domain of the TpsB proteins (Clantin, Hodak et al. 2004). The latter is predicted to have approximately 16-18 transmembrane strands. A third, also distantly related, family is the Haemophilus influenza (hmw1B) Outer Membrane Translocator Family. The members of this family are proteins distantly related to the proteins of the Omp85 family as well as to the TpsB family. There is evidence suggesting that these proteins are involved in the translocation of proteins through the outer membrane. The C-terminal part of the sequence is speculated, based on experimental evidence, to possess a β-barrel structure that forms a pore, whereas the N-terminal part forms a periplasmic chaperone which in the most of the cases consists of a single POTRA domain (Surana, Grass et al. 2004; Surana, Buscher et al. 2006). The first characterized member of the family was found in Haemophilus influenzae, but homologues are found in other Proteobacteria such as Escherichia, Yiersinia, Pseudomonas, Caulobacter and Railstonia. In Porphyromonas gingivalis the PorT outer membrane protein is implicated in the leaderless secretion of various virulence factors (Gingipains/adhesins). PorT seems to be membrane-associated and exposed to the periplasmic space, as revealed by subcellular fractionation and immunoblot analysis using anti-PorT antiserum (Sato, Sakai et al. 2005). Prediction methods suggest that the proteins possess nearly 8-10 transmembrane β-strands. In E.coli, Wzi was found to be involved in the surface assembly of the Escherichia coli K30 group 1 capsule, participating in the translocation of group 1 capsular polysaccharide in co-operation with the Wza complex (Nesper, Hill et al. 2003). Wzi is an outer membrane monomeric β-barrel protein (Rahn, Beis et al. 2003), predicted to possess 16 transmembrane strands. Homologues are also found in Klebsiella pneumoniae, Acinetobacter, Psychrobacter, Shewanella oneidensis, Rhodobacter sphaeroides, Idiomarina loihiensis and Microbulbifer degradans. In Gram-negative bacteria, the components of the outer membrane are synthesized in the cytoplasm or the inner membrane and must thus traverse the inner membrane and the periplasm on the way to their final destination (Bos and Tommassen 2004). LPS (Lipopolysacharide) is an essential component of the bacterial outer membrane and consists of a hydrophobic membrane anchor, lipid A, substituted with an oligosaccharide core region that can be extended in some bacteria by a repeating oligosaccharide, the O-antigen. An OMP is required for the appearance of LPS at the bacterial cell surface (Braun and Silhavy 2002). This protein is known as Imp (increased membrane permeability) or OstA (organic solvent

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tolerance) because E. coli strains expressing mutant versions of this protein showed altered membrane permeability (Bos, Tefsen et al. 2004). It forms probably a β-barrel and it is predicted to have 22 transmembrane strands. Lastly, we have to mention AlgE from P. aeruginosa and AlgJ from Azotobacter vinelandii that are believed to export alginate (an acidic polysaccharide), across the outer membrane of these Gram-negative bacteria (Rehm, Boheim et al. 1994; Rehm 1996). These proteins are predicted to have 18 transmembrane β-strands spanning the outer membrane, thus forming a β-barrel. However the channel properties are different from those of the general porins.

A dhesion Outer Membrane Proteins There are also a large and diverse collection of newly discovered examples of various types of adhesion proteins implicated in pathogenesis. These outer membrane adhesions however, do not show any significant similarity to the already known examples of OmpX, NspA and OpcA of which we know the 3-dimensional structure. One such example is the Moraxella OmpJ (Hays, van Selm et al. 2005), a protein that has been shown to be implicated in the bacterial clearance from the lungs. The members of this family possess a distant similarity with members of the OmpA family and predictions indicate that their membrane spanning β-barrel is formed by 8 transmembrane strands. Intimins are adhesins found mainly in Enterohemorrhagic E. coli (EHEC) and Enteropathogenic E. coli (EPEC), whereas invasins are adhesins found in Yersinia pseudotuberculosis (Niemann, Schubert et al. 2004). Intimins and Invasins, share homology in their N-terminal (500 aminoacids length) segment that probably forms a β-barrel anchoring the protein to the outer membrane (Touze, Hayward et al. 2004). At the C-terminal, these proteins have some Ig-like domains and a C-type lectin domain. Invasin, binds to Integrin, whereas Intimin binds to the Translocated Intimin receptor (Tir) (Luo, Frey et al. 2000). The intracellular bacteria Surface antigen family, includes a number of antigens expressed on the surface of intracellular endosymbiotic pathogens belonging to various species members of the Rickettsiales, such as Anaplasma, Wolbachia and Ehrlichia. It is a diverse family, believed to consist of adhesins having no more than 8 transmembrane strands. The WSP protein of Wolbachia (Braig, Zhou et al. 1998; Baldo, Lo et al. 2005), the P28 antigen of Ehrlichia (Zhang, Guo et al. 2004) and the P44 antigen of Anaplasma (Oberle and Barbet 1993; Huang, Wang et al. 2007) are well-studied examples of such proteins. The Treponema Major Surface Protein is a rather large (474 amino-acids) protein acting as a surface antigen in the outer sheath of Treponema denticola. It is mainly an adhesin, but additionally it has been shown to exhibit channel activity. The channel is estimated to have a pore diameter of 3.4 nm, and prediction methods suggest that the protein possess a transmembrane domain composed of 22 β-strands. Homologues are found also in other pathogenic species of Treponema. However, the β-barrel domain may be considerably shorter since a large portion of the N-terminal is shown to be surface exposed and associated with antigenicity (Egli, Leung et al. 1993; Park, Heuner et al. 2002; Batista da Silva, Lee et al. 2004; Edwards, Jenkinson et al. 2005). The Legionella MomP and its homologues also serve as adhesive molecules for host cells, suggesting and that these proteins play a major role in the virulence of the particular bacterium (Hoffman, Seyer et al. 1992; High, Torosian et al. 1993; Krinos, High et al. 1999). Finally, in Helicobacter pylori which is the causative agent of gastritis and peptic ulceration in humans, there have been identified several outer membrane proteins that are not present in any other Gram-negative bacteria. These OMPs of H. pylori are characterized mainly as adhesins and porins and extensive C-terminal sequence similarity between

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these proteins has been used to define two different families (Doig, Exner et al. 1995; Exner, Doig et al. 1995; Tomb, White et al. 1997; Peck, Ortkamp et al. 2001; Hofreuter, Karnholz et al. 2003)

Uncharacterized Outer Membrane Proteins In this last section we list briefly some examples of probable β-barrel outer membrane proteins that are not yet functionally characterized but there is enough convincing experimental evidence suggesting that they are truly outer membrane proteins. In Acetobacter xylinus BcsC is member of a cellulose synthase operon composed also by bcsA, bcsB and bcsD genes (Wong, Fear et al. 1990). Mutants in the bcsC and bcsD genes were impaired in cellulose production in vivo, even though they had the capacity to make all the necessary metabolic precursors and cyclic diguanylic acid, the activator of cellulose synthase, and exhibit cellulose synthase activity in vitro. S. Typhimurium and E. coli have also cellulose as component of the extracellular matrix (Zogaj, Nimtz et al. 2001), and BcsC is also present in these organisms. Recently, a proteomic analysis of E. crysanthemi (Babujee, Venkatesh et al. 2007), revealed that BcsC is located in the outer membrane. The postulated β-barrel domain is located in the C-terminal of the large protein and probably serves as a membrane anchoring region or a channel for cellulose export. Other domains were also found in the protein, including several tetratricopeptide repeat (TPR) domains, responsible for protein-protein-interactions, and various domains of unknown function. Prediction methods suggest that the C-terminal β-barrel is formed by 16 transmembrane strands. NfrA of E. coli was found to be one of the two genes whose products are required for bacteriophage N4 adsorption (Kiino, Singer et al. 1993). The nfrA gene encodes a 990-residue long outer membrane protein which presumably serves as the phage receptor, whereas the nfrB gene encodes an inner membrane protein and may be a component of the receptor. Besides acting as receptor for N4 bacteriophage the physiological role of nrfA is unknown (Molloy, Herbert et al. 2000). The transmembrane domain of the large protein is located in the C-terminus and prediction methods suggest a barrel of 12 strands. A large N-terminal periplasmic domain of unknown function is also present also as a tetratricopeptide repeat (TPR) domain, which is known to be implicated in protein-protein-interactions. Lastly, we have to mention some examples of newly discovered outer membrane β-barrels with yet unknown function. Such proteins are the Serpulina variable surface protein (McCaman, Auer et al. 1999; McCaman, Auer et al. 2003), the E. coli YfaZ and YaiO outer membrane proteins (Marani, Wagner et al. 2006), and the Salt-stress induced outer membrane protein from Rhodobacter sphaeroides (Xu, Abo et al. 2001; Xu, Kadokura et al. 2001; Tsuzuki, Xu et al. 2005).

C ONC LUSI ON It is now evident that β-barrel outer membrane proteins even though share some remarkable structural features, constitute a large and highly diverse (in terms of functional roles) superfamily of membrane proteins. By reviewing the recent literature we have presented evidence for dozens of previously uncharacterized families of outer membrane proteins implicated in almost any functional role of the bacterial outer membrane. Thus, there are general and specific porins of various families, specific transporters and receptors, translocation channels, enzymes, and adhesion proteins. The importance of identifying such proteins in the completely sequenced genomes is clearly illustrated since such proteins could be

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responsible for the pathogenicity of some medically important Gram-negative bacteria, whereas other proteins could serve as potential targets for drugs or vaccines. One issue that has to be pursued in the near future is the incorporation of such a detailed annotation of the various families, in the publicly available databases. Given that outer membrane proteins are continuously been characterized and the available knowledge is accumulated, we anticipate that such a level of functional annotation should be incorporated soon. Genome-wide computational studies are also needed in order to fully address the issues regarding the distribution of the various families of βbarrel outer membrane proteins in the bacteria with completely sequenced genomes. Concerning prediction methods, the emergence of newly characterized β-barrel outer membrane proteins should be used in addition to the progress of algorithmic techniques used for prediction. Here, two things are of particular interest. First, the coupling of experimentally derived information regarding the topology and the development of prediction algorithms that directly incorporate experimentally derived information in the prediction, similar to the methods implemented for prediction of alpha-helical membrane proteins. Secondly, the development of methods that can locate accurately the transmembrane domain in multidomain proteins. It is worth noting that most of the currently available prediction algorithms fail to correctly predict the transmembrane topology in case of a protein with large periplasmic N- and C-terminal parts. Such prediction methods could be used in turn to identify novel outer membrane proteins that share no sequence similarity with the known families and these proteins could be further submitted as potential targets to experimentalists.

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K ey T erms Beta-Barrel Outer Membrane Proteins: They constitute one of the two major structural classes of transmembrane proteins (the other being the alpha-helical membrane proteins). They have their membrane-spanning segments entirely composed of short amphipathic beta-strands that twist and coil in order to form a barrel (beta-barrel). They have been found up to now only in the outer membranes of Gram-negative Bacteria and presumably (based on low resolution experimental data) on the outer surfaces of mitochondria and chloroplasts. They perform a series of very important biological functions such as membrane transport, receptor activity, and enzyme function or have a structural role. The smallest known transmembrane beta-barrels are composed of 8 beta-strands, whereas the largest are composed of 24 beta-strands even though it is possible that barrels with a larger number exist. Gram-Negative Bacteria: Traditionally, Bacteria are divided according to their behaviour to the Gram staining. Bacteria that are stained by the Gram’s method are commonly referred to as Grampositive, whereas others (that are not stained) are referred to as Gram negative. Gram-negative Bacteria include a number of important classes such as proteobacteria, cyanobacteria, spirochaetes, green sulfur and green non-sulfur bacteria. They all share a common structure in their surface which is composed of a cytoplasmic membrane, a periplasmic space and an outer membrane. Outer Membrane: The term refers to the external (outside) membranes of Gram-negative bacteria, chloroplasts and mitochondria. The outer membrane of Gram-negative bacteria has a unique and un-

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usual structure. The outer leaflet of the membrane is composed of a complex lipopolysaccharide (LPS) whose lipid portion acts as an endotoxin. Another noticeable difference of the outer membrane (at least in Bacteria) is the fact that proteins that are embedded in it (integral membrane proteins), are having their membrane-spanning segments entirely composed of beta-strands (beta-barrel outer membrane proteins), as opposed to integral membrane proteins in any other membrane which have their membrane spanning segments formed by hydrophobic alpha-helices (alpha-helical membrane proteins). Porins: This is the oldest known and well-studied super-family of transmembrane beta-barrels. Porins are large enough to allow passive diffusion i.e., they act as channels that are specific to different types of molecules. They are found in the outer membranes of Gram-negative bacteria, mitochondria and chloroplasts. The amino acid composition of the transmembrane beta strands is unique since polar and non-polar residues alternate along them. This way, the non-polar residues face outwards in order to interact with the non-polar lipid bilayer, while the polar residues face the barrel interior in order to interact with the aqueous channel. Porins typically control the diffusion of small metabolites like sugars, ions, and amino acids. The archetypical general diffusion porins of Gram-negative Bacteria are composed of 16-stranded beta-barrels and are active only as homo-trimers (trimeric porins). However, other families have been found deviating from this motif such as the sugar porins which are trimeric porins composed of 18-stranded beta-barrels or the monomeric porins composed of 14-stranded beta-barrels.

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Section IV

Experimental Techniques for Systems Biology

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Chapter XI

Clustering Methods for GeneExpression Data L.K. Flack University of Queensland, Australia G.J. McLachlan University of Queensland, Australia

abstract Clustering methods are used to place items in natural patterns or convenient groups. They can be used to place genes into clusters to have similar expression patterns across the tissue samples of interest. They can also be used to cluster tissues into groups on the basis of their gene profiles. Examples of the methods used are hierarchical agglomerative clustering, k-means clustering, self organizing maps, and model-based methods. The focus of this chapter is on using mixtures of multivariate normal distributions to provide model-based clusterings of tissue samples and of genes.

INTR OD UCTI ON DNA microarrays are collections of microscopic DNA spots arrayed on a solid surface. Each of these DNA spots will hybridize with a particular target RNA or DNA sequence. Optical measurements are made of fluorophores attached to the target RNA or DNA. DNA microarrays allow us to simultaneously read expression levels of expression levels on thousands of genes. They and other high throughput measurement methods bring many new opportunities in data analysis, but they also create difficulties in taking advantage of this amount of data. A variety of multivariate methods have been used to look for relationships among the genes and tissue samples. Cluster analysis has been one of the most frequently used of these methods. It has been useful in the discovery of gene function and of groups of interconnected biological processes; see Eisen et al. (1998) for examples. Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Clustering Methods for Gene-Expression Data

In medical applications, we are usually interested in the supervised and unsupervised grouping of tissue samples on the basis of the genes expressed. In the latter context, the intent is to identify what subtypes of cancer or other diseases exist, with the aim of assigning patients to these subgroups in order to aid their prognosis and therapy. In biological studies, we are usually interested in partitioning the genes into clusters in which the genes display similar patterns of gene expression across the relevant tissue samples (or cell lines). Genes in the same cluster are perhaps likely to be part of the same biological pathway or otherwise related. It can be seen there are two distinct but related clustering problems with microarray data. One problem concerns the clustering of the tissues on the basis of the genes; the other concerns the clustering of the genes on the basis of the tissues. This duality in cluster analysis is quite common. The aim of clustering is to put items into groups so that they are more similar to each other than they are to members of other clusters. One of the difficulties of clustering is that the notion of clustering is vague. A useful way to think about the different clustering procedures is in terms of the shape of the clusters. The majority of the existing clustering methods assume that a similarity or distance measure or metric is known a priori; often the Euclidean metric is used. But clearly, it would be more appropriate to use a metric that depends on the shape of the clusters. As pointed out by Coleman et al. (1999), the difficulty is that the shape of the clusters is not known until the clusters have been found, and the clusters cannot be effectively identified unless the shapes are known. We will give a brief overview of clustering before we describe its application to microarray data. More detailed accounts of clustering can be found in the many books on this topic; for example, Everitt (1993), Hartigan (1975), and Kaufman and Rousseeuw (1990).

So me H e uristic

Clu stering

Meth ods

In cluster analysis, we wish to group a number (n) of entities into a smaller number (g) of groups on the basis of measurements of some variables associated with each entity. We let yj = (y1j, …, ypj)T be the observation or feature vector of p measurements y1j, …, ypj made on the jth entity ( j = 1, …, n) to be clustered. In discriminant analysis the data belong to g known classes and we wish to create an allocation rule to allow us to assign an unclassified entity to one of these classes on the basis of its feature vector. In cluster analysis, we have no prior knowledge of group membership or structure, except possibly the number of classes. Clustering can have either or both of two aims. We might wish to split the data into several groups with no implication that these groups are a natural division of the data. We might do this for the sake of convenience or mathematical tractability. In this case intergroup boundaries do not necessarily have to be in regions of the feature space with a relatively low density of points. The feature space will be divided into contiguous and at least in some sense compact regions. This is sometimes called dissection or segmentation. Alternatively, we might wish to find a natural subdivision of the entities into groups. In this case the clusters will be regions of the feature space with a relatively high density of points separated by regions with relatively low densities of points. Sometimes the distinction between the two aims is stressed. But often it is not made, particularly as most methods for finding natural clusters are also useful for segmenting the data. Clustering methods can be categorized as hierarchical or nonhierarchical. With a hierarchical clustering method every cluster obtained is a split or merger of clusters obtained at the previous stage. Hierarchical clustering methods can be agglomerative, starting with g = n clusters or divisive starting

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with a single cluster. In practice with hierarchical clustering we usually use agglomerative methods since hierarchical divisive methods can computationally prohibitive unless the sample size n is very small. (There are 2(n--1) – 1 ways of making the first split.) There are methods of carrying out hierarchical divisive clustering that are less computationally intensive, but they will usually not give the optimal partition (Hastie et al., 2001). To apply a hierarchical agglomerative clustering, procedure we first calculate a matrix of distances or of similarities between pairs of observations. We need to choose an appropriate distance metric. Pearson correlation coefficients are common choice for genetic data. They are equivalent to the squared Euclidean distances on data normalized to have zero means and unit variances. We next choose a linkage metric for the between cluster distance. Some examples are single linkage, average linkage, and complete linkage. Single linkage uses the shortest distance between any two objects (one from each cluster). Complete linkage uses the longest distance between any two objects (one from each cluster). Average linkage uses the average distance between pairs of objects (one from each cluster). For agglomerative clustering, we join the two closest clusters, update the intercluster distances and repeat until we have only one cluster. These clusterings can be represented as a tree. We cut the tree at a level that gives a clustering with which we are satisfied; ideally, one which gives well separated coherent clusters. Another approach is Ward’s procedure where we join clusters so as to minimize withincluster variance. With hierarchical clustering poor choices of a join or a split early in the clustering process cannot be corrected by later splits or joins. With single linkage clustering there is a tendency for neighbouring clusters to join into chains. These are often not a natural division of the feature space and the resulting clusters are not compact. Complete linkage tends to create compact groups and seems to perform better than single or average linkage for gene expression data. One of the most popular nonhierarchical clustering algorithms is k-means. It seeks to find k = g clusters that minimize the sum of the squared Euclidean distances between the observations yj and their cluster means; that is, it seeks to minimize the trace of W, trW, where: g

n

W = ∑∑ zij (y j − yi )(y j − yi )

T

i =1 j =1



(1)

is the pooled within-cluster sums of squares and products matrix, and: n

yi = ∑ zij y j j =1

n

∑z j =1

ij



(2)

is the sample mean of the ith cluster. Here zij is a zero-one indicator variable which takes the value one if yj belongs to the ith cluster and zero if it does not. It is impractical to consider all partitions of the observations into g clusters unless n is very small since the number of such partitions is approximately gn /g!; see Kaufman and Rousseeuw (1990). We usually implement k-means by iteratively moving points between clusters so as to minimize trW. One method is to assign each observation yj to the cluster with the nearest centre (sample mean) and then update the cluster centre before repeating the process with the next observation. The initial centre estimates are often a random subsample of k points from the data set to be clustered. A related clustering method is k-medioids (Kaufman and Rousseeuw, 1990) which is similar to kmeans, but which only allows observations yj as cluster centres. Another related method is the self-or-

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ganizing map which constrains the cluster centres to lie on a smooth two-dimensional surface. Another possibility is to seek to minimize the determinant of W, |W|, rather than its trace (Friedman and Rubin, 1967). This will tend to divide the data into ellipsoidal clusters rather than the spherical clusters that k-means tends to create. A difficulty with all the heuristic clustering methods described so far is that they have no objective means of choosing the number of clusters.

C lustering Using Mixture Models We will be focussing on model-based clustering via mixtures of normal densities. In this approach, each observation vector yj is assumed to have a g-component normal mixture density: g

f (y j ; Ψ )= ∑ i =1

i

(y ; j

i

, Σi )

(3)

where φ(yj ;μi , Σi ) denotes the p-variate normal density function with mean μi and covariance matrix Σi and the πi denote the mixing proportions which are nonnegative and sum to one. The vector of unknown parameters, Ψ consists of the mixing proportions πi, the elements of the component means μi, and the elements of the component-covariance matrices Σi. This vector can be estimated by its maximum likeliˆ calculated via the EM algorithm; see McLachlan and Basford (1988) and McLachlan hood estimate Ψ and Peel (2000). This gives a probabilistic clustering defined in terms of the estimated posterior probˆ ), where the latter is the estimated probability that the feature abilities of component membership τi(yj ;Ψ vector with observed value yj belongs to the ith component of the mixture. An outright clustering can be obtained by assigning yj to the component to which it has the greatest estimated posterior probability of belonging. Since clustering methods based on mixture models have an explicit statistical model underpinning them, the clustering obtained is more easily described and interpreted than one not derived from a parametric model. We can perform tests of significance on the results in order to determine whether we have a natural clustering or just a segmentation of the data. We can compare different clusterings (Aitkin et al., 1981; McLachlan, 1987). The clusters can overlap as we would expect some gene and tissue clusters to do. The assumption of normality for the cluster distributions is a potential limitation. However, if an appropriate normalization is done this would appear to be a reasonable assumption for microarray data. We can also use the likelihood ratio to test for the number of components in the mixture, although regularity conditions do not hold for -2logλ to have its usual null distribution of chi-squared with degrees of freedom equal to the difference in the number of parameters between the null and alternative hypotheses, For normal mixture models the most useful of the closed form likelihood based criteria is the BIC. This is equal to -2logλ + d log n where d is the number of fitted parameters. We choose the value of g which maximizes this statistic. While this depends on regularity conditions that do not hold, it often works reasonably well in practice. We can also use a resampling approach (McLachlan, 1987). An advantage of mixture models with elliptically symmetrical distributions such as the normal or more robust models using the t distribution (McLachlan and Peel, 2000) is that the clustering obtained is not affected by changes of location, scale, or by rotation. Proposals have been made for approaches that allow both genes and tissues to be simultaneously clustered (Pollard and van der Laan, 2002; Getz et al., 2000). 212

Clustering Methods for Gene-Expression Data

If the number of elements per vector p is large we might not be able to fit the mixture model described above. This is because the component-covariance matrices Σi are highly parameterized with p(p+1) distinct elements each. Hence if we wish to fit normal mixture models to high-dimensional data we need to use some form of dimension reduction or regularization. A common method of reducing dimensionality is to perform a principal component analysis and use only the first few principal components if they account for a large proportion of the variance. However, the principal components are based on a global model and so they do not necessarily give the directions in the feature space best for revealing the underlying group structure. A global nonlinear method of dimension reduction can be obtained by using mixtures of linear submodels, such as with mixtures of factor analysers. This model provides local dimensionality reduction by imposing on the component-covariance matrices the constraint: Σi = Bi Bi + Di (0 = 1,...,g)

(4)

where Bi is a p x q matrix of factor loadings and Di is a diagonal matrix (i = 1, …, g). Within the ith component of the mixture, it effectively approximates the correlations between the variables by their linear dependence on a small number of (unobservable) latent variables (factors). Model-based methods allow us to perform tests to determine whether the number of clusters g allows a satisfactory division of the data set. If we are using a mixture of factor analysers model we can also test for the number of factors per cluster required for an adequate representation of the variance structure of the clusters For a given number of components g we can make a test for the number of factors using the likelihood ratio λ, where λ = L(Ψ0) / L(Ψ1) where L(Ψ1) and L(Ψ0) are the likelihoods under the alternative and null hypotheses respectively. Regularity conditions do hold for this test for a fixed number of components For the null hypothesis that H0 : q = q0 versus the alternative H1 : q = q + 1, the statistic -2logλ is asymptotically chi-squared with d = g(p-q0) degrees of freedom. However where n is not large relative to the number of unknown parameters we prefer to use the BIC (Bayesian information criterion). In this context, it means that twice the increase in the log likelihood (-2logλ) has to be greater than dlogn for the hypothesis to be rejected.

D ata T ype We now proceed to consider the application of the methods described above to the clustering of microarray data. Normalized expression data from microarray or other genetic experiments can be written as a matrix with M columns and N rows. The M columns correspond to the tissue samples and the N rows correspond to the N genes in the experiment. The expression signature of a tissue sample is the level of the N genes. The expression profile of a gene is the M expression levels across different tissue samples.

T issue C lustering The observation vectors yj used in tissue clustering are the expression signatures of the tissue samples, where yj contains the expression levels of the N Genes. For hierarchical clustering the distance matrix is quite tractable for tissue data as it requires only O(M2N) calculations and storage of a matrix with

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O(M2) values. The number of tissue samples M is usually less than 100; N could be tens of thousands. A problem with these methods is how to choose the number of clusters. Another, especially with single linkage clustering, is that they can put most of the observations into a single large cluster with several singletons. The best performance appears to be from complete linkage (Gibbons and Roth, 2002). We see no reason why we should expect genomic data to form hierarchical groupings. Nonhierarchical methods such as k-means and self-organizing maps typically do better than hierarchical methods, but do tend to divide the data into spherical clusters even when this is a suboptimal representation of the data. Model based methods have recently become a focus of attention (McLachlan et al., 2002). They offer soundly based tests and can reflect the fuzzy nature of some groups. The chief problem with applying them directly to clustering of tissues is that they cannot be directly fitted if the number of genes is large. This is because we have more parameters to be estimated than we have observations to estimate them with. Some form of dimension reduction is necessary, such as with mixtures of factor analysers as described above. The EMMIX-GENE program of McLachlan et al (2002) is designed for the clustering of gene samples using mixtures of factor analysers. However, since the number of tissue samples is usually quite small relative to the number of genes, it might not be practical to fit mixtures of factor analysers to the tissue samples on the basis of all the genes as it would involve a considerable amount of computation time. Thus initially some of the genes may have to be removed. Indeed, the simultaneous use of too many genes in the cluster analysis may only serve to create noise that masks the effect of a smaller number of genes. Using different subsets of the genes can lead to different clusterings of the tissues (Pollard and van der Laan, 2002; Friedman and Meulman, 2004). For example, we might be able to cluster samples by tissue type (cancerous or healthy) and also create a different clustering for the same tissues based for example on progression through the cell cycle (Belitskaya-Levy, 2006). Thus EMMIX-GENE has two optional preliminary steps. The first is to individually screen the genes to eliminate ones which are expected to be of little use in clustering. This is done by testing each gene for the hypotheses that it has a single component t distribution over the tissue samples. After this is done there may still be too many variables. Hence there is a second step available in which the selected genes are clustered into groups on the basis of Euclidean distance. This is done by fitting a mixture of normal distributions with the covariance matrices restricted to being equal to a multiple of the identity matrix. We now cluster the tissue samples on the basis of all or some of the genes in a chosen cluster. Alternatively, we can replace the gene clusters by their means and base our clustering on some or all of these means. The clustering of the genes in this step is more a segmentation for computational convenience than an attempt to seek an informative natural clustering of the genes.

G ene C lustering The data used in gene clustering are the expression profiles of the genes. While hierarchical methods can be used for the clustering of gene profiles, they are less computationally tractable than they are for tissues. This is because the distance matrix is usually much larger, O(N2), and takes more calculations to create, O(N2M), since N is so much larger than M. Difficulties for hierarchical methods with choosing the appropriate number of groups and with chain formation apply to gene clustering as well as to tissue clustering.

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Gene shaving (Hastie et al., 2000) is an example of a nonhierarchical method. This method creates tight clusters of genes with large variation between nonreplicated samples. Replicated samples need to be replaced by their means. It does not necessarily put all the genes into clusters, only the ones with significant differences between samples. The same gene can occur in more than one cluster. Mixtures of normal distributions are again a useful clustering approach. However, up until now, we have clustered the data under two assumptions; namely: a. b.

There are no replications on any particular entity. All the observations on the entities are independent of one another.

The difficulty here is that condition (b) will not hold for the clustering of gene profiles, since not all the genes are independently distributed, and condition (a) will often not hold as there are likely to be replicates of tissues or multiple measurements over time on a tissue. These could be handled by appropriately specifying the component-covariance matrices, but the models created this way may be hard to fit. For example, the M-step may not exist in closed form leading to computational difficulties. The relaxation of assumptions (a) and (b) above can be overcome by using mixtures of linear mixed models, as proposed by Ng et al. (2006). They have developed the program EMMIX-WIRE for the fitting of these models. To describe their approach, suppose that in a gene microarray experiment, we have for T T T the jth gene a feature vector (the gene profile) y j = (y1Tj ,..., ymj ) , where ytj = y1tj ,..., yrttj (t = 1,...m ), and where rt is the number of replicates of the tth distinct tissue. Conditional on its membership of the ith component of the mixture, we assume that the distribution of yj can be modelled by a linear mixedeffects model:

(

yj = X

i

+ Ubij + Vci + ij

)

(5)

In (5), the elements of βi are fixed effects, and bij (a qb -dimensional vector) and cj (a qc -dimensional vector) are the unobservable gene- and tissue-specific random effects, respectively. These random effects T represent the variation due to the heterogeneity of genes and samples, (corresponding to bi = biT1 ,...,Tin and ci, respectively. The random effects bj and ci and the measurement error vector εij are assumed to be mutually independent, and X, U, and V are the design matrices for the fixed and random effects. The distributions of bi and ci are assumed to be multivariate normal, N qb (0, H i ) and N qc 0, ci I qc , respectively, where Hi is a qb x qb covariance matrix and I qc is the qc x qc identity matrix. The measureNM(0,Ai ), where Ai is a diagonal matrix ment error vector εij is also taken to be multivariate normal T constructed from the vector Wξi, where i = i21 ,..., iq2 e and W is a M x qe zero-one design matrix. That is, we allow the ith component-variance to be different among the M microarray experiments. The vector of unknown parameters Ψ can be obtained by the maximum likelihood approach via the EM algorithm, proceeding conditionally on the tissue specific random effects ci as formulated in Ng et al. (2006). The gene-profile vectors yi are not independently distributed due to the presence of the cluster random effects terms ci in the likelihood function. Hence there is difficulty in calculating the latter. It is not needed in the application of the EM-algorithm, but is needed in an assessment of the number of components. In our application of BIC for the number of components, we

(

(

)

(

)

)

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Clustering Methods for Gene-Expression Data

E xamp les As an illustration of the use of the EMMIX-GENE procedure, we applied it to the colon cancer data set of Alon et al. (1999). This consists of n = 2000 genes and p=62 tissue samples. The samples came from 40 tumours and 22 normal tissues. After select-genes was applied to this set, there were 446 genes remaining in the set. These genes were then clustered into 20 groups. These groups were ranked on the basis of -2 log λ, where λ is the likelihood ratio statistic for testing g = 1 versus g = 2 components in the mixture model. If the tumours are clustered on the basis of the second ranked group G2 we have a partition of the tissues in which one cluster contains 37 tumours and 3 normal samples and the other cluster contains 3 tumours and 19 normal samples. This gives an error rate of 6 out of 62 tissues. We have displayed this as heat map where the colour of a square indicates the expression level for a particular gene in a specified tissue. To illustrate the EMMIX-WIRE procedure, we use an example from Ng et al. (2006) who used it to cluster time-course data from the yeast cell-cycle study of Spellman et al. (1998). The data consist of the expression levels of 612 genes at M =18 time points. The design matrix, X used was an 18 x 2 matrix with the (l + 1)th row (l = 0, …, 17)

Figure 1. Heat map of gene expressions from data in Alon et al. (1999)

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Clustering Methods for Gene-Expression Data

(cos 2π (7l/(ω+Φ) sin 2π (7l/(ω+Φ)) where the period of the cell cycle ω was taken to be 53 and the phase offset Ф was set to zero. The design matrices for the random effects parts were specified as U = 118 and V = I18. That is, it was assumed there were random gene effects bij with qb = 1 and cluster random effects, ci1 ,..., ciqc with qc = m = 18. The cluster random effects reflect possible dependence among expression levels within the same cluster at the same time. In the specification of the error matrix, we took W = 118 and φi = σ2i (qe = 1), so that the component variances are common among the m = 19 experiments. The number of components g was determined by using BIC for model selection. It indicated that there were twelve clusters. For each cluster we have plotted the expression level against time for its constituent genes.

Fu t ure T rends With the ever increasing emergence of high-throughput data in biology, there will be increasing use of cluster analysis to reduce the dimensionality of such data to aid in the biological inferences to be drawn. Clustering methods will also be used to study specific problems in genomics, such as the analysis of time-course experiments.

Figure 2. Gene-expression level against time for 12 clusters of genes

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Clustering Methods for Gene-Expression Data

Characterizing the dynamic regulation of gene expression by time is becoming more and more important. Standard methods of cluster analysis are not really applicable to such data as they would give the same clusterings regardless of the order in which the expressions have been observed. Also, they assume the data (the gene profiles) to be clustered are independently distributed. Hence increasing attention is being given to model-based methods, such as mixtures of linear mixed models, that allow the expression levels in the same gene profile to be correlated. They also allow for nonzero correlations between gene profiles in the same cluster (Ng et al., 2006). Model-based methods such as mixtures of normal distributions have already been widely adopted in the clustering of the tissue samples on the basis of the genes. Given that the latter can be present in very large numbers, attention has been given to variable (gene) selection methods in order for the normal components in the mixture model to be fitted without restrictions such as those that take the component covariances to be diagonal (McLachlan et al., 2002).

Co nc lusi on As more high throughput data sets become available, cluster analysis will become more important as part of their analysis. The most commonly used clustering methods have been hierarchical algorithms, but these have problems when they are used to cluster gene-array data. There is no reason to expect clusters of genes or tissues to form a hierarchy and the overlapping nature of likely groupings can lead to poor performance from hierarchical clustering algorithms. Also, these methods provide no criterion for determining the number of clusters. Nonhierarchical heuristic methods do not force a hierarchy on the clustering and can correct a misclassification made at an early stage in the algorithm. However, they often impose other restrictions on the clusters found, such as a tendency towards sphericity. Again they do not provide criteria to decide how many clusters the observations should be partitioned amongst. Mixture model based clustering allows tests of the number of clusters and can reflect differences in dispersion and orientation between clusters. Used in conjunction with some form of variable selection, mixtures of factor analysers provide a good method for clustering tissues, used with some form of variable selection. When clustering genes, correlations between genes and samples should be taken into account. This can be done by fitting mixtures of as linear mixed models. The authors wish to thank Dr. Ian Wood for his comments on this chapter.

R eferences Aitkin, M., Anderson, D., & Hinde, J. (1981). Statistical modelling of data on teaching styles (with discussion). Journal of the Royal Statistical Society A, 144, 419-461. Alon, U., Barkai, N., Notterman, D.A., Gish, K., Ybarra, S., Mack, D., and Levine, A. J. (1999). Broad pat­terns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays, Proceedings of the National Academy of Sciences USA, 96, 6745-6750.

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Belitskaya-Levy, I. (2006). A generalized clustering problem, with application to DNA microarrays. Statistical Applications in Genetics and Molecular Biology, 5, Article 2. Coleman, D., Dong, X.P., Hardin, J., Rocke, D.M., Woodruff, D.L. (1999). Some computational issues in cluster analysis with no a priori metric. Computational Statistics and Data Analysis, 31, 1-11. Eisen, M.B., Spellman, P.T., Brown, P.O., & Botstein, D. (1998). Cluster analysis and display of genomewide expression patterns. Proceedings of the National Academy of Sciences USA, 95, 14863-14868. Everitt, B.S. (1993). Cluster analysis, 3rd edition. London: Edward Arnold. Friedman, H.P., & Rubin, J. (1967). On some invariant criteria for grouping data. Journal of the American Statistical Association, 62, 1159-1178. Friedman, J.H., & Meulman, T.J. (2004). Clustering objects on subsets of at­tributes (with discussion). Journal of the Royal Statistical Society B, 66, 815-849. Getz, G., Levine, E., & Domany, E. (2000). Coupled two-way clustering anal­ysis of gene microarray data. Cell Biology, 97, 12079-12084. Gibbons, F.D., & Roth, F.P. (2002). Judging the quality of gene expression-based clustering methods using gene annotation. Genome Research, 12, 1574-1581. Hartigan, J.A. (1975). Clustering algorithms. New York: Wiley. Hastie, T., Tibshirani, R., Eisen, M. B., Alizadeh, A., Levy, R., Staudt, L., Chan, W.C., & Botstein, D. (2000). Gene shaving as a method for identifying distinct sets of genes with similar expression patterns. Genome Biology, 1, research 003.1-003.21. Hastie, T., Tibshirani, R., & Friedman, J. (2001). The elements of statistical learning. New York: Springer-Verlag. Kaufman, L., & Rousseeuw, P. (1990). Finding groups in data: An introduction to cluster analysis. New York: Wiley. McLachlan, G.J. (1987). On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Applied Statistics, 36, 318-324. McLachlan, G.J., & Basford, K.E. (1988). Mixture models: Inference and ap­plications to clustering. New York: Marcel Dekker. McLachlan, G.J., Bean, R.W., & Peel, D. (2002). A mixture model-based approach to the clustering of microarray expression data. Bioinformatics, 18, 413-422. McLachlan, G. J., & Peel, D. (2000). Finite mixture models. New York: Wiley. Ng, S.K., McLachlan G.J., Wang, K., Ben-Tovim Jones, L., & Ng, S-W. (2006). A mixture model with random-effects components for clustering correlated gene-expression profiles. Bioinformatics, 22, 1745-1752. Pollard, K.S., & van der Laan, M.J. (2002). Statistical inference for simultane­ous clustering of gene expression data. Mathematical Biosciences, 176, 99-121.

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Spellman, P., Sherlock, G., Zhang, M.Q., Iyer, V.I., Anders, K., Eisen, M.B., Brown, P.O., Botstein, D., & Futcher, B. (1998) Comprehensive identifi­cation of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Molecular Biology of the Cell, 9, 3273-3297.

K ey terms EM Algorithm: A method for calculating maximum likelihood estimates of parameters in statistical models in situations where the observed data can be usefully viewed as being incomplete. It proceeds by consideration of the complete data log likelihood, which is formed on the basis of the complete data. The latter comprises the observed data and the ‘missing data’. It is implemented iteratively by alternating two steps known as the expectation (E) step and the maximization (M) step. On the E-step the Q-function is calculated by averaging the complete data log likelihood over the conditional distribution of the complete data given the observed data, using the current value for the parameter vector. This is followed by the M-step in which the current estimate of the parameter vector is updated to that value which globally maximizes the Q-function. Euclidean Distance: A measure of distance between two points. It is the square root of the sum of the squares of the differences between the coordinates of the two points. Factor Analysis: Factor analysis is a statistical technique in which the correlation between the variables is approximated by the linear dependence of the latter on a set of unobservable (latent) variables. Heuristic: An empirical method of solving a problem which does not necessarily reflect the underlying nature of the problem. Likelihood: The likelihood function is found by evaluating the joint density of the random variables in the model defining the random phenomenon under study at their observed values. Maximum Likelihood: The maximum likelihood estimate of a parameter is obtained by consideration of the likelihood (equivalently the log likelihood) function. Typically in the case of a bounded likelihood function it is given by the values of the parameters which globally maximize the likelihood function. Microarray: A slide which contains a grid consisting of a large number of microscopic spots of different DNAs, each of which will hybridize with a particular target RNA or DNA sequence. The target RNA or DNA is generally attached to a fluorescent marker. When the target RNA or DNA binds to the complementary DNA on the slide this binds the fluorescent marker to the slide. The measurements taken are of the intensity of the fluorescence from these markers. Multivariate: A multivariate problem one has more than one response variables. Principal Components: The principal components of data set are the projections of the data vectors onto new coordinate axes that result from a rotation of the centered data set. This rotation is done in such a way that the first principal component (the projection onto the first coordinate axis) has the largest possible variance, the second principal component has the next largest, and so on.

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Chapter XII

Uncovering Fine Structure in Gene Expression Profile by Maximum Entropy Modeling of cDNA Microarray Images and Kernel Density Methods George Sakellaropoulos University of Patras, Greece Antonis Daskalakis University of Patras, Greece George Nikiforidis University of Patras, Greece Christos Argyropoulos University of Pittsburgh Medical Center, USA

abstract The presentation and interpretation of microarray-based genome-wide gene expression profiles as complex biological entities are considered to be problematic due to their featureless, dense nature. Furthermore microarray images are characterized by significant background noise, but the effects of the latter on the holistic interpretation of gene expression profiles remains under-explored. We hypothesize that a framework combining (a) Bayesian methodology for background adjustment in microarray images with (b) model-free modeling tools, may serve the dual purpose of data and model reduction, exposing hitherto hidden features of gene expression profiles. Within the proposed framework, microarray image restoration and noise adjustment is facilitated by a class of prior Maximum Entropy distributions. The resulting gene expression profiles are non-parametrically modeled by kernel density methods, which not only normalize the data, but facilitate the generation of reduced mathematical descriptions of biological variability as mixture models. Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Uncovering Fine Structure in Gene Expression Profile

INTR OD UCTI ON The advent of complementary DNA (cDNA) microarray technologies enabled the simultaneous and specific assessment of the expression levels of thousands of genes (Southern, Mir, & Shchepinov, 1999). The conventional approach to analyze such datasets is to explore quantitative co-expression relations across a variety of experimental conditions prior to invoking putative similarities in gene regulation or function (DeRisi, Iyer, & Brown, 1997; Eisen, Spellman, Brown, & Botstein, 1998). The alternative viewpoint considers gene expression profiles from specific conditions to be informative of distinct molecular signatures that characterize cellular states. Such genome wide, transcriptional signatures have been used to distinguish normal from abnormal samples in benign developmental conditions (Barnes et al., 2005), solid tumors and hematologic malignancies (Febbo et al., 2005; Valentini, 2002) and differentiate distinct disease states of renal allografts (Sarwal et al., 2003). It has been suggested that the thousands of expression values in a microarray experiment are too dense and irregular to be directly interpreted in a holistic manner and that alternative transformations of the normalized gene profiles should be sought after (Guo, Eichler, Feng, Ingber, & Huang, 2006). Nevertheless one could justifiably argue that the irregularity of the gene profiles is due to incomplete modeling and adjustment for the presence of measurement noise. However this alternative hypothesis has not been adequately addressed in the current literature. These considerations underline the impetus for the present work, which aims to: 1. 2.

Establish the role of microarray image background in the irregularity and “featureless” appearance of gene expression profiles (GEP) from individual experimental states. Propose a data and model reduction framework for the analysis of GEP consisting of: a. A probabilistic Bayesian algorithm for background adjustment of microarray images based on Maximum Entropy distributions. b. Non-parametric kernel density estimation methods for the mathematical representation and exploration of the resultant gene expression profiles.

