Current Topics in Membranes and Transport VOLUME 21
ION CHANNELS: MOLECULAR AND PHYSIOLOGICAL ASPECTS
Advisory Board
M . P. Blaustcin G . Blohrl J . S . Cook
P . Liiiiger
P . A . Knoiij” Sir H . L . Kornhc>rg
W . Stoeckcniiis K . J . Ullrich
C . A . Pusterntik W . D . Stein
Contributors
Petrr H . Burry Joun E. Bell R . Brnz Alan Firikrlstriri Peter W . Gage A n ci M u ria Gurcia John W . Hmnruhm D . A . Haydon W . Vrin
S.
B. Hlridky
Richard Horn H.- A . Kol h P . Liiiigc’r
David G . Levirt Sirnon A . Lewis Werner R . L o c w m W h Christ o phor Mill ~r Driessc-he
Current Topics in Membranes and Transport Edited b y
Felix Bronner Department of Oral Biology University of Connecticut Heulth Center Farmington, Connecticut
VOLUME 21
ION CHANNELS: MOLECULAR AND PHYSIOLOGICAL ASPECTS Guest Editor
Wilfred D. Stein Department of Biologicul Chemistry Institute of Life Sciences The Hebrew University of Jerusulem Jerhsulem, Isruel
1984
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Contents Contributors, ix Preface, xi Yale Membrane Transport Processes Volumes, xix
Ionic Selectivity of Channels at the End Plate
PETER H. BARRY AND PETER W. (;AGE
I. 11. Ill. 1V. V. VI.
Introduction, 2 Principles of Equilibrium Ion Selectivity, 3 Principles of Dynamic Ion Selectivity, 9 Experimental 'Techniques. 28 End-Plate Channel Characteristics. 33 Summary and Comparison with Na' and K' Channels in Nerve and Muscles. 47 References. 50
Gating of Channels in Nerve and Muscle: A Stochastic Approach
RICHARD HORN 1. Introduction: Overview and Scope. 53 11. General Properties, 54 111. Stochastic Representation of Chiinncl Gating. 70 IV. Experimental Findings, XX References. 92
The Potassium Channel of Sarcoplasmic Reticulum
CHKISI'OPHER MIILEK, JOAN E. BELI,. AND A N A M A R I A GARCIA Introduction. 99 Electi-ical Behavior of SR K ' Channels. 101 Fluxes in Native SR Vesicles. 122 IV. Standing Problems and Future Directions, 127 Refer-ences, 129
1. 11. 111.
V
vi
CONTENTS
Measuring the Properties of Single Channels in Cell Membranes
H.-A. KOLB I . Introduction, 133 11. Fluctuation (Noise) Analysis o l Multichannel Systems, 13.5 111. Noise Analysis of Non-Channel-Mediated Ion Movement, 147 IV. Methods of Singlechannel Recording. 147 V. I o n Channels in Patched Membranes, 156 VI. Conclusion, 170 References. 171
Kinetics of Movement in Narrow Channels
DAVID G. LEVIT’I
I. II.
lon-Ion Interaction. 182 Water-Water Interactions, 185 111. Ion-Water Interactions, 187 IV. Summary, 193 V. Appendix: Derivation of Eqs. (3) and (4). IY4 References. 196
Structure and Selectivity of Porin Channels
R. BENZ
I.
Introduction, 199 Reconstitution of Porins into Lipid Bilayer Membranes, 200 Single-Channel Analysis. 205 IV. Ionic Selectivity of Porin Channels, 207 V. Properties of the Anion-Selective Channel from Pserrt/orno,itrs crt~r’/r~irio.str Outer Membrane, 209 Vl. Conclusions, 213 References, 217 11. 111.
Channels in the Junctions between Cells
WERNER R. LOEWENSTEIN 1. Introduction. 221 11. The Cell-to-Cell Channel, 222 Ill. Channel Formation. 222
1V. Permeability of the Channel, 231
CONTENTS
V . Regulation of the Channel, 235 VI. Structure and Chemistry of the Membrane Particle in the Gap Junction. 244 References, 247
Channels across Epithelial Cell Layers
SIMON A. LEWIS, JOHN W. H A N K A H A N . A N D W. V A N DRIESSCHE
I. Introduction. 2 5 3 I I . N:I+ Channel. 254 I l l . K ' Chdnnelb, 171 IV. Nonwlective Cation Chamel\. 2x2 V . The H 2 0 Channel, 286 v1. Candidate Channel\. 787 Refeiences. 288
Water Movement through Membrane Channels
ALAN FINKELSTEIN
I.
Water Permeability Coefficients. 296 Water Permeability of Planar Lipid Bilayer Membranes. 298 Water Permeability of Plaarna Menibr;int., 303 IV. Summary. 306 Reference\, 306
11. Ill.
Channels with Multiple Conformational States: Interrelations with Carriers and Pumps
P. I
I . Inlroduction. 309 11. Coupling between Ion Flow and Conlornmational Transitions. 3 10 111. Current Noise in Open Channels, 320 IV. Conformational Transitions Driven by an External Energy Source: Ion Pumps, 321 V . Conclusion. 324 References. 32s
Ion Movements in Gramicidin Channels S. B. HLADKY AND D. A. HAYDON
I . Introduction. 327 11. Structure. 328 111. Channel Formation: Kinetics and Equilibria. 337
vii
viii 1V. V. VI. VI1. VIII.
CONTENTS
Movements of Ions through ihe Pore, 342 Movement of Water through the Pore, 359 interactions of Ions and Water in the Pore, 359 Appendix I, 363 Appendix 11, 366 References, 368
Index, 373 Contents of Previous Volumes, 379
Cont r ibutors Numbers i n parentheses indicate the pages on which the author\' contributions begin
Peter H. Barry, Nerve-Muscle Research Centre. School o f Phyhinlogy and Pharmacology, University o f New South Wales, Kensington, New South Wales 2033. Australia ( 1 ) Joan E. Bell, Graduate Department of Biocheinislry. Hr;mdeis University. Walth;irn, M a sachusetts 03254 (99) R. Benz, Department o f Biology. University o f Konstanl. D-7750 Konstanl. Federal Kcpublic of Germany (199)
Alan Finkelstein, Departments of Physiology and Biophysics and o f Neuroscience. Albert Einstein College of Medicine, Bronx, New York 10461 (295) Peter W. Gage, Nerve-Muscle Keserirch Centre. School o f Physiology and Pharmacology, University of New South Wales. Kensington. New South W;iles 2033. Austl-;ilin (I) Ana Maria Garcia, Graduate Department of Biochemistry, Rrandeis University, W:ilthani. Massachusetts 02254 (99) John W. Hanrahan, Department of Physiology. Yale University School o f Medicine. New Haven. Connecticut 06510 ( 2 5 3 ) D. A. Haydon, Physiological Lihoriitory. Univei-\ity of Cambridge. C;inihritlge CB2 3EG. klngland (327) S. B. Hladky, Department of Pharnlacology. Univenity of Cambridge. Camhi-idge C132 ZQD. England (327) Richard Horn, Department o f Physiology. School o f Medicine, University o f California, 1,os Angeles, 1.0s Angeles, California 90024 ( 5 3 ) H.-A. Kolb, Department of Biology. Universit v of Konstanz. 11-7750 Konstanz. Federal Republic o f Germany ( 133) P. Lauger, Department of Biology. University of Konstanx. 11.7750 Konsranr, Fetleral Kcpublic of Germany (309) David G. Levitt, Department of Physiology. Univei-slty of Minnesota, Minneapolis, Minnzsota 55455 (1x1) Simon A. Lewis, Department of Physiology. Y;ile University School of Medicine. New Haven. Connecticut 06510 (253) Werner R. Loewenstein, Depdrtnient of Phy4ology and Biophybics. Univer.;ity of Miami School o f Medicine. Miami. F-lorida 33101 ( 2 2 1 ) Christopher Miller, Graduate Department o f Biocheiiii\try. 13r.andeis University. W;ilthani. Massachusetts 02254 (99)
W. Van Driessche, 1,ahoratoriurn voor Fy\iologic. KLI I., Campus Gasthuislrerg. 8-3000 Lxuven, Belgium ( 3 3 )
ix
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Preface We seem to be on the brink of understanding how ion channels work. The biophysics of these channels has become much clearer with the ability to measure the electrical properties of single ion channels. In parallel, the application of the techniques of X-ray crystallography and electron microscopy to the isolated channel proteins has established the molecular structure of a few channels. Finally, though more slowly, we are approaching a deeper understanding of the theory of movement through such pores. All these advances allow us to hope that within a few years we shall be in a position to relate structure and function, that is, to predict the selectivity and absolute permeability of an ion channel from a knowledge of its molecular structure. This volume assesses our progress and we hope it will provide guidelines for future progress. The articles, written by experts who have themselves contributed much to the development of the field, summarize comprehensively much of what is known about the molecular and physiological aspects of ion channels in general and of a number of different ion channels in particular. While each contribution deals with a particular aspect of ion channel research problems, a few general comments at this stage are appropriate. The essence of the problem of relating ion permeability to channel properties is as follows: we have, for the channel, a measure of its conductance for a particular ion, that is, we know at a particular concentration of the ion in the bulk solution how many ions flow through the channel when a unit potential difference is applied across the channel. For the ion in question we know also its conductance in dilute solution in the absence of any interaction with the channel. How is this bulk property modified within the channel and how d o the dimensions of the channel determine the measured single-channel conductance'? We can attempt to estimate the cross-sectional area of the channel by observing how it acts as a size-determined filter, selecting among various substances of different cross section. Such data are, as we shall see in this volume, now available for quite a few types of channels. Far more indirectly, we can begin to make an educated guess a s to the length of that region of the channel that forms the filter. From the bulk conductance of the ion in question, together with these estimates ofthe channel dimensions, we can xi
xii
PREFACE
calculate what the single-channel conductance would be were the bulk conductance value to be operative within the channel. Take, for instance, the end-plate channel at the nerve-muscle junction of the rat. This has, at 5"C, a measured single-channel conductance per molar concentration of about 210 pS M - ' for sodium ions (calculated from Hamill and Sakmann. 198 I ) . The equivalent conductance of sodium ions in bulk solution at 100 mM and at 5°C is about 26 S cmz (calculated from Glasstone, 1948). The cross-sectional area of the end-plate channel, as we shall see in the first article, has been estimated as being about 41 We guess the length of this channel to be roughly equal to the length of a gramicidin channel in a lipid membrane (see the last article), namely, about 30 A. The conductance of a channel of such dimensions, assuming that the value of the bulk conductance indeed applies within this channel, will be 26 x 41 X lO-lh/(30 X or 355 x S cm3/g-equivalentNaS or, in molar terms, of 355 pS W ' .This is clearly very close to the measured value, and might suggest that we are close to a molecular understanding of the conductance properties of this channel. The success of this naive calculation suggests that this simple model is essentially correct. But there are numerous unknown factors which might, and apparently do, fortuitously cancel one another and bring about this apparent accord. In the first place, our calculation does not take into account the partitioning of sodium ions between the bulk phase and the channel interior. Since the channel effectively discriminates in favor of cations, the cations must be bound with the channel or at least be at a higher concentration inside the channel than outside. The charged cation ethanolamine crosses the channel three times faster than its uncharged analog ethandiol (Huang et d.,1978). This effect of the charge on the cation might thus increase the conductance to 3 x 355 pS M I. On the other hand, there must be steric effects which limit the access of the sodium ions to the pore. Sodium ions behave within the channel as if they have an equivalent mean diameter of about 4.5 A (as can be concluded from the study of A d a m et d..1980), presumably because of the waters of hydration that they carry. If the channel has a diameter of 6.5 A, the area actually available to sodium ions diffusing through the channel is only the fraction I - (4.5/6.5)', or about one-half, of the whole area. Thus, charge effects and the excluded area effects probably cancel one another. As we shall see in the article by Levitt, any estimate of conductance for narrow channels is likely to be much in error owing to ion-ion and ion-water interactions within the channel. Nevertheless, it remains a goal of the biophysicist to predict channel conductances from a detailed knowledge of channel structure. The second major problem in the understanding of ion channels concerns the gating of these channels. Many channel types, as we shall see,
A'.
PREFACE
xiii
exist in an open or in a closed configuration, and there may be more than one such configuration for either open or closed channels. The act of changing from one conformation to another is generally very fast, too fast to measure, but it is easy to determine the average period of time that a channel exists in an open or a closed conformation. This time period is often strictly controlled by the applied voltage or by the binding of calcium or some specific activator of the channel in question. These conformational changes are of the general class of changes found for many soluble proteins or enzymes. In the same way as they are beginning to be understood at a molecular level in the case of the soluble protein, so, with some delay, are they beginning to be understood in the case of the gated ion channels. The principles are clear, as we shall see in the article by Horn, but the detailed application of these principles needs to be worked out for each system in turn, and we shall in later articles show how a number of these systems are being tackled. How do our authors approach these basic problems of the ion channels? In the first article, Barry and Gage analyze in broad fashion the movements of ions through channels. They compare three theoretical approaches to this problem: the simple Goldman-Hodgkin-Katz approach, the electrodiffusion approach, and the rate theory approach. They distinguish clearly between the principles of selectivity for ions at equilibrium and selectivity during the dynamic process of movement through a channel. ‘The latter requires that ion selectivity be composed of both a binding affinity for a site within the channel and a selectivity due to the differential mobility of ions within the channel. The Eisenman rules apply only to the equilibrium, that is, the binding, selectivities; the Goldman treatment considers only mobilities. Barry and Gage show how the electrodiffusion and rate theory approaches enable one to sort out these two components of ion permeability. On this basis, they analyze the experimental data on ion movements through the end-plate channel, as movement is affected by the applied voltage, and reach the important conclusion that the affinity of ions for charged sites within this channel is in the reverse order to what a naive analysis, based on permeabilities alone, would lead one to suspect. Horn tackles, in the second article, the problem of the gating of ion channels and, in particular, the gating of the end-plate channel. He introduces us to the concept ofgating, to the gating currents, and to the many models of gating, variants of the fundamental scheme of a channel that exists in, and switches between, an open and a closed conformation. I n these variants, there can be numerous “open” states and numerous “closed” states of the channels, interconversion between these states being controlled by voltage or by the binding of some effector, perhaps
xiv
PREFACE
calcium or an agonist such as acetylcholine. Horn gives a full introduction to the stochastic representation of the channel gating and to the theory of Markov processes for gating events that are “memoryless.” We are shown how to estimate gating parameters from experimental data, with examples chosen from channels activated by agonists, by calcium, and by voltage. 1 have chosen to place at this point the article by Miller, Bell, and Garcia which, although dealing with a particular channel-the potassium channel isolated from sarcoplasmic reticulum-surveys very many different approaches to analyze this channel. The channel as portrayed by Miller and colleagues is a beautifully simple one. It is gated by a singly charged site so that a 55-mV voltage change can lead to a 10-fold increase in the equilibrium constant for channel opening. The system has a very high potassium conductance, and its ion selectivity is summarized. The system saturates with increasing ion concentration. From a detailed consideration of the selectivity of the channel for different inorganic and organic ions and of the effect of competitive inhibitors of ion movements, Miller and colleagues are able to draw a striking diagram to explain the mode of action of this channel. The channel appears to be composed of two widemouthed funnels, narrowing to a short selectivity filter situated two-thirds of the way into the membrane. This structure gives the needed high conductance (a short filter) but the required selectivity (a n ~ i r r o w pore). The wealth of biophysical information on this channel makes it one of the best understood at present, although its physical structure remains to be established. The authors address themselves also to the question of the physiological role of the channel. In the fourth article, Kolb shows us how one can go about measuring the conductances of single channels and in a valuable table presents a survey of much of the data that have so far been accumulated. Kolb discusses fully the methods of noise analysis and the advantages and disadvantages of this technique as compared with the single-channel recording (patch-clamp) methods which he also presents. Patch-clamp methods will generally be the method of choice since interpretation of the data is direct and model independent, but for many systems of biological interest noise analysis is still the only method available, and Kolb reveals how much valuable information can be derived from a detailed analysis of noise. Many ion channels seem to be narrow, or as Levitt chooses to call them in the fifth article, they are “no-pass” channels. Ions moving through such a channel cannot pass one another. Water molecules, too, often cannot pass one another within such a channel nor can the ion pass the water molecules that lie ahead of it within the channel. Levitt applies a very general theory to ion-ion, ion-water, and water-water interactions
PREFACE
xv
within such a narrow channel. From his analysis one learns how to test whether a channel is narrow and, having shown that it is narrow, how molecular properties of the channel can be gleaned from a considcration of the interactions between water molecules and ions. I n particular, from the number of water molecules that move through the channel with each ion (as determined from the streaming potential-the measured electrical potential set up a s water flows osmotically through the channel), the number of water molecules can be determined that are present in single file along the channel associated with each ion. As t h e gramicidin channel holds two potassium ions but only one sodium ion (at accessible concentrations), nine water molecules are pushed through the channel with each sodium ion but only four or five with each potassium ion. A n important implication of Levitt's analysis is that the detailed process of ion diffusion along the channel is likely to be determined more by the interaction between water molecules and the wall of the channel than by the interaction between ion and the channel wall. This is because to cross the channel the ion must push out a substantial number of water molecules ahead of it, and each water molecule interacts more or less strongly with the channel wall. In Benz's article we come to a consideration of the numerous spccial pore or channel systems exemplifying the range of such systems present in nature. Bacterial cell outer membranes contain porins, oligomeric proteins which associate to form channels permitting the size-dependent control of access of molecules from the environment to the space between the inner and outer cell membranes. The porins form wide, fairly nonselective, channels. Their conductance can be well fitted by theoretical calculations based on values of the bulk conductances of the ions in question and on reasonable values for channel diameters. As the structure of these porins becomes known through biophysical studies, the relating of structure to function for these simple channels is an exciting, realizable goal. Loewenstein, in the seventh article, discusses a channel of utmost importance to us as metazoans, the channel which connects the different cells comprising an organ. This channel, ubiquitous among the metazoans, has been well characterized biophysically and biochemically. These channels are wide (of the order of 20 A) and discriminate only weakly against anions. They form readily between different cells of animals within a phylum, although not across phyletic boundaries. The channels are strictly controlled by cyclic AMP and by calcium ions and are also voltage controlled. Most importantly, these channels have been identified with the gap junctions seen by the electron microscope, whose structure, currently being solved by Fourier synthesis of electron micrographs, is described by Loewenstein. For the cell-to-cell channel, data
xvi
PREFACE
derived from the evolutionary biology, physiology, molecular biology, and biophysics disciplines are being combined in a synthesis of our understanding of channel behavior. Lewis, Hanrahan, and Van Driessche in the eighth article survey the ion channels that are found in epithelia, such as frog skin and gallbladder. In such salt- and water-transporting epithelia a sodium channel exists at the apical or mucosal surface of the cell. While these channels cannot yet be studied by single-channel methods, noise analysis has been heavily applied in their study. The sodium channel is one of moderate conductance. I t is blocked by the drug amiloride and, from the mucosal surface, can be blocked by sodium ions themselves. Aldosterone and the antidiuretic hormone regulate the number of channels present per unit area of cell membrane but not the properties of the individual channels. Potassium channels also exist at both the apical and the basolateral surfaces for these epithelial cells, and here again noise analysis is the method that has been used to study these channels. A number of nonselective channels also exist in these epithelia, but the most interesting channel here is perhaps the water channel, again under the control of hormones which bring about the insertion into the membrane of channel material preexisting within the cell's cytoplasm. Finkelstein, in the ninth article, continues this theme of water movement and poses the question of how much water movement occurs through the ion channels of the various cell membranes. His thesis is that while water may well move through these channels, this movement is not of quantitative significance for the water balance of the cell since, in general, water that flows across the cell membrane by dissolution in, and diffusion across, the lipid bilayer region of the membrane quite overwhelms that which might flow through the ion channels. Finkelstein feels that there is good evidence for a major part of water flow occurring through specific channels for only two systems. One system is the red blood cell; Finkelstein suggests that the anion transporter is the candidate for being the water channel. The second system is found as the hormonecontrolled water channel of mammalian kidney collecting tubule and of toad urinary bladder, referred to above. These channels are very impermeable to ions. In the course of his account of water flows, Finkelstein considers the detailed data now available on water and ion movements in the gramicidin and nystatin channels. His demonstration that the ion conductance of the former exceeds that of the latter by nearly two orders of magnitude, although the gramicidin channel has clearly the smaller radius, is a chastening example of the dangers inherent in attempting to infer channel radii from ion conductances. Lauger's article puts our studies of ion channels within the wider context of membrane transport systems in general. His argument is that if a
xvii
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channel can exist in more than one open or closed conformation and that if the transformation change between conformations is coupled to ion movements within the channel, the channel is formally and in practice equivalent to a carrier. The concepts of a pure channel and of a pure carricr are limiting cases of a continuum. Liiuger marshalls the evidence pointing clearly to the existence of conformation changes in proteins and in membrane channels. The channels “breathe,” and Liiuger’s analysis is applicable to the accumulating evidence that channels can exist in multiple substates. If the conformation change between channel states can be influenced by an external energy source, the system will pump ions and expend energy in the process. Thus Lauger puts into a single framework the often separated worlds of channel carriers and pumps. The last article by Hladky and Haydon is a deep analysis of the behavior of the gramicidin channel. They discuss the structure of this channel which they themselves used to provide the first direct evidence for discrete single-channel events in conductance measurements. The kinetics of ion movements through this channel is fully discussed and put into the perspective of the large amount of information about the structure of the gramicidin channel. This channel is probably the closest to providing a full description of ion movements in terms of the chemical structure of the channel. Were 1 to be asked how to approach this book, I would say, “Treat it like a good dinner. First have the article by Miller r t t i l . as an aperitif. The hors d’oeuvre will be Levitt’s article. Move on to the sumptuous main course of Barry and Gage, Horn, Kolb, Hladky and Haydon, Benz. and Lewis et ul., but leave for dessert Loewenstein’s article. Take Finkelstein’s article as the stimulating coffee. And, finally, as the after-dinner cigar, read Liiuger’s article and, in the heady fumes of a fine Havana, see thc vision of all of membrane transport in a single formalism and dream of another volume in this serial publication for which the Preface will read, ‘We seem to be on the brink of understanding how membrane carriers work.‘ ”
WILFRED D. STEIN R E FER EN C ES Adams. D.J . . Dwyer. T. M . . and Hille. B. (19x0). The permeability of endplate channels to monovalent and divalent metal cations. J . C h i . Plrysiol. 75, 493-5 10. Glasstone. S. ( 1948). “Textbook of Physical Chemistry,” 2nd ed. Macniillan, London. Hamill. 0. P.. and Sakmann, B.(19x1 ). Multiple conductance states of single acetylcholine receptor channels in embryonic muscle cells. N t i / t i w (Lowdotr) 294, 462-464. Huiing, L-Y. M . . Catterall. W. A , , and Ehrenstein, G . (197X). Selectivity of cations and nonelectrolytes for acetylcholine-activ~il~d channels in cultured muscle cells. J . Giw. Physio/. 71, 397-410.
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Yale Membrane Transport Processes Volumes Joseph F. Hoffman (ed.). (1978). “Membrane Transport Processes,” Vol. I . Raven, New York. Daniel C. Tosteson, Yu. A. Ovchinnikov, and Ramon Latorre (eds.). (1978). “Membrane Transport Processes,” Vol. 2. Raven, New York. Charles F. Stevens and Richard W. Tsien (eds.). (1979). “Membrane Transport Processes,” Vol. 3: Ion Permeation through Membrane Channels. Raven. New York. Emile L. Boulpaep (ed.). (1980). “Cellular Mechanisms of Renal Tubular Ion Transport”: Volume 13 of Cirrrrnt Topics in Mc.mhranes tinti Trtinsport (F. Bronner and A. Kleinzeller. eds.). Academic Press, New York. William H. Miller (ed.). (198I). “Molecular Mechanisms of Photoreceptor Transduction”: Volume I5 of Cirrrcnt Topics in Membrrincjs rind Trri11.sport (F. Bronner and A. Kleinzeller, eds.). Academic Press, New York. Clifford L. Slayman (ed.). (1982). “Electrogenic Ion Pumps”: Volume 16 of Current Topics in Membrritws trnti Trrinsport ( A . Kleinzeller and F. Bronner, eds.). Academic Press, New York. Joseph F. Hoffman and Bliss Forbush 111 (eds.). (1983). “Structure, Mechanism, and Function of the Na/K Pump”: Volume 19 of Cirrrent Topics in Menzhrrrnrs tind Trtrnsporr (F. Bronner and A. Kleinzeller. eds.). Academic Press, New York. James B. Wade and Simon A. Lewis (eds.). (1984). “Molecular Approaches to Epithelial Transport”: Volume 20 of Cirrrrnt Topics in Memhrtines tind Transport (A. Kleinzeller and F. Bronner, eds.). Academic Press, New York.
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Ionic Selectivitv of Channels at the End Plafe PETER H . BARRY A N D PETER W . GAGE Nerve-Mirscle Research Centre School of Physiology and Pharinac~olog.y Univer.sity of Neu, Sortth Wriles Kensington. Ne" South Wales. Aicstruliri
1. Introduction.. . . ...................... Principles of Equ 111. Principles of Dynamic Ion Selectivity . . . . . . . . .
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C. Electrodiffusion Approaches. . . . . . . . . . . . . . . . . . . . . . . . . .
............................. G. Open Time of Ion Channels.. . . . . . . . . . . . . . . . ........... H . Diffusion-Limited Access Effects. . . . . . . . . . . . ........... IV. Experimental Techniques .................... ................ A. Null Potentials . . . . . . . . .............................. B . Noise Analysis.. . . . . . . . . . . . . . . . . . . . . . . . ...................... C. Perturbation Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Single-Channel ( E. Summary of Techniques.. . . . . . . . . . . . . . . . . . . . . . . . .......... V. End-Plate Channel Characteristi
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26 27 28 29
32
B . Null Potential Measuremen C. Conductance-Voltage Rela E. Surface Charge Effects. . . ..................................... F. Channel Block ....................... .....................
H. Charge Transfer Effects. VI. Summary and Comparison wit References.. . .
43 44
Channels in Nerve and
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1 19x4 hy Academic Pres?. Inc. Copyright All rights of reproduction in any form reserved. ISBN 0-12-1?33?1-2
2
PETER H. BARRY AND PETER W. GAGE
I. INTRODUCTION
Both natural and artificial channels in biological membranes exhibit in general a range of selectivities for ions far in excess of the selectivities that might be expected from simple solution properties such as free solution mobilities. For example, the ratio of free solution mobilities of sodium and potassium, calculated from limiting equivalent conductivities, is 0.67 at 18°C. In contrast, resting potassium channels in frog muscle are more than 30 times more permeable to potassium than to sodium ions, whereas the sodium channel responsible for the action potential appears to be about 20 times more permeable to sodium than to potassium ions (for details, see reviews by Diamond and Wright, 1969; and Edwards, 1982, and for properties of electrolyte solutions, see Robinson and Stokes, 1965). In contrast to such selectivities, the end-plate channel has appeared to show remarkably little selectivity toward ions, giving the impression of behaving like a simple “hole” through which ions move with their free solution mobilities. That end-plate channels are really much more complicated than this is strongly suggested by the facts that such channels have no significant anion permeability and also have a low divalent ion permeability (see review by Gage, 1976; and Adams et al., 1980). These facts immediately suggest the presence of negative groups, which would be expected to exert selectivity between ions, within the channel. Indeed, in the light of recent evidence, it has been suggested that there is a much greater selectivity toward cations than would be apparent from considerations of only the permeabilities per se, measured, for example, from null (zero-current) potentials. As in the above examples, selectivity is often used with reference to permeabilities and conductances. More fundamentally, however, it can be used with reference to the actual binding of ions to membrane channel sites and to the mobilities of those ions within the channels. It can then give information about those sites and the actual mechanism of permeation. It is suggested that this fundamental selectivity is most successfully unmasked at the end plate by considering the conductance-voltage relationships for membranes separating asymmetrical cation solutions. This article begins by tracing the thermodynamic principles underlying the selectivity for ions when in an equilibrium distribution between membrane channel sites and aqueous solutions. We then explore the principles underlying dynamic ion selectivity that determine the actual permeability characteristics of the channels to different ions in terms of their fundamental equilibrium selectivities, and we consider the role of permeation modeling in helping to elucidate this. This is followed by a discussion of experimental techniques that have been used to measure channel proper-
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
3
ties at the end plate, together with our interpretation of end-plate channel characteristics in the light of the preceding sections. Finally, some of the selectivity properties of some other channels in muscle and nerve are very briefly discussed for comparison with end-plate channels.
II. PRINCIPLES OF EQUILIBRIUM ION SELECTIVITY
The following (see also Barry, 1974) is an overview of the main principles involved in equilibrium ion selectivity. For more general details the reader is referred to an excellent review on the physical basis of general ion selectivity by Diamond and Wright (1969), and for specific details concerning principles the reader should see, for example, Eisenman (1965, 1969), Krasne and Eisenman (1973), and Krasne (1978). Most ion channels combine selectivities toward ions of the same sign with relative impermeability to ions of the opposite sign. From the beginning of this century it was thought that selectivity sequences obtained, for example for alkali halides permeating across biological membranes, merely reflected frictional resistance, which increased in parallel with ionic radius or, in the case of larger membrane pores, with hydrated radius. In other words, it was suggested that selectivity was simply due to “ion sieving.” The appearance of sequences intermediate between those of increasing ionic and increasing hydrated radius, together with other evidence, resulted in such theories being discarded by physical chemists, in the case of nonbiological systems, before 1930. The high cation/anion selectivity ratio found in most biological membranes, and the pH dependence of this ratio, suggested that cation permeation through ionic channels is controlled by interactions of ions with negatively charged membrane groups. In addition it was found that for the five alkali cations ( L i t , Nat, K + , Rb’, and Cs’) only about I I (plus a few variants) out of a possible 120 ( S ! ) selectivity sequences were observed in nature and that these same sequences were obtained in both nonbiological and biological systems. It was mainly Eisenman, following work with Rudin and Casby, who was responsible both for stressing the role of charged groups within biological membranes and for developing the theoretical framework that could be used to describe and explain such selectivity in biological systems (and in glass electrodes), and to predict these same I I sequences. In order to understand the basic principles, it is helpful to consider the following oversimplified situation in which a hydrated ion in its aqueous environment moves into an ion channel, discards its hydration shell completely. and interacts with an ion site, considered initially by Eisenman
4
PETER H. BARRY AND PETER W. GAGE
for simplicity to be a simple monopole. The partition coefficient for the ion Ki,a measure of the relative concentration of the ion i in the channel with respect to its aqueous concentration, is then dependent on the transfer free energy AF;. This has two components, the hydration energy of the ion A F L and the ion-site interaction energy A F ( , so that
AF;
=
AF;
-
AF:
(1)
and the partition coefficient K i is given by
Ki= exp(-AF[lRT)
(2)
where R and T are the gas constant and temperature in degrees Kelvin, respectively. The basic principles are outlined in Fig. 1. The hydration energy can be estimated to a first order by simply considering the electrostatic energy involved, given the number of water molecules in the
F I G . I . A schematic diagram similar in principle to Barry (1974. Fig. I ) illustrating that the transfer free energy AF, necessary to move a cation (e.g., K') from an aqueous environment to a membrane channel alongside a polar site is made up of two components: the interaction energy AF, with a polar site here drawn to the same dimensions as a model carbonyl group, and the hydration energy AF,, defined with reference to vacuum. The dimensions of the model carbonyl and water molecule relative to K+ were taken from Krasne and Eisenman (1973, Fig. 47).
5
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
primary and subsequent hydration shells. Surprisingly good estimates of relative hydration energy were indeed made by Eisenman on this basis, allowing for an average of 4.8 water molecules for each of the 5 alkali cations. However. hydration energy can be obtained directly and more accurately from available thermochemical data (e.g., Table I). Initially, Eisenman calculated the ion-site interaction energy for ions interacting with a monopolar site using the simple coulombic electrostatic energy equation, expressed now in kilojoules per mole by
AF,
= -138.9
nrn kJ mol ' / ( r -
+ r+)
(3)
where r + and r - represent the radius of the cation and monopolar site in nanometers. The relative partition coefficient or equilibrium constant K,J for two cations i a n d j in the aqueous solution competing for such membrane sites is then given by
K,, = K J K , = exp(-AFy/RT)
(4)
TABLE 1 SOMF PHYSlC'Al PROPFRTIE 5
Ch lonic radius" lonic radius" Hydrated radius' Relative hydration energies" Relative hydration energies' Relative mobilities'
+
0.169 0.181 0.232
o 0
I.05l
K'
Rb' 0.14X 0.166
0.224 -28 -+ 5
-
34
1.059
0 1 THF
~
0.133 0.152 0.218 53 -+ 4
A1 KALl C A T I O N S
Na'
0.05 0.116 0.208 -121 -+ 4
Li
+
0.060 0.090 0.218 -225 -+ 6
n ni n ni nm kJ niol
'
kJ mol
I
- 54
- I42
-251
I ,000
0.682
0.526
" Data are from Pauling (in Diamond and Wright.
Units
-
1969).
Data are from Noyes (in Edwards, 19x2). Ddta from Goldman and Bates: radius of ion and its primary hydration shell (in Edwards, 1982). Data are from Latimer (in Edwards, 1982). Data are from Shannon (in Edwards, 19x2). 1 Based on limiting equivalent conduclances in water at 25°C and summarized by Robinson and Stokes (1965). I'
I'
6
PETER H. BARRY AND PETER W. GAGE
By simply considering the relative transfer free energy difference AFf for ions each interacting with one water molecule and one monopolar site and by allowing for the possibility that different selectivity sequences could arise by virtue of various membranes or channels having different sites with different effective site radii, Eisenman calculated transfer free energies as a function of site strength. This analysis produced 1 1 sequences which were the same as those normally observed. These can be seen in Table 11. This range of selectivities arises because the field due to a tripolar water molecule has a different dependence on radial distance than that due to a monopole (or a dipole). Sequence XI, referred to as a high field strength sequence (corresponding to a site with a small effective radius), is one in which the smallest cation is the most preferred by the site, relative to the water. Sequence 1, referred to as a low field strength site, is one in which selectivity is dominated by hydration energies in which the largest ion (with the smallest hydration energy) is the one most preferred by the site. Although Eisenman's basic model of site and water interactions was very simple, the same 11 sequences are predicted when thermochemical data are used for hydration energies, when hydration of the membrane phase is increased, when multipolar groups are considered rather than TABLE 11 OBSERVED SELECTIVITY SEQUENCES FOR Simple Eisenman sequence
THE ALKALI CATIONS"
Variant sequences Weak field strength site
I
11 111
Rb' > Cs+ > K + > Na' > Li' Rb+ > K + > Cs+ > N a + > Li'
IV V
K' > Rb' > Cs' > Na+ > Lit K + > Rb' > Na' > Cs+ > Lit K + > Na+ > Rb' > Cs' > Li' Na' > Kt > Rb' 1 Cs' > Lit Na+ > K+ > Rb+ > Lit > Cs+ Na' > K + > Lit > Rb+ > Cs' Na+ > Li+ > K + > Rb' > Cs' Li+ > Na+ > K + > Rb+ > Cs+
v1 VII VlII
1x
X XI
Data taken from Krasne (1978).
Ila IIla IVa 1Vp Va VIa
XIa
Cs' > K' > Rb+ 4 Na+ > Li' Rb+ > K' > Na+ > Cs+ > Li' K + > Cs+ > Rb+ > Na+ > Li+ Cs' > Li+ > Rb+ > K' > Na' K' > Rb+ > Cs+ > Lit > N a + K + > Rb+ > Na' > Li+ > Cs'
Na+ > Rb+ 1 K+ > Cs+ > ( L i t ? ) Strong field strength site
7
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
simple monopoles, and when close-site spacing and entropy effects are included, although there are quantitative changes in the magnitude of the selectivity. Differences in field strength can arise from variations in ( 1 ) the distance between ion and ligand groups involved in the site, (2) the number of ligands contributing to a particular site, and (3) any conformational energy involved with an ion-site interaction. However, provided that the ion-site energy falls off with radial distance less steeply than the hydration energy, the above 1 1 sequences are predicted. Not only are these sequences (with a few minor variants) observed for ion-exchange glasses, soils, and antibiotic carriers and channels, but they are also observed for biological membranes. Further complicating influences that would be expected to result in deviations from the above I 1 sequences and that produce some of the variant sequences observed (Table 11) are factors such as polarizability of the sites, which tends to increase the steepness with which the electric field drops off with distance, and conformational changes that occur as a result of the ion being sequestered by the sites. For example, some macrocyclic ionophores such as monactin undergo a considerable amount of conformational change during the sequestration of a cation, whereas others like the cyclic polyether XXXl are quite rigid. This component of conformational energy may be responsible for the very high selectivities obtained with some antibiotics (e.g., valinomycin, PKIPNa 300). The influence of such forces on the selectivity of biological channels is obviously difficult to quantitate but should never be ignored, especially since many channels, including those at the end plate, exist in both open and closed states and the transition from one state to the other may well involve significant conformational energy. Urry ( 1979) implies that the flexibility of gramicidin A channels contributes to the conformational energy component involved in cation permeation, by his suggestion that the channel decreases in diameter so as to increase the interaction energy of the sites with the ion. As already mentioned, there has been in the past a tendency to think of ion permeation merely in terms of ion sieving, and this tendency still persists to some extent. However, even if an ion can enter a channel with part of its hydration shell, the correct thermodynamic way to consider equilibrium selectivities must be in terms of transfer free energies with appropriate contributions from all of the above sources. Of course, simple steric geometry factors must be important when the ion size approaches that of the channel and such reasoning has been used with advantage to determine pore size. By considering a range of different organic cations and by measuring which cations are permeant and which are not, it has been possible to deduce minimum (and probably also maxi-
-
8
PETER H. BARRY AND PETER W. GAGE
TABLE Ill PREDICTED A N D O B S E R V E D SELECTIVITY SEQUENCES
FOR T H E H A L I D E
1
II Ill IV V VI VII
I > Br > CI > F B r > I > C I > F Br > CI > I > F C I > B r > I > F CI > B r > F > I C I > F > B r > I F > CI > Br > I
ANIONS“
Weak field strength site
Strong field strength site
Data taken from Diamond and Wright (1969).
mum) dimensions of end-plate7sodium, and potassium channels. Further details are given in Sections V and VI. Although it might be expected that a particular site could be characterized completely by determining its alkali cation selectivity pattern, it has been found experimentally that different systems (e.g. gallbladder and valinomycin; see Krasne, 1978, for further details) yield the same sequence but have selectivity magnitudes that vary by large factors (in the above example by more than lo5).This suggests that the sites and mechanisms of permeation may be quite different. An alternative approach which can be used to characterize the sites responsible for permeation is to use nonalkali cations such as Tl+ and NHiwhich are more polarizable, and also to use larger organic anions. It has been suggested that T1+ and NHican be used to “fingerprint” the site and that a comparison of TI+ and NHd selectivities, in addition to alkali cation selectivities, can distinguish whether or not two transport systems do indeed involve the same ion-sequestering sites. Examples of this approach are given by Krasne (1978). Not only can the Eisenman approach be applied to the alkali cations but it has also been very successfully applied to anions such as the four halide anions (F-, Br-, C1-, and I-), the channel site being positively charged. Of a possible 24 permuted sequences, only 7 are predicted. Diamond and Wright (1969), in their survey of the literature, found 17 examples of anion sequences and, in every case, the observed sequence was one of those predicted. Tade 111 gives the seven predicted sequences. Sequence I again represents a site of weak field strength in which the transfer free energies are dominated by the hydration energies, and sequence VII, in which the smallest ion is that most selected by the ion-site interaction energies, represents a site of strong field strength. The agreement of the
9
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
OBSERVFD
TAHl E IV SFI FC71VITY S F Q U r N C F \ A1 5 0 P R f
DICTFD
BY SHFRRY FOR THF A l K A I I N I k A R T H 1 0 N S "
"
Data taken from Diamond and Wright (1969).
observed sequences with composite selectivity isotherms in the examples reviewed by Diamond and Wright suggested to them that a knowledge of the relative magnitude of the selectivity of any two of the ions in a particular system is adequate to characterize the complete sequence for all four of the ions. The selectivity patterns for divalent ions such as the alkaline earth ions has also been explained using a similar approach (for a review, see Diamond and Wright, 1969). The only additional factor to be included is the spacing between sites (normally considered to be monovalent), as the divalent ion interacts with two sites at a time. Widely spaced sites tend to select monovalent over divalent ions. and closely spaced sites are more selective for divalent than for monovalent ions. Again, out of 24 possible sequences for the alkaline earths MgZt, Ca?+,Sr2+,and Ba?', Diamond and Wright noted that only 7 had been observed, and these were the same as those predicted by Sherry using Goldschmidt radii for the ions and allowing for hydration entropies. These sequences are given in Table IV. 111.
PRINCIPLES OF DYNAMIC ION SELECTIVITY
A. Channels versus Carriers
The principles derived in Section I1 assume an equilibrium distribution between aqueous phase and site concentrations. Most measurements of ion movements across membranes result in nonequilibrium parameters being obtained and these may not necessarily fit any of the predicted equilibrium sequences. The relationship of these measurements to equilibrium parameters is investigated in this section.
10
PETER H. BARRY AND PETER W. GAGE
In order to explore this relationship, one question that must immediately be asked is whether ions normally cross membranes through channels or whether they are incorporated into some mobile carrier, as occurs with some of the antibiotics such as valinomycin or the actins. It is difficult to imagine how the rectangularly gated currents (e.g., Fig. 7) observed with depolarization-activated sodium and potassium channels and transmitter-activated end-plate channels could be generated by mobile carriers, although the unlikely possibility that some membrane boundary mechanism could control access of ions to the carriers cannot be ruled out. However, strong support for a channel mechanism comes from the very high conductances reported for these three channels, from 4 pS (4 x lo-’* siemens or mhos) to about 32 pS (for a review, see Urry, 1979). These conductances are too high to be explained by carrier transport. Even the low value of 4 pS results in a current of 4 x A, for a driving force of 100 mV, which is equivalent to 4 X lo-” x 6.02 x 1023/96,500= 2.5 x IOh ions sec-I. This is significantly higher than the maximum turnover rate or limiting transport rate of 3 x lo4 ions sec-’ obtained so far for the highly efficient carrier valinomycin (Edwards, 1982). The I-V curves for carrier transport should be sigmoidal even in symmetrical salt solutions: the currents ( I ) are expected to saturate when the applied voltage ( V ) is increased as the maximum turnover rate is reached. In contrast, I-V curves for end-plate channels in symmetrical solutions are linear. An additional observation in favor of channels rather than carriers is the existence of electrokinetic coupling, which occurs in channels but not with carriers. This has been demonstrated for resting potassium channels in giant algal cells and in the squid axon, and has been inferred for active channels in the algal cells (Barry and Diamond, 1984). 6. Ion Channel Conductance
As already mentioned, the ionic selectivity patterns discussed in Section I1 are strictly valid only for equilibrium constants. Can one therefore determine selectivity from conductance or permeability measurements? In order to answer this question, it is necessary to investigate the principles underlying the interpretation of such measurements. Modeling of ion transport through channels, using either electrodiffusional or rate theory, is therefore considered. In order to solve the electrodiffusional flux equations an assumption needs to be made about either the potential profile or the ionic concentrations. The simplest, somewhat arbitrary, assumption that the electrical potential gradient (electrical field) is constant was made by Goldman
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
11
(1943), and was used by Hodgkin and Katz (1949) in their derivation of the equation in its familiar form. For three cations (subscripts I , 2, and 4; generally K + and Na+ inside, and K’ and test cation outside) and an anion (subscript 3 denotes anions), this Goldman-Hodgkin-Katz equation or constant field equation, giving the potential E,, at zero current, is given by
where prime and double prime refer to the outside and inside of a cell, respectively, 3 is Faraday’s constant, and P, is the permeability of ion i relative to ion j . is sometimes referred to as a “null potential” because it is the potential at which the current is zero, or as a “reversal potential” because the current is in opposite directions at potentials on either side of c0. Inherent in the derivation of the above equation is the additional assumption that the ion fluxes are independent. It is therefore totally inappropriate for a situation in which different ions traverse a common channel and compete for sites within it. Nevertheless, in spite of the above very limiting assumptions this equation has enjoyed widespread use. Part of the reason for its success in fitting biological data derives, no doubt, from the fact that under some conditions a number of other models and approaches (with very different assumptions) give rise to an equation identical in form. This is true when only cations are permeant, or when permeant anions are in equilibrium and therefore do not contribute to the membrane potential. In such cases thc null potential equation is given by
formally identical to the Goldman-Hodgkin-Katz equation [ Eq. (6)] in the absence of anions. It is very important to stress that the fitting of experimental data to such an equation [Eq. (7)] in no way necessarily implies the assumption either of a constant field or of flux independence. Nor, since different models imply very different conductance-voltage equations, does it provide any justification whatsoever for using the Goldman-Hodgkin-Katz conductance-voltage equations for determining channel conductance. Unfortunately, Eq.(7) is usually referred to as the Goldman-Hodgkin-Katz equation, and in order to stress the far more general nature of Eq. (7) and to dissociate it from the restrictive and inappropriate assumptions inherent in the Goldman-Hodgkin-Katz equation, we henceforth refer to Eq. (7) as the Generalized Null Potential equation.
12
PETER H. BARRY AND PETER W. GAGE
In the next sections, in order to derive current or conductance expressions for different ions traversing a common channel, either electrodiffusion or rate theory models appropriate for ions competing for sites within the channels are used.
C. Electrodiffusion Approaches
Two particular electrodiffusional models have been suggested for endplate channels (Barry et uf., 1979a,b). Both were originally derived with the underlying assumption that the channels are long in comparison with the Debye length within the channel. This meant that at each point, or more strictly over a reasonable fraction of the channel length, macroscopic electroneutrality is assumed, so that the concentration of cations would be approximately equal to the concentration of negative sites for the “Charged Site” model, or equal to the concentration of mobile anions within the channel for the “Neutral Site” model. Both models are based on the assumption that the mobile cations compete for negative sites within the channel so that the independence principle (an assumption implicit in the Goldman-Hodgkin-Katz equation) is violated. The main difference between the two electrodiffusion models is that in the Charged Site model the charged negative sites must be balanced by mobile cations, whereas in the Neutral Site model the negative polar sites do not huve to be balanced by cations, but are expected to provide electronegative sites with which the cations could interact. In the latter case, electroneutrality is maintained by anions also being able to enter the channel, though a rate-limiting resistance barrier for anions is assumed, in order to significantly reduce their contribution to the total ionic current. In both models the null potential E ( ) , where net ionic current is zero, is given by the same expression (Barry cf al., 1979a). The ideal case assumes no cooperativity effects so that the nonideality cooperativity factor n (which relates activity a to concentration C,by n = yC“, with activity coefficient y) equals I .O. For this case, E ~is) given by the Generalized Null Potential equation [Eq. (7)], which we have already noted is an expression of the same form as that of the Goldman-Hodgkin-Katz equation. However, in contrast to the latter equation, the relative permeabilities in Eq. (7) are now composed of two terms-a relative mobility term 11 and an equilibrium constant (relative partition coefficient) term K , so that P,, is given by
13
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
It can be seen that because the permeability is also dependent on mobility, permeability sequences need not necessarily be the same as equilibrium constant sequences. It is interesting to note that in glass electrodes, although the equilibrium constant term dominates the relative permeability, the mobility ratio is inverted. For example, for one potassium-selective glass, K K / K N=~ 34 but U K / I I N ~= 0.3, and is in the opposite direction to the ratio in free solution (uK/uN<, = 1.5; see Table I). Physically this is reasonable and means that the more tightly bound ion, K + , has the lower mobility. Nevertheless, for that glass, f K / f N a = 10 and is in the same direction as K K I K N ~We . shall see later that there appears to be an even stronger reciprocity relationship between mobility and equilibrium constants in end-plate channels. The expression for the current I in both models is much more complicated than, and is quite different from, the Goldman-Hodgkin-Katz equation. It is a rather complicated function of the potential E. In both electrodiffusion models, the form of the current equation is very 4milar and can be expressed as (cf. Barry ~t d . , 1979a,b)
I
1
B[([U" - U ' ) / ( < C- C')] ( E E E*
-
E*)
= exp(SdHT)
(10)
(I I)
( K T I 9 ) In(C'IC")
+ Kl,rii + Kjltl; C" di + K l l t i ! + K41NI; U' i / t ( i i + UZK:,US+ 144K41N; U" I I I N ; + //~KZIN? + i/4K4,4 C'
(9)
(1;
(12) (13)
i14) (15)
where, for the Charged Site model, B is a constant independent of potential and only dependent on t h e fixed-charged site concentration T o . In such a case B is given by B = (:F'C,,/d)A,
(16)
where d represents the channel length and A , the effective cross-sectional area of the channel. For the Neutral Site model, B is given by a very different expression, though it too is independent of potential: B
=
(S2/(n( K,/y)A, [ici;/O')
-
(~ir;/H")]/ln(c~;B'/ti;8")
i17)
where u3 represents the activity of the anions and 0' and 8" are given by 0' = [ K , a ; / ( ( i ;+ Kzlrli
+
KqIr~i)]~"
(18)
14
PETER H. BARRY AND PETER W. GAGE
and
+
6’’ = [ K 3 a f ( / ( ~ ; ’K ~ ~ u+Z K41ai)]”2
(19)
In the Neutral Site model, an additional term &(E - q)may be added to the right-hand side of Eq. (9) if the effective anion mobility u3 is significant, where E~ is given by e3 =
- ( R T / 4 ) ln(a;/af()
(20)
Two very interesting conclusions can readily be derived from these equations. First, since B is independent of potential in both models, they must each exhibit exactly the same conductance-voltage relationship. Second, both models predict very different conductance-concentration relationships. An inspection of Eqs. (9)-(20) as they stand indicates that, in symmetrical solutions, the current-voltage curves would be linear and hence the conductance would be constant. However, if we consider asymmetrical salt solutions we find that the curves may, in contrast, be very nonlinear. For example, consider an idealized biionic situation with two solutions containing univalent ions, each with concentrations of 100 mM and each having the same anion. Consider also that the external cation ( I ) has an equilibrium constant 10 times the value of the internal cation but a mobility one-tenth of that of the internal cation (i.e., K12 = K I / K z= 10.0; u12 = uI/u2= 0.1) so that Plz = P I / P z= 1.0 and the zero-current null potential would be zero (8” = 0). These values, in fact, are not too different from the Li+/K+experimental values to be discussed in Section V for end-plate channels. For such a case, the conductance-voltage curve fur both models would be as indicated in Fig. 2, the relative conductance values being normalized to give a value of 1.O as V , + --co. The explanation for such a curve is simply that at positive potentials the channel sites would tend to be occupied by the internal cations (2) with their higher mobility, whereas at negative potentials they would be occupied by the external cations (1) with their lower mobility. The ratio of conductances at the two extreme potentials is independent of the equilibrium constant and is given by the ratio of the two mobilities alone, i.e., G ( Vm+-m)/G(
Vm++m) =
UI/UZ
(21)
However, the precise shape of the curve would be dependent on both the relative mobilities and equilibrium constants. It is of interest to note that the steepest, most voltage-sensitive part of the curve encompasses the range from - 120 to +50 mV, a range that is generally explored experimentally. In this example, the null potential of zero, which results from P l / P , =
15
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
1
1.0 +I
4 -00
I
- 1000
I
-500
0.0
0 Vm (mvl
I
500
I
1000
+
00
FIG.2 . The predicted conductance (GI a s a function of membrane potential ( V d of a single channel separating two univalent electrolytes at equal concentrations (cation 1 outside and cation 2 inside the cell). The two solutions share a common anion but have different cations. These values have been calculated using equations derived for the Neutral Site model, which gives the same conductance-voltage curve as the Charged Site model. This curve was calculated for two hypothetical cations with equilibrium constant K I 2= K I / K ?= 10.0 and mobility ratio r r l / r c z = 0. I , so that the permeability ratio P I / P 2= 1.0 and the null potential E , ) = 0. Such values are not too different from those used to fit Li'/K+ data in endplate channels (see Fig. 9B). The conductmce is shown relative lo its value at V,,, = -=, when only the outside cation ( I )would he expected to contribute to the conductance. This relative conductance of 1.0 would also be the value ohtained if the inside cation (7) were to be replaced by cation 1. The curve illustrates the principles underlying the voltage sensitivity of conductance predicted by both the Neutral and Charged Site models. The schematic insets depict the relative occupancy of each cation at the two extreme potentials. At extreme negative (hyperpolarizing) potentials, the channel is occupied only by the external cation ( 1 ) with the lower mobility, and the channel conductance is due only to this ion. At extreme positive (depolarizing) potentials, the channel is occupied only by the internal cation ( 2 ) with the higher mobility, and the relative conductance is now set only by the ratio of the two es (trz/uI= 10.0). The precise shape of the rest of the curve is also determined by KLI in addition to u2/u1and V,. It is interesting to note that the range over which most singlechannel measurements are made (arrows, -120 to +50 mV) at the end plate falls in the steepest portion of the curve.
I .O, gives the impression of a completely nonselective channel. However, the true selectivity can be unmasked using conductance-voltage data and the value of PIIP2obtained from the null potential. Up to this point, the predictions of both models have been the same. An inspection of the equations soon reveals that some divergence would be expected if absolute conductances, or if relative conductances in different cation solutions, were compared. However, the most striking divergence
16
PETER H. BARRY AND PETER W. GAGE
in predictions is the dependence of conductance on external cation concentration. In such a situation, Eq. (16) together with Eqs. (9)-(15) indicate that the conductance would be independent of external cation concentration in the case of the Charged Site model. In sharp contrast, the Neutral Site model predicts that the conductance would vary with external salt concentration. This may be most clearly seen for a symmetrical situation with the same single electrolyte containing univalent ions on each side of the channel (i.e., a ; = a; = a; = a; = a = C ) . In such a case it may readily be shown from Eqs. (17)-(19) that B simplifies to B
=
(9*/d)(KlKj)'''C
(22)
so that B is now directly proportional to the aqueous solution salt concentration C. As it stands, Eq. (22) implies that B , and hence the conductance, would continue to increase with external salt concentration. With a finite number of neutral sites, however, this cannot be. This apparent prediction results because the Neutral Site model of Barry et al. (1979a) was based on the assumption that the salt concentrations were well below site-saturation levels. Such site-saturation effects can be readily incorporated into the Neutral Site model, though they further complicate the equations. Such modifications have been made and some of the predictions presented (Figs. 3 and 4 of Barry et al., 1979b). As expected, when external salt concentration was increased, channel conductance showed saturation as cation concentration in the channel approached site concentration. In addition, as these saturating concentrations were approached, there was a reduction in the magnitude of the predicted voltage sensitivity of conductance in asymmetrical salt solutions. As discussed in more detail in Section V, experimental measurements at the end plate have indicated that single-channel conductance does increase with increasing external salt concentration. The conductance-concentration curve also shows saturation effects at high salt concentrations. These results are consistent with the Neutral Site model, but not with the Charged Site model as it stands. One further test of the two models would be to use in the solution a suitable, preferably impermeant, anion. The Neutral Site model predicts a decrease in channel conductance, whereas the Charged Site model predicts no effect on conductance. There is no experimental evidence for significant anion modulation of conductance, but the question remains to be resolved. In comparing the predictions of these two models, it should be remembered that their fundamental assumption is that electroneutrality applies within the channel. If it is not true that the Debye length is very much less than the channel length (bearing in mind that the Debye length is about 1 nm in a 100 mM aqueous salt solution and about 0.2 nm in membrane
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
17
lipid), then the differences in the conductance-concentration predictions between the two models would tend to disappear. In such a case, the Charged Site model would also be expected to allow conductance to vary with external salt concentration. I n addition, the fact that the other predictions of the two models are identical strongly suggests that the Charged Site model would continue to exhibit the same null potential and voltage sensitivity of conductance in the absence of the electroneutrality assumption. Under these conditions the Charged Site model would behave like the Neutral Site model (with the electroneutrality conditions being obeyed) and its predictions would all be compatible with experimental results at the end plate. The advantage of these electrodiffusional approaches has been the relative simplicity of their predictions in contrast to many of the rate theory models. It has been suggested that electrodiffusional approaches are inadequate for such microscopic channels (e.g., Horn and Stevens, 1980). However, it should be made clear that identical equations can be derived, and the same predictions made, using rate theory approaches, provided that the number of sites is large enough. The difference now is that the mobility 11, is replaced by the rate constant k, for ion i hopping between energy sites. K , again represents an equilibrium constant for the sites with respect to aqueous solution, so that the relative permeability PI, is now given by
Thus the question becomes not whether electrodiffusion or rate theory is more appropriate, but rather how many sites there are in the channel.
D. Rate Theory Approaches Currently, rate theory is widely used for modeling permeation through membrane channels. In part, this arises from the relative simplicity of the approach when dealing with models containing only one or two cationselective sites, although the equations rapidly become more complicated as soon as the number of sites is increased above one and multiple occupancy of the sites is allowed. Evidence is beginning to accumulate that these conditions pertain in at least some channels (eg., K t and gramicidin A channels). It has also recently been suggested (Levitt, 1982) that, in many cases, a continuum Nernst-Planck approach may be more valid for a discrete number of sites. Furthermore, we now show that even for a small number of sites the rate theory model predictions approach those of the electrodiffusional models and in fact are completely equivalent for a large number of sites (multisite model).
18
PETER
H. BARRY AND PETER W. GAGE
In contrast to the electrodiffusion models already discussed, for which it can be shown that the potential profile within the membrane channel is both nonlinear and set by the solution concentrations adjacent to the membrane, most rate theory models assume either a linear potential profile or at least a constant, fixed fraction of the electric field at each energy well. One of the practical problems arising from rate theory modeling is the large number of parameters that are often generated. If, however, it is assumed that the energy profiles are symmetrical, the number of parameters can be halved. In the following analyses we make this assumption and in Section V,C we give experimental justification for it for end-plate channels. In addition, for simplicity, where there is more than one site, it can reasonably be assumed that the sites are uniform. This further radically reduces the number of parameters. A typical, simple rate theory model would be one in which two cations are competing for a two-barrier, single-site channel. Such a model has been analyzed for example by Lauger (19731, Hille (1975a), and Begenisich and Cahalan (1979). These analyses took into account the possibility of site saturation, and Lewis and Stevens (1979) also used an extended version of such a model (incorporating divalent ion permeation) to model ion permeation through end-plate channels. One basic assumption considered was that the binding site must be empty before an ion can enter the channel and bind. In addition, it is obvious that in the steady state, the rate of ion binding to the site must equal the rate of unbinding and also that the sum of the probability that the site is unoccupied and the probability that the site is binding either of the two cations must be unity. Figure 3 depicts the potential- and concentration-independent component of the energy profile for such a model, assuming symmetrical channel energy barriers (a special case of the constant offset energy condition) and a potential gradient across the membrane. Under these symmetrical conditions, the current I for two cations B and C is given by
where potrepresenting the probability that the site is unoccupied, is given by
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
19
FIG.3. Energy and potential profiles for a symmetrical one-site, two-barrier ion channel. The top profile represents the potenlial- and concentration-independent component of the free energy profile FRfor cation B permeating through the channel. The k s represent the potential-independent component o f the rate constants for transitions between the external solution ( 0 ) . the site ( I ) , and the internal solution (2). The lower profile represents the electrical potential E along the channel with fi representing the fraction of the membrane potential E,,, experienced by the cation at the d e . ( I t should be noted that 6 i s not necessarily equal to the fractional distance ofthe site along the channel.) The AHs i n the figure are related to the kRs and the KIIh in the text hy K u A::,/k!, = k?H,/kf!and Alj = kli, = k:?.
and where 6 represents the fraction of the membrane potential E, across the channel which is experienced by the ion at the site. 1 1' and [ 1" respectively represent the concentrations in the adjacent solutions (0 and 2 in Fig. 3). The null potential e0 is then given by E()
=
(f?T/%) In[(P,[B]'
+ Pc[Cl')/(PBIB]"+ PC[CJ")]
(26)
which again is in the form of the Generalized Null Potential equation and, for the null potential only, has the same form as the Goldman-HodgkinKatz equation with the permeability terms P B and PC defined by P* = kBKB
(27)
Pc
(28)
=
kcKc
with relative permeabilities in the form of Eq. ( 2 3 ) . Conductance-voltage curves are shown in Fig. 4 for two cases. Figure 4A shows predictions for symmetrical solutions, with equal concentrations of the same cation on both sides of the membrane, and Fig. 4B
A 4
4
I I I
c+
C' YA
3
----- 1 SITE,
----- 1 SITE, 2 BARRIERS
2 BARRIERS
3 SITES. 4 BARRERS
3 SITES, 4 BARRERS
-MANY SITES, BARRIERS
-MANY SITES, BARRERS -ELECTRODIFFUSiON
-ELECTRODIFFUSION
.
-200
i i
/.
-100
0
Vm (mv)
I
I
I
100
200
-200
1
-100
C 0
Vm (mV)
100
200
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
21
shows predictions for asymmetrical biionic solutions with equal concentrations of cation B in solution’ and cation C in solution”. In both graphs, three different curves are shown. These represent three rate theory models: ( I ) the single-site, two-barrier model just considered, (2) a three-site, four-barrier model, and (3) a multisite rate theory model with many sites and barriers. The first two models assume single-ion occupancy of the channel. The third model, which assumes multiple occupancy, gives predictions identical to those of the electrodiffusion model. Figure 4A is equivalent to the B’ : C” solution case if K B / K c = k s / k c = 1 , For Fig. 4B, values of K B / & = 10. k d k c = 0.1, and hence PB/Pc = 1 were used, equivalent to the electrodiffusion values chosen for Fig. 2. It can be seen that assuming a small number of sites with single-ion occupancy in the channel results in a somewhat parabolic curve of conductance versus potential. However, increasing the number of sites to three and energy barriers to four, but still allowing only single-ion occupancy of the channel. has the effect of reducing this parabolic shape and bringing the two curves closer to those of the multisite rate theory and electrodiffusion models. Presumably, allowing for multiple occupancy of the channel, as assumed by the third model, would bring the other curves even closer to the predictions of the multisite model. We next show that the multisite rate theory and electrodiffusion models give identical predictions. For the purpose of showing equivalence be-
FIG.4. A comparison of rate theory predictions of conductance as a function of voltage for a cation-permeable channel. The figure shows the effect on these predictions of increasing the number of sites in the channel. In the rate theory models with one and three sites and single-ion occupancy, the fraction of potential is equally distributed between sites (i.e., for the one-site model, 6 = 0.5). The predictions of the multisite rate theory model with many sites and barriers are identical to those of the two electrodiffusion models. In each case, the potential V,, (equivalent to E , in the equations in the text) of side” is considered with respect to side’ and the conductance is predicted relative to its value at 0 mV. (A) shows the predictions for a channel separating symmetrical solutions with equal concentrations of cation C on each side of the membrane. This is also equivalent to the situation in which the two solutions contain different ions B and C, but where K s / K c = kB/kc = I . Note that even when the number of sites increases to only three, the curve begins to flatten out (especially in the range between - 150 and +SO mV), approaching the values predicted b y the multisite rate theory model (which is the same as both of the electrodiffusion models discussed in the text). (B) shows the predictions for a channel separating asymmetrical biionic solutions with equal concentrations of cation B in solution’ and cation C in solution”. Values of K l , / K c = 10 and k s / k c = 0. I ( P , / P , = I ) were used for all curves. Note that all curves show the same broad asymmetry, but that. again, as the number of sites increases to three. the curve approaches the values predicted by the multisite rate theory model and the electrodiffusion models. especially in the range from -150 to +50 m V .
22
PETER H. BARRY AND PETER W. GAGE
tween the approaches in such a situation in which there are a large number of sites, we adopt the conditions of the Neutral Site model.’ Figure 5 shows the potential-independent component of the free energy profile for such a channel with n uniform ion-selective sites, together with an accompanying electrical potential profile. Equations identical in form to Eqs. (7)-(15) and (17)-(20) can be derived except that now, for ion i , a rate constant k, replaces the mobility term u,. k, represents the rate constant for “hopping over” the internal barriers and is equal to exp(-AFi,l RT), where AF; represents the potential-independent component of the free energy (or activation energy) between each well and the adjacent barrier (Fig. 5 ) . K , , the equilibrium constant, is related only to the difference in free energy AF;, of the wells above that of the bulk solution (labeled 0 or n + I in Fig. 5 ) by K,
=
exp(-AFt,/RT)
(29)
AFb, equivalent to the transfer free energy (Section 11 and Fig. I ) , is expected to vary considerably between the different cations and is the primary cause of the selectivity of the channel. Furthermore it may be seen that the “hopping” rate constant A, is also related to AF:, by k, =
e-AF:,IRT
= p-F,,/RT e A F $ R l
= e-F,,IRT/~I
(30)
This means that k j is inversely related to the equilibrium constant K i , as discussed in Section III,C, and as noted for ion-selective glasses and for ion permeation through end-plate channels. This also implies that the permeability Pigiven by
Pi= kiKi = exp(-F,/RT) is dependent only on the height F, of the barriers. In contrast to the situation for A F ; and AF;,, it would not seem to be too unreasonable were the barrier heights (Foand all F,s) to remain the same for the different monovalent cations. Thus exp(-FJRT) would tend to be independent of cation species, and the relative permeability of the different cations would tend to be close to 1.0, which indeed it is in end-plate channels. I Without loss of generality we could equally have shown the equivalence of the two approaches by considering the charged site model or any other similar model with or without the electroneutrality condition.
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
23
FIG.5 . Energy and potential profiles for the multisite rate theory model of a channel with a large number n of symmetrical sites. The top profile represents the potential- and concentration-independent component of the free energy F. The ks represent the rate constants for transitions between sites and between sites and bulk solutions. The lower profile represents the electrical potential E along the channel that is set by ion concentration profiles. Asdand As: represent boundary potentials at either end of the channel.
E. Voltage Sensitivity of Single-Channel Conductance As we have seen in the two previous sections (111,Cand 111,D).measurements of null potential with the Generalized Null Potential equation yield values of relative permeabilities ( P ) only. Unless the variations in the equilibrium constants ( K ) are much greater than those of the mobilities ( 1 4 ) or rate constants ( k ) , the permeabilities ( P ) give no information about such equilibrium constants, which represent the most fundamental measure of ion selectivity and give u s direct information about the sites. If, indeed, there is any reciprocal relationship between K and / I values, as there appears to be to some extent in ion-exchange glasses and to an even greater extent at the end plate, then the ion selectivity of the sites would be very effectively masked in null potential measurements. Unless direct measurements of equilibrium constants ( K ) can be made, as is possible in ion-exchange glasses, the only way in which K and 14 (or k ) values can be separated is from measurements of the voltage sensitivity
24
PETER
H. BARRY AND PETER W. GAGE
of conductance. This needs to be done both in symmetrical solutions and in asymmetrical solutions, in which a different cation predominates on each side of the membrane. The simplest channel models to deal with are those with a symmetrical distribution of sites and barriers, as has been assumed in the two electrodiffusion models and in the rate theory models considered in this article. I n these cases, symmetrical solutions result in virtually flat conductance-voltage curves, whereas asymmetrical solutions enable u ( k ) values to be determined from the asymmetry of the conductance-voltage curve and hence K s from the P values (cf. Fig. 4). The immediate question is, how closely are these parameters tied to a particular model? As we have already discussed in Section IILC, identical parameter values are obtained from both the Neutral and Charged Site electrodiffusion models. In Section III,D and Fig. 4,however, we see that even the simple three-site, four-barrier rate theory models are predicting conductance-voltage curves that approach those of the above electrodiffusion models and that have the same parameter values. Thus, the values of these parameters seem to be fairly independent of the model used to calculate them, especially if there are more than three sites in the channel. Another question concerns the assumption that the barrier heights along the channel are symmetrical. If they are not symmetrical, the conductance-voltage curve in symmetrical solutions would no longer be flat but would reflect this barrier asymmetry, and the analyses would have to be modified accordingly. Nevertheless, with appropriate corrections, the same procedure could, at least in principle, still be used to determine values of equilibrium constants ( K ) and mobilities ( u ) or rate constants (k). F. Surface Charge Effects: Screening and Binding
Most biological membranes normally have negative surface charges on both their external and internal surfaces. This can affect permeation in two ways. First, there is a double-layer effect which results in an increase in the concentration of cations and a decrease in the concentration of anions in the vicinity of the membrane surface. Second, a surface boundary potential component A&? is added to the potential profile across the membrane, the potential at the membrane being more negative than that further away in the solution. The relationship between the activity of cations close to, a+(O),and that of cations far from, a+(m),the membrane surface is given as a+(O) = a + ( m ) exp(-z%A&,lRT) (32) where z is the valence number of the cation.
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
25
These two effects tend to be compensatory. Indeed, in the presence of only monovalent cations, which are able to permeate through the membrane channels, the increase in cation concentration is tJxuc.f/ybalanced by the negative surface potential for null potential measurements. The value of the surface charge potential may be obtained from the concentration of surface charge ( ( 7 ) by solving the following (Grahame) equation.
where (T is in coulombs per square meter, C, is in moles per cubic meter, E is the relative dielectric constant, and E~ is the permittivity of free space (= 8.85 x lo-” F m-I), so that ( 2 4 U ‘ ) ” ’ = 1.86 x C m-II2 rnol-”?. For conductance measurements, the compensation between these two opposing effects of increased surface concentration and surface charge potential need not be quite so exact, the precise amount of compensation depending on the actual mechanism of permeation. Obviously any residual effects of the external surface charge are also reduced by similar effects on the internal membrane surface, although the latter is generally considered to have a smaller surface charge density. However, any changes in the external ionic strength directly contribute to changes in the balance of charge effects at the two surfaces. Typical values of surface charge suggested for muscle and nerve membranes range from about 0.02 to 0.16 C m-?. To indicate the order of magnitude of these surface potentials, values for a surface charge density of 0.1 C m-l ( 1 x C cm-?) can be calculated from Eq. (33). For example for such a membrane in a solution containing 120 mM NaCl and 1.8 mM CaCI2, the surface potential is -76 mV. Increasing the Ca2+ concentration to 5 mM would then change the surface potential to -70 mV, whereas decreasing the NaCl concentration to 60 mM would change it to -84 mV. This reduction in the surface potential illustrates the screening effect of ions as expressed in Eq. (33) and occurs at reasonably high concentrations of the ions. Because of the valency term in the exponential of Eq. (33) the contribution of divalent ions is very much greater than that of monovalent ions. In screening there is no direct interaction of the screening ion with the surface charge, and hence there is no differential selectivity in any of the screening for ions of the same valency. In addition to the possibility of screening negative surface charges, ions can also bind to them. As discussed in Section 11, there can be very significant selectivity for different ions being bound by the sites. In contrast to screening, binding can occur at much lower concentrations of the binding ions. D’Arrigo (1978) has proposed a simple physical model to explain the difference between binding and screening.
26
PETER H. BARRY AND PETER W. GAGE
Though we would disagree with some of his assumptions,2 his basic approach is very useful. He suggests very reasonably that in the screening situation one water molecule is between the cation and the surface charge site whereas in the binding situation the cation and site are in apposition. He then calculates the additional energy due to adjacent sites, depending on whether or not they are neutralized. He suggests that as the distance between surface charge sites is increased or as more of the neighboring sites become neutralized (e.g., with decreasing pH), binding predominates over screening. What is certainly unequivocal is that a comparison of the energy for both binding and screening is very dependent on the effective radius of the site and, in the presence of divalent cations, on the separation between the sites. If the binding energy is greater, then binding predominates over screening. As far as its effect on permeability is concerned, surface charge binding merely reduces the effective surface charge concentration and hence the magnitude of any surface potentials.
G. Open Time of Ion Channels There is as yet no well-defined model for describing the average time for which a channel remains open (open time) in terms of external ion concentrations and electrical potentials. There appears to be a loose inverse relationship between ion channel open time and conductance, which is especially evident for the alkali cations at the end plate: under some conditions the product of the conductance and the open time is reasonably constant. It almost appears that there is some counting mechanism or local concentration depletion that closes channels after a certain number of ions pass through. However, in the presence of other ions such as NHd(Takeda et al., 1980), the picture is not so clear. In addition, endplate channel open times are very temperature sensitive (Qlo - 2-3), whereas single-channel conductances are not (Qlo I . 1-1.2). Furthermore there is an exponential dependence of open time (7)on potential ( V,) which may be expressed by
-
T( V,) =
~ ( 0exp() V,/H)
(34)
where H is a voltage sensitivity parameter. Channel conductance has no such dependence on voltage. We would disagree with his use of only the vertical component of the immediate-neighbor energy contribution, and the precise positioning of his divalent cation with respect to the monovalent sites. Upon review of these arguments, J. D'Arrigo (personal communication) is in agreement with our conclusions.
27
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
H. Diffusion-Limited Access Effects When current is funneled through finite-sized channels there can be significant depletion or enhancement of ion concentrations in the unstirred regions adjacent to the channel openings-depletion in one and enhancement in the other. For further details see Neumcke (1975). Lauger (1976), and the review by Barry and Diamond (1984). The magnitude of the concentration change is proportional to rc‘ - t ’ , where t‘ and I’ represent thc cation transport number in the channel and in the appropriate external solution, respectively. The transport number ti for ion i in each case represents the fraction of current carried by that ion and is given by t,
= zirrici1
c
(35)
i,ll;C;
where zi, u;, and Ci represent the magnitudes of the valency, the mobility, and concentration, respectively, of ion i, and the summation is over all ions. For “long” times t it may be shown that C
=
C , - (Air) ( I - r,,(nDr)-”2exp[(r
-
r(,)/rO]}
(36)
where A = (t‘
-
t‘)i,/2~9D
(37)
and where C is the concentration at radial distance r , C, is the ion concentration in the bathing solution, i, is the single-channel current, D is the free solution diffusion coefficient of the ion, and r, is the “capture radius” of the channel given by To = r, - TI (38) where rc and ri are the radii of the channel and ion, respectively. For example, if i, -2 pA = 2 x A, rc = 0.5 nm (similar to the possible dimensions of the inside mouth of end-plate channels, see Section V , A ) , while for K’ ions, ri = 0.22 nm (see Table I), then r,, = 0.28 nm. Hence, if ‘f - 1’ werc taken as 0.S,the long-term concentration depletion at thc channel mouth, for current entering the channel, would be given by ( ( P - r’)/2~9Dr,,li,
=
3.7 mM
If the minimum end-plate channel radius (0.325 nm, Section V,A) were chosen for rc, then ro = 0. I nm and AC would be 10.3 mM. These concentration changes are set up very rapidly-in a matter of nanoseconds-and are very localized in that significant concentration changes occur only within distances less than -10 n m . If the concentration changes approach the absolute concentration of the ions, then of course the effect can limit the magnitude of the current that can traverse the channel.
28
PETER H. BARRY AND PETER W. GAGE
IV.
EXPERIMENTAL TECHNIQUES
A variety of techniques can now be employed to determine the average open time and conductance of channels in biological membranes. Many of these were first developed to characterize end-plate channels, and their application is illustrated for these channels. However, it is clear that the techniques can be applied to any channels. A. Null Potentials
Following its demonstration by Hodgkin and Huxley (1952) for depolarization-activated Na+ and K' channels, it is generally assumed that for other channels there is a linear (ohmic) relationship between current and voltage across the channel. This can be expressed as
i
=
y(V, -
EO)
(39)
where i is the current flow through an open channel, y is the conductance of the channel, V,,, is the membrane potential, and EO is again the null or reversal potential. If a single species of ion is flowing through a channel, measurement of the null potential gives the equilibrium potential for that ion and hence the ratio of its external and internal activities. When, however, there is more than one ion flowing through a channel, null potential measurements give us from Eq. (7) information about relative ionic permeabilities. Generally, studies are made on a population of open channels no, so that the current recorded ( I ) is given by I
=
&')'(Vn, -
Ed
(40)
The null potential can be measured by varying the membrane potential (usually using voltage clamp techniques) and determining the potential at which the membrane current is zero. It is important to determine null potentials by interpolation rather than extrapolation, especially when records are being made from populations of channels. This is best illustrated by making the reasonable assumption that open and closed channels are in equilibrium, and that the probability of channels being closed or open is determined by rate constants a and p, according to the scheme closed
open
The fraction of open channels is equal to @/(a+ p ) and the open time of channels is exponentially distributed with average open time T equal to a-'.
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
29
Now if either (or both) of the rate constants, (Y or p, is voltage dependent, it can be seen from Eq. (40) that the relationship between I and V,, may be nonlinear, as indeed it is at the end plate. A way in which such a complication can be avoided is to measure I immediately following a change in V , before no has changed. However, it is then necessary to contend with capacity currents. The surest way to measure E~ is to determine directly the potential at which I = 0, a measurement that is independent of the number of open channels (unless all channels close at some Vm). It is also important to ensure that ion concentrations are not significantly changed, as this would change G O .
B. Noise Analysis In a situation in which there is an equilibrium between closed and open channels as above, it is expected that there would be fluctuations in the number of open channels about a mean value (for review of the technique of noise analysis, see Neher and Stevens, 1977). The frequency characteristics of such fluctuations would be a function of (Y and p. If current is being recorded through open channels, fluctuations in the number of open channels would cause fluctuations in the current (noise) around a mean value. Such current fluctuations recorded in a voltage-clamped sternomastoid muscle fiber exposed to acetylcholine are illustrated in the lower trace of Fig. 6B. The increase in noise produced by acetylcholine can be seen by comparing this trace with the baseline noise in the lower trace in Fig. 6A. The relationship between power spectral density G(f) and frequency fpredicted from the model is given by
where G(0) is the asymptotic power spectral density (f= 0) and .f;. is the frequency at which G(f) = 1G(O) (,#: is also called the “corner” frequency-see Lewis P I ul., this volume). The power spectral density G ( f ) gives a measure of the square of the amplitude of each spectral component of the current at frequency .f. The form of this spectral density relationship in Eq. (41), with its dependency on the inverse square of the frequency, is often called a Lorentzian curve. A least-squares fit of this equation to points obtained from the noise shown in Fig. 6B is shown as the solid line in Fig. 6D. Measurement of the cutoff frequency.f;. gives a + ,f3 from the relationship a + p = 27rji.. Under conditions in which only a very small fraction of the channels is open (i.e., (Y >> p), ( 2 ~ r f ; . ) -gives ’ an estimate of average channel open time rN.For example, anfc of 160 H z in Fig. 6D gave a value of I msec for T N .
30
PETER H. BARRY AND PETER W. GAGE
FIG. 6 . A miniature end-plate current (A, lower trace) and fluctuations in end-plate current produced by iontophoresis of acetylcholine (B, lower trace), both recorded at the same end plate in mouse sternomastoid muscle. The upper traces in (A) and (B) show membrane potential. (C) A semilogarithmic plot of the decay of the miniature end-plate current in ( A ) giving a time constant 7” (arrow) of 1.2 msec. (D) Triangle5 show a power density spectrum of current fluctuations as shown in (B).The solid line shows a single Lorentzian curve fitted to the points with a cutoff frequencyf, (arrow) of 160 Hz giving a T~ of 1 msec. (Reproduced from Gage and Hamill, 1981, Fig. 3 . )
Under the same conditions of a >> p, and making the reasonable assumption that the channels open independently, it can be shown that the variance of the number of open channels equals the mean number of open channels, so that the ratio of the variance of end-plate current fluctuations induced by iontophoretic application of acetylcholine to the mean endplate current gives the current flow through an individual channel, and hence the channel conductance from Eq. (39).
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
31
Channel conductance can also be calculated from the power spectral density from
C. Perturbation Techniques
In the above two-state scheme. if either a or p is suddenly changed, the rate of development of a new equilibrium is determined by the new values of a and p, according to the equation n d t ) = nJ0)
+
Ino(m)
-
n,,(0)1[1 - exp(-t/dI
(43)
where 7 = ( a + p)-’, n,(O) is the number of open channels before the perturbation, and no(.-o)is the number of open channels long (at “infinite” time) after the change. Mulliplying both sides of Eq. (43) by y ( V , - E ~ , ) gives
1. VOLTAGEJUMP
For many channels, either (or both) a or p may change with membrane potential. For example, at the end plate, a varies steeply with membrane potential, whereas p does not. Measurements of the rate of change of endplate current following a step in clamp potential (with constant acetylcholine concentration) have provided useful measures of average channel open time.
2. MINIATURE END-PLATE CURRENTS A useful perturbation is provided by Nature. A single quantum of acetylcholine secreted from a nerve terminal activates a number of open channels, and then disappears (by hydrolysis and diffusion) before the majority of the channels have closed. Under these conditions, p in the two-state scheme above quickly becomes zero, so that the subsequent current is given by substituting “ 3 0 ) = 0 in Eq. (44) and hence
I ( [ ) = I(0) exp(-f/7) (45) The current waveform, known as a miniature end-plate current, is illustrated in Fig. 6A. The decay of the miniature end-plate current is exponential, as illustrated in the semilogarithmic plot in Fig. 6C in agreement with Eq. (45). Consistent with the two-state model and other assump-
32
PETER H. BARRY AND PETER W. GAGE
tions, the time constant of decay of the miniature end-plate current of 1.2 msec is in good agreement with the average channel open time of 1 msec measured from the power spectral density curve (Fig. 6D) obtained at the same end plate. D. Single-Channel (Patch-Clamp) Techniques
When a channel opens, there is a current flow across the membrane (if V , # E ~ ) .It is now possible to record single-channel currents in a small patch of membrane sucked into the tip of a glass microelectrode. Details of this technique are described in full by Hamill et ul. (1981). The secret of obtaining a useful signal-to-noise ratio is to maximize the resistance of the electrical seal between the glass and cell membrane. A seal resistance of several gigaohms (lo9 a) is necessary if currents of 1-3 pA are to be clearly seen above the baseline noise under voltage clamp conditions. In order to obtain such seals, it is often necessary to clear connective tissue from the surface of cells using proteolytic enzymes. Another approach has been to use cultured cells, which may be obtained with smooth, clean surfaces without enzyme treatment. Single-channel currents recorded from a denervated toad sartorius muscle fiber with a pipet containing 200 nM acetylcholine can be seen in Fig. 7. Open channels have a similar conductance and their open time (strictly, burst length) is exponentially distributed. consistent with the two-state scheme above. E. Summary of Techniques
In summary, average channel open time can be determined by ( I ) noise analysis, (2) perturbation techniques, and (3) single-channel (patch-
50 ms
FIG.7 . Patch-clamp record of currents through single acetylcholine channels recorded in denervated toad skeletal muscle (Bufo marinus) using the gigaohm seal technique. Measurements were done in normal Na' solution at 11°C. V , = -70 mV, filter cutoff of I kHz (Nino Quartararo, unpublished observation).
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
33
clamp) techniques. Single-channel conductance can be determined by measuring the null potential and by ( I ) noise analysis and (2) singlechannel (patch-clamp) techniques.
V.
END-PLATE CHANNEL CHARACTERISTICS
Because of its accessibility, the neuromuscular junction has been the synapse on which much of the pioneering work on the characteristics of ion channels in biological membranes has been done. An added advantage is that it has been possible wing the irreversible ligand, a-bungarotoxin, to identify and extract those receptor-channel proteins activated by acetylcholine, and to visualize receptor-channel complexes using a variety of techniques. End-plate channels play a vital role in neuromuscular transmission. When an action potential propagates into a motor nerve terminal, acetylcholine (ACh) is secreted across the nerve membrane, diffuses across the synaptic cleft, and binds to receptors on the muscle membrane. These receptors are part of a receptor-channel complex, and binding of ACh to specific sites on a receptor converts a closed channel to an open channel. Although sodium and potassium ions can pass through these end-plate channels with about equal ease, normally the end-plate current is carried mainly by sodium ions because of their much greater driving force. The inward current (end-plate current) depolarizes the muscle membrane, setting off an action potential which in turn makes the muscle contract.
A. Molecular Structure of Channels Over the past 5-10 years, the ACh receptor-channel complex has been studied with a wide range of techniques: electron microscopy, X-ray diffraction, and low-angle neutron diffraction. The complex has also been subjected to vigorous biochemical analysis (for reviews, see Karlin, 1980; Horn and Stevens, 1980; Horn and Brodwick, 1980; Dreyer, 1982). Most of this work has been done on membrane-bound ACh receptor-channel complexes from the electric tissue of the electric skates 7orpedo t d i fornica and Torpedo marmorata. The complex has a molecular weight of about 250,000 and a volume of about 300-400 nm?. It appears, from electron micrographic analysis and X-ray diffraction, that the complexes are -I I nm long and protrude beyond the lipid bilayer for -5.5 ? I .O nm on the extracellular side and 1.5 2 0.5 nm on the intracellular side. There also appears to be a central aperture, about 2.5 nm in diameter, on the extracellular side. Low-angle neutron diffraction studies are consistent
34
PETER
EXTRACELLULAR
H. BARRY AND PETER W. GAGE
INTRACELLULAR 5 nm
FIG.8. A hypothetical diagram of two acetylcholine receptor-channel complexes straddling a 5-nm-thick biological bilayer membrane. This figure, which is drawn approximately to scale, is broadly based on an assortment of structural data obtained from the electric ray Torpedo californicu, and is somewhat similar to the one shown in Horn and Stevens (1980, Fig. 1). The lipid bilayer is similar to that depicted by Singer and Nicholson (1972). The 2.5nm channel opening on the extracellular side is suggested by electron micrograph and lowangle neutron diffraction studies; a minimum cross section of 0.65 X 0.65 nm is suggested by electrophysiological evidence. However, the actual internal structure of the channel is unknown. To emphasize this, the sides of the channel have been shown as question marks, some of which could represent the positions of possible ion-binding sites. The size of the solid circles is intended to represent the relative size of a 0.4-nm-diameter hydrated Na' ion. The 10-nm center-to-center spacing of the complexes is suggested by receptor density studies.
with a model in which there is a large disk, 4 nm thick and 9 nm in diameter with a central hole 3 nm in diameter in the extracellular fluid, and a disk 2 nm thick and 6 nm in diameter in the intracellular fluid. The two disks are connected by a hollow tubular section, with internal diame-
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
35
ter of I nm, through the lipid. From receptor density studies it is known that these complexes are closely packed with center-to-center distances of the order of 10 nm. A physical model based on these observations can be seen in Fig. 8, which depicts two of these ACh receptor-channel complexes positioned in a bilayer membrane. Although there is reasonable agreement about the external appearance of these complexes, relatively little is known about the internal structure of the channel. Indirect electrophysiological investigations at the amphibian end plate have led to the suggestion that an open channel has minimum cross-sectional dimensions of 0.65 x 0.65 nm. It has also been suggested that there is only one minimum cross-sectional region, which occurs near the intracellular end of the channel. However, the possibility that there may be two or more such regions symmetrically placed along the main section of channel cannot be dismissed. To emphasize present uncertainty about the internal structure of the channel, the luminal wall in Fig. 8 has been tentatively outlined with question marks; some of these could represent the positions of electronegative sites. From a purely physical perspective, regardless of the models used, electronegative sites are required in the channel to provide an energetically suitable environment for permeant cations. The low (compared with water) dielectric constant (polarizability) of the protein walls of the channel would provide an energy barrier for ion movement into the channel. This would be balanced by the presence of electronegative sites in the channel which could interact electrostatically with the cations. The presence of such sites is also suggested by the selectivity of the channel against anions and the dynamic selectivity between cations, which is discussed in Section V,C.
B. Null Potential Measurements As described above, in the absence of cooperativity effects and significant anion permeation, the null potential equation for monovalent cations [e.g., Eq. (7) or (26)] is essentially model independent and is given by the Generalized Null Potential equation (of the same form as the GoldmanHodgkin-Katz equation), although the permeabilities [Eqs. (81, (23) or (27), (28)] may be expressed as the product of equilibrium (binding) constants and either mobilities (electrodiffusion theory) or rate constants (rate theory). Two possible refinements could be used in these equations. First, activities could be used rather than concentrations. However, internal activity coefficients are not known and, provided the ionic strengths of both external and internal solutions are approximately the same, the ac-
36
PETER H. BARRY AND PETER W. GAGE
tivity coefficients would tend to cancel out. In addition, estimates of internal concentrations that are generally used have been obtained from electrical measurements of equilibrium potentials and knowledge of the external ion concentration. Thus there is consistency in continuing to use concentrations. Furthermore, surface charge effects can alter interfacial concentrations and surface charge potentials. However, as already discussed in Section III,F when only monovalent cations are permeant, errors introduced by the approximations largely cancel each other out and may be neglected. At the end plate, the influence of cations on null potentials has been accurately determined in two ways, using voltage clamp techniques. In the first (Gage and Van Helden, 1979), acetylcholine was iontophoretically applied to an end-plate region of intact muscle fibers “point clamped” with two microelectrodes. The clamp potential at which endplate current became zero was taken as the null potential. The external solution was varied by substituting foreign cations for Na+. The internal concentrations of K+ and Na+ were assumed to be 140 and 10 mM, respectively. In the second way (Dwyer et al., 1980; Adams et al., 1980) a vaseline gap technique was used to voltage clamp end-plate regions of cut muscle fibers. By perfusing the cut ends with appropriate solutions, both internal and external ion concentrations could be changed. The null potential in the presence of iontophoretically applied ACh was again determined by measuring the voltage clamp potential at which zero current flowed. Table V shows permeabilities of monovalent inorganic cations (together with NH& also included in Table VI) measured relative to K+. There is fairly good agreement between permeabilities obtained with the two techniques. The permeability sequence is TI+ > NH;> Cs+ > Rb+ > K + > Naf > Li’. This conforms with Eisenman sequence I, a low field strength sequence, and appears to suggest that the channels behave simply as a free solution shunt. However, this is not an equilibrium constant sequence; the permeabilities are not exactly in the ratio of free solution mobilities and, as we have inferred already, the absence of any significant anion permeability suggests a rather more complicated situation. Using the vaseline gap technique, Dwyer rt a / . (1980) measured 52 different monovalent organic cations, some of which are listed in Table VI for comparison with the alkali cations. It can be seen that there is a simple inverse relationship between relative permeability and molecular weight (or the calculated mean molecular diameter, not shown). It was shown that the permeability sequence agreed fairly well with a frictional pore model for permeation through a circular cylinder with diameter of 0.74
37
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
TAHI,k, V MFASURFMFNI\ 0 1 PFRMFABlI ITY R F I ATIVI K + ( P x / P k )F O R INORGANIC IONI AND NH;
NU1 I POIPNIIAI TO
X
8°C"
TI CI' N H: Rh'
1.24 ? .03 -
K'
I .o 0.98 5 .03 0.90 ? .03
+
Na' Lit
20°C"
1 ?"C"
-
2 26 1.28
1.23
?
I .o
.05
I .ox t .02 0.96 ? .OL
1.61
-
1-17 I .0
-
0.90
I.o 0.9
I .6X I .o o.83
0.78
0.7
-
I .05 I.o I .04 I .o 0.67 0.51
Barry ('I t i / . (197%) in flufit n7t/rit//t.s with SEM. A d a m ct t i / . (19x0) and Dwyer C I t i / . (1980) in Rtrutr pipirw.s. Lassignal and Martin (1977) in eel electroplax. Lewis (1979) at 10- 1 S T for Na. in R . p i p i c ~ mand Takeda P I N / . (1980) at 15°C for NH: in B. niciri/iris. '' From limiting equivalent conductance of X relative to K' at 18°C from Robinson and Stokes i1965). "
I'
nm, after correction for the volume of the permeating ion. Consideration of the largest ions that just permeate (e.g., glucosamine, ethyldiethanolamine, and triethanolamine, Table VI) together with ions that do not seem to permeate (e.g., methylethyldiethanolammonium and tetrakisethanolammonium) suggested that the pore has a square cross section, TABLE V1 Nu1.i. POT-ENI'IAI. M ~ A S U K E M EOF N TPERMEARII.ITY S R E L A T I V E T O K ' (PI(/PK) FOR O R G A N I C C A T I O N S "
X
Molecular weight
Hydroxylaniine (pH 5. I ) Ammonium (NHJ Et hanolamine 4-Aminopyridine Tris (pH 6 3 ) Choline Glucosamine (pH 6.3) Ethyldiethanolamine (pH 6.6) Triethanolamine (pH 6.6)
34.0 18.5 62. I 95. I 122. I 104.2 180.2 134.2 150.2
PxIPK
I .73 1.61 0.65 0.49 0. I6
0. 12
0.03 0.027 0.027
These figures are just a sample of the 52 organic cation permeahilities measured by Dwyer <'/ t//. (19x0) in Rtiwtr pipiei7.s. They have heen reexprcssed relative t o K' by dividing by their value of PK/PN,, = 1 . I 1 . I'
38
PETER H. BARRY AND PETER W. GAGE
0.65 x 0.65 nm?, with 0.05 nm? cut off at each corner (Fig. 10, taken from their Fig. 7). In contrast to the model-independent Generalized Null Potential equation for monovalent permeating cations alone, mixtures of monovalent and divalent cations require null potential equations that become model dependent. This arises because the net ionic current has to be zero, and no longer do the model-dependent factors in the conductance (different for monovalent and divalent ions) cancel out. The Neutral and Charged Site models have not yet been solved for such a mixture of ions, and an analytical solution will probably be extremely difficult, if not imp~ssible.~ Since the Goldman-Hodgkin-Katz equation, which assumes the independence principle, deals with each ionic current separately, its solution for mixed valencies is simply obtained by numerically solving (e.g., by using the Newton-Raphson technique) the following equation (see for example, Lassignal and Martin, 1977) in order to zero the current summed over all the permeant ions
where ii is the ionic current due to ionj, [aj]’ and [uJ” represent the concentrations of ionj on side’ and side” respectively, is the null potential (side” with respect to side’), and the other terms are as previously defined. Although its applicability at the end plate is highly questionable (Sections I1,B and V,C), at least it allows some sort of estimation of relative permeabilities, although any results so obtained should be considered very tentative. Using the above mixed valency version of the Goldman-Hodgkin-Katz equation, Adams et al. (1980) have endeavored to measure the relative permeabilities of divalent ions at the end plate; these results (uncorrected for activity coefficients or surface charge effects) are included in Table VII together with the radius of the ion and of its primary hydration shell. It can be seen that apart from Cd2+,which can form chloride complexes (see discussion in Adams et al., 1980) there seems to be little apparent selectivity among the divalent ions, although all of them are considerably less permeant than monovalent metal cations. When higher concentrations of divalent ions (e.g., 80 mM) were used, there was an apparent drop in the relative permeability ratios, which could be explained in terms of surface charge effects (Adams et a[., 1980). This added factor is discussed further in Section V.E. Lewis and Stevens (1979) have solved the rate theory equations for a single-site, twobarrier model for a mixed valency situation.
39
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
TAHLb V11 N U L LPOTENTIAI M F A S L J RMEF N I S OF PERMEARII-ITY RELATIVE rO K' ( f ' y / P ~ )FOR DIVA1 E N 7 C A r l O N S
X2+ Mg'-
Ca" Sr!' Ba2+ Ni?' Zn" COL' Mn" Cd2-
Ionic radius"
Hydrated radius"
Px/PK'
0.086 0.114 0.132 0. I49 0.083 0.088 0.088s 0.097 0.109
0.214 0.224 0.216 0.222 -
0.23 0.20" 0.16 0.19 0.23 0.23 0.21 0.23 0.12
-
-
Radii in nanometers from Shannon (in Edwards. 1982). Radii in nanometers from Goldman and Bates (in Edwards, 1982). Measurements by A d a m P I ul. (1980) at 12°C in Ranu pipirns using 20-21 mM X?'. No correction was made for activity coefficients or suiface charge effects. The permeabilities have been reexpressed relative to K + . A similar value of 0.14 for Ca?' was obtained by Lassignal and Martin (1977) in eel electroplax (see correction in Edwards, 1982). 1
The problem with null potential measurements is that they do not enable a separation of equilibrium constants and mobilities (or rate constants). Nor do they distinguish between different permeation models (unless mixtures of ions with different valencies are used). As we have already noted (Section III,E) both of these require measurements of conductances or, more specifically, as we shall see in the next section, the voltage sensitivity of the conductance. C. Conductance-Voltage Relationships
Using single-channel conductances obtained from noise analysis and permeabilities calculated from null potential measurements, Barry et al. (1979a) showed that the Goldman-Hodgkin-Katz equation could not explain relative conductances in L i t , Na'. and C s + solutions. A similar conclusion has also been reached by Adams et al. (1981). Nor could the equation correctly predict the experimentally observed conductancevoltage relationship, especially in Lit and Na+ solutions. In the above
40
PETER H. BARRY AND PETER W. GAGE
experimental situation the predominant internal cation was K+. As we have already seen in (Sections III,C, D, and E and Figs. 2 and 4) the asymmetry of the conductance-voltage curve depends primarily on the relative mobilities (or “hopping” rate constants) of the cations within the channels. Experimentally, permeabilities are first obtained from null potential measurements, and then equilibrium constants ( K ) and mobilities ( 1 1 ) or rate constants ( k ) are evaluated (using one of the electrodiffusion or multisite rate theory models) from conductance-voltage curves over as wide a voltage range as possible (generally from - 150 to +50 mV). This is done for test cation X by varying the value of U X / u K (or k x / k K )to best fit the experimental data. This, in principle, gives a unique fit, and the equilibrium constant ratio K x I K K is then determined from the mobility ratio ( U X I M Kand ) the permeability ratio ( P x I P K ) . Figure 9 shows conductance-voltage curves based on noise analysis measurements at the toad end plate for Na+, Li+, and Cs+ solutions (see also Adams rt ul., 1981). The experimental points were fitted by theorelical curves with appropriate values of the mobilities and equilibrium constants. A full set of permeation parameters is given in Table VIII (in these calculations, equilibrium constants were fitted and mobilities obtained from the permeabilities). It may be seen that the equilibrium constant ( K ) A NaCl
1.5
1.0
6
C
LiCl
2.0
CsCl 1.5
/
_____..___----1.5
I
G 0.5
1.0
I
0
.50 Vm
0
(mV)
FIG.9. Experimental values of normalized single-channel conductance G at the amphibian end plate, obtained by noise analysis of acetylcholine-induced noise, as a function of membrane potential V , . The measurements in NaCl (8°C). LiCl (8”C), and CsCl (20°C) solutions are shown relative to the conductance value at -50 mV. Experiments gave very similar results whether done at 8 or 20°C (a full set of data is given in Barry rt d.. 1979aj. The solid lines represent the predictions of the Neutral Site and Charged Site models (which are identical); the broken lines show predictions from the Goldman-Hodgkin-Katz equation (the parameters used were KN;,IKK = 1.7; iiN.,//iK = 0 . 5 8 ; K , , / K K = 7; u t . , ~ i= K 0.14; K J K K = 0.9; U ~ J I ~ = K I .4.For further details see Table V111).‘The figure is taken from Barry c’/ ol. (1979b. Fig. 1).
