Current Topics in Membranes & Transport, Volume 21: Ion Channels: Molecular and Physiological Aspects

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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9 8 1 6 5 4 3 2 1

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 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 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,',

-- 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 ( ~

(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

106

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

Na+ > Rb' > K +; this is identical to the sequence for the depths of the energy wells. Thus, K + displays the highest conduc-

110

CHRISTOPHER MILLER ET AL.

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

111

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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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-

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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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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).

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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

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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

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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 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

270

SIMON A. LEWIS ET AL.

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:

CHANNELS ACROSS EPITHELIAL CELL LAYERS

271

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.

272

SIMON A. LEWIS ET AL.

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.]

CHANNELS ACROSS EPITHELIAL CELL LAYERS

273

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).

274

SIMON A. LEWIS

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

CHANNELS ACROSS EPITHELIAL CELL LAYERS

275

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-

276

SIMON A. LEWIS ET AL.

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.

CHANNELS ACROSS EPITHELIAL CELL LAYERS

277

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 (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

278

SIMON A. LEWIS ET AL.

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.)

CHANNELS ACROSS EPITHELIAL CELL LAYERS

279

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

280

SIMON A. LEWIS ET AL.

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-

CHANNELS ACROSS EPITHELIAL CELL LAYERS

281

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

SIMON A. LEWIS ET AL.

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' (> 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

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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-

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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.

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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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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

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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)

298

ALAN FINKELSTEIN

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.

-

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’,

302

ALAN FINKELSTEIN

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

303

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.

304

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.

WATER MOVEMENT THROUGH MEMBRANE CHANNELS

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, 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)

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S. 6.HLADKY AND D. A. HAYDON

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