BACKGR

OUND

The basic microarray procedure involves hybridization of complementary nucleic acid molecules, one of which (target) has been immobilized in a solid substrate (e.g. glass) using a robotically controlled device (arrayer). Such targets form spots at the vertices of a rectangular lattice on the solid substrate surface; each spot then serves as a highly specific and sensitive detector of the corresponding gene. Technical factors operating at different stages of the microarray pipeline impart the final microarray image with uneven and non-negligible background. Background correction has been considered a necessary step in the microarray pipeline (L. Qin, Rueda, Ali, & Ngom, 2005), which may in fact have a significantly higher bearing on the final results than normalization. This viewpoint is supported by a number of empirical studies showing that conventional approaches to background correction may lead to nonsensical results (e.g. negative gene expression measures) and hinder the ability to detect differential gene expression (L. X. Qin & Kerr, 2004). In spite of the nodal role of background adjustment methods upon the quantification of single gene expression, the effects of de-noising upon the totality of the gene profile remains unexplored. A notable exception is the study by (Kooperberg, Fazzio, Delrow, & Tsukiyama, 2002); the authors argued that incomplete background adjustment is expected to predominantly affect

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the quantification of weakly expressed genes, leading to a reduction in the dynamic range of the GEP. This in turn will result in a “compression” of the left tail of the GEP, which could very well account for its featureless nature of the latter in that signal range. Consequently, proper noise reduction and dynamic range expansion could uncover hidden structure in GEPs and aid the discovery of hitherto unknown elements of transcriptional regulation. In order to facilitate such a discovery process though, it is imperative to supplement the noise reduction algorithms with mathematical model reduction methodologies so as to generate a discrete number of experimentally testable hypotheses about the biological system under investigation. Before addressing this mathematical modeling problem though it is important to properly define the meaning of the phrase “Gene Expression Profile”. The definition we adopt herein is an operational one i.e. we identify the GEP as the output of any step in the microarray pipeline (Figure 1) after the image operations stage. Consequently the GEP is a set of possibly noisy measurements, one for each target printed on the surface of the microarray. Inference about the members of the set, which constitutes the gene expression profile, proceeds in different stages that involve the normalization of the measurements prior to exploratory and formal statistical/machine learning methods. One challenging aspect of the process is how to best represent the GEPs emanating from replicate experiments in a manner that captures the global features of the system under study but also preserve the specific expression pattern within each sample. The issue is further complicated by the fact that a large number of experimental noise sources remain poorly defined or are very difficult to model explicitly.

Figure 1. Microarray pipeline starting from individual cell population to machine learning and inference C e ll S a m p le

C C D c a me ra s C o n fo c a l sca n n e rs P h o s p h o Im a g e r

m R N A I s o la tio n

P32

L a b e lin g

F lu o r e s c e n t D y e s

H y b r id iz a tio n

C h r o m o g e n ic D yes

Im a g e a c q u is itio n

Im a g e o p e r a tio n s ( d e - n o is in g , g r id d in g , s p o t s e g m e n ta tio n ) N o r m a lis a tio n o f m e a s u r e m e n ts

E x p lo r a to r y D a ta A n a ly s is

M a c h in e L e a r n in g

S ta tis tic a l M o d e ls

C lu s te r in g

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Uncovering Fine Structure in Gene Expression Profile

Conventional approaches usually address the effects of residual noise by compressing the GEP from individual samples into a single numerical summary (Guo, Eichler, Feng, Ingber, & Huang, 2006), often after a normalization procedure such as “lowess” has reduced the variability of the dataset in a more or less ad hoc fashion (L. X. Qin & Kerr, 2004). It is important to note that both approaches amount to a considerable degree of data falsification since they operate by discarding “possibly relevant information immanent in the complex, higher-order genome-wide expression pattern”(Guo, Eichler, Feng, Ingber, & Huang, 2006). On the other hand, verbatim use of the GEP is likely to lead to erroneous inferences as sources of noise other than the background of microarray images are not taken into account. Even if it were possible to measure the GEP by a “perfect” noiseless experiment, intrinsic biological variability would carry over to the final results and manifest as “jitter” in a, possibly multidimensional, representation of the latter. It follows that unless one can faithfully control or model all sources of variability (experimental and biological), the best that one can hope for is a probabilistic representation that is based on the gene expression measures obtained in each experiment. However unless one specifies the space that such probabilistic descriptions occupy and the objects that they concern, one has an undefined problem with multiple possible and even conflicting solutions. We postulate that a data driven, bottom-up methodology abstracting the most general features of microarray technology and genome wide transcript abundance quantification is the optimal approach to microarray data and model reduction. The main focus of the present work is the presentation of a bottomup bi-partite quantitative inference approach to address the issues identified in the previous paragraphs. The two pillars of the proposed methodology are a) a probabilistic methodology that utilizes Bayesian methods with the Maximum Entropy prior (Jaynes, 2003), and b) function approximation methods in general and non-parametric kernel density estimation algorithms in particular (Silverman, 1986). The two elements of this framework are used to handle microarray image noise (de-noising) and model residual variability in the global expression profiles respectively. The operational characteristics of this approach are illustrated by applying it on publicly available microarray set (DeRisi, Iyer, & Brown, 1997). We demonstrate that when used in combination, these two different methodologies may facilitate the detection of weak, albeit reproducible, signals, decrease the variability of measures of gene expression and facilitate the detection of global features in the corresponding profiles.

AN OVER VIEW OF BAYESIAN AND MAXIM UM ENTR OPY METH ODS From an epistemological viewpoint, noise reduction in microarray experiments is a problem of quantitative inductive inference that involves the update from a prior probability distribution to posterior probability distribution when new information becomes available. This approach is contingent upon the interpretation of the relevant probabilities in a Bayesian context i.e. as real valued measures of the degree of belief in the truth of a proposition. Two methods to effect the updating of probabilities in a consistent manner have been mathematically established: Bayes’ theorem (Cox, 1946) and Edwin T. Jaynes method of Maximum Entropy (Jaynes, 2003). The choice between the two methods is dictated by the nature of the information at hand (Caticha & Preuss, 2004). When the available information is given by conditional probability distribution between observable quantities and unobserved parameters we should use the Bayes theorem. If however the information at hand concerns expectations about aspects of the general case, the method of Maximum Entropy (MaxEnt) is applicable. The two methods complement each other as evident from the general process of quantitative (Bayesian) inductive inference. In

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order to carry out the latter and reach plausible conclusions in the presence of uncertainty, one ought to proceed in three discrete steps: 1. 2. 3.

Clearly state what the models are, along with all the background information and data. Assign prior (pre-data) probabilities to the different models-hypotheses investigated. Use probability calculus in order to arrive to numerical values for the posterior probability of the hypotheses in light of the available data (inference process).

The tool for updating one’s beliefs about the plausibility of a hypothesis (H) given available evidence (E) and background information (i.e. context I) is given by Bayes theorem:

P( H | E , I ) =

P( H | I ) P( E | H , I ) P( E | I )

(1)

The left-hand term, P(H|E,I) is called the posterior probability, and it gives the probability of the hypothesis H after considering the effect of evidence E in context I. The term P(H|E,I) is just the prior probability of H given I alone; that is, the belief in H before the evidence E is considered. The term P(E|H,I) is called the likelihood, and it gives the probability of the evidence assuming the hypothesis H and background information I are true. The denominator is independent of H, and can be regarded as a normalizing or scaling constant. The information I is a conjunction of all of the other statements (background knowledge) relevant to determining P(H|I) and P(H|I). Within such a framework, Jaynes maximum entropy method corresponds to a formal deterministic, variational algorithm that transforms pre-data constraints into prior probability assignments. The resulting distributions are least informative or “objective” ones in the sense that they are most compatible with the “pre-data” constraints, while being maximally noncommittal about the missing information. The maximum entropy algorithm, proceeds by maximization of the entropy H[p] functional of the prior distribution subject to q pre-data constraints about the numerical values of expectations of functions f k (〈 f k 〉) that depend on the hypothesis H; each such constraint contributes a parameter λk into the final solution thus fixing the functional form of the prior distribution. If the hypothesis H concerns the numerical value of a random variable x taking discrete values {x1,x2,...,xn}, the MaxEnt algorithm generates the following Maximum Entropy prior distribution:  max  H [ p ] = −  fk = −

∑

∂ log Z , ∂ k

i

q   1 pi log( pi )  ⇒  pi = exp(− Z j =1  

∑

fk ≡

n

j

f j ( xi )), Z =

n

 q exp  −  i =1  j =1 n

∑

∑

j

  f j ( xi )     

∑ f ( x) p( x ) = ∑ f ( x ) p i =1

k

i

i =1

k

i

i

(2) (3)

Entropy maximization is a convex optimization problem, and thus the distribution given in Equation 2, is unique. Conceptually the algorithm identifies the distribution that has the maximum uncertainty subject to the constraints in a manner that avoids bias in the process. This can be traced to a mathematical property of MaxEnt distributions i.e. that they assign positive weight to every situation that is not excluded by the given information. Hence by utilizing such distributions to encode the pre-data constraints we are guaranteed not to miss any potential solutions that are compatible with the former.

225

Uncovering Fine Structure in Gene Expression Profile

A PR OBABI LISTIC DE -N OISING A LG ORITHM

F OR MICR OARRAY IMAGES

As a stepping stone for the proposed algorithm, we invoke a very simple additive noise model. This model notes that in any given finite area of the microarray surface there a) may exist both specific and non-specific hybridization sources of fluorescence, and b) fluorescent signals combine additively, and c) there are no quenchers in the hybridization (i.e. the noise is positive). Hence, the “true” signal intensity of a pixel in a microarray image (S), is related to the background noise (B) and the observed pixel value (D) through the relation: D = S + B, {S,B ≥ 0} The Maximum Entropy algorithm takes into account pre-data constraints about the raw microarray images in a formal manner in order to derive the distribution of the background generation process (B) and the signal (S). Subsequently these distributions are utilized in Bayes theorem to derive the posterior distribution for S; this process is repeated for all pixels in the microarray image, leading to a restored version which is then subjected to further processing (spot identification, normalization etc). From an operational standpoint, the proposed algorithm takes into account what is known about the microarray pipeline (“general case”), as well as the data observed in a given experiment (“particular case”) to render a denoised version of the microarray image. The constraints that are built into the algorithm stem from the discrete nature of the microarray measurement scale as well as the different scales of specific vs non-specific and cross hybridization phenomena on microarrays. Qualitatively these constraints correspond to the following discrete predata pieces of information: 1.

2. 3.

Each microarray image can be segmented into two general classes of pixels i.e. Signal (S) and background (B) generated by independent separate, distinct processes. This is nothing more than a consequence of the fact that the arrayed spots occupy only a fraction of the microarray surface; the corresponding pixels are classified as signal and all other ones are designated as background. For the case of the S class the process is one of specific hybridization between labeled mRNA species and spotted target molecules; for the background pixels, non-specific hybridization, noncDNA fluorescent molecules, lateral diffusion of labeled particles, dust etc are responsible. The expected intensity value of the background process is small compared to the dynamic range of the microarray image. The intensity values for both signal and background are expressed in a discrete, bounded, positive, arbitrary scale with M+1 elements e.g. M=65535 for a 16-bit image.

In spite of their crudeness these pre-experimental facts are surprisingly powerful enough to generate useful analytic forms for the prior probability density and likelihood functions of a microarray experiment. For example due to the independence property, one can factorize the probability of observing a particular image (Im) as product density, that is: P(Im) = P(S,B) = P(S)P(B)

226

(4)

Uncovering Fine Structure in Gene Expression Profile

In the absence of any specific information regarding S, the maximum entropy assignment for S considers all possible values equally likely leading to the uniform prior, that is: P(S) = 1/(M + 1)

(5)

The analytic form of the maximum entropy background distribution PME (Bm) can be established on the basis of the general MaxEnt algorithm by setting q = 1, f1(x) = x, F1 = m in the system of equations 2-3. Stated in other terms the conditional distribution of the background is simply the discrete (maximum entropy) density obeying the two constraints of a given expectation and proper normalization (to unity). The resulting distribution is a function of a single Lagrangian λ given by: m=−

M d 1 M +1 + =m⇒ (log( e − b )) ⇒ − − − d e 1 1 e M ( +1) b =0

∑

≅ log (1 + 1/ m )



(6)

The approximate relation between m, λ in the latter equation is a consequence of the second constraint discussed previously. As long as m ≤ M/5, the error between the approximate value log(1+1/m) and the “exact” value for λ obtained by numerically solving Equation 6 is less than 4%. Furthermore, by the change of variables 1+1/m → θ(m), PME (Bm) is identified as a member of the family of modified power series distributions (MPSD) (Johnson, Kotz, & Kemp, 1992):

PME ( B | m) = MPSD( B | M , (m)) =

B

M

∑ x =0

x



(7)

With the prior distributions for signal and background now established (equations 5-7), straightforward application of the Bayes theorem leads to the posterior distribution for S: P ( S | D, m) =

P ( D | S , m) P ( S | m) MPSD( D − S | M , (m)) = = * ( m) S ( | , ) ( | ) ( − | , ( )) P D S m P S m MPSD D S M m ∑ ∑ S

S

D

∑ s =0

*

( m) s ,

*

( m) =

1 ( m)

(8)

Derivation of Equation (8) makes explicit use of the positivity constraint on the values of D, S and the independence of S from B and thus m. Comparison of equations 7 and 8, shows that the posterior distribution for S is also a modified power series one, albeit with a different parameter θ* and support D. In order to restore a microarray image using this distribution, one has to select a numerical summary from the latter. The posterior conditional expectation, is such a summary which can be recovered in a closed and particularly simple form: D

E[ S | D, m] = ∑ S ⋅ P( S | D, m) = D − m + S =0

D +1 (m) D +1 − 1

(9)

One desirable feature of MPSD based models is that they are amenable to numerically tractable, and even analytic procedures for estimation and learning. Specifically in order to estimate m from a sample of “noisy” pixels B = {B1,B2,...,Bn} one has to solve the likelihood equation: (mˆ ) = B

(10)

227

Uncovering Fine Structure in Gene Expression Profile

The aforementioned equation is a functional relationship among the support of the MPSD (M), its first moment (μ), the value of the maximum likelihood estimator (mˆ ) and the sample mean (B ).The value of mˆ is in general close to B , which could thus be used (as we do here) as a convenient first order approximation. For example, the relative error in approximating B with mˆ is less than 3.5% when B ~20-25% of M and drops to 0.0002% for B = M/10. Obtaining such a sample from the microarray image, is facilitated by the deployment of standard clustering algorithms (e.g. Expectation Maximization) that classify image pixels into two classes on the basis of their intensity values. The class with the lower average intensity then corresponds to the background, and its mean sample value is used to estimate the unobserved background intensity m. Having classified each pixel into signal and background classes, one then uses Equation 9 to restore the value of the former, while setting the value of the latter to zero. The end result is a de-noised microarray image which enters the microarray pipeline without any further background adjustment in order to generate a gene expression profile (Figure 1). It is precisely at this point that further open issues of representation and processing arise that we now seek to formally address.

THE RATI ONA LE OF GENE EXPRESSI ON PR OFI LE REPRESENTATI ON BY F UNCTI ON APPR OXIMATI ON METH ODS Gene activity modeling in systems biology ultimately depends on a quantitative description of the amount of transcripts in particular cellular states (Gibson & Jehoshua, 2001). Since cellular identity, judged by both form and function, is determined by biophysical processes that involve bio-molecules interacting in specific stoichiometries, it follows that control of the latter within certain limits is paramount if cellular phenotype is to be preserved. Biological and experimental variability may result in failure to detect the expression of individual genes, but global features such as the relative ordering of gene expression measures should be preserved for the majority of the assayed genes. Without detailed physicochemical modeling one is forced to treat the measurement scale of microarray experiments as a relative one; normalization and representation of replicated profiles of individual states should be limited to a sliding scale approach that seeks to align replicated profiles against each other. To do otherwise would be equivalent to introducing particularly strong hypotheses about the behaviour of the system under examination which may neither be supported by biology nor warranted in light of the available data. In mathematical terms the task is to find a description for the multivariate global expression profile G of an experiment that has quantified the abundance of n genes i.e. G={g1,g2,…,gn} of a particular cellular state. Each individual gene expression measure g j is restricted to lie in the interval [0, M] that is fixed by the microarray apparatus used in the experiment. Since the gene expression measures reported by the image segmentation software are usually moment statistics of a large number of pixels, the discrete nature of the microarray measurement scale is blunted at this stage. Consequently one could treat each g j or better yet log(g j) as real-valued entities; such treatment is facilitated by the positivity constraints enforced by the Bayesian/MaxEnt background adjustment algorithm which ensures that there are no genes with negative expression value. The finite bounded measurement scale of microarray experiments then implies that replicate profiling experiments of the same cellular state C={G1,G2 ,…,Gk} cannot be naively characterized by their coordinates in a n-dimensional space spanned by the log expression measures of individual genes. Firstly, note that as a result of gene silencing, random target failures and/or insufficient signal amplification,

228

Uncovering Fine Structure in Gene Expression Profile

there will be a finite number of genes whose expression is below the detection limit of the experimental apparatus. Such genes will have g j values equal to zero and thus are censored from subsequent analyses carried out in log-spaces. We remark that a similar effect will also be observed if one uses microarrays with different target complements arrayed on their surface. Even if one profiles the same cellular state, the fact that certain targets are missing from one or more array platforms means that the corresponding genes will have a gene expression measure of zero. Secondly, one cannot a-priori rule out the possibility that the expression of certain genes will saturate the dynamic range of the apparatus. By a simple re-ordering of the discrete increments in the digital intensity scale of microarray images, the expression values of the latter genes can be set to zero in this new scale. Therefore symmetry considerations imply that such “saturated” genes should also be disregarded from further analytic and inferential steps. As a result of all these factors, the set of vectors {G1,G2 ,…,Gk} that correspond to replicated experiments of the same cellular state will be of different dimensionality, and thus are not directly comparable. Even though it is relative easy to handle the issue of unequal dimensionalities i.e. by introducing special symbols for the log-expression of zero and M, this solution is not without its own unique problems since the resultant space will be a disconnected one, in need of considerably complicated analytic machinery for further processing. A way out of the conundrum of the previous paragraph is to completely forego multi-dimensional descriptions, and treat each non-zero/non-saturated observation interchangeably. Rather than interpreting each experiment as a point in a multi-dimensional space, one interprets the non-censored observations g1,i , g 2,i ,..., g ni ,i in the ith gene expression profile as repeated measures of a univariate variable Gi. We should point out that this interpretation is strictly epistemological, expressing the modeler’s perception rather than ontological in nature. The latter would imply or -even worse- assert the physical existence of a global transcriptional control mechanism that assigns genes to particular expression levels, which constitutes a particularly strong and possibly unfounded statement about the biology of gene regulation. By limiting ourselves to an epistemological interpretation of the gene expression profile though we are free to handle Gi in any fashion that we deem admissible. For example, one could view Gi as a function to be approximated by almost any statistical learning algorithms, e.g., neural networks, support vector machines, parametric mixture models, Self-Organizing Maps, non-parametric kernel density estimators. To illustrate the potential of function approximation techniques for such a purpose, we opted to use the latter “model-free” technique as an instrument for data and model reduction of gene expression profiles.

{

}

DATA AND MODE L RED UCTI ON OF GENE EXPRESSI ON PR OFI LES BY N ON -PARAMETRIC KERNE L DENSITY ESTIMATI ON METH ODS Non-parametric kernel density estimation methods (also known as Parzen windows) are model-free techniques for the estimation of an empiric distribution from experimental data. Formally such estimators smooth out the contribution of each observed data point over a local neighborhood. In order to apply this estimator to gene expression profile analysis, we assume that the data are of the form discussed in the previous section i.e. g1,i , g 2,i ,..., g ni ,i : g j ,i ~ Gi. Stated in other terms, each gene expression profile is modeled as an independent, identically distributed finite random sample from a random variable Gi. The kernel density approximation ( fˆci ( g )) to the unknown distribution of the latter variable ( f (g)) at each point g is given by the following equation:

{

}

229

Uncovering Fine Structure in Gene Expression Profile

fˆci ( g ) = fˆci (Gi = g ) ≡

1 ni ⋅ ci

ni

 g − g j ,i  ci

∑K j =1

  

(11)

In the latter expression, the function K is known as the kernel and is specified by the analyst while the tunable parameter c is the bandwidth of the estimator and is learned from the actual data. The kernel is usually taken to be a Gaussian function with zero mean and finite variance, although in principle any smooth unimodal function may be utilized. In order for the estimator to be a proper density, an added constraint is imposed on K, i.e. its integral over the space of possible values for Gi should be equal to c. The magnitude of the bandwidth and the shape of the kernel control the contribution of each experimental data point g j,i to the final estimate at point g. Conceptually small values of c make the estimate “rough” and demonstrate spurious features, while large values of c lead to over-smoothed, featureless representations. There exist many criteria for the selection of the optimal size of the bandwidth parameter from data; the criterion most commonly employed is that of minimization of the Asymptotic Mean Square Integrated Error (AMISE) i.e. the second order Taylor series approximation to the Mean Square Integrated Error (MISE): MISE (c) = ∫ E  fˆc ( g ) − f ( g )  dg   G

(12)

A cross-validation strategy is commonly adopted to estimate the value of c that minimizes AMISE but is computationally expensive for datasets with thousands of data points as is typical of microarray based gene profiles. Approximate plug-in or heuristic estimators come then into play, offering a very favorable trade-off between ease and accuracy of computation. For example the normal reference rule (Wasserman, 2006) is an approximate estimate of the optimal bandwidth of the Gaussian Kernel: cGauss = 1.06 ˆ ni −1/ 5 ,

ˆ = min {s, Q75− 25 1.34}

(13)

where s is the sample standard deviation and Q75-25 is the sample interquartile range, i.e., the difference between the first and third quartiles of the sample data. Since the Gaussian kernel is not optimal when derivatives of the density estimator are sought after (Hardle, Marron, & Wand, 1990), the tri-weight kernel and bandwidth estimator were used instead: KTW ( x) = 35(1 − x 2 )3 / 32, x < 1, cTW = 2.978cGauss

(14)

In any case, the kernel estimator of Equation 11 may then be used as a tool for normalization (data reduction), visual exploration and generation of discrete, possibly parametric hypotheses to further reduce the complexity of representation (meta-modeling, model reduction). These roles are facilitated by the closed form of the estimator which is amenable to hybrid symbolic – numerical operations. The least restrictive way to normalize individual replicate gene expression profiles amounts to an alignment operation as discussed in the previous section. During that operation it is assumed that the individual profiles are translated among each other as a result of residual experimental variation, and that estimation of a single constant suffices to bring them in line. In microarray research it is customary to affect such a translation by setting the mean or the median of the sample of intensity values equal to zero but this is not robust with respect to outliers or departures from symmetry. Hence we propose using the mode

230

Uncovering Fine Structure in Gene Expression Profile

of the gene profile derived distribution for such a purpose, whose value is obtained by maximization of the estimator of Equation 11 by repeated evaluation of derivatives of the latter equation by numeric optimization libraries.

UNC OVERING ST UDY

STR UCT URA L FEAT URES IN GENE PR OFI LES : A CASE

As a case study of the proposed methodology we reanalyzed the DeRisi et al dataset concerning the diauxic shift of Saccharomyces cerevisiae (DeRisi, Iyer, & Brown, 1997). The particular dataset was selected for the degree of replication (seven replicates) of its “common reference channel” i.e. a messenger RNA pool prepared from a single cell state. This degree of replication allowed us to explore the effects of the noise correction and profile representation algorithms in adjusting for the technical variability of the data and identifying fine structural features respectively. The impact of the maximum entropy based background correction image upon the seven replicate gene expression profiles is shown in Figure 2 for three alternate background correction methods: a) no correction (NONE), b) the conventional method of subtracting the mean background from the mean intensity for each spot in the image (SBC) and c) the conditional expectation method (COND, Equation 9) In order to generate the data of Figure 2, the seven images were restored with the COND method before or after (SBC, NONE) segmentation with the software SPOT. After segmentation, the three gene profiles were subjected to global mean normalization and the non-parametric density estimators were Figure 2. Effect of different background correction methods upon non parametric density estimates of the gene expression profile. Solid lines: replicate experiments, dashed line: standard normal distribution. PDF: probability density function

231

Uncovering Fine Structure in Gene Expression Profile

generated using Equation 14. For the purpose of comparison, we also graph the probability density function of the standard normal distribution. As compared to the SBC and NONE methods, the maximum entropy corrected images generated more “normal” looking datasets at least around the mode of the distribution (central part of the density estimate). Two important conclusions may be drawn from this figure: a) background correction tends to increase the dynamic range of the microarray measurement scale irrespective of the method used b) the inter-array variation in the dynamic range effected by background adjustment varies for the different methods. With respect to the first point, we note that for the data of Figure 2 NONE is associated with the narrowest dynamic range i.e. 5.71 bits. In contrast, method COND increased the dynamic range (maximum – minimum value in the x – axis) by 210.83-5.71≈35 and the SBC by 214.86-5.71≈568 times. However this performance advantage for the latter method is misleading as it leads to dynamic range increases that are considerably higher than the range of the (12-bit) analogto-digital converter, used to scan the original microarrays. For such an unrealistic increase in the range of a bounded quantity to occur, it is as if SBC “injects” noise in the dataset. Such an effect, which was also noted in different datasets (L. X. Qin & Kerr, 2004) argues against further use of this method. Subsequently we examined the effects of global mode normalization (GMoN) applied to background un-corrected, and conditionally corrected images (upper row Figure 3). When compared to global mean normalization, translation by the global mode rule leads to profiles that are effectively centered on zero. Background adjustment by the MaxEnt based algorithm (Equation 9) has the added benefit of normalizing the profiles. This effect is readily appreciated in the graphs of the average gene expression profile of the experimental cellular state (lower row Figure 3). These graphs result from computing the average of the non-parametric estimate of each replicate experiment: n n ˆf ( g ) = 1 ˆf ( g ) = 1  1 ∑ c ∑ n i =1 i n i =1  ni ⋅ ci

ni

 g − g j ,i  ci

∑K j =1

     

(15)

The average graph of the global-mode-normalized, MaxEnt restored profiles closely parallels the standard normal distribution at its central part that reflects the quantitative behaviour of the majority of the expressed genes. On the other hand, the profiles from the unrestored images exhibit a far from normal behaviour for the majority of the genes (except the ones with a normalized expression of 1 log2). At the far edge of the centre both profiles exhibit a minor peak (around +3 log2), which is a consistent feature in all replications of the experiment (upper row Figure 3).Mode normalization of the profiles generated from the MaxEnt restored images uncovers two additional peaks at intensities -3.54 and -2.34 log2. The latter two peaks are present in all individual profiles (upper right graph of Figure 3), and are also evident in the averaged profiles (lower right graph of Figure 3). It is possible to gather evidence for the presence of these peaks from all experiments by averaging the derivatives of the non-parametric kernel density estimators of the individual experiments, and thus obtain a symbolic data-driven peak detector. For the GEP shown in Figure 3, the values of the derivative of Equation 15 at the points {-3.54,2.34, 0, 3.} is within absolute numerical tolerance of 10 -3 equal to zero (data not shown). Consequently one could model the average profile with a five component Gaussian mixture (the additional component used to represent residual variability); this reduced model is shown in Equation 16 and is graphed along the average profile of Equation 15 in Figure 4):

232

Uncovering Fine Structure in Gene Expression Profile

Figure 3. Effect of global mode normalization upon non parametric density estimates of the gene expression profile. Solid lines: replicate experiments, dashed line: standard normal distribution. Upper row: replicate profiles, lower row: average profile.

2 2 fˆ ( g ) ≅ f approx ( g ) = 0.024e −14.3( g +3.54) + 0.046e −0.32( g + 2.34) + 2

2

2

0.18e −3.11g + 0.24e −0.45( g −0.43) + 0.024e −1.74( g −3)

(16)

In order to estimate the numerical parameters that appear in Equation 16, one regresses a sample from Equation 15 against the finite Gaussian Mixture Model: K +1

GMM ( x | p, , ) = ∑ i =1

2

i

pi e −0.5

i ( x− i )

2



(17)

with K=4 and μ, i.e., the centers of the Gaussians, fixed to values obtained from numerical evaluation of the derivative of Equation 15, while all other parameters are allowed to vary. Once the (epistemological) clusters have been defined, one may invoke ontological models that correspond to experimentally verifiable hypotheses. With respect to the ontological nature of the clusters in Figure 4 the following should be noted: •

•

The “central” massive peak corresponds to (thousands of) genes with “average” expression and thus it is highly unlikely that there is a single mechanism that accounts for their expression. This central peak likely reflects the modulating effect (positive or negative) of multiple transcriptional regulators upon the basal transcriptional rate. The right-most peak includes genes of a limited functional repertoire (e.g. ribosomal genes, translational elongation factors) and thus it is very likely that a small number of transcriptional

233

Uncovering Fine Structure in Gene Expression Profile

Figure 4. Finite Mixture Estimation of average gene expression profile. Solid line: approximation of Equation 16, dashed line: average profile of Equation 15).

•

mechanisms are responsible for its generation and maintenance (Table 1). Furthermore probes of genes with similar function (e.g. the retrotransponson gag/pol genes) that are co-regulated are correctly clustered together adding further weight to the hypothesis that such a peak is the product of actual biological mechanisms i.e. it has an ontological substance. The left most peaks include genes with unknown function and regulation; the nature of the corresponding clusters is purely epistemological at this point. To convert such an epistemic statement into ontology would require targeted experiments that search for common transcriptional mechanisms that explain the common quantitative behaviour.

C ONC LUSI ON In the present work, we propose a novel theoretical framework for data and model reduction of gene expression profiles generated by microarray experiments. In order to avoid inconsistencies we adopted a bottom-up statistical framework approach to the problem of background adjustment. This framework operates on the raw microarray images and utilizes the maximum entropy priors in order to encode testable pre-data information about the background features and the measurement scale of microarray images. Under certain fairly generic conditions on the expected intensity of the background (m) relative to the signal, one can approximate these priors with modified power series distributions paving the way for efficient estimating algorithms for the single parameter of interest (m). Subsequently we formulate the operation of background adjustment as a traditional additive noise inverse problem whose unique solution is obtained by means of the Bayes theorem but which is properly constrained by the prior distributions. An empiric evaluation of the proposed image de-noising algorithm on a real world dataset demonstrates the “uncompressing” effects that the method has upon the gene expression profile which allows one to detect the existence of fine and reproducible structure in the latter.

234

Uncovering Fine Structure in Gene Expression Profile

Table 1. Accession number and function of genes corresponding to the rightmost peak in the profile of Figure 4. Rows with multiple gene identifier entries correspond to probes with similar gene function. Gene Identifier

Gene Function

YCR012W

3-phosphoglycerate kinase

YLR340W

Conserved ribosomal protein P0 similar to rat P0

YNL209W

Cytoplasmic ATPase that is a ribosome-associated molecular chaperone

YDR385W, YOR133W

Elongation factor 2 (EF-2)

YHR174W

Enolase II

YLR167W

Fusion protein that is cleaved to yield a ribosomal protein of the small (40S) subunit and ubiquitin

YPL220W, YKL006W

N-terminally acetylated protein component of the large (60S) ribosomal subunit

YLR075W, YDR012W, YDR418W, YNL067W, YPL131W,

Protein component of the large (60S) ribosomal subunit

YJR123W, YGL123W

Protein component of the small (40S) ribosomal subunit

YNL119W

Protein with a role in urmylation and in invasive and pseudohyphal growth

YML045W, YBR012W-B, YCL019W, YJR027W, BL005W-A, YBR012W-A, YJR026W, YJR028W

Retrotransposon TYA Gag and TYB Pol genes

YDL130W

Ribosomal protein P1 beta

YOL039W

Ribosomal protein P2 alpha

YDR382W

Ribosomal protein P2 beta

YLR109W

Thiol-specific peroxiredoxin

YIL078W

Threonyl-tRNA synthetase

YBL005W

Transcriptional activator of the pleiotropic drug resistance network

YAL003W

Translation elongation factor 1 beta

YKL081W

Translation elongation factor EF-1 gamma

YLR249W

Translational elongation factor

YBR118W, YPR080W

Translational elongation factor EF-1 alpha

In the absence of detailed knowledge about the specific biological mechanisms that control the gene expression profile, one has to forego ontological models of such structure and settle for epistemological ones. By considering the discrete, bounded scale of microarray experimental setups and the potential for over and under-saturation we employed function approximation methods in general, and non parametric kernel density estimators in particular, for the representation of gene expression profiles. Such a representation enables the use of quantitative frequency information about the relative abundance of different transcripts within the same experiment in order to a) normalize the measurements and b) suppress residual noise by averaging (“inverse square root” rule) and thus serve the role of data reduction. The latter underlies the detection (“uncovering”) of subtle structural features in the gene profile which pivot the simplification of the descriptions of the biological system under examination (“meta modeling”, “modeling reduction”). Whereas the non-parametric description uses n+1 parameters (the actual data points and the bandwidth of the kernel, i.e. in excess of 6000 variables in our case), the reduced model utilizes only a handful (i.e. fifteen in the case study of the DeRisi dataset).

235

Uncovering Fine Structure in Gene Expression Profile

It is tempting to justify the use of Gaussian Mixtures parametric descriptions in other situations as a result of their “derivation” as accurate reductions in one typical dataset. Whether normality is an emergent property of our ontological bottom – up (and top down as in Do, Muller, & Tang, 2005) descriptions, or a property of the biological systems grounded in tangible experimentally verifiable mechanisms of transcriptional control remains an open question.

A ckn ow ledgment We thank the European Social Fund (ESF), Operational Program for Educational and Vocational Training II (EPEAEK II), and particularly the Program PYTHAGORAS ΙΙ, for funding the above work.

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Jaynes, E. T. (2003). Discrete prior probabilities: The entropy principle. In G. L. Bretthorst (ed.), Probability theory: The logic of science (pp. 343-371). Cambridge University Press. Johnson, N. L., Kotz, S., & Kemp, A. W. (1992). Power series distributions. In Univariate Discrete Distributions (Second ed., pp. 70-76). John Wiley & Sons. Kooperberg, C., Fazzio, T. G., Delrow, J. J., & Tsukiyama, T. (2002). Improved background correction for spotted DNA microarrays. J Comput Biol, 9(1), 55-66. Qin, L., Rueda, L., Ali, A., & Ngom, A. (2005). Spot detection and image segmentation in DNA microarray data. Appl Bioinformatics, 4(1), 1-11. Qin, L. X., & Kerr, K. F. (2004). Empirical evaluation of data transformations and ranking statistics for microarray analysis. Nucleic Acids Res, 32(18), 5471-5479. Sarwal, M., Chua, M. S., Kambham, N., Hsieh, S. C., Satterwhite, T., Masek, M., et al. (2003). Molecular heterogeneity in acute renal allograft rejection identified by DNA microarray profiling. N Engl J Med, 349(2), 125-138. Silverman, B. W. (1986). Density estimation for statistics and data analysis. CRC Press. Southern, E., Mir, K., & Shchepinov, M. (1999). Molecular interactions on microarrays. Nat Genet, 21(1 Suppl), 5-9. Valentini, G. (2002). Gene expression data analysis of human lymphoma using support vector machines and output coding ensembles. Artif Intell Med, 26(3), 281-304. Wasserman, L. (2006). Density estimation. In All of nonparametric statistics (pp. 125-144). Springer.

K ey TERMS Bayesian Probability: An interpretation of the colloquial term probability, which identifies the latter with the degree of belief of a proposition about the world. This interpretation is firmly grounded in the rules of Aristotelian logic and in fact extends the latter in situations of uncertainty i.e. when the truth or falsity of propositions cannot be ascertained completely. Stated in other terms, the construct of Bayesian Probability and the supporting theory is nothing more than “common sense reduced to numbers”. The major instrument for updating one’s prior beliefs to posterior inferences in light of new information is the computational machinery of the Bayes’ theorem. Epistemological Modeling: Modeling that quantifies one’s perception about the world rather than the world per se. The object of such modeling is to generate coherent descriptions of one’s knowledge usually in the face of uncertainty. Gene Expression Profile: Defined operationally as the output of any step in the microarray pipeline after the image operations stage. Hence the global gene expression profile is a set of possibly noisy measurements, one for each target printed on the surface of the microarray. Inference about the members of the set, which constitutes the gene expression profile, proceeds in different stages that involve the normalization of the measurements prior to exploratory and formal statistical/machine learning methods.

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Maximum Entropy Prior: The distribution that results from application of the variational maximum entropy algorithm. The latter uniquely determines the least biased epistemic (Bayesian probability distribution) that encodes certain testable information is by maximizing the convex functional that information negative entropy defines. The resulting distributions are least informative or “objective” ones in the sense that they are most compatible with the “pre-data” constraints, while being maximally noncommittal about the missing information. Non–Parametric Kernel Density Estimation: Non-parametric kernel density estimation methods are model free techniques for the estimation of an empiric distribution from experimental data. Formally such estimators smooth out the contribution of each observed data point over a local neighborhood. Normalization: The process in which mathematical transformations of the microarray data are undertaken to reduce variability in the expression levels and make data from different experiments directly comparable. Ontological Modeling: Modeling that implies the existence of certain objects in the physical natural world. The distinction between ontological and epistemological modeling is a subtle one; whereas the former is an investigation about natural objects and properties, the latter concerns the analysis of (usually) subjective statements about models of the world. Power Series Distribution: Discrete probability distributions with probability mass function given by: P( y | ) = a y

y

∞

∑a x =0

y

y

1, y ≤ M ay =  . Modified power series distribution (MPSD) are more general 0, y > M

distributions which arise when θ is a function of another (simple) parameter. In such a case we define ∞

the power parameter θ(m) and series function η(θ) by: ( ) ≡ ∑ a y x =0

y

=

M

∑ x =0

y

.Particular choices of the

power parameter render power distributions that are analytic approximations to Maximum Entropy priors over finite domains.

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Chapter XIII

Gene Expression Profiling with the BeadArrayTM Platform Wasco Wruck Max Planck Institute for Molecular Genetics, Germany

abstract This chapter describes the application of the BeadArrayTM technology for gene expression profiling. It introduces the BeadArrayTM technology, shows possible approaches for data analysis, and demonstrates to the reader how the technology performs in comparison to alternative microarray platforms. With this technique, high quality results can be achieved so that many researchers consider employing it for their projects. It can be expected that the technology will gain much importance in the future. The author hopes that this résumé will introduce researchers to this novel way of performing gene expression experiments, thus giving them a profound base for judging which technology to employ.

INTR OD UCTI ON Microarrays have emerged as the most popular technology for performing gene expression profiling. They provide researchers with the means to screen all genes of an organism simultaneously thus alleviating the investigation of complex diseases like cancer or diabetes. Closely coupled with the development of the technology are the reliability issues culminating in the publication of contradictory results achieved on different microarray platforms. While in the starting phase of the microarray technology reliability issues arose from the imperfect technique, e.g. distorted spotting needles, thus requiring a compensation by a sophisticated image analysis (Steinfath,M. et al., 2001, Kamberova, G., 2002) a continuous process of improvement using proved industrial methods gives better but far from perfect results. The BeadArrayTM technology described in this chapter proves that an industrial production process facilitates reliable experiments of high quality. The rest of this chapter is organized as follows. We motivate the BeadArrayTM technology. Subsequently, we describe viable approaches for analyzing data produced with this technology, introducing Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Gene Expression Profiling with the BeadArrayTM Platform

the proprietary software BeadStudio and freely available solutions from the R Bioconductor environment. We introduce our pipeline design for the analysis of bead-summary data. Then we demonstrate the position of the BeadArrayTM technology in comparison to other microarray platforms. Finally, we summarize our experiences with the new technique.

T he B ead A rra y TM techn ology In the first phase of microarray technology probes were spotted by robots at known locations onto a dedicated substrate. Probes were then hybridized with a radioactive or fluorescent labeled target. Thus, the abundance of hybridized material was transformed into a signal which could be read by a scanner. Many error sources influenced the results achieved by this technique: twisted spotting needles, needles transferring different DNA volumes, labelling differences for, e.g. red and green channel, dust on the substrates, systematic local background changes, bad signal-to-noise rates in the scanned image, etc. . A great improvement in quality was achieved by synthesizing oligonucleotides using photolithographic processes known from the semiconductor industry. As a logical consequence the product was called “chip” as a reference to the origin of its manufacturing technique. An alternative approach claiming to reach similar quality benchmarks as the chips is the BeadArTM ray technology. It takes advantage from the ability of beads to be randomly assembled at very high densities. In the literature it has been described that beads of 300nm have been randomly assembled into 500nm wells (Michael et al., 1998). For the BeadArrayTM technology at present a size of 3μm is used for the silica beads. The beads are generated by joining oligonucleotides to their surfaces and are pooled in libraries. They are self-assembled into etched substrates. With the beads randomly distributed over the array the problem of decoding each bead’s information content arises. The solution of this problem is described in (Gunderson, K. et al., 2004) and is an essential precondition for the employment of the technique. The probes consist of a gene-specific 50-mer oligonucleotide and a 23-mer oligonucleotide “address” (see Figure 1). They are immobilized to the beads and decoded by a minimized amount of hybridization steps in the manufacturing process. The number of hybridization stages s is given by: s = logbn where n is the number of different beads and b is the number of different states that can be detected after the image analysis, e.g. b=2 if only red and green can be detected or b=4 if red, green, yellow and black can be detected Thus, every chip is unique and is delivered bundled with media containing the information of the bead locations. (Gunderson,K. et al., 2004) claim to have a misclassification rate of the beads of 1.2 x 10-5 in the mean and 1.4 x 10-4 in the worst case in a random sampling of 100 manufactured array matrices. The misclassification problem can be tackled by using a sufficiently high number of replicates of beads. It is guaranteed that – in average – there are more than thirty replicates and – in minimum – there are more than five. In a random sample of twenty chips the author calculated a median number of 42 replicates of beads. The address oligonucleotides are designed to have low similarity to genetic sequences, minimal complementary sequences versus each other and similar GC content. The probe oligonucleotides, on

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Figure 1. Address and gene-specific part of the more than 100000 oligonucleotides joined to a bead

the other hand, are designed to be specific - also taking into account single nucleotide polymorphisms (SNPs) and alternative splicing. Depending on the spacing between the beads scanners with different resolutions are needed. Two formats exist, one containing 96 samples using a spacing of 6μm works with a scanner resolution of 1μm while the other format containing eight samples using a spacing of 20 works with a scanner resolution of 5μm. For our investigations we used the latter resolution allowing to scan images containing about 1 million x 8 beads.

DATA ANA LYSIS In principle, data analysis can be performed in two different ways: a. b.

Data analysis using the proprietary software solution BeadStudio. Bead-level and bead-summary-level data analysis using manufacturer-independent software, e.g. The R/Bioconductor (Ihaka et al. 1996, Gentleman et al. 2004).

D ata A nalysis with the B eadS tudio The BeadStudio offers a vast variety of functions of which only the main topics will be described here. The software operates on the summarized bead-level-data generated as output from the image analysis modules of the scanner software. Usually this data is in binary format so that it is not readable by the user. By changing the settings in a configuration file also human readable bead-level data can be generated. The BeadStudio enables the access to the data on a per chip-section-basis and the interactive grouping of the data per drag and drop or via a predefined sample sheet. Two types of analysis can be performed: 1.

The gene expression analysis delivers minimum, maximum and mean intensities, standard deviations/errors of samples and of beads, the number of samples, the number of beads and the detection p-values. The detection p-value gives the significance level at which a probe can be distinguished from the background.

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2.

The differential expression analysis delivers the same results as gene expression analysis plus a so-called DiffScore as well as the Concordance value. The DiffScore tells if the probe in the group of interest - usually the treatment group - is significantly higher or lower expressed than in the reference group. The Concordance value compares the number of probes with upregulated signal to the number of probes with downregulated signal.