50
41
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
sequence is Kl.i> KNH4> KNa> K K > K c , , which, for the alkali cations. is Eisenman sequence XI. This implies that in spite of the apparent lack of significant permeability selectivity the sites do in fact have a strong field strength (Table 11). which has been unmasked by the conductance-voltage measurements. In addition, the mobility (or rate constant) sequence is i4ra> i i > ~ ~ N ;> I MNH> ~ u ~ ,I ~ t should . be noted that this is in the opposite direction to the K sequence of equilibrium constants as discussed in Sections III,C and D, and implies that the most strongly bound ion has the lowest mobility or rate constant. Furthermore, the relative values, especially for Li+, are very different from the free solution mobility ratios (obtained from limiting equivalent conductances) given in Table V . Using these parameters, the experimental measurements of conductance in the Lit, Na', and Cs' solutions were fitted within experimental error by the Neutral and Charged Site models, in contrast to the Goldman-Hodgkin-Katz equation predictions (see Table 3 of Barry et a/., 1979a). We have already discussed in general terms in Section III,C the question of the independence of the parameter values from the permeation models, as based on electrodiffusion or rate theory. In addition, two further questions may be raised concerning the evaluation of these permeability parameters. First, how symmetrical are the energy barriers along the channel? Or, rephrasing the question, is the conductance independent of voltage in symmetrical cation solutions (cf. Fig. 4A)? An ideal experiment to answer this question in intact muscle fibers would be simply to use K+ as the external cation. The problem with this, however, is that because of the high resting permeability to potassium, raising its concentration will radikLATIVF.
Li'
TABLE V l l l PERMEATION P A ~ ~ A M F TFOR F R AI ~
0.90 t .03
NH;
1.68
Na+ K'
0.98 ? .03 I .0 1.24 2 .03
cs"
" 1
0.96 2 .05 _+
.05
1.08 2 .02 I.0 1.23 t .05
0.13
rf.
.02
0.42 0.58 i .OX I .o 1.4 ? .4
KAI I C A T I O N S " A N D
0.14
+-
NH;"
721
.05
t 0.45 -
4.2
0.31 0.64 +- . I 0 I .o 1.2 2 .8
Obtained from data of Gage and Van Helden ( 1979) analyLed Obtained from Takeda C I ul. (1980) at I5"C The errors given are the SEM
722'
1.7 I .0 0.9 in
Barry
?
.2 .2
*
1.7 2 I .o 1.0 2 .5
('I t i / . ( 197%).
42
PETER H. BARRY AND PETER W. GAGE
cally depolarize the muscle and cause significant changes in cell volume. An alternative is to choose a cation with a relatively low resting permeability but with an end-plate permeability (and, preferably, mobility) similar to K + . Cs+ fits both of these criteria fairly well. As can be seen in Fig. 9 (see also Fig. 4 of Barry el af., 1979a), the conductance-voltage curve is almost flat, with a slight slope opposite to that of curves obtained with Na+ and Li+, so that conductance was slightly less at depolarized potentials. This certainly seems to suggest that the energy barriers are reasonably symmetrical, at least at the toad end plate, and to justify the analysis and parameters so far evaluated. Furthermore, in excised patches of rat muscle exposed to symmetrical N a + solutions, Horn and Patlak (1980) have shown that the voltage-current curve is close to linear between -100 and +50 mV. Second, we might ask whether there are any particular problems with using the technique of noise analysis to evaluate single-channel conductances. It seems unlikely that errors should depend on the species of cation. However, the best justification for supposing that the conductances so measured are free from significant error is that similar conductance-voltage curves for Li+ and Cs+ over an even greater potential range (- 190 to +50 mV) have been obtained in our laboratory using the patchclamp technique to record single-channel conductance in denervated toad muscle. D. Conductance-Concentration Relationships
Barry et af. (1979) showed that halving the external concentration of NaCl decreased the single-channel conductance, as predicted from the Neutral Site model but not from the Charged Site model. Lewis (1979) has also shown that the single-channel conductance decreased linearly from a value of about 28 pS in normal Ringer’s solution, as the Na+ concentration was decreased, finally reaching a limiting value of 10 pS in Na+-free solution. Takeda et al. (1982b) have found that single-channel conductance, measured with both reduced and increased extracellular sodium concentrations, could be approximately fitted by an equation of the form G
=
G,dNaIo/(Km + “a],)
(47)
where G,,, represents the maximum value of single-channel conductance when all the sites are occupied and K , is something like an effective “affinity” constant for the sites, representing the value of [NaIoat which G = G,,,/2. Electrodiffusion and multisite rate theory models were used to correct for any K tcontribution to conductance and to obtain values for G,,, when the relative Na+ occupancy approaches 1.0. This procedure
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
43
gave values of 78 pS and 423 mM for G,,,, and K , , respectively. The values of relative mobilities (uN;1//fK) and relative equilibrium constants ( K N ~ ~ I K Kobtained ) from analysis of the voltage sensitivity of conductance imply that, as ”a], was decreased, there was a reciprocal increase in K N J K K and decrease in i/N,,/.uK. This is intuitively plausible since a decrease in the occupancy probability of adjacent sites increases the electric potential contribution from unoccupied neighboring sites. This would effectively increase the site strength of the occupied site. The influence of external concentration on conductance distinguishes between the two electrodiffusion models as they stand: the Neutral Site model predicts the dependence of conductance on concentration whereas the Charged Site model predicts a constant conductance as the external ion concentration is varied. These two divergent predictions arise directly as a result of the electroneutrality condition that was imposed on the two models. If it is no longer assumed that the Debye length within the channel is small compared to the channel length, then the electroneutrality would no longer apply and a charged-site model would also predict an approximately linear dependence of conductance on concentration. lndeed, electroneutrality may well not apply in end-plate channels, in which case a “short”-channel, charged-site model would behave like a “long”channel. neutral-site model.
E. Surface Charge Effects
As mentioned in Section III,F, it is more important to take into account surface charge effects when considering divalent ions than when considering monovalent ions. This is because divalent ions contribute far more to the ionic strength of the solutions adjacent to a membrane. At the end plate, Adams et NI. (1980) noted that divalent ion concentrations of 80 mM or more resulted in a decrease in apparent permeability relative to monovalent ions, and suggested that this could be explained if surface charge effects were taken into account. Indeed, allowing for a C cm-? (see Section 1II.F) in a 20 mM Ca2+ surface charge density of solution reduces Pc,,/PKfrom about 0.14 to 0.04 (Takeda rt d., 1982a). Takeda et ul. (1982a) investigated the effects of divalent ions on both single-channel conductance and on open time. The decrease in singlechannel conductance from 24 to 5 pS when 120 m M Na+ was replaced by 80 mM Ca2+probably reflects simply the lower mobility and equilibrium constant of calcium ions in the channel. Divalent ions appear to influence average channel open time in two ways. The first involves screening of surface charge. In solutions containing either 20 mM Ca” or 20 m M Mg?’, channel open time increased by
44
PETER
H. BARRY AND PETER W. GAGE
about 25%. This increase is consistent with simple screening of the surface charge by the divalent ions resulting in an effective hyperpolarization of the membrane, which is known to increase channel open time. The second way involves binding of cations to specific sites, because very low concentrations are needed and the effect is very ion specific. In this case, the presence of Zn2+at concentrations less than 1 .O mM and Ni2+at 1 mM almost doubled the lifetime of the channels. These sites could be surface charge sites or charged sites within the channel. It appears that Ca2+may also bind to these sites since, with 80 mM Ca2+,the increase in open time (slightly more than double control) is too great to be explained in terms of screening effects alone. The binding sequence therefore appears to be Zn2+> Ni2f > Ca2+,Mg*+. It is perhaps not surprising that the apparent permeability sequence (Table VII) obtained by Adams et al., P M>~Pca > P B>~Ps,, is not one of the predicted sequences (Table IV), because it is not actually an equilibrium constant sequence, and also needs to be corrected for surface charge and perhaps for specific binding effects. F. Channel Block
It has been suggested, both on theoretical grounds and from experimental evidence, that a wide variety of ions and molecules (e.g., procaine, curare, gallamine, tetraethylammonium, decamet honium, hexamethonium, atropine, scopolamine, amantadine, histrionicotoxin, barbiturates, and even acetylcholine itself) can block open end-plate channels. If inorganic cations were to compete with these large blocking molecules for an appropriate site in the channel and if this site were the same as those responsible for ion permeation, the kinetics of this competition could give information about the ion selectivity properties of the sites. However, in view of the uncertainties, which are discussed in this section, about the mode of action of these blocking molecules, such information is not yet forthcoming. The classic drug that has been used in developing models for explaining channel block is the local anesthetic procaine, which was suggested to produce end-plate currents with biphasic decays because it entered and blocked end-plate channels, and then came out, leaving an open channel. These events can be represented by a simple, sequential blocking model: closed
/<, & open * blocked I1
where CY and p are rate constants as before, f and b are blocking and unblocking rate constants, respectively, and c is blocking molecule concentration.
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
45
This model predicts end-plate currents with decays (when p = 0) described by the sum of two exponentials, double Lorentzian power density spectra (see Section IV,B), and current relaxations with two time constants following voltage jumps. Such phenomena have been observed at end plates exposed to procaine. Furthermore, “bursting” end-plate channels (in which the channel transiently closes many times during its open time) have been recorded with the patch-clamp technique in preparations exposed to procaine. The integral of the open times within a burst equals the normal open time recorded in the absence of procaine. These observations are also consistent with the above model. (For more on bursts, see Horn, this volume.) However, quantitative comparisons of theoretical predictions with experimentally recorded currents raise doubts about this model. It is possible to show that the current waveform, following a jump in ACh concentration and when p = 0, would be given by
’ [ ( h - r,) exp(-r,r)
I ( r ) = I(0) (rf - r,)
+ (ry - h) exp(-rrifl)J (48)
where rc = ( a + h +.fc) - [cuh/(a + h +Ji.)l and r, = a h / ( a + h + f c ) when a h << ( a + h + fc)*. If the decay of a miniature end-plate current (or endplate current) is fitted by the s u m of two exponentials so that
I(r)
=
At exp(-rft)
+ A, exp(-r,t)
(49)
A1 may be equated with (rl - h ) / ( r l - r,) and A, with ( h - r,)/(rt - r J , It follows that A,/(At A,), the fractional amplitude of the slow exponential component, equals [r,(rf+ r, - a ) l l [ a ( r f- r,)]in the above model. These equations are based on the assumption that ah << ( a + h + .fc)’. More generally, if it is assumed that the total charge movement through an open channel is unchanged by procaine, it can be shown that A,/(Ar + A,) equals [r,(rl - cu)]/[(rf - r J a ] . Thus, the fractional amplitude of the slow phase of a biphasic miniature end-plate current, which can be easily measured, should equal the fractional amplitude predicted from independently measured rate constants. Biphasic miniature end-plate currents, recordcd at different pHs, in the presence of procaine violate these predictions. The effects of some other drugs, which at first sight have appeared to block end-plate channels, have not withstood quantitative comparison with predictions from the above model. For example, hexafluorodiethyl ether produces biphasic miniature end-plate currents, but the slow phase can decay more rapidly than in the absence of the drug, i.e., r, can be greater than a. However, from the model, r, = ah/(a + h + fc) so that it would be predicted that r\ should always be less, never greater, than a . Similar observations have been made with hexanol and 4-octanol, which
+
46
PETER H. BARRY AND PETER W. GAGE
also produce biphasic miniature end-plate currents. It is clear that the temptation to classify ions or molecules that produce biphasic miniature end-plate currents, double Lorentzian spectra, or bursting channels as end-plate channel blockers should be initially resisted until a range of quantitative predictions have been tested. Nevertheless, in view of the qualitative similarities between predictions of the simple blocking model and changes in end-plate currents, power density spectra, current relaxations following voltage jumps, and the bursting channels seen with patch-clamp recording, it is tempting to retain the model, in spite of quantitative difficulties, in the hope that realistic modifications of the simple model may give better quantitative fits between theory and observation. It has also been suggested that alkali cations might “block” ACh-activated cation-selective channels in the sea hare Aplysia. As observed at the end plate, channel conductance and open time vary in opposite ways when foreign alkali cations are substituted for extracellular sodium. The explanation offered was that ions that bound relatively tightly to intrachannel sites held the channel open longer but, by staying on sites longer, reduced the current flow (and hence the conductance) across the channel. This very attractive model fails to explain the effects of some large organic cations that reduce both channel conductance and open time. G. Junctional and Extrajunctional Channels
Normally, acetylcholine-activated channels are restricted to the endplate region of muscle fibers, and are referred to as the junctional channels. However, when a muscle is denervated, additional channels appear over the entire muscle membrane. These extrajunctional channels have different properties from junctional channels: their conductance is about half that of junctional channels, and their open time is longer than for junctional channels. In most other respects (e.g., the influence of membrane potential on channel open time), extrajunctional channels appear to share, at least qualitatively, the properties of junctional channels. Use of the patch-clamp technique should allow their properties to be tested more quantitatively. H. Charge Transfer Effects
Gage and Van Helden (1979) showed that the product of the amplitude and time constant of decay of miniature end-plate currents (which is an
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
47
approximate measure of the charge transferred across the membrane) remains fairly constant when other monovalent alkali cations are substituted for extracellular sodium. This “constant charge” effect is also seen with single channels ( y x T = constant). One possible explanation is that there is current-induced salt depletion or enhancement near the mouths of the channels, as outlined in Section 111,H:the channel would close as a particular salt concentration level was reached. At the moment, such suggestions are purely speculative. The whole picture is further complicated by the fact that other combinations of ions such as NH: together with Na+ do not seem to share the constant charge effect (Takeda et a / . , 1980; see also Adams e t a / . , 19811, although this may be related to peculiarities of the NH: ions themselves and to the possibility that some of their conductance may be due to “proton jumping” (Grotthus conductivity). Another possibility in terms of direct ion binding effects has already been outlined in Section V,F.
VI. SUMMARY AND COMPARISON WITH Na+ AND K + CHANNELS IN NERVE AND MUSCLE A. End-Plate Channels 1. The basic external structure of the acetylcholine receptor channel complex in Torpedo is known and presumably is not too different from that in muscle. A reconstruction is shown in Fig. 8. 2. The ion permeability sequence at the amphibian end plate is P T I : P N H ~ : P c , : P R ~ : P K :=P N2.26: ~ : P1.61: I ~ 1.28: 1.17: 1.0:0.9:0.78. This is a low field strength sequence, though not quite in the order of free solution mobilities, and appears to give the impression that the ion sites in the channel are not very selective. 3. Even when correction is made for surface charge effects, divalent ions are relatively permeant [Pc,,/PK 0.04 (corrected), 0.14 (uncorrected)]. 4. Large organic cations permeate the channel, which may have a minimum cross-sectional area of approximately 0.65 x 0.65 nm2(Fig. 10). The very low anion permeability indicates that there are negative groups within the channel. 5 . The equilibrium constant sequence, obtained from conductancevoltage curves, is KI,l : KNH4: K N , :, KK : KC,,= 7 : 4 : I .7 : I .O : 0.9 (see Table VLlI). This is the Eisenman sequence XI for the alkali cations, a high field strength sequence. The relative mobility (rate constant) sequence is in the inverse order--uc, : l i K : NN., : I I N I ~: 111 ~ = I .4 : I .O : 0.58 : 0.42 : 0.13.
-
I
48
PETER H. BARRY AND PETER W. GAGE
End plate
dlmenslons = 0.6Sx0.66 nm area = 0.403 nmz y=27ps
Na*
K+
dlmenslons = 0 . 3 1 x O . S 1 nm ares =0.168 nm* y =7ps
dlameter = 0.33 nm area = 0.086 nm* y = 4ps
FIG.10. Hypothetical cross sections showing the minimum cross-sectional area or areas available for permeation in amphibian muscle and nerve, drawn with a grid size of 0.1 nm. A comparison can readily be made between the dimensions of the end-plate channel and the Na+ and K+ channels, although the specific conductance of the end plate in pS nm-? is not that much larger than that of the other two channels (see Section V1). The figure, redrawn from Dwyer ct ul. (1980, Fig. 7, and the accompanying data), is based on the dimensions of large permeant and impermeant cations given in that paper and in Hille (1975b).
6. There are opposite changes in conductance and in open time when membrane potential is changed; conductance increases and open time decreases as the membrane is depolarized. For the alkali cations the product of conductance and open time is approximately constant (at any fixed potential). 7. In standard physiological solutions, end-plate conductance is about 27-28 pS in amphibia. The specific conductance per minimum crosssectional area is about 70 pS nm-*. 8. Two permeation models fit the data: either a “long” channel (obeying electroneutrality) lined by a number of neutral sites with high field strength and negative polar ends or, more likely, a “short” channel (violating electroneutrality) lined by a number of charged sites with high field strength. B. Depolarization-Activated Na’ and K+ Channels in Nerve and Muscle
Some of the selectivity properties of sodium and potassium channels are briefly listed here for comparison with end-plate channels. For an overview, see HilIe (1975b), Dwyer et al. (1980), and Edwards (1982).
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
49
1 . SODIUM CHANNELS
I . The permeability selectivity of sodium channels is very much greater than for end-plate channels. For example, in internally perfused squid giant axon P l ~: PNCI l :P K : Pith : Pc, = I : I .0 : 0.083 : 0.025 : 0.016, which is a high field strength sequence between Eisenman sequence XI and sequence X . For frog node of Ranvier, the sequence is PNcI PI, PNH4 : PK = I .O :0.96 0. I 1 0.048. 2. Sodium channels are specifically blocked by tetrodoxotin when applied to the extracellular surface of the membrane. The alkaloids aconitine and batrachotoxin reduce the magnitude of the above selectivity but not the sequence, suggesting that they enlarge any selectivity filters and increase hydration of the channel. 3. Organic cation permeability studies suggest a minimum cross-sectional area of 0.31 x 0.51 nm2 = 0. IS8 nm2, much smaller than the crosssectional area of end-plate channels. 4. The single-channel conductance is -7 pS. The specific conductance per minimum cross-sectional area is -44 pS nm-*. 5. Actual equilibrium constant ( K ) or mobility ( M ) sequences have not been determined. 2 . POTASSIUM CHANNELS 1. The permeability sequence found in frog node of Ranvier is PTI: PK : PRb : PNH4 : Pidl: PNn = 2.3 : I . 0 :0.91 : 0.13 : <0.018 : <0.010. This is more selective in terms of its range of selectivities, but represents an intermediate field strength sequence, Eisenman sequence Va (Table 11). In frog muscle the sequence is P K : P K b :Pc-:PNd: = I .O :0.95 : 0. I I : 0.03 :0.02, which is Eisenman sequence 1V. 2. K t channels are blocked by tetraethylammonium ions and 4-aminopyridine. In squid, tetraethylammonium blocks more effectively when applied to the intracellular surface of the membrane. 3. From organic cation permeability studies the minimum cross-sectional area is a circle, 0.33 nm in diameter, or 0.086 nm2 (Fig. lo), which is very much smaller than in end-plate channels. 4. The single-channel conductance is 4 pS, which gives a specific conductance per minimum cross-sectional area of about 47 pS nm-?, similar to Na+ channels but somewhat less than end-plate channels. 5 . Again, actual equilibrium constant ( K ) or mobility ( u ) sequences have not been measured. ACKNOWLEDGMENTS We would like to acknowledge the support of the Australian Federal CPPER Grant and the Australian Research Grants Scheme during the preparation of this article. We would also
50
PETER H. BARRY AND PETER W. GAGE
like to express our appreciation to Elaine Bonnet and Cynthia Prescott for their help in its preparation and to Drs. G. D. Lamb, R. E. Wachtel, and Nino Quartararo for their helpful comments.
REFERENCES Adams, D. J . , Nonner, W . , Dwyer, T. M.. and Hille. B. (1981). Block of endplate channels by permeant cations in frog skeletal muscle. J . Gen. Physiol. 78, 593-615. Adams, D. J., Dwyer, T. M . , and Hille, B. (1980). The permeability of endplate channels to monovalent and divalent metal cations. J . Gen. Physiol. 75, 493-510. Barry, P. H. (1974). Cation permeability and selectivity in biological membranes. Proc. Aust. Physiol. Phurmucol. Soc. 5 , 10-17. Barry, P. H.. and Diamond, J . M . (1984). Effects of unstirred layers on membrane phenomena. Physiol. Rev. 64, in press. Barry, P. H., Gage, P. W., and Van Helden, D. F. (1979a). Cation permeation at the amphibian motor end-plate. J . Membr. Biol. 45, 245-276. Barry, P. H . , Gage, P. W., and Van Helden, D. F. (1979b). Cation permeation through single end-plate channels. Inr. Conyr. Ser.-Excerpta Med. 473, 174-184. Begenisich, T., and Cahalan, M. (1979). Non-independence and selectivity in sodium channels. Membr. T r u m p . Processes 3, 113-122. D’Arrigo. J . (1978). Screening of membrane surface charges by divalent cations: An atomic representation. A m . J . Physiol. 235, C 109-C 117. Diamond, J . M., and Wright, E. M. (1969). Biological membranes: The physical basis of ion and non-electrolyte selectivity. Annu. Reu. Physiol. 31, 581-646. Dreyer, F. (1982). Acetylcholine receptor. Br. J . Anaesthol. 54, 1 15-130. Dwyer, T. M., Adams, D. J., and Hille, B. (1980). The permeability of the end-plate channel to organic cations in frog muscle. J . Gen. Physiol. 75, 469-492. Edwards, C. (1982). Commentary. The selectivity of ion channels in nerve and muscle. Neuroscience 7, 1335-1366. Eisenman, G. (1965). Some elementary factors involved in specific ion permeation. I n t . Cony. Ser.-Excerptu Med. 87, 489-506. Eisenman, G. (1969). Theory of membrane electrode potentials: An examination of the parameters determining the selectivity of solid and liquid ion exchangers and of neutral ion sequestering molecules. N E S Spec. Publ. ( U . S . )314, 1-56. Gage, P. W. (1976). Generation of end-plate potentials. Physiol. Rev. 56, 177-247. Gage, P. W., and Hamill, 0. P. (1981). Effects ofanaesthetics on ion channels in synapses. I n “Neurophysiology. IV. International Review of Physiology” (R. Porter, ed.), pp. 1-45. Univ. Park Press, Baltimore. Gage, P. W., and Van Helden, D.(1979). Effects of permeant monovalent cations on endplate channels. J . Physiol. (London) 288,509-528. Goldman, D. (1943). Potential, impedance and rectification in membranes. J . Gen. Physiol. 27, 37-60. Hamill, 0. P., Marty, A., Neher, E., Sakmann, B., and Sigworth, F. J. (1981). Improved patch-clamp techniques for high-resolution current recording from cells and cell-free patches. Pfuegers Arch. 391, 85-100. Hille, B. (17Sa). Ionic selectivity, saturation and block in sodium channels. A four-barrier model. J . Gen. Physiol. 66, 535-560. Hille, B. (1975b). Ionic selectivity of Na and K channels of nerve membranes. Membrunes 3, 255-324.
IONIC SELECTIVITY OF CHANNELS AT THE END PLATE
51
Hodgkin, A. I,.. and Huxley, A . F. (19.52). The components of membrane conductance in the giant axon of Loligo. J . Physiol. (Loridon) 116, 473-496. Hodgkin, A . L., and Katz, B. (1949). The effects of sodium ions on the electrical activity of the giant axon of the squid. .I. Physiol. (London) 108, 37-77. Horn, R.. and Brodwick, M. S. (1980). Acetylcholine-induced current in perfused rat myoballs. J . Geri. Physiol. 75, 297-321. Horn, R., and Patlak. J . (1980). Single channel currents from excised patcheh of muscle membrane. Proc. Nu//. Acud. Sci. U.S.A. 77, 6930-6934. Horn, R.. and Stevens, C. F. (1980). Relation between structure and function of ion channels. C O I ~ ~ I ~ IMCoIlI./ Cell. . S Hioplrvs. I, 57-68, Karlin, A. (1980). Molecular properties of nicotinic acetylcholine receptors. In “The Cell Surface and Neuronal Function” (C. W . Cotman, G . Poste, and G. L. Nicolson, eds.). pp. 191-260. ElsevieriNorth Holland. Amsterdam. Krasne, S . ( 1978). Ion selectivity in membrane permeation. 111 “Membrane Phyqiology” (T. E. Andreoli. J . F. Hoffman. and I). D. Fanestil. eds.), pp. 217-241. Plenum. New York. Krasne, S., and Eisenman, G. (1973). The molecular b of ion selectivity. Mernbrunes 2, 277-328. Lassignal, N . L., and Martin, A. R. (1977). Effect of acetylcholine on postjunctional membrane permeability in eel electroplaque. J . Gen. Physiol. 70, 23-36. Lauger, P. (1973). Ion transport through pores: A rate-theory analysis. Biocliirn. Biophys. Acru 311, 423-441. LSiuger, P. (1976). Diffusion-limited ion flow through pores. Biochirn. Biophys. A c / u 455, 493-509. Levitt. D. G. (1982). Comparison of Nernst-Planck and reaction-rate models for multiply occupied channels. Biophys. J . 37, 575-587. Lewis, C. A. (1979). Ion concentration dependence of the reversal potential and the single channel conductance of ion channels at the frog neuromuscular junction. J . P1iv.siol. (Lotidon)286, 4 17-445. Lewis, C. A , , and Stevens, C. F. (1979). Mechanism of ion permeation through channels in a postsynaptic membrane. Memhr. Truiisp. Proc.esses 3, 133- IS1 . Neher, E.. and Stevens, C. F. (1977). Conductance fluctuations and ionic pores in membranes. Annu. Rev. Biophys. Bioeng. 6 , 345-38 I . Neumcke. B. (1975). 1l.f memhrane noise generaled by diffusion processes in unstirred solution layers. Bioplivs. S r r i r c / . M t v l i . 1, 295-309. Robinson. R. A , , and Stokes. R . H. (196.5). “Electrolyte Solutions,’’ 2nd ed. Butterworth, London. Singer, S. J.. and Nicholson, G. L. (1972). The fluid mosaic model of the structure of cell membranes. Science 175, 720-73 I . Takeda, K., Barry, P. H.. and Gage, P. W . (1980). Effects of ammonium ions on end-plate channels. J . G m . Pliysiol. 75, 589-613. Takeda, K.. Gage, P. W . , and Barry, P. H . (1982a). Effects of divalent cations on toad endplate channels. J . Membr. Biol. 64,S5-66. Takeda. K., Barry, P. H., and Gage. P. W . (1982b). Effects of extracellular sodium concentration on null potential. conductance and open time of end-plate channels. Proc,. R . S o c . Loridow. .SPY. B 216, 225-251. Urry. D. W . ( 1979). Molecular perspectives of monovalent cation selective transmembrane channels. Inr. Rev. Neirrobiol. 21, 31 1-334.
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Gating of Channels in Nerve and Muscie: A Stochastic Approach RICHARD HORN Depurtment of Physiology
School of Medicine University of Cnliforniu, Los Angelcr Los Angeles, California
I. Introduction: Overview and Scope.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. General Properties ... .............. ........... A. Voltage Depende ............................................ B . Dependence of Conduct;tnce on Agonists and Drug C. Inactivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Permeant Ion Effects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Temperature Dependence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Single-Channel Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G . Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I I I . Stochastic Representation of Channel Gating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Characteristics of Independent Channels . . . ...................... B. Exponentiiil Distribution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Runs Analysis. . ............... D. Markov Represe E. Waiting Time Distribution5 . . . . . . . . . . . . . . F. Estimation of Parameters in Stochastic Models of Gating . . . . . . . . . . . . . . . . G . Macroscopic and Gating Current\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1V. Experimental Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Agonist-Activated Channel\. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . Calcium-Activated Potassium Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . Voltage-Activated Channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.
53 54 55 61
64 66
69 70 70 73
8.5 86 XX XX 89 91 92
INTRODUCTION: OVERVIEW AND SCOPE
Theoretical examination of ion channels is usually divided into two broad categories, permeation and gating. Loosely speaking, permeation 53 Copyright c 1984 hy Academic Press. Inc. All right5 of reproduction in any form reserved. ISBN o - I ? - I ~ z I - ?
54
RICHARD HORN
describes the biophysical properties of open channels, and gating is the process which underlies the opening and closing of channels. This simplistic view suggests that channels are merely rigid pores which can be opened and closed by a gate. It is becoming apparent, however, that open channels are not necessarily rigid pores, and that gating processes, when fast enough, cannot be distinguished from open channel properties. In spite of this ambiguity, channels often appear to open and close in discrete jumps. This article addresses some of the experimental and theoretical details of this process (for more on the permeation process itself, see Barry and Gage, this volume). Ultimately, the goal in studies of gating is an understanding of the molecular processes underlying the conformational changes which proteins use to regulate ion flow across the cell membrane. This goal requires a knowledge of the structural, biochemical, and electrophysiological properties of the channels of interest. An understanding at this level is not available now for any one type of channel, but the use of a variety of new experimental and theoretical tools suggests that the subdisciplines which aspire to understand the gating of ionic channek will begin to converge on a reasonable molecular description. Because of the vast literature on many types of ionic channels, I am forced to present an overview of the field rather than a comprehensive review. In order to further narrow the scope, I only consider channels in nerve and muscle membranes. My intention is to discuss a number of general themes, which I will illustrate with examples from the recent literature. Since I am most familiar with the properties of acetylcholine receptor (ACh) channels and voltage-activated sodium channels, many of the examples are chosen from studies of these channels. I have deliberately emphasized a viewpoint of gating based on its inherently random nature. The randomness seen in current fluctuations (i.e., noise) and in single-channel recording has been both a nightmare for analysis as well as an incredibly rich source of kinetic information. A synopsis of the theory underlying the analysis of some aspects of random data is presented here. 1 have not discussed the theory relevant to fluctuation analysis, since it has been adequately covered elsewhere (Stevens, 1972; Conti and Wanke, 1975; Colquhoun and Hawkes, 1977; Neher and Stevens, 1977; De Felice, 198 I). 11.
GENERAL PROPERTIES
Several aspects of gating are common to most, if not all, types of ionic channels. These will be discussed in general terms in this section.
GATING
OF CHANNELS IN NERVE AND MUSCLE
55
A. Voltage Dependence Gating of ionic channels is generally dependent on transmembrane potential. The only channel in nerve or muscle which seems to have voltageindependent gating is the calcium-activated nonspecific channel described by Colquhoun et a / . (1981) and Yellen (1981). In other known channels, voltage either is directly responsible for gating (e.g.. the conductances associated with the action potential). or else modulates the gating of a channel (e.g., the ACh-activated end-plate channel). The effects of voltage can be observed in a variety of ways, as listed below. 1. EFFECTOF VOLTAGEON MACROSCOPICCONDUCTANCE
Perhaps the simplest measurement of voltage dependence is that of the macroscopic conductance-voltage (g- V) characteristics of a membrane containing ionic channels. A typical example is given in Fig. Ib, which plots the steady-state g-V relationship for ACh-activated channels in tissue-cultured, embryonic rat muscle. The data points were obtained (Fig. la) by applying a series of command pulses to a voltage-clamped rat myoball in the presence of iontophoretically applied acetylcholine (see Horn and Brodwick, 1980). The current response to a voltage step is a “relaxation” from an initial value to a steady-state value; the latter is then plotted as conductance by dividing the current by its driving force. Since the instantaneous conductance is nearly independent of voltage (Magleby and Stevens, 1972; Horn and Brodwick, 1980), the increased steady-state conductance at hyperpolarized potentials can best be described as an effect of voltage on the probability that a channel is open. This effect can come about in either or both of two ways. Channels may open more frequently and/or stay open longer at hyperpolarized voltages. For the ACh-activated channel it is generally believed that the opening rate has little voltage dependence. Instead. hyperpolarization causes an instantaneous increase in the dwell time in the open state. When the membrane is suddenly hyperpolarized, channels which are open tend to stay open longer. Although the rate of arrival of channels to the open state is not affected by the voltage step, channels which do open tend to get trapped longer in the open configuration. As the number of open channels increases, the current relaxes to its steady-state value. Theoretically one might expect that sufficient hyperpolarization would increase the open time of the channels so much that the probability that a channel is open would approach unity. This limiting relationship has never been found for the ACh-activated channel, partly because it has only a mild voltage dependence. It is found, however, in several other
RICHARD HORN
56
50 nA
.
*-
-aL
10 ms 5 0 ms
8000
v,
-
c
Y
al
g 600-
0 c V 3 U
c 0
0
400-
---
GATING OF CHANNELS IN NERVE AND MUSCLE
57
channels, such as the voltage-activated Na+, K + , and Ca’+ channels of nerve and muscle (see below), and the K’ channel of sarcoplasmic reticulum (cf. Miller et af., this volume). In order to make sense of the macroscopic I-V relationship it is important to consider that the single-channel current is voltage dependent. Suppose the single-channel current is expressed as i ( V ) . If i ( V ) = cV, where c is a constant, then the open channel is ohmic and has conductance c . Some channels are never ohmic (e.g., Ca2+channels; see Hagiwara and Byerly, 1981), and others are ohmic only under particular ionic conditions. For example, if a channel is much more permeable to K+ than to Na+, its i-V relationship in physiological conditions, where [K+] is high only at the intracellular membrane surface, will not be straight, but will tend to show outward rectification, i.e., more conductance at positive than negative voltages (see also Barry and Gage, this volume). Since i ( V ) is generally not linear, the macroscopic I-V relationship is influenced by the shape of the i-V relationship. For simplicity, one can consider that the membrane under study is made up of a homogeneous population of independently gated channels. For studies of gating, the variable of interest is p ( V ) ,the relationship between the equilibrium probability that a channel is open and voltage. (Later 1 will discuss the time dependence of this probability.) Suppose the membrane has N channels. The steady-state current I ( V ) can be written I ( V ) = N p ( V ) i(V). Rearranging gives p ( V ) = I(V V [ N i( V ) ] . The shape of the i-V relationship can be obtained from the “instantaneous” current-voltage relationship (Hodgkin and Huxley, 1952). Then i( V ) is used to correct the measured I-V relationship to give the p-V relationship. In many cases neither N nor i is known at any voltage. Therefore p is also unknown. Howevcr, if p is strongly voltage dependent, the p-V relationship can extend from p = 0 to p = 1.0 within a measureable voltage range. I n this case the p-V relationship can be scaled to give proper values for p without knowing N or the single-channel current. Figure 2a shows the current-voltage (I-V) relationship for steady-state K+ current in squid axon, obtained by measuring the current at the end of a 150-msec depolarization to the indicated voltage. Figure 2b shows the p-V relationship for the same data after correction for instantaneous rectification. Between about -60 and +20 mV the probability that a channel is open increases from 0 to 1.0. Such a sigmoidal relationship can originate from a very simplistic model of gating, in which the rate of opening increases and that of closing decreases, exponentially with voltage (see Ehrenstein and Lecar, 1977). It is noteworthy that the direction of the p-V relationship is not the same in all ionic channels. The channels associated with the action poten-
58
RICHARD HORN
0.21
-50
-25 0 Membrane
25 50 75 Potential ( m V )
FIG.2. (a) I-V relationship for steady-state K + currents from squid axon. Experimental conditions as in Horn er a / . (1980). (b) P-V relationship for the same currents, after correction for instantaneous rectification (see text).
tial tend to be opened by depolarization (e.g., Fig. 2), although a regenerative hyperpolarization has been observed in muscle of the nematode Ascaris (Del Castillo et al., 1964; Byerly and Masuda, 1979). As mentioned earlier the end-plate conductance is enhanced by hyperpolarization.
2. EFFECTO F
VOLTAGE ON K I N E T l C S
Perhaps the most striking effect of membrane potential on the behavior of ionic channels is that on the time course of macroscopic currents. Voltage affects not only the steady-state level of conductance, but also the rate at which it is reached. This can be seen in both Figs. I and 3 , where depolarization speeds the kinetics of macroscopic ionic currents. This effect of voltage can be conceptualized as follows. Suppose an individual channel can exist in either of two configurations, open or closed, and that depolarization favors the open configuration. That is, the closed configuration becomes increasingly unstable as the membrane is
GATING OF CHANNELS IN NERVE AND MUSCLE
59
I nA
FIG.3. Whole-cell recording of Na’ currents from tissue-cultured GH3 cells, using the methods of Hamill ei d.(1981). Cell internally perfused with CsF. Inward currents elicited by a series of voltage steps in 10-mV increments from -60 to +40 mV starting at a holding potential of - 120 mV. Leakage and capacitative currents removed by a P/-4 procedure (Horn rr a / . . 1984). (Data from an unpublished experiment by Dr. Carol Vandenberg.)
depolarized; therefore the “dwell time” in the closed state will become shorter with depolarization. This is equivalent to saying that the rate of transition from closed to open increases with depolarization. The dwell time can be measured on the single-channel level, whereas rates are seen in macroscopic currents. This process can be written as a kinetic scheme as follows I f
?f e0 !.I
where k , and k - , are the voltage-dependent “rate constants,” and C is the closed, and 0 the open, form of the channel. A step depolarization will, in the simplest case, increase kl and decrease k - , , leading to a macroscopic relaxation. The rate of the relaxation is k , + k - , (see Section 111, below), which for a simple model (cf. Ehrenstein and Lecar, 1977) is a concave function of voltage, increasing at both depolarized and hyperpolarized voltages. The time course of the relaxation after a voltage step can, of course, be quite complicated for more complicated kinetic schemes.
3. GATINGCURRENTS Hodgkin and Huxley realized in 1952 that, since the conformations of Na+ and K + channels of squid axon are sensitive to voltage, a transient capacitative current must accompany the gating of these channels. Put simply, voltage causes a rearrangement of charged groups and dipoles in the channel protein. The movement of these charged groups across the membrane, in response to a voltage step, causes a transient current, called either “asymmetry current” or “gating current.” The total charge moved by a voltage step can be caused to move back to its original
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RICHARD HORN
location by stepping the voltage back to its original value. A step depolarization is usually said to induce an “on” gating current, and the return to a negative holding potential causes an “off’ gating current. The total charge carried by these two components must be the same, although in practice slow components of the “off’ current may be difficult to detect. The time course of gating current is similar in many ways to that of the macroscopic ionic current, which in general is not transient. Both can be fitted by sums of exponentially decaying components. The time constants are the same for both types of currents. The differences between these currents are the preexponential weighting factors and the absence of a steady-state value for gating current after a voltage step. This is discussed in Section III,G. The interested reader is also referred to several recent reviews (Almers, 1978; Armstrong, 1981; Bezanilla, 1982; French and Horn, 1983). B. Dependence of Conductance on Agonists and Drugs
A number of ionic channels depend critically for their functioning on interactions with naturally occurring chemicals, such as agonists. Although the end-plate channel is sensitive to voltage, and will open spontaneously in the absence of ACh (Brehm et al., 1983; Sanchez et al., 1983), its primary function is to open in response to a release of ACh by the motor nerve terminal. The same is true for many types of synaptically activated ionic channels. The agonists affect the probability that such channels are open, and therefore the conductance of a patch of membrane containing a population of channels. Stated in this way, the actions of agonists can be considered to be gating mechanisms. Kinetically, an agonist affects the order of a gating transition. For example, suppose a channel has two states, open and closed. The simplest gating mechanism for such a channel is a first-order transition between the states. If the reaction C --., 0 requires the binding of a molecule of agonist to the open channel, the reaction becomes second order, depending both on the agonist concentration and on the probability that a channel is in the closed configuration. A variety of drugs influence the gating of ionic channels in myriad ways. It is beyond the scope of this article to discuss these effects. However, the reaction of quaternary derivatives with ACh-activated channels is worthy of comment. The simplest version of this process is analyzed and discussed by Neher and Steinbach (1978). They suppose that the ACh-activated channel (in the absence of the drug QX-222) behaves kinetically like a two-state channel,
GATING OF CHANNELS IN NERVE AND MUSCLE
61
where p* << a. QX-222 blocks the open channel, adding another kinetic state to the above reaction. Now the kinetics can be described by
The openings occur in bursts, as the QX-222 binds and unbinds from the open channel. The binding rate is linearly dependent on [Q], the concentration of the drug. When the drug unbinds with rate F, the channel returns to the open state. The bursting, or flickering, continues until the channel reaches state C I .The appearance of bursts requires that [Q]G and F be bigger than a . For example, if lQ]G is less than a , an open channel will tend to go to C,, rather than C2. Bursting is a common property of many types of channels, and is discussed briefly in Section II,F,3. C. Inactivation
Most ionic conductances, after being activated by an appropriate stimulus, such as voltage or an aganist, will spontaneously inactivate. Agonistactivated conductances are usually said to “desensitize,” rather than inactivate, but the meaning is the same. Inactivation is a striking feature of the voltage-activated Na+ and Ca2+channels, where it is rapid (nearly on the same time scale as the activation process) and can produce a substantial reduction in the conductance (Fig. 3). In other channel types, such as K + channels or ACh-activated channels, inactivation is a slower process with respect to the activation of channels by voltage or by acetylcholine. The importance of inactivation is easy to understand on a teleological level. Excitable cells are designed to process and transfer information. In most cases information is contained in transient, rather than steady-state, phenomena. A nerve fiber, for example, passes a train of action potentials as a signal. If Na+ channels in a nerve fiber did not inactivate, action potentials would tend to have longer durations, which would limit the fiber’s ability to respond to successive stimuli. Similarly, postsynaptic receptors are often designed to respond to transient releases of agonists. A steady leak of agonist from a presynaptic terminal would, in this view, desensitize this synaptic pathway, rather than continuously activate i t . It is important to distinguish between inactivating a channel and “deac-
62
RICHARD HORN
tivating” it. A channel opened by a depolarization can be deactivated by a hyperpolarization. It is then ready to be activated again. A channel opened by an agonist can be deactivated by removing the agonist. However, an inactivated, or desensitized, channel cannot be opened by intensifying the activating stimulus. On the contrary, the activating stimulus enhances the inactivation process. The mechanisms underlying inactivation are the subject of considerable controversy. This topic has been reviewed extensively, especially for Na’ channels (Meves, 1978; Neumcke et al., 1978; Armstrong, 1981; Bezanilla, 1982; French and Horn, 1983), Ca2+channels (Hagiwara and Byerly, 1981; Tsien, 1983; Eckert and Chad, 1984), and ACh-activated channels (Adams, 1981; Steinbach, 1980; Peper et al., 1982). I will mention only a few important concepts which have emerged from studies of these channels. First of all, inactivation appears to involve, at least for Na+ and AChactivated channels, a conformational change of the channel protein. In the Na+ channel this can be inferred by the fact that inactivation “immobilizes” the gating current associated primarily with the activation gates. Experimentally, charge immobilization is seen from the fact that the activation gating current associated with a step depolarization carries more total charge than the “off’ gating current at the end of the depolarization. The loss of charge depends on the pulse duration, being negligible for very short pulses and increasing, roughly with the same time course as the inactivation of the macroscopic Na+ current at that voltage (Armstrong and Bezanilla, 1977). Conformational changes associated with the inactivation of the AChactivated channel are inferred from the fact that inactivation is accompanied by changes in the affinity of the receptor for a number of ligands, including ACh and histrionicotoxin (Heidmann and Changeux, 1979; Weiland and Taylor, 1979; Neubig et al., 1982). It has been postulated that Na+ channels inactivate by the occlusion of the open channel with a positively charged polypeptide chain which is a component of the channel protein, located at the intracellular surface of the membrane (Armstrong, 1981; Brodwick and Eaton, 1982; Yeh, 1982). The evidence for this viewpoint comes mainly from the fact that a number of reagents, such as pronase, trypsin, and N-bromoacetamide, appear to cleave the inactivation gate from the intracellular membrane surface, leaving a channel which can only activate. The inactivation can then be restored by placing large, charged molecules into the cytoplasmic compartment (Brodwick and Eaton, 1982; Yeh, 1982). Ca2+channels in most preparations (however, see Fox, 1981) have evolved an ingenious variation on this method of inactivation. They use Ca2+ions as the inactivation gate (Hagiwara and Byerly, 1981; Tsien, 1983; Eckert and Chad, 1984). At
GATING OF CHANNELS IN NERVE AND MUSCLE
63
rest, the cytoplasmic concentration of free Ca?+is very low. Upon activation of the Ca? channels, however, Ca'+ enters the cytoplasmic compartment where it can bind to the Ca2+channel and inactivate it. The rate and extent of inactivation depend on the influx of Ca?' ions, and not directly on membrane potential. Both Nat and CaZ+channels use a form of negative feedback control of conductance. In Na+ channels the relevant signal is membrane potential, which activates channels and (either directly or indirectly) leads to inactivation. Effective signal transmission requires a rapid repolarization after an action potential. This is the job of Na+ inactivation. Ca2+ions, on the other hand, are well known to serve a number of functions as intracellular messengers. The relevant signal in Ca2+ channel activation, therefore, may be the intracellular concentration of free Ca2+.Thus it is important to regulate the influx of Ca2+into the cell, regardless of the membrane potential. Ca2t ions do this directly by acting as the inactivation mechanism of the conductance pathway which catalyzes the influx. A final point about mechanisms of inactivation concerns the voltage dependence of Na+ channel inactivation. Depolarization can either close inactivation gates directly, or else lead to inactivation via the opening of the activation gates. The current evidence favors the latter view, although both processes seem to be operative (Armstrong, 1981; French and Horn, 1983; Aldrich et a / . , 1983). It should be noted that some channels have not been reported as showing evidence of inactivation. These include the K + channel of sarcoplasmic reticulum (Miller et uf.,this volume), the voltage-activated Na+ channel in frog oocytes (Baud et ul., 1982; Schlichter, 1983), and the Ca2+-activatedK' channel in rat myotubes (Barrett et ul., 1982). D. Permeant Ion Effects
The Hodgkin and Huxley (1952) treatment of the conductance changes during a voltage clamp pulse considered that open channels were approximately ohmic. Voltage influenced the proportion of open channels by a direct effect on the channels. Gating did not depend, for example, on the type of permeant ion or, for that matter, on the presence of any permeant ion. Gating was also presumed to be independent of the magnitude or direction of current flow through the channels. This idea was tested in experiments with squid giant axon, in which the ionic composition can be controlled on both sides of the membrane. The results were generally consistent with the conclusions of Hodgkin and Huxley (see, e.g., Chandler and Meves, 1965). Other investigations, however, were not consistent with this view. For example, Meves and Vogel(1973) measured an inward current carried by
64
RICHARD HORN
Ca2+ions through the Na+ channel in squid giant axon. The time course of this current is much different from that seen when Na+ carries the current. It is slower, and the inactivation process is less pronounced. More recently Gage and Van Helden (1979) studied the effects of alkali metal cations as permeant species at the end plate of toad skeletal muscle. In general as the ionic radius decreased, from Cs+ to Lit, the singlechannel conductance decreased, and the duration of miniature end-plate currents (mepc’s) increased. Noise measurements also revealed slower fluctuations for smaller ions (Barry and Gage, this volume). Marchais and Marty (1979) found a similar phenomenon at an AChactivated channel in Aplysia neurons. They interpreted their results in the following manner. When the channel is occupied by an ion, it cannot close. (This is reminiscent of the effects of QX-222 on end-plate channels.) Ions which tend to dwell in the channel for a long time have a low conductance, and also keep the channel open longer. The slower rate of closing will lead to slower mepc’s and current fluctuations. It should also lead to longer open times in single-channel measurements. Recent experiments on amphibian end plate are not consistent with this simple idea of the relationship between ion binding and fluctuations in numbers of open channels (Adams et al., 1981; Barry and Gage, this volume). The situation appears to be more complicated. So far the mechanism underlying the effects of permeant ions on the gating of end-plate channels remains a mystery. The most striking example of the effect of a permeant ion on gating is seen in Ca2+channels. As discussed above, the inactivation of Ca2+current in many preparations can be explained by the accumulation of Ca2+ ions at the intracellular membrane surface during a depolarization. Other ionic species, such as Ba2+,which can carry inward current through Ca2+ channels, are much less effective at causing inactivation of the inward current. E. Temperature Dependence
Cooling has the general effect of slowing kinetic processes. Two aspects of the effect of temperature are discussed here: first, the relative effect of temperature on permeation vs gating, and second, the form of the relationship. Permeation can be visualized as the diffusion of ions over one or a series of energy barriers. Provided that the barriers are not too high (in which case the single-channel current would be very small), the effect of temperature on single-channel current should be similar to its effect on the diffusion rates of ions in free solution. In other words the single-
GATING OF CHANNELS IN NERVE AND MUSCLE
65
channel current should have a QI(,of 1-1.5. Gating, on the other hand, is thought to involve conformational changes in membrane-bound proteins. A large enthalpy for such reactions is consistent with the slow rates of gating (on the order of microseconds to seconds, by comparison with nanoseconds for permeation). Typically Qrovalues of 3 or more are found for rates of gating processes ( e . g . , see Magleby and Stevens, 1972; Schwarz, 1980; Beam and Donaldson, 1983). The above discussion, by considering a for gating, assumes that the effects of temperature are simple, i.e., a 10°C increment of temperature will cause a factor of Qlnincrease in the rate of channel gating. But what rate is relevant? All kinetic schemes have at least two rate constants, and usually many more than that. Consideration of such gating schemes makes it unlikely that the temperature dependence will be simple. Suppose, for example, that a channel has the gating scheme
ell,
where C, is a closed state and 0 is an open state. Let each rate constant be expressed using the formalism of absolute rate theory (Glasstone et al., 1941),
k, =
u
exp(-AGilRT)
where u is a vibration, or attempt frequency, on the order of l0l3 sec-I at room temperature, and AGf is the activation free energy change for a particular transition in the usual RT units. The rate constant k, is a reflection of the free energy barrier for a conformational change. This free energy has both enthalpic and entropic components. That is
AGf
=
AH! - TASf
where A H j and AS: are the activation enthalpy and entropy, respectively, for some transition. Combining the above equations gives
In k,
=
In
u -
AHjIRT
+ ASfIR
The relationship between k, and temperature for a given reaction rate is often plotted as In k, vs 1/T, which is known as the Arrhenius plot. The slope of this relationship depends on AW, but not AS:. Therefore, the enthalpic contribution of the activation energy for a given transition will determine its temperature dependence. Usually individual rate constants are not measured in studies of the effects of temperature on gating. Instead time constants, such as the activation, inactivation, or end-plate current time constants, are measured. In complex schemes, such as the four-state model above, the mea-
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RICHARD HORN
sured time constants are a function of all the rate constants (see below), each of which has a different activation enthalpy, in general. Therefore the effects of temperature are expected to be quite complicated. Even if each rate constant could produce a straight line on an Arrhenius plot, the effects of temperature on the time constants will not in general be so simple. This, in fact, is the result observed for potassium currents in mammalian skeletal muscle (Beam and Donaldson, 1983), where the slowest time constant 7nwas examined as a function of temperature. A plot of ln(l/Tn)vs l / T was curved, having a steeper temperature dependence at lower absolute temperatures T . The arguments above also suggest that the time course of macroscopic currents should not, in general, merely be slowed down by cooling. Since the individual rate constants will usually not have the same temperature dependence, the time course of macroscopic currents could be altered by temperature. This also was observed in these experiments of Beam and Donaldson. Only at temperatures above 25°C could the time course of activation be fitted well by the n4 scheme of Hodgkin and Huxley (1952). A similar result was obtained for sodium currents in squid axon, where temperature changes did not produce a simple scaling along the time axis (Bezanilla and Taylor, 1978).
F. Single-Channel Properties
The advent of patch recording has revolutionized studies of gating in biological channels by permitting the direct observation of the opening and closing of individual channels. An example of voltage-activated sodium channels is shown in Fig. 4. The general properties of the gating of single channels are discussed here. I . RAPIDTRANSITIONS BETWEEN CONDUCTANCE LEVELS One might imagine that a channel opens slowly as it undergoes a conformational change from a resting to an activated state. For example, a “gate” could open in tiny increments, with the conductance of the single channel increasing in tiny increments. Alternatively, a channel could flip suddenly into and out of a conducting state. Choosing the correct alternative requires single-channel recording; noise measurements alone cannot do it (Neher and Stevens, 1977). All studies to date show that gates open and close very rapidly. The highest frequency response is obtained with patch recording, largely be1978). Under nearly cause the membrane area is so small (Neher et d., optimal conditions, transitions are as rapid as can be recorded, i.e., <10
GATING OF CHANNELS IN NERVE AND MUSCLE
67
R
?
FIG.4. Single Na' channel currents from outside-out patches of GH3 cells as described in Horn et ul. (1984). The holding potential was -120 mV, and each record shows the current response to a voltage step to -60 mV. Na' currents are random downward events.
psec (Hamill et ul., 1981). Rapid transitions are also observed in channels with multiple conductance levels, such as K t channels in frog sarcolemma (Labarca and Miller, 1981)and ACh receptor channels (Hamill and Sakmann, 1981). The implications of these observations are highly significant for an understanding of gating. Since the observed rates of gating, e.g., from macroscopic currents, are so much slower than the transition rates between conductance states, the process can best be characterized as having a few states with large activation energies for the transitions from state to state. This means that, although a channel undergoes very rapid thermal fluctuations, the probability that a given fluctuation leads to a transition to another state is very low. This view is consistent with an absolute rate theory representation of gating, as discussed above. An alternative viewpoint is that gating is more diffusional in nature, consisting of a great many transitions of low energy (e.g., see Ncumcke ct d.. 1978; Greeff ct al., 1982; Rubinson, 1982). Single-channel recording, at present, is in conflict with the latter conception, since channels seem to dwell at particular conductance levels for longer times than that needed to flip between conductance levels. It is worth considering, however, that the gating process is a mixture of both high- and low-energy transitions. We are a long way from being able to address this conjecture, at least at the experimental level.
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RICHARD HORN
2. EXPONENTIAL DWELLTIMES Fluctuation analysis and single-channel recording show that gating is inherently random. The dwell time of a channel in a particular kinetic state is a random variable. If transitions between states reflect large free energies, then the probability of leaving a state during a short interval At is very low. If this probability does not depend on time, then it can be shown (see Section III,B) that the dwell time Tiin a given state Siis an exponentially distributed random variable. In other words Fi(t) = Prob( Ti It ) = 1 - exp(-hit), where hi is the “hazard rate” for leaving 3;.F i ( t ) is a probability distribution function. Its time derivative, j ( t ) = dFi(t)/dt= hi exp( -hit), is a probability density function. Using the mathematical definition of derivative, f ; ( t ) A t = Prob(t < Ti< t + A t ) for small At. A histogram of dwell times in state Si is theoretically represented by n d f ; ( t ) A t where , the bin size of the histogram is At and the total number of measured dwell times is nd. Theoretically the dwell time within a particular state should be exponentially distributed, and this point could be confirmed by a histogram of dwell times in the state of interest. The difficulty with obtaining this information is that many types of channels have only two conductance levels, open and closed, but more than two kinetic states. For example, a channel may have two closed states and one open state, as in the model C, e CZ$ 0. The transitions between the closed states are invisible from conductance measurements. If a single channel of this type is examined in a patch of membrane, the histogram of dwell times in the open state will be exponentially distributed; however the closed time histogram will generally have two exponentially decaying components (see Colquhoun and Hawkes, 1981, 1982, 1983). Measured dwell times of either open or closed channels are exponentially distributed in several reports (e.g., see Labarca et al., 1980; Fenwick et al., 1982; Sachs et al., 1982; Horn and Standen, 1983; Sakmann et al., 19831, which is consistent with our conception of the energetics of transitions between kinetic states. Nonexponential dwell times (e.g., see Colquhoun and Sakmann, 1981, 1983; Barrett et al., 1982; Cull-Candy and Parker, 1982) may indicate that a channel has either multiple open or multiple closed states. 3. BURSTING Most types of single channels show bursting behavior. A channel may take a long time to reach an open state. Once there it will rapidly flicker open and closed until it reenters a long-lived closed state. This is a burst. Three types of channels which do not show pronounced burstiness are the
GATING OF CHANNELS IN NERVE AND MUSCLE
69
K+channel of sarcoplasmic reticulum (Labarca et al., 1980; Labarca and Miller, 1981), the anomalous rectifier K + channel (Fukushima, 1982), and the voltage-activated Na+ channel (Sigworth and Neher, 1980; Horn et a / . , 1981; Patlak and Horn, 1982; Aldrich ef ul., 1983). The theory underlying the analysis of bursty channels has been thoroughly discussed by Colquhoun and Hawkes (1981, 1982, 1983). G. Memory Memory is a term which has loosely been used in discussions of channel gating. A memoryless process knows only what state (i.e., conformation) it is in. It does not know how long it has been there or by what route it entered this state. A memoryless process can be shown to have an exponentially distributed lifetime, where ‘‘lifetime’’ (used synonymously with “dwell time”) is the random length of time which a process remains in a given state (see Section 111,B). This has many important consequences. Suppose, for example, that a channel has two states, closed and open, each with an exponentially distributed dwell time. An open channel has no memory of when it opened, which means that one can measure dwell time in the open state at any time after a channel has opened. The dwell time in this state will be exponentially distributed with a closing rate that is independent of when the channel opened. This peculiarity has been known for a long time. Its mathematical proof is given Ititer. From this viewpoint, channel gating does not seem to be memoryless in most cases, since single exponential dwell times are not usually found for both open and closed times. On a macroscopic level memory is seen as a dependence of the current at a test voltage on the duration of the prepulse (see Frankenhaeuser and Hodgkin, 1957; Sigworth, 1981). This type of memory is also apparent in “off” gating current, which “immobilizes” as the duration of an activating voltage pulse increases. With this meaning memory can be explained in two ways. First, gating is a random process in which the kinetic states have memory. Second, memory appears in the invisible transitions between memoryless kinetic states which have the same conductance. In the first alternative, the dwell time in a single state will not be exponentially distributed. This is equivalent to saying that the rate of leaving the state depends on when the state was entered. In other words we are no longer dealing with rate “constants.” In mathematical terms this is called a time-inhomogeneous process. The alternative which I favor is that gating is time homogeneous, con-
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RICHARD HORN
sisting of a number of memoryless states, which are either open or closed. Support for this alternative is that measured dwell times can often be fitted well by a discrete sum of exponentially decaying components (e.g., see Barrett et al., 1982; Jackson et al., 1983), which is consistent with a discrete number of states, each with an exponentially distributed lifetime (see below). 111.
STOCHASTIC REPRESENTATION OF CHANNEL GATING
The random nature of channel gating can be seen as a nuisance. In modeling the kinetics, we are usually interested in a reaction scheme with rate constants. Measuring reaction rates in a macroscopic current experiment seems so simple by comparison with trying to make sense out of the apparently chaotic behavior of a small population of channels. The problem with macroscopic experiments, however, is that they provide only minimal information about the underlying kinetics. Single-channel measurements greatly help in decisions about the correct kinetic scheme for a particular process. In this section I discuss some of the expected properties of single-channel gating, from a theoretical viewpoint, and also present some information about the analysis of single-channel data. A. Characteristics of Independent Channels
Typically membrane patches contain more than one channel. A patch may contain, for example, channels of different types, such as sodium and potassium channels. Usually these can be distinguished. Suppose, then, that a patch contains one type of channel. It is important for us to determine whether these channels comprise a homogeneous population. For example, a channel, in the course of its functional life in the membrane, may change its properties as it ages. The changes could be subtle. We would like to be able to detect whether all the channels of the same type, in a patch, have the same properties, i.e., are homogeneous. A related question is the independence of individual channels. A given channel, upon opening, could affect the probability that its neighbors will open. Cooperativity, or anticooperativity, of opening is a form of nonindependence. Unfortunately, there are no precise ways to assess either homogeneity or independence in a population of channels. The usual approach is to examine the behavior of a small population of channels, and ask if it conforms qualitatively with the expectations of an independent, homoge-
GATING OF CHANNELS IN NERVE AND MUSCLE
71
neous population. Qualitative conformity, of course, is not a proof of either independence or homogeneity. Both the binomial and Poisson distributions are stochastic features of a population of independent, homogeneous channels. A brief description follows.
I. BINOMIAL DISTRIBUTION If p ( t ) is the probability that a channel is open at time t , the probability that exactly k channels out of a population of N channels, are open is
where
(T)
N! k!(N- k)!
This is the binomial distribution, which is simply derived from combinatorics for independent channels and the fact that these channels have two conductances, either open or closed. If a channel has three conductance levels (e.g., Labarca and Miller, 1981), a trinomial distribution would be appropriate. The application of Eq. ( I ) to single-channel data requires knowledge of N . This is sometimes trivial (Labarca et al., 19801, but in some cases requires a statistical procedure (Section 111,F).The probability p ( t ) may be a constant for a given set of experimental conditions (e.g., at a constant concentration of agonist), or may vary with time (e.g., for sodium channels after depolarization). In the latter case the process is said to be nonstationary . For a stationary process, p ( r ) = p is estimated by integrating the total time that all channels are open and dividing by Nand by the total time of the observation. The binomial probability, p L ( t ) = PI, is estimated from the fraction of time that exactly k channels are open. The fit to the binomial distribution was excellent both in K' channels of sarcoplasmic reticulum (Labarca et d.,1980) and in calcium-activated K + channels (Barrett et ul., 1982). Nonstationary single sodium channel data were also fitted well by a binomial distribution (Patlak and Horn, 1982; Horn et a / . , 1984). In this case, p ( t ) and pk( t ) must be evaluated at each time point (epoch) after a depolarization. The data consist of the responses to a series of identical voltage pulses. Each response is presumed to be an independent trial, and
72
RICHARD HORN
pk(t) is estimated from the fraction of records having exactly k channels
open. The usefulness of this method of analysis is that it is relatively model independent. One needs to know only that channels have two conductance levels. Other kinetic details are irrelevant. The difficulty with the method is that one does not know what to expect when deviations from independence or homogeneity occur. It is not clear, for example, whether a 10% positive cooperativity would be revealed by an examination of the distribution of the number of open channels. 2. POISSON DISTRIBUTION
It is well known in probability theory that, as the binomial probability p becomes small, the binomial distribution approaches a Poisson distribution, especially if N p remains moderate. In extending our use of the binomial distribution, the probability that exactly k channels are open will be PI
1
(Ak C A ) ) l k !
k
=
0, . . . , N
(2)
where A = N p . This equation is usually not used for this purpose, because of the difficulty in estimating N when N is large and p is small. The Poisson distribution can be used, however, to examine the times when channels open. If the probability that a channel is open is very low, then one might examine the times when an opening event occurs in a population of channels. The Poisson equation in this case is used differently. Suppose that time is divided into At-sized parcels, and that the probability that an opening event will occur during Ar is the constant AAr. The probability that exactly k channels open during A t is Pk(At) =
[(AAr)I
~"'Jlk!
k = 0, . . . , N
(3)
Note that N does not have to be known to use Eq. (3). One might expect that deviations from Eq. (3) would reveal evidence of either cooperativity or inhomogeneity . There are two difficulties with this approach, however. The first is that a single channel often opens in bursts, as mentioned previously. A small population of bursty channels would easily violate Eq. (3), even if they were homogeneous and independent. The violation, explicitly, is that AAt cannot be considered a constant. The second difficulty is that, for N sufficiently large and AAt sufficiently small, an inhomogeneous population of channels will conform to Eq. (3). This will hold even if the kinetics of each channel in the population are complicated. This is an important theoretical result, which will be used later. The proof is given in the following section.
73
GATING OF CHANNELS IN NERVE AND MUSCLE
B. Exponential Distribution
If the times at which a channel opens represent a Poisson process, the waiting time T for the first occurrence of an opening has an exponential distribution. By usual convention, the distribution function for the random variable T is F ( t ) = Prob( T 5 t ) , which is the probability that T is less than or equal to a fixed time C. Now F ( t ) = 1 - Prob(T > t ) =
1 - Prob(na opening events in interval [0, t ] )
I
( At ) " c - ~ ' / O ! - 1 - e-A/ =
-
This is the exponential distribution with parameter (or "hazard rate") A. The associated density function isf(t) = d F ( t ) / d t = he-"'. The probability of a channel opening during the small interval [ t , t + A t ] is approximately
f(W. The exponential distribution has the important Markovian property called "lack of memory." Formally, Prob(7 > t =
+ h I T > t ) = Prob(T > t
(,-A(/+l!l/(,
hl
=
+ h)/Prob(T > t )
Ah
Prob(T > k ) where Prob(T > t + h I T > t ) denotes Prob(T > t + h ) , given that T > t , and where t and h represent intervals of time. The importance of this result is that the time when one begins to sample from a Poisson process is irrelevant. It does not matter, in our previous example, how long channels have been closed when one begins to look for the next opening event, as long as the closed time is exponentially distributed. The time to the next opening event will be exponentially distributed with the same hazard rate. In other words the process does not remember how long the preceding interval was. It only knows that no channels are open at the arbitrary time zero. One of the most important theorems in stochastic processes shows that if the waiting times in successive intervals are independent, the process underlying these waiting times has an exponential distribution. =
THEORLM. Let 7 be a random variable on 10, m] such that Prob(T >
t
+ 12) = Prob( 7 > r).Prob( T > I!).Then T is exponentially distributed.
Proof. Let Y(t ) = Prob( T > t ) and suppose Y'( t ) exists. By assumption Y(r + h ) = Y ( t ) Y ( h )and Y'(t + h ) = Y ' ( t ) Y ( h )
74
RICHARD HORN
or =
Y(t)Y'(h)
depending on whether we differentiate with respect to t or h. Pick any constant h such that Y(h) > 0. Then
Y ( t )= Y'(t + h ) / Y ( h )= [ Y ' ( h ) Y ( t ) l / Y ( h ) If we define A = - Y ' ( h ) / Y ( h ) , then Y'(t) Y ( t ) = e-*(.
=
-AY(t), with the solution
Suppose a membrane patch has many channels, each with rather complicated kinetics. In addition, suppose that the population is not homogeneous, i.e., the channels do not have the same gating kinetics. An important and pertinent result is that if each channel opens only rarely, the times between opening events will be approximately exponentially distributed. The proof is complicated, and uses the theory of renewal processes (Cox, 1962; Feller, 1971). It is presented here because of the simplicity and usefulness of the final result (see Section IV,A). Suppose X I ,X2, . . . are successive random intervals which are independently and identically distributed. The renewal process (S,) is defined by S, = cl=l=, X i . If each X , is distributed as F ( t ) , the renewalfunction of Fk*(t),where FL*(t)denotes the kthe process is defined as U ( t ) = fold convolution of F(t) with itself, and F"*(t)= 1 for t 2 0. It can be shown that U(t) = xF=o Prob(Sk 5 t ) (Cox, 1961). For a given t > 0 there corresponds a chance-dependent subscript N , such that SN,5 t < SN,+1 . Let us define the residual waiting time before the next event after epoch t as SN,+I- t , and denote H ( t , 5) the probability that it is 55. In other words H ( t , 4) is the probability that the first renewal epoch (e.g., channel opening) following epoch t lies between t and t + 5.This occurs if some renewal epoch S, = x 5 t and the following interarrival time lies between t - x and t - x + 5. For a pure renewal process H ( t , 5) = [F(r - x + 5) - F(t - x ) ] d U ( x )
c&o
I,:
(Feller, 1971). For simplicity we denote a ( [ )= F(r renewal theorem states that, in the limit,
=
P
I,: [ I
+ 6)
- F ( t ) . The
-
where p is the expected value of F(t). Now suppose we observe N renewal processes, equivalent to N chan-
GATING OF CHANNELS IN NERVE AND MUSCLE
75
nels. They form a new process in which all their renewal epochs, i.e., openings, form into one sequence. I n general the new process is not a renewal process, but we can calculate the waiting time W for the first opening following epoch 0. Suppose the N renewal processes are mutually independent, but not homogeneous, and the distributions of their interarrival times are F , , . . . , FN with expected values P I , . . , p ~ Let .
.
1/7
= l/p,
+ .. + *
l/p/$
Suppose that the opening of each channel is a rare event. That is, for fixed k and y the probability F d y ) is small and is large. Consider the steadystate situation, where the process has been going on a long time. Let W, be the next opening of the kth channel. Then
For the cumulative process, W is small among the waiting times W,, and hence Prob(W > f) = (I - f / p , ) ( I- dp2). . . ( I - t / p N )= P - " ~ This estimate is made precise as N--, 30. This result shows that in a patch with many channels, each with a low probability of opening, the observed closed time of the patch will be approximately exponentially distributed. This holds even if the closed times of the single channels in the patch have nonexponential distributions. The exponential distribution is frequently used in describing closed times and open times for individual channels. If the kinetics of a channel can be modeled with two states, one open and one closed, then both its open and closed time distributions will be exponentially distributed. For more states the situation becomes more complicated, as we will discover. C. Runs Analysis The detection of randomness can be very difficult. We have already discussed the use of the binomial theorem for examining homogeneity and independence. We have also seen how complicated kinetics can become obscured in membranes containing many channels. How can we test statistically if opening events are occurring at random intervals? Fortunately, a test does exist, based on the technique of riins ancilysis (Feller, 1968; Gibbons, 1971). For simplicity suppose we obtain a continuous record of opening events from a single channel at steady state (Fig. 5 ) . We can arbitrarily divide
76
RICHARD HORN
time into At-sized parcels and ask whether one or more opening events occur in each parcel. Let S indicate a success (meaning at least one opening in a parcel) and F a failure. The continuous record in Fig. 5 can now be represented as a sequence of S’s and F’s. This example yields the following sequence: F, F, F, S, S, F, F, F, F, F, S, S, S, S, F, F, F, F. There are 6 successes and 12 failures in this sequence. One gets the impression from this sequence that successes and failures tend to be clustered, in other words that the order is nonrandom, showing a trend for successes to occur in consecutive parcels. Runs analysis addresses the question of randomness of the ordering of the S’s and F’s. A run is a series of like elements. The above sequence has five runs, which alternate between S’s and F’s. If the S’s tend to cluster together, there will be a tendency for a record to have few runs with many elements in each run. The opposite extreme is for S’s to alternate with F’s. This pattern would produce a large number of runs, each with few elements. Either extreme can be shown to be improbable, if the order of the sequence is completely random. Each parcel of a sequence can be represented as a Bernoulli trial, with a probability a of success and 1 - a of failure. Runs analysis is a simple and elegant use of combinatorial analysis to derive the probabilities of ordering of results of a series of Bernoulli trials. For a sequence having less than 20 successes or failures, Swed and Eisenhart (1943) provided tables of exact probabilities based on the number of runs. For example, in the above example, the most likely number of runs in a sequence of 6 S’s and 12 F’s is nine, which is greater than the five runs observed. The probability of obtaining five or fewer runs is only 0.028. Therefore, we can feel confident in saying that the openings are nonrandomly clustered, since the observed result would occur by chance only about three times out of 100 trials. It is not immediately apparent why one sequence of runs is more probable than another in a series of independent Bernoulli trials. The explana-
FIG.5 . Hypothetical record from a single channel. Current is plotted as a function of time from left to right for two consecutive traces (top, then bottom). The channel opened nine times (see text).
GATING OF CHANNELS IN NERVE AND MUSCLE
77
tion is that there are fewer arrangements of indistinguishable S’s and F’s that give extreme numbers of runs than there are that give intermediate numbers. For example, there are 110 ways to arrange 6 S’s among 18 parcels so that exactly two runs are obtained. On the other hand there are 4125 different arrangements that produce exactly nine runs. For a discussion of the combinatorics involved in this calculation, see Feller (1968). Usually it is possible to obtain much more extensive data than I have shown in this example. Tables of probabilities for numbers of runs are limited; but when the numbers of S’s and F’s are greater than 20 the distribution of the number of runs can be approximated by an asymptotic distribution, forming a standardized random variable Z , with a mean of zero and a variance of one, and
where R i s the number of runs, n is the total number of elements in the sequence, and u , the probability of a success, is estimated by t i S / n , where ns is the number of successes. If Z < - I .5, openings tend to be clustered nonrandomly, since Z has a normal distribution. If Z > 1.5, openings tend to alternate nonrandomly. Intermediate values are consistent with a random ordering. The approximate probabilities can be obtained from a table of the standard normal distribution. The length of the parcel of time used for this analysis can be expected to affect the results. For example, if the time is very long, it will encompass the slow processes causing nonrandom behavior, obscuring them. If the time is too short, then a single long-duration opening could encompass several parcels, which would tend to make random behavior seem nonrandom. A reasonable compromise might be to make the parcels at least long enough to avoid the latter problem. The number of channels will also affect the ability to detect nonrandom clustering, If a patch contains several independent channels, each of which is opening in a nonrandom manner, the openings of other channels will tend to make the process approach Poisson behavior, and thus appear random. The main use of runs analysis could be for the study of slow processes, such as desensitization in ACh receptors (Sakmann el d., 1980), or slow inactivation in Na+ channels (Horn et cil., 1984). It should be added that the theory underlying bursting behavior of single channels can also be used to examine nonrandom clustering of events (Colquhoun and Hawkes, 1981, 1982). An alternative statistical procedure to runs analysis has been used by Gration ef al. (1981).
78
RICHARD HORN
D. Markov Representation of Kinetic Models
Typically, gating models are presented as chemical reaction schemes, with the conformational states of a channel representing “kinetic states” which are connected by rate constants. By assumption, most models are time-homogeneous Markov models. This is a technical term derived from stochastic theory and means that the dwell time in each state is exponentially distributed with a time-independent hazard rate. Again, this implies that each state is memoryless. This is an important, and often untested, assumption. I present some aspects of the theory here, because of its importance and mathematical elegance. Unfortunately, the appropriateness of Markov models is only known in a few types of channels (e.g., the K + channel in sarcoplasmic reticulum, see Miller et ul., this volume). The inability to fit all data to simple Markov models (e.g., see Neumcke et ul., 1978) indicates that other theoretical frameworks are also worthy of consideration. 1. THEORY OF MARKOV PROCESSES’
Consider a finite number of states S I ,S2, . . . , S,. Some transitions are possible between these states. Suppose the system is in state S i . The selection of the next state Sj is made according to the n X n matrix of transition probabilities V = (uij),uji = 0, where vo is the probability that the next state will be S j , given that the system starts in S;. By assumption, the dwell time in Si is exponentially distributed as F;(t)with a mean of p i and a hazard rate A;. The mean dwell time piis the expected value of the lifetime T. If h(t ) = dF;(t ) / d t is the probability density function for the lifetime of S i , its expected value is
Integration by parts shows that p i = l/A;. The successive visits between states constitute a Markov process which is completely characterized by V and by the probability distribution for the initial condition of the process. Let G i j ( t )be the waiting time distribution for the first passage from S; to Sj with a mean of wo. Thus G , ( t ) = Prob(first entry to state S j occurs after a waiting time less than t , given that the process was in Siat time 0). Let P o ( t )represent the proba-
‘
Ediroriul note: Readers who are primarily interested in results, rather than in becoming adept at the theory of Markov processes, might at this stage move on to Section 1II.F.
79
GATING OF CHANNELS IN NERVE AND MUSCLE
bility of being in S, at time t , given that the system was in S, at time 0. The difference between G , ( t ) and P , ( t ) is that the former is only concerned with the time of the first visit to S,. The following theorem shows that the equilibrium probability of being in state S, is the mean dwell time in S,, divided by the mean time between arrivals into S,. THEOREM. lim P , ( t )
= p j ~ ~ ~ , .
I-=
Proof. For i = j ,
This is a renewal equation. It has two parts. The channel begins in S, at time 0. It will remain in S, at time t with probability I - F , ( t ) . If the channel leaves S, before time t , it will be back in S, at time t with probability sh P,,(t - y ) dG,,(y).By the renewal theorem (Cox, 1962). 1 -
lim P , ( t ) = 1-lc
F,(t)ldt
loLdGJ(Y)
= Ph’I,
Y
For i # j the same result is obtained, using the dominated convergence principle. For the above theorem to be useful, we need a convenient way of finding wJ. Clearly,
If all states can, by some path, reach all other states, then a theorem of Markov processes guarantees the existence of an equilibrium distribution I’l = (n,,. . . , nl,)satisfying
and
n; > 0 n; = c n,,ujj I
By this definition I’lj is the equilibrium probability of being in S,. Therefore = P k j ( m )for all k . We now multiply Eq. (4) by n, and sum over i.
80
RICHARD HORN
We now subtract &+j l&wy from both sides and divide by Hi.
Therefore
Using our previous result for Pu(r),
EXAMPLE. We use the following kinetic scheme, s, I I S?=s, k.1
and calculate Pj3(w). Let 8 = k2/(k-l
v=(%
k-2
i ;)
+ k2) and y
= 1
- 8.For this case
Now l l 3 = Xj ll,u,3 = f l 2 ~ 2 3= @Hz, and Ill= yn2. Therefore nz/n3 = 1/43 and IIl/l&= y . We already know that p3 = lIk-2. We only need to calculate w33. W33
= ( I / n 3 > < n l P I + flzE.L2
n3P3>
+ n2/[ll3(k-I + kz)] + + klk-2 + klk2)/(klk2k-2)
= lll/(klll3) = (k-lk-2
llk-2
Therefore P,3(03) = p3h33
= klk2/(k-lk-2
+ klk-2 + klk2)
81
GATING OF CHANNELS IN NERVE AND MUSCLE
The equilibrium probability of being in any state can thus be computed directly. We know that the dwell time in S, is distributed as F,(t) = 1 exp(-Aft). For a continuous time Markov process
A, =
c A,,
A,
2
0,
A,,
=
0
I
where A,, represents the rate constant for movement from S, to S,. Since A, does not depend on time, the probability of moving from S, to S, is V, =
AfJe
All =
Af,/h
i(
At equilibrium the probabilistic flow out of S, must equal the flow into S,. Thus, the equilibrium distribution H I satisfies
This distribution holds if II,A,,= II,A, holds for all i andj. This is called the detailed balance condition, and means that the probabilistic flow from S, to S, is the same as the reverse rate of flow.
2. STOCHASTIC MATRIX It is now possible to derive a differential equation describing the evolution of a continuous time Markov process. As above, let P,(r) be the probability of being in S, at time t , given that the system was in S, at time 0. The Chapman-Kolmogorov relation states that
which simply says that the process can pass through an intermediate state Sk at time t on its way to S, at time t + h. For h << A u - ' , A,-' P,,(h) =
[>-A,',
-- I
-
A,h
and P,,(h) -- A,h
Applying these approximations to Eq. ( 5 ) yields
82
RICHARD HORN
Rearranging and letting h + 0 gives the forward differential equation lim P& + h) - Pi#) h-O = P i ( t ) = -Pij(t)Xj i Pik(t)hkj h k+j
2
The initial conditions for this equation are Pii(0)= 1 and Pij(0)= 0 for i # j . One can explicitly solve for P i j ( t )for a finite number of states. The stochastic matrix for this system is P(t) = (P&)). We also define the matrix Q = (qij), where qij = hv for i # j and qii = - X i = -& Xu. The forward equations can be written as P’(t) = P(t)Q In an analogous manner we can derive the backward equations, P’(t) = QP(t)
The initial conditions can be written P(0) = I , the identity matrix. The solution to the above equations (Colquhoun and Hawkes, 1977; Horn and Lange, 1983) is the matrix exponential P(t) = e@ =
(tkQk)lk! k=O
There are many methods used to compute this matrix exponential, which are beyond the scope of this article (see Moler and Van Loan, 1978). The elements of P( t ) are conditional probabilities which depend on the initial conditions, i.e., the initial probability distribution of the system. We are often interested in the unconditional probability P j ( t ) ,the probability of being in state Si as a function of time. These probabilities can be written as a column vector Pj(t), each term of which is a weighted sum of the rows of P ( t ) . The weighting factors are the initial probabilities of being in each state of the system. These probabilities form the initial distribution and can be expressed as the column vector Pi(0). In summary Pj(t)
=
P(t) Pj(0)
(6)
It is well known that Pv(t)for any i and j is a sum of n-1 exponentially decaying components plus a constant IIj, for an n-state kinetic model. For example, in the two-state model S I 5 S2 P
In general each exponential component has a rate which depends on all of the rate constants, qv, in the kinetic scheme. Each rate is sometimes
GATING OF CHANNELS IN NERVE AND MUSCLE
83
called an “overall rate,” and is an eigenvalue of the matrix Q. The inverses of the overall rates in a kinetic scheme are the time constants of the model. An n-state kinetic process, then, has n-I time constants. If the eigenvalues of Q are distinct, theoretically all time constants can be observed. In practice, however, some exponential components are either weighted too little or have rates too similar to other components to be detectable. E. Waiting Time Distributions
Single-channel records allow one, in some cases, to measure when a channel enters or leaves a particular state. For example, if a channel opens at time 0, the time when it closes can be seen directly. Also, one can measure the time when the first channel opens after a perturbation (such as a voltage jump). These measurements are called “waiting times,” and their distributions can be calculated for a Markov process. The theoretical distributions can be directly compared with data, which are usually collected in the form of histograms. The waiting time distribution for the first visit to state S,, starting in state S,, is denoted G,(t>.For an n-state model it is possible to calculate an n x ti matrix G(t) = (G,,(r)).This matrix is generally easier to calculate than P(t). The method is the same. The only difference is that for each element GJt), the destination state S, is made absorbing. An absorbing state can only be entered, but never left. Therefore, S, is made absorbing by setting = 0 for all k . If the matrix P(t) is already known, and its eigenvalues and weighting factors are represented in terms of the rate constants A,, then P ( t ) can be converted to G(t)by letting A,h = 0 for all k in each element P,(r). In the above two-state example, P I 2 ( t )= a / ( a t p) - I d ( a + p)] expl-(a + pit]. With Sz absorbing, Xzl = /3 = 0. Therefore, Glz(t)= 1 - exp(-at). This is the exponential distribution for the waiting time in S , . It is desirable to be able to calculate dwell times in open or closed states when the kinetic scheme has more than two states. Suppose the system has k states, a of which are open and h = k - a are closed. We can write the Q matrix (Section III,D,2) in partitioned form
where QUU describes the transitions among open states, Quh describes transitions from open to closed states, and Q b h and Qbl, are defined similarly (see Colquhoun and Hawkes, 1977, 1981; Horn and Lange, 1983). In
84
RICHARD HORN
order to determine, for example, the closed time distribution, we make the open states absorbing, i.e., Qoa= 0 and Qob = 0. The modified partitioned matrix Q ' = ( OQho
Qhh O
)
is then used to calculate the matrix exponential exp(tQ'), as above. The number of exponentially decaying components in each element of this matrix exponential equals the number of closed states in this example. Open time histograms will also have the same number of exponential components as that of open states. Because some rate constants are set equal to zero in this calculation, the eigenvalues in the matrix exponential are not the same as calculated for the unmodified matrix Q. As an example, suppose a channel has the kinetic scheme S , e S2 F' S3 S4, where S , and Szare closed and S3 and S4are open. Suppose that at time 0 the channel is in S , . The waiting time for the first opening will be distributed as G13( t ) . It will have two exponentially decaying components. A histogram of waiting times in this case is sometimes called a firstlatency histogram (Fig. 6; also see Fukushima, 1981; Horn et ul., 1981, 1983; Hagiwara and Ohmori, 1984; Patlak and Horn, 1982; Aldrich el d., 1983). Its theoretical equivalent is the waiting time density function, 01' R l d t ) = dGdtVdt. The open time distribution for this channel is G,,(t), and assumes the channel opens at time 0. It also has two exponential components. The closed time distribution usually assumes a channel closes at time 0. Therefore, it is given by GZ3(t),again having two exponential compo-
*
40
m
30
5 3
z
1 10
LT W
v=-50
20
5
10
5
10
15
T I M E T O FIRST O P E N I N G (rnsec) FIG.6. First-latency histograms for Na' channel currents in GH3 cells. Data from Horn et al. (1984, Fig. I ) . Histograms plot latency between onset of a voltage step to the indicated potential and the first opening of a channel. Note that the histograms have a peak at a t > 0 and that channels open sooner at the more depolarized voltage. The holding potential was - 120 mV.
GATING OF CHANNELS IN NERVE AND MUSCLE
85
nents. Note that the first-latency and closed time distributions have identical eigenvalues, but different weighting factors. The densities g , d t ) and g Z 3 ( t )have different shapes for this kinetic scheme. The former has a maximum at a time greater than 0, while the latter is montonically decreasing. One note of caution is appropriate. Waiting time distributions become very complicated for the case of multiple channels (Horn and Lange, 1983). In some cases, however, the first-latency distribution can be derived in a simple manner for multiple channels (Patlak and Horn, 1982). F. Estimation of Parameters in Stochastic Models of Gating
The parameters of interest in gating models include ( I ) the number of channels in a patch of membrane, (2) the number of closed and open states in a model, and how they are arranged, (3) the stochastic matrix, P ( r ) , (4) the initial distribution, P,(0). before a perturbation. and (5) the rate constants, A,, under all conditions of interest (e.g., agonist concentration, voltage, temperature). Estimation of parameters has become increasingly important in kinetic analysis because of the randomness revealed by the “microscopic” data of single-channel recording. A variety of methods have been developed in the last few years to deal with this multifaceted problem. It is reasonable to expect that this aspect of kinetic analysis will experience a rapid expansion in the near future, now that techniques for obtaining single-channel data are already widespread. Because of the complexity of this issue, I will discuss only a few of the methods currently in use. The histograms of open time and closed time are usually fitted to sums of exponentially decaying components. The number of components is important for choosing a kinetic model with an appropriate number of states. Dionne and Leibowitz (1982) considered several methods for obtaining the time constant of a histogram of open time, which they believed to be a single exponential. They examined ( I ) nonlinear, unweighted least-squares procedures, (2) nonlinear, weighted least-squares procedures, and (3) a maximum likelihood method. The weights used for leastsquares analysis were approximately proportional to the variance of each bin of the histogram. Dionne and Leibowitz decided that the unweighted least-squares procedure was best, primarily because it was the least sensitive to the effect of truncating the bins representing long-duration events. These bins contained the fewest elements. Colquhoun and Sigworth (1983) recently discussed a number of strategies for fitting theoretical curves to histograms when more than one exponential component is ex-
86
RICHARD HORN
pected. They used both minimum chi-square and maximum likelihood criteria, and showed examples of the calculation of standard errors for estimated parameters. The decision of the number of exponential components in a histogram is more complicated. One possible method is that of Provencher (l976), in which the number of exponential components is systematically increased until additional components no longer improve the fit. Of course the number of exponential components of histograms is very important in estimating the number of closed or open states. Maximum likelihood methods are finding increasing use in estimating parameters. As mentioned above, they can be used to fit histograms to theoretical functions. They are also used to estimate the number of channels in a patch, the rate constants for a given kinetic model, and the initial distribution, P,(O). The basic method involves the calculation of the likelihood, i.e., probability, of observing the data for a given set of parameters. The parameters are then varied until a set is found which maximizes the likelihood. The values which yield the maximum likelihood are maximum likelihood estimates of the parameters. This method is extremely powerful for a number of reasons. First, maximum likelihood estimators are, on several statistical grounds, “good” estimators (Hoe1 et al., 1971; Rao, 1973), being asymptotically unbiased, consistent, and efficient. Second, standard errors and a covariance matrix can usually be determined for parameters of interest. And third, it is possible to test hypotheses, using the likelihood ratio test (Rao, 1973). The principal flaw of the maximum likelihood method is that in some cases it is computationally demanding, requiring up to several days of computer time for estimation of a single set of parameters (Horn and Lange , 1983). Maximum likelihood methods can simply be used to estimate the number of channels in a patch under either stationary (Sachs et al., 1982) or nonstationary (Patlak and Horn, 1982; Horn et a f . , 1984) conditions. Estimation of open-channel lifetime in kinetic processes with one open state, but possibly several channels, is also straightforward (Horn and Standen, 1983). The estimation of rate constants, A, and the initial distribution, P,(O), requires a more elaborate theory, which has been implemented for nonstationary conditions with as many as five channels (Horn and Lange, 1983; Horn e f al., 1984). G. Macroscopic and Gating Currents
Macroscopic currents can be derived simply from a knowledge of P ( t ) and Pi(0) (Colquhoun and Hawkes, 1977). The relaxation of membrane current after a perturbation, such as a voltage step, will have the time
GATING OF CHANNELS IN NERVE AND MUSCLE
87
course X:=, P I ( [ ) ,where P,(t)is the unconditional probabilty of being in S,, and the sum is over the a open states [see Eq. (6)]. For a membrane with N channels, each with an open-channel current i at the voltage of interest, the macroscopic current Z will be I
z = Ni C P,(t) /=I
Note that P,(r)depends on the initial distribution among the states. This explains the different time course of “tail currents” and activating currents at the same voltage. In the former case, most channels begin in an open state. The voltage step leads to a reduction in the probability of being in an open state, and thus a decreasing current. In the latter case the situation is reversed. The time course of the currents for the two cases, at a particular voltage, may be very different, but the currents have the same time constants and eigenvalues. The differences in time course depend only on the weighting factors for each exponentially decaying component. Gating currents are calculated in a similar manner, except for the following modifications. Gating current is the time derivative of charge movement for each transition in a kinetic scheme (Almers, 1978; Armstrong, 1981; Bezanilla and Taylor, 1982). If charge movement occurs across the membrane field for a particular transition, then that transition is voltage dependent. Formally, each state, S,, in an n-state kinetic scheme can be represented as having M electronic charges located a fractional distance of zI through the membrane field. Let Z be the 1 X n row vector with elements zl. For a patch with N channels, the gating current is the scalar I&)
=
NMZP;(t)
where P;(r) is the time derivative of P,(t), defined in Eq. (6). Since P;(f) has no constant terms, the gating current in response to a voltage step will be transient. Gating currents, in general, have the same time constants (and eigenvalues) as macroscopic currents. This implies that every time constant obtained from either macroscopic or gating currents can theoretically be obtained from the other. Note that the differentiation of PI([) weights the exponentials in such a way that faster transitions lead to larger gating currents. Likewise, large charge movement for a given transition leads to a larger contribution to the gating current. The consequence of this is that slow gating processes with little voltage dependence may be very difficult to detect in gating current measurements, even though they are apparent in macroscopic currents. This may be the reason that gating currents associated with inactivation of sodium currents are difficult to detect (Swenson, 1983; French and Horn, 1983).
88
RICHARD HORN
IV.
EXPERl MENTAL FINDINGS
In this section I will give a few examples of the analysis of gating in a variety of channels found in nerve and muscle membranes. A. Agonist-Activated Channels
The end-plate channel of skeletal muscle opens in bursts of activity (Nelson and Sachs, 1979; Colquhoun and Sakmann, 1981, 1983; Dionne and Leibowitz, 1982; Auerbach and Sachs, 1983; Leibowitz and Dionne, 1984; Sine and Steinbach, 1984). A possible model to explain the observed behavior is the following:
s, A s*
7
k-
I
s3
(open)
k-2
The rate constant k l depends on [ACh] and is very small at usual concentrations. In the study of Dionne and Leibowitz (1982) the number of channels N in a patch was estimated to be on the order of 1000. Yet the probability of observing two channels open simultaneously was extremely low. Thus it is very unlikely that a given channel will reach S2.If it does, it will open with probability u23 = k 2 / ( k -I + k2). If u23 is at least greater than 0.5, openings of a single channel will tend to occur in bursts due to movement between S2 and S3. Eventually, perhaps due to dissociation of an agonist molecule, the channel will reach S , , at which time it remains closed for a long time. A histogram of closed time has two components, one fast, on the order of tens to hundreds of microseconds, and one about 1000 times slower (Colquhoun and Sakmann, 1981; Dionne and Leibowitz, 1982). Loosely speaking, the fast component represents the dwell time in S2and the slow component represents the intervals between the openings of different channels. Suppose we consider what happens to a channel which closes at time 0. The distribution of the waiting time for it to reopen is Gz3(t)(see Section 111,E). This distribution function can be obtained from G(r),and for this case, where k , + 0, G2&)
=
[ k 2 / ( k - ,+ k2)l(l
-
exp[-(k-,
+ k&I)
Note that this distribution is defective (i.e., G z 3 ( ~<) I ) due to the fact that the channels which reach S , will never open. By making k , = 0, S , has , is become an absorbing state. A histogram plots g Z 3 ( t ) which gz3(r)= k2 exp[-(k-l
+ k2)t1
GATING OF CHANNELS IN NERVE AND MUSCLE
89
The fast time constant in the population histogram is thus (kl+ k Z ) - l , the mean dwell time in Sz. What about the N - I channels which did not close at time O? Since N is so large we can assume that the behavior of a channel which has just closed will have little effect o n the overall rate of opening of the whole population (Dionne and Leibowitz, 1982). In other words the probability that a channel will open in some interval Az will be the same, whether or not the population size is N or N - 1. We know from Section III,B that the waiting time for any one of these N - 1 channels to reach the open state will have an exponential distribution. In fact this is the slow component of the closed time histogram. What can be said about its time constant? From the model we know that a channel can only open when it reaches S 1 , which is a rare event because k l is assumed to be very small. One can, however, calculate the equilibrium probability that a closed channel is in state S2. This will be &I = kl/(kl + kI)= k l / k - , . If a channel is in S? it opens with rate kz. In effect k2 is reduced by the factor k l l k P l .This is the expected behavior of a single channel. For N = N - I channels, Prob(no channel in S,) = (1 - k l / k - d N , since the channels are assumed to be independent. Therefore the probability that any one channel is in S, is 1 (1 - k 1 I k - 1 ) = ~ 1 - exp(-Nkl/k-I). The opening rate of the population of channels which did not open at time 0 can now be represented by an approximate model , Clo\ed e Open
where r = [ I - exp(-Nkl/k-,)]kz. The slow component of the closed time histogram will have a time constant of Ilr. This is all we can resolve from the behavior of the N - 1 channels which did not close at time 0. Usually N is not known. If it can be estimated, perhaps from studies of the binding of a-bungarotoxin. then k , can be estimated from the histogram of closed time, since k 2 and k I are ohtained from g 2 d t ) . B. Calcium-Activated Potassium Channels
A calcium-activated potassium conductance has been observed in many invertebrate and vertebrate cells over the last 15 years (Meech, 1978; Schwarz and Passow, 1983). Since 1981 several reports have appeared showing the single-channel properties in both patch recordings and in channels inserted into planar bilayers (see reviews by Latorre and Miller, 1983; Schwarz and Ptissow, 1983; and Miller e f d., this volume). The kinetics of this channel fire somewhat complicated, but it is the best
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RICHARD HORN
studied of calcium-activated channels, in part due to the fact that the single-channel currents are so large. The single-channel conductance is about 200 pS at physiological salt concentrations. An intriguing property of this channel is that it is quite voltage dependent. The probability of being open increases e-fold for about 13-mV depolarization for channels from mammalian muscle (Barrett et al., 1982; Latorre et al., 1982). This is considerably more voltage dependent than ACh channels, but not as voltage dependent as the sodium and potassium channels in nerve axons. The potassium channel in the mammalian muscle has been studied in the most detail, using both patch recording (Barrett et al., 1982; Pallotta and Magleby, 1983) and incorporation into planar bilayers (Latorre et al., 1982; Moczydlowski and Latorre, 1983; Vergara and Latorre, 1983). The results are not entirely comparable and are discussed separately. In patch recordings the open time histograms for a single channel could be fitted by a sum of two exponential components. The time constants were sufficiently different for the individual components to be well resolved (Barrett et al., 1982). Increasing the calcium concentration at the intracellular membrane surface, using excised patches, increased the probability that a channel was open. This was due to three effects. First, the frequency of openings increased. Second, the larger time constant in the open time histogram increased. Finally, the proportion of long-duration openings increased. The effect of intracellular calcium concentration was steeper on the weight of the slow component than on that of the fast component, suggesting that multiple binding of calcium ions to the channel led to longer duration openings. The closed time histograms had three exponential components plus a small fraction of very long duration closings (Pallotta and Magleby, 1983). The kinetic scheme for this channel must have at least two open and four closed states. The effect of calcium suggests that a singly bound channel has a shorter open time than a multiply bound channel. This possibility has been proposed by Dionne et al. (1978) and Colquhoun and Sakmann (1981) for the ACh-activated channel also. Some rate constants in the kinetic scheme must be voltage dependent. The direction of the voltage dependence is consistent with the idea that the binding sites for calcium are located within the membrane field. Thus a depolarization could enhance calcium binding, which enhances the transitions into one of the open states. A simpler kinetic scheme, suggested by Moczydlowski and Latorre (1983), is based on the analysis of single-channel currents from planar bilayers enriched with calcium-activated potassium channels from rabbit muscle. Kinetically, their data are fitted by a two-state scheme, having
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single exponential closed and open time histograms. They can explain the effects of calcium and voltage with the following scheme (rl
fi
c.1
c:, e c, z 0, e 0: The transitions between CI and C2are very rapid, as are those between 0, and 02.Kinetically, movement between CZand 01is rate limiting, and is the only observable transition. The data are consistent with the view that calcium binding is a rapid voltage-dependent step, and that the transition between C2 and O1 is voltage independent. In this scheme CI is unbound, CZ and O1 are singly bound, and O2 is doubly bound by calcium. The binding site on 0, has a higher affinity than that on C I . This model can explain the effect of calcium concentration on the open-channel lifetime. The discrepancy between these results and those from patch recording points out the possibility that the experimental situation can significantly alter the function of a channel. C. Voltage-Activated Channels
A considerable literature has accumulated on the gating of sodium channels in nerve and muscle (see the recent reviews by Armstrong, 1981; Bezanilla, 1982; French and Horn, 1983). Instead of presenting yet another examination of this type of channel, I would like to discuss briefly some recent studies on the single-channel behavior of voltage-activated calcium channels. For an overview of the gating of calcium channels, see the reviews of Hagiwara and Byerly (1981), Lux (1983), Tsien (1983), and Eckert and Chad (1984). Single-channel records from calcium channels have been obtained from both invertebrate (Lux and Nagy, 1981) and vertebrate (Fenwick et a / . , 1982; Reuter et al., 1982; Hagiwara and Ohmori, 1983) preparations. The currents appear to be similar in all preparations (Brown et al., 1982). In patches having a single calcium channel, openings appear in bursts between closed periods of long duration. This indicates the presence of at least two closed states. Accordingly, closed time histograms can be fitted by a sum of two exponentially decaying components (Brown et ul., 1982; Fenwick er al., 1982; Hagiwara and Ohmori, 1983; Lux, 1983). The open time histograms in these studies had a single exponential time course, suggestive of one open state. On the basis of this information two possible kinetic schemes could be
c, = (’: e 0 or
c, = 0 ;t c:
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The latter scheme can be eliminated by the fact that, upon depolarization, the macroscopic activation is sigmoidal (Hagiwara and Byerly, 1981). Also, histograms of first latency after a depolarizing step are not monotonic (Hagiwara and Ohmori, 1983; Lux, 1983). If the scheme CI e CZ e 0 is correct, then the bursts are due to transitions between C2 and 0. The long closed times tend to occur when channels reach C,. A problem with this model has been suggested by Hagiwara and Ohmori (1983). They found that the mean open time and the fast time constant in the closed time histograms were voltage independent over a range of -60 mV. This is difficult to reconcile with the above threestate model, which must account for the approximately m 2kinetics in this preparation over the same voltage range as that in which the rate of activation is changing (Hagiwara and Ohmori, 1982). They propose, instead, that the following model could explain their results: c, = cze 0 e-C3 In this model the flickering is caused by voltage-independent, rapid transitions between 0 and C3, and the slower activation time course is mainly determined by the arrival of channels to the open state from C,. This model will need to be tested further, but it is interesting to note that the bursting behavior of ACh receptor channels may also be caused by a similar kinetic scheme (Auerbach and Sachs, 1983), rather than that described in Section IV,A. ACKNOWLEDGMENTS
I am grateful for many stimulating conversations with Dr. Kenneth Lange about the theory of stochastic processes. I also thank Dr. Julio Fernandez for discussions about gating currents, Dr. Carol Vandenberg for carefully reading the manuscript, and Ms. Lis Greene for typing it. Supported by NIH Grants NS 703-01, KO4 HD00307, NS 186-08, and NSF Grant PCM 81-09702. REFERENCES Adams, P. R. (1981). Acetylcholine receptor kinetics. J . Membr. Biol. 58, 161-174. Adams, D. J., Nonner, W., Dwyer, T. M., and Hille, B. (1981). Block of endplate channels by permeant cations in frog skeletal muscle. J . Cen. Physiol. 78, 593-615. Aldrich, R . W., Corey. D. P., and Stevens, C . F. (1983). A reinterpretation of mammalian sodium channel gating based on single channel recording. Nurirrc, (London) 306, 436441. Almers, W. (1978). Gating currents and charge movements in excitable membranes. Rev. Physiol., Biochem. Pharmocol. 82, 96-190. Armstrong, C. M. (1981). Sodium channels and gating currents. Physiol. Reu. 61, 644-683. Armstrong, C. M . , and Bezanilla, F. (1977). Inactivation of the sodium channel. 11. Gating current experiments. J . Gen. Physiol. 70, 567-590. Auerbach, A., and Sachs, F. (1983). Flickering of a nicotinic ion channel to a subconductance state. Biophys. J . 42, 1-10.
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Barrett, J. N., Magleby, K. L., and Pallotta. B . S. (1982). Properties of single calciumactivated potassium channels in cultured rat muscle. J . Physiol. ILondon) 331, 21 I230. Baud. C . , Kado, R. T., and Marcher. K . (1982). Sodium channels induced by depolarization of the Xeriopus luevis oocyte. Proc. Natl. Acad. Sci. U . S . A . 19, 3188-3192. Beam. K. G . , and Donaldson, P. L. (1983). A quantitative study of potassium channel kinetics in rat skeletal muscle from 1 to 37°C. J . C e n . Ph. Bezanilla, F. ( 1982). Gating charge movements and kinetics o teins. In “Proteins in the Nervo cture and Function” ( B . Haber and R. Perez-Polo. eds.), pp. 3-16. 1 Bezanilla, F., and Taylor, R. E. (1978). Temperature effects on gating currents in the squid giant axon. Biopliys. J . 23, 479-484. Bezanilla, F . , and Taylor, R. E. (1982). Voltage dependent gating of sodium channels. In “Abnormal Nerves and Muscles as Impulse Generators” (W.Culp and J. Ochoa. eds.), Chap. 3, pp. 62-79. Oxford Univ. Press, London and New York. Brehm, P., Moody-Corbett, F., and Kullberg, R. (1983). Functional properties of nonjunctional acetylcholine receptors on innervated muscle. Biophys. J . 41, 67a. Brodwick, M . S . , and Eaton. D. C. (1982). Chemical modification of excitable membranes. I n “Proteins in the Nervous System: Structure and Function” (H.Haber and R. Perez-Polo, eds.), pp. 51-72. Liss, New York. Brown, A . M., Camerer, H . , Kunze, D. L . , and Lux, H. D. (1982). Similarity of unitary Ca2+current in three different species. Nofure (London), 299, 156-158. Byerly, L., and Masuda, M. (1979). Voltage-clamp analysis of the potassium current that produces a negative-going action potential in Ascaris muscle. J . Physiol. (London) 288, 263-284. Chandler, W. K . , and Meves, H. (1965). Voltage clamp experiments on internally perfused giant axons. J . Physiol. (London) 180, 788-820. Colquhoun, D., and Hawkes. A. 0.(1977). Relaxation and fluctuations of membrane currents that flow through drug-operated channels. Proc. R . Soc. London. s e r . B 199, 23 1-262. Colquhoun, D., and Hawkes, A. G. (1981). On the stochastic properties of single ion channels. Proc. R. Soc. London, Ser. B 211, 205-235. Colquhoun. D., and Hawkes, A. 0. (1982). On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. Philos. Trms. R . Snc. London, Ser. B 300, 1-59. Colquhoun. D., and Hawkes, A. G. (1983). The principles ofthe stochastic interpretation of ion-channel mechanisms. I n “Single Channel Recording’’ (B. Sakmann and E. Neher. eds.), pp. 135-175. Plenum, New York. Colquhoun, D., and Sakmann, B. (1981). Fluctuations in the microsecond time range of the current through single acetylcholine receptor ion channels. Nolure (London)294, 464466. Colquhoun, D., and Sakmann, B. (1983). Bursts of openings in transmitter-activated ion channels. In “Single Channel Recording” (€3. Sakmann and E. Neher, eds.), pp. 345364. Plenum, New York. Colquhoun, D., and Sigworth, F. J . (1983). Fitting and statistical analysis of single-channel records. I n “Single Channel Recording” (B. Sakmann and E. Neher. eds.), pp. 191263. Plenum, New York. Colquhoun, D., Neher, E . , Reuter, H., and Stevens, C. F. (1981). Inward current channels activated by intracellular Ca in cultured cardiac cells. Norrtre (London) 294, 752-754. Conti, F., and Wanke, E. (1975). Channel noise in nerve membranes and lipid bilayers. Q . Rev. Biophys. 8, 451-506.
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Cox, D. R. (1962). “Renewal Theory.” Butler and Tanner, London. Cull-Candy, S. G., and Parker, 1. (1982). Rapid kinetics of single glutamate-receptor channel. Nuture (London) 295,410-412. DeFelice, L. J. (1981). “Introduction to Membrane Noise.” Plenum, New York. Del Castillo, J., De Mello, W. C., and Morales, T. (1964). Hyperpolarizing action potentials recorded from the esophagus of Ascuris lunihricoides. Nuture (London)203,530531. Dionne, V. E., and Leibowitz, M. D. (1982). Acetylcholine receptor kinetics: A description from single channel currents at snake neuromuscular junctions. Biophys. J . 39, 253261. Dionne, V . E., Steinbach, J. H., and Stevens, C. F. (1978). An analysis of the dose-response relationship at voltage-clamped frog neuromuscular junctions. J . Physiol. (London) 281,42 1-444. Eckert, R.. and Chad, J . E. (1984). Inactivation of calcium channels. P r o g . Biophvs. M o l . B i d . (in press). Ehrenstein, G., and Lecar, H. (1977). Electrically gated ionic channels in lipid bilayers. Q . R e v . Biophys. 10, 1-34. Feller. W. (1968). “An Introduction to Probability Theory and Its Applications,” Vol. I. Wiley, New York. Feller, W. (1971). “An Introduction to Probability Theory and Its Applications,” Vol. 11. Wiley, New York. Fenwick, E. M., Marty A,, and Neher, E. (1982). Sodium and calcium channels in bovine chromaffin cells. J . Physiol. (London) 331, 599-635. Fox, A. P. (1981). Voltage-dependent inactivation of a calcium channel. Proc. Nut/. Acud. Sci. U.S.A. 78, 953-956. Frankenhaeuser, B., and Hodgkin, A. L. (1957). The action of calcium on the electrical properties of squid axons. J . Physiol. (London) 137, 218-244. French, R. J . , and Horn, R. (1983). Sodium channel gating: Models, mimics, and modifiers. Annu. R e v . Biophys. Bioeng. 12, 319-356. Fukushima, Y. (1981). Identification and kinetic properties of the current through a single Na channel. Proc. N a t l . Acud. Sci. U . S . A . 78, 1274-1277. Fukushima, Y. (1982). Blocking kinetics of the anomalous potassium rectifier of tunicate egg studied by single channel recording. J . P l y i o / . (London) 331, 31 1-331. Gage, P. W., and Van Helden, D. F. (1979). Effects of perrneant monovalent cations on endplate channels to monovalent and divalent metal cations. J . Physiol. (London) 288, 509-528. Gibbons, J. D. (1971). “Nonparametric Statistical Inference.” McGraw-Hill, New York. Glasstone, S . , Laidler, K . J., and Eyring, H. (1941). “The Theory of Rate Processes.” McGraw-Hill, New York. Gration, K . A. F., Lambert, J . J., Ramsey, R., and Usherwood, P. N. R. (1981). Nonrandom openings and concentration-dependent lifetimes of glutamate-gated channels in muscle membrane. Nature (London) 291, 423-425. Greeff. N . G . . Keynes. R . D., and Van Helden, D. F. (1982). Fractionation of the asymmetry current in the squid giant axon into inactivating and non-activating components. Proc. R . Sot. London, Ser. B 215, 375-389. Hagiwara, S . , and Byerly, L. (1981). Calcium channel. Annu. R e v . Neurosci. 4, 69-125. Hagiwara, S., and Ohmori, H. (1982). Studies of calcium channels in rat clonal pituitary cells with patch electrode voltage clamp. J . Physiol. (London) 331, 231-262. Hagiwara, S . , and Ohmori, H . (1983). Studies of single calcium channel current in rat clonal pituitary cells. J . Physiol. (London) 336, 649-661. Hamill, 0. P . , and Sakmann, B. (1981). Multiple conductance states of single acetylcholine receptor channels in embryonic muscle cells. Nuture (London) 294, 462-464.
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Hamill, 0. P., Marty. A,, Neher, E.,Sakmann. B., and Sigworth, F. J. (1981). Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. PJuegers Arch. 391, 85-100. Heidmann, T.. and Changeux. J.-P. (1979). F a s t kinetic studies on the interaction of ii fluorescent agonist with the membrane-baund acetylcholine receptor from Torpedo mirniorur(i. E i o . J . Bioc.hrvi. 94, 255-279. Hodgkin, A . L., and Huxley, A . F. (1952). A quantitative description o f the membrane current and i t s application to aonduction and excitation in nerve. J . Physiol. ( L o n d o n ) 117, 500-544. Hoel, P. G., Port, S. C., and Stone, C. J . (1971). “Introduction to Statistical Theory.” Houghton, Boston, Massachusetts. Horn, R., and Brodwick, M. S. (1980). Acetylcholine-induced current in perfused rat myoballs. J . G e n . Physiol. 75, 297-321. Horn, R.. and Lange, K. (1983). Estimating kinetic constants from single channel data. Biophys. J . 43, 207-223. Horn, R . , and Standen. N. B. (1983). Counting kinetic states: The single channel approach. In “The Physiology o f Excitable Cells” ( A . Grinnell and W. Moody, eds.). L i s s , New York (in press). Horn, R . , Brodwick, M. S., and Eamn. D. C. (1980). Effect o f protein cross-linking reagents on membrane current o f squid axon. A m . J . Physiol. 238, C127-CI32. Horn, R . , Patlak, J., and Stevens. C. (1981). Sodium channels need not open before they inactivate. Nature ( L o n d o n ) 291, 426-427. Horn, R.. Vandenberg. C. A.. and Lange. K . (19x4). Statistical analysis of single sodium channels: Effects o f N-bromoiicetaniide. Biophys. J . 45, 323-335. Jackson, M. H . . Wong, B. S.. Morris. C. E.. Lecar, H., and Christian, C. N . (l9X3). Successive openings o f the same acetylcholine receptor-channel are correlated in their open-times. Biophys. J . 42, 109-1 14. Labarca, P., and Miller, C. (1981). A K+-selective, three-state channel from fragmented sarcoplasmic reticulum o f frog leg muscle. J . Memhr. B i d . 61, 31-38. Labarca. P., Coronado, R . , and Miller, C. (19x0). Thermodynamic and kinetic studies o f the gating behavior o f a K+-selective channel from the sarcoplasmic reticulum membrane. J . G e n . Physiol. 76, 397-424. Latorre. R., and Miller, C. (1983). Conduction and selectivity in potassium channels. J . Membr. Biol. 71, 11-30. Latorre, R., Vergara, C., and Hidalgo, C. (1982). Reconstitution in planar lipid bilayers o f a Ca”-dependent K+ channel from transverse tubule membranes isolated from rabbit skeletal muscle. Proc. N o r / . Acrid. Sci. U . S . A . 79, 805-809. Leibowitz. M. D.,and Dionne. V . E. (1984). Single-channel acetylcholine receptor kinetics. Biophys. J . (in press). Lux. H . D. (19x3). Observations on single calcium channels: A n overview. In “Single Channel Recording” ( D . Sakniann and E. Nehcr, eds.). pp. 437-449. Plenum, N e w York. Lux, H. D.,and Nagy, K. (1981). Single channel Ca” currents i n Helix pornarici neurons. PJuegers Arch. 391, 252-254. Magleby, K. L., and Stevens, C. F. (1972). A quantitative description ofend-plate currents. J . Physiol. ( L o n d o n ) 223, 173-197. Marchais, D., and Marty, A . (1979). Interaction o f permeant ions with channels activated by acetylcholine in Aplysia neurones. J . Physiol. (London) 297, 9-45. Meech (1978). Culciuni-dependent potassium activation i n nervous lissue. Annn. Kc,o. B i o p h y s . Bioenx. 7, I-IX. Meves, H. (1978). Inactivation o f the sodium permeability in squid giant nerve fibres. f r o g . Biophys. Mol. B i d . 33, 207-230.
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341-358. Vergara, C.. and Latorre, R. (19831. Kinetics of Ca"-activated K' channels from rabbit muscle incorporated into planar hilayer\. Evidence for a CaZt and Ba?' blockade. J . Gen. Physiol. 82, 543-568. Weiland, G . . and Taylor, P. (1979). Ligand specificity of state transitions i n the cholinergic receptor: Behavior o f agonists and mtagonists. Mol. P h r n i c i i ~ o l .15, 197-2 12. Yeh, J. Z. (1982). A pharmacologiciil npproach 10 the structure of the N a channel in squid axon. In "Proteins in the Nervous Sy\teni" (B. Haher and K. Perez-Polo, eds.). pp. 17-49. L i s s . New York. Yellen. G . (19X I ). Single Ca?'-activated nonselective cations channels in neuroblastoma. Ntrrrrw ( L o n d o n )2Y6, 3.57-359.
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The Potassium Channel of Sarcoplasmic ReticuIum CHRISTOPHER MILLER. J O A N E . BELL, A N D A N A MARIA GARCIA Graduate Department of Biockrmi,rrn Brundeis University Walthum, Massachusetts
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Introduction ..... ...... ..... Electrical Behavior of SR K ' Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . Methods. .....................................................
C. D.
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....................................... Ion Conduction Behavior.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Blocking Reactions .................... Ion-Water Flux Coupling . . . . . . Modification of Channel Behavior. . . . . . . . . . . SR Channels from Other Species.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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E. F. G. 111. Fluxes in Native SR Vesicles.. . . . . . I V . Standing Problems and Future Directi References. .
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INTRODUCTION
Why is our understanding of excitation-contraction coupling so poor? At first glance, it would seem that the great ferocity of both physiological and biochemical attacks on skeletal muscle contraction mechanisms should have produced a clear picture of the link between electrical events on the plasma membrane and the release of Ca2+from the sarcoplasmic reticulum (SR). For instance, we understand in molecular detail the initiation of electrical signals at the motor end plate; we know the ways in which these signals are propagated along the surface membrane and deep into the muscle interior via the transverse tubules; we can study the biochemical operation of the SR Ca?+-ATPase,which is responsible for 99 Copyright C! 1984 hy Academic Press. Inc. ,411 rights of reproduction in any form reserved. ISBN 0- 12- 15332 1-2
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the storage s f calcium within the SR lumen; and we can identify many of the biochemical and structural changes occurring when Ca2+ interacts with the myofibrillar proteins to trigger contraction itself. But in fact we know next to nothing about the way in which the depolarization of the transverse tubule membrane leads to the massive, rapid release of Ca2+stored in the SR. Probably the most fundamental reason for this unhappy state of affairs is the almost complete inaccessibility of the SR membrane to the types of studies which would immediately provide crucial information about the interactions between these two membranes during Ca2+ release. If we could simply voltage-clamp the SR membrane and directly assay its electrical conductance behavior-the ionic basis of its conductance, the changes occurring upon Ca2+release, and the control of these electrical events by the voltage across the muscle plasma membrane-we would be much farther along the way toward an understanding of excitation-contraction coupling. But the SR, because of its small dimensions, cannot be voltage clamped, and consequently it has never been possible to make direct measurements of SR membrane electrical conductances. Most experimental work on Ca2+release has naturally focused on the movements of the Ca2+ ion itself across the SR membrane (e.g., see Baylor et af.,1982a,b). However, the question of the movements of other ions is also central to the problem, since charge must move to compensate Ca2+movements, and since voltage changes across the SR may occur (Vergara et al., 1978). During the past 8 years, several lines of evidence have developed indicating that permeability pathways to ions other than Ca2+exist in the SR membrane. Although all of these methods are indirect, involving studies of either isolated SR vesicles or vesicles placed in model membranes, the results are, overall, consistent with each other. There is now general agreement that isolated SR vesicles are highly permeable to small ions such as K t and Na+, as well as C1-. Whether this small-ion permeability is an artifact of the isolation procedure or whether the SR in uiuo is also permeable to these ions is not known. However, a candidate for a specific protein mediating the monovalent cation permeability of the SR vesicles has been identified: an ionic channel protein which is specific for monovalent cations, and particularly selective for K + . The properties of this channel have been studied extensively in a model membrane system, the planar lipid bilayer, which can be voltage clamped; in addition, several characteristics of this channel seen in the planar bilayer have been also observed in measurements of monovalent cation fluxes on native SR membrane vesicles. It is the purpose of this review article to describe this channel, and to summarize the conclusions which can be validly drawn about its opera-
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tion. As we shall see, we understand in considerable detail the workings of the channel protein, and we can even draw several tentative conclusions about its physical structure; the physiological function of the channel, and its relation to excitation-contraction coupling, remain unknown. The channel has, however, provided an exceptionally clear example of the way in which an integral membrane channel protein can functionhow such channels conduct ions, and how their most basic processes of opening and closing might work. This article is therefore most concerned with the mechanistic aspects of the channel, as studied in isolated SR membrane systems. Two broad approaches have been used to study the properties of the SR K channels: insertion into planar bilayers and direct flux measurements on isolated SR vesicles. Historically, these two lines of attack have been pursued in parallel by different groups; only recently have efforts been made to relate the properties observed in the two systems in a serious way. +
II. ELECTRICAL BEHAVIOR OF SR K + CHANNELS A. Methods
All studies of the electrical properties of the SR K channel rely on the single experimental method of insertion of channel proteins into planar phospholipid bilayer membranes. The system consists of two aqueous chambers of milliliter size, separated by a well-insulated partition containing a hole 50-500 p m in diameter. A phospholipid bilayer may be formed across this hole by one of two methods. In the “painting” method (Mueller and Rudin, 1969), a solution of lipid in an alkane solvent (usually ndecane) is spread over the hole, the solvent drains away, and a lipid bilayer is left behind. The large amount of alkane solvent known to be included in these painted bilayers gives us pause in relying solely on them for channel studies. Fortunately, a second planar bilayer system has been developed which is nominally solvent free (Montal and Mueller, 1972). These bilayers are formed by first spreading a lipid monolayer film on the surface of each of the two aqueous phases of the bilayer system. The aqueous levels are then raised over the hole in the partition, thus creating a bilayer. Although these “folded” membranes contain much less solvent than painted bilayers, thermDdynamic arguments require that a small amount of solvent be present here as well (White ef a / . , 1976). Once a planar bilayer is formed, channels are incorporated by a process resembling fusion of the SR vesicles with the planar bilayer (Miller and +
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CHRISTOPHER MILLER ET AL.
Racker, 1976). Three parameters control the probability of channel insertion: bilayer lipid composition, aqueous Ca2+concentration, and osmotic conditions leading to swelling of the vesicles. Experimentally, it is possible to insert up to 500 channelshninute under “favorable fusion conditions,” using bilayers rich in phosphatidylethanolamine (PE) and phosphatidylserine (PS), with 1 mM Ca2+ and 100 mM K t in the aqueous medium, and using SR vesicles preloaded with 500 mM sucrose. Channel insertion then spontaneously occurs, and within a short time it is possible to study the macroscopic conductance of a bilayer containing up to 5000 channels. Alternatively, one can reduce the probability of fusion so that only a small number of channels is inserted, allowing the direct observation of unitary fluctuations in current, due to the opening and closing of single channels. Experimentally, it is easy to reduce the fusion probability by reducing the Ca2+concentration, by lowering the sucrose concentration used to load the SR vesicles, and/or by increasing the proportion of phosphatidylcholine (PC) in the bilayer at the expense of PE. A typical experiment is performed by forming a planar bilayer, adding 0.2-1 mM Ca2+to one side of the bilayer, and then adding 1-5 pg/ml of SR vesicles to this side, while applying a holding voltage across the bilayer in order to assay the conductance increase which occurs when the vesicles insert (Labarca er al., 1980). After the desired level of conductance is reached, excess EGTA is added to remove Ca2+,and the vesiclecontaining chamber is extensively perfused with vesicle-free solution. This procedure tends to stop the fusion, or at least to slow it down considerably, so that now a stable bilayer conductance can be studied. Once channels are inserted, they do not “fall out”: we have observed stable macroscopic conductance levels for up to 2 hours after channel incorporation and subsequent perfusion. As we will see, this method allows the insertion of K + channels with a high degree of asymmetry. By a conservative estimate, the degree of channel orientation after insertion is greater than 98% one way (Miller and Rosenberg, 1979a). This asymmetry is probably a consequence both of the high orientation of the preparation of SR vesicles used (nearly 100% right-side out) and of a possible selectivity of the fusion process for rightside out vesicles. In order to distinguish the two sides of the bilayer, we use the following orientation convention. The side of the bilayer to which &heSR vesicles are added is called the cis side; &heopposite side is called trans. Our voltage convention places zero voltage on the trans side. Planar bilayer work does not tell us which side of the native SR membrane is equivalent to which side of the bilayer. However, if our picture of fusion is correct, the cis side is equivalent to the rnyoplasmic side of the SR membrane, while the SR lumen would be equivalent to the trans side. A
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critical discussion of techniques involved in planar bilayer reconstitution presented elsewhere (Miller, 1983) concludes that our understanding of the channel insertion process is so poor that it would be foolish to base any important conclusions about the channel on assumptions about the nature of the vesicle-bilayer interaction. We will see later, however, that independent evidence from SR vesicle flux work argues that the cis side of the bilayer is in fact equivalent to the myoplasmic side of the SR membrane. B. Gating Properties
In any characterization of an ion channel, there are two types of processes to be studied: the “gating” process, by which the channel opens and closes, and the conduction process, by which ions interact with and permeate the open channel. Both of these processes have been investigated in detail for the SR K + channel, and we will treat them separately. In Fig. IA, we see a typical channel insertion event. A trace such as this is interpreted as the fusion into a bilayer of one single SR vesicle containing about six channels, all of which are open at the moment of insertion. Finding themselves in a new environment (with an applied voltage and in an ocean of foreign lipid), they then proceed to close, on the average. The current subsequently fluctuates among five discrete levels, as individual channels randomly open and close. There are several good reasons for assuming that such a trace is due to the presence of multiple channels operating independently, rather than to a single multistate channel complex. Most convincing is the observation that the conductance levels are always equally spaced and that the possibilities of their appearance are binomially distributed (Labarca et a l . , 1980). An example of such a distribution is shown in Fig. IB for a membrane containing 18 channels. More stringent kinetic tests have also confirmed the independent opening and closing of multiple channels (Labarca et al., 1980). Finally, we have occasionally observed the insertion of only a single channel into the planar bilayer, i.e., unitary fluctuations between only two conductance levels; the behavior of these two-state fluctuations is fully consistent with the more commonly seen multiple-level behavior (Labarca et al., 1980). The insertion of only one channel into the bilayer is an extremely rare event; over 99% of insertions involves a “package” of channels, as in Fig. I A . The mean number of channels inserted per package varies from preparation to preparation, in the range of 5-10. We therefore imagine that a single SR vesicle carries about five channels. We will see later that work with whole vesicles forces us to modify slightly
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CHRISTOPHER MILLER ET AL.
s + - J
+--
--
PAL
lo
I 5 sec
B
0
2
4
6
8
10
Level Number i
FIG.I . Insertion of multiple K' channels. (A) A single fusion event recorded in a bilayer held at -50 mV. (B) Binomial test for a multichannel membrane. In this experiment, a bilayer containing 18 channels was held at +35 mV, and records of fluctuations among multiple conductance levels were recorded for approximately 2 hours. The probabilities, J; , of observing the various levels were calculated directly (data points). The solid curve connects the theoretical values expected from a binomial distribution with 18 channels, with an individual channel having an opening probability of 0.25 (measured independently in parallel experiments). (Data taken from J. E. Bell and C. Miller, unpublished.)
this picture of the SR vesicle population. In any case, the appearance of multiple channels in the bilayer is not a hindrance to extracting the fundamental gating properties of the single channel (Labarca et al., 1980). Overall, the gating of this K + channel is remarkably simple. In channels
POTASSIUM CHANNEL OF SARCOPLASMIC RETICULUM
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from rabbit SR, only two levels of conductance are observed (Miller, 1978; Miller and Rosenberg, 1979b; Labarca e t a / . , 1980).A gating mechanism was therefore proposed in which the channel protein can exist in only two conformations, OPEN and CLOSED, the former able to allow K + conduction, and the latter nonconducting. OPEN
G
C’L.OSEl>
(1)
Since it was directly observed in singlc-channel traces that the open state is favored a s voltage is made increasingly positive (Miller, 1978: Labarca P I d . , 19801, the rate constants of opening and closing were proposed to depend upon applied voltage. The treatment of two-state voltage-dependent gating developed by Ehrcnstein and colleagues ( 1970) was adapted to make predictions about the expected gating behavior. In particular, the steady-state membrane conductance g( V ) (after correction for “leaks”) was found to follow the required form: g ( V ) = Ny{I
+ exp[(AG, + z F V ) / R T ] ) - ’
(2)
where N . y . and z are the total number of channels in the membrane, the single-channel conductance, and the effective charge movement during channel opening, respectively; and R , T , and F have their usual meanings. The parameter AG, is the “internal free energy of opening,” i.e., the voltage-independent part of lhe opening free energy, due only to the differences in chemical interactions between the open and closed states of the channel protein (Labarca of d . , 1980). Figure 2 displays the macroscopic conductance-voltage curve of a bilayer with about 5000 channels inserted into it, and it is apparent that the two-state scheme leading to Eq. ( 2 ) is fully adequate to explain the voltage dependence. The parameters z and AGi are easily determined from such curves. We find that the effective charge z is about - I . 1, equivalent to a 10-fold increase in the equilibrium constant of opening per 55 mV, and that this parameter is insensitive to external variables such as aqueous pH, temperature, and lipid composition. In contrast, the internal free energy of opening AG, is quite sensitive to these parameters (Labarca et a / . , 1980). For instance, an increase in the negatively charged lipid concentration used to form the bilayer leads to an increase in AGi, and thus manifests itself as a shift in the g-V curve to the right. Addition of 30% PS to a neutral PE/PC bilayer shifts the g-V curve by about 50 mV to the left (C. Miller, unpublished results). The latter maneuver thus yields a AGi for opening which is 1.4 kcal mol-’ more favorable in a neutral than in 8 charged membrane. Likewise, increasing the medium pH leads to channel opening via modulation of AGi (Labarca
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CHRISTOPHER MILLER ET AL.
0' -100
L
-50
0
50
100
150
V (mV) FIG.2. Macroscopic conductance-voltage relation. The total conductance g of a bilayer formed from soy phospholipid was measured under steady-state conditions as a function of applied voltage. This membrane contained about 5000 channels. Solid curve is drawn according to Eq. (2), with e = - 1 . 1 and AGi = 1.5 kcal/mol. Note small background conductance at negative potentials. (Data taken from Labarca et u / . , 1980.)
et al., 1980). Finally, AGi was shown to have large contributions from both entropic and enthalpic components; in membranes of mixed soy phospholipids, the channel is driven toward the closed state by an increase in temperature. That is, the opening reaction is enthalpically favored (AH = -10 kcal/mol) and entropically disfavored (AS = -35 cal/ mol . K). In the absence of structural information about the channel, there is little that can be said from such analysis, other than to identify a type of behavior easily interpreted in terms of the two-state model. The gating model was further tested by kinetic experiments employing voltage jumps (Labarca et al., 1980). It was found that the opening and closing kinetics are always single-exponential, and that the rate constants depend only on the test voltage, and not upon the previous history of the system. The rate constants of opening and closing were found to depend exponentially upon voltage, again as predicted by the simplest two-state scheme (Ehrenstein et al., 1974). Most of the voltage dependence lies in the opening rate, and relatively less in the closing rate. Both the equilibrium and kinetic behaviors of membranes containing
POTASSIUM CHANNEL OF SARCOPLASMIC RETICULUM
107
many channels were found to agree with the analogous single-channel phenomena (Labarca et al., 1980). Thus, the voltage dependence of the probability of a single channel opening, measured directly from channel fluctuations, parallels precisely the macroscopic g-V curves. Likewise, the opening and closing rates derived from single-channel transition probabilities agreed with those determined using macroscopic relaxation kinetics. These results serve mainly to certify the two-state model as a usable framework for the interpretation of the channel’s gating behavior. They also lead to a strong conclusion: this channel does not operate on the basis of independently diffusing “subunits” that aggregate to form a conducting unit (in contrast, for instance, with the “model” channels, gramicidin A or alamethicin). Rather, the gating reactions are independent of the absolute number of channels in the bilayer, and we can say that this channel operatcs as a single unit. (Of course multiple subunit interactions may be involved in the gating, but any such subunits must act as a tight complex.) C. Ion Conduction Behavior
The SR K + channel has provided an excellent model for the detailed study of specific ion conduction and selectivity through the channel proteins of higher organisms. We shall see that the ion conduction mechanism of this channel displays the properties of ionic selectivity, ion binding, and blocking so familiar in electrophysiological studies of membrane channels of nerve and muscle, In addition, the K f channel of SR can be extensively manipulated in the model membrane system, so we can use the underlying simplicity of its conduction behavior to draw tentative structural conclusions about the K conduction pathway. The channel is absolutely selective for monovalent cations. Careful measurements of single-channel reversal potentials under asymmetric ionic conditions (Coronado ct a / . , 1980) reveal this property, as does the fact that no channel-like conductance behavior can be detected when small monovalent cations are omitted from the medium (Miller, 1978). Among the monovalent cations, a substantial selectivity can easily be demonstrated. In Table I, we have collected values of single-channel conductances for a variety of monovalent cations, at a medium concentration of 400 mM. Among all ions, K displays the highest channel conductance; furthermore, this conductance is unusually high, about 200 pS, 10fold higher than the conductances of the rather nonselective acetylcholine receptor channel and the gramicidin A channel.
TABLE 1 SINGI-E-CHANNEL CONDUCTANCE 400 m M CATIONS" Cation
Y (PS)
Li + Na K' Rh' c s+ NH: Methylammonium Trimethylammonium Choline Diethylammonium Tetramethylammonium Tetraet hylammonium Hydrazinium Methylhydrazinium N,N-Dimethyl hydrazinium Hydroxyet hylhydrazinium Guanidinium Met hylguanidinium Aminoguanidinium Hydrox yguanidinium Hydt-oxylammonium Methylhydroxylammonium Formamidinium Ethanolammonium Triet hanolammonium 2-Methylaminoethanol Tris( hydroxymethy1)aminomethane
7 71 211
+
N.N-dimethy laminoethanol
121
<3 I56 58
2-4
12 4 2-s 4-5
9 S 36
so 6 6
S R vesicles were fused into PE/PC hilayers using symmetrical solutions of 400 mM of the glucuronate o r sulfate salt of the cation indicated. In all cases, the standard error was less than 10% of the listed value. In cases reporting a range of values, channel fluctuations were clearly present, hut the baseline noise was too great to measure the conductance accurately. Cases labeled < I pS correspond to experiments in which there was no discernible noise (below S Hz) on the chart record; in these cases, we would have been able to detect ii channel with I pS conductance. Under the conditions here, all of the compounds with dissociable protons are at least 98% in the ionized state. except for hydroxylammonium, which is only 5% ionized. (Data taken From Coronado ct id., 1980, and Coronado and Miller, 1982.) I'
POTASSIUM CHANNEL OF SARCOPLASMIC RETICULUM
109
Y (PS)
FIG.3. Michaelis-Menten behavior of single K - channels. Single-channel conductance y was measured in symmetrical solutions of either K' or Na'. a s a function of single ion activity u . Scatchard plots of the data are shown, with half-saturation activities and maximum conductances of 50 mM and 230 pS for K + , and 35 mM and 75 pS for Na'. (Data taken from C . Miller and M . Barroll, unpublished.)
In order to analyze the ion conduction mechanism, it is necessary to know how the channel conductance varies with the ion concentration in solution. A study of this (Coronado et al., 1980) revealed that for all conducting ions, the channel conductance is a saturable function of ion activity, as shown in Fig. 3 for K ' and Na'. Indeed, the conductance follows the simple rectangular hyperbolic function demanded by a "Michaelis-Menten" model of the conduction. According to such a model, the channel can bind at mast one ion at a time. The linear increase in channel conductance with low ion concentration5 reprcscnts the secondorder rate procebs of entry into the channel (Hille, 1975; Latorre and Miller, 1983). The limiting value of conductance at high concentration represents the rate at which a n ion leaves Ihe channel (leaving it available for the next ion to enter). LBuger (1973) has presented a general Eyring rate theory analysis of single-ion channels, the major predictions of which have been confirmed for the SR K +channel (Coronado er al., 1980). According to this analysis, the channel conduction pathway may be viewed as a sequence of at least three major energy barriers separating two energy wells, or ion-binding sites. The ionic selectivities of both the peak energies and the binding energies were determined. The peak, or transition state, energies follow the sequence Li+ > Na+ > Rb' > K +; this is identical to the sequence for the depths of the energy wells. Thus, K + displays the highest conduc-
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tance for two reasons: it faces the least unfavorable transition state energy, and it binds the least tightly of these ions. Cs+ could not be included in this analysis because its single-channel conductance is too low to be measured under these conditions; indeed, it is an excellent blocker of the channel, as we will describe below. The single-channel conductance is dependent upon temperature, and the values for the activation enthalpies are consistent with ionic diffusion through an essentially water-like environment. The maximum conductances for K + , Rb+, and Na+ show activation enthalpies of 5-6 kcal/mol, similar to the values for free diffusion, while the value for the conductance of Lit is impressively high, 9-12 kcal/mol (Coronado et al., 1980; C. Miller and M. Barrol, unpublished). The corresponding differences among the ions in activation entropies correlate well with their entropies of hydration, suggesting that a substantial amount of water of hydration is removed from the group IA cations as they traverse the channel (Coronado et a l . , 1980; C. Miller and M. Barrol, unpublished). Possibly the most immediately striking aspect of this channel’s conduction process is the large value of the K + conductance. A maximum conductance of 240 pS at 100-mV driving force corresponds to 150 million K + ions permeating per second; the limiting slope of Fig. 3 at low K + concentrations corresponds to a second-order entry rate constant of the order of 1O1O M-I sec-I. This is consistent with diffusion-limited transport up to the entryway of the channel, if we assume that its “capture” diameter is quite large, about 0.8 nm (Andersen and Procopio, 1980; Latorre and Miller, 1983). A detailed discussion of the possible structural meaning of the combination of high ionic selectivity with high conductance has been presented recently (Latorre and Miller, 1983). Coronado and Miller ( 1982) reported that monovalent ammonium derivatives, if they are not too large, also permeate well through the channel. For example, methylammonium and hydrazine both show conductances higher than the conductance of Na’ (Table I). By examining the dependence of channel conductance on the size of the permeating cation, it was possible to identify a well-resolved “cutoff size” above which permeation could not be detected. The implication was that this size, about 0.4 x 0.5 nm, approximates the narrowest cross section along the ion conduction pathway. Such a constriction would be small enough to force the alkali metal cations to interact strongly with the channel protein. This size is, however, substantially larger than that estimated in a similar way for the much more selective, and much more poorly conducting, delayed rectifier channel of the node of Ranvier in the frog (Hille, 1975; and Barry and Gage, this volume).
POTASSIUM CHANNEL OF SARCOPLASMIC RETICULUM
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D. Blocking Reactions We have seen that many different monovalent cations permeate the SR K + channel, if they are smaller than 0.4-0.5 nm. What about cations larger than this? Are they simply “inert”? One firm rule we can make about the channel’s behavior is that no cation is inert. Every cation that we have ever presented to this channel interacts with it in some way. Indeed, a large class of ions do not permeate the channel, but bind to it and prevent the permeation of conducting ions such as K i . Ions of this class are called blockers, and we have observed three types of blocking reactions in the K + channel: purely voltage-dependent block, purely current-dependent block, and mixed-type block. The voltage-dependent blockers are, at present, the most thoroughly documented.
I . Cs+ BLOCK The first blocking ion found for this channel was Cs+ (Coronado and Miller, 1979; Coronado et nl., 1980). When added to the cis side in the concentration range of 10-50 mM, Cs+ reduces the single-channel K t conductance in a dose-dependent manner, while when added to the trans side, no effect is seen. At a fixed voltage, the reduction in channel conductance follows a simple inhibition law, as though a rapid, reversible Csi binding reaction were competing with K i for a site in the channel. Furthermore, it was found that the apparent Cs+ binding constant is voltage dependent; increasingly positive voltages enhance the blocking affinity, as though the Cs+ ion, in gaining access to its binding site from the cis side, traverses a part of the electric field gradient within the channel. This sort of behavior may be understood in terms of a simple scheme in which the blocker, of valence z , binds to a site located within the channel, such that a fraction 8 of the applied voltage drop is experienced at that site (Woodhull, 1973). Then, it follows that the blocker’s apparent dissociation constant K ( V ) varies exponentially with voltage: K(V) = K ( 0 ) exp(-zGFV/R7)
(3)
where K ( 0 ) is the zero-voltage dissociation constant, and z 8 , the effective valence of the blocking reaction, determines how steeply the block varies with voltage. The Cs+ block shows an effective valence of 0.35, as though the blocker binds to a site 35% of the way down the applied voltage drop, from the cis side (Coronado and Miller, 1979). Further work showed that the Cs’ blocking reaction is competitive with K +;increasing the K concentration relieves the block by lowering the +
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CHRISTOPHER MILLER ET AL.
apparent affinity for Cs+, but leaves the voltage dependence of the pro1980). These two characteristics, the cess unchanged (Coronado e t d., pure voltage dependence and the competition with K + , strengthen the proposal that the Cs+ binding site is located within the channel’s K + conduction pathway. Such a proposal is not surprising, since Cs+ is a close K + analog, and since many Cs+ blocking reactions of a variety of K + channels have long been known (Latorre and Miller, 1983). The aspect of Cs+ block of this channel which remains obscure to us is the basis for the lack of conduction of this cation. K + conductance is at least 50 times higher than that of Cs+, under symmetrical ion conditions (Table I). Since the channel readily allows permeation by organic cations substantially larger than Cs+ (with its 0.3-nm crystal diameter), a steric explanation is ruled out. Likewise, the inherent binding of Cs+ to the channel is only about fivefold stronger than that of K + , and so a “deepwell” blocking explanation is untenable. In spite of these uncertainties, however, the Cs+ blocking reaction appears to be much simpler than the multiple-ion schemes proposed for the interaction of Cs+ with the squid axon K + channel (see, for instance, Adelman and French, 1978; Hille and Schwarz, 1978).
2, MONOVALENT ORGANIC CATION BLOCK Many monovalent “organic cations” derived from ammonium or guanidinium reduce K + currents through this channel, when added to the trans side of the bilayer (Coronado and Miller, 1982). As with Cs’, this effect is purely voltage dependent and is competitive with K + . Furthermore, these blockers lengthen the mean open time for the channel in a dose-dependent way, while leaving the mean closed time unchanged. This behavior is precisely that expected by a model in which the blocker interacts only with the open state of the channel; whenever the channel is occupied by a blocker, it cannot close. These three characteristics-voltage dependence, competition with K +,and lengthening of the mean open timeargue strongly that these compounds act by actually entering and binding to the conduction pathway for K + (Coronado and Miller, 1982). Compounds such as tetraethylammonium, methylguanidinium, glucosamine, and Tris block this channel weakly, with zero-voltage inhibition constants of 50-500 mM. More hydrophobic blockers, such as decyltrimethylammonium and tetrapentylammonium, operate at about 100-fold lower concentrations. But all such blockers appear to interact with the channel in essentially the same way. In one respect, this similarity is very surprising: these compounds all show quantitatively identical voltage de-
POTASSIUM CHANNEL OF SARCOPLASMIC RETICULUM
113
pendence of block, as though they all act at a site located 60-65% of the way down the voltage drop. as measured from the trans side of the biluyer (Coronado and Miller, 1982; Miller, I982a). There are two exception\ to this generalization: compounds containing aromatic rings (such as phenyltrimethylammonium and lidocaine-type local anesthetics), and compounds of size larger than about 0.7-0.8 nm, which display effective valences of about 0.3 (Coronado and Miller, 1982; Y . Kita, C. Smith, and C. Miller, unpublished). We have therefore concluded that on the transfacing side of the channel, there exists a rather wide (0.8 nm) “tunnel” region into which many types of blockers can enter, and that this tunnel abruptly narrows to a 0.4-0.5 nm constriction at a point about 65% of the way through the applied voltage drop (Coronado and Miller, 1982; Miller, 1982b). The “pure” voltage dependence of the blocking reaction is required by the model of the channel as a single-ion channel.
3. BIS-QUATERNARY AMMONIUM BLOCK~RS In attempting to find blockers with affinities stronger than those above, Coronado and Miller (1980) observed unexpected behavior of two divalent blockers of a class called “bisQn” compounds. These are linear alkanes with n methylene groups, and a trimethylammonium “head” on each end. It was found that hexamethonium, bisQ6, displays an effective valence parameter of 0.65, as do the monovalent blockers. Decamethonium, bisQlO, surprisingly shows an effective valence of exactly twice this, I .3. It was suggested that for some reason only one of the charges of bisQ6 is “sensed” by the channel, while both of the charges of bisQlO penetrate to the 65% site. These observations were pursued by studying the block produced by bisQn compounds with chain lengths of 2-12 carbons (Miller, 1982a). It was found that compounds with short chains, two to five carbons, displayed effective valences which decrease with chain length, from a high value of 1 . 1 to a low value of 0.65 (Fig. 4). As chain length is increased further, from five to eight carbons, the effective valence remains constant, at 0.65, the same value as for the monovalent alkyltrimethylammonium analogs, and indeed, for the monovalent blockers described above. This behavior was interpreted by proposing that the applied voltage within the channel falls over a short distance of about I nm, and that one of the charged “head” groups of the bisQn blockers always binds at a site 0.6-0.7 nm of the way into this region from the trans side. The other head group, therefore, is left behind, less deeply in the channel, and consequently senses less of the applied voltage. Once the head-group charges
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CHRISTOPHER MILLER E T AL.
OS
t
0
Monovalent
2
4
6
8
10
12
Number of CH2 groups FIG.4. Voltage dependence of bisQn blockers. The voltage dependence parameter, or “effective valence” 28, is shown as a function of the number of methylene groups on bisQn blockers. Diagrams show the physical interpretation of the voltage dependence in terms of the position of the trimethylammonium head groups inside the channel conduction pathway. (Taken from Miller, 1982c.)
become separated by more than four carbons (0.6-0.7 nm), the second head group does not enter the applied electric field at all, and the blocker is seen by the channel as a monovalent compound. A sudden change in behavior is observed for compounds with chain lengths of nine carbons and greater. The effective valence abruptly doubles to a value of 1.3, as though both charges reach the 65% site. In addition, the affinities of these long-chain blockers become discontinuously stronger (in the 1-10 p M range) than those of the shorter analogs. Most strikingly, the kinetics of the blocking reaction become slow enough so that at 1-msec time resolution, the discrete blocking events due to the entry of single blocker molecules are easily observed. These three types of behavioral change argue that the long-chain bisQn blockers act in a conformation different from that of the shorter chain compounds. It was proposed that the increased hydrophobicity and the flexibility of the longer chain compounds permit them to assume a “horseshoe” conformation within the wide tunnel of the channel, with both charges reaching the blocking site (Miller, 1982a). Such an interpretation would suggest the existence of negatively charged groups near the blocking site, as might be expected if this site were located at or close to a “selectivity filter” (Hille, 1975).
115
POTASSIUM CHANNEL OF SARCOPLASM IC RETlCU LUM
TRANS
FIG. 5 . 1982c.)
Diagram of SK K ’ channel conduction pathway (see l e x l ) . (Taken from Miller,
The accumulated work on organic cation conduction and block has emboldened us to present a structural picture of the channel’s conduction pathway (Fig. 5 ) . First, we envision a critical constriction of 0.4-0.5 nm width as the narrowest part of the channel, consistent with the apparent cutoff size of the conducting cations. It is reasonable to propose that this is the region at which the major interactions involved in ionic selectivity take place. The fact that virtually all monovalent organic blockers show an effective valence of 0.65 leads us to propose that molecules as large as 0.8 nm in diameter can reach a site located 65% of the way down the electric potential drop, from the trans side. For simplicity, we place this site near to the critical constriction, which, we must assume, occurs quite abruptly. Thus, the voltage appears to drop along a “tunnel” about 0.8 nm in width. The physical length of the tunnel is proposed to be about 1 nm, consistent with the variation of the effective valence of the bisQn blockers. Since the channel protein is embedded in a bilayer at least 4-5 nm thick, the short length, along which the applied voltage drop occurs, must be connected to the aqueous phases via wide, low-resistance “mouths.” A picture such us this i\ appealing because it can be used to explain the unusual combination of high conductance and high selectivity seen here, and now also in Ca?+-activated K + channels (Latorre and Miller, 1983); since ion selectivity takes place in a highly localized “active site” of the channel, rather than along a substantial distance, the channel conductance can remain high. The short length of the tunnel also accounts for the single-ion nature of the channel; the ion binding sites are physically so close that electrical repulsion forbids the entry of a second ion
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into a channel already occupied. These points have been discussed in some detail elsewhere (Latorre and Miller, 1983). DENT BLOCKERS 4. CURRENT-DEPEN
Recently, a class of blocking compounds was found which behaves in striking contrast to the voltage-dependent blockers above (Kita et ul., 1984). These are the diaminoalkanes, the primary amine analogs of the bisQn compounds. These compounds block the channel, in the range of 10-100 pM, from both sides of the bilayer in an apparently polaritydependent, but not voltage-dependent way. For instance, diaminodecane added to the cis side reduces the K + current at positive voltages (with K + current flowing cis to trans), but has little effect at negative voltages. Moreover, the inhibition constant at positive voltages is independent of voltage in the range of 20-100 mV. The reverse polarity is seen with the compound added on the trans side, though the inhibition constants are, in general, different on the two sides of the bilayer. In fact it is not the voltage polarity which is sensed by these blockers, but rather the direction of K + current. This was shown by studying the blocking reaction in the presence of K + gradients across the bilayer. Under these conditions, block is always relieved when the direction of current is changed so that K + flows toward the side on which blocker is added. We do not yet fully understand the effects of these compounds. However, they act as though they bind near to the channel mouth, on either side, but do not actually enter the electric field. While occupying its binding site, such a blocker prevents entry of K + ions from its own side; but a K + ion exiting from the channel can knock the blocker off its binding site. This mechanism is not a Maxwellian demon, since it only determines the magnitudes of K + currents, always flowing down their thermodynamic gradients. It is, in fact, similar to the “knock-on” mechanisms used to explain the block of squid axon K + channels by quaternary ammonium ions (Armstrong, 1975). The kinetics of the diaminoalkane block are too rapid to observe, even at 2-kHz resolution, and it has been suggested that the reaction may be diffusion limited (Kita et al., 1984). We do not understand at all why diaminoalkanes show this “pure” current-dependent block, while the quaternary analogs do not, Other compounds, such as long-chain aminoalkanes and guanidinoalkanes, show this effect as well (Y. Kita and C. Miller, unpublished), though in these cases it is impossible to rule out contributions from bilayer surface potential changes caused by the detergent-like molecules. We have observed both voltage- and current-dependent blocking by bisguanidino-n-alkanes (Y. Kita and C. Miller, unpublished), though the complexity of these
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mixed-type blockers has frightened us away from a detailed mechanistic characterization on the single-channel level. E. lon-Water Flux Coupling
Since the SR K + channel necessarily contains a smail constriction within its conduction pathway, it might be expected that K’ ions and water molecules would be unable to pass one another along such a region. Under such conditions, we would expect to see an obligatory coupling between water and ion fluxes through the channel. As shown in detailed studies on the gramicidin A channel (Rosenberg and Finkelstein, 1978; Levitt et ul., 1978; and Leviit, this volume), it is possible to detect such coupling by measurement of streaming potentials. This method was applied to the SR K’ channel by inducing a current of K + against its electrochemical potential gradient by imposing a water activity gradient across the bilayer (Miller. 1982b). It was found that a I-osm osmotic gradient shifts the single-channel zero-current voltage by about I mV. This, in turn, implies that at most twy molecules of water are constrained to move in single file with a K + ion inside the channel, again suggesting that any selectivity constriction within the channel must be short, 0.5 nm or less (Miller, 1982a,c).The fact that urea was as effective as sorbitol in promoting such a streaming potential argues that the permeability of urea through the channel is much lower than that of water itself.
F. Modification of Channel Behavior The planar bilayer system is particularly convenient for studying changes in channel behavior in response to various types of modifications. Both aqueous phases are easily accessible, and, given the complete orientation of the channel in the planar bilayer, modifications can be carried out with unequivocal “sidedness.” We have examined the effects on the SR K channel of various group-specific reagents, proteases, and lipids, and we will briefly review these studies here. +
1. SULFHYDRYL REAGENTS
The channel is sensitive to several types of sulfhydryl-reactive reagents, all of which irreversibly inhibit K conductance. The first studies in this area investigated the effects of transition metal cations on K + channels inserted in bilayers (Miller and Rosenberg, 1979a). It was found that the “soft” transition metal ions, such as Ag’, Hg”, Cu2+,Cd’+, +
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Pb2+,and Zn2+, when added to either side of the bilayer, completely eliminate the channel-mediated conductance; removal of these ions by extensive perfusion or by addition of EDTA in great excess fails to restore channel activity. The rate constants of the inhibition reactions vary over several orders of magnitude; the strongest of these inhibitors, Ag+, causes half-inhibition after a minute at concentrations in the nanomolar range, while Zn2+ requires concentrations in the 100 W M range for a comparable reaction rate. The “hard” transition metal ions, such as Co2+,Mn2+,and Ni2+,do not inhibit the channel. The specificity of this effect was used to argue that sulfhydryl groups are involved. This proposal was strengthened by the observation that organomercurial reagents cause effects similar to those of the transition metals (Miller and Rosenberg, 1979a). The reaction rate of one of these, mersalyl, was found to depend upon the applied voltage in a way suggesting that the residue attacked by the reagent from the trans side of the bilayer is accessible only when the channel is open. On the other hand, inhibition by these reagents added to the cis side occurs equally well whether the channel is open or closed. This observation suggests that the sulfhydryl residue involved in the “cis” inhibition is not located within the K + diffusion pathway. Further confirmation of critical sulfhydryl residues comes from studies showing that methanethiosulfonates also cause rapid inhibition from both sides of the bilayer (B. Breit and C . Miller, unpublished). Unfortunately, none of these reagents is useful in pharmacological manipulation of SR vesicles, since they wreak general havoc on the vesicles, which carry SH-laden Ca2+-ATPaseat very high density.
2. PROTEASES We have found several types of proteolytic modifications of the channel’s behavior, which can be observed after insertion of the channel into planar bilayers. All proteases studied are effective only when added on the trans side of the bilayer; they have no effect from the cis side. The best studied is alkaline proteinase b (APb), an arginine/lysine-specific serine protease derived from pronase (Miller and Rosenberg, 1979b). This enzyme, when added to the trans side, rapidly modifies the channel’s gating in a profound way. In response to the protease, the channel loses its voltage dependence. The macroscopic conductance of a many-channel bilayer, which is normally rectifying, is rendered nearly ohmic by the enzyme treatment. Studies at the single-channel level showed that the enzyme has little effect on the probability of channel opening at zero voltage; here, channels open and close after protease treatment with approximately the same rates as before the reaction. However, the voltage
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dependence of the gating process is entirely altered by APb. The probability of opening becomes almost completely independent of the applied voltage. In other words, the effect of APb is to uncouple the gating from the applied voltage, i.e., to “clip off” the gating charge [Eq. (2)]. This result leads to the speculation that the gating machinery is a rather localized structure, close to the trans side of the channel. Neither the channel conductance nor its ionic selectivity is affected by APb. Another interesting observation that emerged from this work was the finding that the enzyme is unable to react with the closed state of the channel (Miller and Rosenberg, 1979b). as found for the organomercurial reaction described above. The opening reaction, therefore, involves a conformational change large enough to expose to the trans aqueous solution chemical groups which are inaccessible in the closed conformation of the channel. Trypsin, another serine protease, produces the same effect as APb, but with a much lower reaction rate (Miller and Rosenberg, 1979b). Chymotrypsin, which reacts at hydrophobic amino acid residues, brings about an entirely different modification of the K + channel, also from the trans side (C. Miller and B. Breit, unpublished). This enzyme does not change the voltage-dependent gating probabilities, but it increases the opening and closing rates about I0-fold. In addition, the single-channel conductance is lowered to about half after chymotrypsin treatment. This reaction is plainly more complicated than that of APb, and further study is required. Our overall experience is that the channel is quite susceptible to a variety of proteolysis reactions from the trans but not from the cis 4de.
3. LIPIDEFFECTS All studies of the effects of lipid on the function of membrane proteins are fraught with difficulties, and in general we have steered clear of this area. But because the planar bilayer system provides a unique opportunity of varying the lipid environment of an integral membrane protein and examining the consequent changes in behavior on the level of individual protein molecules, we have been tempted into several recent investigations from which quantitative conclusions can be drawn. As mentioned above, the gating behavior of the channel is indeed modified by the lipid composition of the bilayer (Labarca cr a / . , 1980). Increasing the negatively charged lipid components tend to close the channel, i.e., to shift the conductance-voltage curve to the right. Furthermore, the values of the entropy and enthalpy of the opening reaction are sensitive to the lipid environment (Labarca et a / ., 1980). Thus, the channel protein, inserted into the bilayer, “feels” its ocean of
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foreign lipid, which, in a typical experiment, is some five to six orders of magnitude in excess of the native SR lipid carried along when the vesicles fuse. Indeed, a complete exchange of native lipid under these conditions of infinite dilution must be the case, if hydrophobic interactions operate at all as we think they do (Tanford, 1980). A major problem with the lipid effects mentioned above is that the experiments were carried out in “painted” planar bilayers, which contain large amounts of decane, and in which the lipid composition of the bilayer is not known. Furthermore, our picture of the channel’s gating process is not sufficiently detailed to allow us to ask worthwhile questions about lipid effects. For this reason, work on lipid effects has focused on the channel’s conduction process, about which questions exist which can be addressed in a quantitative way by variation of lipid composition. Specifically, we have wondered about the extent to which the channel protein might feel the surface potential set up by charged lipid components in the bilayer (Bell and Miller, 1984). In a negatively charged membrane, for instance, the concentration of K+ at the surface is much higher than that in the bulk solution, due to the electrical double layer (McLaughlin, 1977). The local cation concentration seen by the gramicidin A channel, for example, is very much higher in a PS membrane than in a neutral PE membrane, and this effect can be explained quantitatively by the Gouy-Chapman-Stern model of the electrified interface (Apell ef al., 1979; Alvarez et al., 1983). In contrast with the gramicidin A channel (the “mouth” of which is located right at the lipid bilayer surface), integral membrane proteins might be expected to protrude many nanometers into aqueous solution. The ion conduction process of such a channel would be somewhat insulated from the bulk surface potential. To approach this question for the SR KS channel is a relatively simple matter. Single-channel conductance was measured as a function of K + concentration (from 10 mM up to 1 M )in neutral bilayers formed from PE and PC and in charged bilayers containing PS as well (Bell and Miller, 1984). Care was taken to carry out all experiments in “solvent-free” folded membranes, in which lipid composition is well defined, and to confirm this composition by independent measurements of bulk surface potentials. Figure 6 shows the results of one such comparison. In 70% PS bilayers, the K + conductance is always higher than in neutral bilayers, and the effect of charge becomes increasingly pronounced at lower ionic strengths, as expected by an electrostatic mechanism. The effect of PS, however, is much less than would be expected if the channel mouth were located at the surface of the bilayer. Instead, the data are consistent with the idea that the channel entryway is located 2.0-2.5 nm (20-25 A) away from the bulk surface charge. Furthermore, this distance is the same from
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230 IS
I
I
0
0.3
I
0.6
Concentration (MI FIG.6 . Effect of phospholipid surface charge on K' conduction. SR vesicles were fused with symmetrical bilayers formed from monolayers containing either 80% PE/20% PC or 70%' PS/30% PE. The aqueous solutions contained the appropriate K + (gluconate salt) acid] and 0.5 rnM concentration as well as 5 m M MOPS [3-(N-morpholino)propanesulfonic EDTA. Open circles represent the conductances obtained in PE/PC bilayers, and are well fitted by B rectangular hyperbola with ii diw)ciation constant of 40 rnM and maximum conductance of 230 pS. Closed circles ere the data from the PS/PE membranes. The solid lines are the expected conductance values for a channel protruding the indicated distance in angstroms. from a bil;iyer containing the me;tsurcd hurfiice charge density of I .5 charges/ nrn2 (from Bell and Miller. 1984).
both sides of the channel, as can be studied by analysis of current-voltage relations, and through the use of asymmetrically composed bilayers. This result does not tell us that the channel literally protrudes into solution 2 nm or so. Such isolation could also come about if the entryway were isolated laterally from the lipid bilayer (marshmallow-with-a-hole model). Current work utilizing glycolipids with charges displaced at known distances from the bilayer surface may help to answer this question. G. SR Channels from Other Species All of the work described above was carried out using SR isolated from the fast white skeletal muscle of rabbit. It is notable that channels with qualitatively similar properties have been observed in every SR preparation investigated in this laboratory (C. Hidalgo and C. Miller, unpublished), including SR from chicken and pig skeletal muscle, and from
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canine cardiac and insect flight muscle (A. Williams, unpublished). This interspecies distribution of SR K i channels is of more than academic interest since virtually all work on the physiology of excitation-contraction coupling has been carried out on frog muscle, while the great majority of biochemical studies of SR have used rabbit muscle. For this reason, Labarca and Miller (1981) studied the conductance properties conferred upon planar bilayers by SR vesicles from bullfrog leg muscle. A K+-selective channel was found in this preparation with many properties similar to those described for the rabbit system. The channel was found to display voltage-dependent gating, opening and closing kinetics on the time scale of seconds, a high selectivity to K + , and a voltagedependent Csf block. Qualitatively, then, this channel appears to be the amphibian version of the K+ channel characterized in rabbit. However, one difference in the behavior of the frog channel was at once obvious. The frog channel clearly showed not one but two conducting states, of 50 and 150 pS in 100 mM K+. The transition kinetics between the states suggest that the “large” open state can be reached only from the “small” open state, and not directly from the closed state. These two states were seen with all the conducting alkali metal cations, and the conductance selectivity was in the same order as with the rabbit channel, i.e., K+ > Rb+ > Na+ > Lit > Cs+. The ratio of conductances of the two states was found to be 3 : 1 for each ion. This result was unexpected, since it means that the ionic selectivities of the two conducting states are quantitatively identical, although the absolute conductances differ by a factor of 3. The interpretation of this finding is not obvious, but it was suggested that the change in protein conformation occurring between the two conducting states may lead to changes in nonspecific electrostatic energy, such as image forces or dielectric shielding, rather than to changes in the specific ion-liganding interactions in the channel conduction pathway (Labarca and Miller, 1981). 111.
FLUXES IN NATIVE SR VESICLES
Studies on the electrical behavior of the K+ channel in planar bilayers shed no light whatever on the central question motivating work of this kind: the question of the permeability properties of the SR membrane, and their relation to excitation-contraction coupling. Two fundamental problems with the planar bilayer approach make it all but useless in attacking this question. First, in the absence of physiological information about the K+ permeability of the SR membrane in uiuo (and such information is totally lacking), we cannot be sure of the extent to which we have
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modified the channel by wrenching it out of its native membrane, in our enthusiasm for inserting it into a model system. This is a problem that all membrane reconstitution work necessarily faces, but in most studies of this kind, there is a well-described physiological function that can be used to monitor reconstitution, and the properties of the model system can be checked against a standard of “correct” behavior. Unfortunately, with the SR K + channel in planar bilayers, we have no such standard for guidance. As an assay of correct function, then, the planar bilayer is “blind.” The second failing of the system is the extreme selectivity of the fusion process (Miller, 1983). Experience has shown that some types of membrane vesicles fuse with planar bilayers very easily, while others are extremely resistant to fusion. For example, under similar conditions, rabbit SR vesicles fuse at rates about 50 times higher than do frog SR vesicles. It is possible, therefore, that in studying SR K’ channels, we are selecting a very small population of vesicles that fuse easily with the bilayer, but are not representative of the SR membrane conductance as a whole. When using only the planar bilayer system, it is virtually impossible to address this question even superficially. As an assay of a membrane population, again the planar bilayer is “blind.” Problems of this type have motivated several investigators to study the permeability of the SR membrane to small ions, by measuring passive fluxes directly on SR vesicles. This has the great advantage of being a step closer to the physiological membrane in v i m , and of unequivocally making measurements on the total population of SR vesicles. Thus, neither of the fundamental problems encountered with planar bilayers arises here. Measurement of channel-mediated ion permeability is not without its own difficulties, however. A “typical” SR vesicle of 100-nm radius contains, at 100 mM KCl, about 200,000 K+ ions. If this vesicle carries only a single ion channel, which can pass lox iondsecond, the half-time of passive exchange will be of the order of 1 msec (Miller and Racker, 1979). Thus, the high turnover rates of ion channels conspire with the high surface-to-volume ratio of small vesicles to make conventional isotope exchange techniques unsuitable as a basis for the quantitative assay of channel-mediated fluxes in SR vesicles. The problem is especially severe for the SR K+ channel, since it cannot be rapidly opened or “quenched” by sudden application of agonist or of antagonist. Nevertheless, several studies of the small ion permeability of SR vesicles have yielded useful results, especially with reference to the existence of the K + channel in the native SR membrane. The original impetus of these studies was provided by McKinley and Meissner (1978), who loaded SR vesicles to equilibrium with two radioactive solutes, Rb’ and choline,
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and then followed their passive efflux upon dilution into nonradioactive medium. Both labels were lost from the vesicles over a period of a few minutes, i.e., rather slowly. However, the Rb+ appeared to be effluxing from a total space only a third of the choline space. Since both isotopes must have equilibrated with the same space during the loading step, it was concluded that about 60-70% of the SR vesicles lost their Rb+ before the first sample could be taken for analysis, 20 seconds after dilution. Similar results were obtained using Na+ instead of RbC. The existence of two types of SR vesicles was thus proposed: “type I” vesicles, which are highly permeable to Rb+, K + , and Na+, possessing a monovalent cation permeability mechanism, and “type 11” vesicles, which are devoid of this “cation channel.” Parallel experiments showing that C1- is exchanged within 20 seconds from the entire population of vesicles led to the proposal that an anion transporter exists in both types of SR vesicles. An alternative method of following small ion fluxes in SR is based on the use of voltage-sensitive fluorescent dyes to monitor the vesicle membrane potential. McKinley and Meissner (1978) were able to confirm their conclusions from isotope exchange by monitoring changes in the fluorescence of one of these dyes, diO-C5-(3), upon diluting vesicles loaded with K+ into a K+-free medium, using choline or Tris as substitute. Under such conditions, a fluorescence change is observed, consistent with a K+ diffusion potential. The fluorescence signal dissipates during several minutes, as Tris and K+ slowly exchange. Addition of valinomycin enhances the signal, as if a fraction of the vesicles (type 11) do not carry a K+ permeation mechanism. When Na+ was used as the external ion instead of Tris, no fluorescence change was observed, as if Na+ and K’ exchange essentially instantaneously. Using this method, McKinley and Meissner were able to screen the permeabilities of many cations, and concluded that the “cation channel” responsible for the permeation excludes cations of cross section larger than 0.4 X 0.6 nm. This estimate is in excellent agreement with the K+ channel cutoff diameter of 0.4-0.5 nm determined in later planar bilayer studies, as described above (Coronado and Miller, 1982). Yet another method for measuring small-ion permeability in SR vesicles relies on light scattering changes following an osmotic shock (Kometani and Kasai, 1978; Yamamoto and Kasai, 1981, 1982a,b). Here, SR vesicles are equilibrated in a low-osmolarity medium (10 mM KCI, for example) and rapidly diluted into high osmolarity (100 mM KCl) in a stopped-flow apparatus. The vesicles shrink and then reswell as KCI enters, and this process is monitored by 90” light-scattering changes. The rate of reswelling measures the salt permeability, which in general is limited by the permeability of the slower ion. Using this method, Kometani and Kasai (1978) measured the ionic
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permeability sequence for a variety of anions, cations, and nonelectrolytes. Pertinent to our discussion is the sequence CI- >> K+ > Na’ > Lit >> choline, glucose. The half-time of entry for C1- itself was measured to be 0.2 seconds, while that for K+ was 10 seconds. These results are in direct contradiction with the planar bilayer data, from which we expect K + to permeate more rapidly than C1- (Miller, 1978), with an equilibration rate four orders of magnitude faster than that seen here. We consider, however, that the conclusions of Kometani and Kasai (1978)are invalid because of the existence of the two populations of SR vesicles, as clearly demonstrated by McKinley and Meissner (1978). In measuring reswelling rates, Kometani and Kasai (1978) used only the overall halftime of the relaxation, which for KCI is about 10 seconds. However, the original data show that there are, in fact, at least two components of this relaxation, a rapid one of about 0.4-second half-time, and a slow one of 15-second half-time, as we have confirmed (A. M. Garcia and C. Miller, unpublished). Furthermore, the amplitude of the KCl relaxation is only about 30% as large as that in a similar experiment using choline as the cation. Such behavior is consistent with the idea that the KCI permeability of type I vesicles is so high (higher, indeed, than that of water) that it is altogether missed in a light-scattering assay; in such a case, only 30% of the SR vesicles, the type 11 vesicles, would be seen, and these would be much more permeable to C1- than to K + . Although the light-scattering method is not adequate to measure K + fluxes, it is probably applicable to a similar measurement of choline fluxes, which occur on the much longer time scale of 10 seconds. Yamamot0 and Kasai (1981, 1982a,b) have used this method with choline as a “slow marker” for the cation permeability of SR vesicles. They found that the choline flux is inhibited by Cs+ in the range of 10 mM. Moreover, these authors showed that Ca’’ in the 1-10 p M range induces biphasic kinetics of choline, and that Cs’ inhibits only the Cs2+-independentfraction of these choline fluxes. These results were taken to mean that SR vesicles may contain w o types of cation channels, one of them activated by Ca2+,and one independent of this ion. Further work suggested that the Ca?+-independentcation channel is driven open by increasing SR membrane potential, outside positive (Yamamoto and Kasai, 1982b). Our experience with this light-scattering assay convincea us that although it may be used as a qualitative indication of the time scale of ion fluxes, any quantitative conclusions must be taken with extreme caution. In particular, we have observed light-scattering relaxations in the presence of 1-100 p M Ca2+which are clearly unrelated to ion movements, since they are seen in vesicles permeabilized with nonspecific ionophores (Garcia and Miller, 1984b). Their origin is unclear, but they could result from Ca”-induced changes i n the refractive index of the membranes or of
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the internal Ca’+-binding proteins, or from changes in vesicle aggregation or shape. We should point out, however, that the postulated permeability of vesicles to choline, on a time scale of seconds, is not inconsistent with our failure to detect choline conductance through K+ channels inserted into bilayers. A flux time of 10 seconds would imply a single-channel conductance of the order of 10 fS, well below the limit of the sensitivity of the electrical system. Because of the uncertainties of the light-scattering method, we have begun to apply to SR vesicles another technique for following small cation fluxes on a rapid time scale. This is the method of TIt quenching, developed by Moore and Raftery (1980) to monitor channel-mediated fluxes in Torpedo vesicles. Vesicles are loaded with a hydrophilic fluorescent dye, pyrene tetrasulfonate, and are rapidly mixed with a solution containing TIt,a heavy metal K t analog. The dye fluorescence is quenched by TI’, the entry of which can therefore be followed quantitatively at 5-msec time resolution. This method can be conveniently used to measure the fluxes in SR vesicles of the same ions for which we can directly measure channelmediated conductances in planar bilayers (Garcia and Miller, 1984a,b). SR vesicles are loaded with 100 mM K+ or Lit and 10 mM pyrene tetrasulfonate. The vesicles are then rapidly mixed with an isoosmotic solution, in which 25 mM of the small cation is replaced by TI+. The observed time course of fluorescence quenching can, with proper controls, be converted into a time course of the change of internal TIt concentration (Fig. 7). The thallous ion permeates easily through the SR Kt channel in bilayers. However, the rate of entry of TI+ into the vesicles is limited by the efflux of the slower ions present in the internal space, if care is taken to exclude small anions like CI-. Thus, with choline as the internal ion, TI+ enters slowly, on a time scale of seconds. Thallous ion influx into SR vesicles in exchange for ions known to permeate the Kt channel is rapid (Fig. 7), and behaves qualitatively as expected from McKinley and Meissner’s picture of the SR vesicle population. With all ions, the influx is biphasic, with a slow fraction accounting for about 30% of the total entry, and a fast fraction accounting for the rest. The rate of the slow fraction is not critically dependent on the internal ion, but the rate of the fast fraction shows a substantial ionic selectivity. With K t or N a + as the internal ion, the fast fraction is too rapid to measure, being complete in less than 3 msec. With Lit, however, the fast fraction can easily be resolved, with a half-time of approximately 20 msec. This rate is consistent with the properties of the SR K + channel in planar bilayers (Garcia and Miller, 1984b). In such bilayers, the singlechannel conductance for Lit is 5 pS (Coronado et d.,1980; and Table I).
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288 Time (ms) FIG. 7. TI+ influx into S R vesicles. SK vesicles preloaded with the Huorescent dye
pyrene tetrasulfonate and 100 mM K + or 1 i-’ glutamate were mixed, in a stopped-flow apparatus, with an equal volume of a solution containing 50 mM of the cation replaced by TI+.The concentration of TI+ inside the vesicles was calculated from the decrease in fluorescence of the trapped dye. The continuous line corresponds to fitting of the data by two exponentials. (a) TI+-Li+ exchange of vesicles preincubated with gramicidin A ( I .25 pg/ ml). (b) and ( c ) TI+ exchange with K + (b) or Li’ (c). (d) TI+-Li’ exchange in the presence of 0.5 mM bis-G-I0 ( 1 ,lo-bisguanidinodecane).
If the average type 1 vesicle of 100-nni radius contains five such channels, the expected half-time of Lit entry is 30 msec, in excellent agreemcnt with the observed flux. Our failure to resolve the fluxes of K ’ and Na+ is also consistent with the high conductances of thcse ions in the bilayer (Table I). An additional observation is that the “mixed-type” bisguanidinoalkane blockers (such as bis-GI0 in Fig. 7) inhibit the Lit flux from the inside of the SR. at concentrations comparable to those effective in the bilayer. Calcium has no effect on these rates in the range of 1-100 p M . We have concluded from these experiments that the idea originally proposed by McKinley and Meissner is essentially correct: that SR vesicles are of two populations, with 50-70% carrying a cation channel and the rest only nonspecifically permeable to cations. The behavior of the channels in the type 1 vesicles is consistent, overall, with the properties of the K+ channel in planar bilayers. IV. STANDING PROBLEMS AND FUTURE DIRECTIONS
To the extent that some of the essential attributes of the K+ channel in bilayers appear to be manifest in native SR membrane vesicles, we can reasonably propose that neither of our worries about the “blindness” of
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the planar bilayer system applies in this particular case. The channel is apparently located in a major population of SR vesicles, and its electrical behavior in bilayers does not seem to be an artifactual consequence of insertion into a model membrane. But there are still good reasons to question whether the characteristics of this channel, both in the SR vesicle membrane and in the model system, may not be representative of its function in the SR membrane in vivo. So what does this channel, after all, do? If it behaves in the intact SR membrane as it does in the planar bilayer, how might it contribute to the events of excitation-contraction coupling? Our best guess for the operation of the K+ channel is that it functions as an electrical shunt for the SR membrane. We imagine that under physiological conditions, the channel might reside at a density of about 100/pm2,and on the average might be open, say, 10% of the time. The SR membrane would therefore exhibit a K + conductance in the range of 0.1 S/cm2,a value so high that the membrane potential would always be clamped at the K + equilibrium potential of zero voltage. In this way, K+ would always be easily able to compensate for the massive release of Ca2+causing contractile activation. Two observations from muscle physiology are difficult to reconcile with this picture of K + channels operating as an electrical shunt. The first of these is the observation that Nile blue, a dye thought to monitor the SR membrane potential in frog single muscle fibers, indicates large voltage changes during Ca2+release (Vergara et d., 1978). These changes could not happen if K+ channels were massively shunting the SR membrane. In addition, the total SR membrane conductance implied by the time constant of the dye signals is about 10 pSIcm2, four orders of magnitude lower than it would be if K+ channels in the native membrane behave as they do in the planar bilayer (Coronado et al., 1980). The second piece of evidence bearing on this point is the observation (Somlyo et ~ d . ,1981) from electron microprobe analysis of frog muscle that the calcium lost from the SR lumen after a massive tetanus is not electrically compensated for by the gain of K and Na+. There appears to be an “invisible” charge compensation, perhaps contributed by protons. It is therefore not clear that the limited amount of physiological information on calcium release is consistent with a high-conductance K + channel in the S R membrane. At this point, we can only acknowledge that all of the approaches toward this question are indirect, and that none provides a definitive answer. It will therefore be important in the future to try to find truly specific, strong inhibitors of the SR channel which may be applied to native muscle fibers, in the hope of dissecting out any effects of SR K t conductance which may be present. Another important direction to pursue with this channel is the continu-
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ing characterization of its putative properties in native SR membrane vesicles, along the lines described here. In particular, the high time resolution methods of TI+ flux and possibly of stopped-flow measurements of signals from fast voltage-sensing fluorescent dyes will help us find out which of the properties of the K ’ channel. as observed directly in bilayers, can also be seen in the SR membrane itself. The mechanistic characterization of the channel in bilayers continues to suggest new questions about the ways in which ions interact with this protein. Work on lipid-channel interactions is only just beginning, as are attempts to “map” the structure of the K + conduction pathway with blockers. This type of work is of little direct interest for muscle physiology, but offers a detailed description of a simple integral membrane channel protein as a possible model for more complicated channels. Finally, attaining the biochemical goal of the isolation, purification, and reconstitution of the system may not be far in the future, although this is probably a very minor constituent protein of the S R membrane. Indeed, Young et al. (1981) have recently shown that liposomes formed from detergent-solubilized SR preparations display cation flux properties similar to those of native membrane vesicles. Such a functional reconstitution from the detergent-solubilized state may eventually serve as an assay for purification. We think it likely that all these approaches will be essential in productive future attacks on this system. Only by a combined assault using the tools of membrane biochemistry, the methods of channel biophysics, and the probes of molecular phhrmacology can we hope to gain an understanding of the relationship between the molecular structure and the functional physiology of this elusive channel protein. REFERENCES Adelman. W. J., and French, R. J . (1978). Blocking ofthe squid axon potassium channel by external caesium ions. J . Pliysiol. (London)276, 13-25. Alvarez. 0..Brodwick. M.. Latorre. K.. McLaughlin. A , , Mcl.aughlin, S . . and Szabo. C;. ( 1983). Large divalent calionn and electrostatic potentials adjacent to membranes: experimental results with hexamethonittm. Bioplrys. J . 44, 333-342. Andersen, 0. S . , and Procopio. J . (1980). Ion movement through grarnicidin A channels. On the importance of the aqueous diffusion resistance and ion-water interactions. Ac/u Physiol. Scand., Suppl. 481, 27-42. Apell, H.-J., Barnberg. E . . and LBuger, P. (1979). Effects of surface charge on the conductance of the grarnicidin channel. Biocliim. Biophj)s. Acta 55, 369-378. Armstrong, C . M. (1975). K’ pores of nerve and murcle membranes. Mrmhrunrs 3, 325-
358. Baylor, S . M., Chandler, W. K.. and Marshall, M. W . (1982a). Optical measurements of intracellular pH and magnesium in frog skeletal muscle fibres. J . Physiol. (London) 331, 105-137.
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Baylor, S . M., Chandler, W . K., and Marshall, M. W. (1982b). Use of metallochromic dyes to measure changes in myoplasmic calcium during activity in frog skeletal muscle fibres. J . Physiol. (London) 331, 139-177. Bell, J. E., and Miller, C. (1984). Influence of phospholipid surface charge on ion conduction through the K+ channel of sarcoplasmic reticulum. B k ~ p h y .J~. . 45, 279-288. Coronado, R., and Miller, C. (1979). Voltage-dependent Cs' block of a K+ channel from sarcoplasmic reticulum. Nature (London) 280, 807-810. Coronado, R., and Miller, C. (1980). Decamethonium and hexamethonium block K+ channels of sarcoplasmic reticulum. Nature (London) 288,495-497. Coronado, R., and Miller, C. (1982). Conduction and block by organic cations in a K+selective channel from sarcoplasmic reticulum incorporated into planar bilayer membranes. J . Gen. Physiol. 79, 529-547. Coronado, R., Rosenberg, R., and Miller, C. (1980). Ionic selectivity, saturation and block in a K+-selective channel from sarcoplasmic reticulum. J . Gen. Physiol. 76, 425-446. Ehrenstein, G., Lecar, H., and Nossal, R. (1970). The nature of the negative resistance in bimolecular lipid membranes containing excitability-inducing material. J . Gen. Physiol. 55, 119-133. Ehrenstein, G., Blumenthal, R., Latorre, R., and Lecar, H. (1974). Kinetics of the opening and closing of individual excitability-inducing material channels in a lipid bilayer. J . Gen. Physiol. 63, 707-721. Garcia, A . M., and Miller, C. (1984a). Channel-mediated TI+ fluxes in native sarcoplasmic reticulum vesicles. Biophys. J . 45, 49-50, Garcia, A . M.. and Miller, C. (1984b). Channel-mediated monovalenl cation fluxes in isolated sarcoplasmic reticulum vesicles. J . Gen. Physiol. (in press). Hille, B. (1975). Ionic selectivity of Na+ and K+ channels of nerve membranes. Membranes 3, 255-324. Hille, B., and Schwarz, W. (1978). Potassium channels as multi-ion single file pores. J . Gen. Physiol. 72, 409-442. Kita, Y.,Bell, J. E., and Miller, C. (1984). Current-dependent blocking of sarcoplasmic reticulum K' channels by diaminoalkanes. J . Membr. B i d . (submitted for publication). Kometani, T., and Kasai, M. (1978). Ionic permeability of sarcoplasmic reticulum vesicles measured by light scattering method. J . Membr. Biol. 41, 159-186. Labarca, P., and Miller, C. (1981). A K+-selective, three-state channel from fragmented sarcoplasmic reticulum of frog leg muscle. J . Membr. Biol. 61, 31-38. Labarca, P., Coronado, R., and Miller, C. (1980).Thermodynamic and kinetic studies of the gating behavior of a K+-selective channel from the sarcoplasmic reticulum membrane. J . Gen. Physiol. 76, 397-424. Latorre, R., and Miller, C. (1983). Conduction and selectivity in K+ channels. J . Membr. Biol. 71, 11-30. Lauger, P. (1973). Ion transport through pores: A rate-theory analysis. Biochim. Biophys. Acta 311, 423-441. Levitt, D. G., Elias, S . R . , and Hautman, J. M. (1978). Number of water molecules coupled to the transport of sodium, potassium, and hydrogen ions via gramicidin, nonactin, or valinomycin. Biochim. Biophys. Acta 512, 436-451. McKinley, D., and Meissner, G. (1978). Evidence for a K+, Na+ permeable channel in sarcoplasmic reticulum. J . Membr. Biol. 44, 159-186. McLaughlin, S . (1977). Electrostatic potentials at membrane-solution interfaces. Curr. Top. Membr. Transp. 9, 71-144.
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Miller, C. (1978). Voltage-gated cation conductance from fragmented sarcoplasmic reticulum: Steady-state electrical properties. J . Memhr. Biol. 40, 1-23. Miller, C. (1982a). Bis-quaternary ammonium blockers as structural probes of the sarcoplasmic reticulum K’ channel. J . G w . Phy.rio/. 79, 869-891. Miller, C. (1982b). Coupling of water and ion fluxes in a K’-selective channel of sarcoplasmic reticulum. Biophys. J . 38, 227-230. Miller, C. (1982~).Feeling around inside a channel in the dark. In “Transport in Biomembranes: Model Systems and Reconstitution” ( R . Antolini. A. Gliozzi, and A. Gorio, eds.), pp. 99-108. Raven Preas. New York. Miller, C. (1983). First steps in the reconstruction of ionic channel functions in model membranes. I n ”Current Methods in Cellular Neurobiology” (J. L. Barker and J . F. McKelvy. eds.). Vol. 3. pp. 1-37. Wiley, New York. Miller, C.. and Racker, E. (1976). Ca’ +-induced fusion of fragmented sarcoplasmic reticulum with artificial bilayers. J . Mei?ihr. Biol. 30, 283-300. Miller, C., and Racker, E. (1979). Reconstitution of membrane transport functions. In “The Receptors: A Comprehensive Treatise” (R. D. O’Brien, ed.). Vol. I, pp. 1-31. Plenum, New York. Miller, C., and Rosenberg, R. (197%). A voltage-gated cation conductance channel from sarcoplasmic reticulum. Effects of transition metal ions. L3iochemistr.v 18, I 1381145. Miller, C., and Rosenberg, R. (1979b). Modification of a voltage-gated K’ channel from sarcoplasmic reticulum by a pronase-derived specific endopeptidase. J . Gen. Physiol. 74, 457-478. Montal. M., and Mueller, P. (1972). Formation of himolecular membranes from lipid monolayers and a study of their electrical properties. Proc. Nntl. Acud. S c i . U.S. A . 69, 3561-3566. Moore, H.-P., and Raftery, M. (1980). Direct spectroscopic studies of cation translocation by Torpedo acetylcholine receptor on a time scale of physiological relevance. Proc. Nut/. Acud. Sci. U . S. A . 77, 4509-45 13. Mueller. P.. and Rudin. D. 0. (1969). Himolecular lipid membranes. Techniques of format i o n , study of electrical properties, and induction of ionic gating phenomena. fir “Laboratory Techniques in Membrane Biophysics” ( H . Passow and R. Stiimpfli. eds.), pp. 141-156. Springer-Verlag, Berlin and New Y o r k . Rosenberg, P. A.. and Finkelstein, A . (1978). Interaction of ions and water in gramicidin A . 72, channels. Streaming potentials across lipid bilayer membranes. J . G ~ wPhysiol. 327-340. Somlyo, A. V.. Gonzalez-Serratos, H . , Shuman. H.. McClellan, G.. and Somlyo, A. P. (1981). Calcium release and ionic changes in the sarcoplasmic reticulum of tetanized muscle: An electron-probe study. J . Cell Biol. 90, 577-594. Tanford, C. (1980). “The Hydrophobic Effect: Formation of Micelles and Biological Membranes.” Wiley. New York. Vergara. J . . Bezanilla, F., and Salzherg, B. M. (1978). Nile blue fluorescence signals from cut single muscle fibers under voltage or current clamp conditions. J . Grn. Physiol. 72, 775-800. White, S . H . . Peterson, D. C., Simon. S . , and Yafuso, M. (1976). Formation of planar bilayer membranes from lipid monolayers. A critique. Biopky.~.J . 16, 481-501. Woodhull, A. M. (1973). Ionic blockage of sodium channels in nerve. J . Gen. Pliysiol. 61, 687-708. Yamamoto, N., and Kasai, M. (1981).Studies on the cation channel in sarcoplasmic reticu-
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lum vesicles. I. Characterization of Ca++-dependentcation transport by using a light scattering method. J . Biochem. (Tokyo) 90, 1351-1361. Yamamoto, N., and Kasai, M. (1982a). Characterization of the Ca++-gatedcation channel in sarcoplasmic reticulum vesicles. J . Biochem. (Tokyo)92, 465-475. Yamamoto, N., and Kasai, M. (1982b). Inhibition of a voltage-dependent cation channel in sarcoplasmic reticulum vesicles by caesium studied by using a potential-sensitive cyanine dye. Biochim. Biophys. Acta 692, 89-96. Young, K., Allen, R.,and Meissner, G. (1981). Permeability of reconstituted sarcoplasmic reticulum vesicles. Reconstitution of the K'. Na' channel. Bi0c.him. Biophys. A m 640.409-418.
Measuring the Pro erties of Single Channels in Cell embranes
fvf
H . - A . KOLB Department of Biology University of Konstrrnz Kon.ytan;, Fc~derolReprihlir of Germany
I. 11. A.
The Lol-entzian Spectrum of a Two-State Channel . . . . .
Aulocovariance Function. . . . . . . . . . . . . . . . . . . . . . . . . . Relaxation and Covariance Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. ‘The Analysis of Nonstationary Flucluation~. . . .......... Noise Antilysis of Non-Channel-Mediiiled I ent . . . . . . . . . . . . . . . . . . . Methods of Single-Channel Recording . . . . ...................... A . ion Channel Reconstitution in t‘lmir I ......................... t). Patch-Clamp Method . . . . . . . . . . ......................... C. Patch Clamp of Reconstitirted System\ . . . . . . . . . . . . . . . . . . . . . . . . Ion Channels in Patched Menihranes ................................ A . Chemically Activated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Voltage Activated . . . . . . . ................... C . Calcium Activated.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. D.
111.
IV.
V.
............. V I . Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . ................................................
143 144 147 147 149 150 156
170 171
I. INTRODUCTION
The lipid phase of the membrane is spanned by integral membrane proteins which form a hydroflhilic pathway through the hydrophobic core of the membrane. Early studies with ionophore antibiotics (McLaughlin and Eisenberg, 1975) established the occurrence of discrete and uniform conductance changes in such membranes which could be assigned to the 133 Copyright B 1984 by Audemic Press, Inc All rights of rrproduLtlun in dny form reserved ISBN 0- 12-1 51321 -2
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opening and closing of ionic pathways denoted as channels or pores. Other membrane proteins act by increasing the ion concentration within the membrane as a result of complex formation of ions with mobile membrane-bound molecules. The latter transport systems are usually called carriers (Stark, 1978). These two transport mechanisms can be considered as two limiting mechanisms of ion permeation (see Lauger, this volume). Carrier systems have not been successfully analyzed by electrophysiological measurements on biological membranes, a failure attributable to the low ion transport capacity of a carrier as compared to a channel. But the channels have been very efficiently studied, as we discuss in this article. Much knowledge about ion permeation through cell membranes has been obtained by studying the physical basis of electric cell excitability, and the observed voltage-dependent macroscopic conductance changes have been accounted for in terms of single-ion channels. Indirect evidence for the presence of ion channels was obtained by applying two main techniques: current relaxation and current noise under voltage-clamp conditions. But the invention of the patch-clamp technique (Neher and Sakmann, 1976a) has made discrete current steps visible, those steps being envisioned as the opening and closing of single ionic channels. The number of publications applying this patch-clamp method is increasing almost exponentially, and the observed variability of single-channel properties is increasing in parallel. The properties investigated so far are the single-channel conductance, multiple-channel states, transition rates between channel states and their dependence on voltage, ion selectivity, and the effect of ionic strength and temperature. Questions concerning the shape and dynamics of the internal structure of the channel molecules, the actual movement of the ion within the channel, and its interaction there with ions, water molecules, and the channel itself are largely unsolved. Section I1 presents a simplified treatment of the stationary and nonstationary analysis of macroscopic current fluctuations (or noise), based on the assumption that ion channels open and close independently of each other and can exist in only two states-open and closed. In this simple case of a linear (first-order) kinetic system the analysis of current noise gives an estimate of two important molecular parameters, the mean length of time a channel remains open and the conductance of the open state. In general, analysis of current noise in biological membranes can, however, be explained by several alternative molecular transport models, and therefore measurements of the properties of single ionic channels are needed. In Section IV,A, therefore, the available methods of single-channel recording are characterized. Single-channel behavior can be studied using
MEASURING THE PROPERTIES OF SINGLE CHANNELS
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planar lipid bilayer membranes doped either with ionophores or with biological ion channel systems. For some of these reconstituted biological channel systems, the conductance phenomena of the intact cell membrane can be described well by the derived microscopic data. Sections IV,B and IV,C discuss how the development of the patch-clamp technique has revolutionized the analysis of ion transport through biological membranes. We give a short description of the basic applications of the patch-clamp techniques and of the recently developed method of measuring patches of channel-doped planar bilayer membranes. This is followed by a survey of the reported single-channel data (Section V). In the final section (Section VI) problems of analyzing single-ion channels are briefly discussed. II. FLUCTUATiON (NOISE) ANALYSIS OF MULTICHANNEL SYSTEMS
Historically, electrical measurements on biological membranes were performed on preparations containing a large number of ion transport systems. In general, the contribution of an elementary ion transport pathway such as a channel, a carrier, or an ATP-mediated ion transport is not detectable within the measured overall macroscopic current through the membrane. But, as a natural consequence of the discrete nature of ionic flow, the current across membranes shows a fluctuating or noisy behavior. The basic idea of noise analysis is that the same elementary events give rise both to the macroscopic current and to the fluctuating part of it (for a discussion of the assumptions involved in fluctuation theory in general, see van Kampen, 1976). The elementary event that we will consider is a change in the actual membrane current due to a conductance change of a channel. Fluctuation analysis has been successfully applied to a great variety of biological membranes and has yielded much information about the molecular properties of ion channels, such as the mean lifetime and amplitude of the different conductance states. In the sections that follow, only the most frequently used equations of fluctuation analysis for a two-state channel are outlined. [For more extended reviews of fluctuation analysis, performed mainly on membranes of nerve and muscles, on frog skin, and on doped lipid bilayer membranes, see Verveen and De Felice (1974), Conti and Wanke (1973, Neher and Stevens (19771, De Felice (1977, 19811, Chen (1978), Bevan et al. (1979), Van Driessche and Gogelein (1980), Lindemann (1980), Neumcke (1982), and Frehland (1982).]
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A. The Lorentzian Spectrum of a Two-State Channel
We will consider a pore that can switch between a closed (c) and an open (0)configuration as the standard random (stochastic) event in ion transport through channels. The transitions between these configurations can be described as linear (first-order) chemical reactions with rate parameters a! and p : P
CF====O a
Transitions between the two channel states are generated by thermal activation. Under equilibrium conditions and at constant electrochemical gradient across the channel, these statistical processes cause current fluctuations M ( r ) of the instantaneous current J ( t ) around its time-independent mean value J(t): J(t) =
Jo + 6 J ( t )
(2)
As is well known from the fluctuation dissipation theorem, all displacements from the equilibrium decay on the average with the time constant T , = l/(a + p). Therefore, on the basis of a common reaction scheme, macroscopic relaxation experiments contain the same information about the rate constants as does the corresponding fluctuation analysis. By taking the Fourier transform of the fluctuating component of the membrane current, the spectral density function S c f ) can be derived. Mathematical procedures which allow a transformation of time-dependent random data into spectral intensities are well known (Bendat and Piersol, 1971). S(f) is defined as the intensity of fluctuations in a small frequency band around frequencyf. In order to make clear the physical meaning of the spectral density function, Fig. 1 illustrates one simple method by which it theoretically may be measured. In the case of the two-state channel, the so-called Lorentzian spectrum is obtained: Scf)
=
A41 +
cf/fc)21
(3)
A is the spectral density of S(f)forf-, O.fc denotes the corner frequency given by S(f = fc) = A/2 (see Fig. 1). fc is related to the time constant T~ by T , = 1/(2~h). The amplitude A can also be expressed by the variance of the current fluctuations 6 J ( t ) 2 :
A
=
4TC6J(f)*
(4)
One criterion for the identification of an individual population of twostate channels, by noise analysis of the overall membrane current, is considered to be the finding of a Lorentzian spectrum which behaves as
MEASURING THE PROPERTIES OF SINGLE CHANNELS
137
FIG. 1. Ideal bandpass filter for the determination of the spectral density function of a random current record. For simplicity, assume that the random fluctuation SJ(r)contains no periodic o r dc components. T o determine the spectrum the random current is applied to an ideal bandpass filter whose output is 8 1-0resistor. Let the center frequency of the bandpass filter of width 1 H z be continuously adjustable over the important range of frequencies of the random current fluctuations. By means of an appropriate power-measuring device, the power consumed by the resistor is determined at various center frequencies of the bandpass. If the power per hertz is then plotted a s a function of the adjusted center frequency, the curve appears a s the power density spectrum, also denoted as the spectral density function. The current fluctuations shown were measured on a lipid bilayer membrane (membraneforming solution: glycerylmonoerucinin-decane) doped with the channel-forming antibiotic gramicidin A (Kolb and Bamberg, 1977). A voltage of 30 mV was applied and I M Cs- used as transported ion. The Lorentzian spectrum was drawn according to Eqs. (3) and (4)using variance 6 J 2 = 1.4 X A' and corner frequency .f, = 2.7 Hz. The mean membrane current J(t) = 20.3 nA was measured independently. From Eq. (9) or (10) a mean singlechannel conductance of y = 23 pS is then derived.