The analysis results are presented and saved in a spread sheet that can be easily imported into external table calculation software. For further analysis and quality control linear and logarithmic scatter plots can be generated which provide several functionalities for managing the visualization of the data, e.g. filtering by the detection call or displaying fold change lines. Another feature for follow up analysis is the clustering functionality. Data can be clustered by samples or probes. Thus, it can be evaluated which genes have similar patterns of expression. The same holds for the samples: similar samples regarding the expression patterns are grouped together and displayed in a dendrogram indicating the distances between the samples. For the similarity metrics four different methods are provided: Correlation measures the similarity in terms of the Pearson correlation. Absolute correlation uses also the Pearson correlation, but the absolute value of it – thus, giving good values also for reciprocal dependencies. The Manhattan distance measures the distance as the sum of the edges in a rectangular grid. The Euclidean distance uses the shortest distance between two points which is the square root of the sum of the squares of the components. Quality control information gained from dedicated beads can be displayed in a summarized view but it can be also refined down to the single section. In the summarized view mean and standard deviation of all sections are displayed as bar charts with error bars. The quality control view gives information about hybridization controls, background and noise, Biotin versus high stringency controls, housekeeping genes versus all genes and low stringency controls for perfect matches and mismatches.

D ata A nalysis with the R /B ioconductor Data can be analysed with the R/Bioconductor on bead-summary-level and on bead-level. While the bead-summary-level analysis can be performed on the conventional output of the BeadStudio – the gene profiles – the bead-level-analysis is based upon information about single beads which can be generated by the scanner software changing dedicated configuration parameters in a XML configuration file.

B ead-S ummary-A nalysis with the R /B ioconductor The R/Bioconductor packages beadarray (Dunning,M. et al. submitted), lumi (Lin,S.M. et al. 2007) and BeadExplorer are developed with the purpose of data analysis for the BeadArrayTM technology. The authors suggest to save the bead-summary-data without background correction and normalization via the BeadStudio. The background correction of the BeadStudio produces a higher variance for the lower intensities. This can be examined in a logarithmic scatter-plot of two background-corrected replicates (see Figure 2). The BeadExplorer package offers a GUI (graphical user interface) dialog to specify the bead-summary files while the beadarray and the lumi package are driven by the command line. The lumi package provides the normalization method RSN (Robust Spline Normalization) which combines the quantile (Bolstad, B et al. 2003) normalization and the Loess (Cleveland, W. 1979) normaliza-

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Figure 2. Logarithmic scatter plots of two biological replicates. In the plot to the left the background correction of the BeadStudio was performed, in the plot to the right the correction was omitted. The left plot clearly shows the higher variance in the area of the lower values.

tion methods. However, besides the two packages data can be simply imported into the R/Bioconductor via basic R reading functions for tabulator- or comma-delimited files. Once the data is imported the comprehensive fund of normalization, statistical and plotting functions of R/Bioconductor can be applied. For gene expression analysis the limma package (Smyth, 2005) including several normalization methods as well as the VSN normalization (Huber, 2002) are a good base.

B ead-Level-A nalysis with the R /B ioconductor The bead-level-analysis is only implemented in the beadarray package. For this type of analysis the files containing bead-level data are required. They are generated by the scanner software with dedicated settings in the XML configuration file. It can be considered as an disadvantage that these files cannot be generated “a posteriori” - after the scanning software finished its work. The bead-level analysis provides further facilities like quality control and normalization on a bead-level base. The beadarray package can be used to find local problems on the chips by examining images with the spatial bead distributions. Outlier beads can be removed – a feature also integrated in the standard platform software. On the other hand, the bead-level-data uses large amounts of disk space and a standard analysis without the presence of many bead outliers will yield nearly the same results as the platform software by averaging the bead intensities. Thus, unless the bead-level-data is used for normalization one can stick to the bead-summary-data. Nevertheless bead-level-data should be stored for potential further investigations when disk space is not an issue.

A Pipeline D esign for B ead-S ummary-A nalysis The author established a pipeline for the evaluation of a large series of Illumina bead arrays which is illustrated by Figure 3.

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Figure 3. Pipeline design for the evaluation of BeadArray™ experiments. The first steps from the experiment to the image analysis are under control of Illumina™. The summarized bead data can be generated optionally by a Bioconductor package if the bead-level data is available. Results of the pipeline are on the one hand quality control features like correlation tables and plots and on the other hand tables containing significant genes and pathways as well as statistical and biological descriptive parameters associated with them.

The first steps of the pipeline – from the experiments to the image analysis – are carried out on the Illumina BeadArray™ platform. The standard procedure includes the bead summarization in the BeadStudio but it is also possible to execute this step via the Bioconductor package beadarray as long as the bead-level data is available. In the next step the data is annotated. Here, one could rely on the lookup tables provided by Illumina including RefSeq ids, mouse symbols, descriptions, gene ontolo-

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gies, etc. However, further annotation is required when more complex evaluations are planned, e.g. mapping of chromosomal locations. Furthermore a BLAST (Basic Local Alignment Search Tool) of the oligonucleotide sequences from Illumina against the newest versions of sequence databases keeps track of recent changes whose influences should not be underestimated. After the annotation process the categories of the experiments are determined and integrated into a naming scheme for the bead summary data, e.g. collecting information about tissue, sex and strain in a project comparing differences between strains. These categories again are used to specify data sets from the bead summary data which are incorporated in the dedicated test. The test set itself is usually built up from a control group and a treatment group – more generally speaking - it is built up from two conditions to be compared versus each other. Quality control is regarded as a very important step in the evaluation of the genrerated large data sets. Therefore the evaluation pipeline incorporates multiple quality control methods: • • • •

Inter-array correlation plots and tables Intra-array correlation plots (section correlation, replicates) and tables Heat maps Cluster dendrograms

Sections containing biological or technical replicates are assumed to yield very high correlations. Thus, the average of a section’s correlations to all other sections can be used as quality criterion. This criterion is used to filter bad quality sections applying a dedicated threshold for the correlation coefficient. An automated quality control is enabled this way. However, a visual inspection should complement the automated process at least for some random samples. The quality control phase is followed by the normalization process. The normalization operates on the test sets containing all quality-checked replicates of the control and treatment set. Thus, only the data of interest for the dedicated comparison is considered and external influences are minimized. This would be the drawback of combined normalization of the total data set consisting of all single data sets. By default, we use the quantile normalization algorithm (Bolstad, B et al. 2003) which ranks the values of the data sets, calculates the median values afterwards and finally copies back the median values to the original data sets in the original order. This method brings the data sets’ intensity distributions into line so that the run of the curve is the same for all data sets. The median normalization is a more simple method multiplying each single experiment with a constant factor calculated via the median of the data set so that the median of all data sets is the same. Several statistical tests are performed on the normalized data including Student’s t-test (Press,W et al. 1992), the Welch test, the Wilcoxon test (Wilcoxon, 1945) and a permutation test. The statistical tests result in a p-value addressing the probability that control and treatment have the same mean. Thus, a low p-value indicates a high significance that the dedicated gene is differentially expressed. A threshold of 0.05 – or more strictly – 0.01 is usually applied. The permutation test arbitrarily permutes the samples of the control and the treatment set and determines the percentage of test results less than the Wilcoxon test’s p-value. This percentage itself delivers the p-value of the permutation test. By choosing the equality of control and treatment as null hypothesis the false-positive-rate can be controlled, i.e. the amount of genes yielding a positive test result while in reality they are not differentially expressed. For a series of multiple simultaneous tests the significance is decreased by the multiplicity. This problem can be managed by the false discovery rate adjustment which is calculated by the qvalue method (Storey, 2002).

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In a pathway analysis the significance of the disregulation of pathways is tested. This is achieved by a hypergeometric test comparing the number of significant genes in the dedicated pathway to the total number of significant genes. The pipeline can be parametrized by the threshold for p-value, ratio and detection value. The detection value is delivered by the image analysis telling how good the dedicated beads separate from the background and thus giving a quality criterion of the reliability of the probe. In general, a good detection value corresponds to high intensities. The threshold parameters are used for generating lists of significant genes.

B eadA rrayTM T echnology in C omparison to other Microarray Platforms Ever since microarray technology has been developed reliability has been the crucial factor. Concerning the reliability it can be postulated that experiments should be reproducible on different technology platforms and within one platform a perfect reproducibility is expected. The MicroArray Quality Control (MAQC) project was initiated to investigate reliability issues of microarrays. The project participants tested several microarray and alternative technology platforms – including the BeadArrayTM platform – each at three laboratories selected by the microarray platform provider. They evaluated the intra-platform consistency and the inter-platform comparability across multiple test sites. The tested samples were universal human reference RNA and human brain reference RNA and two predefined mixtures containing 75% universal human reference RNA : 25% human brain reference RNA and 25% universal human reference RNA : 75% human brain reference RNA. The goal of this experimental design was not to perform a representative genetic experiment but to investigate the characteristics and limits of the technologies. The four sample types were tested using five replicate assays. A common subset from all platforms included 12091 Entrez genes extracted from 15615 RefSeq probes contained in the union of all platforms. Genes were matched to probes via a simplifying oneprobe-to-one-gene lookup list. The data for each platform was evaluated with the proprietary software. Therefore the resulting number of probes differed between the platforms depending on the total number of probes provided and the detection calls. Each software solution handles the calculation of the detection calls and the filtering via a threshold in its own way following deviating philosophies regarding the reliability of data. For the study only genes that were detected in at least three of five replicate assays were used for most analyses. The number of genes detected lay in the range of 8000 to 12000 depending on the platform. Within one platform there was only a very small variation in the number of detected genes Different numbers of probes certainly have an impact on the data analysis. In a rough overview the results can be summarized as being measures for the reproducibility within platforms and in between platforms and the accuracy in comparison to a reference technique. As a measure or the reproducibility the coefficients of variation (cv) are calculated telling how much results vary between different platforms and test sites. Here, the values for BeadArrayTM are in the lower range of all platforms at about 0.1 . Another measure is the amount of overlapping genes detected as differentially expressed under predefined conditions in terms of p-value and ratio in different platforms or test sites. Here, the BeadArrayTM platform performed quite well with some overlaps to other platforms and all overlaps within the platform greater than 80%.

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Furthermore, the reproducibility can be measured in terms of the correlation coefficient. Here, the Spearman rank correlation of the log ratios was used. It is calculated by ranking the logarithmic ratios of treatment samples (human brain reference) versus control samples (universal human reference) before calculating the correlation coefficient.. The correlation coefficient ranges between –1 and 1. Good values are close to one, values near zero represent a random dependency and negative values a reciprocal dependency. In this discipline the BeadArrayTM platform performed best for the median to all other platforms. However, the correlation coefficients where only slightly better than those from other competitors and in the intra-platform comparison there were better results from another platform but both were ranging on an excellent level. For these results from the MAQC project see Figure 4.

C ONC LUSI ON The BeadArrayTM platform is a novel promising technology for gene expression profiling. It provides high-throughput data screening and high-quality experiments at a relatively low cost. For data analysis a quite comfortable interactive software solution is bundled with the platform. Furthermore, free software packages from the R/Bioconductor environment can be applied to evaluate the data in combination with the proprietary solution or in a stand-alone fashion. However, since the platform is young of age the software development is in the starting phase and further improvements can be expected, e.g. a state-of-the-art normalization method taking into account GC-content and avoiding negative values, like GCRMA (Wu et al., 2004) for the Affymetrix1™ platform. For the advancement of alternative software

Figure 4. Spearman rank correlations of log ratio values from dedicated platforms compared in the MAQC project. Only genes expressed in both test sites and both sample types were used. ILM_1, ILM2 and ILM_3 are three different test sites for the BeadArrayTM platform. Correlation coefficients less than 0.8 (worst) are the darkest, between 0.8 and 0.9 are the lightest and greater than 0.9 (best) are mid-range. The last row shows the median of the rows above yielding best values for the BeadArrayTM test sites.

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packages the open accessibility of technical specifications, e.g. detailed descriptions of bead-level-data and control probes would be profitable. Nevertheless the existing tools allow for gene expression profiling delivering results of high quality. The data quality as assessed by the MAQC project is located on a high level. In terms of coefficient of variation, overlap of significant genes and correlation coefficient between platforms and within the same platform it always ranges in the upper region of all competitors and sometimes is best. Since the MAQC consortium wanted to investigate the characteristics and limits of the technologies it can be expected that in dedicated biological experiments the quality will not reach the high level of this project. The results of the experiments evaluated by the author confirm this hypothesis. Correlation coefficients of data from technical replicates could reach 0.99. However, when some parameters were changed like the labeling or the batch of chips the quality could be slightly inferior.

ackn ow ledgment Part of this work was funded by the EU project METASTEM.

REFERENCES Bolstad, B., Irizarry, R., Strand, M., & Speed, T. (2003). A comparison of normalization methods for high density oligonucleotide array data based on variance and bias. Bioinformatics, 19(2), 185-93. Cleveland, W.S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74(368), 829-836 Dunning, M. J., Smith, M. L., Ritchie, M. E., & Tavaré, S. (2007). Beadarray: R classes and methods for Illumina bead-based data. Bioinformatics, June 22. Gentleman, R., Carey, V. J., Bates, D. M., et al. (2004), Bioconductor: Open software development for computational biology and bioinformatics. Genome Biology, 5, R80. Gunderson, K.L., et al. (2004). Decoding randomly ordered DNA arrays. Genome Res, 14, 870-877 Huber, W., von Heydebreck, A., Sueltmann, H., Poustka, A., & Vingron, M. (2002). Variance stabilization applied to microarray data calibration and to the quantification of differential expression. Bioinformatics, 18, 96-S104. Ihaka, R. & Gentleman, R. (1996). R: A language for data analysis and graphics. J. Comput. Graph. Stat, 5(3), 299-314. Kamberova, G., & Shah, S. (2002). DNA array image analysis. Nuts & Bolts. DNA Press Lewin, B. (2002), Molekularbiologie der gene. Spektrum Akademischer Verlag. (p. 985). Lin, S.M., Du, P., Kibbe, W.A. (2007), Model-based variance-stabilizing transformation for Illumina microarray data. Accepted by Nucleic Acid Research.

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MAQC Consortium (2006). The microarray quality control (MAQC) project shows inter and intraplatform reproducibility of gene expression measurements. Nature Biotechnology, 24(9), 1151-1161. Michael, K.L., Taylor, L.C., Schultz, S.L., & Walt, D.R.(1998). Randomly ordered addressable highdensity optical sensor arrays. Anal.Chem, 70, 1242-1248. Press, W. H., Teukolsky, S.A., Vetterling, W.T., & Flannery, B.P. (1992). Numerical recipes in C: The art of scientific computing. Cambridge University Press. Smyth, G. K. (2005). Limma: Linear models for microarray data. In R. Gentleman, V. Carey, S. Dudoit, R. Irizarry, W. Huber (eds), Bioinformatics and computational biology solutions using R and bioconducto (pp. 397-420). New York: Springer. Steinfath, M., Wruck, W., Seidel, H., Lehrach, H., Radelof, U., &. O’Brien, J. (2001) Automated image analysis for array hybridization experiments. Bioinformatics, 17, 634-641. Storey, J.D. (2002). A direct approach to false discovery rates. J R Stat Soc B, 65, 479-498. Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1, 80-83. Wu, Z., Irizarry, R. A., Gentleman, R., Martinez Murillo, F., & Spencer, F. A. (2004). Model-based background adjustment for oligonucleotide expression arrays. Johns Hopkins University, Dept. of Biostatistics Working Papers.

K ey T erms Affymetrix: Affymetrix is a trademark of Affymetrix, Inc. . Bead Array: A bead array is an array of randomly assembled beads covered with oligonucleotides representative for an organism’s genome. BeadArray: BeadArray is a trademark of Illumina, Inc. . BLAST: (Basic Local Alignment Search Tool) is an bioinformatics algorithm applied to align sequences versus each other. Clustering: Clustering is an analysis method for grouping of probes and samples by similarity. Similar data sets fall into the same cluster while dissimlar data sets fall into different clusters. For the hierarchical clustering a hierarchy of clusters is determined. Thus, one large cluster comprising all data sets is stepwise subdivided into smaller clusters down to singletons which are clusters containing a single data set. Coefficient of Variation (cv): The coefficient of variation is the standard deviation divided by the mean. It is a measure for the reproducibility. For a low cv data has a good reproducibility, for a high coefficient of variation data contains much variation and thus measured values can only be reproduced very inprecisely. Correlation Coefficient: The correlation coefficient tells how good two data sets correlate. The correlation coefficient ranges between –1 and 1. Good values are close to one, values near zero represent

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a random dependency, negative values a reciprocal dependency. The correlation coefficient calculated directly from the data is called Pearson correlation coefficient. The Spearman correlation coefficient first ranks the data before calculating the (Pearson) correlation coefficient. Thus, it is more robust against outliers than the Pearson correlation coefficient. Gene Chip: A gene chip contains a matrix of photolithographically assembled oligonucleotides representative for an organism’s genome on a dedicated substrate. Gene Expression: Gene expression is the transformation of a gene’s information by transcription and translation (Lewin, 2002) Microarray: A microarray is a collection of genetic substances, - mostly DNA(Deoxyribonucleic acid) - integrated at a large scale..Microarrays can be generated in high-throughput using robots transferring minimal amounts of probes onto substrates. The sample being tested is radioactively or fluorescently labelled and hybridizeded to the probes. A scanner scans the microarrays delivering signals for the labelled and hybrized substance. “Chips” (see Chips) and “bead arrays” (see bead array) can be regarded as subsets of microarrays. VSN (Variance Stabilizing Normalization): The VSN (Variance stabilizing normalization) transforms the data in such a way that the variance remains nearly constant over the whole intensity spectrum. Without this (or another) normalization a dependency between intensity and variance can be observed in may cases which deteriorates the analysis results. XML: XML is the extended markup language. It is a more general version of the Internet description language HTML (hypertext markup language) allowing the detailed description of documents.

endn ote

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Chapter XIV

The Affymetrix GeneChip® Microarray Platform Djork-Arné Clevert Charité Universitaetsmedizin Berlin, Germany and Johannes Kepler University Linz, Austria Axel Rasche Max-Planck-Institute for Molecular Genetics, Germany

abstract Readers shall find a quick introduction with recommendations into the preprocessing of Affymetrix GeneChip® microarrays. In the rapidly growing field of microarrays, gene expression, especially the Affymetrix GeneChip arrays, is an established technology present on the market for over ten years. Used in biomedical research, the mass of information demands statistics for its analysis. Here we present the particular design of GeneChip arrays, where much research has already been invested and some validation resources for the comparison of the methods are available. For a basic understanding of the preprocessing, we emphasize the steps, namely: background correction, normalization, perfect match correction, summarization, and couple these with alternative probe-gene assignments. Combined with a recommendation of successful methods a first use of the new technology becomes possible.

Intr od ucti on Microarrays are the state of the art tool for high-throughput analysis of gene expression. Microarrays allow one to monitor the expression of several thousand genes in parallel in a single experiment facilitating a broad view of the expression state. The genome-wide investigation is basis of the systems biology modeling concept.

Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

The Affymetrix GeneChip® Microarray Platform

The Affymetrix GeneChip® platform was one of the first commercial techniques available on the market. It comes up with a sophisticated design measuring expression of a single gene by several probes on the same chip and providing control sequences for every feature. Chips are available for many species, including popular model species and especially in the biomedical research, where the platform is established. Due to the design and the dissemination of the platform much research has been performed on the analysis of the generated data. It is the main leads and successful results that we wish to describe here. The vast amount of digital and noisy data generated by microarrays requires statistics for its evaluation. Affymetrix provides basic applications for processing the data and collaborates with companies providing Affymetrix recommended software. On the other hand most of the independent research has been carried out on the R software environment with the BioConductor package collection for statistical computing (Gentleman et al., 2004; R Development Core Team, 2005). In an attempt to be concise we shall focus on R/BioC.

D esign of the Platf orm In the GeneChip approach the expression of a gene is measured by several probes. The probes are selected from the transcript sequence of the respective gene. The UniGene database is the reference for the gene sequence. To avoid cross hybridization between several genes, the sequence of the probes has to be chosen unique to the gene. The length of the probes is always 25 nucleotides. A number of such probes collected in probe sets stands for independent measurements of the number of transcripts for the gene. The number of probes in a probe set varies between chip platforms. For example in the popular Human Genome U133 Plus 2.0 array there are eleven probes in each probe set. With the advancement of the human genome sequence and transcript libraries the choice of probe sequences has to be updated from one chip platform to the next. The assignment of the probe sets to genes is updated quarterly and can be retrieved from the NetAffx service on the Affymetrix homepage. In the classic chip designs, each probe is spotted with its perfect match (PM) sequence and the socalled mismatch (MM) sequence. In the mismatch sequence the 13th nucleotide is altered. The idea is, that the mismatch sequence measures the background expression. The perfect match signal then contains the background expression plus the gene expression. In the newer chips Affymetrix spares the space for additional probes and replaces the mismatches with GC-bins. For a given number of G or C nucleotides (between 0 and 25) the GC-bin contains 25mers unrelated to any gene sequence. The assumption is, that sequences with the same GC content show similar expression behaviour. To make the hybridization

Figure 1. Probe sequences are selected from the transcribed regions of the gene sequence

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The Affymetrix GeneChip® Microarray Platform

results independent from the degradation of the transcripts in the cell the probe sequences are selected near the 3’ end of the gene sequence. In the production of the chips, the probes are spotted on slides using a photolitographic method. In the experiment, labeled RNA from the sample under study is injected on the chip. The hybridization result depends non-linearly on the amount of transcripts in the sample. In the analysis of the measurement results this has to be considered by calculating with the logarithm of the hybridization value. The Affymetrix chips are single channel chips. The RNA is labeled using the same dye. The comparison between different samples is done by using several chips. The chip with the hybridized solution is then scanned on the wavelength of the dye. Analysis starts by exploiting the scanner image. An approximate level of hybridization for every probe is inferred from this image.

Prepr ocessing

S teps

In order to analyze and evaluate GeneChip data from an experiment with multiple arrays, the data preprocessing at probe-level is a crucial step. All of the methods have to account for two major disturbing factors, the background signal and the variance of the measurements resulting in noisy data. The composition of the gene signal is not yet completely understood, although several groups develop mathematical models. The use of the models is two-fold, on the one hand the signal can be understood with its disturbance factors and on the other hand the model is applied to correct the measured signal. One effect of the missing understanding is the underestimation of the fold change between two samples. An expression level value is calculated using a four-step procedure, as shown in Figure 2. (1) ‘Background correction’, which removes the unspecific background intensities of the scanner images; (2) ‘normalization’, which reduces the undesired non-biological differences between chips and corrects the signal intensity of the arrays; (3) ‘PM correction’, which removes non-specific signal contributions such as unspecific binding or cross-hybridization from the PM probes by the use of the MM and (4) ‘summarization’, which combines the multiple preprocessed probe intensities into a single gene expression value.

Figure 2. Preprocessing pipeline for Affymetrix GeneChip in BioConductor. Back­ground correction, normalization and PM correction are optional, whereas summarization is a mandatory processing step.

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Errors introduced in one of these steps may corrupt further processing, e.g. spurious correlation with target conditions may appear especially in few tissue samples (arrays) and large number of genes. Most of the methods focus on perfect matches and ignore the mismatch information. Various methods are proposed for preprocessing probe-level data and are the subject of the following sections.

B ackgr ound c orrecti

on Meth ods

The background signal consists of an optical background and a chemical background. The optical background introduced by the scanning of the chip derives from the technical range of the scanning device eventually supplemented by the overshining of the neighboring spots not corrected by the image analysis. The chemical background is explained by the gene signal consisting of gene specific binding and non-specific binding. The gene specific binding is the goal of all the models and normalization methods. The non-specific binding, also called cross-hybridization, is the RNA from other genes and different RNA snippets. Non-specific binding has shorter binding times at the probes and is fortunately much lower than gene specific binding. The background signal differs from probe to probe and thus general estimates for all of the probes have had little success. Recent developments hint at the content of the probe sequence as the main disturbing factor. A higher GC content is associated with a higher binding affinity due to three instead of two covalent bindings for a single nucleotide. The higher affinity leads to higher hybridization values and bigger variance. In ideal circumstances a probe detects the amount of a probe-specific labeled RNA sequence, but actually the measured probe intensity is a mixture of two signals: a probe-specific signal that contains the abundance of hybridized RNA and a non-specific background signal that obscures the observation. To separate these signals one can choose from two methods: 1.

2.

The RMA convolution model, which models the observed probe intensity as the sum of an exponentially distributed signal and a Gaussian distributed background component (Bolstad, Irizarry, Astrand, & Speed, 2003; Irizarry, Hobbs et al., 2003). It is worth noting, that RMA background correction can be improved through correcting probe values for the GC content in the probe sequence. This improvement leads to a method called GCRMA (Wu, Irizarry, Gentleman, Murillo, & Spencer, 2004). The Affymetrix’s MAS 5.0 algorithm, where the chip is partitioned into 16 equally sized segments. For each segment a background is estimated using the lowest 2% probe intensities of each segment. Then each probe value is adjusted based upon a weighted average of each of the background values. Here, the weights depend on the Euclidean distances from a particular probe to the centers of all segments (Affymetrix, 2002).

No rma liza ti on Meth ods Normalization is the process of removing unwanted chip effects that might bias all measured raw probe level data in the similar matter. This bias is introduced during RNA extraction, pipetting, temperature fluctuations, hybridization efficiency and many other sources of variation. (Hochreiter, Clevert, & Obermayer, 2006) discussed these possible sources in more detail. In the following sections we shall

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distinguish between model-based and baseline-based approaches. Model-based methods have made use of information from across all arrays to normalize the probe level data whilst baseline-methods select only one array in the batch as reference, and then normalize all array to that particular one. Affymetrix for instance, proposed to normalize arrays by choosing one baseline array and then to scale all the other arrays to have the same mean intensity as this array. For model-based methods cyclic loess and quantile normalization both serve as examples. The cyclic loess normalization (Yang et al., 2002) is derived from the basic principle behind the MvA-plot, where M is the difference in log expression and A is the average of the log expression values. Ideally, the points of an MvA-plot for normalized data should be centered on M = 0 i.e. the loess curve of that points should be a straight line lying on the A-axis. The rationale of the loess normalization is to project the loess curve onto the A-axis. Given two arrays with probe intensities xi, Mi = log2(xi1/xi2) and Ai = 12 log 2 ( xi1 xi 2 ) are determinated, and then a normalization curve is fitted to the resulting MvAplot using a local regression method called loess. These fits are Mˆ i and M i′ = M i − Mˆ i thus obtain the A +M ′ /2 A +M ′ /2 normalization adjustment. Transforming x1′i = 2 i1 i1 and x2′ i = 2 i 2 i 2 back to linear scale leads to normalized probes intensities of both arrays. (Bolstad, Irizarry, Astrand, & Speed, 2003) proposed to align the distribution of the arrays with an empirical distribution. To determine the empirical distribution, quantile normalization first sorts the intensities for each array and then computes the mean over the arrays for each sorted intensity position. The intensities of each array are then set to the mean value of the according position in the unsorted array. This leads to the fact that all arrays possess the intensity values but for different genes and different positions within a probe set.

Perfect

Match Co rrecti

on Meth ods

Affymetrix GeneChip arrays are so dense, that any non-specific signal contribution such as unspecific binding or cross-hybridization has to be estimated from the probe level data. Therefore, Affymetrix originally adjusted the signal intensity of a PM probe by subtracting the intensity value of the corresponding MM probe. But in (Naef, Hacker, Patil, & Magnasco, 2002) replicate experiments on different arrays were made and the PM values as well as the PM – MM values were analyzed. The authors found that the PM values (PM) have lower noise at low intensity than PM minus MM (PM – MM) whereas for intermediate and high intensities the noise levels for PM and PM – MM were similar. Therefore, recent approaches made use only of PM probes. Affymetrix indirectly supports this aspect due to the retirement of the MM probes in many products. Therefore we shall not address that issue in further detail.

Su mmariza ti on Meth ods In order to establish a single expression value for a gene that is assessed on the array, it is necessary to combine together all intensity values of each of the probes in the corresponding probe set to one value. To tackle this problem several methods have been proposed. In principle it is important to distinguish between single- and multi-array approaches: Single-array methods only use probe level information on an individual array to calculate the expression value (Li & Wong, 2001). Therefore, the calculations are carried out individually chip-by-

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chip, one consequence is that no information from other chips is available to robustify the expression value. For instance Affymetrix suggested in their Microarray Suite 5.0 (MAS 5.0) to apply a one-step Tukey’s Bi-Weight, on the log2 transformed probe level data, to give an expression value. In particular, the algorithm computes a distance measure: dij =

log 2 (PM ij )− M cS +



(1)

where M is the calculated median of the probe level data and S is the median absolute deviation. In addition, c is a constant defaulting to 5 and ε > 0 prevents division by zero. In consideration of dij weight for every data point is calculated from:

(1 − d 2 ) 2 , d ≤ 1 w(d ) =  , d > 1 0

(1.1)

In contrast to the preceding approach, multi-array methods combine the multiple preprocessed probe intensities into a single expression by taking probe information across arrays into account. This is motivated by examining probe patterns across the arrays; Which commonly show that the variability of a single probe across multiple arrays is smaller than the variability between probes of the same probe set. Therefore (Irizarry, Bolstad et al., 2003) proposed to fit a linear additive model through a median polish. This summarization approach is the part of the RMA preprocessing pipeline. As mentioned above, perfect match intensities were modelled by: log 2 ( PM ij ) =

+

i

+

j

+ ij

(2)

where PMij is the intensity matrix of a particular probe set such that j subscripts the probes and i indicates the arrays. Moreover βj descript the probe affinity effect and μ + αi provide an estimation of the log2 expression level. To estimate the parameters, the median polish algorithm is applied. The lack of a standard error estimate is one drawback to this approach. The core of the FARMS algorithm is a factor analysis – a multivariate technique to detect a common structure in the data of multiple probes that measure the same target. The assumption is that the probe intensity measurements of the perfect matches x depend on the true RNA concentration z via: x = λz + ε

(3)

with λ being the loadings for the factor analysis (Hochreiter et al., 2006). In equation (3), a N(0, 1)-distributed z models the common factor in the data x, while the N(0, ψ)-distributed ε models the independent noise in each probe of each array. In essence, model (3) is explaining the observed covariance structure of the data x by representing the data as being N(0, λλT + ψ)-distributed with an individual noise variance ψ and signal variance λλT and is optimized by Bayesian maximum a posteriori estimation. In contrast to other summarization techniques, FARMS provides an unsupervised feature selection criterion that is based on the reliability of the extracted factor. Here, only such probe sets are considered where the model can reliably detect a variation of the latent variable z. (Talloen et al., 2007) discussed the concept and applicability of informative/non-informative calls (I/NI-calls) approach in more detail.

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The Affymetrix GeneChip® Microarray Platform

Va lida ti on R es ources The lack of objective criteria to assess competing preprocessing methods motivated (Cope, Irizarry, Jaffee, Wu, & Speed, 2004; Irizarry, Wu, & Jaffee, 2006) to develop a collection of assessment criteria called ‘Affycomp II’ for the evaluation and comparison of expression measures on the Affymetrix GeneChip platform. Furthermore a web-tool made available at http://affycomp.biostat.jhsph.edu for developers to benchmark their procedures and to help users identify the best method for their application. Here, the benchmark data is crucial. Therefore (Cope et al., 2004) used three well-known evaluation datasets, which were produced by controlled experiments with known target expression values or known mutual relations. The control of input in spike-in and dilution experiments makes it possible to identify features of the data for which the expected outcome is known in advance. Based on this knowledge 17 assessment criteria and several related plots were developed. Nevertheless, we think that from all benchmark criteria the area under the curve (AUC) criterion is best suited to measure the quality of a preprocessing method. The AUC criterion is the area under the receiver operating characteristics (ROC) curve, which plots the true positive rate (sensitivity) against the false positive rate (1–specificity) and serves as a quality measure for classification methods. The AUC criterion can be applied here by defining gene classes: for a pair of arrays class 1 genes are the genes for which expression value differences exceed a certain relative factor (fold change). Now the output of a summarization method can be interpreted as classification by computing the class membership of genes based on the predicted expression values. We prefer the AUC criterion over other measures provided by ‘Affycomp II’ evaluation because it is independent of scaling of the results (log-expression values) and trades sensitivity against specificity. Other quality measures from the ‘Affycomp II’ evaluation, like slope parameter estimation, are often not scaling independent.

Alterna ti ve Pr obe- G ene A ssignments Affymetrix delivers an assignment of probe sequences to probe sets. The number of probes in a probe set is fixed for all probe sets on the chip. Quarterly the probe sets are reannotated to genes and transcripts. In recent time it has come up, that the probe sets do not have to be fixed but the probes themselves can be reattached to probe sets and new assignments have been published (Dai et al., 2005). The alternative assignments have several advantages. The advancement of the sequence databases leads to altered gene sequence. If the probe sequence is not contained in the gene sequence anymore, the probe does not need to be processed. Its signal introduces noise. Also extensive libraries for single nucleotide polymorphisms (SNPs) are meanwhile available. The probe is skipped also if a single nucleotide polymorphism hits the probe sequence. The assignment can be done with a specific sequence database in mind. This eases the path of analysis as the probe sets provide another abstract level between the hybridization values and the gene expression. A drawback of the reassignment is, that there is no fixed number of probes in the probe set anymore. The idea of reassignment leads us to the issue of evaluating its use. On a set of chips from the Human Genome U133 Plus 2.0 arrays we compared two assignments. The Affymetrix assignment and the assignment to Ensembl genes (Birney et al., 2006; Dai et al., 2005). The first discovery is, that one fourth of the probes on the chip is skipped for the reasons given above. For the same set of chips the preprocessing has been executed using two assignments. The two results refer mostly the same genes to be expressed. But one fourth of the genes can be seen to be differentially expressed between the two assignments! The different number of probes in probe set does not lead to 257

The Affymetrix GeneChip® Microarray Platform

a dependency between variation and probe set size. The Kendall correlation between the coefficient of variation and probe set size is –0.06. The mean shows a tendency to high expression for small probe set size. We also processed a set of treatment and control chips with the two assignments and compared the resulting list of differentially expressed genes. The two lists overlap to about 50%. This again shows a major influence of the assignment on the analysis results. From the above considerations we conclude, that the use of alternative probe-gene assignments is recommendable. The new assignments lead to reduced variation and thus reduced noise in the expression values, likewise they improve the sensitivity and specificity of the algorithms and results.

Medica l Use The research or scientific use of microarrays is mostly the comparison of diseased and normal tissue to identify differentially expressed genes. In cases with sufficient disease samples clustering and classification methods can be used to dissect different disease traits. The dissection facilitates the distinction of research results and identifies different causes and developments. Defining expression signatures for the subtraits of an affliction leads into diagnosis of the respective disease traits. Currently there is no chip for diagnostics on the market. But projects are running to push first products towards an admission. With the exact disease trait diagnosed the treatment is optimised using the best possible medicine administered in an adequate dose. Systems biology uses microarrays at several stages of model building (Klipp, Herwig, Kowald, Wierling, & Lehrach, 2005). Genes with altered expression are the basis to develop physiological models. Hybridization results estimate the model parameters and verify model predictions.

Figure 3. On the left hand side are the expression of probe sets for the same target gene for two different assignments compared. On the right hand side we see the variation versus the probe set size.

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The Affymetrix GeneChip® Microarray Platform

E xperiment a l set up Due to the noisy data microarray results always have to be verified. In the lab this is done with complementary RT-PCR experiments for selected genes. In the office, look at the consistency with other published data, although this consistency is often low. The amount of verification is alleviated by the use of statistics in the analysis of the hybridization results. But a solid statistical analysis requires replicates. Normally this is not an issue in industries but in academic laboratories. In technical replicates the same sample is used on several chips and in biological replicates samples from different patients or animals are hybridized each on a single chip. The use of biological replicates is strongly recommended. The following numbers have established by experience: • • • •

Cell culture: 2-3 replicates Animal system: 4-5 replicates Human system: 5-6 replicates Time courses: 4-6 time points with 2 replicates each time point

These numbers imply that it is wise to consult a statistician at the early stage of experiment planning to ensure a reasonable statistical set-up. In the US the MicroArray Quality Control (MAQC) project has started to check for inter- and intraplatform reproducibility of gene expression measurements (Shi et al., 2006). The preprocessing problems raised concerns about the reliability of this technology. The MAQC was initiated to address these among other issues. The study is an important first step pushing microarrays towards clinical and regulatory settings. The experimental setup is described in (Shi et al., 2006). Microarray products from different manufacturers are compared. Affymetrix is presented with a very high reproducibility in- and across test sites with low variance in measurements.

Out look on T echn ologica l A d vances In this chapter we described the established series of gene expression chips from Affymetrix. New chip designs are ahead. A direct enhancement of gene expression chips are exon arrays. They comprise probe sets for every exon. Thus the expression can be dissected into the single transcripts and identify alternative splicing. By collecting the probe sets in so called meta probe sets the gene expression is still included. SNP chips are useful in the help of genotyping with microarrays, avoiding expensive sequencing approaches. On tiling arrays the probes are equidistantly distributed on the genome sequence identifying expression of sequences independent from the gene structure. Because of the equidistant selection of probe sequences not all probe sequences are unique introducing new analysis challenges. Most of the genome is never expressed thus most probes on a tiling array do not return a signal. By now no tiling array is large enough to cover the whole genome. Presenting the different chip designs it must be remarked, that the methods and analysis approaches presented in this chapter are not directly transferable to the new designs. Different biological questions and use of the chips need different processing.

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R eferences Affymetrix. (2002). Algorithms description document. Birney, E., Andrews, D., Caccamo, M., Chen, Y., Clarke, L., Coates, G., et al. (2006). Ensembl 2006. Nucleic Acids Res, 34(Database issue), D556-561. Bolstad, B. M., Irizarry, R. A., Astrand, M., & Speed, T. P. (2003). A comparison of normalization methods for high density oligonucleotide array data based on variance and bias. Bioinformatics, 19(2), 185-193. Cope, L. M., Irizarry, R. A., Jaffee, H. A., Wu, Z., & Speed, T. P. (2004). A benchmark for Affymetrix GeneChip expression measures. Bioinformatics, 20(3), 323-331. Dai, M., Wang, P., Boyd, A. D., Kostov, G., Athey, B., Jones, E. G., et al. (2005). Evolving gene/transcript definitions significantly alter the interpretation of GeneChip data. Nucleic Acids Res, 33(20), e175. Gentleman, R. C., Carey, V. J., Bates, D. M., Bolstad, B., Dettling, M., Dudoit, S., et al. (2004). Bioconductor: Open software development for computational biology and bioinformatics. Genome Biology, 5, R80. Hochreiter, S., Clevert, D. A., & Obermayer, K. (2006). A new summarization method for Affymetrix probe level data. Bioinformatics, 22(8), 943-949. Irizarry, R. A., Bolstad, B. M., Collin, F., Cope, L. M., Hobbs, B., & Speed, T. P. (2003). Summaries of Affymetrix GeneChip probe level data. Nucleic Acids Research, 31(4), e15. Irizarry, R. A., Hobbs, B., Collin, F., Beazer-Barclay, Y. D., Antonellis, K. J., Scherf, U., et al. (2003). Exploration, normalization, and summaries of high density oligonucleotide array probe level data. Biostatistics, 4(2), 249-264. Irizarry, R. A., Wu, Z., & Jaffee, H. A. (2006). Comparison of Affymetrix GeneChip expression measures. Bioinformatics, 22(7), 789-794. Klipp, E., Herwig, R., Kowald, A., Wierling, C., & Lehrach, H. (2005). Systems Biology in Practice. Wiley-VCH. Li, C., & Wong, W. H. (2001). Model-based analysis of oligonucleotide arrays: expression index computation and outlier detection. Proc Natl Acad Sci USA, 98(1), 31-36. Naef, F., Hacker, C. R., Patil, N., & Magnasco, M. (2002). Empirical characterization of the expression ratio noise structure in high-density oligonucleotide arrays. Genome Biol, 3(4), RESEARCH0018. R Development Core Team. (2005). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Shi, L., Reid, L. H., Jones, W. D., Shippy, R., Warrington, J. A., Baker, S. C., et al. (2006). The MicroArray quality control (MAQC) project shows inter and intraplatform reproducibility of gene expression measurements. Nat Biotechnol, 24(9), 1151-1161.

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Talloen, W., Clevert, D. A., Hochreiter, S., Amaratunga, D., Bijnens, L., Kass, S., et al. (2007). I/NIcalls for the exclusion of non-informative genes: A highly effective filtering tool for microarray data. Bioinformatics, 23(21), 2897-2902. Wu, Z., Irizarry, R. A., Gentleman, R., Murillo, F. M., & Spencer, F. (2004). A model-based background adjustment for oligonucleotide expression arrays. Journal of the American Statistical Association, 99(468), 909-917(909). Yang, Y. H., Dudoit, S., Luu, P., Lin, D. M., Peng, V., Ngai, J., et al. (2002). Normalization for cDNA microarray data: A robust composite method addressing single and multiple slide systematic variation. Nucleic Acids Research, 30(4), e15.

K ey T erms FARMS: Factor Analysis for Robust Microarray Summarization, a probabilistic latent variable model for summarizing high-density oligonucleotide Affymetrix GeneChip array data at probe level. Gene Expression: Gene expression is the process by which the inheritable information in a gene, such as the DNA sequence, is made into a functional gene product, such as protein or RNA. Microarray: A microarray (also known as gene chip or DNA chip) is a collection of microscopic DNA spots, commonly representing sequence extracts of single genes, arrayed on a solid surface by covalent attachment to a chemical matrix. DNA arrays are commonly used for expression profiling, i.e., monitoring expression levels of thousands of genes simultaneously, or for comparative genomic hybridization. MM: Mismatch, a probe accompanying a PM, where the 13th nucleotide is changed to its complement (A to T, T to A, G to C, C to G). In the Affymetrix GeneChip design MM are spotted along with the PM aiming to measure the non-specific hybridization to the PM. PM: Perfect match, a probe with the true sequence complement of the targeted sequence. Probe: A probe is a fragment of DNA of 25 nucleotides/basepairs length, which is used to detect in RNA samples the presence of nucleotide sequences (the DNA target) that are complementary to the sequence in the probe. The probe thereby hybridizes to single-stranded nucleic acid (DNA or RNA) the base sequence of which allows probe-target base pairing due to complementarity between the probe and target. Probe Set: a set consisting of all probes addressing the transcripts from the same gene. In the Affymetrix GeneChip design the expression level of a gene shall be measured with several probes.

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Chapter XV

Alternative Isoform Detection Using Exon Arrays Jacek Majewski McGill University and Genome Québec Innovation Centre, Canada David Benovoy McGill University and Genome Québec Innovation Centre, Canada Tony Kwan McGill University and Genome Québec Innovation Centre, Canada

abstract Eukaryotic genes have the ability to produce several distinct products from a single genomic locus. Recent developments in microarray technology allow monitoring of such isoform variation at a genome-wide scale. In our research, we have used Affymetrix Exon Arrays to detect variation in alternative splicing, initiation of transcription, and polyadenylation among humans. We demonstrated that such variation is common in human populations and has an underlying genetic component. Here, we use our study to illustrate the use of Exon Arrays to detect alternative isoforms, to outline the analysis involved, and to point out potential problems that may be encountered by researchers using this technology.

INTR OD UCTI ON Alternative pre-mRNA splicing is a process allowing the production of several distinct gene isoforms from a single genomic locus. The most common type of alternative splicing events in mammals results in cassette exons, where each such exon can be either included or excluded from the mature mRNA. Other events include alternative use of donor or acceptor splice sites, and intron retention. In addition, processes such as alternative promoter usage and alternative polyadenylation, resulting in differences in initiation and termination of the transcript, respectively, further diversify eukaryotic transcriptomes and proteomes. Such processes have been suggested to be at least partly responsible for mammalian Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Alternative Isoform Detection Using Exon Arrays

complexity, which is otherwise difficult to explain in view of our relatively low number of genomic loci - less than 25,000 genes in humans, versus approximately 20,000 in the nematode worm C. elegans (Claverie, 2001). It is estimated that a high percentage of mammalian genes is alternatively spliced, and this frequency is highest in specialized and complex tissues, such as the brain and the liver. Differences in splicing patterns have been shown to exist across species, and within populations of the same species. In humans, splicing defects are known to result in numerous genetic disorders (Faustino & Cooper, 2003) and may confer susceptibility to complex genetic diseases. Thus, the process of alternative splicing attracts the interest of researchers across the entire biomedical sciences spectrum, ranging from evolutionary biology, through development, to medicine. In recent years, alternative transcript investigation in a genome-wide context has been carried out using expressed sequence tag libraries (ESTs). Generally, ESTs (short cDNA sequence reads) are mapped to the genomic sequence, and different isoforms can be inferred from incongruence of splicing patterns (Modrek, Resch, Grasso, & Lee, 2001). However, EST library analyses are prone to sequencing errors, biased towards highly expressed genes, and influenced by cancer-derived ESTs, which may not generally be present in healthy tissues. More recently, microarray platforms have been proposed as a tool for studying gene expression at the isoform level (Black & Graveley, 2006; Lee & Roy, 2004; Zhang et al., 2006). Splicing sensitive microarrays employ a number of exon body oligonucleotide probes, or exon junction probes, or a combination of the two designs, to determine mRNA levels at the resolution of a single exon or splice site. The Affymetrix GeneChip® Human Exon 1.0 ST Array is the first commercially available microarray product designed for genome-wide, exon level expression analysis. The array relies on targeting multiple probes to individual exons and allows simultaneous, exon-level detection of expression intensity for 1.4 million probesets covering over 1 million known and predicted human exons. The Exon Array is a flexible tool, which can be used to perform the function of classical expression arrays and concurrently provide supplementary information on isoform changes. However, because of the complexity of the design, statistical analysis of the data becomes much more intensive, both at the theoretical and computational level. The simplest illustration is the multiple testing problem; whereas in classical expression arrays the number of tests is of the order of the number of genes, in an exon array, the number of tests is over ten-fold higher – and can vary between a few hundred thousand to over 1 million (if computationally predicted exons are included). The statistical approaches need to be able to distinguish between whole gene expression differences and isoform differences, which introduces a new level of complexity. The robustness of measurement is also an issue, since the exon array has on average four probes per probeset, whereas Affymetrix expression arrays relied on more than 10 probes per probeset to estimate expression. In our lab, we have used the Exon Arrays, to investigate differences in splicing patterns among humans. We were able to demonstrate the existence of common variation in splicing, polyadenylation sites, transcription initiation. We also demonstrated genetic linkage and allelic association of the isoform variation to common genetic single nucleotide polymorphisms (SNPs). Our results show that the effects of genetic variants on gene expression are much more complex than previously believed, and constitute an important step towards understanding the functional consequences of such variation. In this chapter, we will use our experiments as a case study, in order to outline the flow of the analysis required to process Exon Arrays. We will also outline problems which may be encountered by potential users of the chips, and describe solutions which we have developed to overcome such problems. We will discuss current advances in statistical analysis and propose future improvements to optimize both the array design and statistical solutions. 263

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MICR OARRAY DESIGN The Exon Array relies on patented Affymetrix technology to provide 5.4 million 25-mer oligonucleotide probes on a single chip. Probes target individual exons, or portions of an exon when prior evidence of alternative splicing exists. Each such potential “splicing unit” is represented by at least one probeset, and each probeset consists, on average, of four individual probes (Figure 1). It should be noted that because of the small size of some exons and limitations in probe placements, many probes within a probeset are overlapping and thus not independent. The array annotation consists of 3 levels: core, extended, and full. The core probesets represent the highest level of annotation confidence; they are supported by RefSeq and GenBank evidence. There are 284,000 core probesets on the array. The extended and full annotations represent less confidently annotated exons, with support from ESTs and comparative genomics, but also de novo gene prediction algorithms. In total there are over 1.4 million probesets interrogating approximately 1 million known and predicted exons. While the extended and full gene annotations have the potential to identify novel exons and transcript variants (Siepel et al., 2007), we expect that most studies will concentrate on the high confidence core annotations. This will greatly limit false positive discovery rates and allow labs to fine-tune their analysis techniques. We recommend that the non-core probesets only be considered by more experienced researchers or in case of follow up analyses targeted to specific transcripts. One significant departure from earlier Affymetrix designs is the absence of mismatch probes. Mismatch probes have previously been used to estimate background hybridization noise levels. Instead, the Exon Array uses a large number of “antigenomic” probes, which do not have a match anywhere in the genome and ideally represent a null signal. Antigenomic probes are grouped by their GC content and used to produce a Detection Above Background (DABG) p-value. A p-value below 0.05 may be used as an indication that a given probe, probeset, or metaprobeset is expressed. It is important to note that, while the Exon Array design targets the entire genome, certain splicing changes are virtually impossible to detect using a purely exon-targeted approach. As an example, if a minor (rare) isoform of a transcript skips a certain exon, even large (several fold) increases in the level of that isoform may not significantly impact the overall mRNA levels of the exon. Such splicing variants would be much more efficiently detected using “junction-arrays” which target their probes to specific exon-exon junctions. However, junction arrays can only target a limited number of junctions (because of the high number of possible combinations) and cannot monitor every hypothetical alternative splicing event. Thus, in order to target every known or predicted exon in the genome, the Exon Array sacrifices sensitivity to certain types of rare isoform changes.

ST UDY DESIGN Genetically controlled variation in gene expression has recently been shown to be common in human populations, and it is believed to be responsible for phenotypic variability and susceptibility to complex diseases (Cheung et al., 2005; Spielman et al., 2007; Stranger et al., 2005). We have a much poorer understanding of the variability at the level of specific transcript isoforms, such as differences in transcription initiation, splicing, and polyadenylation. Despite isolated examples of such differences, to date, no genome-wide studies have been carried out to determine their prevalence and potential impact. We designed a pilot experiment, to investigate the effectiveness of the Exon Array in detecting splicing

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Figure 1. A. Schematic for coverage of probesets across the entire length of the transcript. Light regions correspond to exons, whereas dark regions represent introns. The short dashes underneath the exon regions indicate individual probes of 25 nucleotides in length representing the probeset. B. Flow chart for processing and analysis of chips to validation of alternative splicing events. Total RNA is extracted from the two cell lines (n=15 replicates per individual) and is transcribed to cDNA and labelled with biotin. The total cDNA is then hybridized to the exon chip, followed by washing and staining with an anti-streptavidin antibody. Chips are then scanned and hybridization data is processed and analyzed by the Affymetrix Power Tools software package. A splicing index is calculated and candidate statistically significant differential splicing events are selected using an unpaired t-test. A subset of alternative splicing events predicted between the two are then validated by: 1) reverse transcriptase-polymerase chain reaction (RT-PCR) using exon body primers flanking the probeset of interest; and 2) sequencing of the RT-PCR products (reprinted from Kwan et al., 2007).

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differences among humans by comparing RNA extracted from lymphoblastoid cell lines of two different individuals, and further observing inheritance of the splicing patterns within their families. For the continuation of this study, we used cell lines from 60 unrelated individuals of Northern European descent that have been earlier genotyped for approximately 4 million SNPs by the International HapMap Project (Altshuler et al., 2005). Each cell line was grown in triplicate, in order to minimize stochastic effects of cell growth conditions. RNA was isolated from the cells using standard protocols, and the three “biological replicates” for each individual were used for hybridization. Since all genotypes were already known, we were then able to use the resulting exon-level expression measurement as a quantitative phenotype, and carry out allelic association analysis. Briefly, at each genetic marker the genotypes were coded as 0, 1 or 2, with the heterozygous genotype always given the value of 1. The quantitative phenotype was then regressed on the genotype, and statistical significance and magnitude of the genetic effect were estimated from the regression analysis (Figure 4).

ANA LYSIS All of our microarrays were hybridized and scanned at the Micorarray Platform at McGill University and Genome Quebec Innovation Centre. We used standard protocols, with an enhanced RiboMinus treatment step to improve the reduction of ribosomal RNA. The raw hybridization intensity data was obtained in the form of .cel files. These files can be analyzed using most available microarray software. In our study, we used the Affymetrix Power Tools software package (Affymetrix). The general quality control procedures, such as visual inspection and multivariate analyses aimed at outlier detection (e.g. PCA plots), are common to all microarray analyses and will not be described in detail. Any defective or suspected outlier arrays should be removed from further analyses. The first step of subsequent statistical analysis consists of “normalization”. This step attempts to control for the “chip effect”, which may be caused by slight differences in RNA hybridized to each array or differences across production batches of arrays (if possible, these should be avoided before setting up the experiment). We use the quantile normalization method (Irizarry et al., 2003), which assumes that the distribution of signal intensities across all arrays should be identical. Normalized probe intensities are then “summarized” into a single measurement. Again, this can be carried out using established techniques developed for general microarray use, such as RMA (Irizarry et al., 2003) or PLIER (Affymetrix). However, it is at this stage that the analysis of Exon Arrays acquires its own flavour. The exon array data is summarized at two levels: the probeset level (roughly corresponding to the expression of each exon), and the metaprobeset level (corresponding to an entire transcript). The probeset level signal is obtained by combining an average of four probes per exon. Hence, this signal may be quite noisy. The metaprobeset signal combines the data from all exons within a gene and is thus more robust. However, alternative splicing within a gene may affect the metaprobeset summary and result in erroneous differences in transcription level estimates. This is particularly true for genes with few exons. Both PLIER and RMA claim robustness with respect to rare aberrant signal – e.g. caused by unresponsive of cross-hybridizing probes, or rare alternative exons – and currently we do not filter out such probes. However, to further improve the analysis, algorithms have been suggested to pre-filter inconsistent probes before the summarization step (Xing, Kapur, & Wong, 2006). As a principle, we recommend log-transforming all summary expression levels in order to stabilize the variance.

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One of the biggest challenges in detection of alternative splicing using Exon Arrays is the deconvolution of splicing and transcription. A simple comparison of probeset intensities across samples is not sufficient; if an exon belongs to a transcript that is differentially expressed, the examination of a single exon out of its genomic context will lead to an incorrect conclusion. A very simple and intuitive solution to this problem is the use of the Splicing Index (SI), which is calculated by simply dividing the probeset intensity by the metaprobeset intensity (i.e. exon expression/gene expression), after the addition of a stabilization constant to both the probeset and metaprobeset scores. This simple procedure normalizes the expression level of each exon and accounts for any possible gene expression differences between samples. However, we find that the splicing index has some undesirable statistical properties (arising from large errors in the estimates in both the numerator and the denominator) as well as being prone to methodological artefacts, and should be used with caution. Thus, we have also used a simpler, but more labour intensive method, of carrying out the entire analysis at the probeset level, and relying on visualization and manual curation of the results in order to distinguish splicing and expression differences between samples. While more robust statistical approaches are being developed, we strongly advocate visualization of results in the context of genome annotation and EST evidence in order to filter out false positive signals. We have relied on custom scripts and modifications of the UCSC and ENSEMBL genome browsers, but commercial packages for the Exon Arrays are also available (e.g. Partek Genomics Suite).

RES ULTS T wo S ample C omparison This is the simplest microarray study design. Generally, the two samples may correspond to two different tissues, healthy and affected, or treated and untreated material. In our pilot study, we used RNA extracted from two cell lines originating from two different individuals (Kwan et al., 2007). To analyze splicing differences between the two samples, an unpaired Student’s t-test was performed using the logtransformed SI values of each probeset for 15 replicates (3 biological replicates x 5 technical replicates) of each individual (R statistical package, version 2.3.0). Probesets showing significantly different SI scores were ranked by p-value or fold-change. During the course of the data analysis, we discovered that many pre-processing steps needed to be performed on the SI results, in order to limit false positive rates.

Effect of SNPs We found the primary source of false positives to be the effect of SNPs on probe hybridization levels (Figure 2). A single mismatch in a cDNA sequence can totally prevent the hybridization of the cDNA to its probe (Alberts et al., 2007). Since each probeset consists of only four probes, and a SNP can affect all four overlapping probes in some of the probesets, the final effect of SNPs on genetically heterogeneous samples is substantial. We discovered that the most statistically significant candidate exons were highly enriched in SNP-containing, overlapping probes. A vast majority of those candidates could not be validated using RT-PCR. This effect was easy to verify in our dataset, since the HapMap samples have been thoroughly genotyped and in most cases the mismatch substrate is known before hand, but this may not be the case in many other studies. In our analysis, we conservatively masked (removed

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Figure 2. The effect of SNPs of probe hybridization leads to false positive results. A. The box plots show differences in expression between 4 probes belonging to probeset 2748252. The probe sequences and relative positions are shown under the plots. Two overlapping probes are affected by a single SNP, rs11549015, and show highly statistically significant reduction in intensity in the individual carrying the mismatch allele. B. The probeset 2748252 appears as differentially included in the transcripts of the two individuals (left panel). However, this effect disappears after masking the probes overlapping the SNP (right panel).

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from the analysis) all probes containing known SNPs. While this procedure led to a slight reduction of the available data, it drastically reduced false positive rates. We recommend that this procedure should be followed in experimental setups where samples are genetically heterogeneous (e.g. cancer patients). However, the presence of SNPs should not be a problem in cases where different tissues from the same patient or pooled RNA samples are being studied.

Dataset Reduction In order to reduce the amount of random noise, and decrease the number of tests being carried out, it is useful to exclude all genes which are either not expressed in all of the samples, or more than one of the samples being compared. Such genes, by definition cannot be alternatively spliced across samples. There is currently no reliable procedure on deciding whether a gene is expressed or not, and Affymetrix recommends using an ad hoc expression value of 15, and some additional filters using DABG values of individual exons.

Effect of “Dead” Probesets A probeset which is not expressed – e.g. an exon which is skipped – in all samples under investigation may produce a false positive signal in the splicing index, in the presence of transcript-level variation. All non-responsibe probesets should be removed from the analysis. A DABG-based criterion may be used here, e.g. DABG p-value < 0.05 in at least 50% of the samples.

Additional Filtering Steps Based on the experience of our group and many other researchers using the Exon Arrays, Affymetrix now recommends a number of data filtering steps, which can be found at the company website (www. affymetrix.com).

Splicing Differences We applied three different methods for multiple testing correction. The Bonferroni correction, obtained by dividing the nominal p=0.05 threshold by the total number of probesets yields the most conservative cut-off (p-value=3.159e-7), yielding 1892 candidate probesets (1.2% of expressed ‘core’ probesets) showing differential splicing between the two samples. The false discovery rate (FDR) (Storey & Tibshirani, 2003) at a 0.01 significance level provided the least conservative estimate (p-value=8.915e-4) with 8771 (5.7%) potential splicing events. We also used an empirical null distribution of p-values from the observed data, by shuffling the SI scores for all samples of each probeset (Churchill & Doerge, 1994). At the p=0.05 level, this method estimates 4020 (2.6%) differentially spliced probesets between the two individuals. A small subset of 20 candidates was subjected to validation by RT-PCR using a pair of primers in distinct exons flanking the predicted differential splicing events. We were able to confirm alternative isoforms for 9 of the transcripts, which translates into a 45% validation rate. However, our study evaluates the ability of this microarray technology to identify alternative AS events de novo in genetically diverse populations. Restricting our candidates to those showing EST and cDNA evidence of alterna-

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tive splicing in sequence databases reduces the number of cases from 20 to 12, thereby increasing our success rate to 60% (7 out of 12). As noted earlier, the Exon Array can be used as a de novo discovery platform for alternative splicing, or it can be targeted to the more confident, previously observed events, either by using only the core exons or further limiting the analysis to EST-supported alternative exons. If used as a discovery tool, the false discovery rates will invariably increase, but the benefit of detecting novel events may sometimes outweigh the cost. Judging by our experience, and the experience of other groups, the false positive rates of this platform will generally be non-negligible and may be of the order of 50%. We recommend thorough independent (PCR, Northern blot) validation of the most interesting results.

Heritability of Splicing Differences One of our hypotheses was that differences in splicing between individuals may be heritable, i.e. they have a genetic component. Hence, we carried out genetic linkage analysis within the family of the two tested individuals, using the SI of the 9 validated exons as a quantitative trait. We confirmed linkage to cis-acting SNPs (heritability) for three of the nine exons (Figure 3), and for two of them we were able to identify the SNPs affecting their extended splice-site consensus sequences.

Multiple S ample A nalysis Following the above pilot study, we carried out a full-scale investigation of splicing and isoform level variation in a human population, using cell lines from 60 unrelated CEU HapMap individuals (Kwan et al., 2008). This setup is illustrative of other designs often encountered in microarray experiments, where data subdivided into multiple classes is analyzed simultaneously. In contrast to the two-sample design, ANOVA or regression analysis is used instead of a t-test to detect differences among samples. In our case, we assumed an underlying co-dominant genetic model, where each SNP allele is associated with preferential expression of a distinct isoform. Hence, the heterozygous SNP genotype has an effect intermediate to the two homozygotes, and a linear regression approach is the logical choice (Figure 4). In this part of the study, we decided not to use the splicing index, but rather carry out the entire analysis at the probeset (exon) level. After the filtering steps outlined above, we identified all probesets exhibiting significant association between expression levels and cis-acting SNP genotype. The statistical cut-offs were established using permutation testing and a 0.05 FDR level. Cis-acting SNPs were defined by their proximity within 50kb of the probeset tested. We used a semi-automated classification method, to decide whether a significant association represented an alternative splicing, alternative transcription start, alternative polyadenylation, or whole transcript expression change. This was performed using a simple script which grouped all significant probesets together (in cases where they belonged to a single transcript), determined their location within the transcript (internal, 5’ or 3’) and tested whether the whole gene or just individual exons were significantly associated with the SNP genotype (expression or isoform difference). In addition, we examined all the candidate events by eye, in relation to their genomic context, EST, and mRNA evidence, in order to determine the final classification of isoform differences. Although this may seem like an ad hoc and laborious process, thorough visualization of 324 candidate genes obtained from this analysis was carried out in our lab in a matter of days. It is a relatively minor effort compared to the cost and labour required to set up most microarray studies, and we believe that

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Figure 3. Inheritance of alternative splicing for genes A. OAS1, B. CRTAP, and C. CAST. Left panel shows pedigree structure of CEPH/UTAH family 1444 with the autosomal dominant inherited splice pattern as blue symbols. Haplotypes for each of the eight founder chromosomes are labelled A, B, C, D, E, F, G, and H, and the two inherited haplotypes of each family member are indicated within the symbol. The regulatory haplotype is shown as bold white text. Squares represent males and circles represent females. The right panel shows the two transcript isoforms of the genes. Exon-body primers are shown above the flanking exons of the predicted alternatively spliced exons. Shown below the transcript isoforms are the RT-PCR results. Lanes are numbered from 1-14 according to the pedigree on the left (reprinted from Kwan et al., 2007).

it’s the most effective approach currently available to create a highly confident result set. Some examples of the observed variants are shown in Figure 5. Complete results of this study may be retrieved from our website (www.regulatorygenomics.org). In order to further limit false positives, we also sequenced in multiple individuals 83 candidate events which were supported by a single probeset, and where all

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Figure 4. Analysis steps from identification of a significant probeset in the PARP2 gene to validation. A. Linear regression analysis of expression scores for probeset 3527423 with genotypes of SNP rs4981998, giving a p-value of 2.81x10-30. B. Visualization of probeset 3527423 in the context of all other probesets belonging to the same transcript (metaprobeset 3527418). For each probeset, the significance level (p-value) is indicated by the grey line, along with fold change expression between the mean scores of the two homozygous genotypes (meanTT / meanCC) shown as vertical bars. The solid horizontal grey and black lines represent the significance and fold change expression for the regression analysis at the metaprobeset level against SNP rs4981998. Probeset 3527423 is indicated by an arrow. C. RT-PCR validation of probeset 3527423 using flanking exon-body primers. D. Schematic of 5’ end of two isoforms of PARP2 with Exon Array probesets shown below the exons. The significant probeset 3527423 corresponds to alternative 5’ splice site usage resulting in a larger 2nd exon for NM_005484 (reprinted from Kwan et al., 2008).

probes overlapped and could potentially be affected by a single SNP. As a result of this re-sequencing and discovery of previously un-annotated SNPs, we excluded 27 probesets from further analysis. Again, we proceeded to validate a subset (32) of our candidate events. Putative alternative splicing events were validated using a simple end-point RT-PCR, while promoter and poly-adenylation changes were tested using real time SYBR® Green PCR (Applied Biosystems, Foster City, CA, USA) RT-PCR. We successfully validated 25 of the 32 events. We consider the resulting validation rate (78%) to be extremely high for this type of study. However, this reflects the large amount of processing: statistical (filtering etc.), manual (visualization), and laboratory work (additional sequencing), which contributed to the final dataset.

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Figure 5. Examples of different types of transcript isoform events observed. Each plot corresponds to a transcript, and each data point to an individual probeset. A. Gene expression level changes of LRAP, including alternative splicing of a cassette exon. B. Differential 3’ UTR change of ARTS-1 resulting in long and short isoforms with alternative stop codon usage. C. Expression of two TCL6 transcript isoforms that contain different 5’ and 3’ ends. D. Increasing significance and fold change expression levels towards the 3’ end of the CCT2 gene, suggesting genetic variation associated with mRNA stability (reprinted from Kwan et al., 2008).

C ONC LUSI ON B iology Alternative splicing is rapidly being recognized as an important mechanism regulating numerous biological processes. Identification of alternative splicing and alternative isoform expression provides us with a new venue in understanding the diversity and the complexity of the human genome. Several recent studies have demonstrated the presence of variation in gene expression levels among humans. Furthermore, such variation has been shown to have a genetic basis. It is believed that these expression differences among individuals may be responsible for downstream phenotypic differences, including susceptibility to genetic disorders. In our research, we show that, in addition to gene expression level differences, a significant amount of variation affects the types of isoforms being expressed. This variation also has a strong genetic component, and hence, the effect of common genetic variation in humans is much more complex than previously believed. In fact, we show that the effect of SNPs on isoform expression (initiation, splicing, and termination), is at least as common as the effect on overall levels

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of gene expression. The downstream phenotypic effects are likely to be substantial; some associations with genetic disorders already exist, e.g. a 3’UTR variant of the IRF5 gene has recently been associated with susceptibility to lupus (Reddy et al., 2007). The full extent of the effects of isoform variants will be revealed in the near future.

T echnology Historically, our understanding of alternative splicing has been limited to individual laboratory experiments. Analysis of EST libraries provided the first glimpse into the genome-wide extent of this phenomenon. Splicing-sensitive micorarrays now place the genome-wide analysis into the hands of individual researchers. The Exon Array is the first commercially available tool offering whole-genome coverage, in theory targeting all possible alternative splicing events. Our research, and studies from several other groups (Clark et al., 2007; Yeo et al., 2007) prove that the Exon Array can indeed be used to detect alternative splicing and isoform differences in a variety of systems. We are very excited by this technology and are currently applying it in several experimental settings. However, several words of caution should be given. This is not yet an “out of the box” product. A large number of pre- and postprocessing steps are necessary. Data should be filtered to remove systematic artefacts, such as the effect of SNPs, unresponsive, cross-hybridizing, or saturated probes. Final results must be carefully inspected to determine the type of splicing or isoform event represented by the signal, and whether the signal makes sense in the context of the gene structure or is likely to be a false positive. No automated methods currently exist to perform those steps, and it is unlikely that such a process can be fully automated. Even given specialized visualization tools, such as custom versions of genome browsers or commercial software, the researcher must expect to spend a large amount of time pouring over the final data, rather than simply obtaining a list of genes. Given the massive amount of data produced, false positive results will remain a problem. This may be partially alleviated by development of more appropriate statistics and optimizing array design, but the basic multiple testing problem cannot be avoided. If limiting false positives is a priority, researchers may like to narrow their analysis to a subset of the data by focusing on events only supported by prior data (ESTs) or genes involved in certain biological processes.

F UT URE DIRECTI ONS Whole-genome analysis of alternative splicing has been made possible largely due to recent technological advances, allowing cost-effective manufacture of oligonucleotide microarrays able to interrogate millions of probe sequences. The Exon 1.0 ST Array is the first generation comprehensive splicing array. The current design reveals enormous potential, but also some limitations of the design. The next generation splicing microarrays are likely to combine exon body probes with junction probes. This step should improve the sensitivity and allow of detection of additional types of isoform changes. We foresee that in parallel with the development of appropriate statistical and visualization methods, splicing-sensitive microarrays will facilitate major breakthroughs in investigations of splicing and isoform variations in the coming years. Looking ahead to a more distant future, we expect that high-throughput parallel sequencing will soon become competitive with microarray technology, and may eventually surpass it as a genomewide transcriptome profiling tool. Several groups are currently optimizing parallel sequencing based

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gene expression analyses. With coverage currently reaching 2 billion bases per sequencing run, these methods are likely to produce first results within one or two years. However, in order to simultaneously monitor all splice junctions in a quantitative manner, sequencing coverage will have to reach levels at least 10-fold higher than those necessary for gene expression level analysis. Sequencing-based analysis of alternative splicing will ultimately resemble prior EST-based techniques, where short sequence reads will be aligned to the genome, and the presence and frequency of alternative splicing will be determined by counting the splice variants.

REFERENCES Alberts, R., Terpstra, P., Li, Y., Breitling, R., Nap, J. P., & Jansen, R. C. (2007). Sequence polymorphisms cause many false cis eQTLs. PLoS ONE, 2, e622. Altshuler, D., Brooks, L. D., Chakravarti, A., Collins, F. S., Daly, M. J., Donnelly, P., et al. (2005). A haplotype map of the human genome. Nature, 437(7063), 1299-1320. Black, D. L., & Graveley, B. R. (2006). Splicing bioinformatics to biology. Genome Biol, 7(5), 317. Cheung, V. G., Spielman, R. S., Ewens, K. G., Weber, T. M., Morley, M., & Burdick, J. T. (2005). Mapping determinants of human gene expression by regional and genome-wide association. Nature, 437(7063), 1365-1369. Churchill, G. A., & Doerge, R. W. (1994). Empirical threshold values for quantitative trait mapping. Genetics, 138(3), 963-971. Clark, T. A., Schweitzer, A. C., Chen, T. X., Staples, M. K., Lu, G., Wang, H., et al. (2007). Discovery of tissue-specific exons using comprehensive human exon microarrays. Genome Biol, 8(4), R64. Claverie, J. M. (2001). Gene number. What if there are only 30,000 human genes? Science, 291(5507), 1255-1257. Faustino, N. A., & Cooper, T. A. (2003). Pre-mRNA splicing and human disease. Genes Dev, 17(4), 419-437. Irizarry, R. A., Hobbs, B., Collin, F., Beazer-Barclay, Y. D., Antonellis, K. J., Scherf, U., et al. (2003). Exploration, normalization, and summaries of high density oligonucleotide array probe level data. Biostatistics, 4(2), 249-264. Kwan, T., Benovoy, D., Dias, C., Gurd, S., Provencher, C., Beaulieu, P., et al. (2008). Genome-wide analysis of transcript isoform variation in humans. Nature genetics, Published online: 13 January 2008 Kwan, T., Benovoy, D., Dias, C., Gurd, S., Serre, D., Zuzan, H., et al. (2007). Heritability of alternative splicing in the human genome. Genome Res, 17(8), 1210-1218. Lee, C., & Roy, M. (2004). Analysis of alternative splicing with microarrays: successes and challenges. Genome Biol, 5(7), 231. Modrek, B., Resch, A., Grasso, C., & Lee, C. (2001). Genome-wide detection of alternative splicing in expressed sequences of human genes. Nucleic Acids Res, 29(13), 2850-2859.

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Reddy, M. V., Velazquez-Cruz, R., Baca, V., Lima, G., Granados, J., Orozco, L., et al. (2007). Genetic association of IRF5 with SLE in Mexicans: higher frequency of the risk haplotype and its homozygozity than Europeans. Hum Genet. Siepel, A., Diekhans, M., Brejova, B., Langton, L., Stevens, M., Comstock, C. L., et al. (2007). Targeted discovery of novel human exons by comparative genomics. Genome Res, 17(12), 1763-1773. Spielman, R. S., Bastone, L. A., Burdick, J. T., Morley, M., Ewens, W. J., & Cheung, V. G. (2007). Common genetic variants account for differences in gene expression among ethnic groups. Nat Genet, 39(2), 226-231. Storey, J. D., & Tibshirani, R. (2003). Statistical significance for genomewide studies. Proc Natl Acad Sci USA, 100(16), 9440-9445. Stranger, B. E., Forrest, M. S., Clark, A. G., Minichiello, M. J., Deutsch, S., Lyle, R., et al. (2005). Genome-wide associations of gene expression variation in humans. PLoS Genet, 1(6), e78. Xing, Y., Kapur, K., & Wong, W. H. (2006). Probe selection and expression index computation of Affymetrix Exon Arrays. PLoS ONE, 1, e88. Yeo, G. W., Xu, X., Liang, T. Y., Muotri, A. R., Carson, C. T., Coufal, N. G., et al. (2007). Alternative splicing events identified in human embryonic stem cells and neural progenitors. PLoS Comput Biol, 3(10), 1951-1967. Zhang, C., Li, H. R., Fan, J. B., Wang-Rodriguez, J., Downs, T., Fu, X. D., et al. (2006). Profiling alternatively spliced mRNA isoforms for prostate cancer classification. BMC Bioinformatics, 7, 202.

K ey T erms Allelic Association: A statistical association of a genetic marker allele with a phenotypic trait. Here, we use association analysis to detect SNPs statistically correlated with changes in isoform-level expression. While association does not directly imply causation, it is highly likely that a causative genetic variant is in linkage disequilibrium with the significant SNP marker. Alternative Splicing: A mechanism which results in the production of several mRNA variants from a single genomic locus, by preferential inclusion or exclusion of certain splice sites or exons. EST: Expressed sequence tag. Short sequence reads are produced on large scale from cDNA libraries. EST sequencing allowed quantification of known transcripts, detection of novel genes, and novel isoforms. Exon Array: A type of microarray using probes targeted to individual exons within each gene. Exon Arrays may be used to measure the expression of an entire transcript, but also detect higher level changes, such as alternative splicing and other transcript isoform differences. Pre-mRNA Splicing: A process which removes intronic sequences from the precursor messenger RNA of eukaryotic genes, to produce mature messenger (m)RNA.

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Isoform: In the context presented here, an isoform is one of the transcript variants produced by each locus. A gene isoform can result from alternative splicing, alternative transcription initiation, or polyadenylation. SNP: Single nucleotide polymorphism. SNPs are single base pair mutations which have been driven to detectable frequencies in human populations. On average, two human individuals will differ at 1 polymorphic site for each 1000 bp of DNA. Vast majority of the SNPs are likely to be neutral, but some may affect phenotypic traits.

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Gene Expression in Microbial Systems for Growth and Metabolism Prerak Desai Utah State University, USA Bart Weimer Utah State University, USA

abstract The use of systems biology to study complex biological questions is gaining ground due to the ever-increasing amount of genetic tools and genome sequences available. As such, systems biology concepts and approaches are increasingly underpinning our concept of microbial physiology. Three tools for use in functional genomics are gene expression, proteomics, and metabolomics. However, these tools produce such large data sets that we sometimes become paralyzed trying to merge the data and link it to form a consistent biological interpretation. Use of functional groupings has relieved some of the issues in merging data for biological meaning. Statistical analysis and visualization of these multi-dimension data sets are needed to aid the microbiologist, which brings additional methods that are often not familiar. Progress is being made to bring these diverse data types together to understand fundamental metabolic processes and pathways. These efforts are paying tremendous dividends in our understanding of how microbes live, grow, survive, and metabolize nutrients. These insights allow metabolic engineering to progress and allow scientists to further define the mechanisms of metabolism.

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Gene Expression in Microbial Systems for Growth and Metabolism

Intr od ucti on Systems biology brought a great challenge to the microbial world – produce genome-scale data that is integrated into a complete biological picture using specific genes. In spite of this challenge, systems biology is increasingly underpinning our concept of microbial physiology based on genome sequence. Initially, production of a genome sequence limited implementation of this paradigm. However, the rate at which new genome content is accumulating is staggering and is the basis of new avenues for discovery. Publicly available genome sequence now exceeds 700 finished genomes with an additional 1,700 genomes in process of sequencing that provides access to at least 3,600 individual microbial genomes with an additional 116 metagenome projects underway (GOLD, 2008; www.genomeonline.org). These projects are challenging scientists’ ability to collect, process, and overlay a biologically meaningful interpretation of the data. Application of that information to make biologically informed decisions is also a daunting challenge that requires a fresh perspective and new skill sets that leverage genomic-based tools to answer specific biological questions. The heart of the systems biology discovery lies in the new fields of comparative and functional genomics, along with proteomic and metabolite profiles (Fields, 2000). Comparison of genomes to assess the link between structural similarity and functional expression is fully enabled with access to genome content. Comparative analyses of bacterial genomes provide new information about the dynamic interchange of DNA between microbes (Hughes, 2000). Comparing sequenced genomes is an excellent approach to explore genome plasticity and how it impacts the metabolism of microbes. Approaching microbial metabolism from a systems biology perspective is a new position that requires scientists to think of systems of activities that is composed of multiple individuals to carry out those activities. Use of gene ontologies and (GO) and clusters of orthologous groups (COG’s) are very helpful for this aspect of comparison since specific and common terms are used in a hierarchical classification system, and are essential when using functional genomic tools to drill down to individual conversations (i.e. activities). These tools include gene expression profiling, protein expression profiling, metabolomics profiles, and new statistical methods. Functional genomics must incorporate data from each set of tools to examine how organisms utilize the genome potential (via gene expression initially). Since most genomes have thousands of genes that are monitored the task is like trying to monitor all the individual conversations in a crowded stadium at one moment in time. In essence, functional genomics documents a cell’s many “conversations” as they occur simultaneously. The conversations are defined by genes expression (gene arrays), protein interactions (proteomics), and small molecule biochemistry (metabolomics) that create a multi-dimensional view of the cell. Deciphering these conversations in turn outlines the web of actors in the metabolic networks, providing an unprecedented view of how a living cell carries out the many functions of growth, survival, pathogenicity, and metabolism. Production of multi-dimensional data using these techniques produce very different types of data that need a common thread that links the data types. Such large data sets lead to an interpretational paralysis that limits the linkage between the functional genomics data and biological relevance or meaning. Therefore, the analytical phase must seek to fully integrate all of these tools using new statistical tools that are also unfamiliar to most microbiologists, which often exacerbates interpretation difficulties when the genotype and the phenotype are at odds. Taken together, it is clear that the use of bioinformatics is essential for mining genome content, but also essential to provide bring new scientific abilities that truly bring biologically meaningful insights via systems biology.

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S ystems

B iology and Micr obes

Systems biology brings a new perspective to the life sciences generally, but has specific impact on microbiology due to the nature of the rapid evolution and small genome that is the essence of a microbe. Due to the small genomes in microbes, they lend themselves well to rapid, short-term sequencing efforts because they have limited complexity. Often only a single small circular chromosome with limited extrachromosomal DNA (i.e. plasmids) is found microbes, as compared to eukaryotic organisms that contain multiple chromosomes that are very complex and significantly larger than microbes. Due to the general ease of sequencing microbes the number of microbes projects around the world exploded with isolates coming from various ecologies, including unique environmental organisms and human pathogens (see NCBI-www.ncbi.nlm.nih.gov/genomes/lproks.cgi for a complete listing). This in part is driving the doubling of NCBI’s database every 18 months (Pennisi, 2003). The genome sizes range from 13.03 Mb from the myxobacterium Sorangium cellulosum to 0.16 Mb from the obligate endosymbiont Candidatus Carsonella ruddii PV. While the accumulation of genomes enables more and more fields within microbiology to participate in systems biology shifting from generating more genome sequence to the more difficult aim of comprehending the impact of specific functional genomic patterns is an important and substantial transition that faces microbiology today. Direct comparison of genome alignments enables assessment of organization between strains, species, and genera to give a picture of structural conservation (Figure 1) that is beyond the use of 16S DNA sequence. However, genome structure does not predict phenotype, even among closely related subspecies. For example, the genome structure between Lactococcus lactis ssp. lactis IL1403 compared to Lactococcus lactis ssp. cremoris SK11 is conserved, except for a small inversion. However, the strains behave very differently in the same growth conditions for growth and gene expression (Yie et al., 2004). With the extensive amount of genome information available it is possible to redefine the classification of microbes based on their genome similarity (known as phylogenomics) rather than the 16s DNA or phenotype (Anderssen and Fuxelius, 2005). Gene duplication, translocation, inversion, deletion, and horizontal transfer facilitate genome rearrangement, which is becoming an increasingly common observation in new genomes from environments that have high selective pressure. Presumably, such rearrangements mediate rapid strain evolution allowing adaptation of the strain to the selective pressure (Hughes, 2000). Use of phylogenomics to classify microbes is a complex and emerging area of classification that will produce new phylogeny methods to represent evolution and relatedness between microbes in the near future. Koonin and Galperin (1997) examined this approach with relatively few genomes to inform their conclusions that structure is not conserved, but rather gene exchange in distantly related microbes is common for the conservation of function via many different genome organizational structures. Tools to probe conservation of function are clearly needed to bring focus to the conundrum of the lack of structure conservation with the common phenotypes noticed among genera or species. To aid comparative genomics a technique called comparative genomic hybridization (CGH) is becoming increasingly popular. This is based on use of gene expression arrays that have genomic DNA hybridized to the array rather than labeled cDNA. This allows one to determine genomic similarity without sequencing every strain of interest. Protocols for this approach are being standardized and completely depend on the genome that was used to create the array (Guinane and Fitzgerald, 2008). If genes are missing in the reference genome then no data will be available for the CGH comparison. However, this method is inexpensive, fast, and provides a very rich data set to compare closely related organisms for the conservation of functionally related genes independent of the location on the genome.

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Figure 1. Synteny plots of specific microbes to demonstrate conservation of genome structure

G ene E xpressi on Pr ofi les With a genome in hand creation of a whole genome gene expression array is the next logical step for functional analysis of genome sequence and gene regulation. Construction of gene expression arrays is a critical step to enable creation of reliable and estimates of gene expression profiles (Table 1). This is done by placing probes to various locations in a gene to assess the expression of that gene during growth and environmental treatment. Cellular RNA is isolated from an organism and converted to cDNA (made from RNA using reverse transcription PCR) as a tag is incorporated. Often the tag is fluorescent but other options are available. The tagged cDNA is hybridized to the genome array to produce a signal. Two main types of arrays are in use – spotted arrays and photolithography to deposit the probe on the solid medium for use. Variability in spotting leads to variability in expression data, which has limited use of spotted arrays, except in carefully controlled conditions. Gene expression arrays produce an enormous amount of data for each experiment that requires immense data-handling capacity. For example, an experiment with a DNA array of an entire genome, even a small one with 2,500 genes requires approximately 27,500 individual probes (considering 11 probes per gene) for a single genome. A single experiment done using two treatments (e.g. a single vari-

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Table 1. Options to produce gene arrays for expression and CGH Medium

Probe

Spotting method

Signal

Bead

>50mer oligonucleotide

Ink jet

Dual color

Membrane (nylon)

cDNA

Pin – solid or slotted

Single color

Slide

<25mer oligonucleotide

Photolithography

Chemiluminescent

Solid glass

Use of a linker

Fluorescent

3D glass

Specific or degenerate

Radioactive

Membrane

Direct or indirect label

nanocatilever

Probes per gene

able) and three replications results in 165,000 discrete data points for analysis that need to be acquired, processed, analyzed for validity, and compared statistically before biological meaning can be assigned. Subsequently, these significant genes are associated with a biological function to determine the metabolic difference between the test conditions. The data set balloons to nearly 1 million data points when a time course is done for just six different times. As one can imagine, computer science and statistics become an integral part of the data analysis. Gene expression profiles produce a long list of genes that change during various treatments. Bringing biological meaning is a significant challenge if the variability is too high or treatment conditions are too complex. In some cases protein production and gene expression do not agree. This is more come in eukaryotic data sets than in prokaryotic studies where probe construction is less complex, exon variants do not exist, and experimental conditions are easier to control. Consequently, some investigators prefer to examine the proteome of microbes to assess the proteins that are present during the treatments. One advantage of gene expression profiles is that integral membrane proteins can be observed along with cytosolic proteins in the same sample preparation. Proteomics involves monitoring whole-cell protein expression. This approach uses a more traditional tool, two-dimensional gel electrophoresis (2D), to separate the proteins present in a cell at a specific point in time during growth. Like RNA expression, protein-expression profiles from cells immersed in different environmental conditions can be compared. The protein spots on a 2D gel that differ between conditions are eluted or cut out and digested by specific proteases and subjected to mass spectrometry or tandem mass spectrometry. The resultant mass fingerprint is used to link the 2D gel spot to a specific gene within the genome. Alternatively, more investigations use mass spectrometry coupled to a chromatography interface that does a pre-separation of trypsin-digested proteins before the mass determination. Once the mass is determined a database is searched to determine the protein identification. Using either technology, proteins expressed from the genome are cataloged and monitored and collectively known as the proteome. Whole-cell protein expression profiling provides a fundamentally different, yet complementary, view of cellular systems that is linked to gene profiling. For example, proteins may persist in a cell longer (or degrade faster) than their cognate mRNA transcripts, such that RNA analysis may not give an accurate view of the proteins available in a cell at any moment in time. Conversely, proteome analysis often misses proteins that are bound in the membrane or are not in the water phase of the cell mass. Hence, these complementary methods provide a fuller picture and understanding of cellular gene expression

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when used together. This process provides a wealth of information about the cell and how it responds to the environment. With these data, strategies can be formulated to modulate bacterial survival, as well as modify metabolic processes during different environmental conditions or challenges. An advantage of gene expression over proteomics is that there is no need for cell division to observe changes in expression. Stuart et al. (1998) determined that lactococci lose the ability to produce colonies after carbohydrate exhaustion, which is accompanied by release of methionine and serine into the medium. Ganesan et al. (2006) extended this study using gene expression studies to confirm Stuart’s work and further demonstrate that the cells continue to transcribe RNA even in the absence of colony formation, which is due to repression of the bacterial cytoskeleton ( fts). With the lose of colony formation and the production of amino acids without sugar they hypothesized that global gene expression changes were being regulated by multiple mechanisms to change the metabolism of the non-culturable cell allowing survival. This was proven and creates a link between sugar, regulation of metabolism and colony formation. These “dead” cells are intact, regulate gene expression, and continue to metabolize peptides and amino acids to end products that subsequently change the local environment that again changes the gene expression and metabolism in a complex interplay between the bacterial system and the environment. This is all done in cells that we cannot grow or “see” on a plate. These observations beg the question of gene expression regulation, growth, and how uncultured cells change the community ecology.