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H.-A. KOLB
frequency independent (“white”) at low frequencies and declines with I/.f’forf>>.f, (see Fig. 1). In most reported cases the pure l/f2 behavior of S ( f ) could be followed only over the range of about one order of magnitude in frequency. Neglecting the contribution of further noise sources, the decline of S ( f ) reaches, at higher frequencies, the density of the thermal noise of membrane conductance G, generated by the mean number of conducting channels: Scf) = 4kTG
(5 )
where k is Boltzmann’s constant and T the absolute temperature. At thermal equilibrium (zero net current flowing through the channels) the spectral density function is frequency independent throughout and no information about the underlying rate parameters of ion transport can be extracted from fluctuation analysis. The main advantage of fluctuation analysis is that it allows one to estimate the single-channel conductance, even in the presence of many simultaneously opening and closing channels. In the case just described of a two-state channel, the mean current through a single channel is given by i p , where p is the steady-state probability of the open state at constant voltage V across the channel and i is the current through a single channel. If transitions between the open and closed states occur at random, the steady-state variance of the binominally distributed current pulses is i2p(I - p ) . In case of N identical and mutually independently acting channels one finds
J(r)= Nip
(6)
and the spectral density given by Eqs. (3) and (4) increases by the factor N . Using Eqs. (3) and (4) and the ohmic law, the mean single-channel conductance y is derived:
In the limit of a low probability of channel opening ( p << I ; Poissondistributed current pulses), one obtains the most frequently used equations for an estimation of 7: or
y
=
n.f,S(0)/[2JoV]
MEASURING THE PROPERTIES OF SINGLE CHANNELS
139
Equation (10) shows that the derivation of the Lorentzian spectrum (Fig. I ) and the measurement of the mean membrane current allow an estimation of the mean single-channel conductance even for multichannel systems. But 11s Frehland ( 1982) could show, non-channel-mediated ion transport mechanisms which also yield Lorentzian spectra are conceivable.
B. Interfering Noise Sources and Artifacts
In addition to the background noise arising from fluctuations in the leak current through the membrane and in the current recording system, a further modulation of the current is caused by fluctuations of the channel structure and by the discrete nature of ion current. In the simplest case the different noise sources are independent, although correlations might exist. I . DISTRIBUTION OF C H A N N E L AMPLITUDES For the derivation of Eq. (8), which allows an estimation of the mean single-channel conductance, the intuitive assumption has always been made that all channels adopt the identical conductance value in the open configuration. But even in the simplest case, Gaussian-distributed conductance amplitudes have to be expected. From single-channel experiments on planar lipid bilayer membranes using gramicidin as the poreforming substance, it is known that single-channel conductances show a probability distribution with a variance different from zero (Apell er d., 1977). A similar single-channel amplitude distribution is found for the acetylcholine receptor channel at the snake neuromuscular junction (Fig. 2 ) (Dionne and Leibowitz, 1982). Several explanations have been put forward for this observation. For example, there may be not a single form of a channel, but a whole ensemble of conformational states and different conformations may be frozen in, when the channel forms. If one takes into account the steady-slate variance of channel conductances ((T;), the mean single-channel conductance of Eqs. (8)-(10) has to be substituted by (Kolb, 1980)
The right-hand side of this relation now gives the true mean of the channel conductance distribution. Since in multichannel experiments w; is not known ;I priori, an overestimation of the true mean single-channel conductance is expected. It i s interesting to note that Eq. ( I I ) is also obtained for a single channel which undergoes transitions between differ-
140
H.-A. KOLB
SINGLE-CHANNEL CURRENT (PA)
FIG. 2. Amplitude characteristics of acetylcholine-operated channels at snake neuromuscular junctions. Single-channel amplitude distribution for 2305 events. Amplitude threshold = 1.8 PA. The distribution had a mean and standard deviation of 3.1 2 0.3 pA (Dionne and Leibowitz, 1982).
ent conductance states, while the channel is in the open configuration (Eisenberg cJt d., 1973).The difference between these two mechanisms of channel conductance appears in the different frequency dependence of the corresponding spectral density function. For the latter mechanism a superposition of Lorentzian spectra has to be expected, as found for alamethicin-doped planar bilayer membranes (Kolb and Boheim, 1978). The simultaneous presence of at least two populations of two-state channels, differing in conductance amplitude and rate constants, will also cause a superposition of Lorentzian spectra. This is found for the noise analysis of current fluctuations generated by junctional and extrajunctional acetylcholine receptor channels (Dreyer c’t “I., 1976; Neher and Sakmann, 1976b). Reversible blocking of a switching channel by a blocking (closing) molecule such as the lidocaine derivatives QX-222 and QX3 I4 on acetylcholine receptor channels (Ruff, 1977; Neher and Steinbach, 1978) or the so-called flickering (brief transitions to the closed state) also yielded superimposed Lorentzian spectra (Fenwick ct a/., 1982a). These examples show the strong model dependence of noise analysis of multichannel systems. 2. NOISEI N OPENCHANNELS At least two types of noise behavior are known to be associated with the movement of ions through open pores (Stevens, 1972): (1) thermal noise, correlated with the conductance increase induced by the presence of open channels [see Eq. ( 5 ) ] and (2) shot noise, caused by single-ion
MEASURING THE PROPERTIES OF SINGLE CHANNELS
141
movement through the channel. The time duration of channel crossing is called translocation or transit time. For derivation of a Lorentzian spectrum it is necessary that the transit time is fast compared with the openclosed kinetics of a channel. A finite transit time produces a physical limit to the frequency of the theoretical spectrum, above which the spectral density declines to zero (Chen, 1983). The shot noise contribution is probably unmeasurable, since to see it, the spectral density would have to be determined up to extremely high frequencies. In addition to a pure Lorentzian spectrum, S ( f ) is sometimes observed to vary inversely with frequency ( “ l l f ” spectrum) at low frequencies (see, e.g., Khodorov et ul., 1981). It is believed that Ilfnoise might be generated by ion flow through open channels. But the physical meaning of llfnoise both in general and as a possible consequence of ion movement through channels remains unresolved. The phenomenon of I lf noise will not be discussed here, as a detailed review was given by Neumcke (1978). Also, even small deviations from the steady-state condition of the mean current-such as nonstatianary current baselines-can cause a “ I lflike” contribution to the measured spectrum (Sigworth, 1981a; Conti et ul., 1980). In analysis of current fluctuations, it is difficult todecide whether such sudden and small deviations from the steady state [ 8 J ( t ) = 01 have actually occurred, since the zero-current level cannot be set prior to recording. In this respect, measurement of the autocovariance function (see next section) seems to contain more information. A further source of noise in open channels, observed by Sigworth (1982), could neither be explained by contributions of shot noise nor by l/f noise mechanisms. He found that current fluctuations in open acetylcholine receptor channels exhibited a low-frequency Lorentzian spectrum (fc 300 Hz) plus a constant high-frequency component having about four times the spectral density expected for shot noise. As a physical explanation of this noise source, a structural fluctuation of the channel (channel “breathing”) was proposed (C. Stevens, personal communication). 2
C. Autocovariance Function A mathematical description of the fluctuating behavior of a random process, equivalent to the spectral density spectrum, can be performed in the time domain, yizlding the autocovariance function C(T).The terms autocorrelation function and autocovariance function are often used synonymously, but the autocorrelation function is, in truth, restricted to the normalized covariance function with the initial amplitude normalized to one. C(T)is related to the spectral density function S ( f ) by a Fourier
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H.-A. KOLB
cosine transformation known as the Wiener-Khintchine theorem (Khintchine, 1949):
c(7)=
lom s ( f )COS(2rf7) df
(12)
C(7) gives a measure of the correlation existing between two instantaneous values of the identical current record, separated by a time interval T from each other. A graphical evaluation of this function i s indicated in Fig. 3 . Only for strictly stationary random processes can the autocovariance function and the spectral density function be considered to be equivalent. For the Lorentzian spectrum given by Eq. ( 3 ) the autocovariance function is a single exponential: -C(T)= 8J(t)2 e x p ( - ~ / ~ , ) (13)
Despite the mathematical equivalence of S(f)and C(7),their experimental application is more or less advantageous depending on the type of noise source (Kolb and Frehland, 1980). Also, for the detection of sudden nonstationary events in the current record, the measurement of C(T)seems to be a better tool, as outlined below. Experimentally, to cut out the dc part of the instantaneous current and to achieve a well-defined cutoff frequency at higher frequencies the measured current is filtered by a bandpass filter. Therefore Eq. (12) has to be
t
-r
FIG. 3. Graphical determination of autocovariance curve. L e t f i J ( / ) represent the recorded random current fluctuations with an arbitrary reference point / = 0 as indicated. To evaluate the autocovariance function graphically. the fir51 step i s to form the function f i / O t r , )b y displacing a/(/) by the amount 7 = T , its drawn in the figure. Then the product f i J ( / l . 6 J ( r + r ) . represented by the lower curve. i s obtained. Finally. the time average o f the product curve i s taken b y integration over the finite observation time. This average value is C ( T , )The . procedure i s repeated for ii series of viilues O F T so that ii curve i s determined.
MEASURING THE PROPERTIES OF SINGLE CHANNELS
143
For the simplest case of a rc bandpass withf, < fc < fi (fi and fi are the lower and higher roll-off frequencies), one obtains as Fourier transform of the Lorentzian spectrum (De Felice and Sokol, 1976; Kolb and Boheim, I 978),
That means experimentally that C ( T )cuts the zero line at a T~ value defined by the corner frequencies of the bandpass filter and the time constant of the opening and closing of two-state channels. The influence of signal filtering on the shape of C ( T )and the value of 7 0 is shown in Fig. 4. Nonstationary events in the analyzed membrane current would shift To usually to higher values. D. Relaxation and Covariance Experiments
The kinetics of ion transport mechanisms in biological membranes are usually described in terms of chemical reactions. Two methods for evaluation of the corresponding rate constants are applicable in general: ( 1 ) fluctuation analysis at steady state and (2) relaxation methods, which need an appropriately chosen macroscopic perturbation of the chemical reaction at equilibrium. On the basis of the fluctuation dissipation theorem, both methods contain precisely the same information about the underlying rate constants. The strong model dependency of the interpretation of measured spectral densities (Frehland, 1982) hinders the identification of the underlying elementary ion transport steps. Neher and Sakmann (1975) applied both methods to the analysis of drug-induced conductance changes in frog neuromuscular junction. Similar rate constants for the opening-closing kinetics of acetylcholine-activated ion channel\ were derived in both cases. The analytical background is well described by Colquhoun and Hawkes (1977). Despite the obvious agreement between both ways of analysis, it is possible to find different numbers of time constants (Kolb and Frehland, 1980; Junges and Kolb, 1983b). The appearance of additional time constants in one of the two
144
H.-A. KOLB
'h
1 (s) FIG.4. Effect of bandpass filter on the shape of autocovariance function. The function is plotted in arbitrary units for a characteristic frequencyf, = 1 Hz and various filter settings of a rc bandpass: (a) undistorted function (,fi = 0 Hz.f2+ m); (b)& = 0.1 H z , =~ 10 Hz;(c)f, = 0.5 H z , , ~ = , 5 Hz. 7
methods can be caused by the different contribution of the underlying kinetical process to the corresponding amplitude in the relaxation experiment as opposed to the noise analysis. In a relaxation experiment, this can arise by at least one of the reaction steps being indifferent to the type of macroscopic perturbation chosen. Also, the relaxation amplitude or spectral intensity can assume values below the resolution limit. Both methods therefore need to be used to provide full information for the kinetic description of the ion transport mechanism in terms of chemical reactions. E. The Analysis of Nonstationary Fluctuations
In experimental investigations of stationary but fluctuating ion current, ergodicity of the underlying transport mechanism is mostly assumed. A stationary but random process is called ergodic if the ensemble average is
MEASURING THE PROPERTIES OF SINGLE CHANNELS
145
equal to the corresponding time averages over one realization of the random process [e.g., over one current record J ( t ) of finite length]. In a nonergodic process, the instantaneous fluctuation depends in some random way on the starting conditions. The ensemble average and time averages of fluctuating currents and their variance and higher moments can all be investigated using only a single experimental system. But, a reliable comparison of ensemble fluctuation analysis and the corresponding time analysis (derivation of the autocovariance function) has not been carried out for a fluctuating current with a stationary mean. Ensemble fluctuation analysis was applied to currents which showed a nonstationary behavior of their mean, observed for the desensitization of chemically activated channels (Ruff, 1977)and the inactivation of voltageactivated channels (see below). For systems of two-state channels, methods of ensemble fluctuation analysis were worked out to evaluate the single-channel conductance and the rate constants of the opening and closing kinetics. The experimental procedure is to apply successive, identical voltage jumps to the membrane and to record the corresponding fluctuating current relaxations. The mean transient current of a group of records is then subtracted from each sample of this group. From the remaining current fluctuations, the time-dependent ensemble variance is calculated. A graphical presentation of the method of ensemble averaging is shown in Fig. 5 . Collecting the data into groups is only necessary if a slow macroscopic current drift with time has to be removed. since drift would yield an overestimation of the ensemble variance. From the variance and the corresponding mean current, the single-channel current or conductance can be estimwted (Sigworth, 1980a). Ensemble variance analysis of the sodium current at thc node of Ranvier gave an estimation of the number of single sodium channels in the node and the corresponding conductance (Sigworth, 1977, 1980a; Neumcke c’t d., 1979; Conti et ul., 1980). Ensemble variance analysis could also be used for estimation of single-channel conductance of chemically modified sodium channels (Sigworth and Spalding, 1980). The method also allows analysis of the influence of channel icteraction on the estimated single-channel amplitude, an influence which could not be confirmed for sodium channels at the node of Ranvier (Sigwor-th, 1980b). The opening-closing kinetics of channels contribute to the temporal structure of fluctuations within an ensemble of current records. Those fluctuations can be described by a two-dimensional autocovariance function or by the spectral density function (Sigworth, 1981a). Fewer current records are needed to evaluate the spectral density function if the mean current time course is subtrncted from each current record (Conti et d,,
H.-A. KOLB
b
FIG.5 . Ensemble variance calculation. (a) Eight records of the sodium current aligned with start of the depolarizing pulse (arrow) were obtained on the node of Ranvier. (b) Residual fluctuations from each record after subtracting the mean of eight. Node 8. (c) Ensemble variance estimated from 72 records by the following process: the sum of the squares of the fluctuations was calculated for each time point; the resulting set of squared deviations was scaled and averaged with eight others; finally, the estimated background was subtracted. Each bar represents the mean of the resulting values at four adjacent time points. The smooth curve is the mean current record, scaled by a factor of -0.3 PA. Node 13. Bathing Ringer's solution contained 20 mM TEA CI; cut internodes were in 110 mM CsCI, 10 mM NaCI. Current records were low-pass filtered at 5 kHz (four-pole, Gaussian response) and digitized (12 bits, 156 samples per record) at 100-psec intervals; aperture time jitter was <50 nsec. The thermal noise background was calculated for each current sample, using the measured values for the internode and seal resistances and making use of the instantaneous I-V relation in estimating the membrane slope conductance. The peak value of the background component of the variance in (c) was 7 X lo-**A' (Sigworth, 1977).
1980; Sigworth, 1981b). Comparison of ensemble fluctuation analysis and single-channel recording gave consistent results for the conductance and kinetic behavior of Na+- and Ca*+-selectivechannels in bovine chromaffin cells (Fenwick et ul., 1982b).
MEASURING THE PROPERTIES OF SINGLE CHANNELS
111.
147
NOISE ANALYSIS OF NON-CHANNEL-MEDIATED ION MOVEMENT
In the preceding section, a type of noise was described which is related to the opening and closing of ion channels in the membrane. The fluctuation in membrane current there reflects the fluctuation in the number of open channels in the membrane and the concentration fluctuation theory of chemical reactions could be applied. Another type of noise which has been studied recently is called “transport noise” and is associated with the translocation steps of individual ions or with carrier-mediated ion transport through membranes or open channels. This noise is described in terms of a series of ion jumps from one binding site to the next, over activation energy barriers. Fluctuations of the total membrane current arise therefore from fluctuations in the number of ions crossing the individual barriers. While channel noise is related to fluctuations of concentrations, the transport noise is related to the fluctuation of fluxes of the corresponding chemical reactions (Frehland, 1982). For channel-mediated ion transport, a Lorentzian function or superpositions of Lorentzian functions should be expected, whereas for transport noise caused by the movement of hydrophobic ions or ion-carrier complexes across planar bilayer, the spectra look like an inverted Lorentzian curve (Fig. 6) (Kolb and Lauger, 1977, 1978; Szabo, 1977). A further property of transport noise as compared to channel noise might provide a discrimination between these different noise sources: at nonequilibrium steady state as well as at thermal equilibrium (mean net current equal to zero) an inverted Lorentzian function is obtained for transport noise (Kolb and Prehland, 1980; Junges and Kolb, 1983a). For channel noise at zero mean net current, a frequency-independent spectrum should be measured if reversible binding of the transported ion within the channel can be neglected. It has not yet been possible to analyze channel noise at strictly zero mean net current. Also, transport noise has not been detected in biological membranes, probably owing to the small intensity amplitudes associated with this type of noise.
IV. METHODS OF SINGLE-CHANNEL RECORDING The main aim in studying single-channel properties is to obtain a description of the macroscopic membrane conductances and their changes in terms of molecular conductance events. A subsidiary aim is the identification of molecular structures responsible for ion transport across membranes and their change during cell differentiation and development.
148
H.-A. KOLB
100
500
1000
f (Hz) FIG.6 . Spectral density function of current fluctuations generated by the carrier-mediated ion transport across a lipid bilayer membrane at T = 2°C. Carrier: lo-' M valinomycin; ion: 1 M Rb+; membrane-forming solution: glycerylmonoerucinln-decane(Kolb and Lauger, 1978).
There are several approaches to the direct measurement of single-channel properties. Using planar bilayer membranes doped with channel-forming model substances, such as gramicidin, alamethicin, monazomycin, excitability-inducing material, toxins, and hemocyanin, a molecular description of ion transport through opening and closing multistate channels could be derived. These studies on model systems also give valuable information about the phenomenologically similar ion pathways which occur in excitable membranes. This topic will not be considered here, since excellent review articles have recently appeared by Ehrenstein and Lecar (1977), Hall (1978), Finkelstein and Andersen (1981), Latorre and Alvarez (1981), and Lauger et al. (1981). Other methods are the reconstitution of proteins of biological membranes into planar lipid bilayer membranes, and the electrical isolation of channel proteins within their native surrounding by application of the patch-clamp method. For many years, integration of active transport proteins into planar lipid bilayer membranes was not successful, since many proteins failed to interact with preformed membranes, and the native properties of the proteins were changed by the deleterious effects of detergents and hydrocar-
MEASURING THE PROPERTIES OF SINGLE CHANNELS
149
bon solvents. But more recently, reconstitution procedures have been developed which allow the incorporation of channel-forming membrane proteins (from plasma membranes and membranes of cell organelles) into lipid bilayers and allow the electrical measurement of their conducting properties. Such channel-forming proteins were obtaincd from membranes of Esr.hcvichiu c d i , w-coplasmic reticulum, mitochondrial mcmbranes, and the electric organ of electric eel\ (for reviews see Latorre and Alvarez, 1981, and Montal e f d.,1981). For example, the matrix protcin porin has been isolated from membranes of gram-negative bacteria and incorporated into planar lipid bilayers, in which it was shown (Benz rf d . , 1978; Schindler and Rosenbusch, 1978) that porin forms uniform waterfilled transmembrane channels with a diameter of about I nm (a detailed review is given by Benz in this volume).
A. Ion Channel Reconstitution in Planar Bilayers Two main methods are used in general to reconstitute ion channels within planar lipid bilayers, In the first method protein-containing lipid monolayers are combined into a planar bilayer using the method of Montal and Mueller (1972). The method is fully described by Miller ef al. (this volume). This method has been applied for the incorporation of the matrix protein porin into lipid bilayers (Schindler and Rosenbusch, 1978; Benz, this volume) and in the reconstitution of the acetylcholine receptor channel (Schindler and Quast, 1980; Nelson et ul., 1980) and a voltage-gated anion-selective channel of lwge unit conductance (450 pS in 0.1 M Cl-) from mitochondrial outer membrane (Colombini, 1979, 1980). A similar ion pathway has recently been described by Roos ef al. (1982). for the pore-forming protein in the outer membrane of rat liver mitochondria. The second method is based on the fusion of membrane vesicles with preformed solvent-containing bilayers of the Mueller-Rudin type (Mueller et a / . , 1962). Despite the fact that the mechanism of fusion is not known, there is evidence that fusion could be achieved for the acetylcholine receptor-containing vesicles from the electric organ of Torpedo marmorata (Hanke e f al., 1981; Boheim e t ul., 1981), vesicles of the sarcoplasmic reticulum of rabbit skeletal muscle (Miller, 1978; Miller and Rosenberg, 1979; Miller et ol., this volume), frog leg muscle (Labarca et al., 1980), heart sarcolemm membrane (Coronado and Latorre, 1982), transverse tubule membranes of rabbit skeletal muscle (Latorre et ul., 1982), and rat brain synaptosomas (Nelson and Reinhardt, 1983). There are no general conditions known for fusion but it seems that fusion events are enhanced by using a mixture of anionic phospholipids and phosphati-
150
H.-A. KOLB
dylethanolamine and Ca2+in the aqueous medium (see, e.g., Miller and Racker, 1976; Miller et al., 1976, and Miller et al., this volume). Of the different channels that have been characterized by this method, the acetylcholine receptor channel is described in Section V together with the Ca2+-dependent K+ channel also found in transverse tubule membranes and heart sarcolemma membranes. A further voltage-gated transport system was analyzed by addition of membrane vesicles prepared from the electric organ of Torpedo californica to the aqueous phase of planar lipid systems (White and Miller, 1981). The conductance increase could be explained by single anion channels with a voltage-independent conductance (Table I). In mammalian sarcoplasmic reticulum a voltagegated two-state K+-selective ohmic channel of large unit conductance (Table I) and complex kinetic behavior could be quantitatively studied (Miller, 1978, 1982a,b; Miller and Rosenberg, 1979; Coronado and Miller, 1980, 1982). The K+-selective channel in sarcoplasmic reticulum of frog leg shows three conductance states with similar unit conductances for the fully open state (Table I) (Labarca and Miller, 1981). B. Patch-Clamp Method
In 1976 Neher and Sakmann developed an electrophysiological technique called the extracellular patch-clamp method which, for the first time, allowed the detection and analysis of the single-channel events underlying cellular excitability. In this technique (Neher et al., 1978) a small heat-polished glass pipet with an inner tip diameter of about 0.5-4 pm is pressed against the cell membrane. Under this condition an electrical seal resistance of about 50-200 MR could be achieved. But more recently an improved sealing method (the so-called gigaseal technique) was invented by Neher (1981), a method which is now applied in general. These tight seals (gigaseals) are achieved by applying suction to the pipet interior after the pipet is gently pressed against the cellular membrane. A small omega-shaped part of membrane is sucked in by this maneuver, which is schematically drawn in Fig. 7a. For a successful seal the width of the pipet interior has to be adjusted to the type of membrane used. The gigaseal is formed in a sudden all-or-nothing process by which the seal resistance increases up to three orders of magnitude. A tight seal reduces the leakage of the membrane current into or from the bath solution across the rim of the pipet. Seal resistances of 5-100 GO can be obtained, allowing current recording with an amplitude resolution of 0.1-0.5 pA and a settling time constant of about 60 psec. Details of the electronic design of the amplifying system are described by Sigworth (1983a,b). The mechanism by which a gigaseal is instantaneously formed after suction is un-
MEASURING THE PROPERTIES OF SINGLE CHANNELS
151
known. Also, it is not known which membrane components-the polar head groups of lipids, glyco residues of proteins, or lipids-are actually responsible for the tight contact between the rim of the glass pipet and the membrane surface. Four different configurations of the pipet-membrane arrangement can be used as shown in Fig. 7b (Hamill et al., 1981). ( 1 ) If the pipet forms a seal with the cell and the cell membrane remains intact, the cell-attached configuration is achieved. (2) A cell-free method for recording singlechannel currents across the patched membrane, called the excised insideout patch configuration, was invented by Hamill and Sakmann (1980) (see also Horn and Patlak, 1980). They found that the gigaseal remains intact when the pipet is withdrawn from the cell. The torn-off parts of the surrounding membrane reassemble spontaneously to form a vesicle at the tip of the pipet. On passing the pipet tip through the air-water interface, the outer side of the patched membrane becomes freely accessible to the bath medium. The composition of the medium can now be changed during single-channel recording. The method has the further advantage that it permits the direct control of the transmembrane potential across the patch. (3) By application of a short pulse of suction in the cell-attached configuration, the patch membrane can be disrupted and the current passing through the whole cell membrane flows into the pipet interior. This configuration is called whole-cell recording (see for details Marty and Neher, 1983). Whole-cell recording eliminates most of the shunt resistances due to membrane damage around a microelectrode, as used in the conventional technique, and makes it possible to control the intracellular medium, since the pipet solution diffuses into the cell in less than about 30 seconds, depending on cell size. (4)If, under the condition of whole-cell recording, the pipet is withdrawn from the cell, the torn-off parts of the membrane reassemble to form a membrane across the previously open tip of the pipet, giving the outside-out configuration. In this arrangement the previously outer surface of the membrane again faces the extracellular bath medium. In this configuration &heconcentration dependence of, e.g., drug-activated ion channels can be investigated using a single membrane patch. An analytical treatment and an automated data analysis of drugoperated channels are given by Colquhoun and Hawkes (1981) and by Sachs et ul., (19821, respectively.
C. Patch Clamp of Recongtituted Systems A technique which permits the study of reconstituted channels on a time scale and noise level comparable to cellular patch clamp was developed by Wilrnsen et ul. (1983) and Coronado and Latorre (1983). For this
TABLE I ION CHANNEL CONDUCTANCE y A N D CHANNEL OPENT I M ET
Channel
Cell type
Solution (mM)
Y
(pS)
T ("C)
7
(msec)
V (mV)
References
4
cn
ru
Chemical1y activated * Frog muscle ACh Frog muscle Carb Sub Frog muscle Carb Rat muscle Rat myotubes ACh Rat myoballs ACh Rat myoballs ACh Carb Chick myotube Carb Chick myotube ACh Frog muscle ACh Frog muscle ACh Bovine chromaffin Glutamate Locust muscle GABA Mouse neuron Glycine Mouse neuron
Ringer's Ringer's Ringer's 100 Na' I50 Na+
I50 Na' 137 Na' 137 Na' Ringer's Ringer's 140 Na' 145 C1 142 CI
22 22 22 48 35 35/10 25 48 30 15
23 44 130 23 38
8
8 8 22 23 8 8 20 20 8 8 22 21 22 22
26 II 45 3.2
- I20
I .8 3.5
- 50 -50 -80 - 80 - 80 - 120
II
3 27 2: 12
- 120 - 120
-90
Neher and Sakmann (1976a) Neher and Sakmann (1976a) Neher and Sakmann (1976a) Jackson and Lecar (1979) Horn and Patlak (1980) Hamill and Sakmann (1981) Hamill and Sakmann (1981) Kolb and Wakelam (1983) Kolb and Wakelam (1983) Neher and Sakmann (1976b) Neher and Sakmann (1976b) Fenwick e/ ol. (1982a) Patlak ei trl. (1979) Sakmann P / rrl. (1982) Sakmann e / d.( 1983
Voltage activated Na* channel Rat muscle Tunicate egg Neuroblasroma K ' channel Squid axon Rat myotuhes Tunicate egg CaL- channel Hi4i.r neuron Rat PC 12 Chick neuron Cardiac muscle Bovine chromaffin Rat pituitary
IX
I8 15-20 17 I0
7 5-15
3-4
I1 II 25
2.7 0.5 0.5-1.5
7-8
I .%bunt) I
0 to -30 -50
-50 10 to 30 -5 -4 t o 40
Sigworth and Neher (1980) Fukushima (1981a) Aldrich ('I t i / . (1983) Conti and Neher ( 1980) Ohmori 01 t i / . (1981) Ohmori (1981) Lux and Napy (1981 ) Brown c! t i / . ( 1982) Brown 1'1 t i / . ( 1982) Reuter 1'1 C J / . ( 1982) Fenwick er c d . (1982b) Hagiwara and Ohmori (tY831
Cali activated
K ' channel 3
m GI
Unselective channel
K * channel
Hov ine c h roniaffi n Rat niyotuhey Rat pituitary Frog neuron Rat muscle Chick myotube Cardiac muscle Neuroblastoma Pancreatic acini Ap/yaicr neuron HeLa
140 K -
I80
I40 K -
187'5Y 208
145
K'
2.5 K-. 100 K; I50 K 150 K 137 Na'. 5.4 K' 125 NaI10 Na'. 4.7 K 360 K: IS0 K'
I (n) 240 140 -3
22 30 .. 55
30
Marty ( 19x1) Pallotta " I trl. (1981 1 Wong c'i crl. ( 1982) Adams P I t i / . ( 1982)
Methfessel and Boheiin (1982) Kolh and Schwarze (1983b) Colquhoun 6'1 (I/. ( I98 I ) Yellen (1982) Maruyama and Petersen (19X2a) Siegelbaum P I (I/. (1982) Sauve el crl. (1983) ~~
a
ACh. Acetylcholine: Carb. carbamylcholine: Sub. suberyldicholine: GABA. y-aminobutyric acid.
R
a
I'
LOW RESISTANCE SEAL (50 Ma)
b SUCTION
KCI /Ca'+-FREE PULSE OF SUCTION OR VOLTAGE
/
/
1 \
PULL
aa USING A S M L L CELL
I
lL l n e c d o g r i r 1 IL whole-cell
outside-out inside-out
MEASURING THE PROPERTIES OF SINGLE CHANNELS
155
technique, a lipid-protein monolayer is formed from mixtures of native vesicles and an excess of liposomes. Then a standard patch-clamp pipet is raised and lowered through this monolayer at the air-water interface. A variation of this method, also worked out by Wilmsen rt ul. (1983), allows a fusion of membrane fragments with preformed lipid bilayers under patch-clamp conditions. In this case osmotically loaded vesicles are added to the pipet filling solution and the pipet is oriented vertically to the solution interface. The vesicles fall by gravitation onto the preformed planar bilayer spanning the tip of the pipet and fuse. Recently it became possible to apply the patch-clamp technique to ion channels reconstituted in large liposomes (Tank et al., 1982, 1983). Large liposomes (30 pm) were formed by a freezing and thawing method from small unilamellar vesicles made from Torpedo electroplax plasma membranes. Single voltage-gated CI- channels (Tank et al., 1982) and acetylcholine (ACh) receptor channels could be measured by sealing a patch pipet with the liposome membrane. The properties of ACh receptor channels of Torpedo were found to be similar to those of mammalian muscle membranes (Tank et al., 1983). The following sections summarize the single-channel parameters obtained by patch-clamp recording. This survey clearly cannot be complete, owing to the rapidly increasing number of the publications in this field. Also, a quantitative comparison of the specific channels and their
FIG.7. (a) Schematic drawing of the experimental arrangement. The pipet, approaching the spherical cell, is shown in cross section. The arrow across the cell membrane represents the current I crossing the pipet-covered portion of the cell. This is different from the current I’ being measured, unless there is ideal contact between glass pipet and membrane surface. which, usually, The pipet interior is clamped by the circuit to a command voltage (Ucommand), should be adjusted such that there is zero current flow in the pipet before contacting the cell (see Neher et al., 1978). The output voltage U,,, is proportional to pipet current and feedback resistor R (Neher. 1982). (b) Schematic representation of the procedures which lead to recording configurations. The four recording configurations described are “cell attached,” “whole-cell recording,” “outsidewout patch.” and “inside-out patch.” The uppermost frame is the configuration of a pipat in simple mechanical contact with a cell, as has been used in the past for single-channel recording (Neher et al., 1978). Upon slight suction the seal between membrane and pipet increases in resistance by two to three orders of magnitude, forming what we call a cell-attached patch. The improved seal allows a 10-fold reduction in background noise. This stage is the starting point for manipulations to isolate membrane patches which lead to two different cell-free recording configurations (the outside-out and inside-out patches). Alternatitely, voltage clamp currents from whole cells can be recorded after disruption of the palch membrane if cells of sufficiently small diameter are used. The manipulations include withdrawal of the pipet from the cell (pull), short exposure of the pipet tip to air, and short pulses of suction or voltage applied to the pipet interior while cell-attached (Hamill ct al., 1981).
156
H.-A. KOLB
properties in the different cell species is not given. Quantitative agreement of these parameters is not to be expected, even for one channel type investigated on cells in one culture dish. Thus, a large variation was found for the single-channel conductance of Ca2+-activatedK+-selective channels (Barrett et al., 1982). Several factors might be responsible for this variation of single-channel parameters. It is known that during cell development and synaptogenesis the ACh receptor channel changes its conductance and kinetic properties (Schuetze e l al., 1978; Michler and Sakmann, 1980; Brenner and Sakmann, 1983). Further, modulation of single-channel properties can be caused by phosphorylation and dephosphorylation of proteins involved in ion transport across the membrane. There is evidence that cyclic AMP-dependent phosphorylation regulates the Ca2+-activatedK + current in snail neurons (De Peyer et al., 1982) and, in cultured heart muscle cells, it increases the Ca2+influx during depolarization (Osterrieder et al., 1982; Cachelin et al., 1983). Also, the anchoring of the channel or channel-receptor complex in the membrane can be quite different in different cell membranes or can change during cell development and this may influence the conductance mechanism through specific lipid-protein interaction. For instance a diffusion of ACh receptor molecules is observed in myotomal membranes of Xenopus tadpole (Poo, 1982), whereas sodium and potassium channels in frog skeletal muscle show no visible lateral diffusion (Stuehmer and Almers, 1982; Almers et ul., 1983). V.
ION CHANNELS IN PATCHED MEMBRANES
A necessary condition for the application of the gigaseal technique (in addition to the use of a clean unused pipet tip) is a plasma membrane without a surface coat. Therefore the cell preparations which can be used are limited in number. Membranes of cells present within a tissue have to be cleaned by enzymatic (hyaluronidase, collagenase) treatment. At the neuromuscular junction of frog muscle this approach has been successfully applied (Neher and Sakmann, 1976a). There is evidence, at least for the ACh receptor-channel complex, that enzymatic treatment causes no significant change of the channel properties (Betz and Sakmann, 1973). Enzymatic treatment has also been used for dispersion of tissue-connected cells such as the bovine chromaffin cells (Marty, 1981) and pancreatic acinar cells (Maruyama and Petersen, 1982a) prior to patch-clamp recording. It would be of great interest to perform patch-clamp experiments on the node of Ranvier, for which a large amount of quantitative data on Na+ and K channels is already available from voltage clamp and +
MEASURING THE PROPERTIES OF SINGLE CHANNELS
157
noise analysis (see, e.g., Conti et ( I / . , 1980; Ulbricht, 1981). Recently it has bcen found possible to obtain, by enzymatic cleaning, patch-clamp records on tissue-connected electroplax cells of Elec~troi~liorrrs elrctr.ic.rrs, but in this case only seal resistances in the range of I GiZ could be achieved (Hess e l d., 1983). Gigaseals can easily bc formed with culturcd cells such as nerve cells, muscle cells (myoblasts, myotubes, myoballs), HeLa cells. myeloma cells, lymphocytes, and macrophages. The patch-clamp method has been applied to biological membranes artificially doped with ionaphores such as alamethicin as a probe for membrane composition (Sakmann and Boheim, 1979). The patch-clamp technique was also applied to intact retinal rods, but single, light-sensitive channels were not resolved (Detwiler et a / . , 1982). A. Chemically Activated
Many investigations of single-channel properties have been made on the acetylcholine receptor channel (for the specific properties of this channel, see Barry and Gage, this volume). Acetylcholine is a common chemical transmitter in the peripheral nervous system of vertebrate. In all somatic synapses, in autonomic ganglia, and in most parasympathetic postganglionic synapses, acetylcholine acts as an agonist. The mechanism of acetylcholine action has been quantitatively studied using cultured muscle cells and at the neuromuscular junction, where it generates a membrane conductance change causing muscle cell depolarization. The receptor subunit to which ACh binds is known, whereas the subunit of the molecular complex which forms the channel through which the cations move has not been identified. Little is known about the relative structural arrangement of the receptor subunit in the muscle membrane or about interactions between receptors or between receptor and other membrane components, such as lipids. Two agonist molecules are apparently required for opening the channel. The structural basis and the mechanism of the primary step of activation-the coupling between acetylcholine binding and the opening of the channel-are still unresolved (for a model of this channel, see Barry and Gage, this volume). The ACh receptor-channel complex has two different forms, the muscarinic and the nicotinic, which differ in their pharmacological specificity. The first patch-clamp experiments were carried out on the nicotinic receptor of the neuromuscular form, for which conventional electrophysiological experiments have provided a well-documented description of in uiuo channel activation (Neher and Stevens, 1977). The studies of Neher and Sakmann (1976a) were carried out at the enzymatically cleaned extrasynaptic region of a denervated hypersensitive frog cutaneous pectoris
158
H.-A. KOLB
muscle (see Fig. 8). They showed that the ACh-activated channel could be described well as a two-state system. Similar results were found by Jackson and Lecar (1979) on cultured embryonic rat muscle and by Horn and Patlak (1980) on excised patches of cultured myotubes of neonatal rat thighs. In addition, evidence for saturation of the Na+ current through the channel at high concentrations was found. In recent years, a variety of patch-clamp experiments have been carried out on the ACh receptorchannel complex. In what follows, we discuss first the multistate behavior of the channel, and then recent results concerning the opening and closing kinetics of the channel are presented. It was found that in a single patch of cultured embryonic muscle cell membrane either from rat or from chicken, two distinct populations are visible which differ in their amplitude and mean open time (Hamill and Sakmann, 1981; Kolb and Wakelam, 1983). In adult junctional tissue (which had to be enzymatically cleaned for patch-clamp records) the extra- and subsynaptic ACh receptor appear to be separately organized (Neher and Sakmann, 1976a,b). In denervated frog muscle fibers, a larger amplitude was found for the subjunctional channel than for the extrajunctional channel (Table I). The mean open time of the extrasynaptic channel (about 11 msec) is three to five times longer than that observed for junctional channels. A comparable difference in properties of junctional and extrajunctional channel was observed from noise analysis of ACh-induced current fluctuations in normal human muscle membranes. In
FIG.8. Oscilloscope recording of current through a patch of membrane of approximately 10 pm’. Downward deflection of the trace represents inward current. The pipet contained 2 x lo-’ M suberyldicholine in Ringer’s solution. The experiment was carried out with a denervated hypersensitive frog cutaneous pectoris (Runci pipiens) muscle in normal frog Ringer’s solution. The record was filtered at a bandwidth of 200 Hz. Membrane potential - 120 mV; temperature 8°C (Neher and Sakmann, 1976a).
MEASURING THE PROPERTIES OF SINGLE CHANNELS
159
freshly enzymatically dispersed bovine chromaffin cells (Fenwick et ul., 1982a) only one population was observed of similar amplitude to that measured for channels at the neuromuscular junction of frog but with a mean open time about 20 times longer (Table I). The comparison of AChactivated channel parameters from different membrane species is complicated by the fact that during, cellular development the mean open time of the channel at the neuromuscular end plate of mammals (Michler and Sakmann, 1980) and amphibia (Kullberg et al., 1981; Brehm et al., 1982) shortens. Also, the quantitative difference between junctional and extrajunctional channels and the question as to what extent they express different types of ACh receptors are complicated by the changes that occur during synaptogenesis (Brenner and Sakmann, 1983) and by the fact that a channel can show several conductance states. At least three long-lived conductance states of a single channel were observed by Hamill and Sakmann (1981). At low concentrations of ACh (<1-10 p M ) , responses of individual channels appear as widely spaced square-wave pulses. At higher concentrations of ACh, the mean channel open time is unaffected but the pulses appear in bursts (see Fig. 9) (Neher et al., 1978; Sakmann rt al., 1980) with short transitions to the nonconducting state. These transitions are called “flickers.” The kinetics of flicker were analyzed in frog (Colquhoun and Sakmann, 1981), snake (Dionne and Leibowitz, 19821, and tissue-cultured embryonic chick muscle (Nelson and Sachs, 1979, 1982; see also Horn, this volume). These flickers were also found for glutamateoperated channels in locust skeletal muscle (Cull-Candy and Parker, 1982). It is generally assumed that the flickers are caused by rapid transitions between the doubly liganded open and closed states of the channel. Auerbach and Sachs (1983) found by a close study of the flickering that at least 15% of the short closed periods between channel openings do not reach the baseline but end on a substate. A similar result was obtained by Trautmann (1982). He observed that the nicotinic antagonist curare activated three channel states in ACh-sensitive tissue of cultured rat muscle, observations not confirmed by Morris ef al. (1982). Using the analytical approach of Colquhoun and Hawkes (1981) to the statistical treatment of single-channel events in terms of chemical reaction kinetics, Jackson et al. (1983) found on cultured rat muscle cells that successive channel openings are not independent. They could therefore rule out reaction schemes with a single closed state undergoing transitions to two distinct open states. The question whether these two open states represent separate populations of channels or separate states of a channel remains unanswered at present. The minimal kinetic model usually discussed for the description of channel activation (see for review Sakmann, 1978; Adams, 1981; Dionne and Leibowitz, 1982) contains three closed states (R, AR,
160
H.-A. KOLB
b
0
1
0
~
7
ACh ( p M ) FIG. 9. Agonist concentration dependence of open and closed times during current bursts. (a) Examples of bursts recorded in the presence of three different ACh concentrations as indicated on the left side of each record. All three records were taken at -130 mV membrane potential, 1 I T . As the ACh concentration increases, the duration of intervals between pulses of current decreases. At ACh concentrations <20 wLM ACh, the channels are, during a burst, mostly in the closed state, whereas at >20 p M ACh, the channels are predominantly in the open state. (b) Log-log plot of the inverse of the best fit 7,) and T, values against ACh concentration. Open symbols are values for the channel mean open times, i0, and closed symbols are for the channel mean closed times, 7,. Circles represent measurements at -90 mV, squares at -130 mV membrane potential. The solid lines were drawn through the points taken at - 130 mV; the dotted line was drawn through the points representing mean open times at -90 mV. All lines were drawn by eye. Each point represents the best-fit exponential to histograms made by summation of the histograms from many bursts in the same conditions. Standard error brackets refer to the calculated standard error of the best-fit values of T to their respective histograms. Channel open times are not measurably dependent on ACh concentration but increase with membrane hyperpolarization. The channel closed times are strongly dependent on ACh concentration; the slope of the line drawn was 1.4. No consistent change of mean closed times with changes in membrane potential was measurable (Sakmann el d.,1980).
and A2R)and one open state (AzR"), where A denotes the agonist and R the receptor 2A
f
R
F==
A
iAR
=A2R
F== AzR*
But this sequential reaction scheme includes neither transitions to a low conductance state of the channel (Auerbach and Sachs, 1983) nor transitions from the closed state to two kinetically separated open states of the same channel (Jackson et af., 1983). The origin of the fast component of channel opening and closing is under detailed investigation at present.
1
MEASURING THE PROPERTIES OF SINGLE CHANNELS
161
The glutamate-activated channel responsible for the postsynaptic potential at insect and crustacean neuromuscular junctions was studied directly by Patlak rt d . (1979) using metathoracic extensor tibiae and retractor unguis muscles of locust. The glutamate-activated channel had a conductance almost five times larger than that of the ACh-activated channels at the vertebrate neuromuscular junction (Table I). By variation of the glutamate concentration within the pipet during patch-clamp recording on the extrajunctional membrane of locust fibers, evidence was given by Cull-Candy el a / . (1980) that glutamate receptors also bind two agonists before the corresponding channel opens. The mean channel open time is similar to that for ACh-activated channels and is not markedly dependent on glutamate concentration, whereas the probability for channel opening increases with increasing glutamate concentration and bursts appear. As observed for ACh receptor channels in frog twitch muscle (Colquhoun and Sakmann, 198 I ) , short intraburst closing could be found and was analyzed by Cull-Candy and Parker (1982). Again, it was proposed that the brief intraburst closings (flicker) result from transitions of the channel after closing to the open configuration (reopening) without dissociation of the bound glutamate molecules. Recently, y-aminobutyric acid- (GABA) and glycine-activated chloride channels were found using the patch-clamp technique on spinal cord neurons (Sakmann et al., 1982). Glycine is known as a putative inhibitory transmitter which increases the anion conductance of the soma membrane of spinal neurons. Unit conductances of 23 and 38 pS for GABA- and glycine-activated channels, respectively, were obtained in 0.145 M CI (see also Table I). Evidence was given that two agonists bind in the opening of the C1- channel. Measuring the channel selectivity for anions, Hamill et ul. (1983) found that the ions are not selected according to their hydrated size, implicating a possible interaction between ion and channel structure. 6. Voltage Activated
The propagation of action potentials in nerve and muscle cells depends on the voltage- and time-dependent conductance of membranes. The conductance change is based on voltage-gated sodium and potassium channels (Hodgkin and Huxley, 1952; Armstrong, 1981). 1. SODIUM CHANNELS
The first observations of currents through individual voltage-operated Na+ channels were reported by Sigworth and Neher (1980) on cultured
162
H.-A. KOLB
myoballs from rat embryos. They showed that the shape of the transient macroscopic inward current of sodium following a depolarizing voltage step could be obtained as an ensemble average of up to 300 individual current records (see Fig. 10). The time course of the current thus obtained showed the typical kinetic behavior of a rapid activation followed by a slower inactivation process, if depolarization was maintained. The singlecurrent pulses had a square-wave shape with two conductance statesopen and closed-and a single-channel conductance of about 18 pS (see
7
d FIG.10. Single-channel currents during 10-mV depolarizations. (a) Imposed patch membrane potential. The patch was held hyperpolarized by 30 mV; 40-mV depolarizing pulses were given at I-second intervals. (b) Average of a set of 300 current records elicited by these pulses. (c) Nine successive individual records from this set. The mean channel current was - 1.6 PA, and the lifetime was 0.7 msec. (d) Example of a current record obtained in another experiment where two-thirds of the Na' in the pipet was replaced with tetramethylammonium ion. The patch apparently contained two to three active channels, as estimated from responses to larger depolarizations. The solution in the pipette contained 5 mM TEA. Temperature, 18" (Sigworth and Neher, 1980).
MEASURING THE PROPERTIES OF SINGLE CHANNELS
163
Table I). The mean channel open tinie showed qualitatively the behavior expected from Hodgkin-Huxley kinetics. Horn ot (11. (1981) provided evidence from single Na+ current measurements on rat myotubes that inactivation proceeds independently of activation. Blocking the inactivation process by adding a protein-specific reagent to the cytoplasmic face of an inside-out patch enabled the activation process to be investigated on its own (Patlak and Horn, 1982). A three-state sequential kinetic scheme (two closed, and one open channel state) was proposed for this system in the absence of inactivation. It could be confirmed that the normal mean channel lifetime is primarily determined by the inactivation process. Similar results were obtained on enzymatically dispersed chromaffin cells (Fenwick et ul., 1982b). But at a more hypolarized potential, the decrease of the mean open time could not be explained by the kinetics of the inactivation. The conductance of the open state can be decreased and the probability of channel opening drastically changed by the presence of batrachotoxin (Quandt and Narahashi, 1982). In tunicate egg cell membranes, single voltage-gated Na+ channels properties compatible with those of excitable membranes (except for the lack of tetrodotoxin binding) have been measured by Fukushima (1981a) (see Table I). He estimated a single Na+ channel conductance of about 10 pS. The inactivation and activation process could be described on the single-channel level in terms of the Hodgkin-Huxley model. Recently, Na+ channels were investigated also in neuroblastoma cells (Table I) (Aldrich et ul., 1983).
2. POTASSIUM CHANNELS In nerve cells, three different types of voltage-gated potassium channels are found: the fast-inactivating K + channel, the delayed rectifying channel which is the K + channel of the Hodgkin-Huxley model, and the anomalous or inward-rectifying K' current. Little patch-clamp work has been done on the voltage-dependent K' channel in excitable cells. Conti and Neher (1980) recorded individual K ' channels with a conductance of about 17 pS in squid axon membrane at hyperpolarizing membrane voltages (Fig. 1 1 ; Table I). They used Lshaped patch pipets which were introduced longitudinally into the axon interior for an approach from the inside. The channel showed flickering in the open state as described for chemically activated channels (see above). The mean total burst length was about 12 msec. The Hodgkin-Huxley model (Hodgkin and Huxley, 1952) for the K t currents was not consistent with the single-channel measurements. The anomalous or inward-rectifying K + current was analyzed on the single-channel level for the first time by Ohmori et ul. (1981) on cultured
164
H.-A. KOLB
h
ms . 50
FIG.I I . Several traces of patch recordings of K + currents in squid axons. (a) was taken at -25 mV membrane potential, (b) at -35 mV. The elementary events seem to be bursts of closely spaced pulses. Histograms of open times and closed times of this and nine similar records (a total of 270 bursts) were calculated. The open times were distributed approximately exponentially with a mean open time of 6.1 rnsec. The closed times had a bimodal distribution: short intervals corresponding to interruptions within a burst were superimposed on an approximately exponential distribution of long intervals corresponding to intervals between bursts (Conti and Neher, 1980).
165
MEASURING THE PROPERTIES OF SINGLE CHANNELS
rat myotubes. To increase the frequency of open-close transitions under conditions in which all the channels are in the open state, a small amount of the blocking agent Ba2+ was added to the pipet filling solution. The single-channel conductance was about 10 pS in 0.155 M K t (Table I). In tunicate egg cell membranes, three types of Kt currents are found with properties similar to those in nerve. Fukushima (1981b) measured the anomalous K + rectifier in hyperpolarized tunicate egg cell membranes. Using the patch-clamp technique he confirmed that the openclose kinetics of a single inward-rectifying K ’ channel reflects the reversible closure of blocking by impermeant cations (Fukushima, 1982, 1983), consistent with the blocking kinetics of the total macroscopic anomalous K t currcnt (Ohmori, 1981; Ohmot-i cf d.,1981). The opening rate constant increased almost exponentially with a potential change in the hypcrpolarizing direction. The singlc-channel conductance is roughly proportional to the square root of the K’ conccntration. At 0.2 M K a step size of about 7 pS was obtained (Table I ) . The K’ current through an open channcl was enhanced by the presence of sodium. +
3. CALCIUM CHANNELS Different Ca2+transport mechanisms are assumed to modulate the free Ca2+concentration of the cytoplasm. Cytoplasmic free Ca2+ (Caf+)is known to play an important role in the regulation of numerous cellular activities such as muscle concentration, oscillations in neural discharge, the secretion of transmitters and hormones, the regulation of enzyme activities, and the control of ion permeabilities. Excellent reviews have been written by Hagiwara and Byerly (1981) and Reuter (1983). Using the patch-clamp method, current flowing passively through a voltage-gated Ca?’ channel down its electrochemical gradient was studied on nerve, muscle, and gland cells and recently also on mouse myeloma cells (Fukushima and Hagiwtira, 1983). The first record of single Ca2’selective channels was reported by Lux and Nagy (1981; see also Fig. 12) on neurons of the snail Helixpotnatia under conditions of a pharmacologically blocked Na+ and K + current in the presence of high external Ca2+. These units of single Ca2+ channels resemble those found in cultured dorsal root ganglion cells from chick and in secretary cells of the PC 12 line of cultured rat adrenal medullary tumor cells (Table I ; Brown et d., 1982). In cultured neonatal heart muscle cells with high Ba?+ (0.1 M ) carrying the inward current, it was proved that the probability of channel opening increases steeply over the same depolarizing potential range as that in which activation of the total macroscopic Ca2+ current occurs
166
H.-A. KOLB
100ms Ftc. 12. Ca2+-dependent patch currents during depolarizing cell voltage-clamp steps. Inward- and outward-going current fluctuations during a series of clamp steps to + 10 mV. Patch pipet contained 60 m M CaCI,, 0 NaCl (Lux and Nagy, 1981).
(Reuter et al., 1982). For isotonic extracellular BaC12 an ohmic conductance of about 25 pS was derived. This conductance is similar to that found for snail ganglion (Lux and Nagy, 1981) but smaller than that observed in bovine chromaffin cells (Fenwick et al., 1982b) and in clonal rat pituitary cells (Hagiwara and Ohmori, 1982). The single-channel conductance determined by noise analysis on multichannel systems seems to be substantially smaller (for comparison see Table I) (Akaike et al., 1978a). The selectivity of the Ca2'+channel for Ca2+is less than that previously derived from macroscopic measurements (Hagiwara and Byerly , 1981). For a description of the apparent kinetic properties of macroscopic Ca2' currents in excitable membranes, a three-state sequential scheme for activation was proposed (Akaike et al., 1978b): closed 1
closed 2
=open
In this, the simplest reaction model consistent with the experimental results, ihe Ca2+channel has two closed states and one open state. This reaction scheme was also used by Brown et al. (1982) and Hagiwara and Ohmori (1983). Fenwick et al. (1982b) confirmed this reaction scheme by elaborate patch-clamp studies. They found that brief current pulses often occurred in bursts and that the burst length increased with voltage, whereas the mean channel open time showed only a weak voltage dependency, Therefore it seems that the macroscopic Ca2+ current is mainly determined by the burst kinetics and not by the mean channel lifetime. The observed decline of Ca2+currents with time seems to be explained by the Ca2+ ions in the cytoplasm decreasing the probability that a Ca2+ channel opens.
MEASURING THE PROPERTIES OF SINGLE CHANNELS
167
C. Calcium Activated
It is well known that K+-selective currents, depending on the free cytoplasmic calcium concentration Cat', occur in a wide variety of cell membranes. They appear also to play an important role in the regulation of the repetitive activity in both vertebrate and invertebrate neurons (Meech, 1978; Schwarz and Passow, 1983).
1. POTASSIUM CHANNELS
Using the patch-clamp technique, Caf+-dependentoutward directed K+ channels could be found in a variety of cell membranes. Such channels were first reported in cultured bovine chromaffin cells by Marty (1981) (see also Fig. 13). Similar channels were found in Helix neurons (Lux et af., 1981), rat myotubes (Pallotta et nl., 1981; Barrett et uf., 1982), cultured bullfrog ganglion cells (Adams et ul., 1982), cultured rat myotubes (Methfessel and Boheim, 1982), transverse tubule membranes of rabbit skeletal muscle (Latorre et ul., 1982), clonal anterior pituitary cells (Wong et uf., 1982), and dissociated smooth muscle cells from stomach muscularis of Bufo mariniis (Walsh and Singer, 1983). In each case, the channel shows a high unit conductance of 80-12s pS in normal external K t (5.4 mM) and up to 210 pS in excised patches with symmetrical K + (0.15 M ) across the membrane. The opening frequency and lifetime depend both on voltage and on Cat' concentration. 'There are surprising similarities between this Caf+-activatedchannel and the agonist-operated channel. The binding of two Ca2+ions seem to be required for opening (Barrett et af., 1982; Methfessel and Boheirn, 1982; Moczydlowski and Latorre, 1983), and the channel appears to show brief closures of the open state, as is found for ACh-activated channels (Sakmann et al., 1980; Colquhoun and Sakmann, 1981 ; Cull-Candy and Parker, 1982). The corresponding singlechannel parameters are summarized in Table I. The distribution of all open intervals can be described by two exponentials, suggesting the existence of at least two open channel states. The distribution of all closing events is described by three exponentials. In addition, there are a few longer shut intervals not included in these three exponentials (Magleby and Pallotta, 1983). At present the model first described by Methfessel and Boheim (1982) and extended by Moczydlowski and Latorre ( I 983) seems to explain most of the reported data: closed
KI(V)
Cadosed
P
Ca.open
Kz( V )
===== &*.open
168
H.-A. KOLB
FIG. 13. Large K + unitary currents in isolated patches of bovine chromaffin cells. (a and b) A pipet containing Ca2+-freeRinger's (1 mM Coz+replacing Ca*-) was first used to record from a patch of a cell membrane (a). The bath contained a high-salt solution (in millimolar: 143 KCI, 2 MgCI2, 1 Ca2+-llEGTA buffer, 10 HEPES-KOH, pH 7.3) which presumably brought the cell membrane potential close to 0 mV. The pipet was held at the bath potential, so that the holding potential for the patch was also 0 mV. (a) Potential jumps of 75 mV were applied to the pipet interior to make the patch membrane potential positive. (b) Response to the same voltage pulse after moving the pipet away from the cell (inside-out patch). Unitary outward currents are 12 pA in (a), 10.5 pA in (b). There is a pronounced noise increase during the opening of the channels. (c and d) A pipet containing a high-K' solution (same as the bath solution in a and b) was first applied to a cell bathed in normal Ringer's (c). The pipet interior was held at the bath potential so that the patch holding potential was equal to the cell resting potential (presumably -60 mV). Positive pulses of 100 mV activate large ( I 1 PA) K + unitary currents. (d) Similar currents are obtained after destruction of the initial patch and withdrawal of the pipet when applying 104-mV pulses from a holding potential of -64 mV (outside-out patch). Filtering at 1 kHz (Marty, 1981).
The closed channel has a low-affinity Ca2+site which, in a voltage-dependent step, must be occupied by Ca2+ in order to open the channel (Ca-open configuration). In the open configuration, further Ca2+binding stabilizes the channel in a voltage-dependent step. But this simple reaction scheme does not account for the easily observable low conductance level of the CaT+-activated K+-selective channel. Furthermore, an interesting mechanism blocking this outward Kf current by increasing intracellular Na' can be observed (Moczydlowski and Latorre, 1983; Marty, 1983), a block which can be compensated for by increased extracellular K + (Marty, 1983). This gating mechanism is reminiscent of the membrane-bound Na+,K+-ATPasesystem which has specific binding sites for
MEASURING THE PROPERTIES OF SINGLE CHANNELS
169
Na+ at the cytoplasmic side and for K’ on the extracellular membrane surface.
2.
UNSELECTIVE
CHANNELS
Caf+-dependentNa+-K+ unselective channels have been found in muscle, nerve, and gland cells. Colquhoun ot ul. (1981) using primary cultured rat heart muscle cells observed long-lived and nonselective cation channels, activated by micromolar concentrations of Caf’ . A single-channel conductance of 20-40 pS was measured in isotonic saline. The kinetics appeared to be complex, since the channel opening rate usually declined over a period of several minutes. The channel may be responsible for the transient inward current which produces oscillatory depolarizations in heart cells. In neuroblastoma cells, the Caf +-activated channel showed a similar permeability to Na+, K + , Li’, and Cs’ despite the rather low unit conductance, and was practically impermeable to CaZ+ ions (Yellen, 1982). This type of channel was also found on the basolateral surface of collagenase-isolated rat and mouse pancreatic acinar cells (Maruyama and Petersen, 1982a). It is proposed that this Caf+-activatedinward channel is coupled to the two important physiological processes in acinar cells, fluid and enzyme secretion, and to hormone-receptor interaction. The activation of this channel in pancreatic acinar cells is controlled by a hormone (cholecystokinin) and a transmitter (ACh), through regulation of the concentration of the intracellular “messenger” Cat’ (Maruyama and Petersen, 1982b). D. Channels of Unknown Activation 1. POTASSIUM CHANNELS
A K+-selective channel with characteristic single-channel parameters (large unit conductance, low conductance level, pattern of transitions between open and closed states) was reported by Siegelbaum et ul. (1982) in Aplysiu sensory neurons. The activation of this channel, as well as the kinetic scheme itself, seems to be independent of Car’. The channel is open at resting potential and was therefore denoted as a background K + channel. Evidence was provided that extracellular application of serotonin and injection of cyclic AMP cause an increase of the mean lifetime of the closed state of the channel. Single long-lasting K + currents were also found in HeLa cells (Sauve et al., 1983) and showed a conductance of about 30 pS, similar to that of Ca*+-activated unselective cation channel (see above). The activation
170
H.-A. KOLB
mechanism is unknown. As was observed for the Caf+-dependent K+selective channel (Marty, 1983), an increase of the opening probability was observed with increased K + concentration in the patch pipet.
2. IONCHANNEL OF LARGE UNITCONDUCTANCE A chloride-selective channel of large conductance (-430 pS) was observed in cultured rat muscle cells by Blatz and Magleby (1983). A similar channel of large unit conductance (300-350 pS) was found in a variety of ontogenetically different cells: lymphocytes, macrophages, and primary cultures of myoblasts and myotubes of embryonic chicken muscle cells (Kolb and Schwarze, 1984). This channel resembles the Ca”-dependent K+ channel at high Caf+-concentration of about 1 mM (Barrett et al., 1982) in the unit conductance value and the appearance of a subconductance level, as well as in the pattern of the opening-closing kinetics. But the activation of this channel seems to be independent of Caf+.A remarkable steep voltage-dependent activation and inactivation mechanism was observed (Blatz and Magleby, 1983; Schwarze and Kolb, 1983), but the physiological role of this gating behavior for the regulation of ion transport remains unsolved at present.
VI.
CONCLUSION
Single-channel recording techniques and the noise analysis of multichannel systems enable one to derive single-channel properties such as the channel conductance and the transitions rates between open and closed states of the channel. The single-channel conductance derived from noise analysis of multichannel systems systematically underestimates the true single-channel conductance (see, e.g., Table I), whereas the reverse result might have been expected. The discrepancy perhaps arises from channel interaction, but the origin of this effect remains unclear at present. Noise analysis is a useful tool for investigating channelchannel interactions, but it is clearly an inappropriate method for the amplitude and kinetic analysis of rarely adopted conductance states of channels. In such cases, the recording of single-channel fluctuations by the patch-clamp method is absolutely necessary. Transition rates between different conductance states of a channel are usually described in terms of the kinetics of chemical reactions at equilibrium. But a major difficulty in the application of this theoretical approach is the maintenance (and the proof) of equilibrium conditions. Deviations from equilibrium could be caused by a possible coupling of the current flowing through the channel at nonequilibrium steady state to the opening-closing kinetics, consid-
MEASURING THE PROPERTIES OF SINGLE CHANNELS
171
ered to be at equilibrium. The apparent low conductance states of an open channel are not included in any of the presently studied reaction schemes. Finally it has to be taken into account that the single membrane patch represents only a small part of the total mosaic of the membrane, and the behavior of such a patch may not be representative for the regulation of the overall membrane permeability. Therefore, single-channel recording methods as well as multichannel analysis should be applied in parallel in order to obtain a suitable molecular description of the macroscopic ion currents. REFERENCES Adams, P. R. (1981). Acetylcholine receptor kinetics. J . Menihr. Biol. 58, 161-174. Adams, P. R., Constanti, A.. Brown. D. A . . and Clark, R. B. (1982). Intracellular Ca'+ activates a fast voltage-sensitive K' current in vertebrate sympathetic neurons. NUtitre (London) 296, 746-749. Akaike. N., Fishman, H. M.. Lee, K . S . , Moore, L. E.. and Brown, A. M. (1978a). The units of calcium conduction in He1i.v neurones. Notitre (London)274, 379-382. Akaike, N., Lee, K. S . . and Brown, A. M. (1978b). The calcium current of Helix neurons. J . Gen. Physiol. 71, 509-53 I . Aldrich, R. W., Corey. D. P., and Stevens. C. F. (1983). Kinetic behavior of single sodium channels. Biophys. J . 41, 279a. Almers, W.. Stanfield. P. R., and Stuehmer, W. (1983). Lateral distribution of sodium and potassium channels in frog skeletal muscle: Measurements with a patch-clamp technique. J . P/iy.~iol.336, 261-284. Apell, H.-J., Bamberg, E., Alpes. H., and Liiuger. P. (1977). Formation of ion channels by a negatively charged analog of gramicidin A . J . Mrvnhr. Biol. 31, 171-188. Armstrong, C. M. (1981). Sodium channels and gating currents. Physiol. Reu. 61,644-683. Aseltine, J. A. (1958). "Transform Method in Linear System Analysis." McGraw-Hill. New York. Auerbach, A., and Sachs. F. (1983). Flickering of a nicotinic ion channel to a subconductance state. Bioppliys. J . 42, 1-10. Barrett. J. N.. Magleby, K. L., and Pallotta, B. S. (1982). Properties of single calciumactivated potassium channels in cultured rat muscle. J . Pl7ysiol. 331, 21 1-230. Bendat, J. S . , and Piersol, A. G . (1971). "Random Data: Analysis and Measurement Procedures." Wiley (Interscience), New York. Benz, R.. Janko. K., Boos, W., and Lauger, P. (1978). Formation of large, ion-permeable coli. Biockirn. membrane channels by the matrix protein (porin) of Es~~sr.he.ric.hiti Biophys. ACIN 511, 305-319. Betz, W., and Sakmann. B . (1973). Effects ofproteolytic enzymes on function and structure of frog neuromuscular junctions. J . Physiol. 230, 673-688. Bevan, S ., Kullberg, R., and Rice, J. (1979). An analysis of cell membrane noise. Ann. Stfir. 7, 237-257. Blatz, A. L., and Magleby, K. L. (1983).Single voltage-dependent chlorid-selective channels of large conductance in cultured rat muscle. Biophys J . 43, 237-241. Boheim, G., Hanke. W.. Barrantes, F. J., Eibl, H., Sakmann, B., Fels, G., and Maelicke, A. (1981). Agonist-activated ionic channels in acetylcholine receptor reconstituted into planar lipid bilayers. Proc. Nu//.Acrrd. S(,i. U . S . A . 78, 3586-3590. Brehm, P., Steinbach, J . H . . and Kikidoro. Y. (1982). Channel open time of acetylcholine receptor on Xenopus muscle ce,ll in dissociated cell culture. Deu. B i d . 91, 93-102.
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CURRENT TOPICS IN MEMBRANES 4 N D TRANSPORT. V O L U M E ?I
Kinetics of Movement in Narrow Channels DAVID G . LEVITT Depprrrtmrnt of Physiology Univer.riry of Minnrsorrr Minneripolis, h4inne.i o t r i
I.
Ion-Ion Interaction . . . . . . . . . . . . . . . . . .
............................
IV. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . Appendix: Derivation of Eqs. ( 3 ) and ( 4 ) . . . . . . A. Ion-Ion Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
193 194
The “narrow” in the title of this article refers to the condition in which the diameter of the channel is so small that the molecules or ions in the channel are not able to pass around each other. The actual pore diameter that meets this condition depends on the specific transport process that is being considered. For example, for the analysis of pure water transport the channel diameter should be le\s than about 0.6 nm (i.e., twice the diameter of water) for this condition to be rigorously satisfied. In contrast, if one requires only that two cations cannot pass each other, then, because of the strong electrostatic repulsion, the “narrow” condition could be satisfied for channels that are significantly larger than twice the ion diameter. The significance of this “no-pass” condition (which is a better description than the more commonly used “single-file”) is that it introduces an important simplification into the kinetic equations and allows the derivation of some very general relations. Furthermore, it is a condition that is probably either satisfied or approximated in some region of most biological membrane ion channels. 181
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The first use of this no-pass condition was by Hodgkin and Keynes (1955) to explain the observed K+ flux ratio in the squid axon. Shortly afterward, Harris (1956) applied this same flux ratio equation to the water-water interactions in a no-pass channel to explain the observed difference between the diffusive and hydraulic permeability of water. More recently, attention has been directed toward the implications of the nopass condition for ion-water interactions. These different interaction conditions (ion-ion, water-water, and ion-water) are discussed separately in this article. The theory is illustrated primarily with experimental results for gramicidin A, which provides the best characterized no-pass channel. I. ION-ION INTERACTION
Hodgkin and Keynes (1955) measured the one-way fluxes of K+ across the membrane of the squid axon and showed that the fluxes could be described by an equation of the form
j / j = [ ( K , / K ? exp(zF~/dRT)]” ) (1) where K I and K2 are the K tactivities on the two sides of the membrane, $ is the membrane potential, z is the ion valency, F is Faraday’s constant, R is the gas constant, and T is absolute temperature. If the ion transport is passive and there is no interaction between ions, then the flux ratio should be described by Eq. ( I ) with n = I (Ussing, 1949). Hodgkin and Keynes (1955) found an n (“flux ratio exponent”) significantly greater than I and showed that this could be explained theoretically if the channel was filled with one or more K + ions so that there was interaction between ions in the channel. For the special case in which the channel was always filled with N ions so that when a K+ ion entered one end, and another ion was ejected from the opposite end (“knock on-knock off” kinetics), they showed that n was related to the number of ions in the channel ( N ) by n = N + l
(2)
Hodgkin and Keynes (1955) realized that this “knock on-knock off” model was probably not physically realistic and that a better model was one in which there were vacancies in the channel into which the ion jumped. This “reaction-rate” type of model for ion transport, defined by the condition that ions can only jump to a neighboring site if that site is unoccupied, is now the most commonly used approach for studying ion channel flux kinetics. For the general case, the solution of the kinetic equations for the flux ratio exponent ( n ) can become quite complicated,
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even for relatively simple cases. For example, for the two-site channel with two different ions (e.g., the abundant and tracer species), the complete analytical solution involves 28 different rate constants and nine simultaneous linear equationfi (requiring expansion of a 9 x 9 matrix). The solution is somewhat simplified by considering the equilibrium limit, where Hodgkin and Keynes (1955) showed that II =
(RTIF?)gIJ
(3)
in which g is the conductance in the limit where the applied voltage approaches zero and J is the one-way flux at equilibrium. Heckmann (1972) has discussed the solutions to these equations for a number of different cases. Hille and Schwarz (1978) and Urban and Hladky (1979) have discussed rather general solutions for the two-ion channel. The discussion of the flux ratio is simplified by the use of the following analysis, which is an extension of a recent result of Dawson (1982). Consider a membrane that contains channels that are permeable to only one species of ion which is at equilibrium [i.e., zero electrochemical potential difference (G)across the membrane] and, therefore, has zero flux. Then, an infinitesimal amount of a tracer of this ion is added to the left side. There will be a flux of this tracer ( J " ) across the membrane which, as a result of coupling in the channel, will produce an associated flux of the abundant ion ( J ) . One can then derive (see Section Vj the following relation for the flux ratio exponent ( n j: n =
I'
+
I
I'
=
(J/J*:&,,
(4)
This is a general relation, valid for the near-equilibrium limit (i.e., conditions under which the theory of irreversible thermodynamics is applicable). Consider first the knock on-knock off model. In this case the channel always contains N ions, all of which must be pushed across the membrane for each tracer ion that crosses. Thus, I' = N and n = N + 1 , the result of Hodgkin and Keynes [Eq. (2)]. Next, consider the reaction-rate model for a channel that has two ion sites. In the limit of a low concentration of the abundant species, the channel will usually be empty when the tracer enters so that I' = 0 and n = I . One can also use Eq. (4) to directly derive a relation for 11 in the high concentration limit defined by the condition that the channel always contains either one or two ions. For this condition, when the tracer enters the channel (e.g., from the left) there must be an abundant ion in the right binding site of the channel and this ion must be transported across the membrane when the tracer crosses the channel, contributing a flux of one
184
DAVID G. LEVITT
to J [Eq. (4)]. Also, when the tracer leaves the right end of the channel, this condition requires that there must be an abundant ion at the left binding site of the channel. Now, the value of n depends on the rate constant for entering the channel relative to that forjumping from one site to the next in the channel. If the rate of entering is relatively fast, then, when the tracer leaves the channel from the right channel site, an abundant ion will reenter the channel from the right side (subtracting a flux of one from J ) , so that the net flux ( . I ) of abundant ions is zero ( I ‘ = 0) and I I = 1. If the rate of entering is relatively slow, the abundant species that is in the left channel site when the tracer leaves will jump back and forth between the two ion sites and the abundant ion will jump into the channel with equal probability from either side, so that Y = I and n = 2. Since the rate of entering the channel is proportional to the bulk concentration, at very high concentrations the rate of entering must become relatively fast and n must approach I for the two-site channel. These general qualitative features re illustrated by the specific quantitative analysis of Hille and Schwarz \ ,978). This analysis can be easily extended to the general N-site channel. At concentrations high enough that the channel always contains either N o r N - I ions, I’ = N - 2 ( n = N - I ) if the rate of entering the end is relatively fast, and I‘ = N - 1 ( n = N ) if the rate of entering is relatively slow. Recent measurement for the K + channel of the squid axon indicate that n can reach values of 3 (Begenisich and DeWeer, 1980). This implies that the channel must contain at least three ions, and (if the rate of entering the end is relatively fast) may hold four ions. The experimental value of n for the Na+ channel of the squid axon (Begenisich and Busath, 1981) is not significantly different from 1. This indicates that either (1) the channel has a low probability of holding more than one ion or (2) it contains at most two ions and the rate of entering the channel is relatively fast. For the gramicidin channel, n approaches 2 for Cs+ (Procopio and Andersen, 1979) and Rb’ (Shagina et al., 1978) and does not differ significantly from 1 for Na+ (Procopio and Andersen, 1979) and even at very high Na+ concentrations. These results, combined with other data on the gramicidin channel (see HIadky and Haydon, this volume), suggest that the channel can hold at least two Rb+ or Cs+ ions and that the rate of entering the channel (when the channel contains one ion) is slow compared to the rate of jumping between the two sites in the channel. The interpretation of these measurements of n is based on the assumption of a reaction-rate model in which the ion can jump into a channel site if that site is not occupied by another ion. As is discussed later, this interpretation neglects the importance of the ion-water “no pass” interactions which can significantly alter the interpretation of these measurements.
KINETICS OF MOVEMENT IN NARROW CHANNELS
185
It. WATER-WATER INTERACTIONS'
Harris (1956) was the first to observe that if the channel was so narrow that two water molecules could not get past each other, then, for a knock on-knock off mechanism, the ratio of the osmotic or hydraulic permeability (Pf) to the diffusive permeability (Pd)of water should be equal to N + I where N is the number of water molecules in the channel. The derivation follows essentially the same arguments as were used by Hodgkin and Keynes (1955) for ion channels IEq. ( I ) ] . Lea (1963) presented a somewhat more general and rigorous derivation, again for the knock on-knock off kinetics. Levitt (1974) derived this result using a different approach that did not require any assumptions about the specific mechanism of pore transport. Recently, Dawson (1982) has shown that this relation follows just from the coupling of the flux of the tracer and the abundant species and is independent of the coupling mechanism. A slightly modified version of his derivation is given in Section V . The final result, analogous to the expression [ E q . (411 used in the discussion of the ionic flux ratio, is PfIPd =
I'
+
I
r
=
(J/.I*)Aww=o
(5)
Again, r is equal to the number of abundant water molecules that are coupled or dragged across the membrane for each tracer water molecule that crosses the membrane. It is to be emphasized that these two relations [Eqs. (4) and ( 3 1 are completely general (for the near-equilibrium condition) and do not require any assumptions about the mechanism. For the special case of the nopass channel, r can be related either to the number of ions [Eq. (4)] or the number of water molecules [Eq. ( S ) ] in the channel. The derivation of the relation between r and N (the number of water molecules in the channel) follows the same arguments as were used for the ion-ion case. Since a large energy is required to create a vacancy in the channel, one can assume that the channel always contains either N or N - 1 water molecules (this corresponds to the high concentration limit for the ion case). For knock on-knock off kinetics, r = N and Pr/PC,= N + 1. For reactionrate kinetics, r = N - 1 (PfIPd= N) or r = N - 2 ( P f / P d= N - I ) , depending on whether the rate of water entering the channel is slow or fast, respectively, relative to the rate of water jumping to neighboring sites within the channel. The use of Eq. (5) as a technique for determining N presents some difficult experimental problems. The main problem is in determining Pd, the diffusive permeability of water. First, since one needs to know the I
See also Finkelstein (this volume).
186
DAVID G. LEVITT
value of Pd just for the channel of interest, it is necessary to correct the total membrane Pd for the permeability of the lipid bilayer (which can be significant) and of the other protein systems in the membrane. In practice, in order to measure P d ,one must be able to close or remove the channel being studied in order to subtract out the background Pd. Second, and most important, is the problem of correcting for unstirred layers. For example, the Pd of most pure lipid membranes is in the range of 3 x cm/second which is equivalent to the permeability of a 100-pm layer of water. Rosenberg and Finkelstein (1978b) measured the increase in Pd (and Pf) when the gramicidin A channel was added to bilayers and found a value of r of -5. This equation has recently been used to interpret the results of measurement of PI.and Pd on the channel that is induced by antidiuretic hormone (ADH) in the mammalian collecting duct (Hebert and Andreoli, 1982) and frog urinary bladder (Parisi and Bourquet, 1983). Probably a more generally applicable use of Eq. ( 5 ) is as a method for estimating Pd from measurements of Pf and r . For example, Dani and Levitt (1981a,b) found for the gramicidin A channel a Pfof 6 x 10-14cm3/ second. [Rosenberg and Finkelstein (1978b) found a Pf about six times smaller. Part of this difference may result from the use of different lipids, In the rest of this discussion, the results of Dani and Levitt (1981a,b) are used along with other data from the same laboratory, all of which were obtained with glycerol monoolein membranes.] Using an r of 9, determined from streaming potential measurements (see below), in Eq. ( 5 ) cm3/second. yields a Pd of 6.6 X The no-pass condition not only determines the ratio of P f / P d ,but also has an important influence on the basic kinetic mechanism involved in the transport. For example, for a water molecule to diffuse through a no-pass channel, it must “push” the whole column of water ahead of it. Thus, there are two separate factors that determine the diffusion coefficient ( D ) in the channel: (1) the local water-wall interaction and (2) the influence of the column of water molecules. Levitt and Subramanian (1974) showed that, in the limit where the water-wall interactions are predominant over the water-water interations, the channel D is described by D
=
DoIN
(6)
where N is the number of water molecules in the channel, and Do is the diffusion coefficient the water molecule would have if it were all alone in the channel (i.e., Do represents purely the effect of the water-wall interactions). This relation was verified using a computer simulation of a hardsphere liquid and a channel with diffusely reflecting walls (Levitt and Subramanian, 1974). The diffusion coefficient of water (D,) in the gramicidin channel can be
KINETICS
OF MOVEMENT IN NARROW CHANNELS
187
determined from a knowledge of P,I, N , and L (the channel length) (Dani and Levitt, 1981b): where N A is Avogadro’s number and V , is the molar volume of water. Substituting the values for gramicidin into this equation yields a D, of I .7 X 10 cmVsecond. Substituting this result into Eq. (5) and using the N for grdmicidin (9) yields a Oi, of 1.5 x cm’/second. Thc diffusion coefficient ( D K ,Knudsen) for a hard sphere of diameter h in an ideal diffusely reflecting channel of diameter d is described by (Present, 1958)
’
DK
=
(2/3)(d - h)(2k?/~M)”’
(8)
where M is the mass of the water molecule, and X is Boltzmann’s constant. For d = 0.4 nm and 6 = 0.3 nm, DK= 2 X cm’/second. This is about 13 times larger than the value of DOfor water in the gramicidin channel, indicating that the water apparently spends more time stuck to the pore than in the ideal case in which the water is instantly reemitted after a wall collision. Diffusion in the gramicidin channel can be thought of as essentially diffusion along the proteinlike surface that forms the channel wall. Thus, this value for Do provides a direct measurement of the mobility of water on protein surfaces. The water is clearly not frozen or immobilized on such surfaces since Do is nearly equal to the bulk water value, a result that is consistent with recent measurements of the rate of water movement on the surface of lysozyme (Bryant and Shirley, 1980). In the limit where the channel diameter becomes equal to the solvent diameter, the solvent-solvent collisions become strictly one dimensional (like beads on a string) and it becomes possible to obtain some exact kinetic solutions. For example, one can solve for the detailed time-dependent velocity and spatial correlation functions for the case where the wall interaction is either omitted (Levitt, 1973a) or modeled as an idealized random effect (Levitt, 1973b). 111.
ION-WATER INTERACTIONS
In general, there will be some coupling between the water and ion flux leading to the classical electrokinetic phenomena (streaming potential, electroosmosis, etc.). In the past, these effects have not been an important tool for studying membrane transport because of the interference from unstirred layer effects and the lack of a simple theoretical interpretation for the results. It has been recently recognized that if the channels
188
DAVID G. LEVITT
satisfy the no-pass condition for the ion and water, then these electrokinetic effects can be interpreted in terms of the number of water molecules in the channel. The importance of the information that can be obtained from these measurements (e.g., on artificial bilayer membranes, see below) may be a stimulus to try to overcome the experimental difficulties involved in making them on biological systems. One manifestation of the coupling between water and ions is the streaming potential. The following relation can be derived from a general irreversible thermodynamic analysis (Levitt et al., 1978):
where A* is the change in membrane potential (“streaming potential”) produced by the osmotic pressure A n under open circuit conditions ( I = 0) and I‘ corresponds to the number of water molecules that are dragged by or coupled to each ion transported across the membrane when there is no osmotic pressure difference. It is assumed in Eq. (9) that the imposition of AT (usually by the addition of an impermeant nonelectrolyte) does not alter the ionic activity. This, in general, is not a valid assumption. For example, for an ideal solution, the addition of the pure nonelectrolyte lowers the molarity of the ion in such a way that the Y in Eq. (9) should be replaced by ( I + Y). In general, the change in ionic activity should be measured and corrected for. For a channel that is so narrow that the ion and water cannot get past each other, r can be directly related to the number of water molecules in the channel. Again, the exact relation depends on the events that occur at the channel entrance. For example, if the channel contains at most one ion and the ion enters the channel by pushing the end water molecule ahead of it, then r = N (the number of water molecule in the channel). This corresponds to the “knock on-knock off” type of kinetics. Alternatively, if the ion enters and leaves the channel by exchanging with the water molecule in the channel or bulk solution, respectively, then I‘ = N - 2. As the ion concentration is raised, the channel may become occupied by additional ions which will displace some water, and I’ may decrease. It is assumed in Eq. (9) that only one ion has a significant membrane conductance. That is, the open-circuit condition ( I = 0) implies that there is no ion flux through the channel. If more than one ion is permeable or if there is more than one type of conductance mechanism for the same ion, then, although there may be a macroscopic open circuit, there will still be ion flows in the different channels; and Eq. (9) will be incorrect. The major experimental limitation of this streaming potential measurement is that the effect is small, amounting to about 0.45 mV per water
KINETICS OF MOVEMENT IN NARROW CHANNELS
189
molecule per osmole osmotic pressure difference [Eq. (911. Since the value of N is not likely to be much larger than 10, one must impose a I osm osmotic pressure to observe a change in membrane potential of only 4.5 mV. The concern, of course, is that osmotic pressures of this magnitude will produce artifactual changes in membrane permeability and potential that obscure the small streaming potential. A severe experimental problem results from the electrolyte buildup on one side of the membrane and depletion on the other produced by the convective drag of the 0smotic water flow. This polarization produces a change in membrane potential of the same sign as the streaming potential. This effect probably dominated earlier measurements oft he “streaming potential” (Barry and Hope, 1969a,b: Wedner and Diamond, 1969). The key distinction between the true streaming potential and polarization and other artifactual effects is that the streaming potential develops immediately upon the imposition of the osmotic pressure, whereas these other effects build up with a time constant that can be estimated for the given experimental conditions (Levitt et ul., 19713). Thus, the key requirement for measuring the streaming potential is that the osmotic pressure can be applied rapidly relative to the development of the artifactual effects. Rosenberg and Finkelstein (1978a) and Levitt et ul. (1978) have measured the streaming potential for the gramicidin channel in artificial bilayers. The accuracy of these measurements was somewhat limited by the uncertain correction for polarization effects and for the change in ionic activity produced by the addition of the nonelectrolyte. We have recently repeated these measurements using a technique that eliminates the need for any unstirred layer correction. The method involves establishing the osmotic pressure gradient when the two solutions are separated by a thick membrane. No electrolyte polarization can develop during this time because the water permeability of the thick membrane is negligible. The membrane is then suddenly thinned (in less than a second) and the streaming potential determined before any polarization potential can develop ( I0 seconds or longer). The change in ionic activity is directly measured using an ion selective glass electrode. The results of this new approach as applied to the gramicidin channel are shown in Fig. 1. The value of I’ (water molecules per ion) is plotted versus the activity of either Na’ or K’. For Na’, there are about nine water molecules coupled to each ion with no obvious dependence on the activity up to 6 t n . For K t there are about seven water molecules per ion in the low concentration limit, decreasing to about five water molecules per ion at high activities. There are at least two possible explanations for the I‘ for Na+ being about two water molecules larger than for K + . Sodium is a smaller ion than K’ and has a tighter hydration shell. Thus, when Na+ enters and
190
DAVID G. LEVITT
X X
X 5
0
I
2
3
4
5
Activity (Molal)
FIG. I . Number of water molecules coupled to the transport through the grarnicidin channel of either one Na' (e)or K + ( x ) ion as determined from the streaming potential l r : Eq.
"31.
leaves the channel it may drag an extra water of hydration along with it. Another possibility is that Na' enters the channel by a knock on-knock off mechanism while K + enters by exchanging with the end water. As discussed above, one would expect Y to differ by about 2 for these two mechanisms. Other data on the gramicidin channel (see Hladky and Haydon, this volume) suggest that the channel can be occupied by at least two K + ions but only one Na+ ion. This is consistent with the results in Fig. I since, at high concentrations, the value of Y should decrease for K + because of the presence of the other ion in the channel. In contrast, this decrease would not be seen for Na+ if it could not multiply occupy the channel. This estimate of nine water molecules per channel is about what is expected for the known structure of the gramicidin channel (about 0.4 nm in diameter and 2.5 nm long). One can show that for a channel that becomes occupied by two ions, n is equal to the average number of water molecules between the two ions. That is, each cycle in which an ion moves from, for example, the left to the right site will displace the number of water molecules that are between the two sites. Thus, the value of n = 5 which is found for K + at high
KINETICS OF MOVEMENT IN NARROW CHANNELS
191
concentrations suggests that there are about five water molecules between the two K + sites in the multiply occupied gramicidin channel. There is no detectable streaming potential for H + in the gramicidin channel (Levitt ef al., 1978). This observation is consistent with the relatively high H + conductance through the gramicidin channel which was postulated to result from a proton jump mechanism along the continuous chain of hydrogen-bonded channel water (Myers and Haydon, 1972). In this process, a H + jumps onto the water molecule at one end of the channel, and, after a series of rearrangements, another H + jumps off at the other end. One would not expect any water to be coupled to the H+ flux, and, therefore, the streaming potential should be zero, as observed. Measurements of the streaming potential [or r , Eq. (9)] can still be useful even if the channel does not meet the no-pass criteria for its entire length. For example, Miller (1982; and see Miller et al., this volume) has determined the streaming potential for a K+-selective channel isolated from sarcoplasmic reticulum. The streaming potential was only about 1.1 mV per osmole osmotic gradient (about one-third that found for gramicidin), corresponding to an r of 2.4. Miller’s interpretation of this result was that the channel had a funnel-like mouth with only a short, narrow (nopass) region that gave the channel its ionic selectivity. From the streaming potential measurements, there can be, at most, about four water molecules ( N = r + 2, see above) in this no-pass region. However, since there should be some coupling to water in the wider portions of the channel, the narrow region may only contain one or two water molecules. This picture of the channel is consistent with the observation that this channel has a conductivity about five times that of gramicidin even though it is much more cation selective. This combination of high conductance and high selectivity is consistent with a pore that has a wide mouth and a very short restrictive region. Another application of the no-pass condition for the ion and water is the measurement of Dani and Levitt (198 la) of the equilibrium partitioning of ions into the gramicidin channel. The water permeability of the gramicidin channel was measured as a function of the ion concentration with identical solutions on both sides of the membrane. If the ion and water cannot get past each other, then, under open-circuit conditions, the presence of an ion in the channel will block the flow of water through that channel. As the ion concentration is raised, the average water permeability through the channel should decrease to zero and the equilibrium ion binding parameters can be determined. This prediction was experimentally confirmed (for TI+, K + , and Lit) and the binding constants were in general agreement with other, less direct, cieasurements.
192
DAVID G. LEVITT
Probably the most important aspect of the ion-water interaction is its implications about the general mechanism of channel ion transport. For example, consider the question, What determines the local ion mobility in the channel? The usual assumption in the reaction-rate approach is that this mobility is determined by the local ion-wall interaction. In contrast, in a no-pass channel it may be limited by the water-wall interactions of the nine or so water molecules that must be moved whenever an ion moves. An experimental approach to this question is to determine the local diffusion coefficient (or mobility) of the ion in the channel. Since the diffusion coefficient of pure water in the channel is known [Eq. (7)], these two values can then be compared. If the water-wall interactions were the rate-limiting factor, then the ion diffusion coefficient should be the same as that of water. There are three factors that determined the channel ion conductance: (1) the rate of exchange of ions between the channel and bulk solution; (2) the long-range (electrostatic) forces in the channel, and (3) the local ion diffusion coefficient. Since it is not now possible to independently measure these three factors, the ion diffusion coefficient cannot be directly measured. However, Dani and Levitt (1981b) estimated the ion diffusion coefficient in the gramicidin channel using a theoretical electrostatic calculation for the long-range force and the limiting possible values for the exchange rates of the channel ends. They found that the minimum possible cation diffusion coefficient for Na+ and K' was within a factor of two of the diffusion coefficient in water. These results suggest that the rate-limiting step for these ions is probably the water-wall interaction. These results have obvious implications for studies that attempt to explain the ion conductance from a detailed theoretical analysis of the local ion-wall interaction. Finally, the no-pass condition must be considered in the modeling of the kinetics of ion transport. For example, the most generally accepted model of ion transport is the reaction-rate model in which an ion can jump to a neighboring ion site if that site is unoccupied by another ion. This model is not correct for a no-pass channel where the ion would have to displace all the water molecules and any other ions in the channel in order to move to the next site. For example, one explanation for the observation that the gramicidin channel can hold two K + ions and only one Na+ ion (see Fig. 1) is that Na' (because of its tighter water of hydration) enters the channel by pushing the end water ahead of it. Thus, were there two Na+ sites (one at each end of the channel), then when one ion entered, the other would be pushed out the other end and two ions could not occupy the same channel. One attempt to incorporate these effects into the channel kinetics is a
KINETICS OF MOVEMENT IN NARROW CHANNELS
193
recent application of the Nernst-Planck continuum approach to a multiply occupied channel (Levitt, 1982). The general solution of the continuum equations for a multiply occupied channel is very complicated. However, the no-pass condition introduces a strong coupling between the ions that simplifies the kinetics and allows a numerical solution to be obtained. It is shown that, although the conventional reaction-rate model is probably a good approximation for channels such as gramicidin, it may become inaccurate for channels of larger diameter.
IV. SUMMARY As described in this article, the “no-pass” condition gives rise to two different sets of special effects in narrow channels. First, it provides a physical and mathematical constraint that allows the derivation of some general “thermodynamic” type of relations. The three most important ones discussed here are the relation between the flux ratio and the number of ions in the channel, and the dependence of the streaming potential and of the ratio of the osmotic t4 diffusive water permeability on the number of water molecules in the channel. It is probable that all the important results of this type have now been derived and it is unlikely that they will be significantly extended in the future. The second set of results is concerned with the implications of the no-pass condition for the general kinetic description of transport in narrow channels. Two examples discussed here are the possibilities ( 1 ) that the local mobility of an ion may depend primarily on the mobility of the chain of water molecules in the channel that it must push, rather than on its own ion-wall interaction, and (2) that one ion cannot move in the channel without displacing all other channel ions. Our understanding of these kinetic effects is still in the preliminary descriptive stage. Most of the examples in this article have been from studies on the gramicidin channel, because gramicidin represents the no-pass channel par excellence. It has a uniform, well-characterized narrow channel (about 0.4 nm in diameter) which is too small to permit water molecules to get past ions or other water molecules. The importance of the no-pass condition for biological channels remains, in general, an unanswered question. It is usually assumed that high ion selectivity requires a small diameter “filter” region and, therefore, any highly selective biological channel should meet the no-pass condition for at least a fraction of its length. At present, the implications of the no-pass condition are just beginning to be considered in the analysis of biological channel kinetics.
194
DAVID G. LEVITT
V.
APPENDIX: DERIVATION OF EQS. (3) AND (4)
A. Ion-Ion Interaction
In the linear (near-equilibrium) region the flux of the abundant ( J ) and tracer species ( J * ) of the ion can be related by the general irreversible thermodynamic expression:
where is the electrochemical difference for the two species ( y activity coefficient): -
+
A p = R T ln(al/a2) zFA+ a2
a1 = ylc'l;
=
(A-2)
= Y2C2
Onsager's reciprocity relation (L21= L 2 1 )has been assumed in Eq. ( I ) . Hill (1977) has shown that this relation is valid for the general reactionrate type of ion kinetics near equilibrium. Then, r is defined as the number of abundant ions coupled to the flux of one tracer ion in the absence of an electrochemical potential difference for the abundant species: r = ( J / J * ) Z ~ ;== L12lL22 ~
(A-3)
For the special case where the tracer flux is zero [using Eqs. (A-I) and (A-3)1 -
J* = 0 + Ap* = - r r p
(A-4)
Substituting Eq. (A-2) into Eq. (A-4) ( u ? / u ~ *=) (a2/al)r ~~ exp[-(r
When J * posite:
=
+
l)zFA+/RT]
(A-5)
0. the one-way fluxes of the tracer must be equal and op2- I
I-?
J* h12/hzl =
=
(c;/cT),,
c.TA12 = J * =
=
c;A2,
64-61
(yl~T/y2~:),,
= ( ~ I / ~ ~ ) ( C I I / Lexp[(r I#
+
I)zFA+/RTl
Now, the fundamental assumption of tracer kinetics is that, if the tracer is present at an infinitesimal concentration, the rate coefficients for the
195
KINETICS OF MOVEMENT IN NARROW CHANNELS
tracer flux ( A I z and A z l ) are independent of the tracer concentration. That is, Eq. (A-6). which was derived for the special case of zero tracer flux, is valid for arbitrary tracer concentrations. Using this result [Eq. (A-6)1, the ratio of the one-way fluxes of the abundant species is I-?
?-I
J/ J
?-.I
=
(~~,.l/c.l)/(J*c.?/(.T) = (clA12)/(c2A21)
= 1(ul/u2)e x p ( z F A 1 ~ / R 7 ' ) ] I' )' + =
exp[(r + I)L\CL/RT]
(A-7)
Comparing this result with Eq. ( I ) of the text, (A-8)
n = r + I
B. Water-Water Interaction The above derivation ofthe ion flux ratio [Eq. (A-711 is equally valid for the flux ratio of water: I-!
?-I
J / J
=
exp[(r
+
r
I)Apw/RT]
(J/J*)Ap, = 0
=
(A-9)
where A p , is the chemical potential difference of water and r is the number of abundant water molecules ( J )that are coupled to the flux of one tracer water molecule ( J * ) when ApIl = 0. The net water flux ( J , ) is defined by 1-2
J,=
1-2
'-I
J --J
=
'-I
I-?
J(I - - J I J )
(A- 10)
This diffusive (Pd) and osmotic (P,) permeability coefficients of water are defined by I-?
J
J,
= PL1('u;
)-jWw
=
P~AT/RT
(A-I I )
where cWis the water concentration. I n the dilute solution, equilibrium limit ( A p , + O), using Eqs. ( A - 9 H A - I I ). Ap, = -V,Ap; I-?
i',
PIIP',
= I'
l/V,
1-2
?-I
J,l J = (Ar/RTc,)(PfIPd)= 1
=
J / J
+
1
= (I'
+
I)V,AT/RT (A-12)
196
DAVID G. LEVITT
REFERENCES Barry, P. H., and Hope, A. B. (1969a). Electroosmosis in membranes: Effects of unstirred layers and transport numbers. I. Theory. Biophys. J . 9, 700-728. Barry, P. H., and Hope, A. B. (1969b). Electroosmosis in membranes: Effects of unstirred layers and transport numbers. 11. Experimental. Biophys. J . 9, 729-736. Begenisich, T., and Busath, D. (1981). Sodium flux ratio in voltage-clamped squid giant axons. J . G e n . Physiol. 77, 489-502. Begenisich, T., and DeWeer, P. (1980). Potassium flux ratio in voltage-clamped squid giant axons. J . G e n . Physioi. 76, 83-98. Bryant, R. G., and Shirley, W. M. (1980). Dynamical deductions from nuclear magnetic resonance relaxation measurements at the water protein interface. Biophys. J . 32, 3II. Dani, J . A , , and Levitt, D. G. (1981a). Binding constants of Li’, K’, and TI+ in the gramicidin channel determined from water permeability measurements. Biophys. J . 35, 485-500. Dani, J . A., and Levitt, D. G . (1981b). Water transport and ion-water interaction in the gramicidin channel. Biophys. J . 35, 501-508. Dawson, D. C. (1982). Thermodynamic aspects of radio tracer flow. I n “Biological Transport of Radiotracers” (L. G . Colombetti, ed.), pp. 79-95. CRC Press, Boca Raton, Florida. Harris, E. J. (1956). “Transport and Accumulation in Biological Systems,” pp. 36-38. Academic Press, New York. Hebert, S. C., and Andreoli, T. E. (1982). Water movement across the mammalian cortical collecting duct. Kidney Int. 22, 526-535. Heckmann, K. (1972). Single-file diffusion. In ”Passive Permeability of Cell Membranes” (F. Kreuzer and J. F. G . Slegers, eds.), pp. 127-154. Plenum, New York. Hill, T. L. (1977). “Free Energy Transduction in Biology,” pp. 50-55. Academic Press, New York. Hille, B., and Schwarz, W. (1978). Potassium channels as multi-ion single-file pores. J . G e n . Physiol. 72, 409-442. Hodgkin, A. L., and Keynes, R. D. (1955). The potassium permeability of a giant nerve fibre. J . Physiol. (London) 128, 61-68. Lea, E. J. A. (1963). Permeation through long narrow pores. J . Theor. Biol. 5, 102-107. Levitt, D. G . (1973a). One-dimensional time-dependent distributions. J . Stut. P h y s . 7, 329336. Levitt, D. G . (1973b). Dynamics of a single-file pore: Non-Fickian behavior. Phys. Reu. A 8, 3050-3054. Levitt, D. G. (1974). A new theory of transport for cell membrane pores. I. General theory and application to red cell. Biochim. Biophys. Acftr 373, I 15-131. Levitt, D. G. (1982). Comparison of Nernst-Planck and reaction-rate models for multiply occupied channels. Biophys. J . 37, 575-587. Levitt, D. G . , and Subramanian, G. (1974). A new theory of transport for cell membrane pores. 11. Exact results and computer simulation (molecular dynamics). Biochim. Biophys. Actu 373, 132-140. Levitt, D. G . , Elias, S . R., and Hautman, J. M. (1978). Number of water molecules coupled to the transport of sodium, potassium and hydrogen ions via gramicidin, nonactin or valinomycin. Biochini. Biophys. Acra 512, 436-45 I . Miller, C. (1982). Couping of water and ion fluxes in a K+-selective channel of sarcoplasmic reticulum. Biophys. J . 38, 227-230.