Met ab olic Co nnecti ons t o the G en ome and E xpressi on Pr ofi les In addition to structural gene products metabolism is of interest to understand how microbes grow, persist, produce industrially important chemicals, process toxins, and metabolize the nutrients in their environment broadly. To enable this view various groups produced metabolic reconstruction software that uses gene sequence data to draw the metabolic potential for that specific organism. Importantly, it provides a theoretical touchstone for the possible gene expression profiles to further enable biological meaningful conclusions. Metabolic reconstruction maps (Figure 2) also enables one to conduct comparisons of metabolic capabilities that are predicted by the genome sequence using in silico tools, such as KEGG and Pathway Tools that are designed to predict the metabolic potential from the genome content (Kaneshisa, 2004; Karp et al., 2005). Based on the Pathway Tools platform a generalized inventory of metabolic pathways that is dynamic called MetaCyc allows one to see all of the known biochemical reactions known (Caspi et al., 2006). In the same approach, Biocyc, a web-based database, was created that has over 160 organisms allowing user defined customization to display or compare metabolic pathways (Karp et al., 2005). This provides users with incredible predictive abilities to study the most important pathways and their interconnections to microbial growth and ecosystems. Additional tools for metabolite interconnections are being developed to predict the complex web of metabolism. This approach provides new level of insight into the coupling between genetic, metabolic, and expression events that lead to phenotypic traits. Weimer’s group created a tool as a plug-in to Pathway Tools that allows pathway interconnections to be displayed for any queries of genes, intermediates or proteins. For example, a query using glutamic acid resulted in over 150 interconnections in Lactococcus cremoris SK11 that indicates the central metabolic role of this amino acid. Complexity of metabolism

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for glutamic acid is expected, but it is unexpected to realize the extent of the pervasive connections for this amino acid in lactococcal metabolism. Predictions of metabolism can be verified with gene expression and metabolite analysis. A systems biology view of the microbial cell is more fully enabled using gene expression profiles with metabolic reconstruction maps. However, one still lacks the ability to prove links gene expression profiles with the metabolic processes in a high through put method. Therefore, a more direct measure of the small molecule flow is needed on the same scale as the genome and gene expression profiles to fully enable a system level assessment.

Met ab olomic Pr ofi ling Metabolic profiling is a high through put method to measure the small molecule metabolism via mass spectrometry combined with gas or liquid chromatography. The challenge with metabolomics is based in sample preparation coupled with individual compound identification based on the observed mass. Many compounds have the same or very similar masses, making identification the bottleneck in this technology. Creating libraries of masses coupled with retention times is in progress by a number of manufacturers and academic research laboratories. Metabolomics can be applied to microbial metabolic questions by addressing the profile of compounds, seeking to follow specific compounds, or by determining the interchange of atoms in the metabolites. Each of these areas provides a different answer to the overall question of metabolism that is suggested by gene or protein expression profiling. Metabolite profiling is common at the beginning of projects or communities are being examined. The lack of unique differences between compounds is severely limiting the full integration of metabolite profiling. Hence, it is common to restrict metabolite analysis to specific types of compounds that flux through the cell in response the changes in gene and protein expression due to environmental changes. Often, gene expression profiles need additional or supporting evidence to provide assurance that the metabolism extrapolated from the gene expression pattern is reliable when overlaid to metabolic reconstruction maps. Ganesan et al. (2006) used NMR, gene expression analysis, and metabolic network maps to delineate the exact metabolic pathway to convert branched chain amino acids to branched chain fatty acids. This study demonstrates the usefulness of gene expression to understand complex metabolic pathways and refined the exact genes that enable the committed steps in amino acid metabolism. Further, this study found that we still lack specific understanding of metabolism of central intermediates, such as pyruvate, because the carbon atoms were traded between unexpected intermediates and found in compounds previously unknown to interact in fatty acid production. A systems biology approach seems to always provide unexpected results that challenge the biological dogma. In this light it is critical that one determine how to best use the multi-dimensional data sets of gene expression, protein expression, metabolites, and the in silico prediction models based on the genome content and what is significantly different of just biological noise. Combining these data sets provides a unique look at the cell that requires validation and a perspective of variability due to regulatory networks that are yet to be defined.

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Figure 2. Diagram of “-omics” integration with a metabolic reconstruction map based on the genome sequence of L. cremoris SK11.

Genomics DNA

Regulation

Regulatory Circuits

RNA

Protein

Metabolites

Metabolism

Growth

Survival 285

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B ioinf orma tics and S t atistics Bioinformatics and statistics were first used together to predict gene similarity between organisms, as well as to predict genes among the vast amount of base calls in a genome. They are being used again to merge the vast amount of data produced with gene expression, proteomics, and metabolomics. Methods to merge these multidimensional data sets are factor defining overriding rules or common types of systems. Bioinformatics and statistics are required to provide a systematic context with an estimation of probability that the “real” biology was observed and not just biological noise due to variation in subtle adaptation to the local environment. Systems biology seeks to define the complexity of the system; however a base language and set of common rules are lacking to achieve this task. To bridge that gap use of models is emerging as a preferred method. This approach is borrowing tools and techniques from engineering, circuit design, and control theory to provide a basis of understanding the system. However, this requires biologists, engineers, computer scientists, and mathematicians to communicate on common ground, which is no small feat. The first example of this is software designed to display and analyze the entire genome, but today many examples of analysis exist that predict for genes, intergenic regulatory motifs, metabolic reconstruction from the genome, and metabolic flux. Before higher-level combinations can occur the initial analyses of functional genomic techniques require statistical models that define normalization methods and address the multiple comparison issue of high dimensional data sets. These tools are available and are the beginnings of standardization. For example, it is common to incorporate array normalization techniques called robust multiarray average (Irizarry et al., 2003; Storey and Tibshirani, 2003). Normalization allows comparison between probes and between arrays that is commonly used to determine the fold change. However, one must assess the statistical difference of the change and not rely on the fold change alone. This can be done using a pairwise t-test, except that the large number of probes on an array and the low number of replications causes a bias that needs to be corrected creating a false discovery rate that is reflective of the correction that uses the q-value rather than a p-value (Tusher et al., 2001; Dudoit et al., 2002). Desktop software called SAM is freely available for this analysis (Tusher et al., 2001; www-stat.stanford.edu/~tibs/SAM/index. html). Bioconductor, using the R package (www.r-project.org), is a large worldwide effort that produces statistical solutions for multi dimensional data sets (www.biocondutor.org) that is becoming more accessible to the biologist. The same principles can be applied to gene or protein expression data sets. Once the statistical analysis is completed a list of significantly changing genes or proteins is produced. However, unless additional data are mapped on the significant hits little biological information is derived from the changes. This is where bioinformatics beyond genome structure is burgeoning. Use of GO terms and COG assignments provides a systematic approach to classify the broad (network) changes in the cell. These schemes link function with location of specific genes and gene products. This is very useful in assessing broad changes. For example, Ganesan et al. (2007) used this approach to determine the changes in all the dehydrogenases in the genome due to carbon starvation. Mapping the gene name, function (GO or COG), and change due to the treatment are the beginning steps to define the biological meaning. However, again the limitation is the vast data set that needs additional annotation. This requires additional automated tools to provide these functions for the biologist. Doing this by hand is not possible considering that it is likely the reduced data set will still contain 200 to 1,000 genes per treatment or condition. Method to assess over representation by specific classes of genes or proteins was developed by Gentleman et al. (2004). This method determines statistically significant enrichment within a GO category

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due to changes of specific genes with that GO term. This can be thought of a using the probability that chance will lead to the collective changes in that GO due random chance. If the GO is significant it is unlikely that chance will produce this type of broad change in the genes in the GO. Use of this strategy further allows the biologist to determine a link between the system-wide changes and specific gene or protein changes that are biologically meaningful and relevant for further study. Visualization of the data is very difficult for data with high dimensionality and it is linked to the statistical method used to determine the importance of the results. Clustering and principle component analysis (PCA) are commonly used for each of these data types. Cluster analysis lends itself well to heat maps, while PCA tends to be better with spider plots. Alternatively, one can map the changes on the metabolic reconstruction map to provide a metabolism context. Strategies to visualize the data depend on the question that is asked. Individual genes or reactions are easily defined, but a visualization of the entire system is difficult and still depends on the question of regulation or direct reactions. Traditionally, metabolism is thought of in a linear fashion that is represented by the classical biochemical maps and the metabolic reconstruction maps. However, it is becoming increasingly clear that they are highly interconnected circuits that deviate based on the protein and metabolite present at any point in time. To further link gene expression and proteomic data many scientists are mining microbial genomes for hidden gems of metabolic circuits to create custom metabolic maps that provide a touchstone for interpretation of the genetic possibility in a specific organism. Coupled with develop of high-throughput techniques that allow large-scale biochemistry provide additional insight into the meaning of the merged data sets to define the limits and conditions needed for specific production of metabolic end products. Addition of metabolic flux predictions software is further expanding interpretation.

Su mmar y and Fu t ure T rends With all of these data analysis methods microbiologists are forced to use unfamiliar statistical tools that require computer science skills that are beyond their normal experience and produce a steep learning curve in addition to all the other choices to be made about technology selection. Therefore, while this approach brings many benefits to see the entire cellular conversation at a single time, this course of research is for the committed scientist that really wants to use systems biology for discovery. However, dedication produces a new world of discovery with new perspectives that are likely more realistic of what occurs in the microbial cell in response to its environment. For example new concepts that use these measurements define the cell as a circuit that is “wired” by the genome, but is transduced by proteins and chemical reactions. This approach to systems biology of bacteria brings the absolute need for collaboration between groups that are not traditionally connected – physics, computer science, statistics, biology, and genetics. Communication between these groups is required to make substantial progress to answer biological questions with such large, multi-dimensional data sets. However, this challenge also brings a new view – biological systems that can be described by engineering principles borrowed from communications and control theory that was done by Alan Hodgkin and Andrew Huxley more that 50 years ago in diagramming the circuit of a squid nerve cell. This approach is undeniably possible for a microbe since the genome is limited at any point in time. However, if one allows mutation and genome rearrangement then the task of prediction becomes substantially more difficult. Phylogenomics will likely become more popular as more genomes become available and new comparison tools allow comparison from an evolutionary perspective of genes or proteins, GO or COG’s

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categories, genomes, and ultimately strains or species. The high dimensionality of this approach is somewhat limited by our perspective of evolution, gene transfer, and intimate interaction between microbes in their environment. However, as these perceptions change additional progress will be made in classification systems based on the genome content and expression methods used that ultimately translate into the cell’s phenotype. A newer technique called metagenomics will continue to impact our understanding of microbes and their ecology. The over 116 data sets available were generated with ideas of defining an ecological niche in a shotgun sequencing approach. We immediately learned that our understanding of the complexity of the oceans and soils on earth is sorely lacking during the analysis of the metagenomes that were produced. The allure of metagenomics is the ability to produce genome sequence without growing bacteria. A significantly challenge in most ecologies. However, one can produce enough sequence to create entire genomes without needing to isolate or grow individuals in the community if a strategic approach is used to increase or begin with “staged” complexity in the sample. This approach lends well to extreme environments to determine the community members without the need to understand how to grow the individuals. An example of this strategy is the metagenomes of acid mine drainage, which contained less than five members after the metagenomes was analyzed (Tyson et al., 2004). Additional data analysis tools and methods are needed to quickly link observation to biological meaning. While the statistical methods and databases provide a basis to build the framework of interpretation additional relational structures are needed to fully integrate the perspective of the genetic basis of growth, metabolism, and persistence. Metagenomics is a reasonable method to interrogate complex communities of uncultured organisms, but this brings another dimension and complexity to integrate that requires additional connectivity between biology, computer science, mathematics, and engineering.

R eferences Alon, U. (2007). An introduction to systems biology: Design principles of biological circuits builds a solid foundation for the intuitive understanding of general principles. (3rd edition). Chapman & Hall/ CRC Press. Andersson, S. G. E. & Hans-Henrik Fuxelius. (2005). Phylogenomics for studies of microbial evolution. In Encyclopedia of Genetics, Genomics, Proteomics and Bioinformatics, 4: Bioinformatics. John Wiley & Sons, Ltd. Caspi, R., Foerster, H., Fulcher, C.A., Hopkinson, R., Ingraham, J., Kaipa, P., Krummenacker, M., Paley, S., Pick, J., Rhee, S.Y., Tissier, C., Zhang, P.D., & Karp (2006). MetaCyc: A multiorganism database of metabolic pathways and enzymes. Nucleic Acids Res. 34, D511-6. Dudoit S., Yang, Y. H., Callow, M. J., & Speed, T. (2002). Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments. Statistica Sinica. 12, 111-139. Fields, S. (2000). Proteomics in genomeland. Science, 291, 1221-1224. Gentleman, R. C., Carey, V. J., Bates, D. M., Bolstad, B., Dettling, M., Dudoit, S., Ellis, B., Gautier, L., Ge, Y., Gentry, J., Hornik, K., Hothorn, T., Huber, W., Iacus, S., Irizarry, R., Leisch, F., Li, C., Maechler, M., Rossini, A. J., Sawitzki, G., Smith, C., Smyth, G., Tierney, L., Yang, J. Y., and Zhang,

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J. (2004). Bioconductor: Open software development for computational biology and bioinformatics. Genome Biol. 5, R80. Guinane, C. M., & Fitzgerald, J. R. (2008). Microarray comparative genomic hybridization for the analysis of bacterial population genetics and evolution. Bacterial Pathogenesis: Methods and Protocols 431, 47-53. Hughes, D. (2000). Evaluating genome dynamics: The constraints on rearrangements within bacterial genomes. Genome Biology 1, reviews 0006.1–0006.8. Irizarry, R. A., Hobbs, B., Collin, F., Beazer-Barclay, Y.D., Antonellis, K. J., Scherf, U., & Speed, T. P. (2003). Exploration, normalization, and summaries of high density oligonucleotide array probe level data. Biostat 4, 249-264. Karp, P.D., Ouzounis, C.A., Moore-Kochlacs, C., Goldovsky, L., Kaipa, P., Ahren, D., Tsoka, S., Darzentas, N., Kunin, V., Lopez-Bigas, N. (2005). Expansion of the BioCyc collection of pathway/genome databases to 160 genomes. Nucleic Acids Res. 33, 6083-9. Kanehisa, M., Goto, S., Kawashima, S., Okuno, Y., & Hattori, M. (2004). The KEGG resource for deciphering the genome. Nucleic Acids Res. 32, D277-80. Knudsen, S. (2004). Guide to analysis of DNA microarray data. (2nd Edition). John Wiley & Sons, Inc. Koonin, E.V., & Galperin, M.Y. (1997). Prokaryotic genomes: The emerging paradigm of genome-based microbiology. Curr Opin Genet Dev. 7, 757-63. Liolios, K., Mavrommatis, K., Tavernarakis, N., Kyrpides, N.C. (2008). The genomes on line database (GOLD) in 2007: Status of genomic and metagenomic projects and their associated metadata. NAR 36, D475-D479. Pennisi, E. (2003). Tracing life’s circuitry. Science, 302, 1646-9. Riesenfeld, C. S., Schloss, P. D., & Handelsman. J. (2004). METAGENOMICS: Genomic analysis of microbial communities. Annual Review of Genetics, 38, 525-552. Storey, J. D., & Tibshirani, R. (2003). Statistical significance for genomewide studies. PNAS 100, 94409445. Tusher V.G., Tibshirani, R., Chu, G. (2001). Significance analysis of microarrays applied to the ionizing radiation response. Proc Natl Acad Sci USA, 98, 5116-21. Tyson G.W., Chapman, J., Hugenholtz, P., Allen, E. E., Ram, R. J., Richardson, P. M., Solovyev, V.V., Rubin, E. M., Rokhsar, D. S., & Banfield. J. F. (2004). Community structure and metabolism through reconstruction of microbial genomes from the environment. Nature, 428, 37-43. Xie, Y., Chou, L-S., Cutler, A., & Weimer, B. (2004). Expression profile of Lactococcus lactis ssp. lactis IL1403 during environmental stress with a DNA macroarray. Appl. Environ. Microbiol. 70, 6738-6747.

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K ey T erms Bioconductor (www.bioconductor.org): An open source and open development software project for the analysis and comprehension of genomic data. R (www.r-project.org): R is a language and environment for statistical computing and graphics. R provides a wide variety of statistical (linear and nonlinear modeling, classical statistical tests, time-series analysis, classification, clustering, etc.) and graphical techniques that is highly extensible. Significance Analysis Of Microarrays (SAM; www-stat.stanford.edu/~tibs/SAM/index.html): An Excel plug-in that is used to analyze microarray data.

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Chapter XVII

Alternative Splicing and Disease Heike Stier Charité Universitaetsmedizin Berlin, Germany Paul Wrede Charité Universitaetsmedizin Berlin, Germany Jürgen Kleffe Charité Universitaetsmedizin Berlin, Germany

abstract Alternative splicing is an important part of the regular process of gene expression. It controls time and tissue dependent expression of specific splice forms and depends on the correct function of about 100 splicing factor proteins of which many are the product of alternative splicing itself. It is therefore not surprising that even minor sequence disturbances can cause mis-spliced gene products with pathological effects. We survey some common diseases which can be traced back to a malfunction of alternative splicing including cystic fibrosis, beta-thalassemia, spinal muscular atrophy and cancer. Often cancer also results from even mis-spliced splicing factors leading to randomly spliced non-functional isoforms of several genes.

Intr od ucti on The hypotheses of Beadle and Tatum (1941), that one gene codes for a single uniquely defined protein, has been disproved many times during the past 30 years by discovering a number of ways how one single gene gives rise to different gene products. The differences may result at the transcriptional level, during RNA pre-processing, m-RNA translation or post-translational protein processing and folding. A recent review by Boeckmann et al. (2005) describes the most important ways of gene product modification. Alternative splicing increases the diversity of gene products by deriving different final mRNAs from the same pre-mRNA transcript by alternative definition of introns which are spliced out to derive the Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

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final mRNA used for translation. But whereas the process of splicing, the interaction of different proteins forming the spliceosome and removing an intron, is investigated and described in great detail by Staley and Guthrie (1998), Will and Luhrmann (2001), Nilsen (2003) and Tazi et al. (2005), the process of how the splice sites are selected is not yet fully understood. For each single splicing reaction the spliceosome is newly formed in interaction with the pre-mRNA and acts in two basic steps as seen in Figure 1. Cleavage of the donor site and ligation of the 5’ end of the intron to the branch side (step 1) is followed by removal of the intron by cleavage of the acceptor site, the 3’ end of the intron, and the ligation of the neighboring exons (step 2). About hundred interacting molecular splicing factors, many of them are snRNPs, are known to steer this complex process. Four important signals on the pre-mRNA intron are essential to attract these splicing factors to form the spliceosome and to perform splicing. Theses are the donor site at the 5’ end of the intron, the branch point with the nucleotide A located about 17-40 nucleotides upstream of the acceptor site, the polypyrimidine region, and the acceptor site itself which defines the 3’ end of the intron. Exonic and intronic splicing enhancer or silencer sequence motifs additionally affect attraction of all splicing factors. If hit by mutations, all changed sequence signals are prone to change the pattern of splicing and to seriously affect protein expression, eventually causing death and disease. Krawczak et al. (1992) reported about 15% of all known diseases causing point mutations to directly hit splice sites. This early publication did not consider mutations of exonic or intronic splicing enhancer or silencer signals known to be very important today. The Human Gene Mutation Database published by Stenson et al. 2003 contains 61106 registered mutations of which 5822 affect splicing events. From this set 3633 are point mutations of the GT donor and the AG acceptor splice sites. Skipped exons induced by

Figure 1. The two major steps of splicing; cleavage at the donor site (5’ splice site) and forming the lariat structure (step 1) followed by removing the intron and ligating the exons (step 2)

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these mutations often change the reading frame and create aberrant not functional proteins. Mutations within exons, which do not change the resulting proteins, are considered neutral or silent. Still they can damage splicing enhancer or silencer motifs. Studies of the NF1 (Neurofibromatosis type 1) and ATM (Ataxia telangiectasia) mutated gene by Teraoka et al. (1999) and Ars et al. (2000) found that even 50% of the disease causing mutations imply splicing mistakes. Characterization of these splicing defects can help to understand diseases and to find novel strategies for diagnostics and therapy. Even the normal process of alternative splicing is very complex. Reports by Mironov et al. (1999), Johnson et al. (2003) and Gupta et al. (2004) reported alternative RNA splicing for 35% to 75% of the human genes. Although these numbers must be handled with care, they surely imply that mutations can easily harm the natural balance of alternative splice products and lead to diseases and cancer. After splicing 20-24 nucleotides upstream of the exon-exon junction a so called exon junction complex (EJC) remains on the processed mRNA as found by Le Hir et al. (2000), Tange et al. (2004) and Bono et al. (2006). This complex is important for post-processing of the finally spliced mRNA such as the early stop codon triggered NMD (nonsense mediated decay) pathway decribed by Charlet-B et al. (2002). It can cause complete lack of a protein desired for health. More general the EJC influences mRNA translation, surveillance, and localization. We now provide some interesting examples of wellknown diseases caused by splicing defects.

Alterna ti ve S plicing in Co mmon D isease Cystic fibrosis (CF) is one of the most common hereditary diseases. It causes malfunctions of different organs including lung, heart and liver. Within lungs abnormal thick mucus’ are produced which clog the lung and lead to life-threatening lung infections. Responsible for this disease are mutations described by Kerem et al. (1989) which affect the CFTR (Cystic Fibrosis Transmembrane conductance Regulator) gene. This gene codes for a cyclic-AMP-dependent chloride channel reviewed by Zielenski and Tsui (1995). From 1210 mutations of the Human Gene Mutation Database reported to cause CF, 168 affect splicing. In one of these mutations a C is changed to T which generates a new weakly scoring 5’ splice site within intron 19. It eventually leads to an exon extension by 84 bps which receives a premature stop codon. The ratio between the correctly and aberrantly spliced transcripts determines the degree of affliction. Beta-thalassemia is an inherited blood disorder, mainly affecting people of the Mediterranean regions and causing anaemia. The reason is a mutated Beta-globin gene (HBB) so that the ability to produce haemoglobin is hampered. Within the Human Gene Mutation Database 419 mutations of the HBB gene are registered of which 49 are reported to affect splicing. One of the point mutations is the change of T to G within the poly-pyrimidine tract of intron 2 as shown in Figure 2. This mutation leads to increased binding of the splicing inhibitor hnRNP C protein and down regulates the recognition of the downstream acceptor splice site. Patients with this mutation produce a great proportion of a nonfunctional transcript isoform, that lacks exon 3, and only a small number of full length proteins. The proportion of the full length transcript determines the severity of the symptoms. This observation was described by Sebillon et al. (1995). Another case is the G to A mutation in codon 26 (GAG to AAG) which activates a cryptic 5’ splice site at codon 25 and reduces the amount of the correctly spliced protein. Suwanmanee et al. (2002b) succeeded in blocking this aberrant 5’ splice site by oligonucleotides re-establishing the correct way of splicing.

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Figure 2. The T to G substitution in intron 2 of the ß-globin gene creates a new intronic silencer sequence responsible for hnRNP binding and inhibition acceptor splice site recognition. The next downstream acceptor site is used instead.

Spinal muscular atrophy (SMA) is the most frequent autosomal recessive disorder in human. It happens in one of 10,000 cases and is characterized by a progressive degeneration of spinal cord α-motor neurons which result in skeletal muscle denervation and paralysis. Studies by Lefebvre et al. (1995), Frugier et al. (2002) and Eggert et al. (2006) have shown that more than 96% of the SMA cases are caused by the homozygous loss or mutations of the SMN1 gene (survivor of motor neuron gene 1). In the Human Gene Mutation Database 2 out of 22 mutations of the SMN1 gene are reported to be associated with splicing defects. Meister et al. (2001) describe how the loss of the otherwise resulting SMN1 protein leads to a global defect in pre-mRNA splicing. However, humans have a second, nearly identical copy of the SMN1 gene, the SMN2 gene, which codes for the SMN2 protein and is located in an inverted repeat on chromosome 5q13 as shown in Figure 3. A total loss of both genes leads to early embryonic death. But the SMN2 gene can partially compensate for the loss of the SMN1 gene. It cannot completely replace the SMN1 gene since according to Lorson and Androphy (2000) more than 80% of the mRNA transcribed from the SMN2 gene lack the important exon 7 and lead to a non-functional protein. Compared with gene SMN1 the skipping of exon 7 by transcribing gene SMN2 is caused by a single nucleotide C to T mutation in exon 7. This substitution is silent but, as conjectured by Cartegni et al. (2006), it is supposedly destroying an exonic splicing enhancer motif. For the intact SMN1 gene this enhancer supports the binding of the SF2/ASF splicing factor. The binding of this factor to the considered splicing enhancer strengthens the otherwise weak acceptor splice site of exon 7. Cartegni and Krainer (2003) discuss ways of changing the balance of SMN2 transcripts towards inclusion of exon 7 in order to improve compensation for the loss of the SMN1 gene. Hutchinson-Gilford progeria syndrome (HGPS) is a rare genetic disorder observed for one out of four million humans that causes premature rapid aging shortly after birth. One mutation leading to HGPS is a change from GGC to GGT of codon 608 of the LMNA gene. The LMNA gene codes for A-type and B-type lamins (intermediate filament) which are part of the nuclear lamina. The described

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Figure 3. Location (left) and splicing difference (right) of the SMN1 and SMN2 genes. A single nucleotide C to T mutation within exon 7 presumably damages an exonic splicing enhancer that supports binding of the SR protein SF2/ASF which is important for identification of the 5’ splice site of exon 7.

Figure 4. A point mutation from C to T within exon 11 of the LMNA gene generates a cryptic donor site that causes skipping the rest of exon 11. The resulting protein misses important sites for proper functioning.

mutation creates a cryptic donor splice site within exon 11, making it 150 nucleotides shorter. Hence the resulting protein has an internal deletion of 50 amino acids close to the end of its C-terminal and misses an important internal proteolytic cleavage site as well as some phosphorylation sites which are necessary for normal interaction with lamin C which usually creates heterodimeric multiprotein filaments. A review is given by Pollex and Hegele (2004). Figure 4 shows how the described C to T mutation generates a much stronger but cryptic donor site since a T in intron position 6 is about three times more frequently found than a C. The wild type cryptic donor site is three times weaker and hence remains unused. Myotonic dystrophy (DM) is another exciting story about alternative splicing and disease. DM is an autosomal dominant disorder, affecting one of 8000 humans, the most common form of muscular dystrophy for adults, and is characterized by multiple symptoms like muscle hyperexcitability (myotonia), progressive muscle wasting, defects of the cardiac conduction, alterations in smooth muscle function, ocular cataracts, testicular atrophy, neuropsychiatric disturbances and insulin resistance. Reviews were written by Day and Ranum (2005) and Machuca-Tzili et al. (2005). For DM1, a special version of DM, the only abnormality found on the DNA level is an unusually high number of CTG repeats counting from 80 to 1000 copies, in the 3’ untranslated region of the DMPK gene (DM Protein Kinase) located at chromosome 19q13.3. On the mRNA level DM1 patients show a number of unusually spliced genes like CLC1 (Chloride Channel protein 1), IR (Insulin Receptor), cTNT ( Cardiac Troponin T) which at the first glance have nothing to do with the DMPK gene. However, the mRNA of the DMPK gene with its CTG repeats forms stable hairpin structures, and therefore, is neither translated nor degraded,

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but accumulates within so called ribonuclear foci. As a result the important splicing factor MBNL1 (muscleblind-like mRNA binding protein) irreversibly binds to the double stranded CTG repeat structures and comes short for the regulation of splicing. This leaves more space for CUG-BP, the CUG binding protein which is a member of the CELF-family known as trans-acting splicing regulator and antagonist of MBLN1. The resulting abnormal ratio of the splicing factors MBNL1 and CUG-BP is now responsible for altered splicing patterns of CLC1, IR, cTNT, the Tau protein, and the Myotubularin proteins which cause at least some of the disease related symptoms like myotonia, insulin resistance, cardiac arrhythmia, CNS and myopathic effect, respectively, as shown in studies by Charlet-B et al. (2002), Savkur et al. (2004), Philips et al. (1998), Seznec et al. (2001) and Sergeant et al. (2001). Fokstuen et al. (2001) found that the number of CTG repeats partially determines the onset and the degree of the disease. The longer the repeat region is the more ribonuclear foci are formed and the stronger are the symptoms. The phenotypic similar disease DM2 is caused by CCTG repeats within the first intron of the ZNF9 gene. Figure 5 describes three known examples of how an unbalance of MBNL1 and CUG-BP concentrations affects splicing. For the CLC1 gene CUG-BP binds to the U/G rich repeats upstream of exon 3 of the CLC1 mRNA, and prevents recognition of its 5’ splice site of exon 3. Hence, the upstream 3’ splice site of exon 2 is not used, which leads to inclusion of intron 2 into the final transcript. A premature stop codon leads to a wrongly spliced mRNA that is targeted by the NMD pathway described by Charlet-B et al. (2002). In case of the IR protein, binding of MBNL1 to intron 11 is important to include exon 11 into the final transcript. It facilitates the recognition of the 5’ splice site of exon 11 by a yet unknown mechanism. In the absence of MBNL1, CUG-BP binds upstream of exon 11 and hinders the spliceosome from binding, resulting in exclusion of exon 11. This process was decribed by Dansithong et al. (2005). A study of the cardiacal Troponin T by Ladd et al. (2005) revealed that normally MBNL1 inhibits the recognition of the 3’ splice site of exon 5 of the cTCT mRNA, whereas in DM patients with higher CUG-BP concentration, CUG-BP binds to an enhancer structure downstream of exon 5 leading to an inclusion of the disease causing exon 5. The von Willebrand disease (VWD) is owned by one percent of the German population and is the most frequently inherited blood coagulating disorder. It is caused by defects of the VWF (von Willebrand factor) gene, which is localized on the human chromosome 12p13.3. From 205 cases reported in Human Gene Mutation Database, 11 cause splicing defects. The VWF-protein supports adhesion of platelets to the sites of vascular injury by connecting the sub-endothelial collagen matrix with the platelet-surface receptor complex GPIb-IX-V. Together with the factor VIII it forms a complex which is circulating within the blood delivering the VWF-protein to the site of injury, stabilizing its heterodimeric structure and protecting it from premature clearance from plasma. A new case reported by Gallinaro et al. (2006) describes a C to A substitution within the acceptor splice site of intron 13 which causes production of two alternative transcripts in addition to the normal one. One skips exon 14 by extending intron 13 while the other uses a new cryptic acceptor splice site placed within intron 13 that extends exon 14 by 62 base pairs to the 5’ side. Both transcript variations show a premature stop codon, leading to non-functional proteins. Retinitis pigmentosa (RP) is a group of similar neurodegenerative diseases of the retina with similar clinical symptoms reviewed by Vervoort and Wright (2002). In an earlier stage RP is associated with night blindness due to progressive loss of rod photoreceptor function. In later stages, day vision is also affected. Incorrect expression of three genes, PRPF31, HPRP3, and PRPC8F, is responsible for the

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Figure 5. A proposed mechanism of how high numbers of CTG (CCTG) repeats can affect splicing of multiple genes. Top: Schematic representation of the DMPK gene with untranslated regions shown as grey boxes and exons as grey-shaded (boxes 1, 14, 15). Bottom: Changes of the splicing patterns of three genes caused by the RNA binding proteins CUG-BP and MBLN1 shown as dark grey and light grey ellipsoids, respectively.

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autosomal dominant RP (Liu et al. 2002). Zhou et al (2002) identified the resulting proteins in isolated functional spliceosomes which are all associated with the U4/U6-U5 splicing factors. One protein is called RPGR (Retinitis pigmentosa GTPase regulator) of which 97 variations are reported in the Human Gene Mutation Database. Nineteen of them are due to splicing defects partly described by Vervoort and Wright (2002).

Alterna ti ve S plicing in C ancer Cancer is a generic term for over 100 different diseases, with different progression, prognoses and therapy. The common feature is increased cell proliferation and the formation of tumours. In principal each cell type of an organism could generate tumour cells. Different studies of mRNA expression patterns have shown that cancer tissue is often associated with unusual or unbalanced expression of alternatively spliced isoforms. Brinkman (2004) and Garcia-Blanco et al. (2004) survey cancer type specific isoforms which can be used as diagnostic markers for different stages of cancer progression and therapy. A recent paper by Ritchie et al (2008) found a number of cancer types correlated with significantly increased variation of alternative splicing. The authors conjecture that changes of splicing factor expression may lead to loss of splicing specificity for tissues and developmental stages. Watermann et al. (2006), Karni et al. (2007), Maeda et al. (1999), Zerbe et al. (2004), Fisher et al. (2004) and Stickeler et al. (1999) describe cases of cancer implied up-regulation of splice factors such as SF2/ASF, U2AF-65, SFRS2, SFRS3, SPm160, hnRNP A1/A2 and TRA2-ß. In Table 1 we show a collection of mutations leading to alternative splicing associated with cancer. One example is given by the CD44 receptor which is known for multiple isoforms due to alternative splicing. Its exon 5 is often involved in tumor progression and T-cell activation. It has been shown by Matter et al. (2002) that inclusion of this exon could be mediated by the RAS pathway. This pathway stimulates the extra cellular signal-regulated kinase (ERK), which phosphorylates the SAM68 splicing factor that binds to the AAAAUU sequence within exon 5. The phosphorylation of SAM68 is required for correct inclusion of exon 5 into the final transcript. In non-tumor cells, the RAS pathway is not permanently active, ERK is not stimulated, SAM68 gets not phosphorylated and the AAAAUU site in exon 5 does not trigger splicing and its inclusion into the final transcript. In tumor cells RAS is often found activated by several environmental factors. Also growth factors which are often autoregulated in cancer cells permanently activate the RAS pathway. Cheng and Sharp (2006) describe the regulation of CD44 alternative splicing by the splice factor SRm160 and its role in tumor cell invasion. The BCL-x gene from the BCL-2 gene family is another example for a changed balance of differently spliced isoforms under cancer conditions. The BCL-2 family is important for the regulation of apoptosis, the so called programmed cell death and reviewed by Akgul et al. (2004). There are three different transcripts of BCL-x called BCL-xL (long), BCL-xS (short) and BCL-x¯ which are decribed by Boise et al. (1993) and Ban et al. (1998). The two splice forms Bcl-xL and BCL-xS result from using two different 5’ splice sites within exon 2 of the BCLx gene. The use of the upstream 5’ splice site results in the short BCL-xS transcript and use of the down stream 5’ splice site leads to the long BCL-xL transcript. Both proteins have opposite effects on apoptosis, BCL-xL is anti-apoptotic and BCL-xS is pro-apoptotic. Following Korsmeyer et al. (1993), the balance between these interacting factors determines the normal cell response to external and internal stimuli. In cancer cells the function of apoptosis is often damaged by a high level of BCL-xL and a decreased level of BCl-xS.

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Table 1. Genes and mutations associated with cancer Gene

Mutation

Cancer typ

Reference

AML1b

AML1b transcript lacking exon 6 (AML1b Del179-242)

Ovarian cancer

Nanjundan et al. (2006)

APC

Germline mutations in the tumor suppressor gene APC; exon 4 (c.423G>T), exon 14 (c.1956C>T, c.1957A>G, and c.1957A>C); complete exon skipping due to damage of an exonic splicing enhancer sequence

Familial adenomatous Polyposis (FAP)

Aretz et al. (2004)

ATM

IVS10-6T>G at the 3’ splice site of intron 10; incorrect splicing of exon 11 and exon skipping, resulting in a frame-shift starting at codon 355 and premature stop codon 371.

Breast cancer

Broeks et al. (2003)

BRCA2

Missense mutation in exon 13 (c.7235G>A), results in skipping of this exon, causing a frame shift and generating a premature stop codon in exon 14; mutation site has low homology to an known exonic splicing enhancer sequence.

Breast cancer

Thomassen et al. (2006)

BRCA2

BRCA2 variant 8204G>A is a splicing mutation. The acceptor site of exon 17 is damaged which implies skipping of this exon.

Breast cancer

Hofmann et al. (2003)

BRCA1

IVS10-2A–>C produces an aberrant RNA splicing transcript with missing exon 11.

Breast cancer

Keaton et al. (2003)

BRCA1

G to T mutation at position 5199 of exon 18 implies exon skipping due to changing an ESE sequence. Exon 18 is essential for the DNA repair, transcriptional control and tumour supresssion.

Breast cancer

Liu et al. (2001)

CDKN2A

Two different mutations D153spl (c.457G>T) and IVS2+1G>T imply a 74 bp deletion in exon 2 or complete loss of exon 2, respectively.

Cutaneous malignant melanoma (CMM)

Rutter et al. (2003)

HRPT2

IVS2-1G>A of the AG dinucleotide of the 3’splice site of intron 2 leads to deletion of exon 3 or a by 23 bp shorter exon.

Parathyroid tumors

Moon et al. (2005)

KAI1

Deletion of exon 7causes weaker interaction with integrin α1 leading to increased motility and metastasis of the cells.

Gastric cancer

Lee et al. (2003)

KLF6

IVS1-27G>A: generates a novel SRp40 DNA binding site leading to three alternatively spliced isoforms, antagonizing the wtKLF6 function.

Prostate cancer

Narla et al. (2005)

KIT

Deletion of 30 or 34nt in intron10 and exon 11, respectively, leads to a mis-spliced constitutively activated onkoprotein (KIT).

Gastrointestinal stromal tumors

Chen et al. (2005)

LI-cadherin

Mutation at a putative branch point at IVS6 + 35 A>G in intron 6 leads to loss of exon 7

Hepatocellular carcinoma

Wang et al. (2005)

LKB1

The IVS2+1A>G mutation alters the 5’ splice site of intron 2 (U12-type AT-AC intron)

Peutz-Jeghers Syndrome with increased cancer risk

Hastings et al. (2005)

WT1

Use of an alternative promoter located within intron 1 leads to 147 missing amino acids at the N terminus required for transcriptional repression of sWT1.

Leukemia

Hossain et al. (2006)

This was observed by Cory et al. (2003), Cory and Adams (2002) and Xerri et al. (1996). Hence, changing the balance of these isoforms to increase production of BCL-xS, could make cancer cells more sensitive to chemotherapy.

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Till now unfortunately little is known if cancer causes mis-spliced isoforms or if these isoforms cause cancer. Therefore Hayes et al. (2006) and Pilch et al. (2001) suggest targeting the general RNA splicing machinery as novel strategy for cancer treatment.

Alterna ti ve S plicing and Cl inica l T herapy The growing knowledge about the molecular mechanisms of alternative splicing and how it causes diseases leads to new concepts for clinical therapies. Here we will mention the potential of antisence oligoribonucleotides and modified splicing factors as first strategies to intervene in splicing defects. Kole et al. (2004) and Sazani and Kole (2003) have written excellent reviews about this emerging field. Antisense oligonucleotides (AON) can be used to block splice sites and other signals like splicing enhancers and silencers in order to change the final transcript. Binding of AON to the mRNA creates a short double strand piece of RNA and makes the considered site invisible to splicing factors. However, RNase H, localized in the cell, is able to recognize and destroy double stranded RNA. Therefore the AON has to be chemically modified not to be recognized and degraded by RNase H. The resulting small interference RNA technique has become a widely used tool for down-regulating gene expression and is described by Mercatante et al. (2001), Dallas et al. (2006) and Kurreck (2003 and 2006). Duchenne muscular dystrophy (DMD) is a degenerative muscle disease. Dystrophin is the largest human gene with 2.2 million base pairs and 79 exons. The resulting protein is 3685 amino acids long. Of the 696 mutations reported in the Human Gene Mutation Database 68 lead to loss of exons, shifts of reading frame and non-functional proteins often due to premature stop codons and nonsense-mediated decay as described by Lareau et al. (2007) and Ni et al. (2007). The milder case of DMD is BMD (Becker Kiener disease) in which mutations cause the deletion of less important parts of the dystrophin protein leading to a shorter but more or less functional protein. The most abundant form of DMD is the loss of exon 45 resulting in a frame shift. However, using bioinformatics revealed that an additional skipping of exon 46 re-establishes the reading frame and produces a shortened but probably functional protein. In vitro experiments by Aartsma-Rus and coworkers (Aartsma-Rus et al. 2002; 2003; 2004) with muscle cells from DMD patients having the deletion of exon 45 proved that anti sense oligonucleotides blocking of the splice sites of exon 46 successfully generates functional transcripts which lack both exons 45 and 46. Using the same in vitro method as illustrated in Figure 6 it was possible to skip 11 other exons damaged by DMD. Many cancer cells over express the BCL-xL (long) splice form of the BCL-x gene, which codes for an anti-apoptotically acting protein. Small interfering RNA against the downstream 5’ splice site of its exon 5 leads to a reduced level of BCL-xL and a higher level of its antagonist BCL-xS (short). Experiments by Xie et al. (2006) and Lei et al. (2006) showed that the implied change of balance between these two proteins makes cancer cells more sensitive to chemotherapy and radiation. A similar effect has been shown for another member of the BCL-2 gene family. The expression of the BCL-α isoform is increased in many cancer cells as reported by Real et al. (2002). In vivo experiments by Dias and Stein (2002) and using anitsense oligonucleotides blocking could demonstrate that suppression of the BCL-α isoform inhibits the expansion and progression of tumors. Mutations of the β-globin gene IVS2 within intron 2 create a novel aberrant 5’ splice site and activate a cryptic 3’ splice site finally leading to a premature stop codon. Using AON technique these mutations could be corrected in a culture system reported by Suwanmanee et al. (2002a/b)

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Figure 6. Antisense oligonucleotides blocking induces skipping of exon 46 to re-establish the correct reading frame of the damaged dystrophin gene found in DMD patients lacking exon 45.

A mutation within intron 19 of the CFTR (cystic fibrosis transmembrane conductance regulator) gene creates a novel 5’ splice site and activates an additional otherwise un-present exon. Like in the previous case Friedman et al. (1999) re-established correct splicing by AON. Another example is the correction of the tau gene associated with frontotemporal dementia and parkinsonism linked to chromosome 17. One of the major mRNA changes in this disease is the inclusion of exon 10. Within a tau minigene system and neuronal pheochromocytoma cells, Kalbfuss et al. (2001) was able to stop inclusion of exon 10 using AON against its splice sites. The success of future practical therapy of the discussed diseases by AON naturally depends on the stability of RNA blocking over a certain time. Therefore improved so called locked nucleic acid (LNA) oligonucleotides were proposed by Roberts et al. (2006). These oligonucleotides were observed to bind up to 3 weeks. Oligonucleotide induced recruitment of splicing factors is another approach to control splicing patterns. For example, in the cases of SMA, the SMN1 gene is lost or mutated. The replacement gene SMN2 is less effective since its transcript often lacks the important exon 7. To overcome this problem Cartegni et al. (2006) invented a chimeric protein. With its N terminus it binds to the less functional exonic splicing enhancer located in the skipped exon 7 of SMN2 and on its C terminus it carries a peptide structure similar to other SR proteins which control interaction with the splicing machinery as described by Cartegni and Krainer (2003) and illustrated in Figure 7. In fact, the mimicked SR-protein was observed to work, attracting the splicing machinery and increasing the production of SMN2 mRNA including exon 7 in a dose dependent manner. This technique perhaps opens a general way to restore normal splicing patterns for genes with damaged control signals.

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Figure 7. Inclusion of exon7 into the SMN2 transcript facilitated by a chimeric protein SF** induces recognition of the acceptor site of exon 7.

Co nc lusi on Alternative RNA splicing is the prevailing mechanism of gene expression to generate the great diversity of proteins which is typical for complex forms of life. It is strictly controlled by a complex system of about hundred known splicing factors and a number of complex sequence signals like splice sites, the branch point signal, splicing enhancers and silencers. It is therefore no surprise that sequence mutations and damaged splicing factors can have pathological effects. Our review presented different examples for erroneously spliced gene products which cause severe diseases. The complex process of normal and aberrant splicing offers a number of targets for possible therapies which differ from gene therapy by not repairing genes but making improved use of damaged genes as already known for Duchenne muscular dystrophy. One technology described in this review is the application of complementary oligonucleotides like siRNA in order to suppress unfavourable splice sites, splicing enhancers or silencers (Aartsma-Rus et al.2006). Oligonucleotide induced recruitment of splicing factors is another approach. More research in this direction and focussed on a single important disease like cystic fibrosis (CF) can perhaps soon provide a successful therapy. CF is one of the best studied hereditary diseases and much is known about the process of alternative splicing and other molecular mechanisms related with this disease. The described siRNA technique could soon allow restoring of correct splicing. Another target is increasing the stability and the half-life of correctly or favourably spliced mRNAs in order to produce more functional proteins from each single mRNA template. It could lead to successful treatments of spinal muscular atrophy, myotonic dystrophy and other diseases which are caused by insufficient production of known proteins.