KINETICS OF MOVEMENT IN NARROW CHANNELS
197
Myers, V. B., and Haydon, D. A. (1972). Ion transfer across lipid membranes in the presence of gramicidin A. 11. The ion electivity. Bioclrirn. Biopliv.~.Ac,/ci 274, 3 13-322. Parisi. M., and Bourquet, J . (1983). The single file hypothesis and the water channels induced by antidiuretic hormone. J . Metnbr. Biol. 71, 189-193. Present. R. D. (1958). “Kinetic Theory of Gases.” pp. 55-63. McGraw-Hill. New York. Procopio, J., and Andersen, 0. S. (1979). Ion tracer Huxes through gramicidin A modified lipid bilayers. Biopliys. J . 25, 8a. Rosenberg, P. A , . and Finkelstein, A . (1978a). Interactions of ions and water in gramicidin A channels. Streaming potentials across lipid bilayer membranes. J . Cen. Physiol. 72, 327-340. Rosenberg, P. A , , and Finkelstein, A. (1978b). Water permeability of gramicidin A-treated lipid bilayer membranes. 1.Gtw. fliysiol. 72, 341-350. Schagina, L. V . , Grinfcldt, A . E., and Lev, A . A . (1978). Interaction of cation Huxes in gramicidin A channels in lipid bilayer. meillbrdneS. Nafrrrr (London) 273, 243-245. Urban, B. W.. and Hladky. S . B. (1979). Ion transport in the simplest single file pore. Bioclritn. B i o p k y s . Act11 554, 410-429. Ussing, H. H. (1949). Distinction by means of tracers between active transport and diffusion. The transfer of iodide in the isolated frog skin. Actcr fhysiol. Sccrnd. 19, 43-56. Wedner, H. J., and Diamond. J . M . (1969). Contributions of unstirred-layer effects to apparent electro kinetic phenomena in the gallbladder. J . Mernhr. B i d . 4, 92-108.
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CURRENT TOPICS IN MEMBRANES A N D TRANSPORl. VOLUME 21
Structure and Selectivity of Porin Channels R . BENZ Dcpartmcnt of Biology Univcrsity of Konstanz Konstanz, Fcdcral Republic of Gcrmuny
I . Introduction. ...... 11. Reconstitutio rins in .............. A. Addition of Porin to the Aqueous Phase.. . . . . B. Membrane Formation from C. Fusion of Reconstituted Ve 111. Single-Channel Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Ionic Selectivity of Porin Channels . . . . . . V. Properties of the lective Channel .............. Outer Membrane VI. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I.
199
200 200 203 204 205 207 209 213 211
INTRODUCTION
The cell wall of gram-negative bacteria consists of three different layers, the inner membrane, the peptidoglycan layer, and the outer membrane (Di Rienzo et al., 1978; Nikaido, 1979a).The inner membrane acts as a real permeability barrier and contains, in addition to the respiration chain, a large number of different transport systems for substrates, whereas the peptidoglycan layer prevents lysis of the bacterium. The outer membrane seems to act a5 a molecular filter for hydrophilic wbstances and as a barrier for hydrophobic molecules (Nikaido, 1979b; Nikaido and Nakae, 1979). The sieving property of the outer membrane of gram-negative bacteria resides in a defined exclusion limit for hydrophilic solutes. The permeability of the outer membrane I S associated with the presence in the outer bacterial membrane of a class of major proteins called matrix proteins (Rosenbusch, 1974) or porins (Nakae, 1975, 1976). 199 Copyright CJ 1984 by Academic P r e s . Inc All right\ ot reproduction in dny form reserved
ISBN n-12-153121-2
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Porins have been isolated from the outer membrane of Escherichia coli, Salmonella typhimurium, and Pseudomonas aeruginosa (Hancock et al. , 1979, 1982; Nakae, 1976; Nakae and Ishii, 1978). They form trimers in dodecyl sulfate that are usually stable. Experiments on reconstituted vesicles in the presence of such porin trimers from enteric bacteria have shown that the maximum molecular weight for permeable substances in the case of E. coli and S. typhimurium is between 600 and 700, whereas molecules with molecular weights up to 6000 can penetrate vesicles reconstituted in the presence of porin F from P. aeruginosa (Hancock et al., 1979; Nakae, 1976; Nakae and Ishii, 1978). Experiments on reconstituted vesicles provide valuable information on the presence and the size of the pores formed by a porin. More detailed information about the pore interior and pore selectivity can be obtained from experiments on lipid bilayer membranes. The reconstitution of the porins into lipid bilayers and the properties of the porin channels from E . coli, S. typhimurium, and P. aeruginosa in lipid bilayer membrane are described in this article. In lipid bilayer membranes the porins of these gram-negative bacteria form, in general, large water-filled pores with a poor selectivity for ions. However, there are exceptions. Protein P from P . aeruginosa outer membrane forms highly anion-selective channels in lipid bilayer membranes (Benz et al., 1983; Hancock et al., 1982). II. RECONSTITUTION OF PORINS INTO LIPID BILAYER MEMBRANES A. Addition of Porin to the Aqueous Phase
Three different methods have been used successfully to reconstitute porins into lipid bilayer membranes. Firsi, detergent-solubilized porin is directly added to the aqueous phase bathing a membrane (Benz et al., 1978a); second, the lipid bilayer membrane is formed from reconstituted vesicles according to the Montal-Mueller method (Schindler and Rosenbusch, 1978); and third, the porin is inserted into the planar bilayer via fusion of the reconstituted vesicles with the membrane (Cohen et al., 1982). The simplest method consists of the addition of purified porin from a stock solution containing. 0.1% dodecyl sulfate or Triton X-100 to the aqueous phase bathing a black lipid bilayer membrane (Benz et af., 1978a). Figure I shows such an experiment. Porin from S. typhimuriurn strain SH 5551 (M, 40,000) was added in a final concentration of 100 ng/ml
STRUCTURE AND SELECTIVITY OF PORlN CHANNELS
10-8
201
3 0 10 20 30 LO t (rnin)
FIG.I . Specific membrane conductance as a function of time after addition of 100 nglml trimers of S. tvphinirrrirrm strain SH 5551 ( M ,40.000) to a black membrane from egg phosphatidylcholineln-decane (closed cir'cles, arrow). The open circles represent a control experiment in which only 10 pg/ml SUS was added to another membrane. I M KCI. 25°C.
to a black membrane from egg phosphatidylcholine/n-decane.After an initial lag of 4 minutes, presumably due to diffusion of the protein through unstirred layers, the conductance increased by about three orders of magnitude within about 30 minutes. Only a slight additional increase (as compared with the initial one) occurred after that time. It has to be stressed, however, that in the presence of all porins the membrane conductance increases continuously until membrane breakage. It is interesting to note that detergents had only a small influence, if any, on porin reconstitution. This was shown by using various detergents and detergent-free porin from osmotic shock solution (Benz et id., 1978a,b). Porin trimers dissociated into monomers were found to be inactive in lipid bilayer membranes and reconstituted vesicles (Nakae et a / ., 1979). Since in all the experiments with porins a steady conductance level could not be reached, the dependence of the conductance on various parameters was difficult to determine. A meaningful comparison was possible, however, on the basis pf experiments similar to those presented in Fig. 1, using the conductance value at a fixed time after addition of the protein. Figure 2 shows the influence of the membrane composition on the incorporation of the porins from S . typlzirnrrrium strain TA 1014 ( M , 38,000, 39,000, and 40,000) into the membranes. For membranes made from oxidized cholesterol or monoolein, the conductance is about two to
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Protein concentration (ng/rnl)
FIG.2. Specific membrane conductance A as a function of the concentration of trimers from the Salmonella strain TA 1014 ( M , 38,000, 39,000, and 40,000) in the aqueous phase; 1 M KCI; T = 25°C. Less than 5 pg/ml SDS was present in the aqueous solutions. The membranes were formed from different lipids dissolved in n-decane. The measurements were performed 20 minutes after blackening of the membranes. (0) Oxidized cholesterol; ( W monoolein; ( 0 )brain phosphatidylserine; (0) egg phosphatidylcholine; ( X ) egg phosphatidylethanolamine.
three orders of magnitude larger than for membranes made from phospholipids. A similar “lipid specificity” was also found for the porins from E . coli and P. aeruginosa (Benz et al., 1978a; Benz and Hancock, 1981). It is obvious that many conductive units were incorporated into lipid bilayer membranes in the experiments described above. This allows investigation of the current-voltage behavior of membranes containing a large number of porin trirners. Examples of current-voltage curves of two membranes made from oxidized cholesterolln-decane in the presence of porin trimers of 3. typhimurium strain HN 6017 ( M , 38,000) are given in Fig. 3. The observed current was a linear function of applied voltage up to at least 150 mV. Even for an application of 100 mV for more than 30 seconds no current decrease occurred, but sometimes a slight increase was found-presumably caused by the incorporation of the porin into the membranes, facilitated by the high electrical field. Linear current-voltage relationships were also found for porins from E . coli and P. aeruginosa (Benz et al., 1978a; Benz and Hancock, 1981; Hancock et al., 1982). The results strongly suggest that no voltage is required to initiate the single conductance unit, i.e., the pores are not voltage gated if the porin molecules are reconstituted by addition to the aqueous phase.
STRUCTURE AND SELECTIVITY OF PORlN CHANNELS
203
FIG.3. Current vs voltage characteristics of two membranes from oxidized cholesterol/ n-decane doped with I ng/ml porin ttimers from S. fypypAimitrium strain H N 6017 ( M , 38,000). The aqueous phase contained 1 M KCI and 50 ng/ml sodium dodecyl sulfate; 7 = 25°C.
B. Membrane Formation from Reconstituted Vesicles
Schindler and Rosenbusch (1978) used an alternative method for incorporation of porin molecules into lipid bilayer membranes. Vesicles reconstituted from lipids and porin are added to the aqueous phases on both sides of a thin Teflon foil having a small circular hole (100-200 pm in diameter) above the initial water level. Monolayers form on the surfaces of the two aqueous compartments. It is suggested by Schindler and Rosenbusch (1978) that these monolayers have the same composition as the vesicles. The water levels on both sides of the foil are now raised above the hole and a “folded” membrane is formed across the hole (Montal and Mueller, 1972). No pores are observed in the membrane immediately after formation at low membrane voltages. Membrane potentials around 100 mV are needed to induce the pores in steps larger than one single conductive unit (Schindler and Rosenbusch, 1978, 1981). Figure 4 shows such an experiment taken from Schindler and Rosenbusch (1978). The initial jumps indicate the formation of pore multimers in 0.1 M NaCl at 240 mV, whereas the subsequent decay is due to inactivation of the single conductive unit, caused by the high voltage. Schindler and Rosenbusch (1978) suggested the existence of three pores in a porin trimer. According to their view, all three pores should activate together but inactivate separately (see also Fig. 4). As a consequence of their observations, Schindler
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i -
m
0
05 0
4 0‘
2
10
15
1 20
Time [minl
FIG.4. Initiation of conductance in a porin-containing membrane made from monolayers. The left side shows large current .jumps which appear at 240 m V membrane potential in 0. I M NaCI. Each large increment was followed by a decay in small steps (0.14 pS) as shown on the right side of the figure. (Taken with permission from Schindler and Rosenbusch, 1978.)
and Rosenbusch (1978) proposed a voltage control of the porin pores in the outer membranes of gram-negative bacteria. C. Fusion of Reconstituted Vesicles with Planar Lipid Bilayers
The third possibility of incorporation of porin molecules into planar lipid bilayer membranes is through fusion of reconstituted vesicles with planar bilayers. Miller and Racker (1976) and Miller et a1 (1976; and see Miller et ul., this volume) showed that cytochrome oxidase vesicles and vesicles from sarcoplasmic reticulum could be fused with planar bilayers in the presence of calcium ions. The calcium ions are most probably needed for the close apposition of the vesicles to the membranes. The yield of fusion could be drastically increased if an osmotic gradient hyperosmotic on the cis side (the side of the addition of the vesicles) were applied across the planar bilayer. The osmotic gradient results in a water flux toward the cis side. This water flux for unknown reasons accelerates the fusion process of the lipid vesicles with the planar bilayer. Recently, Cohen et al. (1982) used this method to incorporate porin molecules into planar bilayers. Upon addition of calcium ions to the cis side and establishing an osmotic gradient hyperosmotic at the cis side, the fusion process begins as indicated by a stepwise increase of the membrane current. The fusion process stops after the osmotic gradient is removed by addition of the osmotic active substance to the trans side. Furthermore, Cohen et ul. (1982) could show that water flux into the reconsti-
STRUCTURE AND SELECTIVITY
205
OF PORIN CHANNELS
tuted vesicles without any gradient across the planar bilayer also increases the yield of fusion. It is interesting to note that the fusion process resulted immediately in open pores in the lipid bilayer membranes and that no voltage-induced activation of pores was observed by Cohen et ul. (1982). Only a minor inactivation was found at high voltages prior to membrane breakage.
I II. SI NOLE-CHAN NEL AN ALYSl S The addition of small amounts (1-10 ng/ml) of porins to the aqueous phase bathing a membrane of small surface resulted in a stepwise increase of the membrane current at H given voltage. These current jumps were not observed when only the detergents dodecyl sulfate or Triton X-100 were added to the aqueous phase in the same concentration as the porin. Figure 5 shows an experiment using porin from E . coli. As can be seen from Fig. 5 all steps were directed upward, whereas downward steps are only rarely observed. Similar results are also found for the porins from S. typhirnuriurn and P . aeruginosu. The lifetime of all porin pores was at least I minute, as could be seen from records extending over long times. Only porin F pores observed in the presence of total outer membrane from P . ueruginosa (Hancock and Nikaido, 1978) had a much shorter lifetime, on the order of 50-100 msec, although the absolute level of the pore conduc-
0.5nS 25 pA
FIG.5. Stepwise increase of the membrane current in the presence of 0. I ng/ml porin from E. coli K12 added to the q u e o u s phase containing 0.1 M NaCl; T = 25°C. The membrane was formed from egg phosphatidylcholineln-decane;V , = SO mV. The record starts at the left end of the lower trace and continue5 in the upper trace.
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3 :0 ;1 P
0 0
li
0.1
1
L 02
03
OL
A (ns)
FIG.6. Histogram of the conductance fluctuations observed with membranes from egg phosphatidylcholineln-decanein the presence of porin from E . coli K12, 0.1 M NaCI; T = 25°C. n, the number of single steps; V , = 50 mV.
tance was not changed as compared with purified porin F (Benz and Hancock, 1981). Most of the conductance fluctuations obtained with various porins were not uniform in size but were distributed over similar ranges. A histogram of the conductance steps measured with porin from E . coli is shown in Fig. 6. The fluctuations for the E . coli porin varied about fourfold. Similar distributions were found for all porins. Only the recently discovered anion channel formed by porin P from P . aeruginosa gave a narrow distribution of the conductance fluctuations (Benz et al., 1983; Hancock et al., 1982). Single-channel measurements in the presence of the porin were performed with a variety of different salts and concentrations. From records similar to those given in Fig. 5 the average conductance increment A was obtained by measuring a sufficient number (at least 50) of individual events. For all porins described in this review (except porin P from P . aeruginosa; Benz et al., 1983) the average pore conductance A was a linear function of the specific conductance u of the aqueous phase, i.e., the ratio Alu varied only little in contrast to A, which varied by two orders of magnitude. This is also reflected in Fig. 7, where the average pore conductance A for the porin F of P . aeruginosa and a porin of E . coli are given as a function of u.The data points could be fitted with straight lines. The same is valid for the porins from S . typhiniurium, although the
207
STRUCTURE AND SELECTIVITY OF PORlN CHANNELS
001.
0
FIG. 7. Average pore conductance A of porin from E . coli K I? (open circles) and protein F from P . a ~ r u g i n o s a(closed circles) given as a function of the specific conductance of the corresponding aqueous salt solution; T = 25°C.
ratio Alu showed a much larger variation for E. c d i and S . typhimrrrirrm than for P . creri4g:ino.s~porin F. This can be explained by the larger diameter of the P . uerrrginosu pore. which is also consistent with the larger value of Alu (Fig. 7) and with a vesicle permeability assay using carbohydrates of different sizes (Hancock and Nikaido, 1978; Nakae, 1976). I t is interesting to note that even large organic cations and anions such as Tris', N(CH2CH3);, and HEPES- were able to pass through the porin pores with little or no interaction with the pore interior.
IV. IONIC SELECTIVITY OF PORlN CHANNELS Further information on the structure of the conductance pathway created by the different porins may be obtained by studying the ionic selectivity of the pores using zero-current potential measurements. Figure 8 shows the results of such experiments obtained for E. coli porin oligomers (which contained two different porins called OmpF and OmpC) in mcmbranes from oxidized cholesterolln-decane. The zero-current potential was found to be positive on the more dilute side of the membrane. This indicated that porin oligomers from E. coli form cation-selective pores in lipid bilayer membranes. From the measured V , and the concentration gradient c"Ic' across the membrane, the ratio P J P , of the permeabilities
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c”/c‘
FIG.8. Zero-current membrane potential V , as a function of the ratio of the salt concentrations on both sides of membranes containing porin from E . coli K12. The membranes were made from oxidized cholesterolln-decane; T = 25°C. V , was positive on the more dilute side of the membrane, c’ = lo-* M .The lines were drawn according to the GoldmanHodgkin-Katz equation with the specified values of the permeability ratio P,IP,. ( x ) KCI; (@) NaCI.
P , for cations and Pa for anions was calculated according to the GoldmanHodgkin-Katz equation: RT PCdr+ Pact V , = - In F Pccr t Pact’ where R , T , and F have their usual meanings. Table I shows the permeability ratios P J P , for the different porins with KCI as a salt in the aqueous phase. The observed slight selectivity for cations or anions may be explained by the presence of negative or positive charges, respectively, in or near the pores. The Pho E porin pore is induced in E . coli outer membrane under conditions of phosphate deprivation (Tommassen and Lugtenberg, 1980). The assumption that charged groups are responsible for the selectivity is supported by the pH dependence of the selectivity. The permeability ratio P J P , for the porin pore decreases in the presence of a NaCl gradient from 2.8 at pH 9 to 1.2 at pH 3 (Benz et al., 1979). Further support arises from selectivity changes of chemically modified porin. For example, porin OmpF from E . coli completely loses its cation
209
STRUCTURE AND SELECTIVITY OF PORlN CHANNELS
'TABLE 1 ZERO-CURRENT POTFNTIAI s V,,, FOR
THE
PRESENCE O F A IO-POI
D
DIFFERENT PORINSI N KCI GRADENr"
Porin
pH
V,,, ( m V )
E . co/i OmpF/OmpC (la/lb) OmpF/OmpC (lailb) OmpF/OmpC (Ia/lb) PhoE (Ic)
h 3 9 h
27 t 3 -5 t 2 30 3 -25t5
S. rypliimitrirtm M, 40,000
h
24 t 2
3.2 t 0,s
20
2.4 2 0.4 10
P.
"
3.8 t 0.9 0.80 0. I 4.6 -t 0.9 0.29 t 0.08
*
trerllgitloscl
F P
6 h
'' 4
-57 + 4
V , is the electrical potential of the dilute side (lo-? M ) minus the potentilt1 of the concentrated side (10.' M ) . The membranes were formed from egg phosphatidylcholineln-decane or diphytanoylphosphatidylcholine/n-decane;T = 25°C. The ratios of the permeability P, (cation) and P, (anion) were calculated from the Goldman-Hodgkin-Katz equation. The nomenclature for the E . c d i porins was taken from Lugtenberg (1981).
selectivity after amidation, i.e., PJP,, = 1 (Tokunaga e t a / . , 1981; Benz c't a / . , 1984b). V.
PROPERTIES OF THE ANION-SELECTIVE CHANNEL FROM Pseudornonas oeruginosa OUTER MEMBRANE
The outer membrane of P. u~rrcginosrrobviously has very special sieving properties, which make this organism quite resistant to most antibiotics (Angus rt u/., 1981; Hancock rt d . , 1982). One of these sieving properties is the relatively short lifetime of the porin F channel. Presumably also present in the outer membrane is protein P ( M , 48,000), which is induced when P. creruginow is grown on media with phosphate limitations. Protein P forms anion-selective channels in lipid bilayer membranes. Figure 9 shows zero-current membrane potential measurements on dioleylphosphatidylchol/nemembranes in the presence of protein P and a KCI gradient. The zero-current membrane potential was negative on the more dilute side and could be fitted reasonably well to the Goldman-Hodgkin-Katz equation assuming either a permeability ratio PJP, = 0 (Nernst equation, full line) or PJP,, = lo-* (broken line). According to
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C'/d'
FIG. 9. Zero-current membrane potentials V , of diphytanoylphosphatidylcholine/n-decane membranes measured as function of a KCI gradient in the presence of protein P from P . ueruginosu; T = 25"C, V,,, was negative on the more dilute side of the membrane, c'' = lo-* M . The lines were drawn according to the Goldman-Hodgkin-Katz equation assuming P J P , = 10-' (broken line) or PJP., = 0 (solid line); T = 25"C, pH 6.
this result, chloride permeates through the porin P channel at least 100 times faster than does the potassium ion (Benz et ul., 1983). The current fluctuations of the porin P channel from P . ueruginosu outer membrane are found to be fairly homogeneous, in contrast to the steps in current observed with porins from Salmonella (Benz et al., 1980) or E . coli (Benz et al., 1978a). Figure 10 shows current fluctuations observed with protein P on a diphytanoylphosphatidylcholine membrane. There all current steps were directed upward, closing pores being only rarely observed. This indicates a long lifetime, as is found for the other porin pores. The lifetime of single steps was found to be independent of voltage, and linear current-voltage relationships were observed up to 200 m V for the protein P channels. The single-channel conductance of the porin P channel was found to be independent of the type of cation present in the aqueous phase. For a 100 mM chloride solution the single-channel conductance was 160 pS, irrespective of the size and nature of the cation. A much larger variation of the single-channel conductance A was obtained if the anions were varied. Figure 1I shows the dependence of the single-channel conductance A of
-
21 1
STRUCTURE AND SELECTIVITY OF PORlN CHANNELS
-
1
100 pA
2nS
FIG. 10. Single-channel record of a diphytanoylphosphatidylcholine/n-decane membrane in the presence of 10 ng/ml protein P from P . aerrcginnsci and 1 M KF in the aqueous phase. A voltage of 50 mV was applied through calomel electrodes with salt bridges; T = 25°C.
100 mM salt solutions on the size of the halides. The corresponding cation was in all cases potassium. The conductance appears to be highest for chloride and lowest for iodide. Besides the halides, a variety of other anions, such as nitrate and nitrite, also permeate through the porin P channel, whereas in the presence of salts with large organic anions, such as HEPES- (N-2-hydroxyethylpiperazine-N'-2-ethanesulfonicacid), no conductance fluctuations could be observed at all. The origin of the anion selectivity of the porin P pore from P . ueruginostr outer membrane is, therefore, presumably a selectivity filter with a diameter of -0.6 nm containing at least one positive charge. This structure accounts also for the concentration dependence of the single-channel conductance. Figure 12 shows the dependence of the single-channel conductance on the KCl concentration c in the aqueous phase. A linear conductance-concentration relationship was observed only with KCl concentrations as small as 1 and 10 mM. The single-channel conductance approached saturation for higher salt concentrations, and no further conductance increase occurred above 0.3 M KCI. The conductance concen-
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21 2
3m/
Radius (nml
FIG.11. Single-channel conductance of the porin P channel in diphytanoylphosphatidylcholineln-decane membranes as a function of the ion radius of the anion according to Pauling. 50 mV was applied to the membranes through calomel electrodes with salt bridges; T = 25°C.
Id'
1
FIG. 12. Single-channel conductance of the porin P channel from P . aeruginosa outer membrane as a function of the potassium chloride concentration in the aqueous phase. The membranes were formed from diphytanoylphosphatidylcholineln-decane. 50 mV was applied to the membranes; T = 25°C. The solid line was drawn according to Eq. (2) with the values of Amax= 280 pS, and K = 20 M-I.
STRUCTURE AND SELECTIVITY OF PORIN CHANNELS
213
tration curve A,((.) given in Fig. 12 could be fitted easily assuming single occupancy of the pore (i.e,, one binding site for anions in the pore), using the following equation [Lauger, 1973; see also Eq. (17) of Lauger, this volume]: &(c) = [cK/(I + ~ K ) ] h o , , , , , (2) with the binding constant K = 20 M-' and a maximum conductance of 280 pS (solid curve in Fig. 12). VI.
CONCLUSIONS
Porins isolated from the outer membrane of gram-negative bacteria are able to form ion-permeable pores in lipid bilayer membranes. Three different methods can be used for successful reconstitution of the porins into lipid bilayer membranes; the implications of the different methods are discussed in more detail below. Most investigations were performed by addition of the proteins to the aqueous phase. The insertion into the membranes is in this case presumably controlled by hydrophobic forces because the reconstitution rate shows no dependence on the ionic strength of the aqueous phase (Benz et al., 1978a, 1980). The reconstitution rate has been found to be strongly dependent on the type of lipid used for membrane formation. The conductance and the ionic selectivity of the single conductance unit, however, are independent of the nature of the lipid. We believe, therefore, that the reconstitution rate does not reflect a specific lipid-protein interaction. Moreover, it seems that the insertion of the trimers into the membranes is governed by a kinetic process, for example the replacement of 100 lipid molecules (each of area 0.5 nm?) by one porin trimer (area 50 nm2; Nikaido, 1979a), which may need considerable energy (Benz ct al., 1980). The data presented here support the assumption that large water-filled pores are formed by most, but not all, porins. Let us first consider the large pores. These pores are permeable to the large organic ions Tris+, N(C2Hs):, and HEPES- without detectable interaction with the pore interior. Furthermore, pore conductance shows no saturation with increasing salt concentration in the aqueous phase, and the single-channel conductance was a linear function of the specific conductance of all salt solutions. The current-voltage characteristic was ohmic-which, too, is expected for a wide unselective channel. Nevertheless there exist some differences in the single-channel conductances. The single-channel conductance of porin F from P . nevuginosa was considerably higher than and S. fyphirnrrrirrm (Table conductances observed for porins from E. (di 11). This indicates that the diameter of the porin F pore is considerably
214
R. BEN2 TABLE I1 COMPARISON OF THE PORESFORMED B Y PORINS OF GRAM-NEGATIVE BACTERIA“ Pore
E . coli OmpF (Ia) OmpC (Ib) PhoE (Ic) LamB S . typhimurium M , 38,000 M , 39,000 M , 40,000 P . aeruginosa F P (1
A (nS)
d (nm)
Cross section (nm’)
1.9 I .9 1.7 2.7
1.3 I .3 I.2 I.5
I.3 1.3 1.2 1.8
2.4 2.2 2.3
1.4 I.4 I.4
1.6 1.5 I .6
5.6 0.24
2.2
3.8
-
-
The diameter d was calculated from the pore conductance in
I M KCI according to A = g a r ’ / / (using u = 110 mS cm-l and I =
7.5 nm). The nomenclature for the E . coli porins was taken from Lugtenberg (1981).
larger than the diameters of the other porin pores. Assuming that the porin pores are filled with a solution of the same specific conductivity as the external solution and assuming a pore length of 7.5 nm [corresponding to the thickness of the outer membrane (Di Rienzo et al., 1978; Nikaido, 1979a)], according to the equation
A
= o.rrr2/1
(3)
the average pore diameter d ( = 2 r ) and the cross section can be calculated. Table I1 shows the diameter and cross section for porins from different gram-negative bacteria, calculated from the conductance of the pores in I M KCl (a= 110 mS cm-I). The values for the diameter are consistent with the results of the reconstituted vesicles, in which hydrophilic solutes of molecular weights up to 600 ( E . coli; Nakae, 1976), 700 (S. typhitnurium; Nakae, 1975), and 6000 (P. aeruginosa; Hancock ef al., 1979) were found to be permeable through the porin channels. The properties of the porin P channel from P . aeruginosa outer membrane are quite different from those of the other porins. Whereas most porins have only a limited selectivity, the porin P channel appears highly anion selective, with PJP, > 100. The decreasing single-channel conductance for larger halides indicates a small selectivity filter with a diameter
STRUCTURE AND SELECTIVITY OF PORlN CHANNELS
215
-0.6 nm, compared with a diameter of at least 1.2 nm for the other porins. Furthermore, the single-channel conductance of the protein P channel saturates for salt concentrations greater than 0.3 M . Taking all these findings together, it is obvious that further studies of the porin P channel as a model for anion transport through channels will be of special interest. The outer membrane of gram-negative bacteria acts as a molecular filter for hydrophilic solutes (Di Rienzo et a f . , 1978; Nikaido, 1979a). The results obtained for lipid bilayer membranes support this view. In particular, we found no gating of the porin pores and found that the pores had a long lifetime (of the order of minutes). Only the porin F pores from P . aeruginosa showed a much shorter lifetime (50-100 msec) if total outer membrane, instead of purified porin, was present in the experiments. This is presumably related to the high antibiotic resistance of this organism as has been discussed elsewhere (Angus et a/., 1981). In this case also, a voltage-controlled gating process could not be detected. Furthermore, the vesicle permeability assay (Mancock and Nikaido, 1978; Hancock et a / . , 1979; Nakae, 1975, 1976) is consistent with the presence of open pores in the absence of applied voltage, a fact which supports the results obtained from lipid bilayer membranes. These findings are in contrast to the results reported by Schindler and Rosenbusch (1978, 1981), who studied porin pores from E . c d i with “folded” lipid bilayer membranes formed from reconstituted vesicles. In these experiments no pores were found to be open after membrane formation at zero voltage, and large membrane potentials were needed to switch on ( V , = 100 mV) and switch off ( V , L IS0 mV) the porin pores. However, the control of membrane permeability by voltage-gated pores in the outer membrane of gram-negative bacteria, as suggested by Schindler and Rosenbusch (1978), is difficult to understand. The channel density in the outer membrane of grarn-negative bacteria is about lo’* pores/cm2 (Di Rienzo et af., 1978; Nikaido, 1979b) and the time constant of the membrane is very small under normal conditions (10 nsec at 0. I M salt; Benz c’t a / . , 1980). Any membrane patential will drop immediately to zero, and the Donnan potentials, which have been reported to be about 20-30 mV across the outer membrane of S . typhimirrium and E. coli (Stock et al., 1977), are far too small to reach 100 mV. We believe, therefore, that something other than voltage-gated pores must be responsible for the voltage effects observed by Schindler and Rosenbusch (1978). One explanation could be that the porin molecules are located only in one monolayer and do not penetrate the “folded” membranes. The high electric field could facilitate the insertion of the proteins into both monolayers of the folded membrane and this process could open the pores. Another
216
R. BENZ
explanation could be that for unknown reasons the folded membranes do not contain any active porin after their formation. The attached vesicles, which contain porin, could fuse with the membranes under the influence of the high electric field. The latter possibility would also explain the large conductance jumps observed by Schindler and Rosenbusch (1978, 19811. Similar jumps have been reported for the fusion of porin-containing vesicles with planar lipid bilayer membranes (Cohen et al., 1982). It is still an open question as to whether one porin trimer contains three pores (Nikaido, 1979b: Schindler and Rosenbusch, 1978)or only one pore (Benz et al., 1978a; Di Rienzo et al., 1978). The conductance data presented in Table I suggest that one trimer contains only one pore. For the case of three pores in a trimer, the pore diameter as calculated from the conductance data would be simply too small to account for the permeation of large hydrophilic solutes through the porin pores. The case for one pore per trimer is also supported by the finding that porin monomers have been found to be inactive in reconstitution experiments with vesicles (Nakae et al., 1979). The amino acid composition and the sequence of all three porins of E . coli outer membrane (OmpF, OmpC, and PhoE) have been determined in a number of recent publications (Chen et al., 1979; Inokuchi et al., 1982; Mizuno et al., 1983; Overbeeke et al., 1983). The sequences of all three porin monomers are not particularly hydrophobic. Only a limited number of subsequences with more than three consecutive hydrophobic amino acids have been found in this protein. Furthermore, it is evident from the sequences that the structural genes for the three porins evolved from a common ancestral gene (Mizuno et al., 1983). This shows that the arrangement of the polypeptide chain in the tertiary and quaternary structure is responsible for the pore formation (Chen et al., 1979; Palva and Randall, 1978). The fact that E. coli porin has been shown to contain a large amount of p-sheet structure supports this hypothesis (Nakae et al., 1979). The cation selectivity of the OmpF and the OmpC porin pores arises presumably from the excess of negatively charged amino acids (Inokuchi et al., 1982; Mizuno et al., 1983), whereas the anion selectivity of the PhoE pore may be caused by the appearance of additional lysines in the sequence (Benz et al., 1984a; Overbeeke et al., 1983). The study of porin channels from gram-negative bacteria offers an elegant way to investigate the structure-function relationship of pores. Porin trimers are usually very stable and allow chemical modifications without damage to protein structure (Tokunaga et al., 1981). In particular, it is possible to change the ionic selectivity of porin channels by such chemical modification (Benz et al., 1984b). Of further interest is the study of anion transport through the selective porin from P . aeruginosm (Benz et d.,
STRUCTURE AND SELECTIVITY OF PORlN CHANNELS
217
1983; Hancock c’t d.,1982) and the influence of chemical modification on anion transport (Hancock ct a / . , 1983). REFERENCES Angus, B. L., Carey, A. M.. Caron, D. A. Kropinski, A. M. B., and Hancock, R. E. W. (I98 1). Outer membrane permeability in Pseudomonus ueruginosu: Comparison of a wild-type with an antibiotic-supersusceptible mutant. Antinzicrob. Agents Chemother. 21, 299-309. Benz, R., and Hancock, R. E. W. (1981). Properties of the large ion permeable pores formed from protein I of P.sr14domoncr.s crrrrrginosu in lipid bilayer membranes. Bioc.hinl. Biophys. Actu 646, 298-308. Benz, R., Janko, K., Boos, W., a i d Lauger P. (1978a). Formation of large ion-permeable membrane channels by the matrix protein (porin) of Escherichiu coli. Biochim. Biophys. Actu 511, 305-319. Benz, R., Boehler-Kohler. B. A . , Dieterle, R., and Boos, W. (1978b). Porin activity in the i,oli. J . Bwteriol. 135, 1080- 1090. osmotic shock fluid of E.sc~heric~hiu Benz, R.,Janko, K., and Lauger, P. (1979). Ionic selectivity of pores formed by the matrix protein (porin) of Escherichia coli. Biochim. Biophys. Actu 551, 238-247. Benz, R., Ishii, J., and Nakae, T. (1980). Determination of ion permeability through the channels made of porins from the outer membrane of Salmonella typhimurium in lipid bilayer membranes. J . Membr. B i d . 56, 19-29. Benz, R., Gimple, M., Poole, K., and Hancock, R. E. W. (1983). An anion selective channel from the P.seitdomonus urrrrginosu outer membrane. Biochirn. Biopl7ys. A i m 7-W, 387-390. Benz. R.. Darveau. R. P.. and Hancock, R. E. W. (1984~1).Outer membrane protein PhoE from Escherichiu coli forms anion-selective pores in lipid bilayer membranes. Eur. J . Biochem. (in press). Benz, R., Tokunaga, H., and Nakpe, T. (1984b). Properties of chemically modified porin from Eschrrichiu coli in lipid bilayer membranes. Biochim. Biophys. Actu 769, 348356.
Chen, R., Kramer, C.. Schmidmayer, W., and Henning, U . (1979). Primary structure of major outer membrane protein 1 of Escherichiu coli B. Proc. Nut/. Arad. Sci. U . S . A . 76, 5014-5017. Cohen, F. S . , Akabas, M. H., and Finkelstein, A. (1982). Osmotic swelling of phospholipid vesicles causes them to fuse with a planar phospholipid bilayer membrane. Science 217, 458-460. Di Rienzo, J. M., Nakamura, K., and lnouye, M. (1978). The outer membrane of gramnegative bacteria: Biosynthesis. assembly and function. Annu. Reu. Biochem. 47,481532. Hancock, R. E. W., and Nikaido. H. (1978). Outer membranes of gram-negative bacteria XIX. Isolation from Pseudomonas ueruginosa PA 01 and use in reconstitution and definition of permeability barrier. J. Bacteriol. 136, 381-390. Hancock, R. E. W., Decad, G . M., and Nikaido, H. (1979). Identification of the protein producing transmembrane diffusion pores in the outer membrane of Pseudomonns ueruginosa PA 01. Biochim. Biophys. Acta 554, 323-331. Hancock, R. E. W., Poole, R. K , , and Benz, R. (1982). Outer membrane protein P of Pseudomonas ueruginosu regulation by phosphate deficiency and formation of small anion-specific channels in lipid bilayer membranes. J . Bucteriol. 150, 730-738.
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Hancock, R. E. W., Poole, K., Gimple, M., and Benz, R. (1983). Modification of the conductance, selectivity and concentration-dependent saturation of Pseudomonas aeruginosa protein P channels by chemical acetylation. Biochim. Biophys. Acfa 735, 137-144. Inokuchi, K., Mutoh, N., Matsuyama, S . , and Mizushima, S. (1982). Primary structure of the OmpF gene that codes for a major outer membrane protein of Escherichia coli K12. Nucleic Acids Res. 10, 6957-6968. Lauger, P. (1973). Ion transport through pores: A rate-theory analysis. Biochim. BiophyJ. ACIU 311, 423-44 I . Lugtenberg, B. (1981). Composition and function of the outer membrane of Escherichia coli. Trends Biochem. Sci. 6, 262-266. Miller, C., and Racker, E. (1976). Cat+-induced fusion of fragmented sarcoplasmic reticulum with artificial planar bilayers. J . Membr. Biol. 30, 283-300. Miller, C., Arvan, P.. Telford, J . N., and Racker, E. (1976). Ca++-inducedfusion of proteoliposomes: Dependence on transmembrane osmotic gradient. J . Membr. Biol. 30,271 282. Mizuno, M., Chou, M.-Y., and Inouye, M. (1983). A comparative study on the genes for three porins of the Escherichia coli outer membrane: DNA sequence of the osmoregulated ompC gene. J . Biol. Chem. 11, 6932-6940. Montal, M., and Mueller, P. (1972). Formation of bimolecular membranes from lipid monolayers and a study of their electrical properties. Proc. Natl. Acad. Sci. U . S . A . 69, 3561-3566. Nakae, T. (1975). Outer membrane of Salmonella iyphimurium: Reconstitution of sucrosepermeable vesicles. Biochem. Biophys. Res. Commun. 64, 1224-1230. Nakae, T. (1976). Identification of the outer membrane protein of Escherichia coli that produces transmembrane channels in reconstituted vesicle membranes. Biochem. Biophys. Res. Commun. 71, 877-889. Nakae, T., and Ishii, J . (1978). Transmembrane permeability channels in vesicles reconstituted from single species of porin from Salmonella fyphimurium. J . Bacteriol. 133, I4 12-14 18. Nakae, T., Ishii, J . , and Tokunaga, M. (1979). Subunit structure of functional porin oligomers that form permeability channels in the outer membrane of Escherichia coli. J . Biol. Chem. 254, 1457-1461. Nikaido, H. (1979a). Nonspecific transport through the outer membrane. In “Bacterial Outer Membranes” (M. Inouye, ed.), pp. 361-407. Wiley (Interscience), New York. Nikaido, H. (197913). Permeability of the outer membrane of bacteria. Angew. Chem., f n i . Ed. Engl. 18, 337-349. Nikaido, H . , and Nakae, T. (1979). The outer membrane of gram-negative bacteria. Adu. Microb. Physiol. 20, 163-250. Overbeeke, N., Bergmans, H.. van Mansfield, F., and Lugtenberg, B. (1983). Complete nucleotide sequences of phoE, the structural gene for the phosphate lirnitation-inducible outer membrane pore protein of Escherichia coli K-12. J . Mol. Biol. 163, 513-532. Palva, E. T., and Randall, L. L. (1978). Arrangement of protein I in Escherichia coli outer membrane: Cross-linking studies. J . Bacferiol. 133, 279-286. Rosenbusch, J. P. (1974). Characterization of the major envelope protein from Escherichia coli. J . Biol. Chem. 249, 8019-8029. Schindler, H . , and Rosenbusch, J . P. (1978). Matrix protein of Escherichia coli outer membranes forms voltage-controlled channels in lipid bilayers. Proc. Narl. Acad. Sci. U . S . A . 75, 3751-3755.
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Schindler, H., and Rosenbusch, J. P. (1981). Matrix protein in planar membranes: Clusters of channels in a native environment and their functional reassembly. Prnc. Nut/. Acud. Sci. U.S.A. 78, 2302-2306. Stock, J . B., Rauch, B., and Roseman, S . (1977). Periplasmic space in Salmonelku ryphimurirtm and Escherichia coli. J . B i d . Chem. 252, 7850-7861. Tokunaga, H., Tokunaga, M . , and Nakae, T. (1981). Permeability properties of chemically modified porin trimers from Escherichia coli B. J . B i d . Chem. 256, 8024-8029. Tommassen, J., and Lugtenberg, B. (1980). Outer membrane protein e of Escherichiu coli K-12 is co-regulated with alkaline phosphatase. J . Bacterial. 143, 151-157.
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CURRENT TOPICS IN MEMBRANES AND TRANSPORT, VOLUME 21
Channels in the Junctions between Cells WERNER R . LOEWENSTEIN Department of Physiology and Biophysic,s University of Miami School of Medicine Miami, Florida
I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . .
................................ 111. Channel Formation. .... .................................... 11. The Cell-To-Cell Channel.
A. Conductive Junctio Chosen Regions of Cell Membranes .................................. B. Channel Openings Are Detected as Stable Quanta1 Steps of Conductance. C. A Channel Formation Hypothesis: The Self-Trap Model D. Channel Formation and Cell Adhesion . . . . . . . . . . E. Channels Form between Cells of Different Types F. Cells in Tissues Are Not Completely Promiscuous IV. Permeability of the Channel.. . . . . . . . . . . . . ............. A Wide A 16A. The Channel in Mammalian Cells IIs\ 16-20 and Is 1s Charge Selective . . . . . . . . . . . . . . . ...... . . . . . . . . . . . . . . ...... . . . .......... . . B. The Channel Is Generally Sy ............... in Junctions between Cells of the C. Some Heterologous Junctions Ha V. Regulation of the Channel . . . . . . . . . . ................. A. A Cyclic AMP-Dependent Phosp B. Elevation of Cytoplasmic Ca2+ Ca or H’ Concentration Closes the Channel. . C. The Channel State Depends on Membrane Potential.. . . . . . . . . . . . . . . . . . . D. The Channel Has Two Gates.. .............. ........................ Gates . . . . . . . . . E. Channel Closure Is Basic to Survival of Cell Ensembles . . . . . . . . . . . . . . . . V1. Structure and Chemistry of the Membrane Particle in the Gap Ga Junction.. . . . . . A A.. Structure of 1the Channel and thee Structural Change Produced by Ca” ,. . . B. Chemistry . . . . . . . . . . . . ................................................. . . . . . . . . . . . . . . References ................................. .............. . . . . . . . . . . . . . ...... . . . . . . . . . . .
22 I 222 222 222 224 227 22x 229 230 23 I
231 23 I 232 232 23s 23s 237 241 24 I 241 24 I 243 244 244 245 247 241
I. INTRODUCTION INTRODUCTION
Cells in organized tissues are commonly interconnected at their junctions. The junctional elements are large membrane channels through 221 221 Copyright Copyright 0 0 1984 1984 by by Academic Academic Press. Press. Inc. Inc. All of reproduction reproduction in in any any form form reserved. reserved. All rights rights of ISBN 0-12-153321-2 0-12-153321-2 ISBN
222
WERNER R. LOEWENSTEIN
which a range of hydrophilic cellular molecules can flow directly from one cell interior to another. Such cell-to-cell channels are present throughout the phylogenetic scale in tissues of mesenchymal and epithelial origin, adult and embryonic, from sponges to man. As a rule, a given cell in a tissue is connected with several neighbors, and so whole organs or large organ parts are continuous from within. This ancient connective organelle has adapted to many different functions. It was an elegant solution of the problem that cells faced in their evolution to multicell ensembles, the problem of how to achieve communication between cytoplasms without losing cell circumscription and genetic individuality. In this evolutionary sense, the most basic function of the channel is homeostatic, the evening out of local differences in small molecular concentrations in the ensembles’ cytosols. Other functions were added later: coordination of cell metabolisms, amplification of cellular responses to hormones and sensory stimuli, transmission of electric signals in heart, nerve, and smooth muscle, and, as widely suspected, coordination of cellular growth and differentiation. The functional roles of the channel and the history of the main concepts in this field of intercellular communication have been reviewed elsewhere (Loewenstein, 1979, 1981). Here I deal with the permeability of the channel and its formation, and with related structural aspects. II. THE CELL-TO-CELL CHANNEL
We imagine the cell-to-cell channel as made of two matching, interlocking halves, one contributed by each cell, forming a continuous and direct aqueous passageway between cells (Fig. 1). This concept was originally proposed on the basis of electrical measurements of the whole junctional pathway and of probings with fluorescent tracer molecules (Loewenstein, 1966), but there is now also evidence of the most direct kind. Electrically, the single channels were resolved as quanta1 events of conductance in forming junction, and structurally, they were traced to the membrane particles of gap junction. 111.
CHANNEL FORMATION
A. Conductive Junctional Pathways Form Spontaneously in Randomly Chosen Regions of Cell Membranes
Cell-to-cell channels can form spontaneously when cells come into contact. The first experimental inductions of channels were made by manipu-
CELL-TO-CELL CHANNELS
223
FIG. I . Cell-to-cell channel. (A) Unit as originally inferred from biophysical measurements. Junctional aqueous membrwe channel (C-C) made of a pair of permeable elements (C), one from each apposing cell membrane (0). and insulation (S) of those elements from the exterior. i, Interiors of the two cells. A permeable junction is composed of many such units. (Reprinted with permission from Loewenstein, 1966.) (B) Unit represented as a protein channel. These features are vested in a pair of matching channel halves. made of protein, traversing the membranes. ‘The pair has a continuous aqueous bore (C-C element in part A ) and interlocking walls with hydrophobic exteriors providing continuous insulation (S element in part A). (Reprinted with permission from Loewenstein, 1975a.)
lating into contact cells isolated from sponges or early amphibian embryos, while monitoring the electrical coupling. A conductive pathway developed spontaneously within a few minutes of the cell contact (Loewenstein, 1967a; Ito and Loewenstein, 1969).There was little chance that the cells selected the contact regions by active movement; the cells were pushed together at spots randomly chosen by the experimenters, and in some cases cell-generated movement was blocked by colchicine or low external Ca2+.At the level of the light microscope at least, the conductive pathway seemed to form anywhere on the membrane, not just in certain predetermined regions-a dynamism particularly clear in the am-
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WERNER R. LOEWENSTEIN
phibian embryo cells. With these large cells (nearly 0.5 mm in diameter) communicating junctions could repeatedly be made between a pair of cells by simply pulling the pair apart and putting it together again at a different spot (the pathway sealed upon disjunction) (Ito and Loewenstein, 1969; Ito et al., 1974a). These findings revealed that a large part of the cell membrane of these cells, perhaps all of it, can rapidly develop a communicating junction. They implied that channels, as open entitities, can form on membrane regions where before there were none and gave a basis for the idea that the channels are made of preformed halves, the protochannels in each membrane. B. Channel Openings Are Detected as Stable Quanta1 Steps of Conductance
A further clue about the junction formation process came from work in which cell-to-cell conductance was continuously monitored during the formation of a junction between a pair of cells; the conductance rose gradually over several minutes to a plateau (Fig. 2). In terms of channels, the simple interpretation was that a permeable junction develops by a progressive accretion of chapnel units (Ito et al., 1974b). Thus, with high-enough resolution, one would expect the channel accretion to show itself as a series of quantal increments of cell-to-cell conductance. This, in fact, turned out to be so when the conductance of nascent junction was measured with a phase-sensitive technique against a background of very small, or zero, conductance. During the early phase of junction formation, while few channels were forming, the openings of the channels manifested themselves as discrete, quantal jumps of conductance, moreover as stable quantal jumps. The channels thus detected stayed open over minutes of observation and closures were not seen unless the intracellular calcium concentration was experimentally elevated (Fig. 3) (Loewenstein et al., 1978a). This stability in the open state contrasts with the behavior of other membrane channels, such as the potassium channel, the sodium channel (Neher and Stevens, 1977; Barrett et al., 1982), and the acetylcholine channel (Katz and Miledi, 1972; Neher and Sakmann, 1976), all shortlived. The molecular stability, which this stability in the open state implies, we think, arises as a consequence of the paired nature of the channel, by an interlocking of the two channel halves (Loewenstein et al., 1978b). The gramicidin channel may provide an instructive analogy: it converts from short-lived to stable form on covalent dimer linkage (Bamberg et al., 1978; Urry et al., 1971).
CELL-TO-CELL CHANNELS
225
FIG.2. In uirro formation of a permeable junction. Development of junctional conductance during junction formation between two T r i / i u u . ~embryo cells. The two cells are micromanipulated into contact whilg impaled o n microelectrodes. ( A ) Two such cells (a and b) about 250 pm in diameter, with the three electrodes in position. (B) Record of continuous electrical measurement during development of coupling. Rectangular pulses of current (i = 0.9 X A) are passed between interior of cell I and grounded exterior, and resulting displacements of membrane potential ( V ) are continuously measured in cells 1 and 2. Electrical arrangement i s shown in inset in ( B ) . (C) Junctional resistance ( 2 r ' ) on the sanie time 1974b.) scale. (Reprinted with permission from I t 0 P I d.,
The available data do not rule out the possibility of unstable openings of the cell-to-cell channel in addition to the stable ones. The time constant of the phase detection system used was such that had open states of 300 msec or less occurred, they would have been missed. There were, in fact, occasional conductance transients with half-times of about 1.3 seconds
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WERNER R. LOEWENSTEIN
FIG. 3. (A) Quanta1 development of junctional conductance during formation of cell-tocell channels. Changes in junctional conductance monitored at high resolution. Manipulation of cell pair (Xenopus embryo) and electrode arrangement are as in Fig. 2, but measuring current (i) is sinusoidal and V, and Vz are recorded by phase-sensitive detectors at selectable phase angle with respect to current and converted to proportional dc potentials. Oscillographic record displays V2, VI ( V , at lower gain), and sinusoidal current i. Junctional conductance is directly proportional to V, here. First of three quantal upsteps occurs at (a). At (b) a series of five Ca" pulses is delivered into cell I (spikes on V! trace are capacitive artifacts caused by solenoid that controls injection), which leads at (c) to a series of quantal V ? downsteps. Voltage calibrations: V, = I 0 0 pV; V, = 3 p V ; i = 1.00 x 10VHA (root mean square); 2s Hz.( B ) Time course of quantal conductance development. Cell contact at time 0. Upsteps of V? occur spontaneously; downsteps occur after Ca" injections (arrows) only. In (a) all changes are integer multiples of a unitary value, Vp = 0.6080 t SE 0.0035 p V . In ( b ) downsteps are not integer multiples of upstep quantum. Upstep Vy = 0.6106 t SE 0.0052 pV. (C) Equivalent circuit for coupling cell pair. Terminals represent cells I and 2 and extracellular ground in common for the i-passing and V-recording circuits. A',, Junctional membrane conductance; gI and g 2 . nonjunctional membrane conductances; cI and c?, their corresponding capacitances. gI and g2 are of similar orders of magnitude, and V: is several orders smaller than VI; hence V, is directly proportional tog, and serves as a direct index of nascent g,. (Reprinted with permission from Loewenstein ct d..1978b.3
CELL-TO-CELL CHANNELS
227
which may have reflected unstable channel openings and closings (Fig. 3Ac) (Loewenstein et al., 1978a). C. A Channel Formation Hypothesis: The Self-Trap Model We envision the cell-to-cell channel formation as a two-step process. First, the protochannels interlock with their counterparts from the opposite membrane. Second, they open up. Most simply, the second step may be a structural consequence of the first. Indeed, if the protochannels are made of symmetrical subunits (see below), the structural stabilization of the forming channel unit and its stabilization in the open state could result at once as molecular interactions of the same set of subunits (Loewenstein et al., 1978b). How the protochannels get to the junction and within interaction range of each other-the necessary preliminaries of such channel formationneeds further elaboration. We build on the premise that the protochannels cannot be transferred from one membrane to the other across the junction. There is no justification for this other than that the thermodynamic cost for such an exchange would be steep, and this also was the reason why, since the inception of the cell-to-cell channel concept, the channel was envisaged as a half and half contribution by two membranes. In principle, in agreement with the current ideas about biosynthesis and mobility of membrane proteins, the protochannel material could be directly inserted into the membrane junction, or, if inserted elsewhere, it could reach the junction by lateral movement in the membrane. Schemes of the first kind would require special mechanisms for recognition of the junctional membrane spots, which, given the dynamic behavior of such spots in experimental conditions of disjunction and junction (Section IIl,A), would imply that the recognition system be at least as dynamic. Lateral movement schemes could be simpler. Suppose that the protochannels (or subunits) move randomly in the fluid matrix and that they interlock with their opposite numbers of the other membranes whenever they get within range of van der Waals forces of each other. The chances for such close encounter, nil where membranes are separate, increase steeply where the membranes are joined. There the protochannels would trap each other by their intercellular ends on encounter, and their outward drift is further opposed by the bending moment of the membranes at the margins of the junction (Fig. 4)-a perfect trap. in which the combined energies of attraction between the particles in the pairs and of the bending moment of the membranes by far exceed the particles’ thermal energies.
228
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WERNER R. LOEWENSTEIN
f
/.,. I -
FIG.4. Self-trap model of cell-to-cell channel formation. Protochannels (channel halves or their precursor subunits) move randomly in membrane lipid matrix. At region of membrane apposition (2-5) they get within end-on attractive range of each other, interlock, and open up as complete cell-cell channels (3). Channels concentrate in region with time as protochannels get trapped there by their mutually attractive forces and the bending moment of the membranes (which far exceed thermal energies of protochannel random movement). (Reprinted with permission from Loewenstein, 1981.)
This lateral movement model (Loewenstein, 1981) relies entirely on particle self-interaction. It requires no special bell for channel congregation nor special forces for drawing the protochannels to the junctional site. A humdrum membrane acquires a local organization on joining another membrane. The junction itself (by which 1 mean a close membrane apposition) brings the protochannels within range of molecular interaction and starts the sequence of events leading to protochannel concentration and channel self-assembly. In collaboration with R. Skalak, the model was analyzed quantitatively by Monte Carlo simulation, using particle sizes and membrane appositional areas of gap junctions and diffusion coefficients known for membrane proteins of similar sizes. The model did well: it produced channel clusters of gap junction dimensions, and it did so fast enough even at low initial (dispersed) particle density (cf. Loewenstein, 1981). D. Channel Formation and Cell Adhesion
Cell junction, in the sense used here of a stable junction, implies adhesion between cell membranes. The postulated hookup of the protochannel pairs, of course, is itself an adhesion, but there may be other stable molecular membrane bondings within the boundaries of a permeable junction or in its immediate vicinity. In terms of the model above, such a bonding would be the prelude to cell-to-cell channel formation. Experiments with cells isolated from the sponge Huliclonu have shown that cell adhesion is indeed closely associated with channel formation. These cells need Ca2+or Mg2+and a glycoprotein present on their surface to adhere to each other (Moscona, 1968; Henkart et al., 1973; Burger et
CE LL-TO-CEL L CHANNELS
229
al., 1978). When pairs of cells deprived of these factors were micromanipulated together in vitro, they did not develop electrical coupling until these factors were added to the bathing medium (Loewenstein, 1967a). Cell adhesion and electrical coupling also correlated with respect to zoological specificity. When paired in vitro, cells from Haliclonu fail to adhere (Galtsoff, 1925) and to couple electrically with cells from the sponge Microcionu (Loewenstein, 1967a), a specificity that also extends to their glycoproteins (Humphreys, 1965). Recent experiments with mammalian liver cells treated with antibodies that block cell-cell adhesion are also relevant to this point. Like other higher cells (Edelman, 1983), cells from adult rat liver have specific surface molecules for mutual adhesion, molecules called CAM (Ocklind and Obrink, 1982; Ocklind et ul., 1983). The rat liver cell line RL expresses CAM in culture, and reaggregated cells make junctions that transfer carboxyfluorescein within 20 minutes. Treatment with antibodies against CAM prevents both cell-to-cell adhesion (but not cell-to-dish adhesion, which is mediated by another molecule) and permeable junction formation for as long as there are enough antibodies (fluorescent) on the cell membranes (K. Machida, B . Obrink, and W.R. Loewenstein, unpublished results) . All this indicates that membrane adhesion mediated by elements other than the cell-to-cell channels is necessary for channel formation, at least, for multiple channel formation. E. Channels Form between Cells of Different Types
Cells from different organs and different mammalian species, when paired in culture, will form communicating junctions with each other. Cells from rabbit lens couple to cells from rat liver, hamster kidney, or human skin, for example (Michalke and Loewenstein, 1971). In terms of the channel formation hypothesis this means that the protochannels from these diverse cells can pair. Such compatibility between cell types is widespread in the vertebrate phylum (Azarnia and Loewenstein, 1971; Pitts, 1972; Flagg-Newton and Loewenstein, 1980). Even cells from different zoological orders, such as birds and mammals, couple electrically to each other in culture. Among the arthropods, cells from different homopteran species can couple, but cells from three different ordqs (Homoptera, Lepidoptera, Diptera) probably cannot (Epstein and Gilula, 1977). Interphyla, arthropod and vertebrate cells do not couple (Epstein and Gilula, 1977);the channels of these phyla also are very different in size and permselectivity (Section lV,A).
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There is less information on heterologous junctions in organized tissues, but the indications are that such junctions are not infrequently communicating. In Chironomus salivary gland, where the coupling topology of the entire organ, consisting of 30-35 cells, has been worked out, all cells-which include at least three different cell types-are interconnected (B. Rose, unpublished results). In rat ovarian follicle, cumulus and oocyte cells are connected (Gilula et al., 1978), and in embryonic tissue communicating heterologous junctions are quite common (Furshpan and Potter 1968; Sheridan, 1968; Warner, 1973; Caveney, 1974; Lo and Gilula, 1979). F. Cells in Tissues Are Not Completely Promiscuous in Making Channels
If the channels from various cell types are so broadly compatible, what prevents then the formation of unwanted communication? That there are limits to promiscuity is attested by several examples. In frog skin, the mitochondria-rich cells are not coupled to the interconnected mass of epithelial transport cells with which they are interspersed (R. Rick and H. Ussing, personal communication). In leech ganglion, P sensory neurons couple to L motoneurons, but not to Retzius neurons, a specificity preserved in culture when the cells are placed in close apposition to each other (Fuchs et al., 1981). In mammalian mixed-cell cultures, epithelioid cells from rat liver or human mammary gland make communicating junctions less frequently or more slowly than they make homologous ones (Fentiman et al., 1976; Pitts and Burk, 1976). The self-trap model accounts for such selectivity simply in terms of cell approximation. Who makes channels with whom in mixed-cell populations (with compatible protochannels) would depend on whether the cell membranes get within close (van der Waals) range of each other. To get them that close, the electrostatic cell-repulsive forces must be overcome-a function presumably of the sugar groups belonging to the more or less specific adhesion molecules on the membrane surfaces. Then, whatever keeps cells apart, either lack of adhesive forces or the presence of actual spacer material, would suffice for the cells not forming channels. In this light, one may expect that molecular specificities in cell adhesion (that commonly go under the name of recognition) and “basement membranes” or other spacer material play a part in the selectivity of communication. The question relating to recognition is as yet untouched, but something has been learned about spacers. In experiments in which the collagen coat of mammalian cells in culture was attacked with highly
231
CELL-TO-CELL CHANNELS
purified collagenases, several cell types made more communicating junctions as a result ( C . Laurido and W. R. Loewenstein, unpublished results). IV.
PERMEdBlLlTY OF THE CHANNEL
A. The Channel in Mammalian Cells Is 16-20 and Is Charge Selective
A Wide
Our knowledge of the permeability properties of the cell-to-cell channel comes mainly from probings with four kinds of fluorescent-labeled molecules. One set of probes consists of linear polyamino acids, negatively charged (Fig. 5 ) . They form a series of progressively increasing length and charge. Their width (the abaxial, permeation-limiting dimension) ranges from 14 to 16 A second set consists of neutral linear oligosaccharides,
A.
FIG. 5 . Space-filling models of three examples from the set o f fluorescent, linear polyamino acid channel probes. From top to bottom: DANS-Glu-Glu-Glu: FITC-Leu-Leu-LeuGiu-Glu: LRB-(Pro-Pro-Gly), . The Eluorophore portions are marked. Scale units. 5 (Reprinted with permission from Loewenstein. 1981 .)
A.
232
WERNER R. LOEWENSTEIN
A
polymers of glucose or mannose, a or p linked, that are 16-20 wide. A third set consists of neutral branched glycopeptides that are 20-30 A wide. Finally, use is made of a set of peptides of fixed tertiary structure, which are too wide for permeation: fibrinopeptide, insulin A chain, and polylysine. These molecules are covalently labeled with the fluorophores dansyl (DANS), lissamine rhodamine B (LRB), or fluorescein isothiocyanate (FITC) at an amine group (the sugars are reductively aminated). The molecules are injected into the cells, one or two molecular species at a time, to probe junctional permeability; the three fluorophores have different excitation and emission spectra (Simpson et ul., 1977; Schwarzmann et al., 1981). From the widths of the largest permeants, the channel diameter was estimated at 16-20 A for mammalian cells and at 20-30 A for arthropod cells (Simpson et ul., 1977; Flagg-Newton et ul., 1979; Schwarzmann et al., 1981). This channel is the widest membrane channel known, and is wide enough, probably, to admit most small-molecular cytoplasmic solutes, but not macromolecular ones. The calculated equivalent conductance of the channel is of the order of S (Loewenstein, 1975b). The channel behaves as if guarded by a fixed or induced charge. It discriminates against negatively charged molecules, and this selectivity is particularly prominent in the narrower mammalian channel (Flagg-Newton et al., 1979; Brink and Dewey, 1980). B. The Channel Is Generally Symmetrically Permeable in Junctions between Cells of the Same Type
The channels in junctions between cells of one type (homologous junctions) are generally symmetrically permeable within the resolution of the methods. In moderate electrical fields, the electrolyte conductances are similar and rather linear in both directions across junctions of many kinds, and there are also no major deviations from symmetry in the permeabilities to larger molecules. This was, in fact, one of the reasons why the channel was originally conceived as made of symmetric elements. C. Some Heterologous Junctions Have Asymmetric Channels
In heterologous cell junctions, symmetry is not always preserved. There is evidence for asymmetry of ion fluxes driven by electrical forces as well as more recently obtained evidence for asymmetry of fluxes of larger molecules driven by chemical forces alone.
CELL-TO-CELL CHANNELS
233
1. ELECTRICALLY RECTIFYINGCHANNELS The classic example of an electrical rectifier junction is the crayfish giant motor nerve electrical synapse, discovered by Furshpan and Potter (1959). With small transjunctional potentials, conductance is rather symmetric, but with potentials exceeding a few millivolts, it is markedly nonlinear and asymmetric. Similar rectifiers are found in a few other electrical synapses (Auerbach and Bennett, 1969; Nicholls and Purves, 1972; Rovainen, 1974). In all of these, the low-conductance direction is from negative to positive transjunctional potential. Thus, the rectification fosters one-way, forward transmission of impulses (Purshpan and Potter, 1959) and, where the postsynaptic cell is hyperpolarized by concurrent, synaptic inhibitory transmission, it favors backward transmission of hyperpolarizing current (Nicholls and Purves, 1972). As to mechanisms, this rectification may be similar to that of the shorter, single-ion channels of nonjunctional cell membrane, in which the nonohmic voltage-current relation seems to arise through an interaction of ions moving in single file, with an asymmetric channel charge structure (Lauger, 1973; Hille and Schwarz, 1978). Once again the gramicidin dimer provides an instructive analogy for a double channel: the introduction of a bulky pyromellityl residue and a high density of fixed negative charge (three carboxyls) at one mouth of that channel make its current-voltage relation asymmetric (Apell et al., 1977). 2. CHEMICALLY RECTIFYING CHANNELS
I distinguish between flux asymmetries under electrical gradients (the electrical rectification discussed before) and asymmetries under chemical gradients alone (chemical rectification). An asymmetry of the last kind was found in certain heterologous junction of mammalian cell cultures, and was created by joining, in culture, cells that have cell-to-cell channels of somewhat different permselectivity. For the channel model, this meant the building of a channel with two dissimilar protochannels, a hybrid channel more restrictive on one side than on the other. Such channels exhibited asymmetry. The (downhill) flux of the larger and negatively charged permeants was not simply limited by the more restrictive channel half but was actually favored in one direction over the other; fluorescentlabeled glutamic acid (two negative charges) or diglutamic acid (three negative charges) traversed the junction more slowly in the direction toward the presumptive less restrictive channel half than in the opposite direction (Flagg-Newton and Loewenstein, 1980).
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WERNER R. LOEWENSTEIN
Asymmetries are manifest only with the relatively larger permeants, such as the glutamic acid series, not with the smaller and less charged ones, such as carboxyfluorescein, nor with the electrical currents carried by the inorganic ions. In this regard the hybrid channel, in one direction, . behaves exactly like the more restrictive channel half behaves in a homologous junction, where the channel is permeated readily by these smaller molecules but only marginally by the glutamic acids. The flux asymmetry requires transjunctional concentration gradients. There are no uphill fluxes. There are thus no reasons to believe that the asymmetry is anything more than a saturation phenomenon of passive diffusion. To satisfy the laws of thermodynamics, the permeants must interact with the channel in such diffusion. In analogy with models for electrically rectifying ion channels (Heckmann, 1969; Lauger, 1973 , and this volume; Hille, 1975), we envision that the larger and more charged permeant molecules interact with an asymmetric channel site with kinetics such that their single-file flux through the channels saturates at concentrations different in one direction than in the other. (In terms of absolute reaction rate theory this would mean that there is an asymmetric free energy barrier for permeant movement in the channel that is higher in one direction than in the other.) The interaction is most likely to be electrostatic or a hydrogen bonding (Loewenstein, 1981). Physiologically, these asymmetric channels have interesting potential. They are intercellular directional filters of molecules. No Maxwell demons, they filter only over a range of concentration, but this range may well be physiological. So far, chemical rectifier junctions have only been put together experimentally in culture, and it is not known whether or where they occur naturally. However, their potential for functional partitioning of tissues is so great that it would be small wonder if evolution had not made use of them before the experimenters did. Such junctions could set up subtle internal boundaries in organs and tissues where the traffic for certain molecules is effectively one way. 1 have in mind mainly signal molecules of intercellular communication that are produced “pulse fashion,” that is, generated or destroyed (or lost) fast enough to establish concentration gradients across junctions (the rise times would need not be more than a few seconds). Then, given the right combination of maxima and minima in the channel free energy profile, these junctions could effectively partition tissues into physiologically or morphogenetically different domains. Such directional devices are attractive not only for the economy they would entail in differentiation but also for the flexibility they would have in letting go unhindered the intercellular traffic of small molecules and of all slowly produced and destroyed junction-permeant molecules.
CELL-TO-CELL CHANNELS
V.
235
REGULATION OF THE CHANNEL
The permeability of a cell interface, the degree of intercellular communication, depends on the number of cell-to-cell channels that are in the open state. Two kinds of mechanisms are known for regulating the degree of communication. One, a slow mechanism (operating over hours), controls the number of channels by a CAMP-promoted phosphorylation. This control presumably operates at the level of channel formation. The other, a fast mechanism (operating over fractions of a second), controls the channel aperture. A. A Cyclic AMP-Dependent Phosphorylation Regulates Permeability
The junctional permeability of various mammalian cell types in culture increases when the concentration of their intracellular cyclic AMP ([CAMP],)is elevated, and vice versa. The upregulation of permeability (which goes hand in hand with an increase in the number of gap junction particles) was shown by supplying the cells with exogenous CAMP, by exposing them to phosphodjesterase inhibitor, or by stimulating their cAMP synthesis with choleragen (Flagg-Newton er al., 1981; Flagg-Newton and Loewenstein, 1981; Azarnia et al., 1981). Cells with normal expression of cell-to-cell channels respond by raising their junctional permeability above the base level, and this is the most general finding. But, more spectacularly, the rise can also occur from a zero level: in Cl- I D cells, an aberrant type that lacks detectable cell-to-cell channels in ordinary culture conditions, the channels develop upon experimental elevation of [CAMP],(Azarnia er al., 1981). The upregulation by cAMP takes several hours to develop and depends on protein synthesis. It is blocked by the protein synthesis inhibitors cycloheximide and puromycin (but not by cytochalasin B) (Azarnia et al., 1981). All this, plus the fact that the upregulation involves a proliferation of gap junction particles, leads us to suspect that cAMP promotes channel formation. However, a modulation of unit-channel permeability as an alternative or additional mechanism is not excluded. Is this regulation mediated by phosphorylating protein kinase as it is in other CAMP-dependent cellular regulations (Kuo and Greengard, 1969; Krebs, 1972; Rosen and Krebs, 1981)? Work with mutant mammalian (CHO) cells deficient in CAMP-dependent protein kinase showed this to be the case. Mutant cells lacking kinase type I turned out to be deficient in
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WERNER R. LOEWENSTEIN
permeable junctions, and this channel deficiency could be corrected by supplying the cells with exogenous catalytic subunits of the missing enzyme (Wiener and Loewenstein, 1983).
1. THEUPREGULATION CANBE SET I N MOTIONBY HORMONES The permeability increase can be elicited by hormones that elevate [cAMPIi. This point was made with the aid of two hormone-sensitive cultured mammalian cell types, the rat glioma cell C6, which has P-adrenergic receptors, and the human lung cell WI-38, which has prostaglandin receptors. The junctional permeability of these cells rose upon stimulation with catecholamine (isoproterenol) and with prostaglandin E l , respectively (Radu et al., 1982). The [cAMPIi elevations, in response to these hormones, peak within 15-30 minutes of hormone applications, preceding the permeability rise by several hours. Similarly, the permeability response lags several hours behind [cAMPIielevation when this is produced by short pulses of exogenous CAMP, bypassing the hormone receptors (10-minute pulses are sufficient) (Radu et al., 1982). The mechanism determining the eventual permeability increase thus seems to be set in motion early on, leading one to suspect that the critical CAMP-dependent phosphorylation occurs early on, too. There is evidence for such hormone action also in an organized tissue: gonadotropin produces an increase of permeability at the oocyte/follicle cell junction (Browne and Wiley, 1979). There is further suggestive evidence, of morphological nature: thyroid hormone and estrogens cause proliferation of gap junctions in ependyma (Decker, 1976) and myometrium (Dahl and Berger, 1978; Garfield rt al., 1978), respectively. Although such morphological data alone are not direct evidence for junctional permeability (since it is not possible to infer that the gap junction particles represent open channels), a CAMP-mediated enhancement of junctional permeability seems a reasonable possibility in the light of the findings described in the preceding paragraph and of the knowledge that these hormones cause [cAMPIi elevation elsewhere. Hormones may thus serve as regulators of junctional communication, that is, slow regulators for conditions calling for changes over hours in cellular states. Moreover, the interaction between the junctional and hormonal form of communication confers on the latter a potential for coordjnation of cellular responses-simple, homeostatic coordination or propagation of hormonal responses in tissues (hormonal cellular response amplification) where the hormones’ second messengers are channel permeant (Loewenstein, 1981).
237
CELL-TO-CELL CHANNELS
2.
DOWNREGULATION
We know less about the downregulatory side of this CAMP-dependent mechanism. However, it is clear that cAMP operates in this direction, too; when [cAMP2+],is lowered experimentally by treating cultured mammalian cells with serum or by’stepping up their density, junctional permeability falls, hand in hand with fall in the number of gap junction particles (Flagg-Newton and Loewenstein, 1981; Azarnia ~t ( I / . , 1981). The available data fit a physiological regulation scheme of the following sort: sI + r l + cAMP t + PJt SZ
+ 1’2 -+ CAMPJ,
+ PJJ
where s represents the stimulus and r its receptor, and where up- or downregulation of junctional permeability P, depends on whether r activates or inhibits cAMP synthesis. I use P, rather than number ofchannels, to be safe. However, as already mentioned, the combined electrophysiological and morphological evidence suggests that the number of channels is the variable determining p j here. If this is so, the scheme would demand that the channel be turned over fast enough for the obqerved times of permeability downregulation. This, indeed, seems to be the case, if the turnover rate of the gap junction protein is a valid index (see Section VI,B).
B. Elevation of Cytoplasmic Ca2+or H + Concentration Closes the Channel The channel responds to changes of various sorts in the intracellular milieu by changing its open state. The free ionized calcium appears to play a pivotal role here. The junctional permeability is high at the low Ca2+concentrations normally prevailing in cytoplam (
’
’
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WERNER R. LOEWENSTEIN
FIG.6. Channel closure by Ca2+.Channel permeability in a chain of Chironomus salivary gland cells is probed with fluorescein (330 d). The dark-field micrographs show the spread of this fluorescent dye injected into cell 3: (a) in the intact cell system, (b) after making a hole into cell 2 in Ca,Mg-free medium (fluorescein leaks visibly through the hole, arrow), and (d) in Ca*+-containing(12 mM) medium; here a hole also was made in cell 4, bracketing the injected cell. Calibration, 50 p m . (Reprinted with permission from OliveiraCastro and Loewenstein, 1971.)
demonstration of this action of calcium was given by experiments in which the cytoplasmic free Ca’+ concentration ([Ca2+li)was monitored with the aid of aequorin. Microinjection of Ca2+or elevation of [Ca’+], by treating cells with metabolic inhibitors or Ca2+ionophores caused prompt and reversible channel closure whenever the [Ca2+lirose in the junctional locale (Fig. 7) (Rose and Loewenstein, 1975, 1976).
239
C E LL-TO-C EL L CHANNELS
FIG. 7 . Channel closure by Ca?’. Ca?’ is microinjected into cell 1, while monitoring electrical coupling between cells I and 11 as pictured in Fig. 3 . ( A ) Dark-field TV pictures (bd) of aequorin luminescence produced by three puffs of 5 x 10 M free Ca?*(buffered with EGTA) of increasing magnitude delivered to about the center of the b a 4 region of a Chironomus salivary gland cell. The pictures were each taken at the time of maximum luminescence spread. Cell diameter, 100 pm. Puffs in (b) and (c) do not reach the junction of the cell and do not sensibly affect coupling. The puff in (d) reaches one junction. causing transient uncoupling, as shown by the electrical measurements in (B): chart records of P , E , , Ell, V , , V,, ( i = 4 x A) and plot of coupling coefficient V , , / V , .Note the recoupling upon restoration of normal Ca” activity. (a) Bright-field TV picture of the cells. (A, bottom) Cell diagram showing location of microelectrodes and of Ca” injection pipet (hydraulic); dotted cell preinjected with aequorin. (Reprinted with permission from Rose and Loewenstein, 1976.)
This channel closure mechanism by Ca’+ has been found to operate in a wide variety of animal cells (see Loewenstein and Rose, 1978, for a review). The regulation may be summarized by the scheme TI(.i’ I,
channel open state F=== channel clo\ed state IC.I‘’ I, I
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WERNER R. LOEWENSTEIN
The transitions between the states probably occur in the [Ca2+]irange of M. The threshold concentration for closure is estimated at to 5x M (Chironomus salivary gland and mammalian heart) (Rose and Loewenstein, 1976; Dahl and Isenberg, 1980). There is little as yet to guide us toward the understanding of the molecular mechanism of Ca2+.From the aequorin experiments it is clear that Ca2+acts in the immediate vicinity of the junction and that the channel reacts rapidly to Ca2+.These facts point to a direct membrane action, perhaps a binding reaction leading to a change in the channel's molecular (or fixed-charge) configuration (Loewenstein, 1966, 1975b). Structural data on gap junction particles obtained with isolated membrane preparations agree with such a mechanism (Section VI,A). Is the Ca2f action mediated by a calmodulin? Several observations suggest this to be the case: calmodulin binds to purified protein of the gap junctions of mammalian liver and lens (Hertzberg and Gilula, 1982) and to lens gap junction protein in situ (Welsh et al., 1982), and calmodulin inhibitors (trifluoperazine, chlorpromazine) were found to cause electrical uncoupling of cells in insect epidermis (Lees-Miller and Caveney, 1982) and prevent such uncoupling in vertebrate embryo (Peracchia, 1984). Channel closure can also be produced by cytoplasmic acidification in many cell types (Turin and Warner, 1977, 1980; Rose and Rick, 1978; Reber and Weingart, 1982). In the Xenopus blastomere junction, for example, about half of the channels close on reducing the cytoplasmic pH by 0.6 units (Spray et al., 1981a). The effect is prompt and reversible. 1. Caz+Is SUFFICIENT FOR CLOSING THE CHANNEL
Because acidification generally causes release of Ca2+from intracellular stores (Lea and Ashley, 1978; Connor and Ahmed, 1979; Rink er al., 1980; Rose and Rick, 1978), the question naturally arises whether the effect of acidification is mediated by Ca2+.But there is another side to that coin: elevation of [Ca2+Iican cause release of H+ (Meech and Thomas, 1977) (mitochondria, for example, release Hf as they take up CaZt;Akerman, 1978). Thus the question becomes, which of the two ions mediates the channel closure, or, in experimental terms, which of the two is sufficient? There is a clear answer that Ca2+is sufficient. Injection of pH-buffered Ca2+solutions into Chironomus salivary gland cells causes channel closure when pHi is constant or even when it is raised (pHi, [Caztli, and electrical coupling were monitored simultaneously in these experiments) (Fig. 8) (Rose and Rick, 1978).
CELL-TO-CELL CHANNELS
24 1
As for the sufficiency of H', a definitive answer is still lacking (see also Section VI). C. The Channel State Depends on Membrane Potential The channel open state is influenced by the membrane potential. In Chiroriotiiirs salivary gland cells, depolarization tends to close the chan-
nels (Socolar and Politoff, 1971) and hyperpolarization to open them (Rose, 1970). The factor determining the probability that the channel is in the open state is not the electrical potential along the channel, but the potential across the membrane, most likely across the appositional membrane portions where the channels are embedded, the pc~riclirinndmvnhrtinr (Obaid et d.,1983) (Fig. 9). I n Xrnop/rs blastomeres the channels tend to close when a potential is imposed across the junction (Spray rt (!I., I98 I b). Is the effect of membrane potential on conductance mediated by an ion diffusing to the channel or is a more direct electromechanical transduction, a direct voltage-gated process, at play'? One may hypothesize, for example, a voltage-dependent release of Ca'+ from a reservoir (or a voltage-dependent CaZt affinity of the channel). Indeed, the changes in junctional conductance in response to shifts in potential can take 0.1-4 seconds (Rose, 1970; Socolar and Politoff, 1971; Spray et d . , 1981b; Harris et ul., 1983; Obaid rt a / . , 1983)-the slow kinetics that one expects from a diffusion-mediated process. Furthermore, a change of [Ca?+Jicauses the junctional conductance vs potential curve to shift along the potential axis. This is consistent with a Ca*+-mediated mechanism, but with this constraint: the slope of the curve does not change when the cells are loaded with EGTA, nor does a voltage-insensitive junctional conductance then appear (Obaid et ul,, 1983); the Ca'+ of the reservoir here could not be readily exchangeable with the cytosol. The data on membrane-potential dependence so far available are not, however, incompatible with other models. D. The Channel Has Two Gates
The channel can be closed by an elevation of [Gal'], on either side of a junction (Oliveira-Castro and Loewenstein, 1971) or by a membrane depolarization on either side (Socolar and Politoff, 1971). Thus, in terms of the idea of the channel unit made of two symmetrical halves, a plausible mechanism is that cach channcl half can close independently-a channel
242
WERNER R. LOEWENSTEIN
CELL-TO-CELL CHANNELS
243
with two independent symmetric gates, so to spcak. This point has recently been shown by Obaid et d.(1983): the junctional conductance/ membrane potential relation in Chironomrrs cells is correctly predicted (Fig. 9) by a thermodynamic model in which the conductance is the product of two probability functions, each reflecting the potential of one cell partner of the junction. This fits a channel model with two independent gates in series, but is not compatible with a channel with a single gate nor with a channel of two interdependent gates.
E. Channel Closure Is Basic to Survival of Cell Ensembles The channel closure mechanism allows a connected cell ensemble to seal itself off from an unhealthy member-a functional role recognized early (Loewenstein, 1966). All elements of such a sealing reaction are built into the normal cell system and are critically poised; the steep chemical and electrical gradients drive Ca2+inward, and the channels can rapidly close in the presence of high [Ca?'],. All that is required to set the reaction into motion is a discontinuity in the cell membrane or a depression of the cellular energy metabolism on which the intracellular sequestering and outward pumping of Ca*' depend. It is easy to see, in immediate connection with the Ca2+ mechanism, two general categories of functions for channel closure: ( I ) that of uncoupling a cell community from a cell member with defective Ca*+-pumpingor -buffering mechanisms, and (2) that of uncoupling it from a member with a damaged membrane. The first is likely to apply to cells that reach the end of their life span or that become metabolically poisoned, and the second occurs upon injury to all sorts of tissues. The channel closure mechanism probably arose early in phylogeny, allowing the first multicell interconnected organisms to survive local injury. The mechanism is kept throughout phylogeny. In fact, given the widespread connectivity, one could hardly imagine how our tissues could survive injury or death of even a single cell without some form of channel self-sealing. FIG.8. Elevation of CaZ+closey channels independently of H'. Simultaneous monitoring of [Ca*+],,intracellular pH (pH),, and electrical coupling. Elevation of [Ca"], (pictured in b) during washout of propionate in external medium of Chironornirs salivary gland leads to junctional uncoupling while pH, rises to the alkaline range from 7.4 to 8.5. (A) Sample records of electrical coupling measurement (a); image-intensifier TV picture of aequorin luminescence during intracellular acidification (b); bright-field TV picture of cells (c). (B) Chart records of pH, and extracellular pH (pH,): and V , and V 2 .(Reprinted with permission from Rose and Rick. 1978.)
244
WERNER R. LOEWENSTEIN 101
0.0 -00
-60
-40
-20
0
*20
E (mV) FIG.9. Dependence of junctional conductance g, on membrane potential E . Junctional conductance of a cell pair isolated from a Chironomus salivary gland measured at various, but for the two cells equal. membrane potentials E . (Resting potential, -25 rnV.1 The solid line is the calculated conductance of a thermodynamic model of a channel population where each channel has two independent, potential-sensitive gates in series. (Reprinted with permission from Obaid er d.,1983.)
VI.
STRUCTURE AND CHEMISTRY OF THE MEMBRANE PARTICLE IN THE GAP JUNCTION
A. Structure of the Channel and the Structural Change Produced by Ca2+
Knowledge about the cell-to-cell channel came through transport studies long before intelligence about its structure or even its whereabouts in cell junctions. It is now widely thought that the channel is embodied by the intrarnembrane particles seen electron microscopic!lly in clusters called the gapjunction or nexus. The particles are 60-80 A in diameter in
245
C ELL-TO-CEL L CHANNELS
A
vertebrates and 110-150 in arthropods (Chalcroft and Bullivant, 1970; McNutt and Weinstein, 1973; Peracchia, 1973; Gilula, 1974; Revel, 1974; Makowski et al., 1977). They are in register on the two membranes, forming bonded pairs that span the 20- to 30-A membrane gap (Caspar et al., 1977; Zampighi and Unwin, 1979; Baker et ul., 1983). Each pair probably constitutes a channel unit; the members in a pair probably correspond to the protochannels. By Fourier synthesis of electron microscopic views of particles (from mammalian liver) studied at different tilts, Unwin and Zampighi (1980) arrived at a structure consisting of six rodlike protein subunits, about 25 thick, 75 long, tilted with respect to the membrane plane and the sixfold axis of symmetry, giving the whole a left-handed twist. The subunits surround a central opening 20 A in diameter, outlined by hydrophilic stain (Fig. 10). The opening hasjust been traced through the entire particle, and is a roughly cylindrical channel (P. N . T. Unwin, personal communication). This structure goes into a closed configuration in the presence of Ca” , that is, when the isolated gap-junction membrane preparation is exposed to lo-’ M Ca’+. Exposure to low pH (8-6.6) does not produce the change (Unwin and Ennis, 1983, 1984). I n Unwin and Zampighi’s model the transition is generated by a clockwise rotation of the subunit ensemble, a rotation that straightens the subunits out with respect to the membrane plane and displaces them radially. The \tructure is an elegant rotatory iris diaphragm whose component parts move largely tangentially to the container ring, the membrane lipid. Shutting could thus occur with little disturbance to the lipid and so could be nearly as fast as the movement of the protein oligomer (Fig. 10). The results of these structural studies concerning the diameter of the mammalian channel are in pleasing agreement with those obtained by molecular probings in living cells (Section IV,A), and so are the results concerning closure by Ca2+(Section V,B).
A
A
8. Chemistry
The major protein component of the mammalian gap junction has an apparent molecular weight of 26,000-28,000 (Hertzberg and Gilula, 1979; Henderson et al., 1979; Finbow et ul., 1980), which is about the correct size for a subunit of the above dimensions. The average hydrophilicity of the protein is estimated at about 1000 cal/mol, and the ratio of hydrophilic/hydrophobic amino acid residues is estimated at 0.3222, probably
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FIG. 10. Structure of the cell-to-cell channel, inferred from three-dimensional Fourier synthesis of electron microscopic views of stained membrane particles in gap junction: a tilted hexameric structure with sixfold symmetry traversing the lipid bilayer. This structure would correspond to one channel half in Fig. 1. Structure on the right would correspond to the closed state of the channel. (Reprinted with permission from Unwin and Zampighi, 1980.)
reflecting the existence of large hydrophilic domains (Henderson et al., 1979). About one-fifth of the molecule (derived from rat liver) has been sequenced. There is a hydrophobic stretch towards the N-terminus, 18 amino acids long, probably reflecting an intramembrane section, and the C-terminus seems to be on the membrane’s cytoplasmic side, accessible to protease treatment (Nicholson et al., 1981, 1983), as are other hydrophilic paqts of the protein (Henderson et al., 1979; Keeling el al., 1983). Comparisons with other coupled cell types should soon reveal what sequences are conserved. This aspect is also being illuminated by work with antibodies against the protein (Hertzberg, 1980; Hertzberg et al., 1982; Traub et al., 1983; Janssen-Timmen et al., 1983). The protein turns over rapidly (Revel et al., 1980; Dahl et af., 1981; Traub et al., 1983), with a half-life estimated at 5 hours (mammalian liver) (Fallon and Goodenough. 1981). It is phosphorylated by a cyclic AMPdependent protein kinase (isoenzyme type 1) (Johnson and Johnson, 1982; R. Johnson, personal communication). This together with the turnover may provide a basis for the CAMP-dependent regulation of junctional communication (Section V,A,2).
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REFERENCES Akerman, K. E. 0. (1978). Effect of pH and Ca” on the retention of CaL’ by rat liver mitochondria. Arch. Biochetn. Bioplry.~.189, 256-262. Apell, H . , Bamberg, E., Alpes, H., Gross, E . , Morel], J. L., Harbaugh, J . F., Janko, K.. and Lauger. P. (1977). Ion chtinnels formed by chemical analogs of Gramicidin A. J . M e m h r . Biol. 3, 171-188. Auerbach, A. A,. and Bennett, M. V . L. (1969). A rectifying electrotonic synapse in the central nervous system of a vertebrate. J . Get?.Physiol. 53, 211-237. Azarnia, R., and Loewenstein, W . R. (1971). Intercellular communication and tissue growth. V . A cancer cell strain that fails to make permeable membrane junctions with normal cells. J . Mernhr. Biol. 6, 368-385. Azarnia, R., Dahl, G., and Loewenstein, W. R . (1981). Cell junction and cyclic AMP. 111. Promotion ofjunctional membrane permeability and junctional membrane particles in a junction-deficient cell type. J . Mernhr. B i d . 63, 133-146. Baker, T. S . , Caspar, D. L. D., Hollingshead, C . J . , and Goodenough. D. A. (1983). Gap junction structures. IV. Asymmetric features revealed by low-irradiation microscopy. J . Cell Biol. 96, 204-216. Bamberg, E.. Apell, H., Alpes, H., Gross. E.. Morrell, J . L., Harbauyh, J. F.. Janko, K . , and Lauger, P. (1978). Ion channels formed by chemical analogs of gramicidin A. Fed. Proc.. Fed. A m . Soc. Exp. B i d . 37, 2633-2638. Barrett, J. N . , Magleby. K. L . , and Palotta. B. S. (1982). Properties of single calciumactivated potassium channels in cultured rat muscle. J . Physiol. ( L o n d o n ) 331, 21 1230. Brink. P. R., and Dewey. M. M. (1980). Evidence for fixed charge in the nexus. Nrittrre (London)285, 101-102. Browne. C . L., and Wiley, H . S . (1979). Oocyte-follicle cell gapjunctions in Xenopprts lrievis and the effects of gonadotropin on their permeability. Science 203, 182-183. Burger, M. M.. Burkart, W., Weinbaurn, G . , and Jumblatt. J . (1978). Cell-cell recognition: Molecular aspects. Recognition and its relation to rnorphogenetic processes in general. 111 “Cell-Cell Recognition” (A. S . G. Curtis. ed.). pp. 1-24. Cambridge Univ. Press. London and New York. Caspar, D. L. D., Goodenough, D. A., Makowski, L., and Phillips, W. C . (1977). Gap junction structures. I . Correlated electron microscopy and X-ray diffraction. J . Cell Biol. 74, 605-628. Caveney, J. (1974). Intercellular communication in a positional field: Movement of small ions between insect epidermal cells. Deu. Biol. 40, 311-322. Chalcroft, J . P., and Bullivant. S . (1970). A n interpretation of liver cell membrane and junction structure based on ohhervation of freeze-fractured replicas of both sides of the fracture. J . Cell Biol. 47, 49-60. Connor, J. A . , and Ahmed. Z. (1979). Intracellular calcium regulation by molluscan neurons. Biophys. J . 25, 265a. Dahl, G.. and Berger, W. (1978). Nexus formation in the myometrium during parturition and induced by estrogen. Cell Biol. Int. R P ~2,. 381-387. Dahl, G., and Isenberg. G. (1980). Decoupling of heart muscle cells: Correlation with increased cytoplasmic calcium activity and with changes of nexus ultrastructure. J . Memhr. Biol. 53, 63-75. Dahl, G . , Azarnia, R., and Werner, R. (1981). Induction of cell-cell channel formation by mRNA. Nafure (London)289, 683-685.
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Decker, R. J. (1976). Hormonal regulation of gap junction differentiation. J . Cell Biol. 69, 669-685. Edelman, G . M. (1983). Cell adhesion molecules. Science 219, 450-457. Epstein, M . L., and Gilula, N. B. (1977). A study of communication specificity between cells in culture. J . Cell Biol. 75, 769-787. Fallon, R. F., and Goodenough, D. A. (1981). Five-hour half-life of mouse liver gap-junction protein. J . Cell Biol. 90, 521-526. Fentiman, I. S . , Taylor-Papadimitriou, J., and Stoker, M. (1976). Selective contact-dependent cell communication. Nature (London) 264, 760-762. Finbow, M., Yancey, S. B., Johnson, R., and Revel, J. P. (1980). Independent lines of evidence suggesting a major gap junctional protein with a M.W. of 26,000. Proc. Narl. Acud. Sci. U . S . A . 77, 970-974. Flagg-Newton, J. L., and Loewenstein, W. R. (1980). Asymmetrically permeable membrane channels in cell junction. Science 207, 771-773. Flagg-Newton, J. L., and Loewenstein, W. R. (1981). Cell junction and cyclic AMP. 11. Modulations of junctional membrane permeability, dependent on serum and cell density. J . Membr. Biol. 63, 123-131. Flagg-Newton, J. L., Simpson, I., and Loewenstein, W. R. (1979). Permeability of the cellto-cell membrane channels in mammalian cell junction. Science 205, 404-407. Flagg-Newton, J. L., Dahl, G . , and Loewenstein, W. R. (1981). Cell junction and cyclic AMP. I . Upregulation of junctional membrane permeability and junctional membrane particles by administration of cyclic nucleotide or phosphodiesterase inhibitor. J . Membr. Biol. 63, 105-121. Fuchs, P. A., Nicholls, J. G . , and Ready, D. F. (1981). Membrane properties and selective connexions of identified leech neurones in culture. J . Physiol. (London)316,203-223. Furshpan, E. J., and Potter, D. D. (1959). Transmission at the giant motor synapses of crayfish. J . Physiol. (London) 145, 289-325. Furshpan, E. J., and Potter, D. D. (1968). Low resistance junctions between cells in embryos and tissue culture. Curr. Top. Deu. Biol. 3, 95-127. Galtsoff, P. S. (1925). Regeneration after dissociation (an experimental study on sponges). I. Behavior of dissociated cells of Microniona prolifera under normal and altered conditions. J . Exp. Zool. 42, 183-221. Garfield, R. E., Sims, S . M., Kannan, M. S . , and Daniel, E. E. (1978). Possible role of gap junctions in activation of myometrium during parturition. Am. J . Physiol. 235, C168(2179. Gilula, N . B . (1974). Junctions between cells. In "Cell Communication" (R. P. Cox, ed.), pp. 1-29. Wiley, New York. Gilula, N. B., Epstein, M., and Beers, W. H. (1978). Cell-to-cell communication and ovulation. A study of the cumulus-oocyte complex. J . Cell Biol. 78, 58-75. Harris, A. L., Spray, D. C., and Bennett, M. V. L. (1983). Control ofintercellular communication by voltage dependence of gap junctional conductance. J . Neurosci. 3, 79-100. Heckmann, K. (1969). Zur Theorie der "single-file"-Diffusion. 111. Sigmoide Konzentrations Abhangigkeit unidirektionaler Flusse. Z . Phys. Chem. ( Wiesbaden) [N.S.] 58, 206-2 19. Henderson, D., Eibel, H., and Weber, K. (1979). Structure and biochemistry of mouse hepatic gap junctions. J . Mol. Biol. 132, 193-218. Henkart, P. S., Humphreys, J., and Humphreys, T. (1973). Characterization of sponge aggregate factor; a unique proteoglycan complex. Biochemistry l2, 3045-3050. Hertzberg, E. L. (1980). Biochemical and immunological approaches to the study of gap junctional communication. I n Vitro 16, 1057-1067.
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CURRENT TOPICS IN MEMBRANES A N D TRANSPORT. VOLUME 21
Channels across Epithelial Cell Layers SIMON A . LEWIS," JOHN W . HANRAHAN,* A N D W . VAN DRIESSCHEf *Department of Physiology Yale University School of Mediciniz New Haven. Connecticut and t Laborntorium voor Fysiologie KUL, Campus Casthitisberg Leuven, Belgium
I.
Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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A. Carrier or Channel?. ....................
A. Apical Membrane.. . . . . . . . B . Basolateral Membrane . . . . V . The HzO Channel., . . . . . . . . . . . References . . . . . . . . . . . . .