A ckn ow ledgment This work was supported by the BMBF Germany under contract number 0312705A.

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Thomassen, M., Kruse, T. A., Jensen, P. K., & Gerdes, A. M. (2006). A missense mutation in exon 13 in BRCA2, c.7235G>A, results in skipping of exon 13. Genet Test., 10(2), 116-120. Vervoort, R., & Wright, A. F. (2002). Mutations of RPGR in X-linked retinitis pigmentosa (RP3). Hum Mutat,. 19(5), 486-500. Wang, X. Q., Luk, J. M., Leung, P. P., Wong, B. W., Stanbridge, E. J., & Fan, S. T. (2005). Alternative mRNA splicing of liver intestine-cadherin in hepatocellular carcinoma. Clin Cancer Res., 11(2 Pt 1), 483-489. Watermann, D. O., Tang, Y., Zur Hausen, A., Jager, M., & Stamm, S., et al. (2006). Splicing factor Tra2-beta1 is specifically induced in breast cancer and regulates alternative splicing of the CD44 gene. Cancer Res., 66, 4774-4780 Will, C. L. & Luhrmann, R. (2001). Spliceosomal UsnRNP biogenesis, structure and function. Curr Opin Cell Biol., 13(3), 290-301. Xerri, L., Parc, P., Brousset, P., Schlaifer, D., Hassoun, J., & Reed, J. C. et al. (1996). Predominant expression of the long isoform of Bcl-x (Bcl-xL). in human lymphomas. Br. J. Haematol., 92, 900-906 Xie, Y. E., Tang, E. J., Zhang, D. R., & Ren, B. X. (2006). Down-regulation of Bcl-XL by RNA interference suppresses cell growth and induces apoptosis in human esophageal cancer cells. World J Gastroenterol, 12(46), 7472-7477. Zerbe, L. K., Pino, I., Pio, R., Cosper, P. F., & Dwyer-Nield, L. D., et al. (2004). Relative amounts of antagonistic splicing factors, hnRNP A1 and ASF/SF2, change during neoplastic lung growth: implications for pre-mRNA processing. Mol Carcinog, 41, 187-196 Zhou, Z. H., Licklider, L. J., Gygi, S. P., & Reed, R. (2002). Comprehensive proteomic analysis of the human spliceosome Nature, 218, 182-185 Zielenski, J., & Tsui, L. C. (1995). Cystic fibrosis: genotypic and phenotypic variations. Annu Rev Genet., 29, 777-807.

K ey T erms Alternative Splicing: Alternative choice of introns which are spliced out during pre-mRNA processing. Autosomal Recessive Disorder: Disorder that only occurs if both alleles of a pair of autosomal chromosomes are mutated. Beta-Globin Gene: Gene that codes for the beta globin chain of the hemoglobin protein. CFTR (Cystic Fibrosis Transmembrane conductance Regulator): CFTR is an ion channel protein belonging to the class of ABC transporters. It transports chloride ions through the cell membrane. Dysfunction of this protein causes the Cystic fibrosis.

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Exon: An exon is a part of the pre-mRNA that is not removed during the RNA-splicing process. Exonic Splicing Enhancer/Silencer: A pre-mRNA sequence motif of about six bases within an exon regulating enhanced/silenced splicing at a close by sequence position. Hereditary Disease: A genetic disorder is called a hereditary disease. Human Gene Mutation Database: The Human Gene Mutation Database (HGMD) constitutes a comprehensive core collection of data on germ-line mutations in nuclear genes underlying or associated with human inherited disease (www.hgmd.org). Hyperexcitability: A mutation in a cation ion channel which leads persistent muscle contractions caused by increased cell membrane voltage. Intron: A pre-mRNA fragment that is cleaved out during pre-mRNA splicing. Intronic Splicing Enhancer/Silences: A pre-mRNA sequence motif of about six bases within an intron regulating enhanced/silenced splicing at a close by sequence position. Ligation: The joining of two molecules facilitated by an enzyme called ligase. In our context ligation denotes the joining of exon fragments during pre-mRNA splicing. Spliceosome: The entire assembly of proteins that facilitates pre-mRNA splicing. Thalassemia: Severe heriditary disease caused by mutations in the beta-globin gene sequence.

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Section V

Systems Biology and Aging

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Chapter XVIII

Mathematical Modeling of the Aging Process Axel Kowald Medizinisches Proteom Center (MPC), Ruhr-Universität Bochum, Germany

abstract Aging is a complex biological phenomenon that practically affects all multicellular eukaryotes. It is manifested by an ever increasing mortality risk, which finally leads to the death of the organism. Modern hygiene and medicine has led to an amazing increase in average life expectancy over the last 150 years, but the underlying biochemical mechanisms of the aging process are still poorly understood. However, a better understanding of these mechanisms is increasingly important since the growing fraction of elderly people in the human population confronts our society with completely new and challenging problems. The aim of this chapter is to provide an overview of the aging process, discuss how it relates to system biological concepts, and explain how mathematical modeling can improve our understanding of biochemical processes involved in the aging process. We concentrate on the modeling of stochastic effects that become important when the number of involved entities (i.e., molecules, organelles, cells) is very small and the reaction rates are low. This is the case for the accumulation of defective mitochondria, which we describe mathematically in detail. In recent years several tools became available for stochastic modeling and we also provide a brief description of the most important of those tools. Of course, mitochondria are not the only target of modeling efforts in aging research. Therefore, the chapter concludes with a brief survey of other interesting computational models in this field of research.

W ha t is aging? Looking at the enormous rise of average human lifespan over the last 150 years, one could get the impression that modern research actually has identified the relevant biochemical pathways involved in aging and has successfully reduced the pace of aging. Oeppen and Vaupel (2002) collected data on world

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Mathematical Modeling of the Aging Process

wide life expectancy from studies going back to 1840. Figure 1 shows the life expectancy for males (squares) and females (circles) for the countries that had the highest life expectancy for the given year. Two points are remarkable. Firstly, there is an amazingly linear trend in life expectancy that corresponds to an increase of 3 months per year (!) and secondly there is no leveling off observable. These impressive data suggest strongly that lifespan will also continue to rise in the next years, but it does not show that the actual aging rate has fallen during the last century. Aging can best be described as a gradual functional decline, leading to a constantly increasing risk to die within the next time interval (mortality). The Gompertz-Makeham equation (Gompertz, 1825; Makeham, 1867), m(t) = I ⋅ eG t + E, describes how the exponential increase of mortality depends on intrinsic vulnerability (I), actuarial aging rate (G) and environmental risk (E). All living organisms have a base mortality caused by environmental risks, but it is the aging rate, G, which causes human mortality to double approx. every 8 years. From I

this equation we can derive the following expression for the survivorship function: N(t) = e G

(1−e )− E t. Gt

Figure 1. Male (blue squares) and female (red circles) life expectancy in the world record holding country between 1840 and 2000 based on the annual data of countries world wide (reproduced with permission from Oeppen & Vaupel, 2002).

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Mathematical Modeling of the Aging Process

As expected we see that the number of remaining survivors depends on all three parameters and consequently a change of the average life expectancy (time until 50% of the population has died) can be caused by a modification of any of those parameters. This point is also discussed in more detail by (Kowald, 2002). And indeed, analyzing the survivorship data of the last 100 years more closely, it becomes clear that the aging rate, G, remained constant. The enormous increase in life expectancy was achieved exclusively by changes of intrinsic vulnerability and environmental risk! Because of the drastic social, economical and political consequences that are brought about by the demographic changes of the age structure of the population, it is now more important than ever to understand what constitutes the biochemical basis for a non-zero aging rate, G. Systems biology might help to achieve this goal.

W hy is aging a prime candida te f or systems

bi ology?

Evolutionary theories of the aging process explain why aging has evolved, but unfortunately they don’t predict specific mechanisms to be involved in aging. As a consequence more than 300 mechanistic ideas have been developed (Medvedev, 1990), each centered around different biochemical processes. This is probably due to the fact that even the simplest multicellular organisms are such complex systems that many components have the potential to cause deterioration of the whole system in case of a malfunction. Figure 2 shows a small sample of the most popular mechanistic theories. The spatial arrangement of the diagram intends to reflect the various connections between the different theories. And it is exactly the large number of interactions that makes it so difficult to investigate aging experimentally and renders it ideal for systems biology. To understand this we will look at a few examples. The Telomere Shortening Theory is an important idea that has gained considerable support in the last 10-15 years. Telomeres are the physical ends of linear eukaryotic chromosomes and vital for the

Figure 2. Graphical representation of some mechanistic theories of aging. The topology of the diagram reflects logical and mechanistic overlaps and points of interaction between different theories.

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Mathematical Modeling of the Aging Process

functioning of the cell (Lundblad & Szostak, 1989; Yu, Bradley, Attardi, & Blackburn, 1990). It has been recognized for a long time that linear DNA has a replication problem since DNA polymerases can only replicate in the 5’-3’ direction and cannot start DNA synthesis de novo (Olovnikov, 1973; Watson, 1972). This inability leads to a gradual loss of DNA, which was confirmed experimentally for human fibroblasts in 1990 and consequently proposed as being responsible for aging (Harley, 1991; Harley, Vaziri, Counter, & Allsopp, 1992). Telomere shortening provides the explanation and connection to the Hayflick Limit, the long known phenomenon that most cultured cell types have only a limited division potential. This in turn is by some researcher interpreted as evolutionary selected trait that acts as a cancer prevention system by preventing unlimited cell division. While the direct cause of telomere shortening is the lack of the enzyme telomerase, there is an interaction to oxygen radicals that complicates the mechanism. Oxidative stress was shown to increase the rate of telomere shortening and thus modulating the telomere attrition (von Zglinicki, Saretzki, Docke, & Lotze, 1995). As the figure indicates, free oxygen radicals are also the central hub to several other prominent phenomena affecting the aging process. They damage all kinds of macromolecules, leading to cross linking of proteins and the generation of indestructible waste products that accumulate in post mitotic cells (i.e. lipofuscin). Degraded mitochondria are supposed to be a major fraction of these waste products and certain oxygen radicals are known to damage the mitochondrial membrane. It seems, however, that radical induced somatic mutations of the mitochondrial DNA (mtDNA) are the main route to defective mitochondria, which produce less energy, but generate more radicals (Linnane et al., 1990; Linnane, Marzuki, Ozawa, & Tanaka, 1989; Miquel, Economos, Fleming, & Johnson, 1980). These mutants are capable of taking over the mitochondrial population of the cell, causing a chronic energy deficiency and maybe aging. It is still unclear what the selection pressure and mechanism is that leads to the accumulation of defective mitochondria, but several suggestions have been made (de Grey, 1997; Kowald, Jendrach, Pohl, Bereiter-Hahn, & Hammerstein, 2005; Kowald & Kirkwood, 2000). Supporting evidence has been found for all the above mentioned ideas and the many interdependencies make ageing a phenomenon that is very difficult to study experimentally. If a single mechanism is studied in isolation, it is hard to interpret the results that were obtained without the contribution of the other mechanisms. And if a complex system is studied with all involved pathways, it is expensive, technically demanding and now the results are difficult to interpret because of the large number of factors that might have influenced the results. This is exactly the situation where a systems biological approach is useful. Systems biology aims at investigating the components of complex biochemical networks and their interactions, applying experimental high-throughput and whole genome methods, and integrating computational and mathematical methods with experimental efforts. The growing number of high-throughput techniques that have been developed in the last years is a major driving force behind the wish to utilize computational methods to manage and interpret the high data output. Modelers, on the other side, are keen to use the generated data to develop quantitative models of systems with complex interactions. Because of the large number of parameters such models would not be meaningful without sufficient experimental measurements. In addition, quantitative modeling of complex systems has several benefits. First of all, it requires that each aspect of a verbal hypothesis is being made specific. Before a computational model can be developed, the researcher has to define each component and how it interacts with all the other components. This is a very useful exercise to identify gaps in current knowledge and in the verbal model. It helps to complete the conceptual model, respectively motivates experiments to collect the missing

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Mathematical Modeling of the Aging Process

experimental information. To understand complex systems with components that produce opposing effects it is essential to have a model with quantitative predictions. Purely qualitative models (such as verbal arguments) are not sufficient to decide how a system develops over time if it contains non-linear opposing subcomponents. Computational models are also a convenient way to explore easily and cheaply “what if” scenarios that were difficult or impossible to test experimentally. What if a certain reaction would not exist? What if a certain interaction would be ten times stronger? What if we are interested in time spans too short or too long to observe in an experiment? In the next section we will show in detail how a mathematical model can be constructed for a specific problem in aging research that (i) gives insight into a not well understood phenomenon, (ii) explores several “what if” questions that would be difficult to text experimentally and (iii) makes suggestions for further experiments.

Underst anding

the acc umulati on of defecti

ve mit och ondria

Although a large number of mechanistic theories of aging exist, there are a few that have gained widespread popularity. Probably the most intensively studied idea is currently the free radical theory in combination with the accumulation of defective mitochondria. Large mtDNA deletions were found in post-mitotic tissues (heart, brain skeletal muscle) of aging individuals (Hattori et al., 1991; Linnane et al., 1990). Early studies were performed on tissue homogenates and found that the fraction of defective mtDNAs is well below 1% (Cortopassi, Shibata, Soong, & Arnheim, 1992; Randerath, Randerath, & Filburn, 1996). However, it turned out that the underlying assumption that mitochondrial damage is distributed homogeneously within a tissue is wrong. The combination of PCR amplification of extended sequences together with single cell studies revealed that muscle tissue displays a mosaic pattern of mitochondrial damage. While even in old individuals most cells harbor little or no damaged mitochondria, there are a few cells that contain a large proportion of mitochondrial mutants (Cao, Wanagat, McKiernan, & Aiken, 2001; Gokey et al., 2004; Khrapko et al., 1999). These studies demonstrated that in affected cells the mitochondrial population was apparently taken over by a single mutant, which was different for different cells. This suggests that the cellular accumulation of defective mitochondria proceeds via clonal expansion of a single originating mutant. But how can a single mutant mitochondrial DNA, which lacks essential genes, out-compete the population of wild type mitochondria? The phenomenon that mitochondria form dynamic networks, undergoing constant fission and fusion events has been observed for several cell types, such as yeast, plants, HeLa and human endothelial cells (Arimura, Yamamoto, Aida, Nakazono, & Tsutsumi, 2004; Jendrach et al., 2005; Karbowski et al., 2004; Nunnari et al., 1997; Takai, Inoue, Goto, Nonaka, & Hayashi, 1997; Takai, Isobe, & Hayashi, 1999). This opens the possibility that the shorter replication time of deleted mtDNAs represents the selection advantage, since all the mitochondria of a cell effectively form one large compartment with constant mixing of mtDNA as well as matrix and membrane components. Under these conditions, mtDNA deletions no longer lead to energy and proton gradient deficiencies within a single mitochondrion since there is a common pool of these resources. We therefore developed a model of mtDNA mutation, replication and degradation (Kowald et al., 2005) that should explain the cellular mosaic pattern of mitochondrial damage and the observed distribution of deletion sizes in old rats found by Cao et al. (2001).

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Mathematical Modeling of the Aging Process

T he Model The model was simulated stochastically to explicitly take into account random fluctuations and the discrete nature of the studied biological objects. Mutation events with their inherently small probabilities require a non-deterministic approach to describe adequately the finding that in old animals some cells do contain mitochondrial mutants and others do not. Gillespie developed exact stochastic simulation algorithms that directly calculate the change of the number of molecules of the participating species during the time course of a chemical reaction (D. T. Gillespie, 1977). Thus stochastic algorithms calculate explicitly the time until the next reaction takes place (e.g. A→B+C) and keep track of how the number of molecules in the system is changed by this reaction (A decreased by one, B and C increased by one). Such an approach also deals with the discrete nature of molecule numbers. This is of special importance for self-replicating entities (like mtDNAs) if the number of objects is either zero or one. One mutant mtDNA can multiply and take over the cell, while zero mtDNA molecules obviously cannot. Differential equations, however, assume that variables can attain continuous values, so that 0.001 mtDNAs is a valid simulation result. Because this value is different from zero it is theoretically possible that a population of mutants can recover from such low levels and replace the wild-type: an unrealistic situation which is avoided by stochastic simulations. The free software package Dizzy was used for all simulations (Ramsey & Orrell, 2005). Dizzy is written in Java and implements several stochastic (Gillespie, Gibson-Bruck, Tau-Leap) and deterministic (ODE solvers) simulation algorithms. Models can be described in Systems Biology Markup Language (SBML) (Hucka et al., 2003) or using a proprietary model definition language (CMDL). Because of a special language construct it was possible to define the 4950 mutation reactions with just five lines of code in CMDL. To be comparable with the experimental conditions of Cao et al. (2001), Gillespie’s direct method was used to calculate the fate of a mitochondrial population within a cell for 1100 days, corresponding to 38 months of a rat’s life. On a modern workstation such a calculation took approx. 1 hour. The simulation was then repeated 1000 times on a Linux cluster to have enough information for a statistical analysis of the accumulation process of defective mitochondria.

Mutations In this simulation study only deletion mutations affecting the large arc (Figure 3B) of the rat genome are considered. It is assumed that deletions which include the heavy or light strand origin of replication (OH and OL) are no longer capable of replication and thus cannot accumulate. Deletions affecting exclusively the minor arc are also excluded, since they have not been observed (Cao et al., 2001). To further simplify and speed up the simulation, deletions are modeled with a granularity of 100 bp, i.e. deletions can be of 100, 200 or 300 bp, but not 250 bp. Consequently, the model contains 100 possible classes of mitochondrial genotypes, wild-type (M0) and 99 different types of deletions ranging from 100 bp (M1) to 9900 bp (M99). Note that the name indicates the size of the deletion. Other assumptions that have been made regarding mitochondrial mutations are: 1.

Deletion mutants can suffer from further deletion events (Mx→My, x
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Mathematical Modeling of the Aging Process

Figure 3. A) Overview of the mutations allowed by the model. Different mutants are labeled by numbers and the larger the number, the larger the deletion that this mutant carries. Arrows indicate possible mutations, showing that small (M0→M1) or large (M0→M4) pieces of DNA can be lost in a single mutation event. Mutants can suffer further mutations leading to even smaller mutants (M1→M4 but not M1→ M0). B) Schematic drawing of the rat mtDNA showing OH, the origin of the heavy strand synthesis and OL the origin of the light strand synthesis. The locations of the origins define the minor and major arc with the replication of the strands proceeding in the direction indicated by the arrows. OH

A)

B)

M1

M2

M0

Rat mtDNA . kb OL M4

2.

3.

4.

M3

Since no details are known of the biochemical mechanisms underlying the deletions, we assume that the mutation rate is proportional to the length of the mtDNA molecule and has the dimension per day per kbp. Thus larger mtDNAs have a higher probability of mutation than small mtDNAs. Another important point is the outcome of a deletion event. What is the size distribution of the resulting deletion mutants ? Without knowing the biochemical basis of the deletion process it is not possible to predict if all deletions will be of identical size or what type of distribution to expect. Under these circumstances we assume that the deletion is the result of two random cuts within the large arc. This leads to a distribution with a linearly increasing probability for the occurrence of small deletions. Basically, large deletions are very rare since only a few cut positions exist within the large arc that will result in a large deletion fragment. Finally, we investigate the possibility that the presence of defective mtDNAs increases oxidative stress, and thus the mutation rate, within a cell. It is therefore assumed that the mutation rate is increased by a certain factor (the ‘boost factor’) if 100% of the mitochondrial population is defective. A linear relationship between the fraction of defective organelles and the increase in oxidative stress is assumed, so that a cell with X% mutants has its mutation rate increased by: ‘boost factor * X/100’.

Taking the above points into account the following equation can be constructed that calculates the mutation rates leading from one mutant type to another. The first term describes the effects of increasing oxidative stress caused by mitochondrial mutants (point 4). If there are only wild-type organelles

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Mathematical Modeling of the Aging Process

(M0), the term reduces to one, leaving the mutation rate unchanged, as calculated by the second term. But for a population consisting to 100 percent of mutants (M1 to M99) the first term evaluates to bF, the boost factor. The second term incorporates the assumption that the mutation rate is per kbp and therefore the baseRate is multiplied by the length of the mtDNA of mutant Mi, which is given by (16-0.1*i). Furthermore, we have to take into account that small deletions are more likely to occur than large ones (point 3). There is a 1/1002 chance of placing two random cuts (limited to 100 bp intervals) such that a 10kbp piece results, but there is a 100/1002 chance of placing the two cuts such that a 0.1kbp piece results (i.e. a (100-k)/10000 chance for a deletion size of k*0.1kbp). Since the total mutation rate is distributed among all possible resulting mutants

(∑

100 i =1

)

i / 10000 ≈ 1 / 2 , the resulting equation is given by:

∑

 (bF − 1) ⋅ M i    baseRate ⋅ (16 − 0.1 ⋅ i) ⋅ (100 − k) i =1 + 1 ⋅ mutRateik =  5000 Mi   i =0  

∑

Replication It is assumed that replication time is proportional to the length of the mtDNA molecule. However, because of the special mode of replication of mtDNA, some regions of the mitochondrial genome count twice. The origins of replication of the heavy and light strands of the mammalian mtDNA molecule (OH and OL, respectively) are located at different positions on the molecule (Figure 3B). The replication process proceeds asymmetrically via strand-displacement (Clayton, 2003; Tapper & Clayton, 1981). Leading strand synthesis starts at OH and continues clockwise along the major arc until it reaches and exposes the origin of the lagging strand, OL. Only now can lagging strand synthesis start counter-clockwise through the major arc, while leading strand synthesis continues through the minor arc until it has completed a full round of replication. However, the process is not finished until lagging strand synthesis has also completed the full circle of DNA. The time for the total replication process is therefore the time required for the synthesis of the full length molecule plus the time that the start of light strand synthesis lags behind the start of heavy strand synthesis. For the wild-type molecule this is the time required to synthesize 16 kbp + 10 kbp = 26 kbp so that the major arc effectively counts twice. As a consequence a mutant with a complete deletion of the major arc replicates 26/6 = 4.33 times faster than wild-type and not 16/6 = 2.66 times, as might have been expected. To construct a model that leads to a steady state population of mtDNA molecules we have to add negative feed back such that the total synthesis of mtDNA declines with increasing copy number in the cell. The following equation shows how this feed back enters into the calculation of the replication rate for mutant Mi. The first term is a Hill type product inhibition depending on the total number of genomes, a parameter which controls when the total synthesis rate has reached 50% of its maximum (k), and an exponent determining how sharply the system reacts if the number of mtDNA departs from ‘k’. The term includes a constant specifying the maximum number of mtDNA that can be produced per day (c).

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Mathematical Modeling of the Aging Process

repRatei =

c ⋅ k5   

∑ i

5

 Mi  + k 5 

⋅

26 ⋅ Mi 26 −i⋅0.2 26 ⋅ Mi 26 −i⋅0.2

∑ i

If there are no mtDNA molecules, the total number of newly synthesized genomes is ‘c’, if the number of mtDNAs is equal to ‘k’ the synthesis rate is reduced to ‘c/2’ and if the number of mtDNAs is very large the total synthesis rate approaches zero. We also have to specify how the total amount of synthesized mtDNAs is distributed between the different types (mutants). This is done by the second term that basically weights the different types according to their size advantage and number. If there is only wild-type (M0), the second term simplifies to 1, indicating that all synthesized genomes will be wild-type. If there is a mutant with a 10 kbp deletion (M100) together with equal amounts of wildtype, a fraction 1/(1+26/6) = 0.1825 of the newly synthesized genomes will be wild-type and a fraction (26/6)/(1+26/6) = 0.8125 will be of type M100.

Degradation If new mtDNAs are synthesized some genomes have to be degraded to maintain a stable population size. Unfortunately, little is known about the process of mitochondrial degradation. It is not known if they are selected for degradation according to the amount of membrane damage, as suggested by the SOS hypothesis (de Grey, 1997) or if they are selected randomly. However, here we are exclusively interested in the effects of different mtDNA sizes and in this context degradation of mitochondria means degradation of mtDNA molecules. For the purpose of this study we assume identical degradation rates, and therefore half-lifes, for all types of mtDNAs (M0 to M99). For all simulations shown, the half-life was set to 10 day (see also Table 1).

R esults Figure 4 displays the results for simulations using a mutation rate of 6*10-7 day-1 kbp-1. Part A of the figure is effectively a contour plot showing the accumulation of mtDNA mutants over time. The solid line, for instance, indicates the fraction of cells that contain at least one defective mitochondrial genome (>0% mutants) at a given time. Under the mutation rate used in these simulations, all cells contained one or more mutants after 400 days. Since each simulation run computes the fate of the mtDNA population of a single cell over time, the ‘fraction of cells’ is identical to the fraction of simulation runs performed. The other contour lines represent higher levels of defective mtDNAs. The point marked by the arrow shows that after approx. 200 days, 60% of the cells had a mtDNA population consisting of at least 20% defective genomes. The other parameters used for this simulation are summarized in Table 1. No boost factor has been used (bF=1), i.e. defective mtDNA did not increase oxidative stress. Parameters ‘k’ and ‘c’, necessary for the calculation of the replication rate, were set to 5000 and 1000, respectively. Together with the 10 day half-life of mitochondrial DNA, this resulted in a mtDNA population size of approx. 5500 (data not shown). This is in good agreement with studies of skeletal and heart muscle that find values between 3000 and 7000 mtDNA molecules per cell (Miller, Rosenfeldt, Zhang, Linnane, & Nagley, 2003).

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Mathematical Modeling of the Aging Process

Figure 4. Simulation results for a high mitochondrial mutation rate (6*10-7 day-1 kbp-1). A) Summary of the accumulation pattern of defective mitochondria obtained by following the fate of 1000 cells. The curves show the fraction of cells that contain more than 0, 20, 40 or 60% defective mitochondria, i.e. after 200 days roughly 60% of the cells had more then 20% of defective organelles (marked by arrow). B) Distribution of mitochondrial deletion sizes at four equally spaced time points during the life of a rat. Early in life (day 281) the distribution contains a large fraction of small deletions down to 0.5 kbp. As time progresses, these small deletions disappear until finally (day 1127) the distribution is practically free of deletions smaller than 3.5 kbp. The diagram is based on the results of 1000 simulation runs.

The diagram shown in Figure 4A summarizes the total number of defective genomes that accumulate with time, but does not differentiate among different deletion sizes. For this purpose the histogram of deletion sizes at four different time points (day 281 to day 1127) is shown in Figure 4B. As can be seen, early on many small deletions down to 0.5 kbp are present. But as time progresses, the shape of the distribution changes: small deletions disappear and larger deletions emerge. This resembles very closely the size distribution observed experimentally for old rats (Cao et al., 2001). It turns out that the model assumption that mutants can mutate again is responsible for the disappearance of small deletions over time.

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Mathematical Modeling of the Aging Process

Table 1. Parameters and standard values used for the simulations Name

Value

baseRate

6*10 day kbp

Mutation rate per day and kbp. Order of magnitude is in accordance with (Shenkar et al., 1996).

bF

1

Factor by which the mutation rate is increased if 100% of the mitochondrial population are deletion mutants.

K

5000

If the number of mitochondria is equal to ‘k’, the synthesis rate of new organelles is half maximal. This is related to the number of mtDNAs per cell which ranges from 700 in sperm (Diez-Sanchez et al., 2002), 7000 in heart muscle (Miller et al., 2003) to 25000 in liver (Berdannier & Everts, 2001).

C

1000

degRate

ln(2)/10 day

-7

Description -1

-1

Maximum number of mitochondria that can be synthesized per day. -1

Degradation rate for all mtDNAs. Corresponding to a half-life of 10 days (Huemer, Lee, Reeves, & Bickert, 1971; Korr, Kurz, Seidler, Sommer, & Schmitz, 1998; Menzies & Gold, 1971).

C onclusion In the presented model description we omitted several of the actually performed simulations for brevity, but the main benefits of the modeling approach are clear. The stochastic approach is important to account for the probabilistic nature of mutations, which is likely to be responsible for the mosaic pattern of healthy and impaired cells seen in cross sections of tissues from old organisms. In some of the simulation runs, no mitochondrial mutants were present after 38 months, while in others a deletion event took place and the wild-type mtDNA was replaced by the mutant. A model composed of differential equations could not have captured such a pattern, since that approach is more equivalent to the experimental method of using tissue samples containing millions of cells. The result is in both cases an averaging effect, obscuring the true pattern of accumulation of mtDNA deletion mutants. Furthermore, the model (i) provides the inside that the lack of small deletions might be caused by several successive generations of mutants with increasing deletion size, (ii) it is able to explore several scenarios, which are inaccessible for experiments (high or low mutation rate, different influence of oxidative stress on mutation rate) and (iii) it makes the prediction that the size distribution should be quite different in young animals, with much more small deletions being present.

Tools f or S t ochastic

Mode ling

Most current modeling in systems biology is done using deterministic ordinary differential equations, because many tools exist for this type of modeling and the results are easier to interpret. But as discussed above, there are good reasons to perform stochastic simulations if molecule numbers are low. This approach, however, requires substantially more computing power, since many trajectories have to be simulated for a statistical analysis of the system. The number of software packages capable of stochastic simulations is slowly but constantly growing and in the following we will present a brief survey.

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Mathematical Modeling of the Aging Process

D izzy ‘Dizzy’ (Figure 5) is the software tool we used for the mitochondrial model described above and it has several nice features that make it our favourite tool. It is written in Java and thus platform independent. This is very helpful in heterogeneous environments consisting of Linux/Unix and Windows machines. Furthermore, Dizzy has an easy to use GUI and the results can be directed to a data file or displayed graphically. Another useful feature is the separation of GUI and the number crunching routines. This made it possible for us to calculate thousands of model trajectories on our Linux cluster and analyse the results later. Dizzy not only contains various stochastic solvers (Gillespie direct method, GibsonBruck, τ-leap method), but also a number of deterministic ODE solvers. Without any modifications a model can be simulated stochastically or deterministically. This is very convenient for comparing the two different approaches and for obtaining a fast first view of the model behaviour (by using the ODE solver). A model can be defined in the de facto standard SBML (Systems Biology Markup Language)

Figure 5. Screenshot of the stochastic simulation software package ‘Dizzy’. Three different windows of the GUI are shown. The editor in the background displays a model description, whose simulation results are shown in the window at the top right. In the front window at the bottom the type of simulator (stochastic or deterministic) and the output destination (diagram, table, file) are chosen.

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Mathematical Modeling of the Aging Process

or in a powerful model definition language called CMDL. This was essential for our simulations, since it enabled us to define 4950 mutation reactions with only five lines of code. Dizzy is developed by Stephen Ramsey at the Institute for Systems Biology and is freely available (http://magnet.systemsbiology.net/software/Dizzy).

Other T ools Copasi (http://www.copasi.org) is another popular tool that is also capable of stochastic (Gibson-Bruck) and deterministic simulations. Copasi can read and write SBML models and its major strength is the analysis of existing deterministic models. It performs metabolic control and steady state analysis, calculates Lyapunov exponents and can be used for model parameter estimation using time course or steady state data. Like Dizzy it can be used as a command line version for batch processing. Stocks 2 (http://www.sysbio.pl/stocks) can only perform stochastic simulations but contains, in addition to the standard solvers, also a hybrid algorithm for reaction systems that consist of a mixture of rare and frequent molecular species. Stocks models frequent species using an approximate algorithm and slow reactions with an exact Gillespie algorithm. Species are assigned dynamically to the frequent respectively rare group to take care of concentration changes over time. The Systems Biology Workbench (SBW) (Hucka et al., 2002) is a software infrastructure that enables different tools to communicate with each other (http://www.sys-bio.org). That means all SBW aware programs can use services provided by different modules and in turn advertise their own specialized services. A powerful SBW module that provides stochastic simulation and analysis functions has been developed by the Sauro group and can be downloaded from http://public.kgi.edu/~rrao. Popular model construction tools that are SBW aware are for instance JDesigner (included in SBW) or CellDesigner (http://www.celldesigner.org). The software packages discussed so far are only suitable for spatially homogeneous models, which implies a constant and immediate mixing of all participating species. For stochastic simulations of 3D reaction diffusion systems, MesoRD (Hattne, Fange, & Elf, 2005) is suitable. It is free software, written in C++ and implements the next subvolume method to simulate the Markov process corresponding to the reaction-diffusion master equation. It can be obtained from http://mesord.sourceforge.net.

Su r vey of mathema tica l mode ling in aging

research

While the section about the accumulation of defective mitochondria gave an in depth view of the development and use of a mathematical model for aging research, it is of course only one in a large number of models in this area of research. To provide the reader with a broader picture of the types of models that exist and the types of problems that are tackled, we close this chapter with a brief survey of selected models from the literature. The interaction between oxygen radicals and mitochondria plays a very important role in many aging theories and one of the most complete models of oxidative membrane damage to mitochondria has been developed by Antunes et al. (1996). They developed a system of ordinary differential equations describing more than 80 reactions of lipid metabolism in the inner mitochondrial membrane and surrounding matrix environment. Apart from being an invaluable source of kinetic parameters the main result is that the perhydroxyl radical is the main initiator of lipid peroxidation.

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Mathematical Modeling of the Aging Process

Another publication dealing with mitochondria is by Albert et al. (1996). They model the dynamics of plant mitochondrial genomes, which are composed of a set of molecules of various sizes that generate each other through recombination between repeated sequences. Their stochastic model describes the selection process at the inter-molecular, inter-mitochondrial and inter-cellular level. They show that the inter-mitochondrial level is important for maintaining the entire mitochondrial information in cells. Under those conditions no master circle with maximum fitness is necessary. Since aging is a process that comes about by the interaction of several damage pathways (reflected by the different theories), it is necessary to model the reaction network as a whole. The model of Kowald & Kirkwood (1996) integrates the contributions of defective mitochondria, aberrant proteins and free radicals. It also includes antioxidant enzymes and proteolytic scavengers. The most important result is, that damage accumulation in mitochondria and proteins occurs on different time scales and that the final breakdown seems to be a cooperation of mitochondrial and cytoplasmic reactions. The mitochondria undergo gradual, long term changes, which eventually trigger a short lived cytoplasmic error loop. A rather unusual phenomenon has been observed in Saccharomyces cerevisiae, which are also used as model system for aging. Yeast mother cells have a limited division potential, while young daughter cells start with a fresh division capacity. It has been observed that extrachromosomal ribosomal DNA circles (ERCs) liberate from genomic DNA and accumulate in old yeast cells. A mathematical model was developed that readily explains the observed data, if ERC formation increases with the age of the cell (C. S. Gillespie et al., 2004). Finally, mathematical models have also been used to investigate evolutionary questions about the aging process. The evolution of human menopause is difficult to explain. It has been suggested that there may be little benefit for an older mother in taking the increasing risk of a further pregnancy if existing children depend critically on her survival. Another idea is that post-reproductive grandmothers increase their fitness by assisting their adult daughters. Modeling studies showed that individual theories fail to provide sufficient selection advantage to explain the evolution of menopause, but a combined model can achieve this (Shanley & Kirkwood, 2001). And of course also the evolution of the aging process itself has been modeled. It is not trivial to explain why organisms should grow old and die. What is the selective advantage of this trait and why have different species widely differing life spans ? The disposable soma theory (T. B. L Kirkwood & Holliday, 1986; T. B. L. Kirkwood & Rose, 1991) shows mathematically that aging can be explained as the consequence of an optimal resource allocation between survival and reproduction. The optimal resource allocation (and hence aging rate) differs for different species according to their environmental mortality risk. Mathematical models have been used for many years in aging research to understand phenomena and test explicit predictions of theories. Because aging practically affects all pathways and all levels of a living organism, it is a prime candidate for the emerging field of systems biology. The generation of high throughput data will enable the development of larger models that describe the complex network of interactions underlying the different aging theories.

R eferences Albert, B., Godelle, B., Atlan, A., De Paepe, R., & Gouyon, P. H. (1996). Dynamics of plant mitochondrial genome: Model of a three level selection process. Genetics, 144, 369-382.

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Antunes, F., Salvador, A., Marinho, H. S., Alves, R., & Pinto, R. E. (1996). Lipid peroxidation in mitochondrial inner membranes. I. An integrative kinetic model. Free Radical Biology & Medicine, 21(7), 917-943. Arimura, S., Yamamoto, J., Aida, G. P., Nakazono, M., & Tsutsumi, N. (2004). Frequent fusion and fission of plant mitochondria with unequal nucleoid distribution. Proc Natl Acad Sci USA, 101(20), 7805-7808. Berdannier, C. D., & Everts, H. B. (2001). Mitochondrial DNA in aging and degenerative disease. Mutation Research, 475, 169-183. Cao, Z., Wanagat, J., McKiernan, S. H., & Aiken, J. M. (2001). Mitochondrial DNA deletion mutations are concomitant with ragged red regions of individual, aged muscle fibers: Analysis by laser-capture microdissection. Nucleic Acids Research, 29(21), 4502-4508. Clayton, D. A. (2003). Mitochondrial DNA replication: What we know. IUBMB Life, 55(4-5), 213-217. Cortopassi, G. A., Shibata, D., Soong, N. W., & Arnheim, N. (1992). A pattern of accumulation of a somatic deletion of mitochondrial DNA in aging human tissues. Proc. Natl. Acad. Sci. USA, 89, 73707374. de Grey, A. D. N. J. (1997). A proposed refinement of the mitochondrial free radical theory of aging. BioEssays, 19(2), 161-166. Diez-Sanchez, C., Ruiz-Pesini, E., Lapena, A. C., Montoya, J., Perez-Martos, A., Enriquez, A., et al. (2002). Mitochondrial DNA Content of Human Spermatozoa. Biology of Reproduction, 68, 180-185. Gillespie, C. S., Proctor, C. J., Boys, R. J., Shanley, D. P., Wilkinson, D. J., & Kirkwood, T. B. L. (2004). A mathematical model of ageing in yeast. J. of Theoretical Biology. Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. J. of Physical Chemistry, 81, 2340-2361. Gokey, N. G., Cao, Z., Pak, J. W., Lee, D., McKiernan, S. H., McKenzie, D., et al. (2004). Molecular analyses of mtDNA deletion mutations in microdissected skeletal muscle fibers from aged rhesus monkeys. Aging Cell, 3(5), 319-326. Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality and on a new mode of determining life contingencies. Philosophical Transactions of the Royal Society, 2, 513-585. Harley, C. B. (1991). Telomere loss: Mitotic clock or genetic time bomb? Mutation Research, 256, 271282. Harley, C. B., Vaziri, H., Counter, C. M., & Allsopp, R. C. (1992). The telomere hypothesis of cellular aging. Experimental Gerontology, 27, 375-382. Hattne, J., Fange, D., & Elf, J. (2005). Stochastic reaction-diffusion simulation with MesoRD. Bioinformatics, 21(12), 2923-2924. Hattori, K., Tanaka, M., Sugiyama, S., Obayashi, T., Ito, T., Satake, T., et al. (1991). Age-dependent increase in deleted mitochondrial DNA in the human heart: Possible contributory factor to presbycardia. American Heart Journal, 121(6), 1735-1742. 326

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Linnane, A. W., Marzuki, S., Ozawa, T., & Tanaka, M. (1989). Mitochondrial DNA mutations as an important contributor to ageing and degenerative diseases. The Lancet, 333, 642-645. Lundblad, V., & Szostak, J. W. (1989). A mutant with a defect in telomere elongation leads to senescence in yeast. Cell, 57, 633-643. Makeham, W. H. (1867). On the law of mortality. J. Inst. Actuaries, 13, 325-358. Medvedev, Z. A. (1990). An attempt at a rational classification of theories of ageing. Biological Reviews, 65, 375-398. Menzies, R. A., & Gold, P. H. (1971). The turnover of mitochondria in a variety of tissues of young adult and aged rats. J. of Biological Chemistry, 246(8), 2425-2429. Miller, F. J., Rosenfeldt, F. L., Zhang, C., Linnane, A. W., & Nagley, P. (2003). Precise determination of mitochondrial DNA copy number in human skeletal and cardiac muscle by a PCR-based assay: Lack of change of copy number with age. Nucleic Acids Res, 31(11), e61. Miquel, J., Economos, A. C., Fleming, J., & Johnson, J. E. (1980). Mitochondrial role in cell ageing. Experimental Gerontology, 15, 575-591. Nunnari, J., Marshall, W. F., Straight, A., Murray, A., Sedat, J. W., & Walter, P. (1997). Mitochondrial transmission during mating in Saccharomyces cerevisiae is determined by mitochondrial fusion and fission and the intramitochondrial segregation of mitochondrial DNA. Molecular Biology of the Cell, 8, 1233-1242. Oeppen, J., & Vaupel, J. W. (2002). Broken limits to life expectancy. Science, 296, 1029-1031. Olovnikov, A. M. (1973). A theory of Marginotomy. J. of Theoretical Biology, 41, 181-190. Ramsey, S., & Orrell, D. (2005). Dizzy: Stochastic simulations of large-scale genetic regulatory networks. J. Bioinf. Comp. Biol., 3(2), 1-21. Randerath, K., Randerath, E., & Filburn, C. (1996). Genomic and mitochondrial DNA alterations in aging. In L. E. Schneider & J. W. Rowe (Eds.), Handbook of The Biology of Aging (4th ed., pp. 198-214). London: Academic Press. Shanley, D. P., & Kirkwood, T. B. (2001). Evolution of the human menopause. Bioessays, 23(3), 282287. Shenkar, R., Navidi, W., Tavare, S., Dang, M. H., Chomyn, A., Attardi, G., et al. (1996). The mutation rate of the human mtDNA deletion mtDNA4977. American J. of Human Genetics, 59(4), 772-780. Takai, D., Inoue, K., Goto, Y., Nonaka, I., & Hayashi, J. (1997). The interorganellar interaction between distinct human mitochondria with deletion mutant mtDNA from a patient with mitochondrial disease and with HeLa mtDNA. J. of Biological Chemistry, 272(9), 6028-6033. Takai, D., Isobe, K., & Hayashi, J.-I. (1999). Transcomplementation between different types of respiration deficient mitochondria with different pathogenic mutant mitochondrial DNAs. J. of Biological Chemistry, 274(16), 11199-11202.

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K ey T erms Aging: A biological phenomenon observed in most animals leading to increasing functional impairment and constantly rising mortality rate. Age related changes can be observed at intracellular, tissue and organismic level. Many theories about the mechanism of the aging process exist, but the details are currently still unresolved. Disposable Soma Theory: Popular theory about the evolution of the aging process. Aging is explained as the result of an optimal resource allocation between reproduction and self-maintenance. That means, aging itself has no selection advantage, but is a side product of another selected trait. Species specific life-spans are readily explained by different environmental mortalities. Dizzy: A stochastic simulation tool written in Java. Models can be defined in systems biology markup language (SBML) or a proprietary language and simulated using various stochastic and deterministic algorithms. The GUI and the core engine are separate modules so that Dizzy can also be used for batch calculations on a computer cluster. Life Expectancy: Time until 50% of a cohort of newborn individual have died. Also known as average life-span, although technically it is the median life-span. The life expectancy for humans in industrialized countries is currently between 75 and 80 years, and for women 2-3 years higher than for man. Mitochondria: Cellular organelles present in most eukaryotic cells that are important for calcium homeostasis, apoptosis and energy production. Mitochondria are endosymbionts and probably derived from purple bacteria. A remnant of this origin is the small circular mitochondrial DNA (mtDNA) that is at the center of the mitochondrial theory of aging. Stochastic Modeling: A modeling framework that takes care of microscopic random fluctuations and the discreteness of molecules. Stochastic models explicitly calculate the change of the number of molecules of the participating species during the time course of a chemical reaction. The first exact stochastic simulation algorithms were developed by Gillespie (1977) and are now part of several modeling tools. Stochastic simulations are normally more time consuming than deterministic simulations via differential equations.