I. INTRODUCTION
One of the primary functions of epithelia, as a general class, is the homeostatic regulation of plasma composition. Such a role is possible because epithelia are capable of transporting water, electrolytes, and nonelectrolytes vectorially. The basic building blocks of an epithelium are polarized cells that are joined at their apical (lumen-facing) edge by a continuous hoop called the tight junction, thus forming a planar array. This organization results in two pathways for transepithelial electrolyte 253 Copyright 0 1984 by Academic Press. Inc All rights of reproduction in dny form reserved ISBN 0-12- I5112 1-2
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and nonelectrolyte movement. The first pathway is located between the cells (i.e., through the tight junctions and lateral, intercellular spaces) where solutes and solvent can flow down their respective chemical (and in some instances, electrical) gradients. The second, parallel pathway is through the cells, where passive diffusion and active (energy-requiring) transport of solutes and solvents is a two-step process. For example, transcellular absorption from the lumen (or mucosal side) to the blood (or serosal side) requires entry across the apical membrane followed by selective transport from the cell across the basolateral membrane. Epithelia are often categorized according to the relative permeability of these two pathways. In tight epithelia, the junctions have high resistance so that most passive diffusion occurs through the cell membranes. Leaky epithelia are those in which most diffusion occurs between cells, that is, it is paracellular (for reviews, see Fromter and Diamond, 1972; Diamond, 1978). Electrolytes and hydrophilic nonelectrolytes require a hydrophilic environment for movement through membrane lipid bilayers, such as is offered by integral membrane proteins. These proteins include two important classes: the channels and the carriers. We will follow convention in this article, and define the channel as a selective pore through which substances can move passively without requiring a shuttlelike movement of the protein within the lipid bilayer. To date, four types of channels have been clearly demonstrated in epithelial cell membranes: (1) the amiloridesensitive Na+ channel which is present in the apical membrane of many tight epithelia, (2) K+ channels, which have been found in apical and basolateral membranes of both tight and leaky epithelia, (3) nonselective cation channels, and (4) vasopressin-stimulated H 2 0 channels. This article briefly reviews the properties of these channels and evidence for their regulation by hormones, ions, and voltage. II. Na+ CHANNEL
The first and perhaps best-studied epithelium is the frog skin. In a series of papers which began in the late 1940s, Ussing and co-workers demonstrated and quantified active Na+ transport in the frog skin in uitro, and proposed the classical model for Na+ transport across the frog skin (Koefoed-Johnsen and Ussing, 1958). In this model, Na+ is hypothesized to enter the cell from the mucosal or “pond” side down its net electrochemical gradient. Once inside the cell, Na+ is transported from the cytoplasm to the interstitial fluid via the Na+-K+ exchange pump. This exchange step requires energy since Na+ is transported against a net
CHANNELS ACROSS EPITHELIAL CELL LAYERS
255
electrochemical gradient. Potassium, which is actively accumulated within the cell by this same pump, diffuses back to the serosal side through K+-selective pathways in the basolateral membrane. The end result is a net transfer of Na+ from the pond side to the blood, with a concomitant recycling of K + across the basolateral membranes. This net active absorption of Na+ generates a spontaneous transepithelial potential of 60-100 mV, outside negative. The frog skin model is applicable with only minor changes to a number of other tight epithelia including the urinary bladder of toad (Reuss and Finn, 1974), frog (Davis and Finn, 1982), Necturus (Fromter and Gebler, 1977), turtle (Nagel et al., 1981a),and rabbit (Lewis and Diamond, 1976); the hen coprodeum (Bindslev et al., 1982); and the descending colon (Schultz et ul., 1977) and submaxillary salivary duct (Augustus et al., 1978) of the rabbit. Some features of the Na+ entry step that are common to virtually all these tissues are listed below: 1. The rate of Na+ transport (1,J is a hyperbolic function of mucosal Na+ concentration and can be described by Michaelis-Menten kinetics (e.g., rabbit urinary bladder, Lewis and Diamond, 1976; frog skin, Fuchs ef ul., 1977; toad urinary bladder, Leaf, 1956). 2. The rate of Na+ transport rate is directly proportional to the conductance of the apical membrane. The current-voltage relationship of the Na+ entry pathway follows the constant field equation in frog skin (Fuchs et al., 1977), toad bladder (Li et al., 1982), rabbit colon (Thompson et al., 1982), and Necrurrrs urinary bladder (Fromter et ul., 1981). It should be noted that in order to determine whether Na+ enters by simple diffusion, it is necessary to measure the Na+ conductance of the membrane and the electrical and chemical driving forces (i.e., measure the apical membrane potential and the intracellular Na+ activity using microelectrodes) and then relate these values to the rate of net Na+ absorption. Not all of these parameters have been measured in frog skin, although all have been measured in the rabbit urinary bladder, in which electrodiffusion was confirmed (Lewis and Wills, 1983). 3 . The pyrazine diuretic amiloride reduces apical membrane conductance reversibly, and inhibits I,, and net Na+ absorption (see Benos, 1982). 4. Aldosterone increases sodium absorption after a delay of 45-60 minutes when applied in uiuo or in uitro. This stimulation of Na+ transport is concurrent with an increase in apical membrane conductance. 5. Inhibition of Na+ extrusion across the basolateral membrane by M ouabain reduces the Na+ conductance of the apical membrane. This negative feedback between basolateral Na+ exit and apical Na+ entry
256
SIMON A. LEWIS ET AL.
may be mediated by a rise in intracellular sodium activity, and might serve to protect the cell against excessive swelling when the transport rate is very high, or when the pump rate is reduced by a lack of ATP. 6. Reagents such as PCMBS (p-chloromercuribenzene sulfonate) and BIG (benzimidazolyl-2-guanidine)increase Naf transport and epithelial conductance when added to the mucosal solution of frog skin. These results indicate that there is an external regulatory site on or near the apical Na+ entry pathway (Fuchs et ul., 1977; Dick and Lindemann, 1975). A. Carrier or Channel? 1. MACROSCOPIC EVIDENCE
Is the protein that is responsible for Na+ entry a carrier such as valinomycin, or a channel, like that of gramicidin? Can transepithelial measurements be used to answer this question? Early attempts to distinguish channels from carriers involved measuring I,, as a function of Na+ concentration. It was assumed that channel currents would increase linearly with intramembrane ion concentration whereas carrier current would saturate. Based on this assumption, the Michaelis-Menten-like relationship between net Na+ transport and Na+ concentration certainly indicated carrier-mediated entry (e.g., rabbit bladder, Lewis and Diamond, 1976; frog skin, Fuchs er al., 1977). However, alternate explanations such as the inactivation and/or saturation of channels by high external Na+ seem to be consistent with the following more recent evidence. In frog skin Lindemann and colleagues (Fuchs er ul., 1977) found that I,, increased rapidly and then declined exponentially to a new steady-state level following a step increase in external Na' concentration. The peak current increased linearly with the external Na+ concentration, whereas the steady-state current demonstrated saturation. This observation confirmed the Na+ self-inhibition concept: most channels are open immediately after the solution change, but after a longer exposure time the number of open channels will be smaller at higher external Na+ concentration. Also, the instantaneous current-voltage relationship of the apical Na+ pathway at different external Naf concentrations suggested that apical permeability to sodium varied inversely with mucosal Na+ concentration. The latter observation would be consistent with channel saturation as described for excitable membranes. In summary, measurements of I,, under various conditions suggested that Na+ entry penetrates the apical membrane of tight epithelia through a
CHANNELS ACROSS EPITHELIAL CELL LAYERS
257
channel; however, microscopic studies of membrane conductance were required to rigorously exclude a carrier mechanism. 2 . MICROSCOPIC EVIDENCE Carriers are generally thought to transport ions at a rate slower than that of pores. For example, Kolb and Lauger (1978) report that the carrier nonactin can translocate up to lo4 ions/second compared to about loh for the K + channel in squid axon. Measurement of the “turnover number” for individual transport sites can provide information that is useful for distinguishing between carriers and pores (see Armstrong, 1975; Lauger, this volume). To determine the current carried by a single transport protein, one measures the total current carried by all the transport sites and then divides this by the number of sites. Two experimental approaches can be used. The most direct method is to isolate a single pathway using the patch-clamp technique, and directly record the current and conductance of individual sites. This technique has not yet been used successfully on the apical membrane N a + pathway. The second approach is to clamp the transepithelial potential ( V , )to zero and measure spontaneous or blockerinduced fluctuations in the current. For an ensemble of channels, the macroscopic current per unit area (1,‘) is
I,,
=
iMP,
(1)
where i is the single-channel current, M is the channel density (number of channels per unit area), and Po is the probability that the channel is open (for a spontaneously fluctuating channel) or unblocked (for drug-induced fluctuations). With certain assumptions, described below, these fluctuations can be used to determine single-channel currents and channel density (Anderson and Stevens, 1973). a. Ensemble Analysis of Single Nu‘ Chunnels. The first successful attempt at measuring transepithelial current fluctuations was reported by Lindemann and Van Driessche (1977) for the frog skin. They used an ultra-low-noise voltage clamp to record current fluctuations (for design, see Van Driessche and Lindemann, 1978). The I,, was amplified, digitized, and fast-Fourier transformed to obtain the power density spectrum. Under control conditions, power spectra showed a linear component (typical Ilfnoise) which did not appear correlated with any measurable parameter, and probably reflected ionic diffusion through paracellular pathways and various artifacts. Importantly, the apical Na+ channels did not fluctuate spontaneously in the frequency range measured (0.3-100 Hz).
258
SIMON A. LEWIS ET AL.
Lindemann and Van Driessche reasoned that the reversible blocker amiloride might randomly associate with (“block”) and dissociate from (“open”) the channel and thereby induce measurable fluctuations in the Is,.Indeed, addition of submaximal doses of amiloride produced a Lorentzian-type (single time-constant relaxation) component in the power density spectrum. Increasing the concentration of amiloride in the external solution shifted the corner frequency (see below) to larger values. The Lorentzian-type power spectrum has the form S ( f ) = so41
+ CJ‘/fC,?l
(2)
where S(f’) is the power density (A’ second),J’is the frequency in hertz,./, is the corner frequency (the frequency at which S(f‘) = is,),and S,, is thc plateau value at low frequencies (Fig. 1). For blocker-induced fluctuations, fc is related to the time constant (T) of the chemical process (i.e., association-dissociation of the blocker) by 7 =
(3)
1/(27rf,)
(For power spectrum analysis as applied to end-plate channels, see Barry and Gage, this volume.) For the simplest possible reaction scheme (see Verveen and DeFelice, 1974):
where R is the receptor and A is amiloride and kol and k l o are the rate constants for association or closing rate (in mol-l sec-’>and dissociation or opening rate (in sec-I) of amiloride with the channel. When the concentration of channels is negligible compared to that of amiloride, these rate constants are related to T by
I/T
=
[Alkol
+ kin
and to the amiloride dissociation constant KA = kidkoi
K A
(5)
by (6)
One can determine both the association and dissociation rate constants by plotting the corner frequency as a function of amiloride concentration. It is important to note that such a plot must be linear for the model to be valid. The probability of the channel being open ( P o )or blocked ( P , ) can then be calculated for any concentration of amiloride as and
259
CHANNELS ACROSS EPITHELIAL CELL LAYERS
10-22
1
01
10
I
100
1000
FREQUENCY ( H r )
FIG. I . Power spectrum density (PSD; A’ second) recorded transepithelially from an in vitro rabbit urinary bladder. Curve C is from a control bladder and demonstrates low-frequency noise or Ilfnoise. To date, the source of this noise has not been clearly identified; however, it is not correlated with the magnitude of the amiloride-sensitive current. Addition of 1.4 yM amiloride to the mucosal solution dramatically alters the shape of PSD (curve A ) to one expected for a single time-constant relaxation process (or Lorentzian spectrum) plus a linear low-frequency component (Ilfor flicker noise). The Lorentzian form is predicted for a simple open-closed configuration of a channel which can occur spontaneously or may be induced by a reversible blocker, i.e., amiloride. Curve D is the PSD from the voltage clamp amplifier using a dummy network of resistors and capacitors similar in value to that measured for curve C.
Thus the corner frequency of the Lorentzian component provides information about amiloride binding kinetics. In addition, the plateau So can be used to estimate channel density M and single-channel current i using the following equation:
9,
=
4ri2MaP,P,
@a)
SIMON A. LEWIS ET AL.
260 A 30 /2 KA 4o07
4
25
20
PI
2nf
c
?
(sec-')
X 0
I
-a
2nfc = KO1(A) + K1O
I5
N
0
10
o
v)
1
2
3
4
E
.
r
AMlLORlDE ( r M ) 5
0 0
I
2
4
3
5
6
AMlLORlDE ( r M )
B 30-
25-
-
l c
20-
5! X V
I
IS-
-a
N
0
10-
10
20
30
.O
so
60
TRIAMTERENE ( r M ) 112 K A
1
5-
0 0
10
20
30
40
50
60
TRIAMTERENE (MM)
FIG. 2. Relationship between the plateau value (So) of a Lorentzian process and the concentration of blocker: amiloride (A) or triarnterene (B). Equation (8) predicts for this function that So starts at zero, peaks at a value equal to MA, and then decreases toward zero
CHANNELS ACROSS EPITHELIAL CELL LAYERS
261
or, combining Eqs. ( I ) and (7a), So = 471,iUP,
(8b)
where u is area and Z, is the amiloride-sensitive I,, that remains after adding a submaximal dose of amiloride. Equation (8) predicts that S , will be zero at [A] = 0 mM, and will increase as amiloride concentration increases, reaching a peak value when the amiloride concentration is equal to IKA. Finally, So should decline toward zero as the amiloride concentration approaches infinity and most of the channels become blocked.
6 . Is the Two-Stute Model Adequate? As outlined above, fluctuation analysis offers three simple predictions that can be used to test the validity of the two-state model for amiloride-Na' interactions. First, a plot of 2nfCversus amiloride concentration must be linear. In all epithelia studied so far, the relationship between 27& and amiloride concentration is indeed linear (e.g., Fig. 2 ) and yields reasonable estimates of the association and dissociation rate constants for amiloride with the channel (see Table I). Second, the plateau value must be zero at 0 mM amiloride, increase to a peak value at one-half the K A , and then decline gradually back to zero (Fig. 2). The relationship between S, and blocker concentration is difficult to show experimentally at very low blocker concentrations because the plateau value (and corner frequency) occurs at frequencies below the experimental frequency range (0.2 Hz). The analysis of the fluctuations in current at lower frequencies is hampered by (1) the time needed for the analysis and (2) the presence of the low-frequency llf noise. Consequently, So is usually determined at blocker concentrations which are greater than I K A ,i.e., where So is already decreasing. However, So can be determined at low amiloride concentrations in rabbit urinary bladder (Lewis et ul,, 1983). We found that S , increases, peaks, and then declines as expected when amiloride concentrations are elevated from zero. Triamterene (an amiloride analog) is a Na' channel blocker with higher intrinsic rate of dissociation than amiloride and generates a Lorentzian component having higher corner frequencies at low blocker concentrations. Moreover the association rate of this blocker with receptor is large as blocker concentration saturates. Value5 for association-dissociation rate constants (shown in the inserts) are from rabbit urinary bladder and given in Table I, for a channel density of 10 x IOVcrn?. Of interest ih that the ratio for So of amiloride to triamterene at $KA is equal to the corresponding ratio for the corner frequency of triamterene to arniloride: SSlSl; = fflf,".
TABLE I KINETICSFOR Na-, AMILORIDE. AND TRIAMTERENE BINDINGTO Na+
Amiloride
KN= (mM)
@M-I KA Ki (sec-I) sec-I) ( p M ) ( p M )
Frog skin Rana esculenta (depolarized) Rana temporaria Rana pipiens (nondepolarized) Toad urinary bladder (depolarized) Rabbit Descending colon (37°C) Urinary bladder (37°C) Hen coprodeum (34°C)
Na' CHANNEL^
Triamterene
KOi Preparation
THE
Koi
Kio
14
-
12.2
-
-
-
-
-
-
-
-
-
22
2.5
15
-
7.42
Kio
(sec-')
KA KI sec-I) ( p M ) ( p M )
(pM-'
Y (pS)
(PA)
M (106/cm')
I
Reference
-
2.8
18.2
5.5
0.3-0.46
-
19.2
12.4
1.61
-
-
0.46
17
0.2
-
-
-
-
-
0.59
38.7
0.18
0.42
-
-
-
-
3.6
0.18
77
Li et a / . (1982)
68.4
0.19
0.23
-
-
-
-
4.0
0.4
593
Zeiske et a / . ( 1982) Lewis et at. (1983) Christensen and Bindslev (1982)
-
62
11.6
52.1
0.24
0.25
78.2
2.4
41.4
53.6
5.3
0.64
2-19
32
-
-
-
-
25.5
9.5
30.8
49.9
4.0
0.30
580
Li and Lindemann (1981); Van Driessche and Lindemann (1979) Hoshiko and Van Driessche (1981) Helman et a!. (1981)
" KNs. the mucosal Na' concentration for half-maximal reduction in channel density; K o l .the dissociation rate constant for receptor and blocker: K A . the inhibition constant (= K i o / K , ) i )KI. : the concentration of blocker required to reduced Na' transport by half; i. the single-channel current; y . singlechannel conductance: and M , the channel density. Depolarized indicates that the serosal solution was a K'-Ringer's solution designed to reduce basolateral membrane resistance and voltage. All measurements were conducted at room temperature except where noted.
CHANNELS ACROSS EPITHELIAL CELL LAYERS
263
enough to obtain an increase in h at blocker concentrations above KA. The S , for triamterene also peaked near BKA, and then declined toward zero, consistent with the two-state model (see Fig. 2, and Hoshiko and Van Driessche, 1981). Third, the inhibition constant for amiloride (macroscopic K J must equal the microscopic association constant ( K A ) ,obtained from Eq. (6). As shown in Table I, this criterion is met only by the rabbit urinary bladder; in all other tissues, K1 is larger than K A . Li et af. (1982) have suggested that this discrepancy between K 1 and K A reflects competition between external Na+ ions and amiloride for binding to the channel. The kinetic model shown in Eq. (4) is undoubtedly an oversimplification because it does not include the Na+ self-block discussed above. Li et al. (1982) expanded the model for amiloride-sensitive Na+ channels in toad bladder to include three \tates: open, N a + blocked, and amiloride blocked. According to their analysis, the dissociation rate constant for amiloride determined by plotting 27~hagainst amiloride concentration would be overestimated by an amount equal to the association rate constant for sodium times the Na+ concentration. If the rate constant for amiloride dissociation is larger than the Na' dissociation rate constant, then the apparent K 1for Naf can be calculated using the macroscopic and microscopic inhibition constants at any given Na+ concentration. At first glance one must conclude that the two-state model is overly simplistic and does not adequately describe the interaction of amiloride and Na' with the channels, Validation of the model and estimates of channel properties must await independent measurements of single-channel properties, for example, through use of the patch-clamp technique (Hamill et a / . , 1981). However values for single-channel currents and channel densities calculated from the simple model are probably reasonable estimates at high blocker concentrations, and are consistent with the concept that a channel, rather than a carrier, is involved in these movements of sodium. B. Properties of the Na+ Channel
1. MACROSCOPIC PROPERTIES a. Selectivity. The ionic selectivity of the Naf channel has been investigated in both the frog skin (Benos et al., 1980a) and toad urinary bladder (Palmer, 1982). In the frog skin only Lit and Nat could permeate the channel, while other ions compete for the Na+ binding site but do not traverse the channel. The selective binding sequence is Lit > N a ' > TI + > NH,' = K + . These permeability and binding sequences indicate that Na' moves through the channel in an unhydrated form.
264
SIMON A. LEWIS ET AL.
b. Voltage Dependence. Is there a dependence of apical Na+ permeability on the voltage across the apical membrane? To address this question, numerous investigators have measured the near-instantaneous current-voltage relationship (I-V) of the amiloride-sensitive Na+ conductance of the apical membrane. To avoid complications due to the parallel non-amiloride-sensitive pathways (e.g., K+ channels and the tight junctions), the I-V relationship of the amiloride-sensitive pathway was calculated as the difference in current I in the absence and presence of a saturating dose of amiloride. In frog skin (Fuchs et a/., 1977), toad urinary bladder (Li et al., 1982), and rabbit descending colon (Thompson et al., 1982), the Goldman-Hodgkin-Katz constant field equation adequately describes the I- V relationship. The simplest interpretation of these results is that Na+ channels are not voltage gated (at least for the duration of the voltage step) and all voltage sensitivity is a reflection of asymmetrical ionic activities. The possibility of voltage gating with steady-state voltage pertubations has not been studied. c . Chemical Modification. Considerable insight into channel architecture has been gained for excitable membrane channels by studying the effects of chemical modifications. However, similar success has not been attained for the amiloride-sensitive channel. Table I1 summarizes the reagents that have been employed and their effects on two parameters: macroscopic Na+ current and amiloride binding. The most striking feature of this table is that no single reagent has any consistent effect on Na+ transport among different epithelia. As an example, PCMBS can stimulate I,, (Rana escufenta),stimulate and then irreversibly inhibit I,, (Rann catesbeiana), irreversibly inhibit I,, (rabbit urinary bladder), or have no effect on I,, but inhibit amiloride binding (rabbit descending colon). Similar variability occurs in the actions of PCMB and the carboxyl reagent EEDQ (I-ethoxycarbonyl-2-ethoxy- 1,2-dihydroquinoline). One can only conclude that the architecture of this channel is complex and species dependent.
2. MICROSCOPIC PROPERTIES t i . Single-Chtinnel Current. Table 1 lists the single-channel currents, i, and Na+ channel densities, M , of various epithelia (amphibian, mammalian, and avian). There is remarkable agreement between estimates of the single-channel currents, considering the diversity of the preparations and experimental conditions under which current fluctuations were measured. One might expect the calculated parameters to vary with (1) the kind of preparation and animal species used; (2) several experimental conditions,
T A B L E 11 EFFECTOF REAGENTS ON N:i* Preparation Frog skin Rana caresbeinnu R u u PSCIIIC~~W Rcrncr icniporcrri(/
Rabbit Urinary bladder Descending colon Toad urinary bladder ( B ~ f inu/rinu.\ ) )
TRANSPORT A N D
AmiliNa'
PCMBS
PCMB
PCMB-Dex
Noncomp C-P Comp
t 1 lrrev t t
1 lrrev
1 Rev
r
T
AMILORIDE BINDING" TNBS
EEDQ
Inh amil
f)
Reference
Benos
c't ti/ ( 19XOb)
7Ktckc 4 I9784
1 lrrev
Zeiske and Lindemann (I975), Lindemann and Voute (1977)
lrrev
Park and F;ine\til (198.;)
J lrrev Inh amil
Comp Comp
tf
Comp
T
The first column indicates whether amiloride and Na' are competitive (comp) o r noncompetitive (noncomp) inhibitors of the Na* channel. PCMBS (a sulfhydryl reactive agent). p-chloromercuribenzene sulfonate: PCMB-Dex. p-chloromercuribenzoate (with 01- without a n attached dextran: M , 40,000): TNBS (an amino reagent). 2.4.6-trinitrobenzenesulfonicacid; EEDQ (the carboxyl reagent). I-ethoxycarbonyl-2-etho~y1.2-dihydroquinoline. t 1 The agent first stimulates then inhibits Na' transport either rever.;ihlv (Rev) o r irrever.;ibly (Irrev): T . the agent reversibly stimulates Na' transport: 1 the agent decreases N a - transport either reversiblv ( R e v ) o r irreversibly (Irrev): ++. the agent has n o effect o n Na' transport: Inh amil. the agent inhibits amiloride action o n Na' transport. 'I
.
.
SIMON A. LEWIS ET AL.
266
such as temperature, composition of solutions used, etc.; and (3) the extent to which the current noise signals are attenuated by the presence of the basolateral membrane in series with the apical noise source. Based on estimates of the driving force for Na+ entry, single-channel conductances y are also in good agreement between preparations, ranging from a low of 3.6 to a high of 5.5 pS (see Table I). Even this narrow range of the conductances might reflect different conditions (i.e., ionic concentrations and driving forces) rather than intrinsic differences in channel properties per se. A channel parameter which is independent of ion activities and voltage is the single-channel permeability Pk;,. To determine this we assume that single channels are in a constant field and that they obey the GoldmanHodgkin-Katz equation relating current to permeability: F2
INa = - P;,l.,VF u,Na+
RT
I
-
q N a + exp(-VFF/RT) exp(-VFF/RT)
(9)
where iNi, is the mean single-channel current and has a value which is tissue dependent; V F is the apical membrane potential under short-circuit conditions; u,Na+ and uiNaf are extra- and intracellular Na' activities, respectively; and R, T, and F have their usual meanings (for a discussion of this equation, see Barry and Gage, this volume.) The only preparation in which there are adequate data (membrane potentials and Na' activities) for this calculation is the rabbit urinary bladder. We can insert measured values into Eq. (9) for i N a (0.64 PA), u,Na+ (104 mM), uiNa+ (7 mM), and VF (52 mV), and calculate a single-channel permeability of 32 X lopt5cm/second. Future studies using fluctuation analysis should include intracellular potential and ion activity measurements as part of the experimental protocol. b. Control of Channel Density by N a + . In at least three epithelia there is strong evidence that lowering extracellular "a+] increases the Na+ permeability of the apical membrane, and that this involves an increase in the number of functional channels. Van Driessche and Lindemann (1979) showed that the number of functional channels in the frog skin apical membrane increased when external Na+ concentration was lowered. A similar inverse relationship between external sodium concentration and channel density has been described for the hen coprodeum, the toad urinary bladder, and most recently the rabbit urinary bladder. Using frog skins bathed with high-K+ Ringer's solution on the serosal side, in order to lower basolateral membrane resistance, Fuchs et ul.
CHANNELS ACROSS EPITHELIAL CELL LAYERS
267
(1977) found that the macroscopic current-voltage relation of the apical border fitted the constant field equation and that Na+ block could be described by the Michaelis-Menten kinetic equation:
P N =~ k ' g i x / ( l -I N,Na'/KN,)
(10)
where PNdis the apical Na+ permeability for any extracellular Na' activity (a,Na+), P E x is apical Na' permeability at zero extracellular Na+ activity, and K N is~ the concentration of Na+ which results in half-maxima1 inhibition. Since macroscopic permeability is simply equal to the product of singlechannel permeability and functional channel density, Eq. (10) can be expressed as M
=
M"""/(I
+
N , , N'IKN.!) ~
(I I)
Table 1 lists the K Nfor ~ Na+ self-block in preparations in which it has been measured using this method. In the epithelia so far studied, external Na' blocks the Na+ channel with half-maximal inhibition between 14 and 62 mM Na+. Whether the site for Na+ self-block is the same as that for amiloride binding/blocking is not known, although there is evidence that Na+ competitively inhibits arniloride binding (Li et ul., 1982). There may be two sites of Nat interaction: Na' self-block might be independent of amiloride, occurring at some external location on channel, while amiloride and Na+ also compete at a site near (or in) the mouth of the Na' channel. Whether Na+ occludes the channel when associated with this latter site remains to be determined. Perhaps these alternative kinetic schemes will eventually be distinguished using enzymatic digestion or pharmacological manipulations that eliminate Na+ self-block while leaving amiloride-Na+ competition intact. It is difficult to make meaningful comparisons of channel density in different epithelia because the density depends on extracellular Na+ concentration, hormonal factors, and intracellular ion concentrations (Na+or Ca2+).The reported values range from less than 1 per 50 pm2 membrane area up to a maximum of 50/pm2 (counting both open and Na+-blocked channels). This translates into transepithelial Na+ transport rates of between 1.5 and 3500 pA/cm2 assuming single-channel currents of 0.7 pA and the channel densities shawn above. While it is well established that extracellular sodium blocks the amiloride-sensitive Na+ channel, there is also some evidence that intracellular Na+ controls this pathway (see Taylor and Windhager, 1979). Modulation may be indirect and may be mediated by changes in intracellular Ca2+ activity. The experimental evidence that suggests this "negative feedback" by intracellular sodium is that inhibition of Na' extrusion from the
268
SIMON A. LEWIS ET AL.
cell (i.e., inhibiting the Na+-K+ pump) causes an increase in cell Na+ and a decrease in apical Na+ permeability, the latter approaching zero in rabbit urinary bladder when aiNa+ exceeds 25 mM (Wills and Lewis, 1980). This decrease in Na+ permeability might reflect a decline in singlechannel permeability or a decrease in channel density; however, the latter seems most likely because Erlij and Van Driessche (1983) have recently shown, using fluctuation analysis, that the density of Na+ channels in frog skin declines when Na+ exit from the cell is blocked by ouabain. They also reported that the channel density increases following Na+ removal (which would lower aiNa+ and reverse the direction of the Na+ current). Despite large (eightfold) changes in channel density in their studies, single-channel currents were not affected. In short, intracellular sodium appears to regulate the number of functional channels in the apical membrane of tight epithelia but not their unit conductance. Amiloride inhibits Na+ current by reducing the number of open channels, but apparently does not affect currents flowing through those which remain open. In contrast, when the transepithelial potential is clamped away from zero, the single-channel currents change as predicted on the basis of the alteration of the driving force for Na+ across the apical membrane. To date, there are no reports of chemical or voltage gating of the amiloride-sensitive Na+ channel, although amiloride binding is reportedly voltage sensitive (Palmer, 1983). c . Hormonal Control. Sodium transport across many epithelia is regulated by two plasma-borne hormones, aldosterone and antidiuretic hormone (ADH). In recent years it has been demonstrated that aldosterone, after a lag period of 45-60 minutes, increases the rate of apical membrane Na+ entry by increasing the apical membrane Na+ conductance. The lag phase might represent synthesis of new channels which are subsequently inserted, of an activator protein for quiescent channels already located in the apical membrane (e.g., release from Na+ self-block), or of some modifier protein that increases the permeability of individual channels. These possible mechanisms cannot be easily distinguished using macroscopic methods, but can be studied using fluctuation analysis to measure singlechannel properties. Palmer et al. (1982) showed that aldosterone initially stimulates Na+ permeability in toad urinary bladder by increasing the number of functional channels rather than the conductance of single channels. Sodium self-block was not affected by aldosterone. On the average, aldosterone increased channel density by 2.2-fold after incubation for 4-6 hours. Do these "new" channels preexist in the apical membrane or are they recruited from some cytoplasmic pool?
CHANNELS ACROSS EPITHELIAL CELL LAYERS
269
If aldosterone causes the synthesis and insertion of new channels, we might predict that the hormone-stimulated rate of Na’ transport would be relatively independent of the baseline (i.e., control) rate, and that it would be insensitive to pretreatment with chemical reagents. On the other hand, if channels preexist in the apical membrane and are simply activated by aldosterone, then the size of stimulation would be proportional to the baseline current and the hormonally stimulated component would be susceptible to prior modification by reagents. Palmer and Edelman (1981) used DSA (diazosulfanilic acid) to modify apical membrane Naf channels and then measured the responsiveness of Na+ transport to aldosterone. They found that baseline I,, and aldosterone-stimulated I,, were both reduced 60-70% after 1-hour exposure to DSA ( I mM), implying that aldosterone activates quiescent (i.e., nonconducting) channels that are already present in the apical membrane before addition of the hormone. A similar, proportional increase in Na’ transport has been measured in rabbit urinary bladder (S. A. Lewis. unpublished observations) following endogenous treatment with aldosterone. The peptide vasopressin (or ADH) also stimulates Na’ transport across many epithelia. However, unlike the aldosterone response, Nat transport increases rapidly and reaches a peak value only IS minutes after serosal addition of ADH and therefore cannot involve protein synthesis. As with aldosterone, Li et al. (1982) found that the increase in Na+ transport rate across toad urinary bladder was a consequence of increased channel density and not a change in single-channel properties. Employing the same DSA pretreatment method i ~ for s aldosterone, Palmer and Edelman (1981) concluded that ADH also activates quiescent apical Na+ channels. The same conclusion was reached by Helman et al. (1981) for ADH stimulation in frog skin. In the latter study, an interesting finding was made that some frog skins did not increase transport upon ADH challenge. The reason for this difference in responsiveness is apparently related to the intracellular levels of prostaglandin and of cyclic AMP in the two sets of frog skins; inhibition of cellular PGEz (prostaglandin E?) synthesis by indomethacin reduces Na+ transport across frog skin and addition of CAMP or theophylline (which inhibits the breakdown of endogenous CAMP) reverses the effects of indomethacin. Thus sodium channel density is regulated not only by an exogenous steroid hormone but also by a peptide hormone and by endogenous prostaglandins.
d . Channel Turnover. All biological systems are dynamic rather than static, and it seems reasonable that channels would “wear out” due to contact with the external environment. Two strategies are available to the cell to overcome a steady loss of channels. First, there could be constant
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replacement by the internalization and degradation of old channels and the synthesis and insertion of new ones. Alternatively, the entire cell might simply age, desquamate, and be replaced by a new healthy cell containing a full complement of channels. Many epithelia probably utilize a combination of both these processes. The best evidence for channel turnover in epithelial membranes comes from a series of experiments performed recently on the rabbit urinary bladder. These findings are summarized below: 1. Two distinct conductive pathways for Na+ have been identified in the apical membrane using microelectrodes (Lewis and Wills, 1983). One of these channels is amiloride blockable while the other is not. 2. Lewis and deMoura (1982) demonstrated that rabbit bladder accommodates an increase in urine volume by smoothing out macroscopic epithelial folds, then by flattening out folds in the apical membrane, and finally, by a movement of vesicles (mediated by microfilaments) from the cell cytoplasm into the apical membrane. Importantly, electron micrographs indicate that the entire apical membrane is composed of fused vesicles (Minsky and Chlapowski, 1978); thus, during a series of expansion-contraction cycles, the apical membrane is apparently replaced by membrane of cytoplasmic origin. 3. The amiloride-sensitive Na+ permeability of newly inserted membrane is eightfold greater (per unit area) than membrane that has been exposed to urine (Lewis and deMoura, 1982). 4. Using fluctuation analysis, it has been demonstrated that the density of channels in the newly inserted membrane is greater than in the apical membrane, and that single-channel currents and amiloride binding for “old” and “new” channels are not significantly different (Loo et al., 1983). 5. Multiple washing of the apical membrane with Ringer’s solution reduces the amiloride-insensitive pathway, suggesting that an unstable (partially degraded) channel may be removed by this treatment,
These findings strongly suggest that channels are degraded during exposure to the acidic urine in vivo and that new channels can be inserted by the fusion of cytoplasmic vesicles with the apical membrane. Are the amiloride-insensitive channels partial degradation products of the amiloride-sensitive pathways or are they a’ completely different channel species? Support for the idea that there may be a common link between the two channel populations in rabbit bladder comes from the following observations:
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I . Serotonin (5-hydroxytryptamine) reversibly blocks the amiloridesensitive and -insensitive pathways, suggesting that both channel proteins have a binding site for this molecule. 2. Trypsin irreversibly inhibits the amiloride-sensitive pathway, demonstrating its susceptibility to enzymatic degradation. 3. Human urokinase, a plasniinogen-activating enzyme (resembling trypsin) which is found in the urine, decreases the number of amiloridesensitive channels in rabbit urinary bladder. Concurrent with this decline in channel density, conductance of the amiloride-insensitive pathway increases. Interestingly, after removing urokinase, the leak current declines to values which are lower than those observed before enzyme treatment (S. A. Lewis and W. P. Alles, unpublished observations). In summary, amiloride-sensitive Nat channels from a diverse group of vertebrates possess similar properties. The stimulation or inhibition of macroscopic Na+ absorption results largely from changes in the number of conducting Na+ channels in the apical membrane. Channel density is regulated by steroid and peptide hormones, by endogenous prostaglandins, and by intra- and extracellular Na+ concentrations. The molecular mechanisms involved in modulation of the amiloride-sensitive Na+ channels are not well understood. Competition between different blockers for particular sites on the channel is still uncertain, and in some cases might be species dependent (see Benos, 1982). It is obvious that detailed study of the properties of epithelial Na' channels has just started, and that studying the effects of chemical and enzymatic modifications will yield deeper insight into the mechanisms of Na' channel regulation. 111.
K t CHANNELS
A. Apical Membrane Electrophysiological studies have revealed significant K+ conductance in the apical membrane of rabbit gallbladder (Henin and Cremaschi, 1975), Necturus gallbladder (Reuss and Finn, 1975), frog skin (Hirschmann and Nagel, 1978; Nagel and Hirschmann, 1980), and rabbit colon (Clausen and Wills, 1981). This pathway may serve as the exit step for active K + secretion in the colon (Wills and Biagi, 1982; Halm et al., 1983; McCabe et al., 1982) and gallbladder (Gunter-Smith and Schultz, 1982). Its function in frog skin has not been established, although we would like to speculate that it plays an important role in K + secretion in K+-loaded animals, e.g., after digestion of insects.
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1. GALLBLADDER
The first evidence that apical potassium conductance results from channels was obtained by analyzing microscopic current fluctuations in shortcircuited toad gallbladders (Van Driessche and Gogelein, 1978; Fig. 3). When bathed bilaterally with NaCl Ringer's solution, about one-third of the preparations showed a Lorentzian-type component in the power density spectrum (Fig. 3A), consistent with a single population of channels that open and close spontaneously with a relaxation time (7)of 41 msec. To identify the source of current fluctuations, Van Driessche and Gogelein used triaminopyrimidine (TAP) to reduce paracellular cation conductance (Moreno, 1974). When 20 mM TAP was added to both sides, transA
B
C .
**..
a
a
FIG.3. Power spectra of the current fluctuations through the toad gallbladder epithelium in control conditions and after the addition of various agents. (A) Curve a, spontaneous Lorentzian noise spectrum recorded with Na+ Ringer's solution on both sides. The plateau A*second c m 2 and the corner frequency isf, = 5.3 Hz. Curve b, value is S, = 4.3 x fluctuations are depressed to levels comparable to the amplifier noise after the addition of 3 m M KCN t 3 mM sodium iodoacetate. Because of the capacitive reactance component in the membrane impedance, the amplifier noise increases in the high frequency range and may become larger than the excess noise of the preparation. This explains the increase of the spectral density observed at higher frequencies. (B)Influence of ouabain. Curve a, spectrum recorded in control conditions: So = 2.7 x IO-Iy A?second cm-* andf, = 5.7 Hz. Curve b, IS minutes after the addition of ouabain to the serosal solution: So = 1.2 x A* second c w 2 and f c = 17.1 Hz. Curve c was recorded 35 minutes after the addition of ouabain. (C) Influence of TEA.Curve a, Lorentzian recorded with Na Ringer's solution on the serosal side and with Ringer's in which all Na+ was replaced by K+ on the mucosal side: So = 3.1 X A2 second cm-* andf, = 4.7 Hz. Curve b, the addition of 5 mM TEA to the mucosal solution abolished the current fluctuations. [Van Driessche and Gogelein (1978). Reprinted by permission from Nature (London),275, No. 5681, pp. 665-667, 0 1978 Macmillan Journals Limited.]
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epithelial resistance increased threefold without blocking the Lorentzian component. They concluded that fluctuations do not arise in the paracelMar pathway (Van Driessche and Gogelian, 1978). More recently, TAP has been shown to reduce apical membrane K + conductance (Reuss and Grady, 1979) and current fluctuations somewhat (Gogelein and Van Driessche, 1981). Despite this effect, the independence of current fluctuations and paracellular conductance still argues that relaxation noise must originate in the cellular pathway. The Lorentzian component was abolished following exposure to cyanide ( 3 mM) and iodoacetate (3 mM) (Fig. 3A, curve b), or after serosal addition of I mM ouabain (Fig. 3B), presumably because of a reduction in the driving force for K + across the apical membrane, a force that probably favors efflux from cell to niucosa as in the Necturus gallbladder (Zeuthen, 1978; Reuss and Weinmann, 1979). In support of this hypothesis, relaxation noise also disappeared when the outward driving force for K + was reduced by elevating the external K + concentration to 38 mM, and noise reappeared when mucosal [K+] was increased further to produce an inward-directed gradient (Van Driessche and Gogelein, 1978). Moreover, a continuous increase of the relaxation noise with elevation of the serosal K + concentration was observed over the entire concentration range (2-1 17 mM). These observations provided further evidence that the noise source resides in the cellular pathway and localized the source to the mucosal side. The latter suggestion was confirmed by the fact that the K + channel blocker, tetraethylammonium (TEA+),added to the mucosal side (Fig. 3C), abolished the Lorentzian component whereas serosal addition of TEA+ had no effect. In those tissues that did not show spontaneous current fluctuations, or when current noise was abolished using inhibitors, a Lorentzian component could be induced by imposing a large transepithelial K+ gradient (Van Driessche and Gogelein, 1978). The potassium channel in toad gallbladder does not rectify, because similar Lorentzian components were produced whether high K+ ( I 17 mM) Ringer's solution was placed on the mucosal or serosal side (Fig. 3C, curve a). Spontaneous fluctuations in I,, have been observed in a variety of epithelia, including the Necturir~gallbladder (Gogelein and Van Driessche, 1981a,b). Spectral analysis revealed spontaneous relaxation noise in dnly 20% of the gallbladders tested because the Lorentzian component was usually obscured by a linear, "low-frequency" (LF) component.' TAP (at I This LF noise is a common feature of transepithelial power spectra, and may result from ionic diffusion in the paracellular pathway (Gagelein and Van Driessche. 1981a.b; Van Driessche and Gullentops, 1982) or nonselective "leak" pathways in the apical membrane (Lewis et a / . , 1983; Loo et a / . , 19x3).
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ET AL.
8.5 mM) in the active (cationic) form reduced the LF component, but had, in addition, two other effects; it increased the corner frequency of the Lorentzian component (suggesting a stimulation of the overall open-close reaction rate), and reduced So (consistent with a decline in open channel density and/or single-channel conductance). As in toad gallbladder, maneuvers that would alter the driving force for K+ across the apical membrane had the expected effects on the power spectrum. The plateau value of the Lorentzian was enhanced by a serosa-to-mucosa Kf gradient, abolished by raising mucosal K t concentration to 36 mM while leaving NaCl Ringer’s solution on the serosal side, and restored by elevating mucosal [K+] further to 57 mM. The Lorentzian component, which was TEA+ sensitive, was enhanced by clamping the transepithelial potential (V,) to mucosa-negative values (which would increase the outward driving force for K+ across the apical membrane), and was reduced by clamping V , to more positive potentials. Finally, all these effects of clamping V , were reversed when a K+ gradient oriented from mucosa to serosa was established. In order to study the selectivity of the apical membrane K+ channel, it was necessary to reduce LF noise by adding TAP to both sides (Gogelein and Van Driessche, 1981a). Rubidium gradients could then be seen to produce Lorentzian-type spectra with the same corner frequency as those with K+ gradients, suggesting that the open-close kinetics of the channel are the same for K+ and Rb+. However, plateau values were slightly lower in spectra obtained using Rb+. No Lorentzian component was detectable in the presence of a cesium gradient. Potassium and rubidium current fluctuations were both blockable by mucosal TEA+ (5 mM) but not by Cs+ (10 mM). Adding Baz+(5 mM) to the mucosal side or lowering mucosal pH from 7.4 to 6.0 reduced So without changingf,. These effects of TAP+, Ba2+,and protons would be consistent with reductions in the number of functional channels and/or their unit conductance. Single-channel currents were calculated indirectly for gallbladders bathed in NaCl Ringer’s solution as follows. The measured values of So were corrected for the large attenuating effects of basolateral membrane and paracellular pathways. Macroscopic K+ current across the apical membrane was calculated from literature values for the net electrochemical gradient (Reuss and Weinmann, 1979) and the Kf conductance (Reuss and Finn, 1975). The estimated single-channel conductance was in the range of 6.5-40 pS (Gogelein and Van Driessche, 1981a). Gogelein and Van Driessche (1981b) also used fluctuation analysis to test whether the apical K+ channel in Necturus gallbladder is voltage gated. The gallbladder was modeled as two resistance-capicitor networks
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in series; one representing the epithelium and the other a polarization impedance. “Peaking,” a distortion of the power spectrum that became noticeable at mucosa-negative potentials, was explained as an artifact of polarization, which would attenuate current fluctuations more strongly below a characteristic frequency of - I Hz (Gogelein and Van Driessche, 1981b; Van Driessche and Gullentops, 1982). No voltage gating needed to be assumed. Interestingly, a second (high-frequency) relaxation component appeared in the power spectrum when the mucosal side was bathed with KCI Ringer’s solution and clamped to + 18 mV. Unlike the low-frequency Lorentzian component, the kinetics of the fast process depended strongly on voltage; i.e., fc increased from 10 to about 50 Hz at mucosa-positive potentials. This difference in voltage sensitivity was taken as evidence that the two Lorentzian components result from different K+ channels, rather than a single population of channels having multiple kinetic states. Studies of the macroscopic conductance of this membrane have shown that lowering mucosal pH (over range of 8.0-6.0) or adding divalent cations (5 mM Mg2+,Ca2+,Sr*+,or Ba2+)reduced K + conductance (Reuss et al., 1981). Two mechanisms were proposed for the inhibition by protons: a nonspecific titration of fixed negative charge, or a specific inhibition of the K + channel. These mechanisms were also offered as possible explanations for proton-inhibited K+ secretion in rabbit cortical collecting duct (Boudry et al., 1976)and for H+-induced depolarization of Necturus proximal tubule cells (Khuri, 1979). Some interaction (in addition to screening surface charge) was postulated for Ba2+and Sr2+because they were more potent blockers than were Mg2+and Ca2+. In summary, the apical membrane of the gallbladder normally has a high KS conductance and this results from selective channels which fluctuate spontaneously. In the following sections we review the evidence for apical K+ channels in tight epithelia.
2. FROGSKIN Potassium-dependent current fluctuations were first observed in shortcircuited skin from the frog Rana temporaria by Zeiske and Van Driessche (1978a). The site of fluctuating structures was not apparent because this membrane has traditionally been considered to be Na+ selective. However, in an independent microelectrode study, significant apical membrane K+ conductance was observed in about 15% of the preparations examined (Hirschmann and Nagel, 1978; Nagel and Hirschmann, 1980) and it is now clear thaf K+ channels are present in the apical mem-
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brane. Unlike other epithelial K+ channels described to date, this K+ channel rectifies, conducting only inward currents. Van Driessche and Zeiske (1980a) also found that the plateau value observed immediately after imposing a mucosa-to-serosa K+ gradient was greater when tissues were preequilibrated with sodium than with choline. To explain this difference, they suggested that an electrogenic Na+ pump in the basolateral membrane could leave the apical membrane hyperpolarized, thereby increasing the initial driving force for K+ across the apical membrane. Alternatively, intracellular Na+ might regulate apical membrane K+ permeability directly (Nagel and Hirschmann, 1980) although the influence of other intracellular modifiers such as Ca2+,elevated K+, and voltage cannot be excluded. The apical K+ channel in frog skin was readily blocked by cesium, rubidium, and barium (Hirschmann and Nagel, 1978; Zeiske and Van Driessche, 1978b; Van Driessche and Zeiske, 1980b; Nagel and Hirschmann, 1980). Inhibition by Cs+ was rapid, reversible, and competitive, with half-maximal inhibition ( K , ) ranging between 6.6 and 8.5 mM, depending on the length of time that skins were exposed to high-K+ Ringer's solution (Zeiske and Van Driessche, 1979; and see below). Because thef, of the spontaneous Lorentzian component declines with mucosal [Cs'], Van Driessche and Zeiske (1980a) have suggested that cesium interacts with the channel and induces current fluctuations at a frequency that is too high to be resolved experimentally. Rubidium was about half as effective as Cs+ in reducing the macroscopic K+ current and in depressing the Lorentzian component of the power spectrum. Barium blocked the current with a K I between 40 and 80 p M , increased the corner frequency of the spontaneous component slightly, and reduced its plateau value by -30% (Van Driessche and Zeiske, 1980b). In addition, mucosal Ba2+at low (8 p M ) concentrations induced low-frequency relaxation noise. The corner frequency of the blocker-induced Lorentzian component varied linearly with barium concentration between I p M and 1 mM (Van Driessche and Zeiske, 1980b). Individual association (k02) and dissociation (k20) rate constants (280 sec-I mM-' and 22.5 sec-I, respectively) have been calculated for barium block by assuming that channel-Ba2+ interactions are pseudo-first order and that spontaneous fluctuations do not affect the Ba2+-inducedrelaxation noise (Van Driessche and Zeiske, 1980b). Barium probably blocks by competing with K+; however, this was difficult to show experimentally because Ba2+ seemed to introduce a shunt pathway at low external K+ concentrations. It was clear that the K+ channel would have to remain open most of the time (in the absence of barium) in order to reconcile the measured values of ,402 and ,420 with Ba2+ block at high concentrations.
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Using a three-state model,
in which kol and k l oare the rate constants for spontaneous channel closing and opening, respectively (Van Driessche and Zeiske, 1980b),the singlechannel current ( 1 .O t 0.14 pA) and channcl density (0.18 -+ 0.02 p m ?) were calculated from the Ba2+-inducedfluctuations. From values of i and M, the probabilities for the channel being open or closed during spontaneOUJ Jluctrtations were back-calculated to be -0.95 and 0.05, respectively. Zei\ke and Van Drie\\che (1981) \tidied the effects of proton\, Ca”, and voltage on current fluctuations. Lowering mucosal pH from 7.4 to 4.4 reduced /L and increased S,,, but had little effect on the macroscopic K’ current. Similar results were obtained when mucosal Ca?’ concentration was raised from 0 to 20 mM or when the mucosal side was clamped to positive potentials (Fig. 4). Ca”, Sr?+,Mg?’, Cs2+,Ni?’, Mn2+,Zn2+,and La3+all increased So by 25-30% and reducedf, by 20-35 Hz. They suggested that Calf, protons, and voltage act on K + channel kinetics in frog skin by similar mechanisms because their effects interfere. For example, addition of 10 mM Ca’+ increased S,, and reducedf, while causing both parameters to become independent of mucosal pH. If the single-channel current remains constant when mucosal concentrations of H f and Ca2+are raised, these cations must act by reducing the rate of channel opening. Raising mucosal [Ca2+]from I to 10 mM increased mean closed time by 50% but had negligible effects (<0.4%) on mean open time. Zeiske and Van Driessche (1981) proposed that H’, Ca?+,and other divalent cations influence the rate of channel opening by screening fixed negative charge. Recently, Zeiske and Van Driessche (1981, 1983) studied the selectivity of the apical K+ channels in frog skin. It was found that TI+, Rb+, and NH,+also pass through the apical K + channels. On the other hand, small organic cations like hydrazinium, hydroxylammonium, and guanidinium do not permeate. The macroscopic current depended strongly on the species of the permeating cation present in the mucosal solution, and displayed the following sequence: TI’>K +>Rb+ = NH;. The macroscopic current could be reduced by Ba2+;however, the Ba?’ concentration needed to depress 50% of the current K& depended strongly on X, the species of the permeating cation: KiB > 10 mM. K i d = 80 p M ,Ki: = 2 mM, Ki,”4 = 15 pM. Among the permeating cations, TI+ displayed special characteristics, in that TI’ ions not only permeated through the K f
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A
10
20
[Ca2+Io ImM)
‘
ii
0
\,
0
30
0
1
20
pA2/dl 10
0
- 40
0
40
80
PD (mV)
FIG.4. (A) K+ current (short-circuit current, SCC, A). Lorentzian plateaus (So,0)and corner frequencies & 0) as functions of the mucosal Ca2+concentration [Ca2+],. Mucosal solution contained (in m M ) I15 KCI, 5 Tris (pH 7.4) without/with CaCI2. (B) Dependence of the transepithelial steady-state current I (A) and the Lorentzian parameters So (0)and,f, (0) on the transepithelial potential difference. Potential difference values are given with respect to the serosal side, no mucosal Ca2+. (Reprinted by permission from Zeiske and Van Driessche, 1981.)
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channels, but were also able to block the passage of K + . This was clearly demonstrated by recording the transepithelial current with different K+TI+ mixtures, keeping constant the total concentration ( I 15 mM). Such a mole-fraction experiment revealed a minimum in the transepithelial current at a ITI+]/[K'] ratio of about IO%. Analysis of the current fluctuations revealed a spontaneous Lorentzian component in the power spectrum with K + , T1+, Rb+, or NH,+ as the main mucosal cation. This observation confirmed the finding that these cations pass through the fluctuating K+ channels. The corner frequencies of the Lorentzian curves recorded with K + , T1+, and NHd were comparable (60-90 Hz), while a much higher value was obtained with Rb+ (= 200 Hz). Like the inhibition of the macroscopic current, fluctuation analysis showed that the interaction of Ba2+with the K + channel strongly depended on the cation species passing through the K + channel; the analysis of the Ba2+-inducedfluctuations showed that the association as well as the dissociation rate for Ba?+ varied with the mucosal cation species. The Michaelis-Menten constants calculated with these rate constants were in agreement with the values obtained from the inhibition of the macroscopic current. From this study, Zeiske artd Van Driessche (1983) concluded that ion translocation through the apical K t channels can be described by singlefile diffusion through a channel with at least two binding sites and three barriers. 3. OTHERPREPARATIONS Maneuvers that are known to elevate intracellular CAMPin frog gastric mucosa also induce net K ' secretion when a serosa-to-mucosa K + gradient is imposed under I,, conditions (Zeiske et al., 1980). I,, was blocked by adding 5-10 mM Ba2+to either side, and Ba2+induced a shoulder in the power density spectrum when the mucosal side was clamped to negative potentials. Unfortunately, data obtained from the gastric mucosa were difficult to interpret because of its complex ultrastructure, which requires use of a model with distributed resistance in the crypt lumen (Clausen et a / . , 1983). The power spectrum from rabbit colon also displays a spontaneous Lorentzian component, particularly when a transmural driving force for K+ is imposed (Wills et al., 1982). This channel does not rectify since similar Lorentzian curves were obtained regardless of the direction of the K+ gradient. The spontaneous Lorentzian curve had a corner frequency of -16 Hz and a plateau value which ranged between 4 and 17 x lo-'" A2 second/cm2,depending upon the size of the driving force. Mucosal addition of TEA+ (10-30 mM) or Cs+ (10 mM) partially inhibited So without
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affecting the corner frequency. However, unlike most other epithelia, mucosal Ba2+had no effect (Wills et al., 1982). Two lines of evidence suggest that K+-dependent relaxation noise originates at the apical membrane of rabbit colon. Mucosal addition of nystatin (40 U/ml), which causes a drastic decline in membrane resistance, abolished the spontaneous Lorentzian component whereas addition of nystatin to the serosal side had no effect (Wills et al., 1982).This result can be easily understood because nystatin would reduce electrical and chemical gradients for K+ across the apical membrane and would also have a shunting effect on apical current fluctuations. A second argument for localization of this relaxation noise to the apical rather than basolateral membrane comes from their relative resistances: any current noise arising at the basolateral membrane should normally be attenuated to unmeasurably low levels (see Van Driessche and Gullentops, 1982). In addition to the results in gallbladder and frog skin mentioned above, macroscopic techniques have revealed a large apical membrane K+ conductance which is sensitive to luminal Ba2+ and H+ in rabbit cortical collecting ducts (O’Neil, 1982a,b). Apical K+ conductance is sensitive to luminal Ba2+ in flounder intestine, and also depends on the rate of CIabsorption (Krasny et al., 1982).
6. Basolateral Membrane
Basolateral potassium conductance is an important feature of the Koefoed-Johnsen and Ussing model because it provides a pathway for K+ taken up by the Na+-K+ exchange to return to the serosal side. Since the Na+,K+-ATPaseis found in the basolateral membrane of nearly all epithelia, we might also expect basolateral Kf channels to be of widespread importance. Indeed, electrophysiological experiments have shown that basolateral K+ conductance is invariably high. Unfortunately, basolateral K+ channels have been difficult to study using noise analysis because current fluctuations are normally attenuated. Recently, pore-forming antibiotics such as nystatin and amphotericin B have been used to reduce apical membrane resistance in the bladder and colon, thereby permitting studies of macroscopic K+ conductance (Lewis et al., 1978; Wills et al., 1979; Kirk and Dawson, 1983) and K+ current fluctuations from the basolateral membrane (Van Driessche et al., 1982; Wills et al., 1982). For example, spectral analysis of the I,, in R . temporaria revealed a Lorentzian component cf, = 45-70 Hz) when nystatin (3520 U/ml) was added to the luminal surface in the presence of a mucosal-to-
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serosal gradient of potassium ions (Van Driessche et d., 1982). Serosal Ba?+ (5 mM) blocked the current elicited by ny\tatin, reduced transepithelial conductance, and aboli\hed the LorentLian component of the power spectrum. Serosal Ba2+was acting on K’ current in these experiments because removal of the K’ gradient also abolished the Lorentzian component. In power spectra obtained from rabbit colon, a Lorentzian curve having a corner frequency of 201 Hz and So of 3 X lo-” AZsecond/ cmz was observed after treating the apical membrane with a Large dose of nystatin (Wills ef ( i / . , 1982).This current noiw wa\ dependent on a transepithelial K ‘ gradient and wa\ blocked by 5 mM \ero\al Ba” . Power spectra obtained from tadpole skin also showed a Lorentzian component under these conditions, and had a corner frequency between 60 and 100 Hz (Van Driessche e? a/., 1982). Barium-sensitive K’ conductance has been reported in the basolateral membrane of gastric mucosa(Pacifico rf a / . , 1969).frog skin (Nagel, 1979; Nielsen, 1979; Hillyard, 1982; Cox and Helman, 1983), rabbit proximal tubule (Biagi et a/., 1981; gello-Reuss, 1982), turtle colon (Kirk et al., 1980), rabbit colon (Wills et ul., 1982), trachea (Welsh, 1983), Manduca sexla midgut (Moffett and Koch, 19821, Necturus urinary bladder (Demarest and Finn, 1983). and locust hindgut (Hanrahan ef al., 1983). In larval toad skin, Ba2+ blocks when added to the serosal side and when added apically in the presence of mucosal nystatin (Hillyard, 1982). The effects of pH on basolateral K’ channels have not yet been studied using fluctuation analysi\; howevar, proton\ (Biagi of a / . . 1981) or low \ero\al HCOT (Bello-Reuss, 1982) reduce Ba”-sensitive K+ conductance at the basolateral membrane of rabbit proximal tubule. Cesium block is voltage dependent at the basolateral membrane of rabbit colon, blocking only inward K’ currents (Wills et al., 1979). Basolateral conductance (macroscopic) has been studied in turtle colon by imposing a transmural K’ gradient in the presence of mucosal amphotericin B and serosal ouabain (Kirk and Dawson, 1983). I,‘ equals net 42K+ flux under these conditions, but the flux ratio is greater than that expected for simple diffusion. Several results suggest that cations interact within the basolateral K’ pathway: ( 1 ) Ba’+-sensitive 42K flux ratios can be fitted to the model for single-file diffusion (Hodgkin and Keynes, 1955) by assuming that the parameter n’ equals 2 (Kirk and Dawson, 1983). (2) K+dependent I,, is inhibited by adding Rbt to the opposite (trans) side whereas cis addition has little effect. (3) Imposition of a Rb+ gradient in the presence of potassium generates a net K + flux, indicating positive coupling between K’ and Rb+ (Kirk and Dawson, 1983). In the presence of a Kf gradient, addition of Rbt to both sides inhibits the Ba?+-sensitive current and the 42K+flux, with the degree of inhibition varying inversely
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282
with potassium concentration (Germann and Dawson, 1983). The permeability sequence of the basolateral K+ conductance is PK = PTI= 10 PRb. It may prove interesting to study epithelial K+ channels in invertebrate animals. For example, K+ is often the main extracellular cation in insects (>100 mM) and is transported at extraordinarily high rates (reviewed by Harvey, 1982). As in vertebrate preparations, basolateral K+ conductance is high in insect epithelia (see Hanrahan, 1982) and is Ba2+-sensitivein K+-secreting (Moffett and Koch, 1982) and K+-absorbing tissues (Hanrahan et al., 1983). The locust hindgut passively absorbs K+ at high rates from the lumen via conductive pathways in the apical and basal membranes (Hanrahan, 1982). Under CI--free conditions, 1 mM cAMP lowers the resistance of the apical membrane in this tight epithelium, permitting the analysis of basolateral membrane K+ current fluctuations with minimal attenuation (Hanrahan et al., 1983). A large, K+-dependent lscoccurs during cAMP exposure in the presence of a K+ gradient. Barium has no effect when added to the mucosal side; however, serosal Ba2+is inhibitory (Ki = 2.9 mM) and induces a Lorentzian component in the power spectrum. Like the apical K+ channels in the frog skin (Van Driessche and Zeiske, 1980b), there is a bell-shaped dependence of So on [Ba2+],and fc increases linearly with [Ba2+]over the range 1-14 mM. Basolateral K+ channel density is estimated to be -150 x 106/cm2macroscopic tissue area and single-channel currents are approximately 0.6 pA under these conditions (J. W. Hanrahan, N. K. Wills, and S . A. Lewis, unpublished observation). IV. NONSELECTIVE CATION CHANNELS A. Apical Membrane
Spontaneous fluctuations in I,, have been measured (see Table 111) using larval bullfrog skins when bathed with NaCl Ringer’s solution on the serosal side and with K+, Rb+, Cs+, or NH; Ringer’s solutions on the mucosal side (Hillyard et al., 1982). In each case, power spectra had a Lorentzian component that was abolished by mucosal nystatin. As expected, the relaxation noise observed with “K+-like” cations was blocked by Ba2+(5 mM) or TEA+ (10 mM). A more surprising result was that mucosal amiloride or benzimidazolyl-2-guanidine(BIG), an analog of amiloride which stimulates apical Na+ conductance, enhanced the noise observed with K+-like cations and also induced a Lorentzian component when tissues were bathed bilaterally with Na+ or Li+ Ringer’s solution. Because of their poor selectivity and their interactions with Na+ and K+
CHANNELS ACROSS EPITHELIAL CELL LAYERS
283
channel blockers, it was suggested that these cation channels might be precursors of the “normal” adult Na+ channels (Hillyard et af., 1982). This would be consistent with earlier work on toads where it was found that the skin does not distinguish between Na+ and K+ immediately after moulting (Katz, 1978). Van Driessche and Zeiske (1983a,b) have recently found a cation-selective channel in the apical membrane of Rana catesbeiana and Rana ridibunda. A relaxation noise component was observed in the spectrum of fluctuations in I,, with different mucosal monovalent cations. The plateau values displayed the following sequence: TI+ > K+ > Na+ > Rb+ = NH: = Cs+. With Na+ as the main mucosal cation, the plateau value was augmented when Na+ uptake through the Na+-selective channels was blocked with amiloride. This observation provided evidence for the existence of a nonselective pathway in parallel with the amiloridesensitive Na+ channels in the apical membrane. ( I ) The driving force for Na+ through the non-selective pathway is increased by amiloride through hyperpolarization of the intracellular potential (Nagel et al., 1981b) and a reduction of the intracellular Na+ concentration. (2) As a consequence of the augmented resistance of the apical membrane, the attenuation of the noise signal is reduced under these conditions. The macroscopic currents through this nonselective pathway recorded with the different permeating cations were less than 1 pAlcm2 and therefore difficult to analyze. The existence of the nonselective channels can only be demonstrated in the absence of Ca2+in the mucosal solution. It was also found that all divalent cations (Ca2+,Sr2+,Mg2+,Ba2+,Cd”, Ni2+,Mn2+)at concentrations of 0.1 mM abolished the Lorentzian component completely. Finally, it was shown that this pathway was occluded at low pH and that more transport sites were opened when the pH was elevated (Zeiske and Van Driessche, 1983b). B. Basolateral Membrane
A Ca2+-activatedcation channel has been identified in the basolateral membrane of pancreatic acinar cells using the patch-clamp technique (Maruyama and Petersen, 1982a,b). This channel is apparently involved in stimulus secretion; the channel does not distinguish between Na+ and K + ,does not rectify, and has a mean conductance of 27 and 33 pS in NaCl and Na2S04solutions, respectively. The mean open time ranges between 0.3-1 second and is dependbnt on internal [Ca2+].The channels, which are usually closed in cell-attached patches, open in response to externally applied cholecystokinin or acetylcholine, and this response is mediated by a rise in intracellular calcium. Based on their estimates of single-
SPONTANEOUSLY FLUCTUATING
TABLE 111 K' A N D NONSELECTIVE CATION
CHANNELS
Spect ru rn'l
.L
Preparation N
03
P
Apical membrane Gallbladder Bufo rnarinrrs Nectrtrus mu-
SO
Rectification
4.0
37
No
TEA' (100%)
2.1-6.3
4.8-340
No
Ba" (reduces So only), TEA+ (100%~). H' (
IS (with rnucosal to serosal K'
10
clllosus
Rabbit Skin (Roncr fernporurirr )
Blockers
Selectivity
K' >> Cs'. not choline Na+ K' > Rb'. not Cs'. Na'
gradient) - I 1 (22°C)
NRb
NR
NR
PNR
34 (37°C) 81
I .5
Yes
Ba". Cs'. TI': at low conc. Rb'. H' (pH < 4.4). not TEA'
TI'. K
3 Rb' -NH;. not Cs'. Na'. Li'
References
Van Driessche and Gogelein (1978) Gbgelein and Van Driessche (1981a) Cogelein and Van Driessche (1981b) Unpublished results Van Driessche and Zeiske I980a. b: Zeiske and Van Driessche ( 198 I . 1983)
.
Colon (rabbit)
15.6 (37°C)
7.0
N0
Larval frog skin ( R ~ I I I(‘tit(’.\~I
30-40
1-10
NR
hrirrrrcr )
Adult skin
(Rotitr
100-300
1
NR
45-70
NR
NR
100-150 (37°C)
NR
NR
NR
Wills er
C\- K’. Rh’. NH;. Na’. Li’
Hillyard e / t i / .
TI* > K A . Na’
Van Drie5sche and Zeiske (19X3a.b)
Ba”. Cs’ (not voltage dependent) Ba’-. cs- (voltage dependent)
NR
Wills er c i l . (1982): Van Driessche (’I t i / . (1982) Wills 8 1 crl. (1982): Van Driessche t’r
Ba’-
NR
TEA’ (33-50%). Cs- ( l8-7C% ). not Ba” Ba”. TEA+. stimdated by amiloride. BIG Divalent cations
c~trteshuicrncr
Basolateral membrane Skin (Rancr /ernporcrrirr )
Colon (rabbit)
NR
I’
NR
ti/.
(1982)
(19x2)
t r l . ( 19x2)
At V, = 0 and room temperature unless otherwise stated:./; is in hertz. S,, is x 10’” A’ second cm NR. not reported.
Van Driessche ( ’ I nl. (1982); Hillyard (1982)
’.
286
SIMON A. LEWIS ET AL.
channel current and published values for the membrane area of the acinar cells, Maruyama and Petersen (1982a) calculated that the maximal current through these channels in the basolateral membrane would be more than sufficient to account for the macroscopic current measured during acetylcholine-evoked Na+ secretion. In all respects, this nonselective cation channel resembles those described in cultured cardiac muscle (Colquhoun et al., 1981) and neuroblastoma cells (Yellen, 1982). V. THE H20 CHANNEL
In the previous sections we emphasized the properties and regulation of cation channels; however, there is increasing evidence that hormonestimulated water permeability in the apical membrane of tight epithelia is mediated by the insertion of water channels from a cytoplasmic store. Transepithelial hydraulic conductivity of toad urinary bladder increases dramatically following serosal addition of antidiuretic hormone (ADH). Net water flux is increased 100-fold when an osmotic gradient favoring flow from lumen to plasma is present. Morphological studies utilizing freeze-fracture have shown that ADH causes the appearance of particle aggregates in the apical membrane (Kachadorian et al., 1975). These particles seem to originate in the cytoplasm because cytoplasmic tubule vacuoles contain identical aggregates. Furthermore, morphometric analysis has shown a loss of aggregates from the cytoplasm and a gain of aggregates in the apical membrane during ADH challenge. Removal of ADH reverses this process, causing particles to reappear associated with tubule vacuoles. Additional evidence for vesicle translocation comes from the increase in apical membrane area (i.e., capacitance) which closely parallels the water response (Warncte and Lindemann, 1981; Stetson et al., 1982; Palmer and Lorenzen, 1983). Selective inhibition of the ADH response by methohexital (Stetson et al., 1982) results in a parallel inhibition of the membrane area changes. The hydroosmotic response is blocked by agents that are known to interfere with microfilaments and microtubules (Taylor et al., 1973), providing further support for the contention that movement of HzO channels into the apical membrane requires the cytoskeleton. The results described above are suggestive, but they do not establish that water moves through channels, or that the particle aggregates are channel proteins. The best evidence that H 2 0does flow through channels comes from the work of Gluck and Al-Awqati (1980). These investigators reasoned that if ADH induces aqueous channels, then the proton permeability of the membrane should also increase because protons would be
CHANNELS ACROSS EPITHELIAL CELL LAYERS
287
capable of jumping from water molecules in the bulk solution to those in the channel. On the other hand, if ADH stimulates H20 permeability by increasing membrane fluidity, then the low dielectric constant of the membrane would prevent any increase in proton conductance. In the presence of a pH gradient favoring H+ entry across the apical membrane, addition of serosal ADH increased the net flux of protons by 300% and reduced cell pH from 6.7 to 6.12, suggesting the presence of water channels in the apical membrane (Gluck and Al-Awqati, 1980). In addition to increasing water permeability, ADH also stimulated apical Na+ and urea permeabilities. To exclude the possibility that protons diffuse through these other pathways, the effects of specific inhibitors on proton conductance were also tested. Amiloride caused proton flux to increase (presumably due to a more negative membrane potential), indicating that protons do not permeate through the amiloride-sensitive Na+ channel. Phloretin, which blocks urea permeability in toad bladder, had no effect on proton flux or conductance, suggesting that water and urea move through different pathways. The final evidence for proton permeation through the H 2 0 channels was obtained by correlating changes in proton conductance with these in water permeability (as measured with tritiated H20). Water permeability and proton conductance were linearly correlated (Gluck and Al-Awqati. 1980). In summary, there is good evidence that ADH increases apical water permeability in tight epithelia by causing the insertion of H 2 0 channels from a cytoplasmic store into the apical membrane, and that these channels conduct protons. It is not yet known whether the H2O channels fluctuate spontaneously, or whether there is a correlation between the number of particle aggregates and number of channels. VI.
CANDIDATE CHANNELS
We have been quite strict in selecting pathways that we consider to be well-established ion channels (e.g., demonstration of Lorentzian-type power spectral density using fluctuation analysis, or direct single-channel recording using the patch-clamp technique). Other possible channels that have not yet been demonstrated in epithelia are the Ca2+-activatedK + channel and the Ca2+ channel. A most obvious “candidate channel” would be the C1- Conductance, which is important in secretion by a number of epithelia. Evidence for epithelial CI- channels is lacking because ( I ) no spontaneous Lorentzian has been measured for CI-, (2) there is no reversible blockers for epithelial C1- conductance which might be used to induce fluctuations, and (3) the impedance properties of those prepara-
SIMON A. LEWIS ET AL.
288
tions known to transport CI- do not favor fluctuation analysis. It is hoped these problems will be overcome in the near future. For now, we must apologize to any reader whose channel has not been included. ACKNOWLEDGMENTS We wish to thank Drs. C. Clausen, J. Diamond, M. Ifshin, D. Loo, N. Wills, and W. Zeiske for their collaborations and help over the past years, and W. Alles for technical assistance. This work was supported in part by NIH Grant AM 20851 to S.A.L. and a postdoctoral fellowship to J.W.H. from NSERC (Canada). REFERENCES Anderson, C. R., and Stevens, C. F. (1973). Voltage clamp analysis of acetylcholine produced end-plate current fluctuations at frog neuromuscular junction. J . Physiol. (London) 235, 655-691. Armstrong, C. M. (1975). Evidence for ionic pores in excitable membranes. Eiophys. J . 15, 932-933. Augustus, J., Bijman, J., and Van Os, C. H. (1978). Electrical resistance of rabbit submaxillary main duct: A tight epithelium with leaky cell membranes. J . Membr. B i d . 43,203226. Bello-Reuss, E. (1982). Electrical properties of the basolateral membrane of the straight portion of the rabbit proximal renal tubule. J . Physiol. (London) 326, 49-63. Benos, D. J. (1982). Amiloride: A molecular probe of sodium transport in tissues and cells. A m . J . Physiol. 242, C131-CI45. Benos, D. J., Mandel, L . J., and Simon, S. A. (1980a). Cationic selectivity and competition at the sodium entry site in frog skin. J . Gen. Physiol. 76, 233-247. Benos, D. J., Mandel, L. J., and Simon, S. A. (1980b). Effects of chemical group specific reagents on sodium entry and the amiloride binding site in frog skin: Evidence for separate sites. J . Membr. B i d . 56, 149-158. Biagi, B., Kubota, T., Sohtell, M., and Giebisch, G. (1981). Intracellular potentials in rabbit proximal tubules perfused in uitro. A m . J . Physiol. 240, F200-F210. Bindslev, N., Cuthbert, A. W., Edwardson, J. M., and Skadhauge, E. (1982). Kinetics of amiloride action in the hen coprodaeum in uitro. PJuegers Arch. 392, 340-346. Boudry, J. F., Stoner, L. C., and Burg, M. B. (1976). Effect of acid lumen pH on potassium transport in renal cortical collecting tubules. A m . J . Physiol. 230, 239-244. Christensen, 0.. and Bindslev, N. (1982). Fluctuation analysis of short-circuit current in a warm-blooded sodium retaining epithelium: Site, current density and interaction with Triamterene. J . Membr. Eiol. 65, 19-30. Clausen, C., and Wills, N. K. (1981). Impedance analysis in epithelia. In “Ion Transport by Epithelia” (S. G. Schultz, ed.), pp. 79-92. Raven Press, New York. Clausen, C., Machen, T. E., and Diamond, J. M. (1983). Use of AC impedance analysis to study membrane changes related to acid secretion in amphibian gastric mucosa. Eiophys. J . 41, 167-178. Colquhoun, D., Neher, E., Reuter, H . , and Stevens, C. F. (1981). Inward current channels activated by intracellular Ca in cultured cardiac cells. Nature (London) 294, 752-754. Cox, T. C., and Helman, S. I. (1983). Barium effect at the basolateral membrane of isolated epithelia of frog skin. Fed. Proc., Fed. A m . Soc. Exp. B i d . 42, 1101.
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Davis, C. W . , and Finn. A. L. (1Y82). Sodium transport inhibition by amiloride reduces basolateral membrane potassium conductance in tight epithelia. Scicncc. 216,525-527. Demarest. J . R., and Finn, A, L. (1983). Serosal Ba inhibits apical membrane conductance in Nc~irrrusurinary bladder. Fed. Proc.. Fed. A m . Soc. Exp. B i d . 42, 1282. Diamond, J. M. (1978). Channels in epithelial cell membranes and junctions. Fed. Pro(,., Fed. A m . Soc. Exp. Biol. 37,2639-2644. Dick, H. J . , and Lindemann, B. (1975). Saturation of Na-current in frog skin epithelium abolished by PCMB. Pjurgers Arch. 355, R72. Erlij, D.. and Van Driessche, W. (I(m3). Noise analysis of inward and outward Na current in ouabain treated frog skins. Fed. Proc., Fed. A m . Soc. Exp. B i d . 42, 1101. Fromter, E., and Diamond, J. M. (1972). Route of passive ion permeation in epithelia. Nutitre (London)New Biol. 285, 9- 13. Fromter, E., and Gebler, B. (1977). Electrical properties of amphibian urinary bladder epithelium. Ill. The cell membrane resistances and the effect of amiloride. Pjhteger~v Arch. 371, 99-108. Fromter, E., Higgins, J . T . , and Gabler. B. (1981). Electrical properties of amphibian urinary bladder. IV. The current-voltage relationship of the sodium channels in the apical cell membrane. I n "Ion Transport by Epithelia" (S. G . Schultz. ed.), pp. 31-45. Raven Press, New York. Fuchs. W.. Larsen, E. H . , and Liedemann. B. (1977). Current voltage curve of sodium channels and concentration dependence of sodium-permeability in frog skin. J . Phy.vid. (London)267, 137-166. Germann, W. J., and Dawson, D. C . (1983). Cation interaction in a basolateral potassium channel in turtle colon. Fed. Proc.., F'cvl. A m . Soc. Exp. B i d . 42, 1100. Gluck. S . , and Al-Awqati, Q. (1980). Vasopressin increases water permeability by inducing pores. Nutiire (London) 284, 631-632. Gogelein, H., and Van Driessche, W. (1981a). Noise analysis of the K' current through the apical membrane of Nectirrus gallbladder. J . Mrnihr. Biol. 60, 187-198. Gogelein, H., and Van Driessche. W. (1981b). The effects of electrical gradients on current fluctuations and impedance recorded from Nec,t/rri~vgallbladder. J . Mcvnbr. B i d . 60, 199-209.
Gottlieb, G . P., Turnheim, K., Frizzell, R. A,. and Schultz, S. G. (1978).p-Chloromercuribenzene sulfonate blocks and reverses the effect of amiloride on sodium transport across rabbit colon in uitro. Biophys. J . 22, 124-129. Gunter-Smith, P. J . , and Schultz. S. G. (1982). Potassium transport and intracellular potassium activities in rabbit gallbladder. J . Mernhr. Biol. 65, 41-48. Halm, D., Bynum, E.. and Frizzell. R. A. (1983). Active potassium secretion across rabbit colon stimulated by 0-adrenergic agonists. Fed. Proc.. Fed. A m . Soc. E x p . B i d . 42, 1980. Hamill, 0. P., Marty, A., Neher, E., Sakmann. B.. and Sigworth, F. J. (1981). Improved patch-clamp techniques for high-resolution current recording from cells and cell-free Arch. 391, 85-100. membrane patches. P'uegrrs Hanrahan, J. W. (19821. Cellular mechanism and regulation of KCI transport across an insect epithelium. Ph.D. Dissertation, University of British Columbia. Vancouver, Canada. Hanrahan. J. W., Wills. N. K.. and Lewis, S . A. (1983). Barium-induced current fluctuations from the basal membrane of an insect epithelium. Proc. 2Yrh Int. Conxr. Plzysiol. Sci., p. 457. Harvey, W. R. (1982). Membrane physiology of insects. 1n "Membrane Physiology of
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Li, J. H. Y., Palmer, L. G . , Edelman, I. S., and Lindemann, B. (1982). The role of sodiumchannel density in the Natriferic response of the toad urinary bladder to an antidiuretic hormone. J . Membr. B i d . 64, 77-89. Lindemann, B., and Van Driessche. W . (1977). Sodium-specific membrane channels of frog skin are pores: Current fluctuations reveal high turnover. Science 195, 292-294. Lindemann, B., and Voilte, C. (1977). Structure and function of the epidermis. In “Frog Neurobiology” (R. Llinas and W. Precht. eds.), pp. 169-210. Springer-Verlag, Berlin and New York. Loo, D. D. F., Lewis, S. A., Ifshin, M. S . , and Diamond, J. M. (1983). Turnover, membrane insertion, and degradation of sodium channels in rabbit urinary bladder. Science 221, 1288-1290. McCabe, R., Cooke, H . , and Sullivan, L. (1982). Potassium transport by rabbit descending colon. A m . J . Physiol. 11, 81-86. Maruyama, Y., and Peterson, 0. H. (1982a). Single channel currents in isolated patches of plasma membrane from basal surface of pancreatic acini. Nature ( L o n d o n ) 299, 159161.
Maruyama, Y., and Petersen, 0. H. (1982b). Cholecystokinin activation of single-channel currents is mediated by internal messenger in pancreatic acinar cells. Nature ( L o n d o n ) 300,61-63. Minsky, B. D., and Chlapowski, F. J. (1978). Morphometric analysis of the translocation of luminal membrane between cytoplasm and cell surface of transitional epithelial cells during the expansion-contraction cycles of mammalian urinary bladder. J . Cell Biol. 77, 685-697. Moffett, D. F., and Koch, A. R. (1982). Ba” as a probe of K’ uptake mechanism of insect midgut. A m . Zool. 22, 891. Moreno, J . (1974). Blockage of cation permeability across the tight junctions of gallbladder and other leaky epithelia. Nictitre ( L o n d o n ) 251, 150-151. Nagel, W. (1979). Inhibition of potassium conductance by barium in frog epithelium. Biochim. Biophys. A c t a 552, 346357. Nagel, W., and Hirschmann, W. (1980). K+-permeabilityof the outer border of the frog skin ( R . temporaria). J . Membr. Biol. 52, 107-113. Nagel. W., Durham, J . H., and Btodsky, W . A. (1981a). Electrical characteristics of the apical and basolateral membrane in the turtle bladder epithelial cell layer. Biochirn. Biophys. A c t a 646,78-87. Nagel, W., Garcia-Diaz, J. F., and Armstrong, W. McD. (1981b). Intracellular ionic activities in frog skin. J . Memhr. Biol. 61, 127-134. Nielsen, R. (1979). A 3 to 2 coupling of the Na-K pump responsible for the transepithelial Na transport in frog skin disclosed by the effect of Ba. Acru Physiol. Scund. 107, 189-191. O’Neil, R. G . (1982a). Effect of luminal H A and Ba++ on the apical cell membrane K+ conductance of the cortical collecting tubule (CCT). Fed. Proc.. Fed. A m . Soc. E x p . B i d . 41, 1006. O’Neil, R. G . (1982b). Microelectrode assessment of the luminal cell membrane ionic conductive properties of the cordcal collecting tubule (CCT). Physiologist 25, 334. Pacifico, A. D., Schwartz, M., MacKrell, T. N., Spangler, S. G . , Sanders, S . S., and Rehm, W. S . (1969). Reversal by potftssium of an effect of barium on the frog gastric mucosa. A m . J . Physiol. 216, 536-5418. Palmer, L. G. (1982). Ion selectivity of the apical membrane Na channel in the toad urinary bladder. J . Memhr. Biol. 67,91-98. Palmer, L. G. (1983). Voltage dependence of amiloride inhibition of apical membrane Na conductance in toad urinary bladder. Biophys. J . 41, 186a.
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Palmer, L. G . , and Edelman, I. S . (1981). Control of apical sodium permeability in the toad urinary bladder by aldosterone. Ann. N . Y . Accrcl. S'f,i. 372, 1-14. Palmer, L. G . , and Lorenzen, M. (1983). Antidiuretic hormone-dependent membrane capacitance and water permeability in the toad urinary bladder. A m . J. Physiol. 244, F19SF204. Palmer, L. G . , Li, J. H. Y . , Lindemann, B., and Edelman, I. S. (1982). Aldosterone control of the density of sodium channels in the toad bladder. J. Mernbr. Eiol. 64, 91-102. Park, C. S., and Fanestil, D. D. (1983). Chemical, hormonal, and metabolic control of Na' entry step across the apical membrane of toad urinary bladder. Fed. P r o c . , Fed. A m . Soc. Exp. Biol. 42, 1282. Reuss, L., and Finn, A . L. (1974). Passive electrical properties of toad urinary bladder epithelium: Intercellular electrical coupling and transepithelial cellular and shunt conductances. J. Gen. Physiol. 64, 1-25. Reuss, L., and Finn, A . L. (1975). Electrical properties of the cellular transepithelial pathway in Nectitrus gallbladder. 11. Ionic permeability of the apical cell membrane. J . Membr. Biol. 25, 141-161. Reuss, L., and Grady, T. P. (1979). Triaminopyrinidinium (TAP+)blocks luminal membrane K conductance in Necuturus gallbladder epithelium. J. Mernbr. B i d . 48, 285-298. Reuss, L., and Weinmann, S. A. (1979). lntracellular ionic activities and transmembrane electrochemical potential differences in gallbladder epithelium. J. Mernbr. Biol. 49, 345-362. Reuss, L., Cheung, L. Y . , and Grady, T. P. (1981). Mechanisms ofcation permeation across apical cell membrane of Necturus gallbladder: Effects of luminal pH and divalent cations on K+ and Na+ permeability. J. Membr. Eiol. 59, 21 1-224. Schultz, S. G . , Frizzell, R. A., and Nellans, H. N. (1977). Active sodium transport and the electrophysiology of rabbit colon. J. Membr. Biol. 33, 3.51-384. Stetson, D. L., Lewis, S . A., Alles, W., and Wade, J. B. (1982). Evaluation by capacitance measurements of antidiuretic hormone induced membrane area changes in toad bladder. Biochim. Biophys. Actu 689, 267-274. Taylor, A . , and Windhager, E. E. (1979). Possible role of cytosolic calcium and Na-Ca exchange in regulation of transepithelial sodium transport. Am. J. Physiol. 236, FSOSF512. Taylor, A., Mamelak, M., Reaven, E., and Maffly. R. (1973). Vasopressin: Possible role of microtubules and microfilaments in its action. Science 181, 347-349. Thompson, S. M., Suzuki, Y . , and Schultz, S. G . (1982). The electrophysiology of rabbit descending colon. 1. Instantaneous transepithelial current-voltage relations and the current-voltage relations of the Na+-entry mechanism. J. Mernbr. B i d . 66, 41-54. Van Driessche. W.. and Gogelein, H. (1978). Potassium channels in the apical membrane of the toad gallbladder. Nature (London)275, 665-667. Van Driessche, W . . and Gullentops. K . ( 19x2). Conductance fluctuation analysis in epithelia. "Techniques in Cellular Physiology." Vol. P123. pp. 1-13. Van Driessche, W., and Lindemann, B. (1978). Low-noise amplification of voltage and current fluctuations arising inepithelia. R e v . Sci. Instrum. 49, 52-57. Van Driessche, W., and Lindemann, B . (1979). Concentration dependence of currents through single sodium-selective pores in frog skin. Nutrrre (London)282, 519-520. Van Driessche, W., and Zeiske, W. (1980a). Spontaneous fluctuations of potassium channels in the apical membrane of frog skin. J. Physiol. (London) 299, 101-1 16. Van Ihiessche. W . , and Zeiske. W. ( 198Ob). B;i?+-inducedfluctuations of potassium channels in the apical membrane of frog skin ( R a m temporariu). J . Membr. Biol. 56, 3142.
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Van Driessche, W., and Zeiske, W. (1983a). Cation-selective channels in the apical membrane of frog skin. Fed. Proc.. Fed. A m . Soc. Exp. Biol. 42, 1101. Van Driessche, W., and Zeiske, W. (1983b). Cation-selective channels in the apical membrane of frog skin unmasked by decreasing external [Ca2+]and intracellular [H’]. Arc,h. Int. Physiol. Biochim. (in press). Van Driessche, W., Wills, N. K., Hillyard, S . I)., and Zeiske, W. (1982). K+ channels in an epithelial “single-membrane” preparation. Arch. f n t . Phvsiol. Biochim. 90, P12-PI4. . Mol. Biol. 28, Verveen. A. A,, and DeFelice, L. J . (1974). Membrane noise. P r ~ gBiophys. 189-265. Warncke, J . , and Lindernann, B. (1981). Effect of ADH on the capacitance of apical epithelial membranes. Adu. Physiol. Sci., Proc. Int. Congr., 28th, 1980, pp. 129-133. Welsh, M. J. (1983). Barium inhibition of basolateral membrane potassium conductance in tracheal epithelium. A m . J . Plrysiol. 244, F639-F645. Wills, N . K . , and Biagi. B. (1982). Active potassium transport by rabbit descending colon epithelium. J . Membr. B i d . 64, 195-203. Wills, N . K., and Lewis, S. A. (1980). lntracellular Na’ activity as a function of Na+ transport rate across a tight epithelium. Biophys. J . 30, 181-186. Wills, N. K . , Eaton, D. C., Lewis, S. A,, and Ifshin, M. S . (1979). Current-voltage relationship of the basolateral membrane of a tight epithelium. Biochim. Biophys. Actu 555, 5 19-523. Wills, N . K., Zeiske, W., and Van Driessche. W. (1982). Noise analysis reveals K’ channel conductance fluctuations in the apical membrane of rabbit colon. J . McJmbr.B i d . 69, 187- 197. Yellen, G. (1982). Single Caz+-activuted nonselective channels in neuroblastoma. Nature ( L o n d o n ) 296, 3.57-359. Zeiske. W. (1978). The stimulation of Na’ uptake in frog skin by uranyl ions. Biochirn. Biophys. A c t a 509, 218-229. Zeiske, W., and Lindemann, B. (1975). Blockage of Na-channels in frog skin by titration with protons and by chemical modification of COO-groups. tfluegers Arch. 355, R71. Zeiske, W., and Van Driessche, W. (1978a). The origin of K+-dependent current fluctuations in frog skin ( R . t e m p . ) . PJliregars Arch. 373, R48. Zeiske, W., and Van Driessche, W. (1978b). K+-uptakeacross the outer border of frog skin ( R . t e m p . ) and its inhibition by Cs-ions. P’uegers Arch. 373, R48. Zeiske, W., and Van Driessche, W. (1979). Saturable K’ pathway across the outer border of frog skin ( R a n a temporaria): Kinetics and inhibition by Cs’ and other cations. J . Memhr. Biol. 47, 77-96. Zeiske, W., and Van Driessche, W. (:1981).Apical K’ channels in frog skin (Runa temporuria): Cation adsorption and voltage-gating kinetics. PJluegers Arch. 390, 22-29. Zeiske, W.. and Van Driessche, W. (1983). The interaction of “K’ like” cations with the apical K + channel in frog skin. J . Memhr. B i d . 76, 57-72. Zeiske, W., Van Driessche, W., and Machen, T. (1980). K+ current noise in frog gastric rnucosa. J . G e n . Physiol. 76, 9a. Zeiske, W.. Wills, N. K . . and Val1 Driessche, W. (19x2). Na’ channels and miloride induced noise in the mammalim colon epithelium. Bioc,/iirrt. Biophy.~.Ac/u 688. 201210. Zeuthen. T. (1978). Intracellular grgdients of ion activitics in the epitheliiil cellx of the N c ~ t r r r u sgallbladder recorded with ion-\elective niicroelectrodes. J . Mc~mhr. Biol. 39, 1x5-218.
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CURRENT TOPICS IN MEMBRANES A N D 'TRANSPORT. VOLUME ?I
Water Movement through Membrane Channels ALAN FINKELSTEIN Departments of Physiology and Biophysics nnd of Neuroscience Albert Einstein College of Medicine Bronx, N e w York
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I. 11. A.
Unmodified Membrane.. ,
111. IV. Summary . . . . . . . . .
..........
The movement of ions and water across plasma membranes has been of interest to physiologists for over 100 years. It is now clear that most, if not all, ionic conductance associated with these membranes is attributable to channels, that is, to high dielectric constant, hydrophilic regions spanning the low dielectric constant, hydrophobic bilayers of cell membranes. Presumably these same channels are also permeable to water, although at present there are no data bearing directly on this point. Ion-conducting channels also occur in artificial lipid bilayer membranes; indeed, the first studies of single-channel behavior were made on channels in these model membranes (Ehrenstein et af., 1970; Hladky and Haydon, 1972). For two of these channels, those formed by gramicidin A and the polyene antibiotics nystatin and amphotericin B , water permeabilities have also been determined (Rosenberg and Finkelstein, 1978b; Holz and Finkelstein, 1970), providing the only direct data on water transport through "biological-like'' channels. In addition, water permeabilities of unmodified lipid bilayers are known. This article is a review of the findings from water permeability studies on both unmodified and channel-modified planar 295 Copyright B 1984 by Academic Press, Inc All nghts of reproduction in any form reserved
ISBN 012-153321-2
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ALAN FINKELSTEIN
lipid bilayers, with particular emphasis on the latter, and a discussion of their implications for water transport across plasma membranes. The interesting topic of water-ion interaction within channels is also touched upon in the course of the discussion; a more extensive treatment is given in the article by Levitt in this volume. I. WATER PERMEABILlTY COE FFlClENTS
Before considering water permeability studies on lipid bilayer membranes, let us recall some general definitions and interpretations of water permeability coefficients. On any membrane, two different water permeability measurements can be made, each giving rise to a different water permeability coefficient. In one, a difference in concentration, Ac,, of an impermeant solute is placed across the membrane, causing an osmotic flow of water, @, (expressed as moles per unit time). The relation between @, and Acs is expressed through the osmotic, or filtration, water permeability coefficient ( P I )by the equation @,
=
P f A Ac,
(1)
where A is the membrane area. [In principle, Pf can be obtained by applying a hydrostatic pressure difference (AP),instead of an osmotic pressure difference (AT = RT Acs; where R is the gas constant and T is absolute temperature), across the membrane; that is why the osmotic permeability coefficient is also called the filtration permeability coefficient. In practice, water flow is almost always experimentally generated across lipid bilayers and cell membranes by osmotic pressure differences.] In the other type of measurement, a difference in concentration, Ac*, of isotopic water is placed across the membrane, giving rising to an isotopic flux, @*. The diffusional water permeability coefficient Pd expresses the proportionality between @* and Ac* through the equation @* = -PdA Ac*
(2)
If water transport across a membrane occurs through channels, the corresponding equations are Qw = t ~ p lAc, Q * = -I
Ac*
Z ~ J
(la) (221)
where n is the number of channels in the membrane, and pl and pd are the
WATER MOVEMENT THROUGH MEMBRANE CHANNELS
297
water permeability coefficients p r r d w m i d . These single-channel permeability coefficients, having dimensions of cubic centimeters per second, are related to the corresponding macroscopic permeability coefficients, having dimensions of centinieters per sccond. by the identities p, =
rj,~i~~
(3a)
Pd = PcjA/n
(3b) From the ratio of Pf to P d , interferences can be drawn about the physical nature of the water transpart pathway. If the membrane consists of an organic phase in which water is poorly soluble, then both bulk and isotopic water movement occur by a solubility-diffusion mechanism, and it can easily be shown that PflPd = 1 (Cass, 1968). On the other hand, if water transport is through channels, then, in general, PflPd > 1 , and the larger the channel radius, the larger thc ratio. This is because osmotic water transport occurs by laminar, or quasi-laminar flow (Mauro, 1957). whereas isotopic water transport is diffusional in nature. In fact, insofar as macroscopic hydrodynamic equations are still applicable at the molecular level, which is (surprisingly) often the case (Einstein, 1905: Finkelstein and Rosenberg, 19791, channel radii can be calculated from the value of P,.lPCl(Pappenheimer, 1953; Solomon, 1968). The exceptions to the dependence of PfIP,I on channel radius are those channels which are s o narrow that water molecules cannot pass one another: that is, single-file transport occurs. In those cases, P,/P,I = N , where N is the number of water molecules in single-file array (Levitt, 1974).This surprising result is a consequence of the unusual nature of the diffusion process (which determines P d ) ,in which a water molecule can traverse the channel only if all of the other water molecules ahead of it do so first (Finkelstein and Rosenberg, 1979). In summary, PflPd
=
1
solubility-diffusion trtinsport through hydrophobic phase
transport through channels of radius R > RHZO
single-file transport, where N = number of water molecules in single-file array.
(4a)
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II.
WATER PERMEABILITY OF PLANAR LIPID BI LAYER MEMBRANES
A. Unmodified Membrane
Molecules, including water, cross lipid bilayer membranes by a solubility-diffusion mechanism, and consequently, PfIPC1= 1 (Finkelstein and Cass, 1968). Of greater interest are the actual values of Pr (or P d )in these membranes. Depending on temperature, cholesterol content, chain length, and degree of saturation of fatty acid chains, water permeability coefficients span a 500-fold range from 2 X lop5 (Finkelstein, 1976a) to 1 x cmhecond (Huang and Thompson, 1966). These values encompass almost the entire range of values reported for plasma membranes, a point to which we shall return in our discussion of water movement across cell membranes. In the determinations of water permeability coefficients for nystatin and amphotericin B channels and for gramicidin A channels, discussed in the following sections, the background permeability of the membrane is always subtracted from the measured values. B. Modified Membranes 1. NYSTATIN A N D AMPHOTERICIN B
Nystatin and amphotericin B, which are polyene antibiotics (the former a tetraene, the latter a heptaene), have almost identical chemical structures (Fig. 1); their effects on lipid bilayer membranes are so similar that for purposes of this discussion I shall generally not distinguish between them. Membranes treated with these polyenes “sieve” nonelectrolytes; permeability coefficients decrease with increasing molecular radius for molecules up to the size of glucose (radius = 4 A),above which they are zero (Holz and Finkelstein, 1970). This fact, combined with molecular model building, leads to the belief that nystatin and amphotericin B form transmembrane channels of about 4 A in radius, with the polar interior of the channel lined by hydroxyl groups (Fig. 2) (Finkelstein and Holz, 1973; deKruijff and Demel, 1974). In fact, it appears that these polyenes can form either “single-length’’ or “double-length” channels, the latter being twice the length of the former (see legend to Fig. 21, and that because of flexibility in bilayer structure and thickness, both of these channels can completely span the bilayer (Marty and Finkelstein, 1975). Recent experiments have shown that the ratio of urea permeability to glycerol permeability is the same for single- and double-length channels, thus con-
299
WATER MOVEMENT THROUGH MEMBRANE CHANNELS
OH
0
OH
OH
OH
OH
0
HOOC
0
OH
0
OH
OH
OH
OH
0
OH Arnphotericin B
FIG. I . The structural formulas of nystatin and amphotericin B. (After Medoff and Kobayashi, 1980.)
firming that they have essentially the same radius (Kleinberg and Finkelstein, 1984). As expected for water transport through a channel, PI > P d ; in fact (Holz and Finkelstein, 19701, P I I P ~= 3
(nysttitin and amphotericin B channel)
(5)
The calculated single-channel permeability coefficients for urea are 23 X 10-16 and 3.6 x cm3/second for single- and double-length nystatin channels, respectively (Kleinberg and Finkelstein, 1984).' Since Pfis 42 times greater than Pd (urea) for nystatin channels (Holz and Finkelstein, I Nonelectrolyte and water permeability determinations are, by necessity, made on membranes containing many channels (- lo9channels/cm2),as water flow or isotope flux through fewer channels is experimentally unmeasurable. On the other hand, because of the exquisite sensitivity of electrical measurements, conductances of individual channels are measured on membranes containing one or a few channels. Single-channel permeability coefficients to water and nonelectrolytes are calculated by dividing the measured permeability coefficients by the number of channels in the membrane. The latter is computed by dividing the membrane conductance by the single-channel conductance. on the assumption that the singlechannel conductance in membranes containing lo9 channelskm? is the same as that in a membrane containing one or a few channels. Electrostatic interactions among neighboring channels in close proximity may modify single-channel conductances and hence cause errors in the estimations of the number of channels in the membrane. This, in turn, will cause errors in the calculations of single-chbnnel permeability coefficients. This caveat pertains to all single-channel permeability coefficients discussed in this article.
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ALAN FINKELSTEIN
300
4 \
4
FIG.2. Diagram of a single-length nystatin or amphotericin B channel. Each nystatin (or amphotericin B) molecule is schematized as a plane with a protuberance and a solid dot. The shaded portion of each plane represents the hydroxyl face of the hydroxyl-containing chain, the protuberance represents the amino sugar, and the solid dot represents the single hydroxyl group at the nonpolar end of the molecule. The interior of the pore is polar. whereas the exterior is completely nonpolar. Note that the ring of hydroxyl groups at the top of the figure can hydrogen bond in the middle of the membrane with an identical structure from the other side to form a double-length channel. (From Finkelstein and Holz, 1973.)