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Systems Biology Workbench: The Systems Biology Workbench (SBW) is a software systems that enables different modeling programs to communicate with each other and provide or use specialized analysis services. In this way SBW acts as broker for services like deterministic and stochastic simulation engines, stability and bifurcation analysis, model optimization and graphical model building. Popular tools that are SBW aware are among others JDesigner, CellDesigner and Dizzy.

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The Sebaceous Gland: A Model of Hormonal Aging Evgenia Makrantonaki Dessau Medical Center, Germany and Charité Universitaetsmedizin Berlin, Germany Christos C. Zouboulis Dessau Medical Center, Germany and Charité Universitaetsmedizin Berlin, Germany

abstract This chapter introduces an in vitro model as a means of studying human hormonal aging. For this purpose, human sebaceous gland cells were maintained under a hormone-substituted environment. This environment consisted of growth factors and sex steroids in concentrations corresponding to those circulating in young and postmenopausal women. The authors suggest that hormone decline, occurring with age, may play a significant role not only in the maintenance of skin homeostasis but also in the initiation of aging. Furthermore, skin, the largest organ of the body, offers an alternative approach to understanding the molecular mechanisms underlining the aging process.

SKIN AGING AND H ORM ONES Signs of aging become evident with time, whereas skin provides the first obvious evidence of this process. Since the collection of specimens from internal organs, such as brain, heart, vessels, bones and endocrine glands throughout life for experimental research purposes is associated with major practical and ethical obstacles in humans, interspecies research but also the use of human skin as a common research tool offer promising alternative approaches. Among multiple factors been involved in the process of skin aging the hormone environment plays a distinct role (Makrantonaki & Zouboulis, 2007). Alterations in appearance due to declining skin quality

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are common complaints in postmenopausal women. The postmenopausal skin state is associated with a rapid worsening of skin structure and functions, which can be at least partially repaired by hormone replacement therapy (HRT) or local estrogen treatment (Brincat, 2000). Improvement of epidermal skin moisture, elasticity and skin thickness (Fuchs, Solis, Tapawan, & Paranjpe, 2003), enhanced production of surface lipids (Sator, Schmidt, Sator, Huber, & Honigsmann, 2001), reduction of wrinkle depth, restoration of collagen fibers (Schmidt, Binder, Demschik, Bieglmayer, & Reiner, 1996) and increase of the collagen III/I ratio (Affinito et al., 1999) have been reported. Further potential benefits of longterm HRT are the prevention of osteoporosis and atherosclerotic cardiovascular diseases (Hulley et al., 1998). There has been considerable interest in the possibility that HRT may also be protective against the risk of developing neurodegenerative diseases e.g. Morbus Alzheimer. This remains controversial and the benefit is at present unproven (Yaffe, Sawaya et al., 1988). Conventional contraindications to HRT include a history of breast cancer or endometrial cancer, recent undiagnosed genital bleeding, active, severe liver disease or a history of thromboembolism. In addition, several current studies, which have shown that the unwished effects are more serious and severe than the advantageous ones have entirely changed the strategy of HRT and limited it in certain cases only (Rossouw et al., 2002; Solomon & Dluhy, 2003)

THE SEBACE OUS G LAND Sebaceous glands or holocrine glands are skin appendages and are found over the entire surface of the body except the palms, soles and dorsum of the feet. They are largest and most concentrated in the face and scalp where they are the sites prone for acne. The normal function of sebaceous glands is to produce and secrete sebum, a group of complex oils including triglycerides and fatty acid breakdown products, wax esters, squalene, cholesterol esters and cholesterol (Downing et al., 1987; Nikkari, Schreibman, & Ahrens, 1974; Ramasastry, Downing, Pochi, & Strauss, 1970; Thody & Shuster, 1989). The most accepted function of sebum is skin lubrication in order to protect it against friction and to make it more impervious to moisture. Furthermore, sebum lipids transport antioxidants in and on the skin and exhibit a natural light protective activity. They exhibit an innate antibacterial activity and have a pro- and anti-inflammatory function. The sebaceous gland can regulate the activity of xenobiotics and is actively involved in the wound healing process (Zouboulis, 2004). It possesses all enzymes required for the intracellular androgen metabolism and confers upon the skin an independent endocrine function (Fritsch, Orfanos, & Zouboulis, 2001). With advancing age the size of sebaceous gland cells tends to decrease, while their number remains approximately the same throughout life (Zouboulis & Boschnakow, 2001). Sebaceous gland cells show an age-related reduced secretory output, which results in a decrease in the surface lipid levels and skin xerosis (Engelke, Jensen, Ekanayake-Mudiyanselage, & Proksch, 1997; Pochi, Strauss, & Downing, 1979) - a major characteristic of aged skin. Hormone substitution with estrogens in vivo could significantly reverse skin xerosis indicating a hormone-dependent function of the sebaceous gland cells (Dunn, Damesyn, Moore, Reuben, & Greendale, 1997). Human SZ95 sebocytes are sebaceous gland cells derived from facial skin and transfected with the SV-40 large T antigen and offer a unique model for investigations on the physiology of aging. They constitute a better alternative to animal research and they functionally behave in a manner concomitant

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Figure 1. Illustration of a human sebaceous gland connected to a hair follicle on the skin surface (face) of a 70-year old man. The sebaceous gland constitutes of sebaceous gland cells which are responsible for the sebum production.

to nontransfected human sebocytes. SZ95 sebocytes show a similar epithelial morphology to normal sebocytes and they can produce squalene and wax esters, as well as triglycerides and free fatty acids, even after 25-40 passages (Patents and patent applications: WO0046353, EP1151082, AU770518, US2002034820, CA2360762, CN100366735C, JP2002535984, IL144683D, PL194865, HU0200048, AT1151082, BE1151082, CH11151082, DE19903920, DK1151082, FR1151082, GB1151082, IE1151082, IT1151082, KR689120) (Zouboulis, Seltmann, Neitzel, & Orfanos, 1999).

IN VITR O MODE L OF H UMAN H ORM ONA L AGING Using models of animal aging, such as the nematode Caenorrhabditis elegans, the fly Drosophila melanogaster, and the mouse Mus musculus, the importance of hormonal signals on the aging phenotype has been already documented. Suppression of the levels of hormones, such as insulin-like peptides, growth hormone (GH) and sterols (Tatar, Bartke, & Antebi, 2003) or of their receptor expression has been shown in animals to increase lifespan and delay age-dependent functional decline. Conboy et al. (2005) showed that the age-related decline of progenitor cell activity of mice could be reversed by

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exposure to young serum and that the cells could retain much of their intrinsic proliferative potential underlining the great importance of the systemic environment (Conboy et al., 2005). Within the scope of the Explorative Project ‘Genetic aetiology of human longevity’ supported by the German National Genome Research Network 2 (NGFN-2) an in vitro model of human hormonal aging has been developed. Human sebaceous gland cells (SZ95 sebocytes) were maintained under a hormone-substituted environment consisting of growth hormone (GH), insulin-like growth factor I, estrogens, androgens and progesterone in concentrations corresponding to those circulating in 20- and in 60-year-old women (Makrantonaki et al., 2006). Upon 15,529 tested genes 899 genes showed a differential expression between SZ95 sebocytes under the 20- and 60-year-old hormone mixture, respectively. This result demonstrates that hormones interact in a complex fashion, and changes in their circulating blood levels may significantly alter the development of cells by regulating their transcriptome. Among the 899 genes, genes were regulated, which are involved in stress response, chaperone activity, ubiquitine-proteosome activity, cholesterol biosynthesis and fatty acid metabolism, eicosanoid biosynthesis, synthesis of extracellular matrix, nucleotides and ATP metabolism, and DNA repair mechanisms - biological processes which are hallmarks of aging. The most significantly altered signaling pathway identified was that of transforming growth factor-β (TGF-β). The TGF-β signaling pathway is involved in different biological processes during embryonic development and plays a distinct role in adult organisms in tissue homeostasis (Massague, 1998). In human skin, the TGF-β signaling pathway has been shown to regulate many cellular processes, such as differentiation and proliferation of keratinocytes and fibroblasts and the synthesis of extracellular matrix proteins (Massague, Freidenberg, Olefsky, & Czech, 1983). In addition, a disturbed function of this cascade has been associated with tumorigenesis, i.e. in pancreatic, prostate, intestine, breast, and uterine cancer (Levy & Hill, 2006). A differential expression of TGF-β isoforms, activins, basal membrane proteins, MADHs/SMADs, and other components of the TGF-β signaling cascade was shown at SZ95 sebocytes under the 60-year-old hormone mixture. These data suggest that age-specific hormonal changes are likely to play a determining role not only in the healthy aging process, but also in tumorigenesis. Interestingly, genes expressed in signaling pathways operative in age-associated diseases such as Huntington’s disease (Luthi-Carter et al., 2002; Sipione et al., 2002), dentatorubral-pallidoluysian atrophy (Luthi-Carter et al., 2002), and amyotrophic lateral sclerosis (Jiang et al., 2005) were also identified. According to these results, a disturbed hormone status may act a part into the generation of neurodegenerative diseases.

C ONC LUSI ON The fundamental aim of the aging research is the better understanding of the mechanisms involved and the prevention of age-associated diseases by early identification of individual molecular risk profiles. Recent data suggest that skin represents an adequate model for aging research and that change of hormone levels occurring with age plays a major role in the generation of aging. Thus, these results could be a basis for an integrated and interdisciplinary approach to the analysis of aging.

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KEY TERMS Aging: A complex process that defines the changes observed throughout the organism’s lifespan and cannot be defined by a single pathway or a single cause. Aging is controlled by both environmental factors and the genetic constitution of the individual and has been described as a progressive decline of the ability to withdraw stress, damage and disease. Furthermore, it is characterized by an increase of degenerative and neoplastic disorders. Endogenous Skin Aging: Endogenous aging, otherwise called intrinsic or chronological aging, is influenced by genetics, hormonal changes and metabolic processes, which appear at advanced age. Endogenous skin aging can be viewed on non UV-exposed areas of the body and can be considered as model of the aging process taking place in internal organs. Exogenous Skin Aging: Exogenous aging, otherwise called extrinsic aging, takes place in exposed areas of the body (e.g. head, neck) which are constantly influenced by various environmental factors including ionizing and non-ionizing irradiation, air pollution, natural deleterious gases (e.g. ozone and high concentrations of oxygen), smoking, invasion of pathogenic bacteria, viruses, xenobiotics and mechanical stress. Among them UV-irradiation is the most fundamental one, as it can damage skin to such an extent, that makes it seem prematurely aged (photoaging). This premature aging process is cumulative with sun exposure and affects more individuals of skin phototypes I and II. Hormone: (from Greek όρμή - “to set in motion”) A chemical messenger from one cell (or group of cells) to another. The function of hormones is to serve as a signal to the target cells. Endocrine hormone molecules are secreted (released) directly into the bloodstream, while exocrine hormones (or ectohormones) are secreted directly into a duct, and from the duct they either flow into the bloodstream or they flow from cell to cell by diffusion in a process known as paracrine signaling. Skin: The largest organ of the body, exhibits multiple functions, among them it serves as a protective barrier between internal organs and the environment and is a complex organ with multiple cell types and structures. It is divided into three major compartments: epidermis, dermis and subcutaneous tissue. Sebaceous Glands: Can usually be found in hair-covered areas where they are connected to hair follicles to deposit sebum on the hairs, and bring it to the skin surface along the hair shaft. The structure consisting of hair, hair follicle and sebaceous gland is known as pilosebaceous unit. They are largest and most concentrated in the face and scalp where they are the sites prone for acne. Sebum: (Latin, meaning fat or tallow) Is produced by sebaceous glands and its main function is to protect and waterproof hair and skin, and keep them from becoming dry, brittle, and cracked. It can also inhibit the growth of microorganisms on skin. In the sebaceous glands, sebum is produced within specialized cells and is released as these cells burst; sebaceous glands are thus classified as holocrine glands. In humans, the composition of sebum is as follows: 25% wax monoesters, 41% triglycerides, 16% free fatty acids and 12% squalene. SZ95 Sebocytes: Are sebaceous gland cells derived from facial skin and transfected with the SV-40 large T antigen. They functionally behave in a manner concomitant to nontransfected human sebaceous gland cells.

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Section VI

Systems Biology Applications in Medicine

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Chapter XX

Systems Biology Applied to Cancer Research R. Seigneuric GROW Research Institute, University of Maastricht, The Netherlands N.A.W. van Riel Eindhoven University of Technology, The Netherlands M.H.W. Starmans GROW Research Institute, University of Maastricht, The Netherlands

C.T.A. Evelo University of Maastricht, The Netherlands B.G. Wouters GROW Research Institute, University of Maastricht, The Netherlands P. Lambin GROW Research Institute, University of Maastricht, The Netherlands

A. van Erk University of Maastricht, The Netherlands

abstract Complex diseases such as cancer have multiple origins and are therefore difficult to understand and cure. Highly parallel technologies such as DNA microarrays are now available. These provide a data deluge which needs to be mined for relevant information and integrated to existing knowledge at different scales. Systems Biology is a recent field which intends to overcome these challenges by combining different disciplines and provide an analytical framework. Some of these challenges are discussed in this chapter.

Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Systems Biology Applied to Cancer Research

Intr od ucti on Systems Biology is emerging as a promising answer to the increasing need for analytical approaches in molecular medicine. Its goal includes modeling interactions, understanding the behavior of a system from interplay of its components, inferring models from data, data integration, confronting the prediction of the model to data, proposing most promising experiments. Solutions to these challenges are often interdisciplinary, and Systems Biology intends to provide such a framework beyond scientific communities ‘dialects’ or differences in approaches (Lazebnik, 2004). Cancer is too complex a disease to be solely and completely described by the existing clinical variables (e.g.: age of the patient, size of the tumor, histological grade, etc.) which are currently used in practice. It is therefore necessary to identify new biomarkers which will provide additional information about the cancer type, origin, or aggressiveness for instance. Within a decade, high-throughput assays have revolutionized biology and are now being introduced in the clinic. Among these techniques, we focus on DNA microarrays which can monitor the expression of tens of thousands of genes in parallel and offer a means to individualize treatment. This should contribute to guide clinicians toward tailored therapies which will lead to reduced over treatments and costs by an improved prognosis, the design of targeted drugs, as well as more accurate application of drugs. Since this is quite a recent field where each analysis requires a large number of steps, consensus has not yet been reached. Furthermore, researchers involved come from various backgrounds (e.g.: Statistics, Engineering, Biology …). Applying tools from all these fields result in a wide spectrum of approaches that may be confusing at first. Nevertheless there are some trends in the biomedical research community that we review in this chapter in the context of cancer. The outline of the chapter is meant to follow a practical analysis pipeline and URLs for accessing resources (i.e.: softwares and data) are provided in Table 1.

W ha t is a Micr oarra y? Quite suited to monitor many genes at once, a DNA microrarray is an inert, solid, flat and transparent surface (e.g.: a microscopic slide) onto which 20,000 to 60,000 short DNA reporters (often called probes) of specified sequences are orderly tethered. Each reporter on the microrarray corresponds to a particular short section of a gene. More and more, a single gene (e.g.: VEGF) is covered by several reporters which span different parts of the gene sequence. Firstly available in the mid 1990’s, companies are nowadays developing micorarrays with increased feature density (i.e.: the number of molecular detectors per array) to scan the genome at regular intervals (‘tiling’ arrays) that are re-usable for instance.

A Micr oarra y E xperiment After a careful experiment design (Kerr & Churchill, 2001; Y. H. Yang & Speed, 2002) to start with, biological samples are collected either from an in vitro or an in vivo experiment. Then, the RNA is extracted and labelled (e.g.: with a fluorescent dye). The central reaction is when the labelled RNA is hybridized (bound) to the microarray reporters. Unbound RNA is subsequently washed out so that the amount of bound and labelled RNA can be measured. The intensity of the signal of the reporter is indicative for the relative expression of the corresponding gene. DNA microarrays measure a surrogate

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Table 1. Systems Biology approach to link microarray data to individualized treatment in molecular oncology: websites referring to possible alternatives for the analysis steps presented in this chapter. Microarray General Y.F.Leung

http://ihome.cuhk.edu.hk/%7Eb400559/

Microarray bibliography

http://www.nslij-genetics.org/microarray/

Pubmed Entrez

http://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed

MGED

http://www.mged.org/

MIAME

http://www.mged.org/Workgroups/MIAME/miame.html

ArrayExpress

http://www.ebi.ac.uk/arrayexpress/

GEO

http://www.ncbi.nlm.nih.gov/projects/geo/

SMD

http://genome-www5.stanford.edu/

Oncomine

http://www.oncomine.org/main/index.jsp

Rembrandt

http://tr.nci.nih.gov/rembrandt

Data sets repositories

Quality controls Bioconductor

http://www.bioconductor.org/ (package affyQCReport)

dCHIP

http://biosun1.harvard.edu/complab/dchip/

GCOS

http://www.affymetrix.com/products/software/specific/gcos.affx

Genomatix

http://www.genomatix.de/

RMA

http://www.bioconductor.org/ (package affycomp)

RMAExpress

http://rmaexpress.bmbolstad.com/

GCRMA

http://www.bioconductor.org/ (package gcrma)

BRB Array Tools

http://linus.nci.nih.gov/BRB-ArrayTools.html

Cluster & Tree View

http://rana.lbl.gov/EisenSoftware.htm

SAM

http://www-stat.stanford.edu/~tibs/SAM/

BRB Array Tools

http://linus.nci.nih.gov/BRB-ArrayTools.html

GenePattern

http://www.broad.mit.edu/cancer/software/genepattern/

TM4

http://www.tm4.org/

Normalization

Unsupervised & supervised Analyses

Analysis Suite

Time series STEM

http://www.cs.cmu.edu/~jernst/stem/

EDGE

http://www.biostat.washington.edu/software/jstorey/edge/

SAM

http://www-stat.stanford.edu/~tibs/SAM/

CAGED

http://genomethods.org/caged/ Annotation & Gene Ontology

NCBI

http://www.ncbi.nlm.nih.gov/

Ensembl

http://www.ensembl.org/index.html

continued on the following page

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Table 1. (continued) NetAffx

https://www.affymetrix.com/site/login/login.affx

Onto Express

http://vortex.cs.wayne.edu/projects.htm

David Ease

http://david.abcc.ncifcrf.gov/ease/ease.jsp

Gene Ontology

http://www.geneontology.org/

Gene Ontology Annotation

http://www.ebi.ac.uk/GOA/

KEGG

http://www.genome.jp/kegg/

BioPax

http://www.biopax.org/

GSEA

http://www.broad.mit.edu/gsea/

KEGG

http://www.genome.jp/kegg/

GenMAPP

www.genmapp.org/

PathVisio

http://www.pathvisio.org

WikiPathways

http://www.wikipathways.org

Ingenuity

http://www.ingenuity.com/

GeneGo

http://www.genego.com/

GeneXpress

http://genexpress.stanford.edu/

Genomatix

http://www.genomatix.de/

Jaspar

http://jaspar.genereg.net/

Maps & Pathways

Transcription Factors

Network Inference, Visualization & Integration CARRIE

http://zlab.bu.edu/CarrieServer/html/

Cytoscape

http://www.cytoscape.org/

Patika

http://www.patika.org/

NIH Roadmap

http://nihroadmap.nih.gov/

SBML

http://sbml.org/index.psp

Physiome Project

https://www.bioeng.auckland.ac.nz/physiome/physiome_project.php

eCell

http://www.e-cell.org/software/e-cell-system

Virtual Cell

http://www.nrcam.uchc.edu/

BioModels Database

http://www.ebi.ac.uk/biomodels/

Systems Biology & Mathematical Modeling

of RNA abundance with either 1 or 2 channels. Two colour arrays (e.g.: Stanford microarrays) measure by competitive hybridization the relative expression under a given condition (fluorescent red dye Cy5) compared to its control (labelled with a green fluorescent dye, Cy3). The other type of platform only has 1 channel (e.g.: Affymetrix GeneChip) and thus measures absolute expression levels. Whatever the platform, the expression levels are usually converted into log scales. Distribution of the intensities is then no more skewed to the high intensities treating up and down regulated genes symmetrically. The variation is also less dependent on the absolute magnitude (the relative difference between high and

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low expression levels is smaller in the log scale). Expression levels are normalized to a control level, visualized in black. In this situation, overexpression is represented in red, repression in green.

T ypes of S t udies Using Micr oarra y E xperiments The most common applications of microarrays are for class comparison, class prediction and class discovery, although they are often combined in research papers. In the context of class comparison, classes are defined independently of the gene expression levels. Classes can be defined by a pathologist looking at the shape of cells under the microscope, or when the labels of the samples are known (e.g.: control versus treated design). The goal is then to determine if expression differs between theses classes and find which genes are differentially expressed. In the case of class prediction, a classifier (or predictor) is already available and the objective is to accurately predict the class of a new sample based on the expression levels of the genes of the predictor. Class discovery aims at identifying expression structures within a set of samples where classes are not predefined. Even though microarrays are meant to monitor transcription, some authors have also quantified changes in translation in cancer cell lines by polysome assays (Koritzinsky et al., 2005). The authors showed dramatic differences between these 2 levels of regulation of protein expression. Indeed, under a hypoxic environment a major repression at the transcriptional level was shown to not necessarily imply a major repression of protein translation. On the contrary, some genes related to angiogenesis and the unfolded protein response for example were highly translated. The regulation of translation is rather complex and different means have been suggested as the role of functional internal ribosomal entry sites, or micro RNAs (short RNA sequences - about 20 nucleotides long).

R ep osit ories of Micr oarra y S t udies Due to the large use of microarrays, data repositories have flourished world-wide. Three of the largest databases of gene expression are GEO, the Gene Expression Omnibus, of the National Center for Biotechnology Information (NCBI), its European homolog ArrayExpress hosted at the EMBL-EBI in the UK, and the Stanford Microarray Data Base (SMD). Databases dedicated to cancer have also been created such as Oncomine and the REpository of Molecular BRAin Neoplasia DaTa (REMBRANDT). They can be searched for data sets or even to test hypotheses. In Rembrandt for instance, it is possible to compute survival curves on line. Good practices or MIAME (Minimum Information About a Microarray Experiment) are being developed by the MGED (Microarray Gene Expression Data) workgroup. This group of biologists, computer scientists and data analysts aims to set standards to ensure an unambiguous interpretation and the reproducibility of the results.

Initia l q uesti on, hyp othesis

and the fishing

experiment

The starting point usually stems from a peculiar (or even paradoxical) finding that needs to be further investigated. The aim of the study can be to provide a better description of a given system (in a new context and/or with a new combination of assays for instance) or to test a hypothesis. The former ap-

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proach is known as the ‘fishing experiment’. It consists in running an experiment, then analyzing the data to find out inherent structure embedded into the data.

D ata G eneration Design This is one of the key steps that need to be carefully addressed (Churchill, 2002). One of the few points of consensus is that a sound experiment requires positive and negative controls as well as biological replicates. Any experiment is sensitive to 3 sources of variation: biological variation, technical variation and measurement error so that every measurement contains actually a convolution of the 3. Replicates can either be technical or biological (Churchill, 2002; Quackenbush, 2002). The former monitors a biological sample from the same source (e.g.: two microarrays -ideally identical but only similar in practice- are used to assess the expression level of genes from the same patient biopsy. Because the origin of the samples is meant to be the same, the variability in the results is expected to be mostly explained by technical differences (e.g.: microarrays from a different batch, or differences in the procedure or handling). Biological replicates mean repeating a certain number of times a complete assay. In this case, for the same patient, a biopsy would be taken and hybridized on a microarray. This procedure would be repeated twice for example. The variability is then a combination of technical and biological origins (Churchill, 2002). Different designs are possible depending on the goals of the experiment (control versus treated, time series, etc.). Clinical studies are essentially static in the sense that the data is collected from patients without the possibility to assign retrospectively a precise starting point before the first diagnostic (observational studies). In the contrary, in a controlled environment (e.g.: in vitro culture of cancer cell lines) times series are quite suited to assess the behavior of complex systems after an experimental perturbation (Bar-Joseph, 2004). Two essential issues in experiment design are bias and chance, the former being the hardest to address (Ransohoff, 2004). It requires a detailed description of the procedure to be detected. Unfortunately, when a study suffers from bias, hardly anything can be done to compensate for it so that it is often said that ‘bias times 12 is still bias’. Before running the full experiment, one might consider a pilot study. Samples of interest can be selected to provide the expected highest information gain (Tibshirani, 2006).

Protocol & Quality Controls of Samples The design should result in a detailed written protocol carefully followed by the investigators. Regardless of whether the RNA comes from an in vitro or in vivo studies, the primary importance is to yield samples of excellent quality in order to avoid the situation of ‘garbage in, garbage out ‘. At this stage, quality controls are essentially attained with the Nanodrop and the Bioanalyzer (Agilent Technologies, Santa Clara, CA) assays. The former assesses material quantity whereas the later measures the integrity, purity and quality of the sample.

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Microarrays & Quality Controls DNA microarrays can be divided in 2 groups depending on their number of channels. The cDNA microarrays have 2 channels (red and green), but we will focus on the Affymetrix microarray (1 channel) which is currently one of the most widely used commercial platform. A set of quality controls has been developed in the open software R. The corresponding packages can be downloaded from the Bioconductor website and run from the R environment or Excel with BRB Array Tools for instance (see Table 1 for details).

D ata Preprocessing Filtering for Artefacts, Outliers and Controls After a careful examination of the microarray, this step intends to remove bad spots, subtract background, and deal with controls. Control reporters which are highly expressed or even saturated need to be removed.

Normalization Normalization is an attempt to correct for systematic errors in the data (e.g.: one channel of a twochannel array is much higher than the other). Thus it allows comparing the data in an even way for proper analysis. A common normalization assumption is that the expression level of most genes does not change (e.g.: Affymetrix platform). Although normalization is quite suitable, it can not compensate for data of poor quality such as the ‘garbage in, garbage out’ situation already mentioned or insufficient number of samples. How to combine this information detected by different reporters for the same gene is also a part of the normalization step (Quackenbush, 2002), and an area of intense research. Different normalization algorithms have been developed over the years. For the Affymetrix platform, the most common ones are GCOS, RMA, GCRMA, and dChip. These algorithms combine the reporter intensities for a given gene to define a measure of expression that represents the amount of the corresponding mRNA species. They have a profound effect on the detection of differentially expressed genes. This was exemplified in the context of lung cancer where the number of common genes found with 3 different algorithms was quite small (P. Yang et al., 2004). Since no method is clearly established as more reliable than others, the authors suggested combining the genes selected by more than one method. In contrast to these findings, these authors found that once the data was pre-processed, the different analytical tools used to extract genes differentially expressed (see below) gave very similar results (concordance ~ 90%).

Filters for Noise and/or Intensity In order to decrease the risk of spurious findings, it is necessary to filter for noise and absence of variation. Different procedures have been used but no consensus exists yet. Regardless of the experimental design and microarray platform, the idea is to discard reporters with low intensities (probably noisy measurements) or which expression levels remain roughly constant in the conditions studied (e.g.: both

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control and treated samples). Some platforms provide a measure of the reliability of detection (e.g.: the present or absent call for Affymetrix microarrays).

C urse of D imensionality & D ata R eduction T echniques A massive amount of data arises from DNA microarrays. Typically, the number of reporters on a microarray varies between 20,000 to approximately 60,000 while the number of samples is relatively small. Currently, typical (static) in vitro cancer studies contain roughly 50 samples (less than 10 usually for time series). The largest clinical studies span approximately 300 samples but the usual size is around 100 patients. It is thus a challenge (or the so-called ‘curse of dimensionality’) to select a set of genes of interest when the number of potential candidates outreaches by far the number of samples. Data reduction techniques can be helpful to downsize the data set to a more manageable size. In the so called expression space, each experiment is represented by an axis (dimension). For each gene, its expression level (coordinate) is reported in log scale units along the corresponding axis. In the case where just 3 experiments would be run, the axes experiment1-experiment2-experiment3 would be similar to the x-y-z basis used in three-dimensional geometry. A distance can also be defined to measure the closeness (similarity in expression) of 2 or more points (genes). Like in geometry, the Euclidean metric is a common similarity distance but Pearson correlation, Manhattan, etc. similarity measures can also be selected depending on the purpose of the analysis. Although it is not possible to represent it, similarity measures between genes can be computed in the expression space extended to any number of dimensions. Principal Component Analysis (PCA) is based on the singular value decomposition and remains one of the most common techniques to perform data reduction. The idea is to rotate the cloud of data points in the expression space so as to identify the direction of greatest variation (1st principal component). Iteratively, each next component gets the most of the remaining variance. Due to data representation issues, only the 2 or 3 first principal components are computed. These first ‘superaxes’ represent the major part of the total variance in the dataset and may allow the detection of different clusters of data points.

D ata A nalysis Gene Expression Profiling This step provides the list of genes of interest (also called gene expression-based signature or gene signature) which are supposed to be differentially expressed between 2 or more conditions (the control and the treated experiments for instance). The two main ways to tackle this are by an unsupervised or by a supervised approach. Both methods rely on defining a similarity measure which is used to group the genes with similar expression. In general, the choice of the similarity measure is more important than the algorithm to compute it. The differentially expressed genes or gene signatures can be used to identify specific subtypes within individual human tumors and predict their influence on patient treatment. Such gene ‘signatures’, ‘metagenes’ (linear combinations of gene expression values extracted to predict phenotype) or ‘modules’ (sets of genes that act in concert to carry out a specific function) are identified to represent the molecular behaviour of the response, phenotype or function under study. Predictive gene signatures have also been identified from tumor samples (van de Vijver et al., 2002).

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Recently, gene signatures have also been extracted from in vitro experiments with cell lines cultured under defined conditions (Chang et al., 2004; Chi et al., 2006; Seigneuric et al., 2007); with subsequent application to publicly available clinical data sets. Starting from in vitro studies allows not only to record gene expression in very controlled and reproducible situations but also to reduce the chances of overfitting. Overfitting occurs when an identified pattern is actually based on existing random features within the data (a consequence of the curse of dimensionality and of a poor procedure to detect structures embedded in the data). Therefore, the pattern can not be generalized to new, similar data sets.

Unsupervised Methods Unsupervised clustering relies on an algorithm without any a priori knowledge about the number or the type of classes it should find. In this respect, it is unbiased as it seeks to determine inherent structures (clusters) embedded into the data set. Cluster analysis is extremely common to assess shared functions and common regulation often referred to as ‘guilt by association’. It is often done by average-linkage with a Euclidean distance to focus on the highest expression changes. Data can be clustered and visualized with the popular software Cluster & TreeView (Eisen et al., 1998) for instance. Then, the user selects a group or cluster of genes for further analysis. Unsupervised approaches have been used to identify ‘molecular portraits’ of tumors and improve the classification of breast cancer (Perou et al., 2000). To improve breast cancer diagnosis for instance, one would like to refine the pathologist’s classes (e.g.: histological grade) assessed with a microscope by discovering new subclasses on the molecular level based on gene expression. A collection of samples belonging to the same grade is interrogated by an unsupervised algorithm to detect groups of samples that exhibit different expression patterns between the groups while maintaining similarity within the groups. This approach has been applied to provide a means to reduce overtreatment (Wang et al., 2005).

Supervised Methods This approach is based on identifying genes that fit an a priori determined feature (e.g.: pattern of expression). It requires to first define classes based on a different criteria than expression (e.g.: time point for a time series) and assign each sample to its class. The common pitfalls in the building of a predictor for cancer outcome have also been recently addressed in detail (Dupuy & Simon, 2007). A wide variety of algorithms (coming from the statistical and the machine learning communities) is available: the t-test, ANalysis Of Variance (ANOVA), Linear Discriminant Analysis (LDA), Support Vector Machine (SVM), etc. It is in fact necessary to restrict one to the simplest possible tools (e.g.: by starting an analysis with LDA rather than with SVM) to reduce the risk of overfitting. This is known as Occam’s razor after the Franciscan logician from the 14th century who stated that: ‘entities should not be multiplied beyond necessity’. This law of parsimony requires keeping the simplest model which can explain the data at hand. Since the number of samples in microarray data studies is always a limiting factor, some strategies have been selected to get the most out a given data set. One such approach is the Leave-One-Out-Cross-Validation (LOOCV). It consists in identifying genes differentially expressed in all samples but one, and to use the predictor to classify the remaining sample. With n samples this procedure is repeated n times. To decrease overfitting and provide more robust predictors, it is necessary to apply the LOOCV to the full procedure.

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List of D ifferentially E xpressed G enes Independent Validation The list of differentially expressed genes needs to be validated by an independent assay, usually by Reverse Transcription-Polymerase Chain Reaction (RT-PCR). Although the magnitude of the change may be different, it is important that its direction (up- or down-regulation) holds. Because the gene signatures are often large (presently ranging from 11 genes up to more than 500 in oncology), one option may be to select randomly a representative fraction of the (up- and down-regulated) genes to be tested.

Univariate Analysis: Kaplan-Meier Survival Curves Kaplan-Meier curves are used to show the clinical relevance of the gene expression based signature on patient data. Data sets containing gene expression from tumor specimens together with follow-up and clinical variables (e.g., age, tumor size, grade…) can be downloaded from the databases mentioned above and listed in Table 1. They span many cancer types including leukemias and carcinomas. Since clustering is the main method used to stratify patients in groups dependent on the expression of the genes in the signature, Kaplan-Meier survival analysis is the most widely used method to evaluate a gene signature. Log-rank tests are applied to test whether this results in a statistical difference in survival between the groups. Meta-analyses allow merging of small (homogeneous) data sets and therefore increase statistical power.

Multivariate Analysis In the context of molecular oncology, the objective of the multivariate analysis is to quantify the prognostic power of a list of biomarkers (e.g., a gene signature) with respect to the existing multiple variables as: age of the patient, tumor size, grade, mutation status of the gene coding for the essential protein p53 (called the ‘guardian of the genome’), etc. Additional methods are necessary to characterize and validate gene signatures (e.g., area under the curve, sensitivity, specificity or the concordance index).

Gene Ontology In order to get some insight into the biological theme of the list of genes, one often runs a gene ontology query. Ontology is a data model that represents a set of concepts within a domain and the relationships between those concepts (http://en.wikipedia.org/wiki/Ontology_(computer_science)). The current gene ontology contains approximately 20,000 terms to assign the biological process, the cellular component and the molecular function of genes. A wide variety of programs exists to find which of these are overrepresented in the list at hand (links are provided in Table1). Due to the a priori constraints imposed in a supervised analysis, it is harder to define its biological theme relatively to an unsupervised approach.

Pathways Involved An additional step in the analysis is to find the pathways in which the genes of interest are actually involved. This relies on our current understanding and representation of these pathways. The KEGG (Kyoto Encyclopedia of Genes and Genomes) initiative was launched in 1995 in order to link genomes 348

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to biological systems and its implementation has been recently up-dated by the use of Markup Language and API (Application Program Interface which allows customization). The pathway maps (for metabolic, genetic information processing, information processing and disease) are drawn manually and a z-score quantifies those maps where the genes of interest are overrepresented . The Gene Microarray Pathway Profiler (GenMAPP) software is designed for viewing and analyzing gene expression data in the context of biological pathways. Microarray data can be superimposed on existing maps to visualize up and down regulations. Pathways in GenMAPP can be edited and visualized with the PAthway VISualizatIOn (PathVisio) program which is also meant to display additional types of data (e.g.: proteomics data). A collective effort now intends to develop pathways important to biological research communities on the web (http://www.wikipathways.org/index.php/WikiPathways). Recently, the Biological Pathway eXchange (BioPax) initiative was launched to create a data exchange format for biological pathways in order to integrate knowledge from multiple sources in a coherent and reliable way. BioPax is based on Web Ontology Language (OWL). This language is meant for ontology construction and deployment to evolve from a human-readable graph to a machine-readable format for pathways analysis softwares.

Network Inference The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins and small molecules. Due to the massive number of such components and interlocking positive and negative feedback, feedforward loops, formal methods and computer tools are needed to unravel the relevant interactions and their topology. Depending on the goal (fine vs. coarse-grain model) and the collected data, different approaches have been proposed for inferring, modeling and simulating genetic, metabolic and signaling pathways: interaction graphs (Radulescu et al., 2006), Bayesian networks, Boolean networks (and their generalizations), ordinary and partial differential equations, qualitative (piecewise linear) differential equations, stochastic equations, and rule-based formalism. Bayesian Networks (BNs) and their temporal extension the Dynamic Bayesian Networks (DBNs) have received a wide interest. Indeed, unlike most other approaches, BNs and DBNs can handle missing data thanks to hidden variables. It allows circumventing the fact that most of the time, a study focuses on one level (e.g.: gene or protein expression). If one is monitoring gene expression data only (e.g.: by microarrays) no information is available on the protein level. In our perspective, DBNs are of special interest because they can overcome a limitation of BN which are restricted to infer network without feedback loops. DBNs do so by untangling their Directed Acyclic Graph (DAG) as a function of time, allowing reconstructing feedback and feedforward loops essential in biology. Network can be reconstructed from this framework allowing the identification of highly connected nodes (hubs) and apply other analyses using methods from graph theory. Performing experiments on such hubs (e.g.: RNAi, overexpression) will provide optimized set-ups for the molecular biologist who will maximize the effect of his experimental perturbation. Comparison between experiments and reconstructed network will fine tune the model while allowing one to select the most interesting experiments.

Mathematical Modeling Model is a common word which happens to be often misleading depending on the background of scientists using it. A model is a set of hypotheses or concepts that allows a simplified description and understanding of the system of interest. 349

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For a molecular biologist for instance, a model will be a (mouse) model where cancerous cells are injected to create tumor xenografts. The behaviour of cancer cells can thus be studied in a more controlled manner. But in the same field, a model can also be a molecular device which is used to change the expression status of a gene of interest. In gene therapy, the property of certain types of bacterias (like salmonella) to preferentially be located in hypoxic environments is exploited to target tumors. In this context, a model may be a flip-in construct to switch ON or OFF a specific gene. In molecular biology, a model can also be a breast cancer cell line (e.g.: MCF7) which represents an (in vitro) model for monitoring gene expression. In the field of data mining, this could be a (machine learning) model that is a set of rules identified from a specific data set. With an engineering sciences background, a model could be a (mathematical) model composed of equations containing parameters and variables. This is the meaning of ‘model’ within this paragraph. There is an increasing need for developing mechanistic systems models (van Riel, 2006) in biological sciences as outlined by the National Health Institute RoadMap (http://nihroadmap.nih.gov/). The Hyper Text Markup Language (HTML) language provides tags to give meaning and (hierarchical) structure to a web document. A more flexible version, eXensible Markup Language (XML), can be customized to create and define such tags. This feature is widely used in the Systems Biology Markup Language (SBML) language which aims at representing in a computer-readable format: pathways, biochemical reactions and gene regulations. SBML also provides simulations tools for quantitative modelling as well as a model repository (e.g.: curated cell cycle or MAPKKK cascade models). Numerical attempts to mathematically model and simulate the human heart (Cardiome) and the whole human body (Physiome) are based on this language. With ordinary differential equations, quantitative detailed descriptions spanning large temporal and spatial scales are provided to better understand physiological conditions. Both projects are collaborative efforts of several laboratories world-wide which exemplify some applications of Systems Biology.

Perspecti

ves

Any microarray study is composed of a succession of several steps which were discussed in this chapter. Each one of this step (with many options) represents an active field of research by its own. Due to such a situation (‘moving target’) it is a rule rather than an exception that investigators get somewhat different results. The requirement of the design, the raw and analyzed data on publishers’ website may greatly help clarifying the results and thus our understanding of the molecular biology of cancers. Our body is composed of 100,000,000,000,000 cells from about 250 different types, yet, it is working in harmony as a whole. It is made of organs, tissues, cells, genes, proteins, etc. which span many temporal and physical scales, from less than nanoseconds to tens of years and from atoms to a whole body. These different scales require various assays so that going from the wetlab to the bedside is a challenging endeavor which is indeed by essence multidisciplinary.

Co nc lusi on Systems Biology is a promising framework to improve our current understanding of the biology of tumors for instance. By unraveling the function of key genes, it may lead to individualized treatment

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instead of the ‘one size fits all’ approach. In the future, this may help developing better drugs or identifying beforehand patients who will be most likely to develop drug resistance or who will most benefit from a treatment.

R eferences Bar-Joseph, Z. (2004). Analyzing time series gene expression data. Bioinformatics, 20(16), 24932503. Chang, H. Y., Sneddon, J. B., Alizadeh, A. A., Sood, R., West, R. B., Montgomery, K., et al. (2004). Gene expression signature of fibroblast serum response predicts human cancer progression: Similarities between tumors and wounds. PLoS Biol, 2(2), E7. Chi, J. T., Wang, Z., Nuyten, D. S., Rodriguez, E. H., Schaner, M. E., Salim, A., et al. (2006). Gene expression programs in response to hypoxia: Cell type specificity and prognostic significance in human cancers. PLoS Med, 3(3), e47. Churchill, G. A. (2002). Fundamentals of experimental design for cdna microarrays. Nat Genet, 32 Suppl, 490-495. Dupuy, A., & Simon, R. M. (2007). Critical review of published microarray studies for cancer outcome and guidelines on statistical analysis and reporting. J Natl Cancer Inst, 99(2), 147-157. Eisen, M. B., Spellman, P. T., Brown, P. O., & Botstein, D. (1998). Cluster analysis and display of genome-wide expression patterns. Proc Natl Acad Sci USA, 95(25), 14863-14868. Kerr, M. K., & Churchill, G. A. (2001). Statistical design and the analysis of gene expression microarray data. Genet Res, 77(2), 123-128. Koritzinsky, M., Seigneuric, R., Magagnin, M. G., van den Beucken, T., Lambin, P., & Wouters, B. G. (2005). The hypoxic proteome is influenced by gene-specific changes in mrna translation. Radiother Oncol, 76(2), 177-186. Lazebnik, Y. (2004). Can a biologist fix a radio? -- or, what i learned while studying apoptosis, (cancer cell. 2002 Sept. 2(3), 179-82). Biochemistry (Mosc), 69(12), 1403-1406. Perou, C. M., Sorlie, T., Eisen, M. B., van de Rijn, M., Jeffrey, S. S., Rees, C. A., et al. (2000). Molecular portraits of human breast tumours. Nature, 406(6797), 747-752. Quackenbush, J. (2002). Microarray data normalization and transformation. Nat Genet, 32 Suppl, 496501. Radulescu, O., Lagarrigue, S., Siegel, A., Veber, P., & Le Borgne, M. (2006). Topology and static response of interaction networks in molecular biology. J R Soc Interface, 3(6), 185-196. Ransohoff, D. F. (2004). Rules of evidence for cancer molecular-marker discovery and validation. Nat Rev Cancer, 4(4), 309-314. Seigneuric, R., Starmans, M. H., Fung, G., Krishnapuram, B., Nuyten, D. S., van Erk, A., et al. (2007). Impact of supervised gene signatures of early hypoxia on patient survival. Radiother Oncol. 351

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Tibshirani, R. (2006). A simple method for assessing sample sizes in microarray experiments. BMC Bioinformatics, 7, 106. van de Vijver, M. J., He, Y. D., van’t Veer, L. J., Dai, H., Hart, A. A., Voskuil, D. W., et al. (2002). A geneexpression signature as a predictor of survival in breast cancer. N Engl J Med, 347(25), 1999-2009. van Riel, N. A. (2006). Dynamic modelling and analysis of biochemical networks: Mechanism-based models and model-based experiments. Brief Bioinform, 7(4), 364-374. Wang, Y., Klijn, J. G., Zhang, Y., Sieuwerts, A. M., Look, M. P., Yang, F., et al. (2005). Gene-expression profiles to predict distant metastasis of lymph-node-negative primary breast cancer. Lancet, 365(9460), 671-679. Yang, P., Sun, Z., Aubry, M. C., Kosari, F., Bamlet, W., Endo, C., et al. (2004). Study design considerations in clinical outcome research of lung cancer using microarray analysis. Lung Cancer, 46(2), 215-226. Yang, Y. H., & Speed, T. (2002). Design issues for cdna microarray experiments. Nat Rev Genet, 3(8), 579-588.

K ey T erms Biomarker: By definition any bio(logical) marker like a gene or a protein. In molecular oncology, due to the complexity of cancer diseases, highly parallel techniques are needed to identify a set of biomarkers rather than a unique biomarker. Sets of biomarkers are believed to be stronger predictors since they would reflect more reliably the multidimensionality of cancer. Cancer: A genetic disease emerging when cells have acquired at least six important factors contributing to pathogenesis. These hallmarks include evading apoptosis, self-sufficiency in growth signals, insensitivity to anti-growth signal, limitless replicative potential, sustained angiogenesis, and tissue invasion and metastasis. Complex System: Such systems (e.g.: a cell, an organ, a whole human body) are complex because of the large number of players involved and/or because of their time and context dependent interactions. The nature of these interactions or regulatory motifs (e.g.: positive or negative feed-back loop, feed-forward loop) increase the complexity of even a simple system with only a handfull of variables. Microarray: DNA microarray is a technique to monitor the abundance of tens of thousands RNA transcripts at once (by extension, gene expression). Molecular reporters corresponding to complementary sequences of genes of interest are orderly deposited on a glass surface. This is today the most mature of the highly parallel techniques. Model: A commonly used but very misleading term which heavily depends on the background of the investigator. In the broad sense, a model is used in any attempt to describe and explain a system of interest which can not be directly observed. A set of hypotheses are required to represent a simplification of it (i.e: a model).

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Network Inference: The attempt to discover the relationships between the components (or nodes such as genes, proteins, metabolites) of the network. It is a form of the inverse problem where one starts from the observations (gene expression levels from DNA microarrays for instance) and intends to identify the causes that led to such observations. Due to the very large number of potential players, this is a non-trivial problem which requires a massive amount of data. Normalization: The correction for known systematic biases in the data to allow a fair comparison. Omics: Due to the recent advent of highly parallel assays, it is now possible to monitor the behavior of not just one or a couple of variables but rather tens of thousands of variables at once. A growing number of disciplines with the ‘-omics’ suffix like genomics, transcriptomics, metabolomics and so on, intend to describe and understand completely a given level. Systems Biology: A field which studies complex biological systems at different levels to decipher the interactions of its key components and provide a mathematical model integrating this heterogeneous information.

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Chapter XXI

Systems Biology Strategies in Studies of Energy Homeostasis In Vivo Matej Orešič VTT Technical Research Centre of Finland, Finland Antonio Vidal-Puig Institute of Metabolic Science, Addenbrooke’s Hospital, UK

abstract In this chapter the authors report on their experience with the analysis and modeling of data obtained from studies of animal models related to obesity and metabolic syndrome. The complex interactions of genetic and environmental factors contributing to the failure of energy balance that lead to obesity, as well as tight systemic regulation to maintain energy homeostasis, require application of the systems biology strategy at the physiological level. In vivo systems offer the possibility of investigating not only the effects of specific genetic modifications or treatments in selected tissues and organs, but also to elucidate compensatory allostatic mechanisms induced to maintain the homeostasis of the whole system. A key challenge for systems biology is to characterize different systems’ responses in the context of activated pathways. One possible strategy is based on reconstruction of tissue specific pathways using lipidomics, or metabolomics in general, in combination with proteomic and transcriptomic profiles. This approach was applied to obese mouse model and revealed activation of multiple liver pathways that may lead to metabolic products, which may impair insulin sensitivity.

Intr od ucti on The system controlling the energy balance is tigtly regulated. The failure of mechanisms controlling the energy balance may lead to obesity. The causes of such failure may be genetic defects in the mechanisms Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Systems Biology Strategies in Studies of Energy Homeostasis In Vivo

controlling food intake, energy expenditure, partition of nutrients towards specific organs, expandability of the adipose tissue, or genetically inherited traits leading to inactivity. The environmental factors interacting with genetically determined traits are clearly involved, as the obesity is a rather recent problem of the last few decades. The biological redundancy adds another layer of complexity. Since energy homeostasis is so central to survival, the system has evolved towards a tightly regulated redundant system characterised by: (1) similar responses induced by different pathways and (2) compensatory mechanisms systems aiming to restore the steady state of energy homeostasis. Systems biology investigations aiming to address the complexity of obesity should therefore not only consider identification of mechanisms that may lead to obesity, but also aim to identify the compensatory biological strategies that are found in vivo. Some of these compensatory mechanisms may be targeted to increase the success rate of current strategies to lose weight. As obesity may lead to a number of complications such as diabetes and cardiovascular disease, a systems biology approach may be applied to identify early pathways that may lead to obesity-related complications, before they result in clinically identifiable specific diseases.

Lipid omics Lipids play an important role as structural components (e.g., cell membranes), energy storage components (triglycerides in adipose tissue), and as signalling molecules (Vance & Vance, 2004). For example, changes in lipid function due to peroxidation, imbalanced fatty acid composition or their increased flux to peripheral tissues may contribute to development of disorders such as atherosclerosis, diabetes, metabolic syndrome or Alzheimer’s disease (Watson, 2006; Wenk, 2005). Traditional clinical lipid measures quantify total amounts of triglycerides, cholesterol, or lipoproteins. However, serum lipid profile is much more complex at the molecular level. However, the modern lipidomics and metabolomics platforms enable quantitative characterization of 100s of diverse lipid molecular species across multiple lipid classes such as sphingolipids, phospholipids, sterol esters, and acylglycerols. In most cases, exact fatty acid composition for each detected lipid can be determined. Lipid metabolism is regulated both by genetic and environmental factors. For example, using a unique monozygous twin study design in which young adult obese monozygous twins were compared with their non-obese co-twins, we have recently shown that that obesity already in its early stages and independent of genetic influences is associated with deleterious alterations in the lipid metabolism known to facilitate atherogenesis, inflammation and insulin resistance (Pietiläinen et al., 2007). The study also demonstrated the sensitivity of the metabolomics platforms since subtle pathophysiological changes were detected well prior to changes in commonly utilized clinical measures. Of special interest and clinical relevance was the finding that the atherogenic lipid profile of the obese co-twins was associated with whole body insulin resistance, something that could not be detected using classical lipid measures and inflammatory markers only.

IN vivo st udies Lipidomics is increasingly utilized in functional characterization of genetic or environmental interventions in vivo. In vivo systems offer the possibility of investigating not only the effects of specific genetic

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modifications or treatments in selected tissues and organs, but also to elucidate compensatory allostatic mechanisms (McEwen & Wingfield, 2003) induced to maintain the homeostasis of the whole system. For example, in the context of energy balance, we have observed marked differences in adipogenesis and fat deposition between in vivo and in vitro models. In fact, whereas lack of proadipogenic transcription factor PPARγ2 in vitro results in markedly impaired adipogenesis and fat deposition, its genetic ablation in mice results in normal development of adipose tissue, thus suggesting robust compensatory mechanisms operating in vivo to facilitate fat deposition in adipose tissue. Remarkably, despite its normal adipose tissue appearance, lipidomic analysis revealed qualitative and quantitative differences in the repertoire of lipids stored. We found that lack of PPARγ2 resulted in accumulation of more immature lipids characterized by decreased long chain triacylglycerols and accumulation of lipid precursors such as specific phospholipid species (Medina-Gomez et al., 2005). Lipotoxicity is rapidly emerging as an important concept in the pathogenesis of multiple diseases as well as in aging (Slawik & Vidal-Puig, 2006; Summers, 2006; Summers & Nelson, 2005; Unger, 2002). The lipotoxicity is attributed to products, i.e. toxic lipids such as ceramides, of excessive non-β-oxidative metabolism of fatty acids in peripheral tissues such as skeletal muscle, pancreas, and myocardium (Unger, 2002). High levels of lipotoxic lipids in peripheral tissues are believed to be associated with diabetes, insulin resistance, cardiovascular disease by disrupting cell function and by promoting programmed cell death (lipoapoptosis). In order to investigate the effect of lipid overflow in adipose tissue, and its effect on peripheral tissues, the PPARγ2 KO was also studied in the obese mouse model background (ob/ob). Indeed, this approach allowed the identification of potentially pathogenic ceramide lipid species in adipose tissue. We are currently using this lipidomic approach to identify and characterise lipotoxic dysregulated metabolic networks in relevant metabolic organs for diabetes (Medina-Gomez et al., 2007). The use of this information may identify not only organ specific lipotoxic pathways suitable for pharmacological intervention in the context of the metabolic syndrome but also specific metabolic signatures with prognostic value.

Lipid pathw ay rec onstr ucti on fr om iN vivo st udies of lipot oxicity One question that may arise from the studies of lipotoxicity in vivo is which specific pathways leading to accumulation of reactive lipids in peripheral tissues are being activated. This immediately leads to a problem, as lipidomics today studies characterizes lipids at the intant molecular level, while the common pathway databases such as KEGG (Kanehisa, Goto, Kawashima, Okuno, & Hattori, 2004) contain information only at the generic lipid class level, although it is expected that with advent of lipid bioinformatics (Fahy et al., 2005; L. Yetukuri, Ekroos, Vidal-Puig, & Oresic, 2008) the information on lipids available in public databases will rapidly grow in the future. For example, cardiolipin contains four fatty acids. Assuming there are approximately 40 most common naturally occuring fatty acids in human, there are theoretically approximately 404=2,560,000 possible cardiolipin molecular entities. However, only one entry for cardiolipin exists in KEGG. It is thus not difficult to imagine that reconstruction of complete lipid metabolism at the molecular pathway level would lead to a combinatorial explosion. As a possible solution to the combinatorial explosion problem, we recently proposed a method for bridging the experimental knowledge with known lipid pathways in combination with omics data

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(Yetukuri et al., 2007). Each compound entry is linked to the available information on lipid pathways (e.g., based on KEGG) as well as contains information necessary for identification from the lipidomics experiments. The pathway instantiation is performed for selected lipids based on identification of Figure 1. From metabolomics data to instantiated pathways. Adapted from (Yetukuri et al., 2007).

G ro u p 1

G ro u p 2

L -S e rine

M etabolic profiles

M etabolic profiles

T ranscriptional and other data

T ranscriptional and other data

C er(d 1 8 :1/18:0 )

C oe x p ressi o n n etwo rks

P athw ay in s tan tiatio n, e.g., f o r C er(d18:1 /18:0)

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coregulated lipid species (Figure 1). Using our new methodology, we have recently reconstructed the lipotoxic pathways in fatty livers of obese mice (Yetukuri et al., 2007). We found that two ceramide synthesis pathways are upregulated in fatty livers: (1) de novo ceramide synthesis pathways due to increased flux of fatty acids into the cells, (2) glucosylceramidase and galactosylceramidase pathways, leading to release of ceramide from the membrane glycosphingolipids. Reassuringly, recent study showed that pharmacological inhibition of glucosylceramide synthase enhances insulin sensitivity in the obese mouse model (Aerts et al., 2007).

Co nc lusi on Systems approaches to the studies of in vivo systems must address the regulation of biological pathways in the physiological context. Characterization of pathways as either causal or compensatory requires knowledge of changes at the systems level. Studies of lipid metabolism as related to regulation of energy balance is one such example. As shown in this chapter, many practical bioinformatics and computational challenges remain for in vivo systems biology due to the need to bridge multiple special and temporal scales, which will require close cooperation between the theoretical and experimental work.

R eferences Aerts, J. M., Ottenhoff, R., Powlson, A. S., Grefhorst, A., van Eijk, M., Dubbelhuis, P. F., et al. (2007). Pharmacological inhibition of glucosylceramide synthase enhances insulin sensitivity. Diabetes, 56, 1341-1349. Fahy, E., Subramaniam, S., Brown, H. A., Glass, C. K., Merrill, A. H., Jr., Murphy, R. C., et al. (2005). A comprehensive classification system for lipids. J. Lipid Res., 46(5), 839-862. Kanehisa, M., Goto, S., Kawashima, S., Okuno, Y., & Hattori, M. (2004). The KEGG resource for deciphering the genome. Nucl. Acids Res., 32(Database Issue), D277-280. McEwen, B. S., & Wingfield, J. C. (2003). The concept of allostasis in biology and biomedicine. Horm. Behav., 43(1), 2-15. Medina-Gomez, G., Gray, S., Yetukuri, L., Shimomura, K., Campbell, M., Curtis, K., et al. (2007). PPAR gamma 2 prevents lipotoxicity by controlling adipose tissue expandability and peripheral lipid metabolism. PLoS Genet., 3(4), e64. Medina-Gomez, G., Virtue, S., Lelliott, C., Boiani, R., Campbell, M., Christodoulides, C., et al. (2005). The link between nutritional status and insulin sensitivity is dependent on the adipocyte-specific Peroxisome Proliferator-Activated Receptor-{gamma}2 isoform. Diabetes, 54(6), 1706-1716. Pietiläinen, K. H., Sysi-Aho, M., Rissanen, A., Seppänen-Laakso, T., Yki-Järvinen, H., Kaprio, J., et al. (2007). Acquired obesity is associated with changes in the serum lipidomic profile independent of genetic effects - A monozygotic twin study. PLoS ONE, 2(2), e218.

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Slawik, M., & Vidal-Puig, A. J. (2006). Lipotoxicity, overnutrition and energy metabolism in aging. Ageing Res. Rev., 5(2), 144-164. Summers, S. A. (2006). Ceramides in insulin resistance and lipotoxicity. Prog. Lipid Res., 45(1), 4272. Summers, S. A., & Nelson, D. H. (2005). A role for sphingolipids in producing the common features of Type 2 Diabetes, Metabolic Syndrome X, and Cushing’s Syndrome. Diabetes, 54(3), 591-602. Unger, R. (2002). Lipotoxic diseases. Annu Rev Med, 53, 319-336. Vance, D. E., & Vance, J. E. (Eds.). (2004). Biochemistry of lipids, lipoproteins and membranes (4th ed.). Amsterdam, The Netherlands: Elsevier B. V. Watson, A. D. (2006). Thematic review series: systems biology approaches to metabolic and cardiovascular disorders. Lipidomics: A global approach to lipid analysis in biological systems. J. Lipid Res., 47(10), 2101-2111. Wenk, M. R. (2005). The emerging field of lipidomics. Nat. Rev. Drug Discov., 4, 594-610. Yetukuri, L., Ekroos, K., Vidal-Puig, A., & Oresic, M. (2008). Informatics and computational strategies for the study of lipids. Mol. BioSyst., 4(2), 121-127. Yetukuri, L., Katajamaa, M., Medina-Gomez, G., Seppänen-Laakso, T., Puig, A. V., & Oresic, M. (2007). Bioinformatics strategies for lipidomics analysis: characterization of obesity related hepatic steatosis. BMC Syst. Biol., 1, e12.

K ey T erms Adipose Tissue: Loose connective tissue composed of fat cells or adipocytes. Its main role is to store energy in the form of fat, although it also cushions and insulates the body. Allostasis: The process of achieving stability, or homeostasis, through physiological or behavioral change. Allostasis is generally adaptive in short term, and can be carried out, e.g., by cytokines, autonomic nervous system, or metabolome. Ceramide: Sphingolipid which can induce apoptosis and is a key mediator of lipotoxicity. It consists of sphingosine linked to fatty acid via an amide bond. Structural and signaling molecule. Lipids: A diverse class of biological molecules that play a central role as structural components of biological membranes, energy reserves, and signaling molecules. They are broadly defined as hydrophobic or amphipathic small molecules that may originate entirely or in part by carbanion based condensation of thioesters, and/or by carbocation based condensation of isoprene units. Metabolomics: Metabolomics is a discipline dedicated to the global study of small molecules (i.e., metabolites), their dynamics, composition, interactions, and responses to interventions or to changes in their environment, in cells, tissues, and biofluids .

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Lipidomics: Lipidomics as a subfield of metabolomics aims at characterization of lipid molecular species and their biological roles with respect to the expression of proteins involved in lipid metabolism and function including gene regulation. Lipotoxicity: Accumulation of (lipo)toxic reactive lipids such as ceramides in non-adipose tissues of metabolically important organs such as pancreatic β-cells, skeletal muscle, liver, and heart. Pathway Instantiation: Reconstruction of possible activated pathways, originating from a specific molecular entity (e.g., protein or metabolite). based on molecular interactions and enzymatic reactions.

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Chapter XXII

Approaching Type 2 Diabetes Mellitus by Systems Biology Axel Rasche Max-Planck-Institute for Molecular Genetics, Germany

abstract We acquired new computational and experimental prospects to seek insight and cure for millions of afflicted persons with an ancient malady. Type 2 diabetes mellitus (T2DM) is a complex disease with a network of interactions among several tissues and a multifactorial pathogenesis. Research conducted in human and multiple animal models has strongly focused on genetics so far. High-throughput experimentation technics like microarrays provide new tools at hand to amend current knowledge. By integrating those results the aim is to develop a systems biology model assisting the diagnosis and treatment. Beside experimentation techniques and platforms or rather general concepts for a new term in biology and medicine this chapter joins the conceptions with a rather actual medical challenge. It outlines current results and envisions a possible alley to the comprehension of T2DM.

Intr od ucti on Type 2 Diabetes mellitus (T2DM) is the most common metabolic disease with more than 170 million patients worldwide. It rapidly increases in the developed and developing countries and is a huge, growing burden for health care systems. In the USA T2DM already accounts for over 130 billion Dollar of the health care costs (Stumvoll, Goldstein, & Haeften, 2005). In the past, T2DM was rarely seen in young people and thus called age-onset diabetes. But its prevalence increases due to changes in the lifestyle. For babies born in 2000 an estimated chance of 33%50% to develop T2DM leads to 11 to 18 years reduced life expectancy. Several risk factors account for this prevalence including genetics, nutrition, low physical activity and low birthweight. The genetical prevalence is identified by looking at the offspring of diabetic patients, a positive family history confers for a 2.4 fold increased risk for T2DM. For first-degree relatives to an afflicted person the risk is Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.

Approaching Type 2 Diabetes Mellitus by Systems Biology

increased by 15% to 25%. In twin studies the difference of the concordance rate between monozygotic and dizygotic twins returns an estimate of the genetic contribution, as dizygotic twins only share 50% of the genetic code. The concordance rate is 35% to 38% for monozygotic twins and 17% - 20 % for dizygotic twins. Prevalence merges with the environment. Increased availability of food combined with reduced physical activity lead to obesity which itself becomes the major influencing factor. In the USA 1991 12% of the population have been classified to be obese, increasing to 20.9% in 2001 and even 30% today resulting in an anticipated epidemic increase of T2DM in the next decades. Physical inactivity is a controllable factor, so 20 minutes exercise per day is enough for a noticeable improvement in treating T2DM. Unhealthy diet with a surplus of fatty acids completes the problem. Several molecular mechanisms are proposed to link obesity to T2DM. But the connection to the pathophysiology still remains unknown. Less than 10% of the T2DM variants are monogenic disease forms, on the other hand a high number of susceptibility genes is accounted for T2DM. Alterations in an entire network of genes is thought to be responsible for the disease. Most of the costs do not derive directly from diabetes but from its associated complications like macrovascular and microvascular diseases or accelerated atherogenesis. In an unclear pathogenesis, T2DM is preceded by impaired glucose tolerance, where glucose needed for cell energy cannot penetrate the cell wall anymore. Followed by an impairment in insulin action, increased adiposity drives a progression into insulin resistance. Since available T2DM therapies are of limited effectiveness, new insight into the disease by biomedical research must be sought. The classic genetic approaches have been more successful in monogenic diabetes like maturity-onset diabetes in the young or mitochondrial diabetes. The unknown hereditary mode poses a challenge, so far resulting in a number of candidate genes. Transgenic and knock-out mice are helpful in dissecting the transcriptional regulatory network. With the dawn of high-throughput methods a novel way to tackle these challenges arises. Microarrays allow us: 1. 2. 3.

To dissect the diversity of the disease primarily on the transcriptomic level. To identify transcription factor target sets using ChIP-on-Chip. To search for single nucleotide polymorphisms (SNP) using genotyping arrays.

The complex pathophysiological interactions between the tissues fat, muscle, liver, pancreas and brain are captured in distinct expression profiles for different mouse strains and different diets. On the

Figure 1. Different influences on the metabolism cause T2DM with its subsequent complications

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level of proteomics one now knows the secretory proteins in adipose tissue (Chen, 2005), while massspectrometry experiments are pursued in several labs. In this chapter, systems biology is defined as the development of mathematical models by the aggregation of experimental results. In the following we give an overview of the physiology of T2DM to sketch the complexity of the disease. T2DM is under study in several animal models based on different changes in the genomes. These genetic changes have been the most promising approach in the last years, now complemented by high-throughput gene expression, proteomic or metabolic surveys. The results are merged in the discipline of systems biology to generate and validate mathematical models.

T ype 2 D iabetes

Me llit us: Physi ology

In this subchapter the biologic topic, T2DM, shall be outlined. Central parts of the metabolism are affected. There is no space to address T2DM exhaustively, but only to comprehend the complexity of the affliction. The first paragraph distinguishes different types of diabetes, afterwards we look at the physiological interplay to subsequently describe the pathogenesis, and we finally link this topic to medicine with the diagnosis criteria.

D iabetes The main characteristic of diabetes mellitus is an abnormally high level of glucose in blood (Dean & McEntyre, 2004; Stumvoll et al., 2005). Normal people can mediate their blood glucose, whereas in diabetics glucose levels remain high. Insulin mediates the blood glucose level, and in diabetes insulin is not produced at all, insufficiently or not as effectively as needed. Most common forms are the autoimmune disorder type 1 diabetes (5% of the cases) and obesity associated type 2 diabetes (95%). Some rare variants exist, for example by single gene mutations. T2DM generally occurs in obese adults. Many underlying factors contribute to high blood glucose levels. An important factor is a resistance of the body to insulin, ignoring its insulin secretions. Therefore T2DM is a combination of deficient secretion and deficient insulin action. The rise of obesity in the population is the driving force behind the increase of diabetes. Today it can be difficult to maintain healthy body weight in the presence of abundant food and a sedentary life. Being overweight or obese is defined by looking at the Body Mass Index (BMI). A BMI of 18-25 is healthy, 25-30 overweight and above that level obese.

Physiology Here we follow the interaction of the key players for energy control in the human body. Three interactors are discussed and subsequently the involved tissues: • • •

Glucose, an essential energy source for the body Insulin, regulator of glucose and energy balance Glucagon, opponent of insulin

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Blood glucose levels are variable depending on the needs of metabolism, rising for three reasons: diet, breakdown of glycogen or hepatic synthesis of glucose. Glucose is regulated by several hormones, in particular by insulin. When glucose is abundant, insulin is released from pancreas and stimulates: • • • • •

Muscle and fat to remove glucose from the blood Cells to convert glucose in ATP Liver/muscle tissue to store glucose as glycogen Fat tissue to store glucose as fat Cells to use glucose in protein synthesis

Glucagon opposes the action of insulin and rises in scarcity. Insulin activates formation of glycogen and glucagon activates glycogen breakdown. Glucagon also helps the body to use alternative resources such as fat and protein. Fasting results in a fall of blood sugar level, leading to lower insulin and higher glucagon. Glucagon raises blood glucose by calling of glycogen from the liver short term reserve and glucose production by converting amino acids in the liver. Glucagon level is stimulated by several causes, like protein-rich food or stress. By fasting for a couple of days, the liver is exhausted by glycogen but continues to make glucose from amino acids and glycerol in fat. When glycogen stores are full, lipogenesis converts glucose into fat. Insulin supports lipogenesis by increasing transporters, mediated release of fatty acids and inhibition of fat breakdown, lowering fatty acid in blood. Insulin also stimulates entry of amino acids into cells and protein production. Four tissues are affected by this interplay: • • • •

Liver: Buffers and produces glucose Fat: Stores energy Skeletal muscle: Stores energy as glycogen Pancreas: Insulin is produced, stored and released from the pancreatic islets.

One of the most important organs in this interplay is the liver. It produces and consumes glucose and buffers glucose levels. From digestion the liver receives glucose-rich blood and removes large amounts of glucose to mediate the blood glucose level. Rise of blood glucose detect the pancreatic beta cells and respond with the release of insulin. This rise of glucose also lowers the release of glucagon and thus the production of glucose from other sources.

Figure 2. Insulin as main regulator

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Approaching Type 2 Diabetes Mellitus by Systems Biology

In every tissue inside the cell, glycolysis uses some of the glucose. Glycolysis is a central pathway of carbohydrate metabolism which occurs in all body cells and releases energy and carbohydrate intermediates for use in metabolism.

Pathogenesis In the pathogenesis of T2DM, insulin is no more able to stimulate the glucose usage in fat and muscle and to inhibit the glucose production adequately. Impaired insulin sensitivity and glucose intolerance are early phenomena, leading to hyperglycemia, hylerlipidemia and, eventually, to a failure of pancreatic β cells to produce and secrete a sufficient amount of insulin. However, most genes and their associated molecular network contributing to the onset and course of the disease are yet unknown. An understanding of the interplay between obesity and insulin resistance is crucial but not completely resolved (Kahn & Flier, 2000; Stumvoll et al., 2005). Obesity and physical inactivity is strongly associated with insulin resistance. Several mechanisms mediating this relationship are identified. Circulating hormones, cytokines and metabolic fuels from the adipocytes influence insulin action. Sometimes lipids are related to skeletal muscle insulin resistance, highlighting excessive fat storage in non-adipose cells.

D iagnosis Diabetes mellitus is diagnosed on the basis of WHO recommendations from 1999, which includes both fasting and 2h after 75g glucose load criteria into a practicable diagnostic classification (Table 1). impaired fasting glucose and impaired glucose tolerance are conditions predisposing overt diabetes mellitus. If not treated a substantial part of people with these problems will progress to overt diabetes (Stumvoll et al., 2005).

S pecies For the means of molecular biology different tissues of an organism are analysed. Due to ethical restrictions, human tissue is rarely available. To bypass this problem animal models are used in research. In the following some of the most important strains are presented. As mentioned it is difficult to get human tissue for analysis demanding the cooperation of many medical doctors for statistically meaningful samples. In addition, nutrition and lifestyle are not under

Table 1. Diagnostic criteria of diabetes mellitus and other categories of hyperglycaemia (mmol / L)

Fasting

2h after 75g glucose load

Diabetes mellitus

≥ 7.0

or

≥ 11.1

Impaired glucose tolerance (IGT)

< 7.0

and

7.8 – 11

Impaired fasting glucose

6.1 – 6.9

and

< 7.8

Normoglycemia

< 6.1

and

< 7.8

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control in contrast with lab mice. On the other hand the heritable predisposition for the disease is observable in family studies, twin studies and ethnic or population differences. In the chapter about the genetics I describe approaches to track involved genes. With animal models more finegrained study designs are possible by controlled conditions with regard to nutrition and lifestyle but also genetics. Time series for different disease states and back crossing experiments for genetical insight are further features. T2DM affects the basic metabolic process and therefore is traceable in organisms from mice and rats down to Caenorhabditis Elegans, where we find the most relevant pathways as aging pathways. Although rat models for T2DM exist like the Zucker Diabetic Fatty rat (ZDF rat) or Zucker Fatty rat, most of the available high-throughput screens and genome-wide genetical studies are performed in mouse, now pointed out in more detail. A complete overview about the mouse models used in T2DM research is provided by (Clee & Attie, 2007) highlighting the history of the mouse strains and their susceptibility to impaired glucose tolerance or T2DM. For example the C57BL/6, which accounts for 14% of the experiments, shows diabetessusceptible and diabetes-resistant aspects. With a so-called ob mutation in the Leptin gene, the same mouse strain is severely diabetic. Likewise the BTBR strain shows strong diabetes-susceptibility. The New Zealand Obese (NZO) mouse is a polygenic mouse model reflecting the whole metabolic syndrom, surrounding obesity and T2DM. All of the described mice models are available from the Jackson Labs including the focussed T2DM models (Jackson Labs, 2006). Insight into the metabolism and insulin resistance drawn from mouse models is described in (Nandi, Kitamura, Kahn, & Accili, 2004). The authors break down the plurality of knock-out and transgenic mice by phenotypes and tissue to find unsuspected players, e.g. transcription factors, which emerge from the underlying studies. In summary, major findings can arise from a variety of organisms to understand human metabolism. A caveat is, that the disease in the animal models may have causes different from the human setting. So the results lack comparability and have to be reproduced in different models. To understand the missing comparability we continue with a look at the methods for analyzing differences in genetic code.

G enetics T2DM is clearly associated with a genetic prevalence which is demonstrated for example in family studies. A positive family history is related to a 2.4 fold increased risk (Stumvoll et al., 2005). Twin studies contributed distinguishing non-genetic from genetic factors. For impaired glucose tolerance concordance rates were 88% in monozygotic twins. The two main strategies are the genome-wide scanning and the candidate gene approach. In genomewide scanning different genomes from the same species are compared to each other to narrow down disease related regions. In the candidate gene approach gene sequences of physiologically important proteins are compared among population samples. Both approaches seek to isolate causative genetic changes.

G enome-W ide S canning For the genome-wide scanning in human association studies are performed on patient cohorts raised over years using genotyping microarrays isolating chromosomal regions or, more advanced, single nucleotid polymorphisms (Permutt, Wasson, & Cox, 2005; Sladek et al., 2007).

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In a variant, called linkage approach, the entire genome of affected family members is compared using genetic markers, to combine the alterations with the family genealogy over several generations and affected sibling pairs to look for associations between parts of the genome and the risk of developing diabetes. This locates genes by the rationale, that family members not only share the phenotype but also chromosomal regions surrounding the involved gene. Positive associations are found in one or more studies, but the following positional cloning of causative genes has mostly been unsuccessful. To make the genetic quest more complicated a possibility arose of a relation of T2DM to imprinted genes. Imprinted genes are genes for which expression varies depending on the sex of the transmitting parent. The genome-wide scan is also used in mice. Through backcrossing between susceptible and unsusceptible strains, arbitrary quantitative trait loci are isolated with a similar goal, with a much smaller demand of individuals as in the human case (Permutt et al., 2005). In the animal model it is more easy to follow and direct the family history. The chromosomal regions linked to the trait, here T2DM, are called quantitative trait loci. Recently the genetic component has been directly linked to the expression level using expression microarrays and genotyping arrays on backcrossed mouse strains (Lan et al., 2006). Thus, it integrates two different information levels and results in narrow genomic candidate regions. Genetic linkage and association to a phenotype, like T2DM, often has a poor replicability, which is regularly attributed to a number of factors amongs others ethnic stratification, population-specific linkage disequilibrium between markers and causal variants but also gene-by-gene and gene-by-environment interactions. Because of the late onset of T2DM, susceptibility gene variants may exist in the control group and reduce the power of genetic-linkage and association analyses.

C andidate G ene A pproach The candidate gene approach examines specific genes on their role in T2DM. In unrelated individuals, the statistical association of an allele and the phenotype T2DM or impaired glucose tolerance is tested. Obvious biological candidates for insulin resistance have been examined (Dean & McEntyre, 2004; Parikh & Groop, 2004). But the candidate gene approach had minor success in identifying causative factors. In many candidate genes, like ABCC8 or GCGR, variants were extensively analysed, but mostly the initial association could not be replicated in subsequent studies (OMIM, 2000). The candidate gene approach is scientifically more simple focussing on disease status and alleles or haplotypes in insulin signalling or glucose metabolism. (Dean & McEntyre, 2004; Parikh & Groop, 2004) describe work and results performed on the most promising candidates. In the animal models genetical manipulation is possible often leading into mouse models as described above (Clee & Attie, 2007).

S ummary Due to the heterogeneity, genetic studies produced very diverse results. At this time their incorporation into a systems biology model is a challenge, as most of the models do not account for changes in genetic code but focus on the physiology. An exhaustive collection of entangled genome regions is provided by OMIM under the identifier #125853 (OMIM, 2000). Mutations of a single gene can result in disease. This happens in rare forms of diabetes. Such mutations can be investigated with sequencing to find responsible alterations in the DNA, so called single nucleotide polymorphisms (SNP). T2DM is assumed to be polygenic. Disease genes may show subtle but common differences in the gene sequence. It is difficult to link these common gene variations to an

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increased risk of developing T2DM. Therefore it is a remarkable result, that microarray study results converge on the same functional modules by deriving metabolic pathways from expression results (Toye & Gauguier, 2003).

G ene E xpressi on in T 2DM DNA microarrays present a powerful tool for studying the mechanisms of complex diseases and have been used to dissect every aspect of T2DM (Sun, 2007). Behind physiologic and pathologic conditions the technology permits a more comprehensive understanding of the multiple genes involved in the mechanisms of the disease. Microarrays allow the categorization of disease states according to the changes in the mRNA expressed. This is used in parallel in several tissues and different cells at the same time or in the same cell type at several time points. (Sun, 2007) outlines the current status of DNA microarray applications in the field of obesity and T2DM. A number of high-quality microarray data sets can be found at (mult., 2002). Animal models and cultured cells analysed with microarrays are used in a variety of studies. In T2DM they returned a tremendous amount of information about the pathophysiology. Studies in vivo and in vitro profiling adipocytes from intra-abdominal and subcutaneous adipose tissue lead to coordinated depotspecific differences in expression of multiple genes in embryonic development and pattern specification. In the case of the liver the nonalcoholic fatty liver disease is related to lipid metabolism, extracellular matrix remodeling, liver regeneration, apoptosis and detoxification process. In rat skeletal muscle the activation of the hexosamine biosynthesis pathway – a nutrient-sensing mechanism – decreased genes involved in oxidative phosphorylation. Diet effects alter the expression of hundreds of genes primarily related to lipid metabolism and transcription factors in adipocyte differentiation. Expression profiling in the central nervous system is only possible in animals by finding the cytokine signalling box-containing protein 4 expressed in brain areas linked to energy homeostasis. In human analog studies are carried out, like in adipose tissue returning disperse results, e.g. linking genes to lipid and glucose metabolism, membrane transport and promotion of the cell cycle. In liver, for patients with nonalcoholic steatohepatitis gene groups related to (also) lipid metabolism and extracellular matrix remodeling are differentially expressed. In skeletal muscle probably the most important finding is the upregulation of the oxidative phosphorylation pathway in accord with the rat results (see above). The current application of microarrays is accompanied by some problems and challenges. A set of guidelines called Minimum Information about a Microarray Experiment (MIAME) is introduced by the International Microarray Gene Expression Data Society. However there are still some issues to be considered. The total number of probes on a microarray and the selection of the probe sequences from the gene/transcript sequences differs between the chip manufacturers and therefore hinders comparability. Direct comparisons may focus on the overlapping part, in all other cases the differences have to be accounted when interpreting the results. Biological parameters are to keep constant in the experiment like age of the animals or patients, balanced gender ratio and sample collection at same time points in the menstrual cycle. Data analysis is complex due to the large amount of genes and possible study designs. A small number of samples is most often the biggest issue resulting in low power of the study. Microarray experiments mostly result in a list of differentially expressed genes. A plurality of tools has been developed to enhance the expression results, and only selected approaches can be mentioned. (Jensen & Steinmetz, 2005) discuss the comparability of array results in terms of integrating data sets to

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raise the power and confidence in the results. The number of available experiments suggests to perform first meta-analyses identifying core processes underlying T2DM. A simple way to ascend from the gene expression level to biological function in terms of metabolic or signalling pathways is enrichment. The technique has originally been introduced in (Mootha et al., 2003) as “gene set enrichment analysis”. In (Liu et al., 2007) an advanced approach, “gene network enrichment analysis”, is used to identify network models for T2DM (see below). Not only sets of apparently dependent genes are taken into account but rather subnets of the protein-protein-interaction network. The gene networks are compared with the results of several microarray data sets from (mult., 2002). Altogether the analysis of the transcriptome with microarrays is a valuable ressource of data for systems biology. The mass of data may be frightening and data quality issues are regularly brought up. Nevertheless the alternative, RT-PCR, returns only selective results and thus high-throughput methods support the systems biology approach outlined in the next subchapter.

S ystems

B iology f or T 2DM

Systems biology comprises different aspects exemplified in this chapter. It is sustained by genetical analyses and high-throughput methods on different species. The center is the aggregation of the different evaluations to a comprehensive model (Klipp, Herwig, Kowald, Wierling, & Lehrach, 2005).

S ystems B iology S tarts with D ata Integration On first-level heterogenous resources, like experimental data sets or databases are integrated to parse data and query information. Several types of data sets are described above and can be set in relation to gene or protein sequence databases, interaction data or pathway data for several organisms. In a second level correlations across different sources lead to a more comprehensive and coherent picture. For example the genetic hints by now do rarely correlate with results from expression analysis. On a third level the newly gained information is casted into networks and pathways for the understanding of T2DM on a cellular level.

S ystems B iology is Modeling T2DM is a complex process not following any elementary principles, at least we are not aware any. The outcome from the genotype and lifestyle cannot be foreseen by experience. The properties of an appropriate model let us distinguish between system states, for example T2DM – healthy, obese – lean or high-fat diet – healthy diet. The variables, parameters and constants of the model clear up our possibilites to regulate and control the disease. The substantial changes in T2DM are on the metabolic level. Perhaps a single model cannot serve all purposes. Metabolism is a generic term for catabolic and anabolic reactions. These metabolic reactions transform molecules from one type into molecules of a different type. Metabolic reactions are modeled on three levels of abstraction: • • •

Enzyme kinetics study the dynamic properties of the reactions. Stoichiometric analysis describes the network character. Metabolic control analysis (MCA) quantifies the effect of perturbations in the network. 369

Approaching Type 2 Diabetes Mellitus by Systems Biology

Figure 3. Systems biology facilitates to attain new perceptions

Gene expression can be modelled in two ways. The expression of one to few genes can be described with transcription, translation, including binding of transcription factors and RNA polymerases to DNA and effect of activators or inhibitors and subsequently the different stages of maturation of mRNA. This is not appropriate for microarray experiments with ten thousands of measurements. Reverse engineering methods reconstruct the underlying regulator networks. This approach neglects the complex regulatory machinery covering a larger fraction of genes in a cell and focussing on activators and inhibitors.

S ystems B iology Uses C omputers and Internet Modeling tools help formulate theoretical hypotheses and extract information relevant to the hypotheses. General purpose tools like R, Matlab or Mathematica have a steep learning curve. Focussed tools for the special needs of biologists are easier to use like PyBioS (Wierling, Herwig, & Lehrach, 2007), where the handling of the differential equations is covered behind a web interface. Parameters and kinetics are controlled through this interface. Exchange of models meanwhile is standardized by the systems biology markup language (SBML) also used for some of the models described below. With the rapid increase of biological data the need to organise and structure the data increases and so does the number of databases in the internet. No comprehensive database with the focus T2DM is available. But different databases provide the information needed for the modeling. E.g. several microarray datasets are available at (mult., 2002) or the KEGG pathway database provides the topological model of a T2DM signalling pathway.

S ystems B iology Models S erve D ifferent Purposes A descriptive model elucidates causes and developments or explains the expression signatures that we observe in the experiments. Already projects are under way to use expression signatures in the diagnosis of certain diseases. After the refined diagnosis an optimized drug treatment uses the best possible medi-

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cine administered in an adequate dose. The admission process for new treatments could be facilitated if accompanying models show that it complies to the restrictions.

Mode ls of T 2DM In the last subchapter we discuss mathematical modeling in the context of T2DM. This subject is not new, but known as physiological modeling for years. New are the computer-assisted techniques and the support by high-throughput data resulting in models of increased scale. The body glucose balance and T2DM itself has been subject to modeling for several years. But despite the availability of these models, we still miss key aspects explaining the pathogenesis or adequate drug targets. Here we first discuss the topic of mathematical modeling and then present five examples of models in this research subject.

Mathematical Modeling The goal of the Systems Biology approach is to create a comprehensive representation of all of the biochemical reactions in human and to understand the control of signalling pathways in complex networks. Therefore mathematical models of descriptive, predictive or elucidative nature are used. Ultimatively a quantitative, kinetic model reflects the outcome of the experiments. Such models are rare by now and none exists for T2DM comprising all tissues and aspects of the disease. Mathematical models have the advantage to be cheap and reduce the number of necessary animal experiments and, at the same time, facilitate the conceptual clarification of the disease and observed biology, independent of the kind of the model, a graph, network model or kinetic, differential equation model (Klipp et al., 2005). Special challenges in T2DM are a suspected entanglement of the mitochondrion, the influence of nutrition and genetic prevalence. No templates exist to incorporate such aspects into a model.

S elected Models Here we present 5 examples of models for T2DM. (Kansal, 2004) or the introduction of (Jiang, Cox, & Hancock, 2007) review several approaches to the topic and are recommended for further reading. The models are intentionally chosen to present different modeling approaches and therefore do not have much in common but the subject T2DM. Model I and V are differential equation models and return numerically exact results. Model II is a large scale model incorporating a maximum of components. Model III and IV are interaction maps for discussion of known interactions in terms of control theory as well as highlight previously unevaluated protein-protein-interactions for possible relationship to T2DM.

Model I 1979 the “minimal model” is presented in (Bergman, Ider, Bowden, & Cobelli, 1979). It models glucose clearance for understanding the action of insulin. It comprises two coupled differential equations: dG (t ) = − {SG + X (t )}⋅ G (t ) dt dX (t ) = p2 ⋅ I (t ) − p3 ⋅ X (t ) dt 371

Approaching Type 2 Diabetes Mellitus by Systems Biology

where G is the concentration of glucose in the plasma, I is the concentration of insulin in the plasma, X is the concentration of insulin in remote compartment. SG is the glucose effectiveness and p2 and p3 are model parameters. For a glucose injection the two equations describe the glucose decline and insulin movement from blood to insulin-sensitive tissue. The first equation is the decline of glucose as an insulin-independent process and an insulin-dependent process. The second equation stands for the insulin removal from blood dependent on the available blood insulin as well as the insulin already in the insulin-sensitive tissue. The model is successful as a clinical tool und meanwhile has been checked and extended in various directions. It is shown here (Figure 4) for its simplicity.

Model II For skeletal muscle the authors of (Pollard et al., 2005) present a large scale model with 157’000 molecular components and more than 210’000 relationships between those components. Building on several microarray data sets, the authors take the challenge to model the entity of the skeletal muscle cells. For an approach of this size reactions cannot be composed by hand but have to be built computationally. On the other hand the intricate complexity of large scale schemes is reduced by restricting expression changes to three categories: expression increased, unchanged or decreased in T2DM. Thus it is directly set up as a qualitative, discrete model reducing parameter space and computation time. The authors apply their model to the treatment of T2DM with different drugs or post-transplant diabetes mellitus.

Model III An interaction map is presented in (Kitano et al., 2004) like in terms of control theory, clearly separating the interactions between the tissues. The robustness of the body energy balance is discussed highlighting several feedback loops for unstable food supply. The interaction map elucidates cross talk between tissues and pathways. This is the only model so far to divide and link the related tissues. In model IV tissues are intermingled and models II and V are focussed on one tissue type each.

Figure 4. Modelling and simulation of the minimal model with PyBioS

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Approaching Type 2 Diabetes Mellitus by Systems Biology

Model IV In (Liu et al., 2007) the authors identified an insulin signaling and a nuclear receptor network consistently and differentially expressed in several occurences of insulin resistance. Integrating different microarray data sets from (mult., 2002) and combining the results with the protein-protein-interaction network in this model the authors determine the two subnetworks of the protein-prote