1970), we calculate that pf is 9.7 x and 1.5 x cm3/second for single- and double-length nystatin channels, respectively.
2. GRAMKIDINA This pentadecapeptide (Fig. 3) is believed to form channels that are about 2 A in radius. This belief is based both upon molecular model building (Urry, 1972) and upon observations that gramicidin A-treated membranes are permeable to water but not to urea or other small nonelectrolytes (Rosenberg and Finkelstein, 1978b). For the gramicidin A channel (Rosenberg and Finkelstein, 1978b) P f / P d= 5
(gramicidin A channel)
(6)
301
WATER MOVEMENT THROUGH MEMBRANE CHANNELS
CHO
-
L-Val - G l v - L-Alo - 0-Leu
L-Alo - 0-Val - L-Val
L-Trp
-
D-Leu
-
-
D-Val
- L-Trp - D-Leu
L-Trp - D-Leu - L-Trp
-
NHCH2CH20H
FIG. 3. Structure of valine-gramicidin A. Each horizontal row of amino acids corresponds to approximately one helical turn of Urry’s &-helical model (Urry, 1972). The two diagonal lines represent peptide bonds connecting the three helical turns. (After Finkelstein and Andersen, 1981.)
In such a narrow channel, single-file transport of ions and water must occur. The number of water molecules N in single-file array can be determined either from the ratio of PFto P,’ [Eq. (4c)l or from streaming potential measurements. [For the theory behind the latter method for determining N, see Levitt ct d., (1978). Levitt (this volume), or Finkelstein and Rosenberg (1979).] Streaming potential measurements yield values of about 6-7 (Rosenberg and Finkelstein, 1978a) or 8-9 (Dani and Levitt, 1981b) for N . The reasonablc agreement between these values for Nand that determined from P~IP,I[ Eq. ( 6 ) ] provides additional cvidence for single-file transport through the gramicidin A channel. The osmotic water permeability coefficient ( p r ) for this channel has been calculated to be - I x cm3/second by Finkelstein and Rosencm7/secondby Dani and Levitt (1981a). (For a berg (1979) and -6 x possible cause of the sixfold difference in values, see Footnote I . ) I t is noteworthy that the rate of movement for an ion such as Nat from one end of the channel to the other is the same as that for a water molecule (Finkelstein and Andersen, 1981; Dani and Levitt, 1981b). Both require the movement of N water molecules in single-file array; the equality of the two rates means that the movement of these N water molecules is the major barrier to ion transport. In other words, ion-wall interactions and electrostatic energy barriers are minor impediments to ion movement through the channel. There is an additional barrier, however, for ion transport at the end of the channel (the exit step), and this makes the transport rate of ions across the entire channel (as opposed to the transport rate from end to end) less than that for water. This raises the interesting possibility that the water permeability of a gramicidin A channel could be salt dependent; that is, the water permeability of a channel occupied by an ion could be considerably less than that of an unoccupied one (Finkelstein and Rosenberg, 1979). In essence the ion can block the channel to water flow. Dani and Levitt (1981b) report such an effect with Lit, K’,
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and TI+, but Finkelstein (reported in Finkelstein and Andersen, 1981) saw no such effect with Na+. 3. COMPARISON OF NYSTATIN A N D AMPHOTERICIN B CHANNELS WITH GRAMICIDIN A CHANNELS It is instructive to compare the water permeability of the 4-A-radius nystatin and amphotericin B channels with that of the 2-A-radius gramicidin A channel, particularly since these are the only channels in lipid bilayer membranes, or plasma membranes, for which more or less complete information is available. Table I summarizes the results presented in the previous section, along with additional relevant information about these channels. I wish to draw the readers' attention to three points in that table: first, although the radius of the gramicidin A channel is smaller, by a factor of 2, than that of the nystatin and amphotericin B channels, the ratio of Pf to P,! for the gramicidin A channel ( - 5 ) is larger than that for the polyene channels (-3). This is contrary to the general trend for PflPd to decline with decreasing radius [Eq. (4b)], but is not unexpected given the unique nature of the diffusional process in single-file transport, as reflected in Eq. (4c). Second, the values of pr (the osmotic permeability coefficients per channel) differ by up to only an order of magnitude with those calculated from a naive application of Poiseuille's law to these channels of molecular dimension. As noted previously (Finkelstein and Rosenberg, 1979), macroscopic hydrodynamic equations, derived from a continuum theory of fluids, have a way of retaining validity at the molecular level. Third, the conductance of the 2-A-radius gramicidin A channel is COMPARISON
OF
TABLE I GHAMlClDlN A A N D NYSTATIN CHANNELS pr (crn'/second)
Radius
Length
Conductance in 100 mM
Channel
(A)
(A)
KCI ( S )
PSlP,,
Experimental ( x i 0 14)
Grarnicidin A Nystatin (single length) Nystatin (double length)
2
25-30
in
5.3 (3)
1-6 ( 3 . 4 )
3
4
21-25
2.5 x lo-" (2)
-
9.7 (2)
50
4
42-48
1.3 x
in
3.3 (4)
1.5 (2)
25
11
(1)"
13
(2)
Poiseuille's law ( X I O 14)
~~
References: (I) Hladky and Haydon (1972); (2) Kleinberg and Finkelctein (1984); (3) Rwenberg and Finkelstein (l978b); (4) Dani and Levitt (1981a).
WATER MOVEMENT THROUGH MEMBRANE CHANNELS
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almost 100-fold greater than that of the 4-A-radius nystatin channel. Although this article is not directly concerned with ion permeation through channels, 1 feel it is appropriate to point out with this example that it is very risky to infer, as is often done, channel radius from channel conductance. It is obvious that charges associated with a channel can have enormous effects on ion permeability; it is particularly striking in the present examples, however, that a large anomalous conductance difference arises between channels lacking any charge groups. 111.
WATER PERMEABILITY OF PLASMA MEMBRANES
As remarked at the beginning of this article, ion transport through channels in plasma membranes is now well established, and undoubtedly water also passes through these same channels. In this section we will consider the significance of this pathway for water transport, as opposed to diffusion through the bilayer proper of plasma membranes. Because of the large variety of cells and channel types, and the limited data on water permeability through channels, it is not reasonable to expect a single, allembracing answer. What I hope to provide, however, is a general outlook and point of view that is useful in analyzing specific examples. It might be thought that an excellent criterion for the importance of channel pathways in water transport is the value of PtIP,; in particular, values significantly greater than I would clearly indicate that channels were a major contributor to water movement. Unfortunately, with the exception of erythrocyte data, unstirred layer problems cause the values of Pdto be so underestimated that the large values commonly reported for PflPd cannot be attributed to channels in the plasma membrane (Dainty, 1963). We must therefore invoke other arguments in deciding this tissue. The reported range of permeability values for plasma membranes2 excmlsecond for tends over four orders of magnitude-from 1 X Fundulirs eggs (Dunham et a/., 1970) to 2 x cmlsecond for erythrocytes (Side1 and Solomon, 1957); most values fall around 2 x cml second. As was noted in an earlier section, the water permeability coefficients determined for various unmodified lipid bilayers cover most of this to I x lo-* cmIsecond), so that the magnitude of the range (from 2 x water permeabilities of most cell membranes can be accounted for simply I shall not deal with the large water permeability coefficients of “leaky” epithelia, in which the major pathway for water transport may be intercellular (Levitt, 1981). Later in this section, however, 1 consider the large values of PI induced by antidiuretic hormone in the luminal plasma membranes of “tight” epithelia such as toad urinary bladder.
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ALAN FINKELSTEIN
from the properties of the bilayer backbone of the plasma membrane. The very low water permeabilities of plasma membranes such as that of Fundulus eggs presumably result from lipid bilayer compositions with even lower H2O partition and diffusion coefficients than those so far studied in the planar bilayer model membranes. It is worth noting at this point that from a physiological standpoint, most cells do not need or require high water permeabilities, and therefore one does not expect their plasma membranes to have evolved special channels for water t r a n ~ p o r t[Eggs .~ which develop in tidal pools, where osmolarity can vary over wide ranges, must be protected from the vicissitudes of tonicity changes. This they have apparently accomplished both by evolving a bilayer composition and structure that is very impermeant (perhaps because of a high phase transition temperature), and by having a small surface-to-volume ratio (i.e., by being large).] Thus, if a large fraction of the water movement across a cell membrane occurs through channels, this must be incidental to other functions of those channels (e.g., ion permeability) and is not their primary purpose. With this in mind, let us see how things stand with most cells. We may assume that the water permeability of plasma membrane channels will not be significantly greater (and probably in general will be less) than that of single-length nystatin channels. (I base this on the assumption that the ion-selective regions of plasma membrane channels are probably considerably narrower than the 4-A-radius nystatin channel, although these regions may be somewhat shorter than 25 A in length.) Therefore, to account for a Pfof 2 x cm/second, a value around which most cell membrane permeability coefficients lie, there must be approximately loio of these channels ( p f= cm3/second)per cm2 (-lo2 channels/pm2). Single-channel conductances for many channel types in a variety of cells have been measured, and their values tend to be around lo-” S (see, for example, other articles in this volume). On the other hand, the conductances of most cell membranes fall around S/cm2; in other words, they have about lo8 ion-conducting channels/cm2. The Pf attributable to these channels is therefore cm/second, or only about 1% that of the actual value for the cell. In short, there are too few ion-conducting channels in most cell membranes to uct as a sign$cant pathway for water movement; by implication, most of a membrane’s water permeability is attributable to its bilayer structure. The interested reader can apply the above general arguments to his favorite cell, if Pfand single-channel data are available. An exception is the luminal plasma membranes of “tight” epithelia, which are considered later in this section.
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305
An interesting exception to the above considerations is the erythrocyte membrane. The magnitude of P f ( - 2 x 10-I cm/second) (Side1 and Solomon, 1957), the nonunity value of P f l P d (-3) (Paganelli and Solomon, 1957), and the effects of chemical modifications of the cell membrane on water permeability (Macey and Farmer, 1970) provide convincing evidence that a significant fraction of the water movement into and out of the cell occurs through channels. Yet, the conductance of the erythrocyte membrane is very low,
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ALAN FINKELSTEIN
1979). [The channels responsible for the large water permeability of the erythrocyte membrane, presumably the chloride-bicarbonate “carriers,” also have a very small ion conductance (Hunter, 1977).] This is another illustration of my earlier remark that for a channel of a given radius there is an enormous latitude in its possible ion permeability. IV. SUMMARY
The only direct data on water transport through “biological-like” channels come from studies on the channels formed in planar lipid bilayer membranes by gramicidin A and the polyene antibiotics nystatin and amphotericin B. These data were reviewed along with water permeability measurements on unmodified lipid bilayer membranes. From the water permeability coefficients for single nystatin or gramicidin A channels, one can estimate the number of channels required in plasma membranes to account for their water permeability. The general conclusion is that there are too few channels in most plasma membranes to represent a significant pathway for water movement, and therefore, by implication, the major route for water transport across most plasma membranes is through their lipid bilayers. Two exceptions are noted: the erythrocyte membrane and the luminal membranes of certain “tight” epithelia. It appears that a major pathway for water permeation across the erythrocyte membrane is through the anion “carrier” protein. This water transport is incidental to the main function of the “carrier.” Indeed, it is pointed out that most cells do not require high water permeabilities, and therefore one does not expect to find in their plasma membranes channels specifically devoted to water movement. An exception are the luminal membranes of such “tight” epithelia as toad urinary bladder and cortical collecting tubule. The ADH-induced water permeability of these membranes is through specific channels that are permeable to water and very little else. Since the water permeability of these membranes is of great physiologic concern to the organism, it is not surprising to find channels in them especially devoted to water transport. ACKNOWLEDGMENT This work was supported by NIH Grant GM 29210-06. REFERENCES Brahm, J . (1982). Diffusional water permeability of human erythrocytes and their ghosts. J . Gen. Physiol. 79, 791-819.
WATER MOVEMENT THROUGH MEMBRANE CHANNELS
307
Cass, A. (1968). Water and ion permeability of thin lipid membranes. Doctoral Thesis, pp. 119-121. Rockefeller University, New York. Dainty, J. (1963). Water relations of plant cells. Adu. Bot. Res. I, 279-326. Dani, J. A., and Levitt, D. G . (1981a). Binding constants for Li’. K + , and TI’ in the gramicidin channel determined from water permeability measurements. Biophys. J . 35, 485-500. Dani, J . A., and Levitt, D. G . (198lb). Water transport and ion-water interaction in the gramicidin channel. Biophys. J . 35, 501-508. deKruijff, B . , and Dernel, R. A. (1974). Polyene antibiotic-sterol interactions in membranes of Acholeplusmu laidlawii cells and lecithin liposomes. Ill. Molecular structure of the polyene antibiotic cholesterol complexes. Biochim. Bioplrys. Acrci 339, 57-70. Dunham, P. B.. Cass, A., Trinkaus, J . P., and Bennett, M. V. L. (1970). Water permeability of Fi~nditluseggs. B i d . Bull. ( Woods Hole, Muss. ) 139, 420-421. Ehrenstein, G . , Lecar, H., and Nossal, R. (1970). The nature of the negative resistance in bimolecular lipid membranes containing excitability-inducing material. J . Gerr. Physiol. 55, 119-133. Einstein. A. (1905). On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat. [Translated from Atin. Phys. ( L e i p z i r ) [4] 17,549-560.1 In “Investigations on the Theory of the Brownian Movement by Albert Einstein” (R. Furth, ed.; transl. by A. D. Cowper), pp. 1-18. Dover, New York, 1956. Finkelstein, A. (1976a). Water and nonelectrolyte permeability of lipid bilayer membranes. J . Gen. Physiol. 68, 127-135. Finkelstein, A. (1976b). Nature of the water permeability increase induced by antidiuretic hormone (ADH) in toad urinary bladder and related tissues. J . Gen. Physiol. 68, 137143. Finkelstein, A., and Andersen, 0. S. (1981). The gramicidin A channel: A review of its permeability characteristics with special reference to the single-file aspects of transport. J . Membr. Biol. 59, 155-171. Finkelstein, A,. and Cass, A. (1968). Permeability and electrical properties of thin lipid membranes. J . Gen. Physiol. 52, 145s-172s. Finkelstein, A., and Holz, R. (19731. Aqueous pores created in thin lipid membranes by the polyene antibiotics nystatin and amphotericin B . I n “Membranes 2. Lipid Bilayers and Antibiotics” ( G . Eisenman, ed.), pp. 377-408. Dekker, New York. Finkelstein, A., and Rosenberg, P. A. (1979). Single-file transport: Implications for ion and water movement through gramicidin A channels. Membr. Trunsp. Proc,es.ses 3, 73-88. Hladky, S. B., and Haydon, D. A . (1972). Ion transfer across lipid membranes in the presence of gramicidin A. 1. Studies on the unit conductance channel. Biochim. Biophys. Acta 274, 294-3 12. Holz, R., and Finkelstein, A. (1970). The water and nonelectrolyte permeability induced in thin lipid membranes by the polyene antibiotics nystatin and amphotericin B. J . Gen. Physiol. 56, 125-145. Huang, C.. and Thompson, T. E. (1966). Properties of lipid bilayer membranes separating two aqueous phases: Water permeability. J . Mol. Biol. 15, 539-554. Hunter, M. J . (1977). Human erythrocyte anion permeabilities measured under conditions of net charge transfer. J . Physiol. (London) 268, 35-49. Jones, M . N., and Nickson, J. K. (1981). Monosaccharide transport proteins of the human erythrocyte membrane. Biochim. Biophvs. Actu 650, 1-20. Kleinberg, M. E., and Finkelstein, A. (1984). Single-length and double-length channels formed by nystatin in lipid bilayer membranes. J . Memhr. B i d . (in press).
308
ALAN FINKELSTEIN
Knauf, P. A. (1979). Erythrocyte anion exchange and the band 3 protein: Transport kinetics and molecular structure. Curr. Top. Mefnbr. Trump. 12, 249-363. Levitt, D. G. (1974). A new theory of transport for cell membrane pores. I. General theory and application to red cell. Biochim. Biophys. Acta 373, 115-131. Levitt, D. G. (1981). Routes of membrane water transport: Comparative physiology. Alfred Benzon Symp. 15, 248-257. Levitt, D. G . , Elias, S. R., and Hautman, J. M. (1978). Number of water molecules coupled to the transport of Na’, K’, and H+ via gramicidin, nonactin, or valinomycin. Biochim. Biophys. Acta 512, 436-451. Macey, R. I., and Farmer, R. E. L. (1970). Inhibition of water and solute permeability in human red cells. Biochim. Biophys. Actu 211, 104-106. Marty, A., and Finkelstein, A. (1975). Pores formed in lipid bilayer membranes by nystatin. Differences in its one-sided and two-sided action. J . Gen. Physiol. 65, 515-526. Mauro, A. (1957). Nature of solvent transfer in osmosis. Science 126, 252-253. Medoff, G., and Kobayashi, G. A. (1980). The polyenes. In “Antifungal Chemotherapy” (D. C . E. Speller, ed.), pp. 3-33. Wiley, New York. Paganelli, C. V., and Solomon, A. K. (1957). The rate of exchange of tritiated water across the human red cell membrane. J . Gen. Physiol. 41, 259-277. Pappenheimer, J. R. (1953). Passage of molecules through capillary walls. Physiol. Rev. 33, 387-423. Rosenberg, P. A., and Finkelstein, A. (1978a). Interaction of ions and water in gramicidin A channels. Streaming potentials across lipid bilayer membranes. J . Gen. Physiol. 72, 327-340. Rosenberg, P. A , , and Finkelstein, A. (1978b). Water permeability of gramicidin A-treated lipid bilayer membranes. J . Gen. Physiol. 72, 341-350. Sha’afi, R. I., and Feinstein, M. B. (1977). Membrane water channels and SH-groups. Adu. Exp. Med. Biol. 84, 67-83. Sidel, V. W., and Solomon, A. K. (1957). Entrance of water into human red cells under an osmotic pressure gradient. J . Gen. Physiol. 41, 243-257. Solomon, A. K. (1968). Characterization of biological membranes by equivalent pores. J . Gen. Physiol. 51, 335s-364s. Solomon, A. K., Chasan, B., Dix, J. A . , Lukacovic, M. F., Toon, M. R., and Verkman, A. S. (1983). The aqueous pore in the red cell membrane: Band 3 as a channel for anions, cations, nonelectrolytes and water. Ann. N . Y . Acad. Sci. 414, 97-124. Urry, D. W. (1972). Protein conformation in biomembranes: Optical rotation and absorption of membrane suspensions. Biochim. Biophys. Acta 265, 115-168.
CURRENT TOPICS IN MEMBRANL S A N D TRANSPORT. VOLUME 21
Channels with Multiple Conformational States: Interrelations with Carriers and Pumps P . LAUGER Department of Biology University of Konsfanz Konstanz, Federal Republic of Germany
1. Introduction.. .......................................................... 309 11. Coupling between Ion Flow and Conformational Transitions. . . . . . . . . . . . . . . . . 310 A. Properties of a Two-State Channel with Single Binding Site . . . . . . . . . . . . . 310 B . Carrierlike Behavior of Channels..................................... 316 C. Nonequilibrium Distribution of Long-Lived Channel States. . . . . . . . . . . . . . 317 111. Current Noise in Open Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 IV. Conformational Transitions Driven by an External Energy Source: Ion Pumps. 32 I V. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 References . . . . . . . . . . . . . . ......... .... 325
1.
INTRODUCTION
The transport pathway of an ion across a channel may be visualized as a sequence of energy wells separated by activation barriers. According to this picture ion movement within the channel is described as a series of thermally activated jumps over energy barriers. In the traditional treatment of ionic channels, the energy levels of wells and barriers are considered to be fixed, i.e., independent of time and independent of the movement of the ion. This description, which corresponds to an essentially static picture of protein structure, represents a useful approximation in certain cases. Recent studies of protein dynamics, however, suggest a more general concept of channel behavior. A protein molecule in thermal equilibrium may assume a large number of conformational states and may rapidly move from one state to the other 309 Copyright 0 19x4 hy Academic Prey\. Inc All rights ot reproduction in m y form reyerved IFBN 0-1?-1573?1-?
310
P. LAUGER
(Frauenfelder et al., 1979; Karplus, 1982). Evidence for fluctuations of protein structure comes from X-ray diffraction and Mossbauer studies (Huber et af., 1976; Parak et al., 1981), from optical experiments (Lakowicz and Weber, 1980), and from the kinetic analysis of ligand rebinding to myoglobin after photodissociation (Austin et af., 1975). These and other studies have shown that internal motions in proteins occur in the time range from picoseconds to seconds. The existence of conformational substates may be inferred from the observed electrical properties of a channel. Transitions between long-lived substates can be directly detected in records of single-channel currents (Hamill and Sakmann, 1981). Short-lived substates may escape detection because of the limited bandwidth of the measuring circuit, in which case the observed single-channel current represents an average over unresolved conductance states. As is discussed below, the existence of such “hidden” substates may strongly influence the measurable properties of (average) single-channel conductance. Of particular interest is the possibility that transitions between conformational states of the channel protein may be coupled to the translocation of the ion within the channel (Frehland, 1979). In this case the permeability of the channel depends explicitly on the rate constants of conformational transitions. An extreme situation arises when a channel can assume two conformations, one with the binding site accessible only from the left, and the other with the binding site accessible only from the right. In this case-in which ion translocation through the channel is limited by the rate of interconversion of the two states-the channel exhibits a carrierlike behavior. Another interesting consequence of coupling between ion translocation and conformational transitions is that if ions are driven through the channel by an external force (a difference of electrochemical potential), a nonequilibrium distribution of conformational states is created. As discussed below, this may result in an apparent violation of microscopic reversibility, i.e., in a situation in which the frequency of transitions from state A to B is no longer equal to the transition frequency from B to A. II. COUPLING BETWEEN ION FLOW AND CON FORMATIONAL TRANS ITIONS
A. Properties of a Two-State Channel with Single Binding Site
In order to analyze the effects of coupling between ion flow and conformational transitions, we consider a channel which fluctuates between two
CHANNELS WITH MULTIPLE CONFORMATIONAL STATES
31 1
FIG.1. Energy profile of a channel with two conformational states. v' and v" are the frequencies of jumps from the solutions into the empty site; p' and p" are the jumping frequencies from the occupied site into the solutions. c ' , c " and $"are the ion concentrations and the electrical potentials in the left and right aqueous solutions, respectively.
conductance states A and B. We assume that the rate of ion flow through the channel is limited by two (main) barriers on either side of a single (main) binding site (Fig. 1). In series with the rate-limiting barriers, smaller barriers may be present along the pathway of the ion (this corresponds to a channel consisting of a wide, water-filled pore and a narrow part acting as a selectivity filter-see, for instance, Miller et al., this volume). Since the binding site may be empty or occupied, the channel may exist in four substates (Fig. 2): A": conformation A, empty; A*: conformation A, occupied; Bo: conformation B, empty; and B*: conformation B, occupied. In general, the rate constants for transitions between A and B depend on whether the binding site is empty or occupied (i.e., k i f~ k i and ~ ktA # kgA).The coulombic field around the ion tends to polarize the neighborhood by reorienting dipolar groups of the protein, and in this way the probability of a given transition may be strongly affected by the presence
FIG.2. Transitions between four substates of a channel with one binding site. A": conformation A , empty; A*: conformation A , occupied; B": conformation B, empty; B*: conformation B, occupied.
312
P. LAUGER
of the ion in the binding site. Transitions between empty and occupied states occur by exchange of an ion between the binding site and the left or right aqueous phase (Fig. I): VA
=
va
VB
=
VL
PA
+ u i = c ’ p a + c”pi + uh = c’pk + c”pL Px;
+
(1)
(2)
(3) In Eqs. (1) and (2) it is assumed that ions in the energy wells outside the rate-limiting barriers are always in equilibrium with the corresponding aqueous phase. The jumping frequencies v i , vi, u;, and u: into the empty side are then proportional to the aqueous ion concentrations c ’ and c”, whereas the rate constants p i , p i , pk, and p i for leaving the site are independent of c’ and c”’. p A , p i , p b , and p i are concentration-independent rate constants. The principle of microscopic reversibility requires that the rate constants obey the following relation (Lauger et id., 1980): P A
=
f
PB = PL
Pi
where z is the valency of the ion, u is the voltage across the channel, and uo the equilibrium voltage of the ion, both expressed in units of RTIF ( R , gas constant; T, absolute temperature: F, Faraday constant): u = (I//’ -
$”)/(RTIF)
(5)
zuO = ln(c”/c’)
(6) where $‘ and $” are membrane potentials on either side of the membrane (compare Fig. 1). Using the equilibrium constants KO and K* between the conformational states, (7) the stationary ion flux CD through the channel from solution‘ to solution” is obtained as (Lauger et al., 1980) KO
= (l/a)[I
=
kiB/k:A;
K*
= kiB/k$A
- eXp(ZU0 - Z U ) ] [ U A p . k ( 1
+ VB/kiA + pB/kgA)
+ VL&(KOK* + K * U A / k ! A + KO/.LA/k$A) + K*Uk/.AL + K”U&A] (1
+
KO)
+ (I + -k
(PA
+
K*PB
(8)
+PAPB~~~A)
+ K”UB + U A V B / k i A ) UA,UB(K*/kiA + I / k g A ) f UBpA(KOIk&j + l / k i A ) K * ) (UA
(9)
313
CHANNELS WITH MULTIPLE CONFORMATIONAL STATES
The ion flux @ is proportional to the driving force [ I - exp(zuO- z u ) ] = [l - exp(-Afi/RT)], as expected (Afi is the electrochemical potential difference of the ion). Equation (8) has the interesting property that @ explicitly depends on the rate constants k I B ,k i B , k i A . and kgA. This is an expression of the phenomenon of coupling between ion translocation and conformational transitions. Similarly, it is found that the equation for the probability of a given conformational state not only contains the equilibrium constants K O , K * , V A / ~ A and , V B / ~ B but , depends explicitly on the translocation rate constants pa, p i , p;J, and p:. An essential condition for the occurrence of coupling is the assumption that transitions between the two conformations can take place both in the empty and in the occupied state of the binding site. If transitions can start only from one of the states ( k ; ~= k ; = ~ 0 or k i =~ k i A = 0) then the dependence of @ on the rate constants of conformational transitions is lost. Conformational transitions with a rate that is comparable to or slower than the rate of ion translocation between binding sites may be important for the conduction mechanism in the gramicidin channel (Andersen, 1975; Urry et al., 1981).
I . CONCENTRATION DEPENDENCE OF CONDUCTANCE c"
The ohmic conductance A of the channel under the condition c.' = c is obtained from Eqs. (8) and (9) in the form
R ( c ) = ( z ? F 2 / R T [) c ( a + /3c)/(y + 6c
+ EC~)]
=
(10)
The parameters a,/3, y , 6, and E are concentration-independent combinations of the rate constants: (Y
papA(I
+ pg/k$A) + ~ ; ~ ; I K ' ( K * + pA/kgA)
+ P a p L K * + PLpAK"
(11)
p
(PBPkPk
(12)
Y
(1 +
(13)
6
~ A / . L B (l / k ; ~
E
+ ( I + K*)(PA + ~ B K " ) pApe(l + ~ * ) / k i A
KO)
+ pApbpbK*)/k!A (PA + ~ B K *+ p A p d k $ A )
+ K*/ktA) +
l / k i ~+
K"/~$A)
(14) (15)
+ pi
(16) It is seen from Eq. (10) that N c ) is a nonlinear function of ion concentration containing terms which are quadratic in c . This behavior may be compared with the properties of a one-site channel with fixed barrier PA
pi f pi;
PB
pb
314
P. LAUGER
structure which always exhibits a simple saturation characteristic of the form (Lauger, 1973; Lieb and Stein, 1974) A(c) = ( z 2 F 2 / R T )[ p c l ( p + pc)l (p’p’’lp)
(17) It can easily be shown that for certain combinations of rate constants A(c) goes through a maximum with increasing ion concentration. Such a nonlinear concentration dependence of conductance is usually taken as evidence for ion-ion interaction in the channel or for the existence of regulatory binding sites. In the channel model discussed here the nonlinearity of A(c) is a direct consequence of the coupling between ion flow and conformational transitions. For the further discussion of Eq. (10) it is useful to consider two limiting cases in which conformational transitions are either much slower or much faster than ion translocation.
2. SLOWCONFORMATIONAL TRANSITIONS Under this condition k i ~ k ,i A , k f A<< pa, p l , pk, p:, u a , u x , mean lifetime of a given state is much longer than the average time an ion spends in the energy well, which may be as short as lo-” seconds. Since many ions pass through the channel during the lifetime of the individual state, a well-defined conductance can be assigned to each state. On the other hand, the frequency of transitions between state A and state B may still be much too high to be resolved in a single-channel record. The observed current is then averaged over the two rapidly interconverting conductance states. Under the conditions given above, Eq. (10) reduces to ub , u i ) , the
N c ) = PAAA+ (1 - PA)AB
(18)
where A A and RB are the conductances of the channel in states A and B , respectively, which have the form of Eq. (17). p A is the probability of finding the channel in state A (Aoor A*) which, in the vicinity of equilibrium, is given by (with KA = P A / p A , K B = PB/pB, and K*KA = KOKB) P A = (1
+ C K A ) / [+~ K o + (1 + K * ) C K A ]
(19)
According to Eq. (Is), A is equal to the weighted average of the conductances in states A and B. Since not only AA and AB but also pA contains the ion concentration c , the concentration dependence of A is different from the simple saturation characteristic given by Eq. (17). Furthermore, it is interesting to note that the conductance A in Eq. (18) contains only the equilibrium constants K O and K* (through P A ) but not the single rate constants of conformational transitions. This means that in the limiting
CHANNELS WITH MULTIPLE CONFORMATIONAL STATES
31 5
case considered here ion flow is no longer coupled to conformational transitions. If the frequency of conformational transitions is so low that discrete conductance states can be observed in a single-channel current record, the mean lifetimes T A and rB of the two conductance states can be deter~ the conditional probability that the channel is in mined. If p i = p i / p is state An (given that it is in state A" or A*) the transition frequency I / T A is + ( I - p i ) k z ~This . yields, in the limit of slow conformaequal to tional transitions, T A = (PA
+
+
vAY(/JA~~B
vAkiB)
(20) + VR)/(PBk;A + V B k g A ) Thus, the mean lifetimes depend on ion concentration (through vA and v B ) . Only when the transition frequencies are unaffected by the presence of the ion in the binding site ( k i = ~ k i ~k ,i A = k $ ~are ) the lifetimes given by the usual concentration-independent relations T A = l / k h and 713 = 78 = (pi3
I/k;A.
3. FASTCONFORMATIONAL TRANSITIONS When interconversion of states A and B is much faster than ion transfer between binding site and water ( k i ~ k&, , k i A , k g >> ~ PA, kug, V A , V B ) , coupling between ion translocation and conformational transitions is, again, lost. This is because states A and B are always in equilibrium with each other, even for nonzero ion flow through the channel. This equilibrium may be described by introducing the probability p i that an empty channel is in state A and the probability p i that an occupied channel is in state A: p i = l / ( l KO); 0; = I / ( ] -k K * ) (21) Under the condition of fast conformational transitions Eq. (10) reduces to the simple form of Eq. (17) when the following substitutions are introduced:
This means that in the limit of fast interconversion of states the equation for A becomes formally identical with the corresponding equation derived for a channel with fixed barrier structure, provided that the rate constants are replaced by weighted averages of the rate constants in the two states. This result, which can be generalized to multisite channels with more than
316
P. LAUGER
two conformational states (Lauger et al., 1980), has to be expected since under the above conditions the lifetime of a given conformation is much shorter than the time an ion spends in the binding site and therefore the ion "sees" an average barrier structure. Despite the formal identity of the conductance equation with Eq. (17), the interpretation of the transport process in a channel with variable barrier structure is different; since an ion will preferably jump over the barrier when the barrier is low, this means that the jump rate largely depends on the frequency of occurrence of conformational states with low barrier heights. B. Carrierlike Behavior of Channels
A special situation (with strong coupling) occurs when in state A the barrier to the right is very high (binding site mainly accessible from the left) while in state B it is the barrier to the left that is high (binding site mainly accessible from the right). In this case neither state is conducting, but ions may pass through the channel by a cyclic process in which binding of an ion in state A from the left is followed by a transition from A to B and release of the ion to the right (Fig. 3). In this case the channel approaches the kinetic behavior of a carrier. (A carrier is defined as a transport system with a binding site that is exposed alternately to the left and to the right external phase.) Indeed, in the limit p i = p: = 0 , pa = pb
A0
A*
t
FIG.3. Carrierlike behavior of an ionic channel results from transitions between two conformational states A and B, where in state A the binding site is accessible (mainly) from the left and in state B accessible (mainly) from the right. During the cycle Ao+ A* + B* -+ Bo+ Ao an ion is translocated from left to right.
CHANNELS WITH MULTIPLE CONFORMATIONAL STATES
317
From these considerations it becomes clear that channel and carrier mechanisms are not mutually exclusive possibilities. Rather, a carrier may be considered as a limiting case of a two-state channel with coupling between ion flow and conformational transitions. Apart from mobile (translatory) carriers of the valinomycin type (Lauger er al., 198 1) which represent a distinct class of transport systems, carriers in cellular membranes are likely to function by cyclic conformational transitions in which only part of the carrier molecule moves with respect to the membrane. The idea that carrier operation may involve conformational transitions switching a binding site from a left-exposed to a right-exposed state has been extensively discussed in the literature (Patlak, 1957; Jardetzky, 1966; LeFevre, 1975; Klingenberg rt al., 1976). Experimental evidence for the existence of a conformational state differing in the orientation of the binding site has been obtained, for instance, in case of the ADP/ATP exchange system in mitochondria (Klingenberg et al., 1976). C. Nonequilibrium Distribution of Long-Lived Channel States
In this section we consider a channel with a single binding site and three conformational states, A, B, and C. The lifetimes of the states are assumed to be sufficiently long so that transitions may be directly observed in current records (Fig. 4).In this case, again, many ions enter and leave the binding site during the lifetime of a given conductance state. A macroscopically observable transition, for example A to B, can result, at the microscopic level, from a transition A('+ B" (binding site empty) or from a transition A* + BY (binding site occupied). The distinction between these two elementary processes is meaningful as long as the actual duration of a conformational transition is shorter than the mean lifetimes of the
P. LAUGER
318
t current
time + FIG. 4. Single-channel record showing transitions between three different conformational states of the channel. fAB andfBAare the observed frequencies of transitions A 3 B and B .+ A , respectively.
empty and occupied states of the binding site. Accordingly, the microscopic description of the transition frequencies may be based on the scheme shown in Fig. 5 . Transition frequenciesfxy from state X to state Y (X, Y = A, B, C) may be obtained from single-channel current records such as that shown schematically in Fig. 4 (Hamill and Sakman, 1981). For a cyclic interconversion of three states, A S B
%4! C
the principle of microscopic reversibility requires that under equilibrium conditions the transition frequencies in both directions be the same (fxY = .fyx). If, however, transitions between conformational states are coupled to ion translocation, one may expect that the symmetry relationfxy = fYx no longer holds when ions are driven through the channel by an external force. Deviations from the symmetry relation have recently been observed in studies of acetylcholine-activated channels (Hamill and Sakman, 1981).
C' FIG.5 . Transitions between three conformational states A , B, and C of a channel. A", B", C": binding site empty; A*, B*, C*: binding site occupied.
319
CHANNELS WITH MULTIPLE CONFORMATIONAL STATES
The expectation that f x y and f y x may become unequal in the presence of a driving force for ion flow is borne out by an analysis of the reaction scheme of Fig. 5. In order to simplify the formal treatment, we assume that in states A and C the binding site is always in equilibrium with the left-hand solution (solution') and in state B with the right-hand solution (solution"). This means that even for nonzero ion flow the ratio of the probabilities of occupied and empty states is given by the corresponding equilibrium constant:
P ~ I P= ~V!~,//..L;E Q A pi/p; = u~~I/..L~QB p:/py, = "[./py,= Q c
Microscopic reversibility requires that the following relations hold:
(X, Y
=
A. B , C)
The total transition frequency f x y of a single channel results from transitions Xo .+ Yoand X* + Y'. Thus, fxu
=
P ~ G+Yp i k &
(35)
The asymmetry in the transition frequencies may be expressed by the quantity p x y : PXY
= (fXY
-
fYX)/(fXY
+ fYX)
p x y is obtained by calculating the probabilities
(36)
p i and p g in the stationary
state. The result reads =
(QB/EAB)[I
PAC = (QB/EAC)[1
exp(zm
-
exP(ZU -
-
wdl(kk3kikkCA - kFBkLkAC) zLlO)l(kFBkiAkAC -
EAC E
k i y
+ Qxk;y
(X, Y
=
A, B, C )
(37)
k i ~ k k k ~(38) ~ )
+ k C B ) + ~ A B ~ B C+ ~k BAA k A C k C B ~ ~ A C ~ C A (+~ ~B BA C )+ ~ A B ~ B C ~+C ~A B A ~ A C ~ C B 2kABkBA(kCA
EAB
kxy
-
(39)
(40) (41)
An analogous expression for p c ~= -pBc is obtained from Eq. (37) by interchanging the subscripts A and C. The result contained in Eqs. (37)( 4 1 ) may be summarized in the following way. The transition frequencies
320
P. LAUGER
are asymmetric (pxy # 0) as long as a driving force for ion flow is present. On the other hand, the asymmetry disappears ( p x y = 0) near equilibrium, where exp(zu - zuo) approaches unity. This has to be expected, since the asymmetry of transition frequencies is a manifestation of a nonequilibrium distribution of conformational states created by ion flow through the channel. It may also be shown using Eqs. (33) and (34) that ~ A and B PAC vanish when the transition rate constants for empty and occupied binding site are the same (&OXy = kZy). In general, however, k i y and k g y are different since the presence of a charge in the binding site changes the electrostatic interaction of the channel with the external field. 111.
CURRENT NOISE IN OPEN CHANNELS
Acetylcholine-activated channels have recently been shown to exhibit random current fluctuations in the open state of the channel (F. Sigworth, 1983, personal communication). An obvious contribution of current noise in open channels results from the statistical nature of ion translocation over barriers (Stevens, 1972; Lauger, 1978; Frehland, 1980). This “transport noise” which is frequency independent up to very high frequencies is likely to represent only a minor noise component in the case of the acetylcholine receptor channel, however. Evidence for a second noise source comes from the large amplitude and the dispersion in the millisecond range of the current fluctuations. A likely explanation for the predominant component of the observed noise is that conductance fluctuations are induced by thermal fluctuations of channel structure (C. F. Stevens, personal communication). Indeed, a protein channel which can assume many conformational states will exhibit conductance fluctuations with a frequency spectrum that is determined by the relaxation times of the protein molecule. The spectral intensity Sl(w) of current noise may be expected to be of the form (w is the angular frequency):
The time constants T ; and the amplitudes Ai are functions of the transition rate constants. Even for the two-state channel with a single binding site discussed above, the expressions for the T~ and A ; are rather complex (Frehland, 1979). In fact, Sl(w) contains as limiting cases the frequency spectra of ion carriers and of channels with simple open-closed kinetics, which are entirely different in shape (Neher and Stevens, 1977; Kolb and Lauger, 1978).
CHANNELS WITH MULTIPLE CONFORMATIONAL STATES
321
For a two-state channel with simple open-closed behavior (k(j4” ~ / T A ,k i A = k g = ~ I/Q) the spectral intensity is given by
=
k i =~
sl(W)
= (/A
- le)’[4T’/(TA
T = TATB/(TB
+ T ” ) ] [ l / ( l + W2T2)]
(43)
+ TB)
(44)
where I A and I B are the single-channel currents in states A and B and T,j and TB are the mean lifetimes, If the experimentally accessible frequencies w are much smaller than I / T only white noise of intensity SI(0)can be observed. According to Eq. (43), SI(O)vanishes when the transitions , + 0). become very fast ( T ~T~~ When a channel carries out random transitions between many conformational substates and when the single transitions cause only minor conductance changes, then a pseudocontinuous behavior results (“channel breathing”). The analysis of such open-channel current noise may be expected to yield important information on the dynamics of channel proteins. IV. CONFORMATIONAL TRANSITIONS DRIVEN BY AN EXTERNAL ENERGY SOURCE: ION PUMPS
The concept of channels with multiple conformational states may be used as a basis for the description of active ion transport. An ion channel functions as a pump when the energy profile of the channel is transiently modified in an appropriate way by an energy-supplying reaction (Patlak, 1957; Jardetzky, 1966; Lauger, 1979). Absorption of a light quantum, transition to another redox state, or phosphorylation of the channel protein may alter the binding constant of an ion-binding site in the channel and, at the same time, change the height of adjacent barriers. In this way an ion may be preferentially released to one side of the membrane, while during the transition back to the original state of the channel another ion is taken up from the opposite side. As a specific example we consider a proton pump driven by the hydrolysis of ATP, such as the proton-translocating ATPases in fungi and higher plants (Goffeau and Slayman, 1981; Poole, 1978). A minimum model of the pumping cycle is depicted in Fig. 6. It is assumed that in the dephosphorylated state (HA) of the pump a proton is located in a binding site which is accessible from the left-hand (cytoplasmic) medium but separated from the right-hand (extracellular) medium by a high barrier. Phosphorylation creates a state HB in which the barrier heights are changed in such a way that the proton is released preferentially to the external medium. After dissociation of H ithe protein is dephosphorylated and relaxes back to a conformation with a low barrier
322
P. LAUGER
H+”
HA*m
ADP
A,
FIG.6. Channel mechanism for an ATP-driven proton pump. The energy profile of the channel is transiently modified by phosphorylation of the channel protein. In the dephosphorylated state HAlA the proton binding site is exposed to the left-hand (cytoplasmic) medium (’) and in the phosphorylated state HB/B to the right-hand (extracellular) medium (”). During the cycle HA + HB + B A + HA a proton is translocated from the cytoplasmic to the extracellular medium. --$
on the left (cytoplasmic) side (B +. A). The original state is restored by uptake of HS from the cytoplasmic side (A +. HA). During the cycle a proton is translocated from the cytoplasm (phase’) to the extracellular medium (phase”). The rate constants for the transitions between HA and HB (Fig. 6) may be written as
where cT,c D , and cp are the concentrations of ATP, ADP, and inorganic phosphate (Pi),respectively. In Eqs. (45) and (46) it is assumed, for generality, that HA may be phosphorylated not only by ATP but also by direct reaction with Pi and that dephosphorylation may take place either by transfer of Pi from the protein to ADP or by release of Pi to the aqueous medium. It may easily be shown that the rate constants p , q , r, and s are connected by
qrlps
=
CTICDEP = 1IK
(47)
where CT, C D , and Cp are equilibrium concentrations and K is the equilibrium constant of ATP hydrolysis. For the rate constants of uptake and release of the proton the same notation is used as in Fig. I and Eqs. (1)(3).
CHANNELS WITH MULTIPLE CONFORMATIONAL STATES
323
If the pump starts to work at zero initial voltage ( V = +' - +" = 0) and equal proton concentrations in both aqueous phases ( c ' = c " ) , a difference in the electrochemical potential pH of H+ builds up, which consists partly in a voltage V and partly in a pH difference. With increasing A&, the rates of the reverse processes (B + H+"-+ HB, HA + A + H+') are enhanced so that eventually a limiting value of At& is reached at which the net rate of proton translocation vanishes. The limiting value of At;iHIF ( F is the Faraday constant) is the so-called protomotive force (pmf) of the pump which is obtained as (Lauger, 1984)
The quantity X is related to the free energy AG of ATP hydrolysis:
For a pump with ideally asymmetric barriers which has the binding site in state A accessible only from the left and in state B only from the right (pA = plf)= V X = V L = 0), Eq. (48) reduces to pmf
RT F
= - In
X 1
+ drcn + s/rcD
If, in addition, phosphorylation-dephosphorylation and proton translocation are perfectly coupled, i.e, if the rate of spontaneous dephosphorylation is small (s << rcD), the protomotive force becomes pmf
=
(RTIF) In X
=
-AG/F
(52)
Under these conditions the pump works with maximum thermodynamic efficiency, converting chemical free energy completely into (electro)osmotic energy. The maximum turnover ratefof the p u m p may be defined as the limiting proton flux (referred to a single pump molecule) which is observed
324
P. LAUGER
under short-circuit conditions for infinitely large driving force (c‘ = c” = c, V = 0, CD = c p = 0, CT + 03). Introducing the proton dissociation constants in the dephosphorylated and phosphorylated state, KA = pilpk and KB = p i l p i , the maximum turnover rate of a pump with ideally asymmetric barriers is obtained as
I KA - -
[.pi
1
-1
1
1
p B
@A
+,+-(1
+&)I
-I
(53)
It is interesting to note that the expression for the protomotive force (Eq. 51) does not contain the proton dissociation constants KA and KB. This means that a pK difference between the phosphorylated and dephosphorylated state is not necessary for a large pmf. The essential feature of the pumping mechanism is a chemically induced change of barrier structure which switches the proton binding site from a left-exposed to a rightexposed state. On the other hand, as seen from Eq. (53), a low pK of the phosphorylated state (KB >> c) and a high pK of the dephosphorylated state (KA << c) is favorable for a high turnover rate of the pump.
V.
CONCLUSION
The notion that the conformation of ionic channels fluctuates in time is suggested by recent studies on the dynamics of proteins. Whereas longlived substates may be directly observed in records of single-channel currents, fast transitions may merely contribute to open-channel noise or may escape detection altogether. Such “hidden” substates nevertheless influence the measurable properties of channels such as the dependence of conductance on ion concentration. Since ions interact with the ligand system of the channel, transitions between different conformational substates will depend in general on whether a binding site is empty or occupied. If the rate of conformational transitions is comparable to the jumping rates of ions in the channel, coupling between conformational transitions and ion flow occurs. In this case the permeability of the channel depends explicitly on the rate constants of conformational transitions. A two-state channel that in one state has the binding site accessible only from the left and in the other state only from the right exhibits carrierlike behavior. Many biological transport systems are likely to function by mechanisms intermediate between a “pure” carrier and a “pure” channel mechanism.
CHANNELS WITH MULTIPLE CONFORMATIONAL STATES
325
The concept of a channel with multiple conformational substates may also be applied to ion pumps. A channel acts as a pump when the barrier structure of the channel is transiently modified by an external energy source in such a way that an ion binding site is switched from a leftexposed to a right-exposed state. In this way cyclic conformational changes driven by an external energy source are coupled to vectorial ion translocation. KEFEKENCES Andersen, 0. S. (1975). I o n specificity o f gramicidin A channels. Proc. 3/11 Inr. Eiophvs. Congr., p. 112. (Abstr.) Austin, K . M . . Heeson. K . W., Eixnstein. L., Frauenfelder, H., and Gunsalus, I. C. (1975). Dynamics of ligand binding to niyoglobin. Bioclrc~rriistry 14, 5355-5373. Frauenfelder, H.. Petsko, G. A., and Tsernoglu, I). (1979). Temperature-dependent X-ray diffraction as a probe o f protein structural dynamics. Narure ( Loridon) 280, 558-563. Frehland, E. ( 1979). Theory o f transport noise in membrane channels with open-closed kinetics. Riopliys. Strrrcr. Mer:h. 5 , 91-106. Frehland, E. (1980). Nonequilibrium ion tran\porl through pores. The influence of barrier structures on current fluctuations, tranuient phenomena and admittance. Biopliys. S/rrii./. Mcjch. 7, 1-16. Goffeau. A,. and Slaynian. C. W. (19x1). The ploton-translocating A'I'Pase o f the fungal plasma menibrane. Bioc,/fi/ri.8iophy.s. A(.rrr 639, 197-223. Hamill. 0. P.. and Sakmmn, B. (1981). Mulliple conductance states o f single acetylcholine receptor channels in embryonic muscle cells. Ntrrrirc (London) 294, 462-464. Huber, K . . Deisenhofer, J., Colman. P. M . . Matshushima. M., and Palm. W . (1976). Crystallographic structure studies o f an IgG molecule and an Fc fragment. Nrrrctrc ( L o w don ) 264, 41s-420. Jardetzky, 0. (1966). Simple allosteric models for membrane pumps. Nrrliirc, ( Loridori ) 211. 969-970. Karplus, M. ( 1982). Dynamics of proteins. Ecr. Btrnsc,ri~e.s.Phys. C/ic,iri. 86, 386-395. Klingenberg. M., Kiccio, P., Aquila. H . . Buchanan, 13. B . , and Grebe, K . (1976). Mechanism o f carrier transport and the ADP. ATP carrier. I N "The Structural Basis of Membrane Function" ( Y . Hatefi and L. qjavadi-Ohaniance, eds.), pp. 293-31 1. Academic Press, New York. Kolb. H.-A,. and Liiuger. P. ( 1978). Spcctral analysis o f current noise generated by carriermediated ion transport. J . Merrihr. Biol. 41, 167-187. Lakowicz, J. K . . and Weber, G . ( I1)XO). Nanosecond segmental mobilities o f lryptophan residues in proteins observed by lifetime-resolved fluorescence anisotrophy. Biopliys. J . 32, 591-600. Liiuger, P. ( 1973). Ion transport through pores: A rate-theory analysis. Bioc./iiiri. Biopl7y.s. A[./
326
P. LAUGER
LBuger, P., Stephan, W., and Frehland, E. (1980). Fluctuations of barrier structure in ionic channels. Biochirn. Biophys. Ac/o 602, 167- 180. L h g e r , P., Benz, R., Stark, G . . Bamberg, E., Jordan, P. C., Fahr, A., and Brock, W . (1981). Relaxation studies of ion transport systems in lipid bilayer membranes. 9. Reu. B i o p h y s . 14, 5 13-598. LeFevre, P. G . (1975). The present state of the carrier hypothesis. Citrr. T o p . M m b r . 7rcrnsp. 7 , 109-215. Lieb, W . K . , and Stein, W . D. (1974). Testing and characterizing the simple pore. Biochirn. Biop/iy.s. Ac/ci 373, 165-177. Neher. E., and Stevens. C. F. (1977). Conductance fluctuations and ionic pores in membranes. Annic. Rcw. Biophys. Bioeng. 6 , 345-381. Parak. F., Frolov, E. N . , Mossbauer, R. L.. and Goldanskii, V . I . (1981). Dynamics of metrnyoglobin crystals investigated by nuclear gamma resonance absorption. J . Mo/. Biol. 145, 825-833. Patlak, C. S. (1957). Contributions to the theory of active transport: 11. The gate type noncarrier mechanism and generalizations concerning tracer flow, efficiency, and measurements of energy expenditure. B i d . M ~ JBiophys. . 19, 209-235. Poole, R. J . (1978). Energy coupling for membrane transport. Annic. R m . Plan/ Physiol. 29, 437-460. Stevens. C. F. (1972). Inferences about membrane properties from electrical noise measurements. Biophys. J . 12, 1028-1047. Urry. D. W., Venkatachalam, C. M . , Prasad. K. U., Bradley, K. J., Parenti-Castelli, 0.. and Lenaz, G. (1981). Conduction processes of the gramicidin channel. In/.J . Q I / L I I I / I ~ Chew.. Qucin/rcm Biol. S y m p . 8, 385-399.
CUKKliNT 'IOPIC'S IN MEMHKANI-S A N D 'I'KANSKOKI'. VOLUMF. 21
Ion Movements in Gramicidin Channels S . B . H L A D K P A N D D . A . HAYDON?
* Depurtmenr
of Piiurtnuidogv f P h y s i o l o g i i d Lahorcitory University o] Ccrmhridge
oritl
Comhriclgc~,EnRlurrd
I. 11.
Introduction . . . . . . . . . . . . . . . . , . Structure . . . . . . .
327 328 328 329 332 332 335
111.
and Physical Properties . . . . . . . . . . . . . . . . . . .
IV. Gramicidin Forms Poreti B . General Features of Ion C. Models for Ion Transpor D. Analysis of Ion Fluxes:
A.
337 340 342 342 342 . . . . . . . . . . 346
..........
348 354 F. Analysis of Ion Fluxes: Flux Ratios.. . . . . . . . 356 357 358 V . Movement of Water through the Pore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 VI. Interactions of Ions and Water in the Pore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 VII. Appendix I . . . . . . . . . . . . . . . . . . .... 363 VIM. Appendix II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 References . . , . , . . . . . . . , . . , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
1.
INTRODUCTION
Gramicidin has the distinction of being the first clearly idcntified and structurally well-characterized ion channel known to function in lipid 327 ('opyripht C ) 19x4 hy Academic Press. Inc. All rights of icproduction in m y form reserved. ISBN 0-12-1?33?1-?
S. B. HLADKY AND D. A. HAYDON
328
bilayers and biological membranes. It has, moreover, remained the only well-characterized channel for over a decade. In a structural sense, gramicidin may not resemble very closely channels of more obvious physiological importance, such as those of the nerve and synapse, but it has a number of properties in common with these channels, and its study has considerably advanced our understanding of the fundamentals of ion permeation. The conductance selectivity, water permeability, and singlefiling characteristics of gramicidin have received particularly close attention. As a polypeptide in a lipid membrane, its stability as a function ofthe membrane structure has also attracted some interest. In this article gramicidin is discussed first with respect to its structure and why it is believed to be a channel, second, with regard to its stability and kinetics of formation and decomposition in lipid membranes, and third, in relation to its ion and water permeability. II. STRUCTURE A. Origins and Primary Structure
The gramkidins, of which there are several, are linear 15-amino acid polypeptides produced by Bacillus hreuis. The naturally occurring gramicidin is a mixture of gramicidin A, B, and C in the approximate ratio 72 : 9 : 19 (Glickson et al., 1972). Gramicidin A (Fig. 1) differs from B and C in that the L-tryptophan in position 1 I is replaced by L-phenylalanine and L-tyrosine, respectively. Most ion permeability studies have been carried out either on gramicidin A or on the natural mixture. There are differences in the single-channel properties of the three polypeptides (Bamberg rr al., 1976), but these are sufficiently small that results obtained for the natural mixture would, in many instances. not be readily distinguishable from those for the pure A analog. The primary structure of gramicidin A (Sarges and Witkop, 1964, 1965) is unusual in several respects. For example, it has a heavy preponderance of hydrophobic amino acids, it has alternating D and L configurations, it Formyl-L-Val-Gly-L-Ala-D-Leu-L-Ala-D-Val-L-Val-D-Val1 2 3 4 5 6 7 8
L-Trp-D-Leu-L-Trp-D-Leu-L-Trp-D-Leu-L-Trp-NHCH CH OH 2 2 9 10 11 12 13 14 15 FIG.I . The amino acid sequence of valine gramicidin A (Sarges and Witkop, 1965). Note the alternation of D- and L-amino acids and the formyl and ethanolamine end groups.
ION MOVEMENTS IN GRAMlClDlN CHANNELS
329
has no ionizable side chains, and the ionic end groups are blocked. The substance is very insoluble in water (probably to 5 1W"' mol liter I) but is soluble in ethanol, dioxan, and other relatively nonpolar solvents, and adsorbs very strongly at air-water interfaces and lipid membranes (Haydon and Hladky, 1972). Despite this, the functional role of gramicidin in B . hrruis is by no means clear. As Ivanov and Sychev (1982) have pointed out, the evidence available suggests that, rather than acting as an inducer of ion permeability, the primary biological purpose of gramicidin is the inhibition of RNA polymerase, with the subsequent development of sporulation. 6. Structure of the lon-Conducting Channel
Ion conduction by gramicidin occurs by pore formation and the pores are made up of two molecules of the polypeptide. These conclusions were reached initially on the basis of electrical measurements of lipid bilayers (Hladky and Haydon, 1970, 1972; Krasne ei d.,1971; Bamberg and Lauger, 1973; Veatch el d.,1975). However, no details of the chemical structure of the channel were revealed by these experiments, and a discussion of the ion conduction is postponed until a later section. The early indications of the likely structure of the conducting channel were obtained from spectroscopic studies of solutions of gramicidin in organic solvents. As a result, Urry (1971), Urry et a / . (1971), and Ramachandran and Chandrasekaran ( I 972) proposed that gramicidin A existed as a left-handed helix, described as a rrl,Dhelix. Urry ef a / . (1971) considered that a range of such helices, differing in the number of amino acids per turn, were theoretically possible. It was also proposed that these helices could form head-to-head (head = formyl end) hydrogen-bonded dimers. so accounting for the fact that two molecules are required for channel formation. The selection of the helix actually involved was made from consideration of the requirements that the channel should be sufficiently long to span a bilayer and that it should permit the passage of ions as observed from conduction studies. The result was the head-to-head --*
(&A
t-
rrf;;) structure with 6.3 amino acid residues per turn, having a length of approximately 28 A and an internal diameter of 4-5 A (Fig. 2a). Six hydrogen bonds link the twa molecules. This rather attractive picture was confused by the discovery by Veatch ef nl. (1974) that, in nonpolar media, gramicidin A forms four dimers which are in equilibrium with each other and with the monomer. It was suggested that these structures were double helices which could either be parallel ( t rrrr) or antiparallel ( t 1rrrr). Since their overall lengths and
330
S. 6. HLADKY AND D. A. HAYDON
a
32
.)-
-+
FIG.2. Left-handed nt:nt:, (a) and t 3. n ni$ (b) helical dimers of gramicidin A . (The hydrogen bonds and the amino acid side chains are omitted for clarity.) [From Ivanov and Sychev. The gramicidin A story. In “Biopolymer Complexes” ( G . Snatzke and W. Bartmann, eds.), pp. 107-125. 0 1982. Reprinted by permission of John Wiley & Sons, Ltd.]
internal diameters were similar to those of the head-to-head helices (Fig. 2b), they were obviously candidates for the conducting structure in the bilayer. Considerable effort has been devoted to trying to distinguish which of the proposed structures is predominent in lipid membranes. A summary of much of this work has been given by Ivanov and Sychev (1982). From recent papers in which nuclear magnetic resonance and circular dichroism techniques have been applied to gramicidin in phospholipid vesicles (Weinstein et al., 1979, 1980; Wallace e t a / . , 1981; Nabedryk et ul., 19821, it now seems beyond reasonable doubt that the effective ion-conducting structure is the head-to-head dimer originally proposed (Fig. 2a). Further, Wallace et ul. (1981) conclude that in a lipid membrane the width and
ION MOVEMENTS IN GRAMlClOlN CHANNELS
331
--t
FIG.3. The Corey-Pauling-Koltun model of lwo molecule\ of gramicidin A in the
7r::)
t
I$: conformation.
length of the channel are not uffected by the binding of ions. The number of and most probable positions of ions in the channel are discussed in more detail in Section IV but it should be mentioned here that ions have been detected in gramicidin channels by X-ray crystallographic techniques (Koeppe rt id., 1979). Two binding sites were found, one close to each end of the channcl. The polypeptide complexes were. howevcr, obtained by crystallization from organic solvents and, although they were helical, it is not clear precisely which helices were present or whether the findings are wholly relevant to ion conduction in membranes. Lipid bilayers of stearoyl or oleoyl lipids in the liquid crystalline state have hydrocarbon region thicknesses of approximately 27 A. The length of the gramicidin channel is thus well adapted to span such a membrane. Moreover, the numerous lipophilic side chains of the constituent amino acids are distributed exclusivcly over the outside of the channel and are thereby in contact with the lipid chains and mostly out of contact with water. The interior of the channel is bounded by the basic peptide chain stabilized by -C=O--H-Nbonds oriented parallel to the axis of the complex. A Corey-Pauling-Koltun model of the dimer is shown in Fig. 3.
332
S. B. HLADKY AND D. A. HAYDON
111.
CHANNEL FORMATION: KINETICS AND EQUILIBRIA
A. Unit of Conductance and the Properties of a Single Channel
One of the properties of gramicidin which has greatly facilitated its study is its readily measurable single-channel conductance and duration (Hladky and Haydon, 1970). Figure 4 shows a typical record of channels opening and closing in a black lipid membrane to which a small amount of gramicidin has been added. Qualitatively similar phenomena can be observed in solventless bilayers as formed by Montal and Mueller (1972) or in bilayers formed from monolayers over the end of patch-clamp pipets (Coronado and Latorre, 1983). For a given lipid, electrolyte solution, and temperature, the conductances of the single channels, as calculated from the height of the smallest current pulses, lie within a very narrow range of values. Thus, only one molecular species appears to be responsible for conduction. It is also found that, for low concentrations of channels, the single-channel conductance is only weakly dependent on membrane thickness (Hladky and Haydon, 1972; Kolb and Bamberg, 1977). This is presumably because the passage through the channel is the rate-determining step for an ion crossing the membrane and, if the channel is of fixed dimensions, then the structure of the lipid surrounding the channel should be of minor importance. This result was one of the first pieces of evidence for pore, as opposed to carrier, transport by gramicidin and is illustrated in Fig. 5 . A further demonstration of the same principle is provided by the experiments of Krasne ct ul. (1971) from which it may be inferred that the channel conductance does not change appreciably as the surrounding lipid undergoes a phase transition. The polar groups of the lipid do, however, influence the channel conductance. Thus, in bilayers of dioleoylphosphatidylcholine the conductance is only -50% of its value in mem-
FIG.4. Conductance transitions in a bilayer of monoolcin + n-hexadecane to which a small amount of gramicidin A has been added. The aqueous phase was CsCl ( I M ) , the applied potential 100 mV, and the temperature 23°C. (From the records ofJ. R . Elliott, with permission.)
333
ION MOVEMENTS IN GRAMlClDlN CHANNELS
branes of monoolein (Zingsheim and Neher, 1974; Bamberg and Lauger, 1974). Further data pertinent to this question have been obtained by Neher and Eibl (1977) in experiments in which the structure of the polar group of a phosphatidylcholine analog was changed systematically. How the polar groups of the lipid affect the channel conductance is not understood. It is not clear, for example, whether the lipid influences the electrolyte ions directly or whether it does so by perturbing the amino acid disposition at the mouth of the channel. Apell et ( I / . (1979) have studied the influence of the negatively charged phosphatidylserine. While the negative charge had the expected effect of increasing the channel conductance at low ionic strengths, no quantitative treatment of the observations was found to be very successful. Studies of the statistics of channel opening show that at low concentrations in the membrane this is a random process; that is, there are no indications of interaction or cooperativity. It is also found that the frequency of occurrence of channels with any given duration declines exponentially as the duration increases (Hladky and Haydon, 1972) (Fig. 6). This is consistent with a closure process which is first order, as would be required if a dimer were to dissociate into monomeric units. Determinations of the temperature dependence of the mean channel duration yield activation energies in the range of 70-80 kJ mol-I. This corresponds satisfactorily with the notion that several hydrogen bonds have to be broken in the dissociation reaction (Hladky and Haydon, 1972; Bamberg and Lauger, 1974). Unlike the single-channel conductance, both the frequency of opening of channels and the mean channel open time or duration are strong funcaqueous solution
7
-Pgromicidin
bilayer
3
JL
channel 0
b
FIG.5 . A schematic illustration of gramicidin A dimeric channels in lipid hilayers. (a) A bilayer of total thickness comparahlp to the length of the channel, e.g.. o f monopalmitolein + squalene. ( b ) A bilayer such as of nionoolein + u-decane which. with the polar groups included. is some 25 A thicker t h m the length of the channel. The single-channel conductance in the thinner membrane is approximately 25%' higher.
334
S. 8.HLADKY AND D. A. HAYDON 1250
-!+
a1000
.-E c
B
Y4-
O
5n
750
0
-ma C
{
500,
'6
ki
n
250,
0 time t
(5)
FIG.6. A cumulative frequency histogram of single-channel durations for gramicidin A in lipid bilayer membranes of monopalmitolein t n-decane. The curve is a single exponential corresponding to a mean channel duration of 1.71 seconds. (Data of Elliott, 1981, with pcrmission.)
tions of the membrane lipid. This becomes clear from a few qualitative experiments. The frequency of opening, however, is meaningful only with a knowledge of the amount of gramicidin in the membrane since, obviously, dimer formation requires encounters between monomers. Unfortunately, there is no simple and precise method of determining the membrane concentration of gramicidin A, and the opening frequency has to be determined by another method to be described below. The variation of channel duration with membrane composition is, by contrast, readily measured. Figure 7 shows records of single-channel events in two membranes, each of monoolein but with different hydrocarbon solvents. This effect is discussed in Section III,C. In the course of testing the dimer hypothesis, a number of chemically linked gramicidin dimers have been synthesized and examined for their conduction properties (Urry et a / . , 1971; Bamberg and Janko, 1977; Fonina et a/., 1982). The linkages have been achieved by means of deriva-
335
ION MOVEMENTS IN GRAMlClDlN CHANNELS
a
3 P A l 10s
b
10s
FIG.7. An effect of membrane composition on single-channel duration: (a) monoolein + squalene; (b) monoolein + decane hilayer. The temperature and applied potential were 23°C and 100 mV, respectively. The aqueous phase in (a) was KCI (0.5 M ) and in (b) was CsCl ( I M).(From the records of J. R . Elliott, with permission.)
tives of dicarboxylic acids [HOOC(CH~),COOHl,and head-to-head, head-to-tail, and tail-to-tail dimers have been produced. It has been shown that the dimers form channels without the need for further association and that their conductances are similar to, though usually less than, that of the normal hydrogen bond-linked gramicidin A dimer. The ion selectivity also remained es3entially unchanged. The mean open time for the chemically linked species was, however, usually one to two orders of magnitude longer than for the hydrogen-bonded channel. B. Multichannel Membranes: High Levels of Conductance
At relatively high concentrations of gramicidin, the unit conductance events shown in Figs. 4 and 7 occur so frequently that many channels are
336
S. 6.HLADKY AND D. A. HAYDON
open simultaneously and the membrane conductance can rise to levels many orders of magnitude larger than that of a single channel. The study of membranes with such high conductances has helped greatly in the elucidation of the kinetics and equilibria of the channel formation reaction. The rate constants of both the formation and the dissociation reactions can be determined by the use of a voltage jump relaxation technique. The equilibrium between conducting and nonconducting gramicidin species in a lipid membrane which contains appreciable amounts of hydrocarbon solvent is strongly dependent on the membrane potential. This is primarily because the forward and back reactions depend upon, among other things, membrane thickness, and the thickness is a function of the membrane potential. Thus, a step change in potential produces a relaxation of the membrane conductance to a new equilibrium value. The half-life of this process depends upon both the rate constants, and these can be extracted by analysis of the conductance transient (Hladky, 1972; Bamberg and Lauger, 1973). The results obtained by Bamberg and Lauger (1973) and Zingsheim and Neher (1974) were consistent with the equations derived for the reaction G + G & Gb,
(1)
where G and G2 represent the gramicidin monomers and dimers, respectively, in the membrane. In other words, the forward reaction was found to be approximately of the second order and the back reaction first order. The dissociation rate constant (k,,) was in close agreement with the values of the same parameter calculated from the single-channel mean duration ( 7 ) where kD = I/T. The forward rate constant ( k R ) was concluded to be several orders of magnitude smaller than the diffusion limiting value. This, it was suggested by Bamberg and Lauger, may be attributed to the fact that a rearrangement of the lipid around the polypeptide is necessary for channel formation. Since the studies were carried out using monoolein- and dioleoylphosphatidylcholine-n-decane membranes of hydrocarbon thickness -48 A it is possible that the local thinning necessary for the monomers to make contact in the middle of the bilayer (Fig. 5 ) is a major inhibitory factor. The experiments of Bamberg and Lhuger and Zingsheim and Neher showed that the channel formation was second order but did not prove that it was bimolecular. This, however, was demonstrated convincingly by Veatch et a / . (1975) by the use of an analog of gramicidin A, dansylgramicidin C. This analog is strongly fluorescent but has conductance properties similar to those of gramicidin A. The fluorescence enabled the
ION MOVEMENTS IN GRAMlClDlN CHANNELS
337
concentration to be determined in planar bilayers simultaneously with the conductance. A quadratic dependence of the conductance on the fluorescence intensity was accurately obeyed in a system in which nearly all the gramicidin was monomeric, showing that the channel is indeed a dimer. Veatch ct a / . also showed thut the equilibrium constant for the monomerdimer reaction was strongly dependent on the lipid composition of the membrane, as had been inferred qualitatively from single-channel studies. Further evidence in support of the dimer model was provided by the synthesis of another analog of gramicidin A , o-pyromellitylgramicidin (Apell rt a / . . 1977). This derivative is appreciably water soluble and, unlike gramicidin A itself, reaches a relatively clear and reproducible adsorption equilibrium with a lipid membrane. When added to the aqueous phase on only one side of the membrane, o-pyromellitylgramicidin increases the conductance very slowly but, when on both sides. it immediately yields the highly conducting membranes found for gramicidin A. It is also found that the conductance increases with the square of the aqueous concentration. Thus, in addition to substantiating the dimerization mechanism, these experiments also suggest that the dimers are formed by the interaction of monomers from opposite sides of the bilayer. C. Dependence of Channel Stability on Membrane Composition and Physical Properties
The equilibrium constant K for the dimerization of gramicidin may be expressed conventionally as
By the use of o-pyromellitylgramicidin, the value of K has been examined in monoolein bilayers in which the hydrocarbon thickness and surface tension have been varied by equilibrating the membranes with different hydrocarbon solvents. For membranes of monoolein + n-hexadecane, K was some lo4 times larger than for membranes of monoolein + n-heptane. It is known from measurements of mean channel duration (7)that k,, is smaller for the hexadecane than for the heptane membrane but this difference is little more than one order of magnitude; the remaining responsibility for the difference lies in kit. The large variation in K has been accounted for in terms of the work required to deform the bilayer during channel formation (Hendry et d.,1978). Thus, in Fig. 5a where the thickness of the bilayer is equal to the channel length no extra work is required but, in a situation such as i n Fig. Sb, the deformation of the membrane involves a displacement of the lipids from their normal positions. The
338
S. B. HLADKY AND D. A. HAYDON
work done may be estimated roughly by assuming a square-well deformation of the surface (radius r ) and a constant surface tension (u)(Fig. 8). An expression for the equilibrium constant may then be deduced and tested. To a first approximation,
K
=
KOexp[-2~r(u/2)(h - ho)/kTl
(3)
where h and ho are, respectively, the thickness of the membrane and the length of the channel, k is the Boltzmann constant, and T is the absolute temperature. KO is the equilibrium constant when h = ho. With ho = 28 A, r = 8 A, and with h and u/2 determined respectively from capacitance and contact angle measurements (Requena rt ul., 1973, Eq. (3) was found to hold to within experimental error (Hendry Pt al., 1978). If this model is correct, therefore, the forward rate constant k R in particular should depend strongly on the thickness and surface tension of the bilayer in which the channels are forming. As yet very little is known about how k R depends on other variables such as the chemical nature of the lipid polar groups. The factors which determine the dissociation rate constant k D have been more thoroughly examined. Correlations between In kD and the membrane surface tension have been found (Neher and Eibl, 1977; Rudnev et ul., 1981). However, it seems that thickness must also play some part. Thus, in monoglyceride bilayers of decreasing thickness, k D eventually becomes roughly constant when the channel length and membrane er +I
,a12
I
I I
I I /
aqueous phase
FIG.8. An illustration of the parameters used in Eqs. (3) and ( 5 ) . (r/2 is the Gibbs surface tension of one side of the lipid bilayer; r is the radius of the equivalent square-well deformation of the membrane; H is the angle between the lipid surface and a normal to the plane of the membrane; k and h,, are, respectively, the thickness of the membrane and the length of the channel.
ION MOVEMENTS IN GRAMICIPIN CHANNELS
339
thickness are similar (Elliott et ul., 1983). This observation can be rationalized by supposing that the membrane tension tends to destabilize the dimeric channel only when it has a component acting parallel to the axis of the channel, i.e., when the angle 6' in Fig. 8 is less than 90". It can then be argued that the activation energy AGq:needed to raise the conducting complex to its transition state would be smaller by an amount AG:determined by the magnitude of the surface tension and the distance 5 through which it acts. In the conventional notation of Eyring rate theory kD =
v exp(-AG$kT) exp(-AG:/kT)
where v is a frequency factor and AGtis the activation energy when 90". AG; may be written AG:
=
51((~/2)cos 0
(4) 6, =
(5)
where I is the effective perimeter of the channel and 5, a/2, and 8 are as described above. For a range of monoglyccride membranes for which ( ~ / 2 was known and 8 could be crudely estimated, the plot of loglokl, versus ( d 2 ) cos B was, as required, fairly linear (Fig. 9) (Elliott el a / . , 1983). The
((U2)cos e (mN rn-')
FIG. 9. A test of Eqs. (4)and (5). k ~ is, the dissociation rate constant of gramicidin. A dimeric channels in lipid bilayers foknied from monoglycerides and hydrocarbons. (r/2 is the Gibbs surface tension of one side ofthe bilayer and His the angle a( which the tension acts on the channel (see Fig. 8). The three points which lie on the ordinate are for membranes of thickness less than or equal to that of the channel and for which H has therefore been taken as 90".(From Elliott e l d.,1983; with permision.)
340
S. B. HLADKY AND D. A. HAYDON
results of Neher and Eibl (1977) and of Rudnev rt ( I / . (1981) for membranes of other lipids yield, as far as can be seen from the more limited data, plots which are roughly parallel to that for the monoglycerides. This suggests that, although the chemical nature of the lipid is of considerable importance in determining A c t o r v (or probably both these parameters), variations in surface tension and perhaps also thickness still influence kl, in the same way. A curious feature of the results is that for any reasonable value of the channel perimeter I, 5 is relatively large (- 15 A). This implies that, in the transition state, the two monomers are much further apart than needed for the breakage of the hydrogen bonds between the two polypeptide helices. However, as Elliott et a / . (1983) have pointed out, it is possible that a water bridge is formed in the center of the bilayer when the monomers move apart. The ends of the gramicidin molecules are hydrophilic and the channel is permeable to water. There is consequently some reason to think that water would tend to fill a hole transiently produced between the two parts of the channel. D. Effects of Anesthetics A large variety of relatively inert lipophilic or amphipathic substances, including many general anesthetics, perturb the ion-conducting channels of the nerve and synapse (Seeman, 1972). The mechanisms by which these substances act are not well understood owing largely to the complexity and unknown structure of the channels involved. It is therefore of interest that some, at least, of the same substances have a marked effect on the conducting properties of gramicidin. The influence of hydrocarbons has already been described in the previous section where it was shown that, although the single-channel conductance was not changed, the rate constants for formation and dissociation of the channels were respectively decreased and increased. For the shorter chain n-alkanes (i.e., smaller than n-decane) in monoolein membranes at concentrations approaching saturation in the aqueous phase, the changes in the formation rate constant and in the equilibrium constant were very large. Although substances other than the hydrocarbons have not been investigated so thoroughly, some results for the n-alkanols and halothane are available (Pope et ul., 1982; 0. Brandt and D. A. Haydon, unpublished results). In common with the alkanes, little effect is found on the singlechannel conductance but, again, there is a marked increase in the dissociation rate constant. Figure 10 shows how the mean channel duration (= l l k D ) varies with the aqueous phase concentration in three instances.
341
ION MOVEMENTS IN GRAMlClDlN CHANNELS
halothane
, 0
0 ‘lipid
C,,
(mM)
2
C,,
L
ImM)
FIG.10. The dependence of gramicidin mean channel duration on anesthetic concentration. The lipid bilayers were of monoolein + squalene (or squalene) and contained 5 5 % (v/v) of this hydrocarbon. The condentrations of n-decane correspond roughly to the fractional saturation in the aqueous solution. The electrolyte in each instance was 0.5 M KCI and the temperature 23°C. (The data fot n-decane are from Elliott ef d.,1983; the n-hexanol 1982; and the halothane data are unpublished results of 0. results are from Pope ef d., Brandt and D. A. Haydon.)
The concentrations of n-hexanol and halothane for the blockage of the nerve impulse in sciatic nerve are 6 and 5 mM, respectively (Seeman, 1972). No quantitative measurements of either the equilibrium constant or the formation rate constant have been reported, although it appears that for n-octanol neither of thesa parameters changes by more than an order of magnitude at nerve block concentrations (J. R. Elliott, personal communication). The n-alkanols and halothane do not affect membrane thickness appreciably (Elliott and Haydon, 1979; Elliott, 1981; J . P. Dilger, personal communication). The n-alkanols, like the n-alkanes, do however increase bilayer surface tension (Elliott and Haydon, 1979; Elliott, 1981) and it seems probable that halothane would do so too. Since single-channel mean duration is known to be sensitive to membrane surface tension, the effects of the n-alkanols and halothane may therefore be explicable in these terms. On the basis of the simple model described in Section 1II.C it would be necessary for the membrane thickness to be greater than the effective channel length. This appears to be true for the monooleinsqualene bilayers used in the anesthetics experiments (Elliott cf d.,1983).
6
S. B. HLADKY AND D. A. HAYDON
342
IV. MOVEMENT OF IONS THROUGH THE PORE A. Gramicidin Forms Pores A pore spans the membrane and has a hole through it, occupied by components of the aqueous phases. The measured currents through individual gramicidin-conducting units, called channels (see Figs. 4 and 7), leave no doubt that each channel is a pore. Some of the observations which led to this conclusion are (Hladky and Haydon, 1972; Myers and Haydon, 1972; Haydon and Hladky, 1972) (1) the single-channel currents at high ion concentrations are large and insensitive to large changes in the thickness of the membrane, (2) the channels are simultaneously adsorbed to both surfaces of the membrane, and (3) the selectivity and conductance-activity relations imply that ions are transported partially hydrated and that hydrogen is transported via a chain of water molecules. In addition, (4) there are plausible conformations of gramicidin which would make pores (Urry et al., 1971; Ramachandran and Chandrasekaran, 1972) and would be consistent with the observed function (Haydon and Hladky, 1972; Bamberg r t al., 1977; Weinstein c't al., 1979), and ( 5 ) the osmotic and tracer fluxes of water through the channels display the long pore or single-file effect and the movements of ions and water are coupled (Rosenberg and Finkelstein, 1978a,b; Levitt et d.,1978).
6. General Features of Ion Transport
The conductance in solutions of the alkali chlorides first increases with ion concentration, then reaches a limiting or maximum value as shown in Fig. 1 I . The limit or maximum indicates that permeant ions compete for occupancy of the pore and that pores will usually have at least one associated ion at concentrations greater than I M . For any reasonable model of the pore, the volume of the lumen is small compared to the volume per ion in the aqueous phases at I M and thus it is clear that permeant ions are more concentrated in the pore than in the aqueous solutions. Only small monovalent cations and neutral molecules are significantly permeant. Single-channel conductances are not observable in CaCI2, MgCI2, TEA-CI, choline-CI, or Tris-CI solutions, but they are in solutions of sodium or potassium with a variety of anions. Furthermore the reversal, or zero-current, potentials in concentration gradients of NaCl, KCI, TIOCOCHj, TINO3, RbCI, and CsCl demonstrate perfect cationic selectivity within experimental error (Myers and Haydon, 1972; Urban r t d.,
343
ION MOVEMENTS IN GRAMlClDlN CHANNELS
I
f
I
100 -
activity
. (0). FIG. I I . Conductances at 5 0 mV versus niolal activity for NaCl (U),KCI ( 0 )CsCl and TIC1 (0). The curves are drawn according to Eq. ( A - I ) using the constants of Fit G-a in Table I l l . Experimental points from Urban c/ N / . (1980) and Neher el (11. (1978).
1978, 1980: Rosenberg and Finkelstein, 1978a: Schagina et ul., 1983).The size limit for monovalent cations is larger than cesium, methylammonium, and formamidinium but is smaller than dimethylammonium and guanidinium (Hladky and Haydon, 1972; Eisenman et al.. 1977: Urban, 1978). The size limit for neutral molecules lies between water and urea (Finkelstein, 1974). These cutoffs suggest a pore radius of about 2 A which was the principal criterion for deciding between the various possible 7 ~ l . l )helices (the single-stranded /3 helices). The accumulation of cations and exclusion of anions must be explained in terms of the properties of the pore wall. The only polar groups available to form the wall and to interact with the ions and water are the oxygens and hydrogens of the peptide bonds. I n the structures proposed for the pore these are aligned parallel to the walls of the pore and are hydrogen bonded. Presumably the cations can “bind” to the oxygens with sufficient
344
S. 6. HLADKY AND D. A. HAYDON
strength to account for their accumulation. The absence of anion permeability then indicates that anion interaction with the peptide hydrogens is not sufficiently strong. Urry et ul. (19824 propose as a structural basis for this difference that the carbonyl bonds tilt, shifting the oxygens into the lumen while no such movement is possible for the hydrogens. The failure of any divalent ion to permeate is at least partly a consequence of the attraction between its charge and that of the counterions in the solution. The potential of this force, called an image potential, is proportional to the square of the charge on the ion. Thus, if the image potential lowers the concentration of ii monovalent ion I0-fold in the middle of the pore relative to the ends, it will reduce that of a divalent ion by lo4, i.e., sufficiently to render such an ion impermeant (Hladky, 1972). Divalent cations do appear to bind to the pore near the ends, where they reduce the fluxes of monovalent ions (Hladky, 1972; Bamberg and LBuger, 1977; Urban, 1978). Further evidence for divalent ion binding is obtained from 13C NMR spectra of gramicidin incorporated into lysolecithin micelles (Urry et al., 1982b). Barium, sodium, and thallium ions all shift the NMR spectra of the same carbonyl groups located near one end of the molecule. The selectivity of the transport process among small cations is most simply displayed by either the ratio of conductances or the ratio of the permeabilities, at ion concentrations sufficiently low that these two ratios are equal. The permeability ratios are easier to determine. These ratios (Urban ct a / . , 1980) are compared with aqueous diffusion constants and conductances at 0.01 M (Neher e l ad., 1978; Urban et ul., 1980) in Table I . With the exception of thallium, the sequence is the same as for aqueous diffusion. This sequence could arise in several ways. It would, of course, be seen if the ions diffused fully hydrated through a large hole. However, if so, the pore would not be able to discriminate against chloride, dimethylammonium, calcium, and urea. Furthermore, the permeant ion concentration in the pore would not be increased above that in the aqueous phases. The sequence would arise in a very different manner if transport were proportional to the binding of ions to sites, the ions preferred water to the sites, and the ions were fully dehydrated within the pore. However, these conditions predict strong selectivity, no accumulation of ions, and a very small flux of hydrogen ions, all of which are in marked contrast to the experimental results. Finally the aqueous sequence would arise if the rate-limiting process in transport were the escape of the ion from part of its water of hydration. This explanation is consistent with all other evidence as discussed below. The high permeability of hydrogen in the pore, as in aqueous diffusion,
345
ION M O V E M E N T S IN GRAMlClDlN C H A N N E L S TABIdE I C'OMPARlbON OF S F L t C T I V l l l t S U E T W E F N IONS
K'
Kb'
Cs'
0.77
1.47
1.55
0.29' 0.33c 0.3Y
2.9
1.54 3.5
2.9
Li Aqueous mobilities" P , / P N at , I mM" G,/C;N, at 0.01 M 50 mVI
+
2.6
3.0
H'
NH;
'11'
6.98 5s
1.47 4.6
1.49 X.2'
26.5
2.3"
4.3
Ratio of limiting aqueous mobilities, from Robinson and Stokes (1965). Biionic permeability ratios at low ion concentrations. from Urban e/ a/. (1980). Ratio of conductances at 0.01 M , from Neher P / ul. (1978). Value at 0.1 M , from Myers and Haydon (1972). Value at 0.01 M , from Eisenman ct crl. (1977). Value at 0.1 m M , calculated as lhe sum ofthe biionic potentials for TI'IK' at 0.1 mM and K'INa' at I mM. K gL, (0.01 M ) = 0.3 pS extrapolated from the data of Neher el ul. (1978) using the parameters in their Table 2. Value adjusted from data at 12.5 mM. from Urban e? [ I / . (1980). L
reflects a different mechanism of transport than for the alkali cations, e.g., proton exchange along a chain of water molecules (Haydon and Hladky, 1972). This mechanism implies the presence of water molecules in the pore, as has been confirmed hy measurement of the water fluxes. Electroosmotic experiments also demonstrate directly that hydrogen transport is different from transport of the alkali cations since the latter produces a flux of water while that of hydrogen does not (Rosenberg and Finkelstein, 1978a; Levitt r t d.,1978). Current-voltage relations provide an indication of the location of the rate-limiting step. At high activities, ions can be supplied to the pore as rapidly as they can be transported, and the superlinear current-voltage relations reflect the movements of ions through and out of the pore. At low ion activities, in which arrival of ions at the pore is much less frcquent, the sublinear current-voltage curves indicate that the potential sensitive steps are now faster than ion access1(Hladky and Haydon, 1972; Hladky et NI., 1979; Eisenman ef u l , , 1982). Andersen (1983a,b) has shown for 0. I M salts that, at high potentials where transport within the pore should be faster, the rate of the limiting step is very weakly potential dependent, and it is reduced by sucrose in the aqueous phases even
' In the two-ion. four-state model. this shift in the site ofthe rate-limiting step is possible o n l y if exit from singly occupied pores is potential dependent or second ion entry can occur (Hladky. 1972).
346
S. B. HLADKY AND D. A. HAYDON
though sucrose cannot enter the pore. Thus the rate-limiting step almost certainly occurs at or just outside the mouth of the pore. Access can be limiting only if transfer through the pore is faster than is ion exit. The maximum or limiting value in the conductance-activity curves demonstrates that ions compete for occupancy of the pore. In fact there is now extensive evidence that the pore can be occupied simultaneously by two ions, at least transiently. While this evidence is independent of any particular model, the possibility of double occupancy greatly increases the range of kinetic phenomena which can occur. These are much easier to discuss with a definite model in mind. C. Models for Ion Transport through the Pore
Any kinetic model must be consistent with the structure of the pore. From the proposed structures there are many potential binding sites for ions; the probable number corresponds roughly to the number of carbonyl oxygens in the wall of the lumen, say 20. However, these are not all equivalent. Different side chains of the amino acids may result in interaction with some carbonyl groups being stronger than with others, and, furthermore, the image force will tend to hold ions near the ends of the pore. The number of sites occupied at least 5% of the time that an ion is in the pore is therefore unknown. Ideally a kinetic model would be based on a known structure for the pore and on the actual interactions of the ions and water in the pore with each other and with the pore wall. Such calculations are at present impossible even numerically, though the principle has been illustrated by molecular dynamics calculations using a greatly simplified model for the pore and completely ignoring the water (Fischer et ul., 1981). A less satisfactory approach, but one which still refers to real sites, is to use a type of Eyring rate theory for the jumps between the sites. The exponential potential dependence assumed for the rate constants in this type of theory is probably reasonable as long as the individual jumps are short. The calculations are tractable for pores which are never more than singly occupied (Lauger, 1973), or for pores which never have more than one vacancy (Kohler and Heckmann, 1979). However, the theoretical expressions entail so many arbitrary constants that kinetic data can never supply values for them. Fortunately under some circumstances, which are likely to include gramicidin, a simpler and less ambitious approach is possible, based on transitions between the possible occupancy states of the pore, rather than
ION MOVEMENTS IN GRAMlClDlN CHANNELS
347
on jumps between binding Sites. Imagine a motion picture of ions going through the pore. Look at the individual frames of the film and catalog these into a small number of groups corresponding to different states of the pore, for example (1) pore is empty, or (2) there is one ion and it is to the left of center. Thc numbcr of frames in each group represents its frequency of occurrence. Whencver two successive frames differ in state, a transition has occurred. These are also tabulated to obtain the frequencies of transitions. If the ends of the pore are preferred to the middle and the pore can be doubly occupied, the smallest possible number of such states is four. These occur with frequencies X,,,, for empty, Xlofor one ion on the left, Xolfor one ion on the right, and X I Ifor two ions, one at each end. I n reality each of these states must represent a collection of many configurations of the ions, water, and pore wall. The kinetic model consists of stating that the list of states is adequate and that the frequency of transitions between states is proportional to the probability that the pore was in the initial state times “rate” constant. This rate constant depends on external factors, e.g., the applied potential and the concentrations in the aqueous solutions, but it must not depend on the past history of the pore. This last point is not trivial. For instance if an ion arrives at the left from the right, it is immediately available for transfer back to the right. However, if the ion arrives from thc left-hand solution, it must traversc a distance of at least I nm before it can cross to the right. Thus the value to be assigned to the rate constant for the transition is in general different for these two prior histories. The assumption that the history does not matter is appropriate if an ion at one end is almost always at one particular site or if it is almost always at one of several sites connected by rapid exchange reactions. The use of an occupancy state description of the pore greatly simplifies the equations rclative to models which refer to a realistic number of jumps. But there is a price to pay. The transitions between states now involve the movement of ions over considerable distances. Thus it is no longer reasonable to assumo without evidence that the “rate” constant has any particular potential dependence. With this difference the two-ion, four-state model is mathematically equivalent to a two-site model. Fortunately, the potential dependence of those ratios of constants which describe equilibrium properties is still simple (see Urban ef d., 1980). The two-ion, four-state model is the simplest which can treat ion interaction within the gramicidin pore. Nevertheless it still requires a minimum of five rate constants (listed in Table 11) to describe the possible transitions at zero potential and additional functions to specify how the rates vary with potential. The full theory extended to treat two species of
S. B. HLADKY AND D. A. HAYDON
348
TABLE I I RATE CONSTANTSUSEDI N THE TWO-ION, FOURSTATE MODEL TO PREDICTTHE CONDUCTANCES AT Low APPLIED POTENTIALS Constant
Transitions
Description
A
00- 10 00- 01 lo-* 00 01 -+ 00 01+ I I 10- II I I +01 II 10
Access to empty pores
B
D E K
-
10 01 01 -+ 10
Exit from singly occupied pores Access to singly occupied pores Exit from doubly occupied pores Transfer between the ends of the pore
ion simultaneously present has been set out by Urban and Hladky (1979) and that paper should be consulted for the equations and references to earlier work. D. Analysis of Ion Fluxes: Conductances, Current-Voltage Relations, and Permeability Ratios
Two large collections of data exist, both pertaining to pores embedded in membranes made from glyceryl monooleate. At 0.01 M the ratio of the conductances (Urban et al., 1980; Neher et ul., 1978) differs from the low concentration limit of the permeability ratio for each pair of ions investigated’ (Urban et ul., 1980), and hence from the low concentration limit of Since the conductances vary with potential the (biionic) permeability ratio and the conductance ratio should be compared at the same potential. Andersen (1983a) and Decker and Levitt (1983) have both reported that the conductance ratio for potassium and sodium measured at 10 mM and at the biionic potential, 27-28 mV, is in fact the same a s the limiting permeability ratio, 2.9. Andersen (19833). however, found that the conductance ratio was the same from 25 to IS0 mV, which contradicts the single-channel results of Urban r / ti/. (1978. 1980). Neher cf d.(1978), and Decker and Levitt (1983). as well as the currentvoltage relations with membranes containing many channels measured by Eisenman (’/ d . (1982). Thus there must be an experimental error either in Andersen’s results or in all of these other studies. Decker and Levitt (1983) find that the ratio at 100 mV is 2.45, in agreement with Urban ef al. (1980), but that it increases to 2.9 at 27 mV. Alternative estimates of the conductances at 27 mV can be obtained in two ways. First, the conductance ratio at 100 mV, where the single-channel currents are much larger, is 2.4.5 (Decker and Levitt, 1983). and the ratios of the currents at 27 and 100 mV measured with the same
ION MOVEMENTS IN GRAMlClDlN CHANNELS
349
the conductance ratio (see Table 1). These deviations result from competition for occupancy of the pore. The minimum apparent binding constant K , consistent with these data can be estimated by assuming that at low concentrations the binding of sodium ions is negligible and the conductances G of the other ions follow a simple Michaelis-Menten relation G = GmaAK2,u/(l + K,u)
(6)
where u is the concentration of the ion in question. Then for each ion, when it is paired with sodium, (P,/P~,),,=o/(Gi/G~;~)~,~oin)s = I + KL(0.009)
(7)
These minimum values for the apparent binding constants for ions to the pore are roughly 10 M - ’ for potassium, 25 M - ’ for cesium, 40 M - ’ for ammonium. and 150 M - ’ for thallium. The actual binding constants could be much larger. A similar conclusion follows from the conductance-activity curves at low activities as shown in Fig. 12 (Neher Pt ul., 1978). These data are presented as Eadie-Hofstee (or Scatchard) plots. since whenever the conductance follows a Michuelis-Menten curve the Eadie-Hofstee plot is a straight line (see Fig. 13) whose slope ( - I/K;,)and intercepts (IS,,,;,, for Gla + 0, n + a,and G,,, K , for G + 0, u + 0) immediately provide the constants of the empirical relation. Furthermore, by using this type of plot any deviations, at low concentrations, from the simple binding curve are displayed prominently. At low concentrations (i.e., high G/u) it is clear that for potassium, cesium, and thallium the plot has a “tail,” i.e., G increases only slightly as Gl’a falls. In other words, even at these concentrations competition occurs and K,u > 1. The limiting slope of the Eadie-Hofstee plot at low concentrations provides an estimate of K , (see Fig. 13b and Appendix I). dCld(G1~~) = - IIK,
(8)
The experimental value of this slopc and thus of the apparent binding constant are crucially dependent on the accuracy of the low concentration data and are thus difficult to determine from the data. The tails are consissolutions, i.e.. without indifferent electrolyte. are I.18 for sodium and 1.27 for potassium. The conductance ratio at 27 rnV is therefore 2.63. Second. it is unlikely that the changc in ratio from 27 to 50 mV will exceed that from SO to 100 niV. The experimental values at 100 and 50 m V are 2.45 and 2.56 (Neher C I a/., 1978). respectively and thus the estimates for 27 niV is less than 2.45 t 2(2.S6 - 2.45) = 2.67. The discrepancy between these two estimates and the 2.9 reported by Decker and Levilt may be a consequence of the increased in racy which is inevitable when single-channel measurements at low Concentrations are attempted at low applied potentials.
350
S. 6. HLADKY AND D. A. HAYDON
1
I
I 30
I
I
I
80
120
a
a 80
I G/a lpS/M)
G/a IpSIM)
G/a lpS/M)
FIG. 12. Eadie-Hofstee plots of the conductance-activity relations: (a) NaCI, (b) KCI, (c) CsCI, (d) TIOCOCH, (0 and 0) and TIF (0). The curves are drawn according to Eq. (A-1) using the constants of Fit G-a in Table 111. In the dashed line in (d),B is changed to 2.35 x lo5 sec-I. Open data points from Neher ef a / . (1978); closed data points from Urban el NI. ( 1980)
tent with apparent binding constants of 10-40 M-' for potassium, 30-100 M - ' for cesium, and greater than 800 M - ' for thallium. The apparent saturation of the conductance at low activities revealed for potassium, cesium, and thallium by both of the methods discussed
351
ION MOVEMENTS IN GRAMlClDlN CHANNELS
a
t Gla
(Gla),
=
K,Gma,
b
segment
above must be reconciled with the obvious increases in conductance which occur at higher concentrations. These increases must rcpresent the effects of additional ions. In the two-ion, four-state model, entry of the second ion induces ion exit from the doubly occupied pore. If this induced exit can be followed by rapid transfer between the ends, the conductance can increase above the limit for first ion exit. The two-ion process is in turn limited at the highest activities as a result of two effects. First, ion reentry into the vacated sitas becomes faster than internal transfer (Dri >> 2 K ) (see Table 11 for definitions of rate constants) which leads to wasteful filling and emptying of the pore ends, and second, the pores become tied up in the blocked, doubly occupied state (Drr >> E ) . The Eadie-Hofstee plot for an ion which can be tl-ansported by the twoion mechanism (i.e., for which 2E. 2 K >> B ) will have the general appearance shown in Fig. 1%. At the lowest activities, corresponding to the tail, the conductance is iimited by first ion entry, while for activities
S. B. HLADKY AND D. A. HAYDON
352
corresponding to the bottom of the straight segment it is limited by second ion entry. Thus the true value of Gla at G = 0 (a = 0) is closely related to A while the intercept is related to D . The limiting slope of the tail provides an estimate of the first binding constant, while the slope of the straight D / 2 K . The remaining relation segment is closely related to D/2E needed to determine the constants is provided by the downturn at the highest activities which is described by EKID. The equations relating the constants to the Eadie-Hofstee plots for the case discussed and the alternative cases 2 K 5 B and D = 0 are set out in Appendix 1. Curves generated from this model as examples are included in Fig. 12. The constants used for sodium, potassium, cesium, and thallium are compared with those of previous fits (Urban, 1978; Urban et a l . , They should be regarded as rough estimates. 1978, 1980) in Table
+
' There have been three other attempts to fit data for monoglyceride membranes. Neher el (1978) used an expression with seven adjustable constants which was based on a four-site equilibrium binding model. Eisenman and co-workers no longer support the equilibrium binding assumption. The first binding parameter K" in Table 2 of Neher rt d.is calculated in the same manner as K , here. Levitt (1978b) used the two-ion, four-state model to fit the data of Hladky and Haydon (1972), Myers and Haydon (1972). and Hladky (1974). His fitted constants are not listed for three reasons: ( I ) he asumed that the ratio of the rate constants for entry A I D was the same a s for the equilibrium binding constants, AEIBD, i.e., that B = E which contradicts the data; (2) he assumed that AEIBD was correctly given by a theoretical calculation of the effects of the image force, but this value is not consistent with the data; and ( 3 ) in his analysis of the permeability ratios, he assumed that ions cannot enter pores already occupied by an ion ofthe other species. Finally Sandblom i ~ td . (1983) have divided the pore into four regions instead of two and have developed a four-site, 16-state model. Kinetic data cannot possibly determine the large number of constants available in the general form of this model (roughly 28 for each species of ion at zero potential), and the equations derived from it are extremely cumbersome. Sandblom P I f i / . choose to simplify the model by assuming that the outer regions remain at equilibrium with the aqueous phases. Eisenman and Sandblom (1983) have used the resulting equations to fit the conductanceactivity and current-voltage relations measured with monoglyceride membranes and tlux ratio exponents (see Section 1V.F) measured with phospholipid membranes (Procopio and Andersen, 1979: Finkelstein and Andersen, 19811. Inevitably, with so many adjustable constants, they succeed. However, the binding constants they calculate for the outer sites preclude their equilibrium assumption. If the outer sites are to remain at equilibrium with the aqueous phases, then the rate constant for dissociation from these regions must be Fast (>10' sec I). But then since the rate of entry cannot be faster than diffusion to within about 2 A of the pore [see Eq. (lO)l, the maximum binding constant to an outer region is o n l y 1.5 x 10' M-I ~ e c - ~ / 1sec--I 0 ~ = 1.5 M - I . The values calculated by Eisenman and Sandblom for rubidium, cesium, and thallium are orders of magnitude larger. Eisenman and Sandblom also propose that triple and quadruple occupancy of the pore is common. Much clearer. more direct evidence is required before this conclusion can be accepted. Sandblom et t i / . (1983) assert that the conductance-activity and flux ratio data cannot be fitted simultaneously unless higher occupancy occurs, but Finkelstein and Andersen ( 1981)have succeeded, using the two-ion, four-state model. (I/.
353
ION MOVEMENTS IN GRAMlClDlN CHANNELS
TABLE 111 COMPARISON O F THRFE SETSO F VALUESFOR THE RATF CONSTANTS“ Constant A (10’ M-I s e c - ’ )
D ( lo7 M I sec-I) K
(lo7sec
I)
BIAA ( m M )
Bik
(X
iooo)
E ( lo7 sec
EIB [I
I)
Na’
4.8 5.5
K’ 6.7 I6
6 I8
(9)
5.3 (6) I .6 1.3 1 .5
14
1 I00 X
500 3400 34
2000 75 26 20 6.7
9.7 9 4.3 2.6 4.5 290 2.5 100
450 IS
200 I0
20 9.9 I1
CS‘
7.4 18 (14) 23 16 14
8.0 8.2 I? 240 I .h 10 22 3.6 12 20 16 12.3 87.9
TI
Fit
+
53.8 (23.5)”
37. I 23.5
I I1 G-a 1 11
6.7 6
G-a I I1 G-a
0 .1 I 2”
I1 G-a
1
0.09 8”
1.5 3.9 83
Values of A and D in parenthe\es were calculated assuming A Values subject to large errors if A > D (see text)
1 11
G-a I 11 G-a G-a =
D.
The fits for potassium, cesium, and thallium proceed much as outlined above. For sodium the conductance data can be fitted using several very different combinations of constants. Finkelstein and Andersen (1981) have argued that for sodium the decrement in conductance from the expected line (Fig. 12a) is a secondary effect and that only one sodium ion can enter the pore. If this view were correct, sodium would not only bind less strongly than potassium, but would be qualitatively different from the other ions. The data are also consistent with equal rates of first and second ion entry. The predicted first ion binding is still weak if transfer between the ends, K , is not fast compared to first ion exit, 5 (case 2, Appendix 1). Values of 2 KJB near I would satisfy this condition and be consistent with the change in shape of the current-voltage relations (Hladky and Haydon, 1972; Hladky, 1974). The values given in Table I11 as Fit G-a assume 2 K I B = I and L) = A . The values given as Fit I 1 (for which transfer is fast compared to first ion exit) also fit the conductanceactivity and current-voltagc data, but they predict strong binding. It has not been possible to restrict the values of the rate constants for
354
S. 6.HLADKY AND D. A. HAYDON
rubidium sufficiently to warrant entering them in the table. In the EadieHofstee plot (Fig. 3 in Neher e t a / . , 1978) there appears to be a small short tail, i.e., the conductances at low activities are higher than expected for a single occupancy pore. If the tail is treated as an artifact, then the binding is weak and the curves are fitted much as for sodium. Weak binding such as that suggested for sodium would be surprising since the conductances for rubidium are more like those for cesium and potassium. On the other hand if the tail is real, then its limiting slope must be small and it must extend to larger values of G l a (corresponding to smaller G's) than have been resolved. The fitting parameters listed by Neher et d.(1978) indicate that they were of this opinion. The rubidium data then suggest a value D = A -- 15.lo7M-I sec-' while BIK and BIA are unspecified but could be considerably smaller than those for cesium. This possibility is interesting since in ox brain lipid membranes the flux ratio data suggest that BIK is indeed much smaller for rubidium (Schagina et d.,1983). For thallium the conductance data specify D = 25 x lo7 M - ' and the sum D / 2 E + DI2 K -- 5 M - ' . The values to be assigned to A and B depend crucially on the data at and below I mM. If A = D , then B 25 X 10' sec-I; if A is larger than D, B can be much smaller. The values for E and K can be reversed without changing the conductance-activity relation. Urban et uf. (1980) found K substantially greater than E for thallium. The ability of thallium to block the fluxes of other ions such as sodium (Neher, 1975) also suggests an unusually small value of E (Urban and Hladky, 1979). Veatch and Durkin (1980)have used equilibrium dialysis to measure the binding of thallium to gramicidin pores in dimyristoylphosphatidylcholine vesicles. They calculate a first binding constant to the pore ( 2 A A I B ) of 500-1000 M - I . However, in their calculations they took no account of the Donnan potential which develops when thallium binds to the gramicidin present on one side of the dialysis membrane and not on the other. This potential reduces the concentration of the free thallium in the region of the gramicidin. Thus the true binding constant is larger than that calculated by an amount which depends on the exact concentration of bound thallium. It could be as much as three- to fourfold larger.
-
E. Interpretation of the Rate Constants
The rates of entry are high. It is instructive to compare them with the maximum possible rate of access from the aqueous phase which is given by the rate of diffusion of ions, J , up to a hemisphere at the mouth of the pore, J = D~TYuNA (9)
ION MOVEMENTS IN GRAMlClDlN CHANNELS
355
where m is the concentration in the bulk solution in moles per unit volume, D is the diffusion constant, N, is Avogadro's number, and r is the radius of the hemisphere. There is ambiguity in the appropriate choice of r ; one reasonable choice is the smallest possible distance between the centers of the mouth of the pore and of a fully hydrated ion. This is roughly 2 A. Thus for D = 2 x lo-' cm? sec-l
which is about 3-10 times larger than the observed values. Thus as concluded earlier (Hladky, 1972; LBuger. 1976; Urban et d.,19XO), diffusion (free from contact with the pore) is not limiting. Andersen (1983a,b) has shown that for high applied potentials the rate of the limiting step in access is very weakly dependent on applied potential and it is reduced by the presence of sucrose in the aqueous phases. Sucrose cannot enter the lumen. These results require (at least for high potentials) that the slow step occurs outside the lumen. The obvious suggestion which satisfies all the requirements is that the rate is limited by the partial dehydration which must occur before the ion can fit into the lumen (Hladky and Haydon, 1972; Hladky, 1984). It is apparent from all three fits to the data that the rates of first and second ion entry are similar, while the second ion binding constants, DIE, are much smaller than the first, AIB. The reduction in the binding constant when two ions are present presumably arises from some combination of electrostatic repulsion of each ion by the other and compression of the water molecules trapped between them. Electrostatic repulsion will be identical for all species if they bind to the same sites, while repulsion resulting from compression of the water will also be the same if each species enters accompanied by the same number of water molecules. The similarity of the two rate constants for entry suggests that the limiting step occurs near the mouth of the pore where electrostatic repulsion will be weak (Levitt, 197th) and water can move out of the way before the ion enters. The rate constant for first ion exit. B . and hence the values of B/2A and BIK in Table 111, vary greatly from one fit to another. The value of B affects the conductances only at low activities. Very few conductances at sufficiently low activities ware included in the data analyzed for Fits I and 11. Fit G-a emphasizes the low activity data of Neher et ul. (1978), but even so the values in the table represent a somewhat arbitrary choice from a range of possible values. For instance for potassium, fits to the data in Fig. 12b could be obtained for at least a fivefold range. A definitive value will not be available until a set of constants has been shown to
356
S. B. HLADKY AND D. A. HAYDON
describe both the conductance-activity curves and either the concentration dependence of the permeability ratios4 or the concentration dependence of the flux ratios (see below). The rate constant for transfer, K , varies remarkably little between ion species. This observation suggests that transfer along the chain of oxygens lining the pore is limited by nonspecific factors such as the image force and the water movements which must also occur. These Factors are discussed further in the section on ion-water interaction (Section VI). The listed values for the rate constant of exit from doubly occupied pores are those obtained without regard to any possible secondary effects at very high ion concentrations (Urban rt al., 1980; Finkelstein and Andersen, 1981; see Appendix I). If repulsion between ions within the pore is independent of species, then the combination of constants AEIDB should be the same for all species (Urban er d.,1980). In the present fit, labeled G-a in Table 111, this condition has not been imposed and it is not satisfied. There are two plausible explanations. Some or all of the values of E may be wrong as discussed in Appendix 1; those for sodium and potassium are the principal suspects. Alternatively the repulsion may vary with the ion species present. F. Analysis of Ion Fluxes: Flux Ratios
The analyses of permeability ratios and of flux ratios are similar in that both depend on unidirectional fluxes. The flux ratios are, however, much simpler in one crucial respect, that only one ion species is present. They are, however, also more difficult experimentally since a large flux must exist for a long time to transfer enough tracer to be measured. Glyceryl monooleate membranes have not as yet been thought sufficiently long lived to allow these experiments. The flux ratio exponent n is an empirical constant defined as
j/j
= [(u"/u')exp(zeAV/kT)I"
( 1 1)
Andersen (l983b) has proposed that when the fluxes are limited by an external access step, which he calls diffusion, the conductance-activity relation yields an underestimate of the first binding constant, and the permeability ratios are concentration dependent for reasons not included in the two-ion, four-state model. As discussed elsewhere (Hladky, 1984). his calculations are based on the assumption. incorrect for gramicidin, that the external steps are not affected by the occupancy of the pore. When access is limited close to the mouth of the pore (see Hladky, 1984, for details). the equations become equivalenl to those used by Urban iif c i l . (1980). It is also worth noting that the principal difficulty in fitting the permeability ratio data is to restrain the predicted increase with concentration. There is no need to invoke additional mechanisms.
357
ION MOVEMENTS IN GRAMlClDlN CHANNELS
where J is the unidirectional or tracer flux in the direction of the arrow: 11' and (1'' are the ion concentrations on the left and right side of the membrane. respectively; z is the ion valence; and c is the charge of the proton. Whenever Eq. ( 1 I ) is satisfied, Glj
=
(12)
(z?e?lkT)n
applies in the limit of low applied potentials. The two-ion, four-state model predicts in this limit (Hladky ct (11.. 1979) ti =
1
+ 2KDcrl[(Dm)' + Drr(3B + 2K) + 2B? + 4KBl
(13)
Thus whenever both the conductance and the unidirectional fluxes can be measured over a sufficient rttnge of concentrations, KIB and DIB can be evaluated simply from the data. Schagina el d.(1983) have found for RbCl and membranes made from ox brain lipids that at 2 x 10 ?, 10 I , and I M , IZis 1.6, 2 , 2, and 1.5, respectively. For 0.1 M CsCl and 0. I M NaCI, they observe 1.7 and 1.2. They argue, using the theoretical results of Kohler and Heckrnann (1979, 1980). that only two ions can be in the pore at once. Using Eq. (13), their results for rubidium imply that 1000 BIK 5 0.67 and 8/20 0.17 mM. If the maximum values of n for CsCl and NaCl are those reported these values would indicate 1000 BIK - 20, BI2D 5 mM and 1000 BIK - 1000, Bl2D 17 mM, respectively. Unfortunately. no single-channel conductances have been reported for membranes made from ox brain lipids. Finkelstein and Andersen (1981) briefly reported conductances and tracer fluxes (see Procopio and Andersen, 1979) for CsCl and diphytanoylphosphatidylcholine membranes. From the flux ratio exponent which reaches 1.6 at 1 M ,2KIB 2 20 and DIB 10 to 20 M - ' . With these values known, the conductance-activity relation specifies A = D = 1.4 x 108M-I sec-I and thus B = 8 x lo6 sec-I and K > 8 x 10' sec-I. This minimum value of K can be calculated without using conductance data obtained at concentrations above 1 M . Instead Finkelstein and Andersen used all of the data and found K = 9 x lo7 sec-' and E = 5 x 10' sec-I.
-
-
-
-
G. Analysis of Transitions: Spectroscopic Evidence
There is insufficient space in this article to discuss in any detail the N M R spectroscopy of gramicidin incorporated into lysolecithin micelles. Urry and collaborators have now amassed considerable evidence (see Urry et (11.. 1980a,b) that gmmicidin can be incorporated into these micelles in a porelike conformrttion which binds two ions. They have esti-
358
S . B. HLADKY AND D. A. HAYDON
mated binding constants and on and off rates for sodium ions (Urry rt ul., 1980a) which are very close to those listed in Table 111 as Fit 11.5 The conductance data for sodium on glyceryl monooleate membranes can be fitted using a variety of rate constants including those suggested by Urry et al. However, comparison with constants which fit the conductance data for potassium makes it unlikely that the first or tight binding constant in the membrane is as large as proposed by Urry et al. for gramicidin in micelles. The flux ratio data for ox brain lipid or diphytanoylphosphatidylcholinemembranes exclude these values (Finkelstein and Andersen, 1981; Schagina et al., 1983). Dielectric relaxation measurements (Henze et ul., 1982) using 10 mM thallium and gramicidin incorporated into what were apparently multilayered lysophosphatidylcholine liposomes demonstrate a charge movement which could be an ion shifting between sites within the pore. The rate constant calculated, K = 4 X lo6 sec-I, is surprisingly slow, however. H. Location of Ion Binding Sites
The current-voltage data demonstrate that access and exit of ions are respectively very weakly and weakly dependent on the applied potential (Urban et al., 1980; Andersen, 1983a,b). Thus, in agreement with expectation, the ions appear to spend most of the time near the ends of the pore. When the pore is doubly occupied it is difficult to see how this could be otherwise, since water and the ion at the farther end must emerge before a new ion can enter much deeper than is allowed by exchange with a single water molecule. Spectroscopic evidence can provide more detailed information. Sodium and thallium both perturb the N M R resonances of the carbonyl groups in the first turn of the helix (Urry et u/., 1982a,b).These experiments demonstrate a preferred binding site at this location (for gramicidin in lysophosphatidylcholine micelles) but they do not exclude weaker binding anywhere else. To demonstrate the weaker binding the concentration must be raised, but this increase leads to occupation of the preferred sites and exclusion of binding to the weaker sites. The data do show that in the presence of a bound ion, second ion binding is much weaker and is only appreciable at the far end of the pore. Urry et ul. state that in their fit of the two-site model D > A , yet the values they report are D = 6 x lo7 M-I sec-l and A = 5.2 X lo7 M-' sec-I, which are insignificantly different. Similarly they never state the value of K used to predict the conductances. However, since they obtained this value by fitting the data of Urban et ul. (1980), it must have been near lo7 sec-I.
ION MOVEMENTS IN GRAMlClDlN CHANNELS
V.
359
MOVEMENT OF WATER THROUGH THE PORE
Gramkidin increases the water permeability of lipid membranes as measured either as a volume flow in an osmotic gradient or as the flux of a tracer. The permeability measured in osmotic experiments was about five times larger than that determined in tracer experiments (Rosenberg and Finkelstein, 1978b). This finding is the equivalent for water of the result for ions that the flux ratio exponent is greater than I . It is clear evidence that the movement of one water molecule is affected by the movements of many others. For a single-file pore such as gramicidin containing a small number of water molecules, the ratio of the osmotic and tracer permeabilities is not given directly by the number of water molecules in the pore (Kohler and Heckmann, 1979, 1980)-juut as there is no immediate relation (see Urban and Hladky, 1079)between pore occupancy by ions (governed by AIB and DIE) and the flux ratio exponent (governed by KIB and DIB). However, it seems that the ratio of the water permeabilities is an underestimate of the true number. If the pores are almost always full (entry faster than all other processes), Kohler and Heckmann (1980) find that for a permeability ratio of 5 , the number of molecules per pore could be six, seven, or eight depending on the precise relation between transport and the number of vacancies. There is, of course, no guarantee that the pore usually contains the maximum number of water molecules. Levitt et al. (1978) have estimated from models of the pore that it could hold 10 water molecules. It should be emphasized that at present there is no serious proposal for how water in the pore is organized, how water interacts with the walls (there are presumably about 20 binding sites but neighboring sites cannot be occupied simultaneously), or how large the fluctuations are likely to be in the number of water molecules in the pore. VI.
INTERACTIONS OF IONS AND WATER IN THE PORE
When there is a net flux of water through the pore, any ions which enter will tend to be swept along with the water. Under short-circuit conditions, this generates a current, while on open circuit the current generates a streaming potential which builds up until it is large enough to bring the current to zero. The conversq effect, called electroosmosis, is the production of a net flux of water by current flow. Both effects have been observed for gramicidin (Rosenberg and Finkelstein, 1978a; Levitt ct al., 19713). Using either effect, together with irreversible thermodynamics, it is possible to calculate N , the number of water molecules transferred per
S. B. HLADKY AND D. A. HAYDON
360
ion. At low ion concentrations this number is apparently somewhere between 6 or 7 (Rosenberg and Finkelstein, 1978a) and 9 (Dani and Levitt, 1981a). Rosenberg and Finkelstein found the same number for 0.01 and 0.1 M solutions of NaCI, KCI, and CsCl, while Levitt et uf. saw no difference between NaCl and KCI at 0.15 M. At higher ion concentrations the pores will usually be occupied by more than one ion. The number of water molecules transferred per ion is then equal to the number between the ions when the pore is doubly occupied (Rosenberg and Finkelstein, 1978a). This number will in general be different from the number transferred per ion at low concentrations. Rosenberg and Finkelstein report that the number transferred per ion drops to 5 for 1 M NaCI, KCI, and CaCl while Levitt et al. found that it dropped to 6 for 3 M KCI or NaCI. The transition between the low and high concentration behavior should coincide with the transition from the one-ion to the two-ion mode for ion transport (Hladky, 1983). It thus depends on the ratio DIB and not on single or double occupancy of the pore as had previously been assumed. At 0.15 M CsCl (for which DIB = 17 M - l is the smallest anyone proposes), the results already represent primarily the high concentration behavior. The absence of any variation with concentration or between species below 0.15 M t h u s suggests that the numbers transferred per ion are similar for the two modes of ion transport (compare footnote 4 in Finkelstein and Andersen, 1981). Some other explanation must be sought for the fall in N at concentrations above I M. A nonspecific effect is quite possible since the fall apparently occurs for the same concentrations with NaCI, KCI, and CsCI. Finkelstein and Andersen suggest that the number of water molecules in the pore is reduced by the high osmolality of the solution. If so, the fractional change in the number of water molecules in the pore would need to be greater than 20%, which far exceeds the change in mole fraction of water in the bulk phases. Darri and Levitt (1981a) have used water permeability measurements to determine ion binding in the pore. They assumed that on open circuit, where the current is zero, no water could flow through a pore occupied by an ion and thus in effect that Pob(~)/Po,(O) = X(N,= 1/11
+ (2AaIB) + (ADa'IBE)]
(14)
This expression is in fact only an approximation,6 but it is good enough for estimations of B/2A. Dani and Levitt (1981a)found 115 mMfor lithium, Water can be transported at open circuit when all channels are occupied by at least one ion if either ( I ) the number of water molecules transported per ion is different in the one-ion and two-ion modes, or (2) the number of water molecules transported per ion is different in the two directions of transport. The second condition is theoretically possible in the pres-
361
ION MOVEMENTS IN GRAMlClDlN CHANNELS
69 mM for potassium, and 2 mM for thallium. When the large errors possible in both types of analysis are taken into account, these values are very similar to those determined from the conductance activity data: 127 mMfor lithium [where Kh in Table 2 of Neher ef crl. (1978) equals I .S AIB if 2K = B], 50 mM for potassium (Fit G-a, Table 111). and 1 mM for thallium (see previous section). Despite this rough agreement some caution is required. Dani and Lcvitt rcport that the water permeability is 6 X cm3 sec-I pore-’ when there are no ions. This value is six times larger than that reported by Rosenberg and Finkelstein (197%). Dani and Levitt (1981b)also pointed out that the osmotic water permeability of singly occupied pores (at short circuit) can be calculated from the conductances at low ion concentrations if the fraction of pores which arc singly occupied is known. Thus as shown in Appendix 11, it follows to a good approximation that
pI 7 ( V , G R T ! ~ , ) ( N / Z F ) ~
(15)
where PI is the osmotic water permeability of a singly occupied pore, V , is the partial molar volume of water. G is the conductance, J; is the fraction of pores which are singly occupied, N is the number of water molecules transferred per ion, R is the gas constant, and F is Faraday’s constant. The three parameters P I ,G , and ,fi must be determined at the same concentration. The ratio G / f ;at low concentrations cannot be determined directly from the tail of the Eadie-Hofstee plot since the limiting slope is not the reciprocal of the binding constant (see Appendix I ) and the intercept on the G axis is not the proper G,,,,. However, the ratios (G/ a),,,(, and (f’,/u)(,-,, are easily (though not always accurately) determined from the Eadie-Hofstee plots and from either the data of Dani and Levitt (1981a) or the fits in Table 111, respectively. These values and the calculated water permeabilities for ion-occupied pores are listed in Table 1V. The results suggest that at low ion concentrations the presence of an ion in the pore substantially reduces the water permeability, e.g., for thallium cm3 to roughly 3 X the permeability drops from more than sec-I. The large reductions for cesium and thallium occur primarily as a result of the slow exit of ions from the pore. At higher ion concentrations the water permeability of singly occupied pores calculated using Eq. ( I S ) increases. Theoretically, using the predictions of the two-ion, four-state model for G andJ;, the relation becomes
PI
=
(N2Vw/2N,4)[K(B + D N ) / ( ~+K B
+ Da)]
(16)
ence of a large osmotic gradient. particularly if the large change5 in the number of water molecules in the pore referred to earlier are genuine. These factors become important when P(a)IP(O)becomes small, i.e., they must be taken into account to estimate values of DIE (Hladky. 1983).
362
S. B. HLADKY AND D. A. HAYDON TABLE 1V CALCULATION OF THE WATERPERMEABILITY OF OCCUPIED PORES AT Low ION CONCENTRATIONS From data of Dani and Levitt (1981a)
Li+ Na' K+ Cs+ TIi
34.8" 95 260 450 750
8.7
-h
14.5
I .46
-h
6.5 0.55
so0
From Fit G-a
5.9" 2.5 20 200 1000
2.15 14 4.7 0.82 0.28
~~
Taken from Table 2 in Neher et al. (1978). Dani and Levitt do not provide a value offila nor do they state how they calculated a value for P I .
where N A is Avogadro's number. Thus according to the model the increased water permeability is allowed by second-ion entry and induced ion exit. For second-ion entry faster than transfer between the ends, the permeability approaches a maximum limit of Pyax= N2VwKl2NA
For the values in Table 111 these limiting values range from 1.8 x cm3 sec-l for sodium to 1.5 X lo-" cm3 sec-' for cesium. The prediction of a maximum value for the rate constant for transfer from data on water movements requires certain assumptions. Perhaps the simplest are (1) only transfer between the ends is coupled to water movements, (2) transfer occurs by a vacancy diffusion mechanism in which the ions can only enter holes left by the previous movement of a water molecule, (3) ion and water movements into holes occur at the same rates, and (4) the water movements into holes occur at the same rate regardless of the presence and position of an ion. It then follows that (see Finkelstein and Andersen, 1981) 2 ~ K 5 N2Vw
4 -
~5 x lo7 p sec-l ~
(Dani and Levitt, 1981a)
2 x lo7 sec-I
(Finkelstein and Andersen, 1981)
(18)
where Po is the osmotic water permeability of an ion-free pore. The values of K for cesium and thallium in Table III and that for cesium reported by Finkelstein and Andersen (1981) all violate this inequality. Thus at least one of the assumptions used to derive it is wrong.
363
ION MOVEMENTS IN GRAMlClDlN CHANNELS
The discrepancy between the observed rate of transfer and the maximum possible by a vacancy diffusion mechanism is larger than suggestcd by this comparison. Thus as noted by Dani and Levitt (1981b) in vacancy diffusion, water movements determine the local mobility or diffusion constant for the ion, but the ion is also subjected to the image force. The stronger this force, the larger must be the diffusion constant to yield any particular value of the rate constant. The comparison given above assumes no image force. The actual maximum rate constant consistent with vacancy diffusion and with Pyx= Po must be considerably smaller. Andersen and Procopio (1980) have suggested that for high applied potentials, ion movements through the pore are so fast that ions must be able to push some water molecules ahead of them. If the same were true at low applied potentials it could explain the high values of the rate constant for transfer. VII.
APPENDIX I
The conductance-activity relation predicted by the two-ion, four-state model is G-' = - (zeP
kT
2Aa
ADuBE
B
Dn + 2K
(A- 1)
where z is the ion valence and P is the electronic charge. From Eq. (A-I) the behavior at very low activities can always be described by
Thus in the limit of low concentrations (A-3) and the initial slope is (see Fig. 13b)
The conductance relation can lead to straight line segments (see Fig. 13b) on an Eadie-Hofstee plot in three ways.
364
S. B. HLADKY AND D. A. HAYDON
I . When only one ion can enter, i.e., D
=
0, (A-5)
which yields a straight line on a Eadie-Hofstee plot for all activities. 2. When exit from singly occupied pores is faster than transfer between the ends, i.e., the ends are at equilibrium with the adjacent solutions, Eq. (A-1) simplifies to G
(ze12 K 2Au kT 2
+ 7+ BE
= -( - ) ( T ) / ( l
which gives a straight segment at low and medium concentrations. The curve drops below the line for high concentrations (low Gla) where DulE 2 0.5. In practice Eq. (A-6) will appear to fit the data whenever B 2 2K. 3 . For sufficiently rapid ion entry that AalB >> 1 and DalB >> 1 the conductance in Eq. (A-I) becomes
which for either Dul2E < 0.5
Da/(B + 2 K ) < 0.5
or
(A-8)
is approximately KE Da(2E + B + 2K) G = -(ze)' (2E + B + 2 K ) [ 2E(B + 2 K ) Da(2E + B + 2K) kT I + 2E(B + 2K)
(A-9)
Thus provided there is a range of concentrations for which either 2E >> Da >> B
or
2K >> Da >> B
(A-10)
the Eadie-Hofstee plot in this range will be a straight line with slope
=
-2E(B
+ 2K)/D(2E + B + 2 K )
(A-11)
and intercepts
(ze)'
G G , ~ ==oR T 2E
KE
+ B + 2K
(A- I 2 )
(ze)' DK (Gla)(;=o= kT 2(B + 2 K )
(A- 13)
and
365
ION MOVEMENTS IN GRAMlClDlN CHANNELS
Thus when these conditions are satisfied, the intercept on the abscissa is related to the true low activity limit by (GI~)inteI.cep(I(Gln)o
=
D/2A
(A- 14)
It must be emphasized that the simple relation between the intercept and the value of D is correct only when the inequalities are strictly obeyed. For instance the curve for potassium shown in Fig. 12 was generated with A A / ( B + 2 K ) = 260 pS, and I1 = A , and t h u s the intercept predicted by Eq. (A-14) is 130 pS M - ' . The intercept obtained by laying a straight edge on the plot is nearly 200 pS M-I. There are several difficulties encountered in fitting the conductanceactivity, current-voltage, and permeability ratio data. First. the product K E is determined solely from data at very high concentrations (22 M ) .At these levels changes in concentration may have secondary effects (Urban ef ( I / . , 1980). Finkelstein and Andersen (1981) have observed that 5 M urea reduces the conductance of 1 M NaCl by 23% and that of I M CsCl by 44%. and that this provides evidence for an indirect effect of high solute concentrations. They propose as a possible mechanism that the high osmolality of the solutions reduces the pressure inside the pore which results in a reduction in pore diameter. This mechanism might account for a greater effect on larger solutes. At 5 M the osmotic pressure would indeed be of the order of 100 atm which as a driving force for water transport is very impressive. However, a negative pressure of 100 atm within a cylinder of radius 2 A would induce a tension in the wall of only 2 dyn cm-' which is almost certainly negligible. If there is an effect of osmolality per se it is much more likely to be a change in the number of water molecules in the pore (Urban et (11.. 1980; Finkelstein and Andersen, 1981). The decrease in the mole fraction of water between distilled water and a 5-osm solution is roughly 10%. If the change within the pore were as large, it would represent a decrease of one in the number of water molecules per pore for half of the time (see also Section VI). Second, the conductances specify lower limits for K and E but they do not reliably specify which is which. This assignment must be based on another type of data. Urban ct N / . used the concentration dependence of both the permeability ratios and the shape of the current-voltage relations. For sodium, potassium, and cesium they found K < E , while for ammonium and thallium, K > E . Eisenman et d.(1982) have attempted to evaluate K I B from the current-voltage relations at low activities and rate constants which vary exponentially with potential. Unfortunately, without the exponential assumption the data can be fitted for a large range of values of K I B . For instance at low activities the data can always be fitted if the assumed potential dependence of A is adjusted to fit. using KIB-, Eisenman and co-workers (1980) also conclude that the pore must be
366
S. B. HLADKY AND D. A. HAYDON
divided into more than two regions since three steps in series, each varying exponentially with potential, cannot fit the current-voltage relation. Without the exponential assumption, the conclusion no longer follows. Third, Urban at al. assumed that repulsion between ions within the pore was independent of ion species, i.e., that AEIDB was a constant for all species. The fit to their data was insensitive to changes in B (i.e., large changes could occur in the fits), thus any errors in E will have been imposed on the values of B by this assumption. Finally, in the present fits, relations derived for very low potentials have been used to interpret data obtained at SO mV. This problem is purely technical but can perturb the calculated values of the constants. The conductances at SO mV should be corrected to the values at 0 mV using measured current-voltage relations. These corrections can be of the order of 10%. In practice, the values of K calculated without correction are probably about 30-S0% too high. In the curve fitting of Urban at (if. ( l980), the full expressions using potential-dependent rate functions were employed and thus no correction of the data was necessary. VIII.
APPENDIX II
The osmotic water permeability of ion-occupied pores is related to the conductance since water movements in an ion-occupied pore require the ion to move as well. From the usual equations of irreversible thermodynamics (see Dani and Levitt, 1981b) J~ = (V,P,,IRT)AT
+ (V,NGIZF)AJI
(A-15)
and
(A-16) I = (V,NG/ZF)AT + GAJI where JV is the volume flow, AT is the difference in osmotic pressures between the two sides of the membrane, and AJI is the difference in potential. Thus the water flux at short circuit, AJI = 0, is
4:
=
JVIV, = (PEIRT)AT
(A-17)
-1
(A-18)
while on open circuit
PE V G N2 P:: G = [m -( zF I zF ) AT = -RT AT Thus
V,G RT(NIzF12 = PE
-
Po's 13
(A-19)
367
ION MOVEMENTS IN GRAMlClDlN CHANNELS
follows without any assumptions about the transport process. Dani and Levitt (1981b) made two further assumptions. First, on open circuit they assumed that all the water flows through the fraction Xo of pores which are ion free and thus that P::
=
X,P,
(A-20)
Second, they assumed that the flow on short circuit can be divided into flows via ion-free, one-ion, two-ion, etc., pores, i.e.,
P: = X , P ,
+ X I P , + X,P, +
..
+ XJJ,,
(A-21)
where the P values are constants. Substituting these into Eq. (A-19) gives their working equation. Their first assumption is correct if the number of water molecules transferred per ion is the same for conduction by the oneion and two-ion mechanisms and the same for transfer in the two directions (Hladky, 1983). It will be a reasonable approximation for low ion concentrations. The second assumption is not correct for the two-ion, four-state model. In that model and using the same assumptions about the number of water molecules transferred, the difference between the shortcircuit and open-circuit water fluxes becomes
It follows directly from Eq. (A-22)and the definition of the permeabilities that
P:;
-
P::
=
fi PI
(A-23)
where the osmotic permeability of an ion-occupied pore is
+ Da) RT G + B + Du) - -zF2 N ? V wfi-
N2Vw K(B
P, = 2N.4 (2K
-
(A-24)
It should be noted that the permeability of singly occupied pores varies with concentration and that the permeability for doubly occupied pores is zero. At very low ion concentrations
KB p , =--N'V, 2N.4 2 K + B
(A-25)
while at high concentrations
P,
=
N2VwK12NA
(A-26)
368
S. 6.HLADKY AND D. A. HAYDON
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ION MOVEMENTS IN GRAMlCDlN CHANNELS
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Index A
Acetylcholine receptor channel, .xec Endplate channel Active ion transport, .ree Ion pumps Adenosine triphosphate. ion pump model. 322 Agonists ion channel gating, 60, 88-89 Alkaline earth ions selectivity sequences, 9 Amiloride binding, 265 Amiloride-insensitive channels, 270-271 Amiloride-sensitive pathway. s w Sodium channel, epithelia Ammonium, permeability, end-plate, 41 Amphotericin B structure, 299 channel formation. 340-341 Anesthetics effect on gramicidin channel, 340-341 Anions, see ulso Ions selectivity, 8 porin channels, 209-213 Apical membrane, gallbladder, 272-275 Asymmetry, cell-to-cell channel, 232-234 Autocorrelation function, 141-142 Autocovariance function, 141-143
0
Bacteria anion selectivity, 209-213 cation selectivity, 207-209 porin channel, 199-216 Barium potassium conductance inhibitior), epithelia, 281
Basolateral membrane, potassium conductance, 280-282 Binding sequence, see also Selectivity sequence end-plate channel, 44, 47 BisQn blockers. sarcoplasmic reticulum potassium channel, 113-1 14 Black membrane. .set’ Lipid bilayer membrane Bladder, Lorentzian spectrum, 259 Block end-plate channel, 44-46 epithelia, 284-285 aniiloride, 258, 260. 262 triamterine, 260. 261, 262 gramicidin channel. water permeability, 30 1 potassium channel, basolateral membrane, 281 frog skin, 49, 276 sarcoplasmic reticulum, 1 I 1-1 17 sodium channel, frog, 49 Bursting, 68, 92
C
CAMP. see Cyclic adenosine monophosphate Calcium effect on cell-to-cell channel structure, 245 effect on cell-to-cell permeability. 23724 I effect on epithelium channels, 283, 286 Calcium channel gating, 63, 64, 91-92, 165 inactivation, 63 patch-clamp, 165-166 single-channel measuremcnts. 161- I63 373
INDEX Carriers, 3 16-3 17 evidence against, end-plate channel, 10 water permeability, 305 Cation channels, nonselective, epithelia, 282-283 Cation selectivity, porin channel, 207-209, 212 Cations conductance, sarcoplasmic reticulum potassium channel, 108 permeabilities, end-plate channel, 39, 41 physical properties, 5 selectivity sequence, 3. 6, 36 Cations, monovalent permeabilities, end-plate, 41 Cell-cell adhesion, cell-to-cell channel formation, 228-229, 230 Cell-to-cell channel, 221-247 formation, 222-23 I mixed-cell populations, 230, 233 structure, 223, 227, 231-232, 245-246 Cell compatibility, cell-to-cell channel, 229-230 Cell junction, see Cell-to-cell channel Cesium. potassium channel blocking, I I I I12 Channel breathing, 321 Channel density, epithelia, 266-268 Channel incorporation, potassium channel, 102-103 Channel noise, see Noise Channel turnover, epithelia, 269-270 Charged site model, end-plate channel, 1217, 41, 43 Conductance measurement, see also Single-channel conductance end-plate channel, 29-33, 39, 41 Conductance-concentration relationship end-plate channel, 42-43 sarcoplasmic reticulum potassium channel, 109 two-state, single-site channel, 313-3 14 Conductance models, 10-22 Conductance-voltage relationship, endplate channel, 23-24, 39-41, SS-56 Conformational states, ion channels, 310315 Conformational transitions, coupled to ion BOW,310-325 Current fluctuations, see Noise
Current-voltage relationship, sodium channel, 57 Cyclic adenosine monophosphate-promoted phosphorylation, 235
D Deactivation of channel, 62 Debye length, 16 Desensitization, see Inactivation Downregulation, cell-to-cell permeability , 237 Drugs end-plate channel block, 44-45, 61 ion channel gating, 60-61 Dwell times, 68, 69, 70, see also Open times
E
Eisenman sequence, 6, 8, 41 Electrodiffusion model end-plate channel, 12-17 ion transport, 12-17 Electrodiffusional flux equations, 12-17 Electroosmosis, gramicidin channel, 359 End-plate channel, 2-49 agonist-activated, 60, 88-89 current noise, 320 gating, 55-57, 88-89 inactivation, 62 ion selectivity, 2-49 structure, 33-34 Ensemble fluctuation analysis, 145- 146 Epithelial channels, 253-293 Excitation-contraction coupling, 99, 122, 128 Extrajunctional channels, 46
F
Filtration permeability coefficient, 296 Fluctuation analysis, see Noise analysis Flux measurements, sarcoplasmic reticulum vesicles, 123-127 Flux ratios, ion fluxes, 356-357
INDEX
375
Frog skin potassium transport, 275-279 sodium channel, 254-271 G
Gallbladder, potassium channel, 272-275 Gap junction, see ulso Cell-to-cell Channel Gap junction protein, cell-to-cell channel regulation, 237, 240 Gating cell-to-cell channel, 243-244 ion channels. 53-92 potassium channel, sarcoplasmic reticulum, 103-107. 118 temperature dependence, 64-66 voltage effect. 55-60 Gating current, 59-60, 86-87 Gating model. Markov model, 78-83 Gigaseal, 150, 151, 154. 156 Goldman-Hodgkin-Katz equation, 1 1 , 12. 13, 19, 208, 264 mixed valency version, 38 Gramicidin, structure, 328-329 Gramicidin channel conformational transitions, 3 13 formation and dissociation, 332-341 formation kinetics, 336-337 ion transport, 342-358 kinetics, 192 streaming potential. 189- 190. 301 structure, 302. 329-331, 338 two-site model, 192 water permeability, 186-187, 191, 300303
end-plate channel, 62 sodium channel. 62-63 Inhibition, see Block Ion, see ulso Alkaline earth ions; Anions; Cations Ion channels gating currents, 59-60 nonselective, 169 Ion conductances. 152-153 gramicidin channel, 348-349, 353-356, 358 sarcoplasmic reticulum vesicles, 123-127 Ion pumps, 321-324 Ion selectivity, see also Alkaline earth ions; Anion selectivity; Cation selectivity; Selectivity sequences end-plate channel, 2-49 gramicidin channel, 343-345 potassium channel, frog skin, 277 potassium channel, sarcoplasmic reticulum, 107 equilibrium, thermodynamics, 3-27 porin channel, 207-213 sodium channel, epithelium 263 Ion-ion interaction, 182-184, 194-195 flux ratio equations, 194-195 Ion-water interactions gramacidin channel, 359 narrow channels, 187-193 sarcoplasmic reticulum potassium channel, I17 Irreversible inhibition, potassium conductance, 117-1 18
K H
“Hopping” rate constant, 22, 40 Hormones effect on cell-to-cell permeability, 236 effect of sodium channel, epithelium, 268-269 effect on water permeability, 305 I
Inactivation calcium channels, 63
“Knock on-knock o f f ’ model, 182-183, I88
L
Lifetimes, see Conformational transitions: Dwell time; Open time Lipid bilayer membrane porin channel formation, 200-205 potassium channel, 100-129 single-channel measurement, 148-149 water channel, 298-303
376
INDEX
Lorentzian spectrum, 136-141 set' trlso Noise analysis basolateral membrane, 280-281 cation channels, epithelium, 284-285 epithelia, 258-260, 284-285 frog skin, 278-279 gallbladder, 272-273 two-state channel, 136-139
M Macroscopic currents and gating currents, 86-87 Matrix proteins, see Porins Maximum likelihood method open time estimation, 85-86 Memory, gating, 69-70, 73 Microscopic reversibility , 318 Model end-plate channel, 12-23 gramicidin channel, 347-348, 351, 363366 ion transport, 12-23, 183-184 knock on-knock off, 182-184 multisite, 19-23 rate theory, 17-23 reaction rate, 183-184, 192 single-site channel, 18-20, 317-320 single-site, two-state, 310-316. 317 three-state channel, 3 17-320 two-site, 183- 184 two-site, four-state, 347-348. 351, 363366 Model membrane, see Lipid bilayer membrane Multichannel systems, noise analysis, 135146 /
N
Neuromuscular junction, see End-plate channel Neutral site model, end-plate channel, 1217, 41, 43 Nexus, see Cell-to-cell channel No-pass, see Single-file Noise, in open channels, 140-141
Noise analysis, see also Lorentzian spectrum, 135-147 end-plate channel, 29-30 gallbladder, 274-275 Nonelectrolytes. single-channel permeability coefficients, 299 Nuclear magnetic resonance spectroscopy, gramicidin channel, 357-358 Null potential measurement, 28-29 end-plate channel, 35-39 Nystatin, structure, 299 Nystatin channel, 298, 300, 302 0
Open channel noise, 140-141 Open times cell-to-cell channels, 224-227 end-plate channel, 26, 29-32, 143 estimation, 67, 71-77, 85-86 gramicidin channel, 333-335 ion channels, ,52-,53 porin channels, 205 Open-close kinetics agonist dependence, 160 calcium channels, 166 measurement, 143, 145-146 potassium channel, calcium-activated, 167 Open-closed state, cell-to-cell channel, 235-244 Osmotic permeability coefficient, 296 gramicidin channel, 301, 366-367 P
Patch homogeneity, 70 Patch recording, gating studies, 66-69 Patch-clamp, see a h Open times; Singlechannel conductance measurements; Single-channel recording Patch-clamp method, 150-156 end-plate channel, 32, 157-161 Permeability, see Conductance Permeability sequence, see Selectivity sequence Perturbation technique, open time measurement, 31-32
INDEX
Phospholipid surface charge, effect on sarcoplasmic reticulum potassium channel, 119-120 Phosphorylation, effect on cell-to-cell permeability, 235-237 Planar bilayer membrane, see L i p d bilayer membrane Plasma membrane, water permeability, 303-304 Pore size, see ulso Single-file channel, I8 I - I95 calculated from ion size, 7 cell-to-cell channel, 231-232 determining cation transport, 27 end-plate channel, 34, 37, 38, 48 gramicidin channel, 302, 343 porin channel, 213-214 potassium channel frog muscle. nerve 48, 49 sarcoplasmic reticulum, I10 sodium channel, frog muscle, nerve, 48. 49 water channel, 297, 302 Porin channel preparation, 200-205 structure, 213-217 Potassium channel calcium-activated, 89-91, 167-169 epithelia, 271-282 gating, 89-9 I , 163 invertebrates, 282 ion selectivity at end plate, 49 single-channel recording, 163- 164. 169 Potassium conductance irreversible inhibition, 117-1 18 sarcoplasmic reticulum, 117-1 18 Potassium flux single-file channels, 182- I84 Procaine end-plate channel block, 44-45 Protease effect on sarcoplasmic reticulum potassium channel, 118-1 I9 Protein conformation, see Conformational states Protochannels. 224. 227-228, 229, 233, 245 Proton concentration, effect on cell-to-cell permeability, 237-241
377 R
Rate theory model end-plate channel, 17-23 multisite, 19-23 single site, 18-20 Reaction-rate model gramicidin channel, 192 ion flux, 183-184 Rectification, cation channels, epithelia, 284-285 Rectifying channels, cell-to-cell channel, 233 Runs analysis, 75-77
S Sarcoplasmic reticulum potassium channel, 99-129 blocking reaction, I 1 1-1 17 effect of phospholipid surface charge, 118-119 effect of proteases, 118-1 19 streaming potential, 191 structure, 115 Sarcoplasrnic reticulum vesicles, flux measurement, 123- 127 Selectivity, water channel, 305 Selectivity sequence, .set’ c i / . c o Ion selectivity epithelia, 263 frog skin, 277 alkaline earth ions, 9 anions, halide, 8 apical membrane, 283, 284-285 cations, 3. 6 end plate, 47 gramicidin channel, 345 potassium channel, 49 sodium channel, 49 Self-block, sodium channel, epithelia, 265. 267 Self-trap model, 227-228, 230 Single-channel conductance concentration effect, 42-43 end-plate channel, 39-43 epithelia, 264. 266 gallbladder, 274
378 gramicidin channel, 302, 332-333, 342343 nonselective channels, 169 porin channel, 210-212 potassium channel, frog, 49 sarcoplasmic reticulum potassium channel, 108-110 sodium channel, frog, 49 sodium channel, GH3 cell, 67 voltage sensitivity, 24-26 Single-channel conductance measurement end-plate channel, 32-33 fluctuation analysis, 138-140 Single-channel permeability coefficients, 296-297 Single-channel recording, 133-171, 315 patch-clamp, 156- 17I porin channel, 205-207, 210-212 potassium channel, calcium-activated, 167- 169 statistical analysis, gating, 71-87 three-state channel, 318 Single-file channel, 181-195, 297, 301 potassium, 182-184 water permeability, 297 Single-site channel conformational transitions, 3 10-320 Sodium channel epithelium, 254-271 gating, 57-92, 161 inactivation, 62-63 kinetics, voltage-dependent, 58-59 selectivity, 49 single-channel recording, 161- 163 Sodium transport, epithelia, 265 Spectrum density, see Lorentzian spectrum Squid axon, see Sodium channel Streaming potential gramicidin channel, 359 sarcoplasmic reticulum potassium channel, 117 single-file channel, 188-191, 359 Surface charge, effect on single-channel conductance, 25-26, 43-44 Surface concentration, effect on singlechannel conductance, 25 Symmetry, transition frequencies, 3 18-3 19
INDEX
T Three-state channel, conformational transitions, 317-320 Tight junction, 253-254 Transition metal ions, inhibition of potassium channel, 117-118 Transport noise, 147, 320-321 Two-gate model, cell-to-cell channel, 243, 244 Two-site model, gramicidin channel, 192 Two-state channel conformational state, 310-316, 317, 321 noise analysis, 136-146
U
Upregulation cell-to-cell permeability, 236
V
Vesicles reconstituted with porin channel, 204205 sarcoplasmic reticulum, flux measurements, 123-127 Voltage-activated channels, 91 -92 Voltage dependence cell-to-cell channel, 241-243 sodium channel, epithelia, 264
W
Waiting time, 73-75, 83-85 Water channel, epithelia, 287 Water permeability, 295-306 epithelia, 286-287 gramicidin channel, 359-363, 366-367 single-file channel, 185-193, 359-363, 366-367 Water-wall interactions, 192 Water-water interaction, 185-187, 195 flux ratio equations, 195
Contents of Previous Volumes plasmic Reticulum Function ANTHONY MARTONOSI The Role of Periaxonal and Perineuronal Spaces in Modifying Ionic Flow across Neural Membranes JR. A N D Y. PALTI W. J. ADELMAN. Properties of the Isolated Nerve Endings GEORGINA RODRfGUEZ DE LORES DE ROBERTIS ARNAIZA N D EDUARDO Transport and Discharge of Exportable Proteins in Pancreatic Exocrine Cells: In Vitra Studies J . D. JAMIESON The Movement of Water across Vasopressin-Sensitive Epithelia RICHARD M. HAYS Active Transport of Potassium and Other Alkali Metals by the lsolated Midgut of the Silkworm WILLIAM R. HARVEYA N D KARLZERAHN Aitrhor Index-Subject Index
Volume 1
Some Considerations about the Structure of Cellular Membranes MAYNARD M. DEWEYA N D L ~ O Y D BARR The Transport of Sugars across lsolated Bacterial Membranes H. R. KABACK Galactoside Permease of Esclierichiu coli ADAMKEPES Sulfhydryl Groups in Membrane Structure and Function ASERROTHSTEIN Molecular Architecture of the Mitochondrion DAVIDH. MACLENNAN Author Index-Subject Index Volume 2
The Molecular Basis of Simple Diffusion within Biological Membranes W. R. LIEBA N D W. D. STEIN The Transport of Water in Erythrocytes ROBERTE. FORSTER Ion-Translocation in Energy-Conserving Membrane Systems A N D M. MONTAL B. CHANCE Structure and Biosynthesis of the Membrane Adenosine Triphosphatase of Mitochondria ALEXANDER TZAGOLOFF Mitochondria1 Compartments: A Comparison of Two Models HENRYTEDESCHI Author Index-Subject Index
Volume 4
The Genetic Control of Membrane Transport CAROLYN W. SLAYMAN Enzymic Hydrolysis of Various Components in Biomembranes and Related Systems MAHENDRA KUMARJ A I N Regulation of Sugar Transport in Eukaryotic Cells HOWARDE. MORGAN AND CAROLF. WHITFIELD Secretory Events in Gastric Mucosa P. DUREIN RICHARD Author Index-Subject Index
Volume 3
The Na+,K+-ATPaseMembrane Trmsport System: Importance in Cellular Function ARNOLDSCHWARTZ, GEORGEE. LINDENMAYER, AND JULIUS C. ALLEN Biochemical and Clinical Aspects of Sarco-
Volume 5
Cation Transport in Bacteria: K', Na', and H + FRANKLIN M. HAROLDA N D KARLHEINZ ALTENDORF
379
CONTENTS
Pro and Contra Carrier Proteins: Sugar Transport via the Periplasmic GalactoseBinding Protein WINFRIED Boos Coupling and Energy Transfer in Active Amino Acid Transport ERICHHEINZ The Means of Distinguishing between Hydrogen Secretion and Bicarbonate Reabsorption: Theory and Applications to the Reptilian Bladder and Mammalian Kidney AND WILLIAM A. BRODSKY THEODORE P. SCHILB Sodium and Chloride Transport across Isolated Rabbit Ileum STANLEY G. SCHULTZ AND PETERF. CURRAN A Macromolecular Approach to Nerve Excitation ICHlJl TASAKIA ND EMILIOCARBONE Subject Index Volume 6
Role of Cholesterol in Biomembranes and Related Systems JAIN MAHENDRA KUMAR Ionic Activities in Cells A. A. LEV A N D W. McD. ARMSTRONG Active Calcium Transport and Ca2+-Activated ATPase in Human Red Cells H. J. SCHATZMANN The Effect of Insulin on Glucose Transport in Muscle Cells TORBEN CLAUSEN Recognition Sites for Material Transport and Information Transfer HALVORN. CHRISTENSEN Subject Index Volume 7
Ion Transport in Plant Cells E. A. C. MACROEBtE H+ Ion Transport and Energy Transduction in Chloroplasts RICHARDA. DILLEYA N D ROBERTT. GIAQUINTA
OF PREVIOUS VOLUMES
The Present State of the Carrier Hypothesis PAULG. LEFEVRE Ion Transport and Short-circuit Technique WARREN S. REHM Subject Index
Volume 8
Chemical and Physical Properties of Myelin Proteins M. A. MOSCARELLO The Distinction between Sequential and Simultaneous Models for Sodium and Potassium Transport P. J. GARRAHANA N D R. P. GARAY Soluble and Membrane ATPase of Mitochondria, Chloroplasts, and Bacteria: Molecular Structure, Enzymatic Properties, and Functions RIVKAPANETA N D D. RAOSANADI Competition, Saturation, and InhibitionIonic Interactions Shown by Membrane Ionic Currents in Nerve, Muscle, and Bilayer Systems AND ROBERTJ. FRENCH WILLIAMJ. ADELMAN, JR. Properties of the Glucose Transport System in the Renal Brush Border Membrane R. KINNE Subject Index
Volume 9
The State of Water and Alkali Cations within the Intracellular Fluids: The Contribution of NMR Spectroscopy MORDECHAI SHPORER AND MORTIMER M. CIVAN Electrostatic Potentials at MembraneSolution Interfaces STUARTMCLAUGHLIN A Thermodynamic Treatment of Active Sodium Transport S. ROYCAPLANA N D AL.VINEssic Anaerobic Electron Transfer and Active Transport in Bacteria WIL N. KONINGSA N D JOHANNES BOONSTRA
CONTENTS OF PREVIOUS VOLUMES
38 1
Techniques for the Analysis of Membrane Gly coproteins R. L. J U L I A N O Glycoprotein Membrane Enzymes JOHN R. RIORDANA N D GORDON G. FORSTNER Membrane Glycoproteins of Enveloped Viruses w. COMPANS A N D RICHARD MAURICE C. KEMP Erythrocyte Glycoproteins J . A. TANNER MICHAEL Biochemical Determinants of Cell Adhesion Volume 10 LI-OYDA. CULP Mechanochemical Properties of MemProteolytic Modification of Cell Surface branes Macromolecules: Mode of Action in StimE. A. EVANSA N D R. M. HOCHMUTH ulating Cell Growth Receptor-Mediated Protein Transport into KENNETH D. NOONAN Cells. Entry Mechanisms for Toxins, Glycoprotein Antigens of Murine LymphoHormones, Antibodies, Viruses, Lysocytes soma1 Hydrolases. AsialoglycoprotEins. MICHELLE LETARTE and Carrier Proteins Sithjrc~rIndex JR. A N D DAVIDM. NEVILI-E, TA-MIN CHANG The Regulation of lntracellular Calcium AND ERNESTO CARAFOLI Volume 12 MARTINCROMPTON Calcium Transport and the Properties of a Carriers and Membrane Transport Calcium-Sensitive Potassium Channel in Proteins Red Cell Membranes VIRGILIOL. LEW A N D Isolation of Integral Membrane Proteins HUGOG. FERREIRA and Criteria for Identifying Carrier ProProton-Dependent Solute Transport in teins Microorganisms MICHAEL J. A. TANNER A. A. EDDY The Carrier Mechanism Siibjecl Index S. 9.HLADKY
Protein Kinases and Membrane Phosphorylation M. MARLENE HOSEYA N D MARIANO TAO Mechanism and Physiological Significance of Calcium Transport across Mammalian Mitochondria1 Membranes LEENAMELA Thyroidal Regulation of Active Sodium Transport F. ISMAIL-BEIGI Subject 1nde.r
Volume 11 Cell Surface Glycoproteins: Struoture, Biosynthesis, and Biological Functions
The Cell Membrane-A Short Historical Perspective ASERROTHSTEIN The Structure and Biosynthesis of Menibrane Glycoproteins JENNIFER STURGESS, MARIOMOSCARELLO, AND HARRYSCHACHTFR
The Light-Driven Proton Pump of Huloh r i c w i u n i hubhiurn: Mechanism and Function AND MICHAEL EISENBACH S. ROY CAPLAN Erythrocyte Anion Exchange and the Band 3 Protein: Transport Kinetics and Molecular Structure PHILIPA. KNAUF The Use of Fusion Methods for the Microinjection of Animal Cells R. G. KULKAAND A. LOYTER Siibjrc.1 Index
382 Volume 13 Cellular Mechanisms of Renal Tubular Ion Transport
PART 1: ION ACTIVITY AND ELEMENTAL COMPOSITION OF INTRAEPITHELIAL COMPARTMENTS lntracellular pH Regulation
CONTENTS OF PREVIOUS VOLUMES
Changes in Cell Membrane Surfaces Associated with Alterations of Transepithelial Ion Movement MICHAELKASHGARIAN The Dimensions of Membrane Barriers in Transepithelial Flow Pathways AND LARRYW. WELLING DANJ. WELLING Electrical Analysis of lntraepithelial Barriers EMILEL. BOULPAEP AND
WALTERF. BORON Reversal of the pH,-Regulating System in a Membrane Selectivity and Ion Activities of Snail Neuron Mammalian Tight Epithelia R. C. THOMAS SIMONA. LEWIS,NANCYK. WILLS, How to Make and Use Double-Barreled A N D DOUGLAS C. EATON Ion-Selective Microelectrodes Ion Conductances and Electrochemical THOMAS ZUETHEN Potential Differences across Membranes of The Direct Measurement of K, C1, Na, Gallbladder Epithelium and H Ions in Bullfrog Tubule Cells LUISREUSS MAMORUFUJIMOTO, A Kinetic Model for Ion Fluxes in the KUNIHIKO KOTERA,A N D Isolated Perfused Tubule YUTAKAMATSUMURA BRUCEBIAGI,ERNESTOGONZALEZ, lntracellular Potassium Activity MeasureAND GERHARD GIEBISCH ments in Single Proximal Tubules of Necof Voltage Clamping on Ion The Effects turus Kidney TAKAHIRo K ~ B~~~~~B , ~~ ~ ~Transport ~, ~Pathways , in Tight Epithelia ARTHURL. FINNA N D PAULA A N D GERHARD GIEBlSCH ROGENES lntracellular Ion Activity Measurements in Tubular Permeability to Buffer CompoKidney Tubules nents as a Determinant of Net H Ion RAJA N. KHURI Fluxes Intracellular Chemical Activity of PotasG. MALNIC,v. L. COSTASILVA, S . s. sium in Toad Urinary Bladder CAMPIGLIA, M. DE MELLOAIRES, JOEL DELONGA N D A N D G. GIEBISCH MORTIMER M. CIVAN Quantitative Determination of Electrolyte Ionic Conductance Of the Membranes and Shunts of Necrurus Proximal Tubule concentrations in Epithelial Tissues by GENJIROKIMURAA N D Electron Microprobe Analysis KENNETHR. SPRING ROGERRICK, ADOLFD ~ R G E , Luminal Sodium Phosphate Cotransport as RICHARD BAUER,FRANZBECK, the Site of Regulation for Tubular PhosJ U N E MASON,CHRISTIANE ROLOFF, phate Reabsorption: Studies with Isolated AND KLAUSTHURAU Membrane Vesicles HEINIMURER,REINHARDSTOLL, CARLAEVERS,ROLF KINNE, PART 11: PROPERTIES OF 1NAND JEAN-PHILIPPE BONJOUR, TRAEPITHELIAL MEMBRANE BARRIHERBERTFLElSCH ERS IN THE KIDNEY The Mechanism of Coupling between Glucose Transport and Electrical Potential Hormonal Modulation of Epithelial Strucin the Proximal Tubule: A Study of Potenture tial-Dependent Phlorizin Binding to IsoJAMESB. WADE
383
CONTENTS OF PREVIOUS VOLUMES
lated Renal Microvillus Membranes PETERS. ARONSON Electrogenic and Electroneutral Na Gradient-Dependent Transport Systems in the Renal Brush Border Membrane Vesicle BERTRAM SACKTOR
Volume 14 Carriers and Membrane Transport Proteins
Interfwe between Two lmmiscible Liquids as a Tool for Studying Membrane Enzyme Systems L. I. BOGUSLAVSKY Criteria for the Reconstitution of Ion PART 111: INTRAMEMBRANE CARRITransport Systems ERS AND ENZYMES IN TRANSEPIADlL E. S H A M 0 0 AND TH ELI AL TRANSPORT WILLIAM F. TIVOL The Role of Lipids in the Functioning of a Sodium Cotransport Systems in the ProxiMembrane Protein: The Sarcoplasmic mal Tubule: Current Developments Reticulum Calcium Pump R. KINNE, M. BARAC,A N D H. MURER J . P. BENNET,K. A. MCGILL,A N D ATPases and Salt Transport in the Kidney G . B. WARREN Tubule The Asymmetry of the Hexose Transfer DE L A MARGARITA PEREZ-GONZALEZ System in the Human Red Cell Membrane MANNA,FULGENCIO PROVERBIO, A N D W. F. W ~ D D A S GUILLERMO WHITEMBURY Permeation of Nucleosides, Nucleic Acid Further Studies on the Potential Role of an Bases, and Nucleotides in Animal Cells Anion-Stimulated Mg-ATPase in Rat AND PETERG. W. PLAGEMANN Proximal Tubule Proton Transport ROBERTM. WOHLHUETER E. KINNE-SAFFRAN A N D R. K I N N E Transmembrane Transport of Small PepRenal Na+-K+-ATPase: Localization and tides Quantitation by Means of Its K+-DepenD. M. MATTHEWS A N D J. W. PAYNE dent Phosphatase Activity Characteristics of Epithelial Transport in I11 A N D R E I N I E BEEUWKES R Insect Malpighian Tubules SEYMOUR ROSEN S. H. P. MADDRELL Relationship between Localization of N+Subject Index K+-ATPase, Cellular Fine Structure, and Reabsorptive and Secretory Electrolyte Volume 15 Transport STEPHENA. ERNST, Molecular Mechanisms of CLARAv. RIDDLE, A N D Photoreceptor Transduction KARLJ. K A R N A K JYR,. Relevance of the Distribution of Na' PART I: THE ROD PHYSIOLOGICAL Pump Sites to Models of Fluid Transport RESPONSE across Epithelia JOHNW. MILLSA N D The Photocurrent and Dark Current of DONALDR. DIBONA Retinal Rods Cyclic AMP in Regulation of Renal TransA N D D. A. BAYLOR G. MATTHEWS port: Some Basic Unsolved Questions Spread of Excitation and Background THOMAS P. DOUSA Adaptation in the Rod Outer Segment Distribution of Adenylate Cyclase Activity K.-W. YAU. T. D. LAMB,A N D in the Nephron P. A. MCNAUGHTON F. MOREL.D. C H A B A R D ~ S , Ionic Studies of Vertebrate Rods A N D M. IMBERT-TEBOUL W. GEOFFREY OWENA N D Subject Index VINCENT TORRE
384 Photoreceptor Coupling: Its Mechanism and Consequences GEOFFREY H. GOLD PART 11: THE CYCLIC NUCLEOTIDE ENZYMATIC CASCADE AND CALCIUM ION First Stage of Amplification in the CyclicNucleotide Cascade of Vision LUBERTSTRYER, JAMESB. HURLEY, A N D BERNARD K.-K.FUNG Rod Guanylate Cyclase Located in Axonemes DARRELL FLEISCHMAN Light Control of Cyclic-Nucleotide Concentration in the Retina THOMASG. EBREY,PAULKILBRIDE, JAMESB. HURLEY,ROGERCALHOON, A N D MOTOYUKI TSUDA Cyclic-GMP Phosphodiesterase and Calmodulin in Early-Onset Inherited Retinal Degenerations Y. P. LIU, G. J . CHADER, G. AGUIRRE, R. T. FLETCHER, R. SANTOS-ANDERSON, A N D M. T'so Control of Rod Disk Membrane Phosphodiesterase and a Model for Visual Transduction A N D E. N. PUGH,JR. P. A. LIEBMAN Interactions of Rod Cell Proteins with the Disk Membrane: Influence of Light, Ionic Strength, and Nucleotides HERMANN KUHN Biochemical Pathways Regulating Transduction in Frog Photoreceptor Membranes M. DERICBOWNDS The Use of Incubated Retinas in Investigating the Effects of Calcium and Other Ions on Cyclic-Nucleotide Levels in Photoreceptors ADOLPHI. COHEN Cyclic AMP: Enrichment in Retinal Cones DEBORA9. FARBER Cyclic-Nucleotide Metabolism in Vertebrate Photoreceptors: A Remarkable Analogy of an Unraveling Enigma G. L. WHEELER, M. W. BITENSKY, A. YAMAZAKI, M. M. RASENICK, AND P. J. STEIN
CONTENTS OF PREVIOUS VOLUMES
Guanosine Nucleotide Metabolism in the Bovine Rod Outer Segment: Distribution of Enzymes and a Role of GTP HITOSHISHICHI Calcium Tracer Exchange in the Rods of Excised Retinas ETE Z. S z u r s The Regulation of Calcium in the Intact Retinal Rod: A Study of Light-Induced Calcium Release by the Outer Segment H. GOLDA N D GEOFFREY JUANI. KORENBROT Modulation of Sodium Conductance in Photoreceptor Membranes by Calcium Ions and cGMP ROBERTT. SORLII PART 111: CALCIUM, CYCLIC NUCLEOTIDES, AND THE MEMBRANE POTENTIAL Calcium and the Mechanism of Light Adaptation in Rods BRUCEL. BASTIANAND GORDONL. FAIN Effects of Cyclic Nucleotides and Calcium Ions on Bufo Rods JOELE. BROWN A N D GERALDINE WALOGA The Relation between Ca2+and Cyclic GMP in Rod Photoreceptors STUARTA. LIPTONA N D JOHNE. DOWLING Limits on the Role of Rhodopsin and cGMP in the Functioning of the Vertebrate Photoreceptor E. OSTROY, SANFORD EDWARD P. MEYERTHOLEN, PETERJ . STEIN, ROBERTA A. SVOBODA, AND MEEGANJ. WILSON [Ca2+],Modulation of Membrane Sodium Conductance in Rod Outer Segments I1 A N D BURKSOAKLEY LAWRENCE H. PINTO Cyclic-GMP-Induced Depolarization and Increased Response Latency of Rods: Antagonism by Light WILLIAM H. MILLERA N D GRANTD. NICOL
385
CONTENTS OF PREVIOUS VOLUMES
PART IV: AN EDITORIAL OVERVIEW Ca'' and cGMP WILLIAM H. MILLER Index
Volume 16 Electrogenic Ion Pumps
PART 1. DEMONSTRATION O F PUMP ELECTROGENICITY IN EU KARY OTIC CELLS Electrophysiology of the Sodium Pump in a Snail Neuron R. C. THOMAS Hyperpolarization of Frog Skeletal Muscle Fibers and of Canine Purkinje Fibers during Enhanced Na+-K' Exchange: Extracellular K' Depletion or Increased Pump Current? DAVIDC. GADSBY The Electrogenic Pump in the Plasma Membrane of Nitellir ROGERM. SPANSWICK Control of Electrogenesis by ATP. Mg'+. H', and Light in Perfused Cells of Clrurti MASAHITAZAWA AND TERUOSHIMMEN
PART 11. T H E EVIDENCE IN EPITHELIAL MEMBRANES An Electrogenic Sodium Pump in a Mammalian Tight Epithelium S . A. LEWISA N D N. K . Wll.L5 A Coupled Electrogenic Na+-K+ Pump for Mediating Transepithelial Sodium Transport in Frog Skin ROBERTNIELSEN Transepithelial Potassium Transport in Insect Midgut by an Electrogenic Alkali Metal Ion Pump MICHAEL G. WOLFERSBERGER, AND WILLIAM R. HARVEY, MOIRACIOFFE
The ATP-Dependent Component of Gastric Acid Secretion G. SACHS,B. WALLMARK, C. SACCOMANI, E . RABON, H. B. STEWART,D. R. DIBONA,A N D T. BERGLINDH PART 111. REVERSIBILITY: ATP SYNTHESIS DRIVEN BY ELECTRIC FIELDS Effect of Electrochemical Gradients on Active Hi Transport in an Epithelium QAISAL-AWQATIA N D TROYE. DIXON Coupling between H+ Entry and ATP Synthesis in Bacteria PETERC. MALONEY Net ATP Synthesis by H+-ATPase Reconstituted into Liposomes YASUO KAGAWA Phosphorylation in Chloroplasts: ATP Synthesis Driven by A$ and by ApH of Artificial or Light-Generated Origin PETERGRABER PART IV. SOME THEORETICAL QUESTIONS Response of the Proton Motive Force to the Pulse of an Electrogenic Proton Pump ERICHHEINZ Reaction Kinetic Analysis of CurrentVoltage Relationships for Electrogenic Pumps in Neurospora and Acetuhiiluriu DIETRICH GRADMANN, AND ULF-PETER HANSEN, CLIFFORDL . SLAYMAN Some Physics of Ion Transport HAROLDJ. MOROWITZ PART V. MOLECULAR MECHANISMS O F CHARGE SEPARATION An H+-ATPSynthetase: A Substrate Translocation Concept I. A. KOZLOVA N D V. P. SKULACHFV Proton Translocation by Cytochrome Oxidase MKRTENWIKSTROM
CONTENTS OF PREVIOUS VOLUMES
Electrogenic Reactions of the Photochemical Reaction Center and the UbiquinoneCytochrome hlc2 Oxidoreductase P. LESLIEDUTTON,PAULMUELLER, DANIELP. O’KEEFE, NIGELK. PACKHAM, ROGERC. PRINCE,A N D DAVIDM. TIEDE Proton-Membrane Interactions in Chloroplast Bioenergetics R. A. DILLEY,L. J . PROCHASKA, G. M. BAKER,N. E. TANDY,A N D P. A. MILLNER Photochemical Charge Separation and Active Transport in the Purple Membrane BARRYHONIG Mitochondrial Transhydrogenase: General Principles of Functioning 1. A. KOZLOV Membrane Vesicles, Electrochemical Ion Gradients, and Active Transport ti. R. KABACK PART VI. BIOLOGICAL SIGNIFICANCE O F ELECTROGENIC ION PUMPS The Role of Electrogenic Proton Translocation in Mitochondria1 Oxidative Phosphorylation JANNAP. WEHRLE Electrogenic Reactions and Proton Pumping in Green Plant Photosynthesis WOLFGANG JUNGE The Role of the Electrogenic Sodium Pump in Controlling Excitability in Nerve and Cardiac Fibers MARIOVASSALLE Pumps and Currents: A Biological Perspective FRANKLIN M. HAROLD Index Volume 17 Membrane Lipids of Prokaryotes
Lipids of Prokaryotes-Structure and Distribution HOWARDGOLDFINE Lipids of Bacteria Living in Extreme
Environments THOMASA. LANGWORTHY Lipopolysaccharides of Gram-Negative Bacteria OTTOLUDERIZ, MARINA A. FREUDENBERG, CHRISGALANOS,VOLKERLEHMANN, AND ERNST TH. RIETSCHEL, DEREKH. SHAW Prokaryotic Polyterpenes: Phylogenetic Precursors of Sterols GUYOURISSON A N D MICHELROHMER Sterols in Mycoplasma Membranes SHMUELRAZIN Regulation of Bacterial Membrane Lipid Synthesis 0. ROCKA N D CHARLES JOHNE. CRONAN, JR. Transbilayer Distribution of Lipids in Microbial Membranes SHLOMOROTTEM Lipid Phase Transitions and Regulation of Membrane Fluidity in Prokaryotes DONALDL. MELCHIOR Effects of Membrane Lipids on Transport and Enzymic Activities RONALDN . MCELHANEY Index Volume 18
PART I. ADENYLATE CYCLASERELATED RECEPTORS Hormone Receptors and the Adenylate Cyclase System: Historical Overview B. RICHARDMARTIN The Elucidation of Some Aspects of Receptor Function by the Use of a Kinetic Approach A. M. TOLKOVSKY The p-Adrenergic Receptor: Ligand Binding Studies Illuminate the Mechanism of Receptor-Adenylate Cyclase Coupling JEFFREYM. STADELA N D ROBERT J . LEFKOWITZ Receptor-Mediated Stimulation and Inhibition of Adenylate Cyclase DERMOTM. F. COOPER
387
CONTENTS OF PREVIOUS VOLUMES
Desensitization of the Response of Adenylate Cyclase to Catecholamines JOHNP. PERKINS Hormone-Sensitive Adenylate Cyclase: Identity, Function, and Regulation of the Protein Components ELLIOTTM. Ross, STEFNE. AND PEDERSEN, V I N C E N TA . FLORIO The Regulation of Adenylate Cyclase by Glycoprotein Hormones BRIANA. COOKE The Activity of Adenylate Cyclase Is Regulated by the Nature of Its Lipid Environment A N D LARRY M. MILESD. HOUSLAY GORDON The Analysis of Interactions between Hormone Receptors and Adenylate Cyclase by Target Size Determinations Using Irradiation Inactivation B. RICHARD MARTIN
PART 11. RECEPTORS NOT INVOLVING ADENYLATE CYCLASE Vasopressin Isoreceptors in Mammals: Relation to Cyclic AMP-Dependent and Cyclic AMP-Independent Transduction Mechanisms SERGEJARD Induction of Hormone Receptors and Responsiveness during Cellular Diflerentiation L. MICHAEL C. LIN A N D SUZANNE BECKNER Receptors for Lysosomal Enzymes and Glycoproteins VIRGINIA SHEPHERD, PAUL SCHLESINGER, AND PHILIP STAHL The Insulin-Sensitive Hexose Transport System in Adipocytes J. G L ~ E M A N AN ND W. D. REES Epidermal Growth Factor Receptor and Mechanisms for Animal Cell Division MANJUSRI DAS The Linkage between Ligand Occupation
and Response of the Nicotinic Acetylcholine Receptor PALMER TAYLOR, ROBERTDALEBROWN. A N D DAVIDA. JOHNSON The Interaction of Cholera Toxin with Gangliosides and the Cell Membrane S I M O NVAN H E Y N I N G E N Subject Index
Volume 19
PART I . THERMODYNAMIC ASPECTS OF MEMBRANE TRANSPORT What is a Coupled Vectorial Process’? WILLIAM P. JENCKS The Membrane Equilibrium with Chemical Reactions FRIEDRICH A. SAUER
PART 11. STRUCTURAL ANALYSIS O F Na-K-ATPase Structural Aspects of Na-K-ATPase ROBERTL. POST Detergent Solubilization of Na,K-ATPase MIKAELESMANN Methods for the Cleavage of the Large Subunit of Na,K-ATPase and the Resolution of the Peptides Produced HENRYRODRIGUEZ. RICHARD HARKINS. A N D JACKKYTE Selective Purification of Na.K-ATPase and Ca?+,Mg’+-ATPasefrom Eel Electroplax L. M. AMENDE,S. P. CHOCK,A N D R. W. ALBERS High-Performance Gel Chromatography of Horse Kidney Na.K-ATPase MAKOTONAKAO.TOSHIKO NAKAO, TOMOKO OHNO,YOSHIHIRO FUKUSHIMA. Y U K I W HARA, I AND MASAKOARAI Native Membranes from Dog Kidney Outer Medulla, Enriched in Na,K-ATPase, and Vesicular in Nature 111 BLISSFORBUSH
388 Ultrastructure of Na,K-ATPase in Plasma Membranes Vesicles ELISABETH SKRIVER, ARVID B. MAUNSBACH, A N D PETERLETH JORGENSEN Electron Microscope Analysis of TwoDimensional Crystals of Membrane-Bound Na,K-ATPase ARVID B. MAUNSBACH, ELISABETH S K R I V E R , HANSHEBERT,AND PETER LETHJORGENSEN Organization of the Transmembrane Segments of Na-K-ATPase. Labeling of Lipid Embedded and Surface Domains of the aSubunit and Its Tryptic Fragments with I”’llIodonaphthylazide, [’?P]ATP, and Photolabeled Ouabain PETERLETHJBRGENSEN, A N D CARLOS STEVENJ . D. KARLISH, GITLER Structural Studies on Lamb Kidney Na,KATPase J . H. COLLINS,BLISSFORBUSH Ill, L. K. L A N E ,E. LING, ARNOLD SCHWARTZ, A N D A. (REEVES) ZOT Two Slightly Different &-Subunit Components of Kidney Na,K-ATPase Induced by Heat Treatment T. OHTA,M. KAWAMURA, T. HASECAWA, H. ISHIKURA, A N D K. NAGANO Radiation Inactivation Analysis of Na,KATPase PAUL OTTOLENCHI, J . CLIVE ELLORY, AND ROGERA. KLEtN Stoichiometrical Binding of Ligands to Less than 160 Kilodaltons of Na,KATPnse H. M A T S U I , Y. HAYASHI, H. HOMAREDA, A N D M. TAGUCHI The Active Site Structure of Na.KATPase: Location of a Specific Fluorescein Isothiocyanate-Reactive Site CYNTHIA T . CARILLI, ROBERTA. FARLEY, A N D LEWISC. CANTLEY Subunit Distribution of Sulfhydryl Groups and Disulfide Bonds in Renal Na,KATPase M. KAWAMURA, T. OHTA,A N D K. NACANO
CONTENTS OF PREVIOUS VOLUMES
Lipid Regions of Na,K-ATPase Examined with Fluorescent Lipid Probes KIMBERLY A. MUCZYNSKI, WARDE. HARRIS,A N D WILLIAM L. STAHL Role of Cholesterol and Other Neutral Lipids in Na,K-ATPase J.J.H.H.M.DEPoNT,W.H.M. PETERS,A N D S. L. BONTING PART 111. LIGAND INTERACTIONS: CARDIAC GLYCOSIDES AND IONS Cardiotonic Steroid Binding to Na,KATPase 111 BLISSFORBUSH Binding of Monovalent Cations to the Na,K-ATPase M. YAMAGUCHI, J . SAKAMOTO, AND Y. TONOMURA Half-of-the-Sites Reactivity of Na,KATPase Examined by the Accessibility of Vanadate and ATP into Enzyme-Ouahain Complexes OTTO HANSEN Binding of Rb’ and ADP to a PotassiumLike Form of Na,K-ATPase JORGENJENSENA N D PAUL OTTOLENGHI Side-Dependent Ion Effects on the Rate of Ouabain Binding to Reconstituted Human Red Cell Ghosts T. J . C A L L A H A N , H. H. BODEMANN, A N D J . F. HOFFMAN H. REICHMANN, Intracellular Sodium Enhancement of Ouabain Binding to Na,K-ATPase and the Development of Glycoside Actions TAI AKERA,KYOSUKE TEMMA,A N D SATOSH~ YAMAMOTO Lithium-Catalyzed Ouabain Binding to Canine Kidney Na,K-ATPase GEORGER. HENDERSON Ouabain Binding and Na,K-ATPase in Resealed Human Red Cell Ghosts A N D P. K. LAUF D. G. SHOEMAKER Stereoelectronic Interaction between Cardiotonic Steroids and Na,K-ATPase: Molecular Mechanism of Digitalis Action F. DITTRICH,P. BERLIN, K. KOPKE, A N D K . R. H. REPKE
CONTENTS OF PREVIOUS VOLUMES
Use of Prophet and MMS-X Computer Graphics in the Study of the Cardiac Steroid Receptor Site of Na,K-ATPdse DWIGHTS. FULLERTON. DOUGLAS C. ROHRER.KHALILAHMED,ARTHUR H. L. FROM.EITAHO KIl-ATSUJI, A N D TAMHOUE I~EFFO Photoaffinity Labeling of the Ouabajn Binding Site of Na,K-ATPase E. CLIFFORD C. HALL.A N D ARNOLD RUOHO New Ouabain Derivatives to Covalently Label the Digitalis Binding Site BERNARD Rossi. M A U R I C E GOEL-DNER. GILL.ESPONZIO. CHRISTIAN HIRTH.A N D MICHEL LAZDUNSKI Ouabain Sensitivity: Diversity and Disparities JOHNS. WILLISA N D J. CLIVE ELLORY
389 of Na,K-ATPase Regulated by Na' Ions on Both Sides of the Plasma Membrane HORSTWALTER Structurally Different Nucleotide Binding Sites in Na,K-ATPase A N D DORIS HERMANN KOEPSELL OLLIG Study of Na,K-ATPase with ATP Analogs WILHELM SCHONER, HARTMUT GEROLD PAULS,E N G I NH. SERPERSU. RE.MPETERS, ROSEMARIE PATZELT-WF:NCZLER, A N D MARION HASSELHERQ Affinity Labeling Studies of the ATP Binding Site of Canine Kidney Na.KATPase JAMESB. COOPER,CARI.JOHNSON, A N D CHARLES G . WINTER 31P['nO]NMRKinetic Analysis of '"0 Exchange Reaction between P, and HzO Catalyzed by Na,K-ATPase A. STEPHENDAHMSA N D JOEI.I.EE. MIARA
PART IV: LIGAND INTERACTIONS: NUCLEOTIDES, VANADATE, AND PHOSPHORY LATION Ligand Interactions with the Substrate Site of Na,K-ATPase: Nucleotides. Vanndate, and Phosphorylation JENSG . NORBY Conformational Changes of Na,K-ATPase Necessary for Transport T. LEWISC. CANTLEY, CYNTHIA CARILLI, RODERIC 1,. S M I T H , A N D DAVIDPERLMAN On the Mechanism behind the Abilily of Na,K-ATPdse to Discriminate between Na+ and K' JENSCHR.SKOU Characteristics of the Electric Eel Na,K-ATPase Phosphoprotein ATSUNOHU YODAA N D SHIZUKO YODA Sulfhydryl Groups of Na,K-ATPase: Effects of N-Ethylmaleimide o n Phosphorylation from ATP in the Presence of Na' t Mg'+ MIKAEL ESMANN A N D IRENA KI.ODOS Alternative Pathways of Phosphorylation
PART V. CONFORMATIONAL CHANGES, STRUCTUREIFUNCTION, AND ACTIVE SITE PROBES Principal Conformations of the @-Subunit and Ion Translocation PETERL. J0RGENSEN Magnesium-Induced Conformational Changes in Na,K-ATPase S. L. BONTING, H . G . P. SWARTS,W. H. M. PETERS,F. M. A. H. SCHUURMANS STEKHOVEN. AND J. J. H. H. M. DE PoNi Rubidium Movements in Vesicles Reconstituted with Na,K-ATPase, Measured in the Absence of ATP and P,, in the Presence of Either Ligand, and in the Presence of Both Ligands: Role of the "Occluded State" in Allowing for the Control of the Direction of Ion Movements S. J . D. KARLISHA N D W. D. STEIN Eosin: A Fluorescent Probe of ATP Binding to Na,K-ATPase J. C. SKOUA N D MIKAELESMANN
390 Interaction of Divalent Cations with Fluorescein-Labeled Na,K-ATPase JAMESG. MARCIASTEINBERG, KAPAKOS,A N D PARIMAL C. SEN Cation Activation of Na,K-ATPase after Treatment with Thimerosal MANISHAD. MONEA N D JACKH. KAPLAN Alteration of Conformational Equilibria in Na,K-ATPase by Glutaraldehyde Treatment DAVIDM. CHIPMAN, E. ELHANANY, R. BERGER,A N D A. LEV Conformational Transition between ADPSensitive Phosphoenzyme and PotassiumSensitive Phosphoenzyme KUNIAKI KAZUYATANIGUCHI,
CONTENTS OF PREVIOUS VOLUMES
Interaction of Na+, K', and ATP with Na,K-ATPase P. J. GARRAHAN, R. ROSSI, AND A. F. REGA Sodium Ion Discharge from Pig Kidney Na,K-ATPase YUKICHIHARAA N D MAKOTONAKAO ADP Sensitivity of the Native and Oligomycin-Treated Na,K-ATPase ANNS. HOBBS,R. WAYNEALBERS, A N D JEFFREY P. FROEHLICH Three (at Least) Consecutive Phosphointermediates of Na-ATPase I. KLODOS,J. G . NORBY,A N D N. 0. CHRISTIANSEN Aspects of the Presteady State Hydrolysis of ATP by Na,K-ATPase S U Z U K I , A N D S H O l C H l IlDA A. G . LOWEA N D L. A. REEVE Relation between Red Cell Membrane Identity of the Na Activation Sites in ATPase with the K Activation Sites in pNa,K-ATPase and Band 3 ERICT. FOWL AND A. K. SOLOMON Nitrophenylphosphatase L. A. PARODI, J. F. PINCUS, L. D.J. SORCE, AND s. R . JOSEPHSON, PART V1. REACTION MECHANISM AND KINETIC ANALYSIS SIMON On the Existence of Two Distinct Hydrolysis Cycles for Na,K-ATPase wilh Only Kinetic Analyses and the Reaction MechaOne Active Substrate Site nism of the Na,K-ATPase IGORW. PLESNER JOSEPHD. ROBINSON Kinetic Analysis of the Effects of Na' and Evidence for Parallel Pathways of PhosK+ on Na,K-ATPase phoenzyme Formation in the Mechanism LISELOTTEPLESNERA N D IGORW. of ATP Hydrolysis by Ekctrophorus PLESNER Na,K-ATPase Divalent Cations and Conformational JEFFREYP. FROEHLICH, ANN S. States of Na,K-ATPase HOBLIS,A N D R. WAYNEALBERS JOSEPHD. ROBINSON Evaluation of the Reaction Mechanism of the Sodium Pump by Steady-State Kinetics JOHNR. SACHS PART VII. ION TRANSLOCATION Kinetic Evidence in Favor of a ConsecuAND REACTION MECHANISM tive Model of the Sodium Pump D. A. EISNER AND D. E. RICHARDS Na,K-ATPase: Reaction Mechanisms and Kinetic Models of Na-Dependent PhosIon Translocating Steps phorylation of Na,K-ATPase from Rat PAULDE WEER Brain J. DONALDM. FOSTER, STANLEY Existence and Role of Occluded-Ion RUSSELL,AND KHALILAHMED Forms of Na,K-ATPase Reinvestigation of the Sequence of SensiI. M. GLYNNAND D. E. RICHARDS tivity of Phosphoenzyme of Na,K-ATPase Na and K Fluxes Mediated by ATP-Free to ADP and K + during the Presteady State and ATP-Activated Na,K-ATPase in of the Phosphorylation by ATP Liposomes Y. FUKUSHIMA AND M. NAKAO BEATRICEM. ANNER
CONTENTS OF PREVIOUS VOLUMES
Sidedness of Cations and ATP Interactions with the Sodium Pump L. BEAU& A N D R. DipoLo Sidedness of Sodium Interactions with the Sodium Pump in the Absence of K.I RHODABLOSTEIN Magnesium Dependence of Sodium PumpMediated Sodium Transport in Intact Human Red Cells A N D V. L. LEW P. W. FLATMAN K+-Independent Active Transport of Na+ by Na,K-ATPase A N D GILBERT CHIN MICHAELFORGAC ADP-ATP Exchange in Internally Dialyzed Squid Giant Axons PAULDE WEER,GERDAE . BREITWIESER, BRIAN G. KENNEDY, A N D H. GILBERT SMITH Sodium Pump-Catalyzed ATP-ADP Exchange in Red Blood Cells: The Effects of Intracellular and Extracellular Na and K Ions JACKH. KAPLAN Ouabain-Sensitive ATP-ADP Exchange and Na-ATPase of Resealed Red Cell Ghosts J. D. CAVIERES Effect of Internal Adenine Nucleotides on Sodium Pump-Catalyzed Na-Na and Na-K Exchanges GORML U N N , BRIANG. KENNEDY, A N D JOSEPH F. HOFFMAN N d K Pump in Inside-Out Vesicles Utilizing ATP Synthesized at the Membrane ROBERTW. MERCER,BEVERLEY E. FARQUHARSON, A N D PHILIP B. DUNHAM Anion-Coupled Na Efflux Mediated by the Na/K Pump in Human Red Blood Cells S. DISSINGA N D J. F. HOFFMAN Effect of Trypsin Digestion on the Kinetic Behavior of the Na/K Pump in Intact Erythrocytes DONNAL. KROPP Sodium Movement and ATP Hydrolysis in Basolateral Plasma Membrane Vesicles from Proximal Tubular Cells of Rat Kidney F. PROVERBIO, T. PROVERBIO, A N D R. MARfN
391 Stoichiometry of the Electrogenic Na Pump in Barnacle Muscle: Simultaneous Measurement of Na Efflux and Membrane Current M. T. NELSONA N D W. J. LEDERER PART VIII. BIOSYNTHESIS, MULTIPLE FORMS, AND IMMUNOLOGY Regulation of Na.K-ATPase by Its Biosynthesis and Turnover J. KARIN A N D NORMAN JOHNs. COOK Biosynthesis of Na,K-ATPase in MDCK Cells J. SHERMAN, T. MORIMOTO. A N D D. D. S A B A T I N I Possible Functional Differences between the Two Na,K-ATPases of the Brain KATHLEEN J. SWEADNER Antigenic Properties of the a, p, and y Subunits of Na,K-ATPase WILLIAM BALL,JR., JOHNH. COLLINS, L. K. LANE,A N D ARNOLDSCHWARTZ Antibodies to Na-K-ATPase: Characterization and Use in Cell-Free Synthesis Studies ALICIA MCDONOUGH, ANDREW HIA.TT. A N D ISIDORE EDELMAN Inimunoreactivity of the a- and a ( + ) Subunits of Na, K-ATPase in Different Organs and Species IRENEV. GERARDD. SCHELLENBERG, PECH, A N D WILLIAM L. S T A H L Role of Na’ and Ca” Fluxes in Terminal Differentiation of Murine Erythroleukemia Cells 1. G. MACARA,R. D. S M I T H , A N D LEWIS c. C A N T L E Y Na/K Pumps and Passive K + Transport in Large and Small Reticulocytes of Anemic Low- and High-Potassium Sheep P. K. LAUFA N D G. VALET Enhancement of Biosynthesis of Na,KATPase in the Toad Urinary Bladder by Aldosterone But Not T3 K. GEERING, M. GIRARDET, C. BRON, A N D B. C. J.-P. KRAEHENBUHL, ROSSlER
392 Na,K-ATPase Activity in Rat Nephron Segments: Effect of Low-Potassium Diet and Thyroid Deficiency LALC. GARGA N D C. CRAIGTISHER Axonal Transport of Na,K-ATPase in Optic Nerve of Hamster SUSANC. SPECHT PART IX. Na,K-ATPase AND POSITIVE INOTROPY; ENDOGENOUS GLYCOSIDES Positive Inotropic Action of Digitalis and Endogenous Factors: Na,K-ATPase and Positive Inotropy; “Endogenous Glycosides” ARNOLDSCHWARTZ Endogenous Glycoside-Like Substances GARNER T. HAUPERT, JR. Monovalent Cation Transport and Mechanisms of Digitalis-Induced Inotropy H. THOMASW. SMITHA N D WILLIAM BARRY Effects of Sodium Pump Inhibition on Contraction in Sheep Cardiac Purkinje Fibers AND D. A. EISNER,W. J. LEDERER, R. D. VAUGHAN-JONES Quantitative Evaluation of [3H]Ouabain Binding to Contracting Heart Muscle, Positive Inotropy, Na,K-ATPase Inhibition, and saRb+ Uptake in Several Species ERLANDERDMANN, LINDSAY AND BROWN,KARLWERDAN, WOLFGANG KRAWIETZ Contractile Force Effects of Low Concentrations of Ouabain in Isolated Guinea Pig. Rabbit, Cat, and Rat Atria and Ventricles GUNTERGRUPP,INGRIDL. GRUPP,J. A. GHYSEL-BURTON, T. GODFRAIND, DE POVER,A N D ARNOLDSCHWARTZ Difference of Digitalis Binding to Na,KATPase and Sarcolemma Membranes I. KUROBANE, D. L. NANDI, A N D G. T. OKITA Pharmacological and Biochemical Studies on the Digitalis Receptor: A Two-Site Hypothesis for Positive Inotropic Action ARNOLDSCHWARTZ, INGRIDL. GRUPP.ROBERTJ. ADAMS,TREVOR
CONTENTS OF PREVIOUS VOLUMES
POWELL,CUNTERGRUPP,A N D E. T. WALLICK Hypothesis for the Mechanism of Stimulation of the Na/K Pump by Cardiac Glycosides-Role of Endogenous Digitalis-Like Factor T. GODFRAIND, G. CASTAREDAJ. UHYSEL-BURTON, HERNANDEZ, A N D A. DE POVER Immunochemical Approaches to the Isolation of an Endogenous Digoxin-Like Factor KENNETHA. GRUBER, JANICEM. WHITAKER, A N D VARDAMAN M. BUCKALEW, JR. Demonstration of a Humoral N d K Pump Inhibitor in Experimental Low-Renin Hypertension MOTILALPAMNANI, S T E P H ~HUOT, N DAVIDCLOUGH,JAMESBUGGY,A N D FRANCIS J. HADDY Absence of Ouabain-Like Activity of the Na,K-ATPase Inhibitor in Guinea Pig Brain Extract GEORGER. KRACKE Brain Na,K-ATPase: Regulation by Norepinephrine and an Endogenous Inhibitor ALANC. SWANN Inhibitory and Stirnulatory Effects of Vanadate on Sodium Pump of Cultured Heart Cells from Different Species KARLWERDAN,GERHARD B AURIEDEL , WOLFGANG KRAw IETZ , A N D ERLAND ERDMANN Endogenous Inhibitor of Na,K-ATPase: “Endodigin” K. R. WHITMER, D. EPPS, A N D ARNOLDSCHWARTZ PART X. PHYSIOLOGY AND PATHOPHYSIOLOGY OF THE Na/K PUMP Disorders in Molecular Assemblies for Na Transport in Essential Hypertension MITZYL. CANESSA, NORMAC. ADRAGNA, ISABELBIZE, HAROLD AND DANIEL C. TOSTESON SOLOMON, The Na-K Cotransport System in Essential Hypertension R. P. GARAY,C. NAZARET,A N D P. HANNAERT
393
CONTENTS OF PREVIOUS VOLUMES
Loss of Na,K-ATPase Activity during Cataract Formation in Lens P A R I M AC. L SEN A N D DOUGLAS R. PFEIFFER Na/K Pump: Effect of Obesity and Nutritional State M. DELUISE. P. U S H E R , A N D J. F L I E R Decreased Na.K-ATPase Activity in Erythrocyte Membranes and Intact Erythrocytes from Obese Man DAVID M. MOTT, 1WAR KLIMES.A N D RANDILL . CLARK Functionally Abnormal Na/K Pump in Erythrocytes from a Morbidly Obese Subject J . FLIER. P. USHER. A N D M. DLLUISE Specific Insulin Binding to Purified Na.KATPase Associated with Rapid Activation of the Enzyme J U L I EE. M. MCGEOCH Mechanism for Cholinergic Stimulation of Sodium Pump in Rat Submandibular Gland DAVIDJ. STEWART A N D A M A R K K. SEN Evidence for an Aldosterone-Mediated. NaDependent Activation of Na,K-ATPtise in the Cortical Collecting Tubule KEVINJ . PETTY.J U H A P. KOKKO, AND DIANA MARVFR Vanadate and Somatostatin Having Divergent Effects on Pancreatic Islet Na.KATPase R. KENJIIKEJIRI A N D SEYMOUR LEVIN Phosphorylation of a Kidney Preparation of Na.K-ATPase by the Catalytic Subunit of CAMP-Dependent Protein Kinase SVENMKRDH Modulation of Na,K-ATPase Activity in Rat Brain by Adenosine 3',S'-Monophosphate RUSSEI.LB. L I N G H A AMN D A M A R K. SEN Stimulation and Inhibition by Plasma of Ouabain-Sensitive Sodium Efflux in Human Red Blood Cells A. R. CHIPPERFIELD Inhibition of the Na Pump by Cytoplasmic Calcium in Intact Red Cells A. M. BROWNA N D V. L. LEW
Involvement of Calmodulin in the Inhibition of Na.K-ATPase by Ouabain LIONEL G. L E L I ~ V RM. E , T . PIASCIK, J . D. POTTER.E . T. WALLICK. AND ARNOLDSCHWARTZ It1dex
Volume 20
PART I . FREQUENCY DOMAIN ANALYSIS O F ION TRANSPORT Fluctuation Analysis of Apical Sodium Transport T. HOSHIKO Impedance Analysis of Necturirs Gallbladder Epithelium Using Extra- and IntracelM a r Microelectrodes J . J . L I M ,G. KOTTRA, 1,. K A M P M A N NA. N D E. F K O M T E H Membrane Area Changes Absociated with Proton Secretion in Turtle Urinary Bladder Studied Using Impedance Analysis Techniques A N D TROYE. DIXON CHRISCLAUSEN Mechanisms of Ion Transport by the Mammalian Colon Revealed by Frequency Domain Analysis Techniques N. K. WILLS Analysis of Ion Transport Using Frequency Domain Measurements SIMON A. LEWISA N D WILLIAM P. ALLES Use of Potassium Depolarization to Study Apical Transport Properties in Epithelia LAWRENCE G . PALMER
PART 11. USE O F ANTIBODIES TO EPITHELIAL MEMBRANE PROTEINS Biosynthesis of Na+.K+-ATPasein Amphibian Epithelial Cells B. C. ROSSIER Use of Antibodies in the Study of Na+.K'ATPase Biosynthesis and Structure ALICIA A . MCDONOUGH
394 Encounters with Monoclonal Antibodies to Na+,K+-ATPase MICHAELKASHGARIAN, DANIEL BIEMESDERFER, A N D Bi.rss FORBUSH I11 Monoclonal Antibodies as Probes of Epithelial Cell Polarity A N D DORISA. GEORGEK. OJAKIAN HERZLINGER Immunolabeling to Frozen Thin Sections and Its Application to the Study of the Biogenesis of Epithelial Cell Plasma Membranes IVANEMANUILOV IVANOV,HEIDE PLESKEN,DAVIDD. SABATINI, AND MICHAELJ. RINDLER Development of Antibodies to Apical Membrane Constituents Associated with the Action of Vasopressin JAMESB. WADE,VICTORIA GUCKIAN, AND INGEBORC KOEPPEN Molecular Modification of Renal Brush Border Maltase with Age: Monoclonal
CONTENTS OF PREVIOUS VOLUMES
Antibody-Specific Forms of the Enzyme BERTRAM SACKTOR A N D UZI REISS PART 111. BIOCHEMICAL CHARACTERIZATION O F TRANSPORT PROTEINS Sodium-D-Glucose Cotransport System: Biochemical Analysis of Active Sites R. KINNE,M. E. M. DA CRUZ,A N D J. T. LIN Probing Molecular Characteristics of Ion Transport Proteins DARRELL D.FANESTIL, RALPHJ. KESSLER,A N D CHUN S I K PARK Aldosterone-Induced Proteins in Renal Epithelia MALCOLMCox AND MICHAELGEHEB Development of an Isolation Procedure for Brush Border Membrane of an Electrically Tight Epithelium: Rabbit Distal Colon MICHAELC. GUSTINA N D DAVIDB. P. GOODMAN Index
