Ionic channels and gating currents in excitable membranes.

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Ann. Rev. Biophys. Bioeng. 1977. 6:7-31 Copyright © 1977 by Annual Reviews Inc. All rights reserved

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IONIC CHANNELS

-:-9085

AND GATING CURRENTS IN EXCITABLE MEMBRANES Werner Ulbricht

Department of Physiology, University of Kiel, 0-2300 Kiel, West Germany

INTRODUCTION Nerve fibers transmit information encoded as sequences of uniform impulses, the action potentials, which consist of brief changes in membrane polarization. In most nerves, but also in skeletal muscle fibers, the action potential is brought about by a transient flow of Na+ into the fiber that is followed by an outflow of K+. Flow of these ions is passive, i.e. down their respective (and opposite) electrochemical gradients. It has long been suggested that this movement of ions takes place at discrete membrane sites and there is now considerable evidence that these sites are pore-like structures, so-called ionic channels (1-3). This paper reviews recent publications in which the behavior of these channels is studied. This field was covered 5 years ago by Ehrenstein & Lecar ( 1) in these Annual Reviews and this article may to some extent be considered a sequel of this earlier review. To accommodate the entirely new topic, gating currents, the scope had to be limited by omitting some subfields (e.g. surface charges) altogether and by concentrating on voltage clamp experiments on axon and skeletal muscle mem branes. The technique of voltage clamping (e.g. 4), which forces the membrane potential to follow command signals, has proved to be particularly successful in studying excitable membranes. Other pertinent reviews have appeared during the last 5 years (5-11), some stressing the pharmacological approach (12, 13). Reviews of work on special aspects are mentioned in context.

BEHAVIOR OF CHANNELS Channel Types

In the axon membrane at least three types of ionic channels seem to exist whose average behavior can best be deduced from the current pattern that is observed when 7


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the membrane is suddenly depolarized, say to 0 mY, in a voltage clamp experiment. The immediate effect is a brief surge of capacity current that is largely over when the voltage step is completed; the surge roughly corresponds to the charge or discharge of the membrane capacity of about I p,F cm-2. A small, slower component of this current is considered in more detail in connection with the gating currents. Following the capaciity current is an inward current (of positive charge) that reaches its peak within less than 1 msec at room temperature. The current then subsides, changes its sign, and reaches a steady outward level within a few mil liseconds. In their classical analysis Hodgkin & Huxley (14) showed that what follows the brief capacity current is the sum of a transient Na inward current and a delayed K outward current. It was soon suggested that the pathways for Na+ and K+ are separate; this review defines two types of channels whose average response is derived from the current pattern. The first kind of channel promptly opens on depolarization but slowly closes again by inactivation. Since these channels nor mally let pass mostly Na+ they are called Na channels. By analogy I postulate another type of channel that opens more slowly, and after some delay, but stays open as long as the membrane is depolarized. This kind of channel is normally and predominantly used by K+ and hence is termed K channel. Both Na and K channels promptly close on repolarization.· Of course, these kinetic terms only reflect the average behavior of channels; the individual channel possibly exists in only two states,. fully opened or eompletely closed. This point is discussed in more detail in a chapter on noise anallysis (15). During a hyperpolarizing impulse a steady inward current, the so-called leakage current, is observed; it is thought to flow through a third type of channel that is permanently open, the leakage channel. Hence leakage also contributes a small current during depolarization. Leakage channels little discriminate among monova lent cations (16). The channel types diltfer in their ability to distinguish between ion species and in their response to chang1es in membrane potential. The latter property is the essence of excitability and is commonly attributed to the channel gate, as discussed in later sections. The former property is usually termed selectivity of the channel and is dealt with in the subsequent section. Selectivity of Channels DEFINITIONS The current carried by the movement of an ion species through the membrane is, in most general terms, the product of a permeability coefficient and the driving force acting on these ions. The most widely used equation describing this fact is the Goldman-Hodgkin-Katz flux equation (17, 18), which for the ion species Sis Is

p F/RD PS z2S EF2 [SI 0 [SI i ex (zsE 1 exp (zsEF/RD RT -

=

-

with Is density of current carried by S, ters per second), Zs = charge on S, [S]o external activity of S, [S]i =

=

1.

IONIC CHANNELS AND GATING CURRENTS IN NERVE

9

activity of S, and E membrane potential (inside with respect to outside); F, R, and T have their usual meaning. If several ion species, say Na+, K+, and Cl-, move through the membrane the potential, Er, for which the total ionic current becomes zero is given by the Goldman-Hodgkin-Katz potential equation =


RT PK [K+]o +PNa [Na+]o +PCI [Cl-]j In E = F r PK [K+] j +PNa [Na+lj +P C1 [el 10'

2.

Equations I and 2 were originally derived from the Nernst-Planck flux equation with several assumptions that most probably do not hold for ionic channels in nerve membranes; this point is extensively discussed in Hille's (19) comprehensive article on ionic selectivity of Na and K channels. Nevertheless the two equations have proved very valuable for the description of electrical membrane phenomena. The current flowing through the Na channel becomes outward, i.e. reverses its sign for depolarizations beyond the so-called reversal potential that for intact axons bathed in physiological saline is virtually identical with the Nernst potential for the Na+ distribution. Interestingly, in squid axons internally perfused with a K-rich but Na-free solution, an early outward current is observed in K-free sea water at large depolarizations that, obviously, cannot be carried by Na+ moving out. Chandler & Meves (20) have shown that this current was carried by K + passing, though less readily, through the Na channel. In this situation where [Na+] , = [K+ ] o 0 and PCI = 0 as suggested by independent evidence, equation 2 yields for the reversal potential =

RT 1 PNa [Na+]o n E = r

F

3.

PK [K+lj

Hence the permeability ratio P K/P Na can be calculated from Er when the ion activities are known. This ratio is 1/12 in squid axons and may serve as a measure of selectivity of the Na channel for K ions. In preparations such as myelinated nerve fibers or muscle fibers where internal perfusion is not feasible, the permeability ratio can be obtained from the difference of reversal potentials in the presence of (external) Na+, E,.Na' and E r.X after substi tuting Na+ with another monovalent cation, X+. We then have _RT

Px[X+]

o In Er,x - Er,Na - F P Na [Na+] 0

'

4.

assuming no change in internal ion concentration, P xlP Na could also be obtained from current ratios, at constant E, as derived from equation I for monovalent cations: _Px [X+lo -[X+lj exp(EF/RT) INa - PNa [Na+lo -[Na+lj exp (EF/RT)' Ix

5.

This derivation implies, as does equation 1,that the independence principle is valid. This principle states that the chance of an ion to cross the membrane is independent of the presence of other ions, of the same or other species (21 ). Often considerable

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deviation from independence is observed; possible reasons are saturating sites, long pore flux coupling, etc. Hence it is not surprising that for a number ofNa substitutes equation 5 yields different permeability ratios than equations 3 and 4, which are more universally valid. SODIUM CHANNELS The discriminating ability of the sodium channels has been studied for quite a number of cations. In most cases reversal potentials, E" were measured in the voltage clamp and permeability ratios, Px/ PNa> were calculated with equations' 3 or 4. Table 1 shows that Px/ PNa is comparable in the four preparations listed and that the permeability sequence is, with very few exceptions, identical. Chandler & Meves (20) were the first to measure, in squid axons, the complete selectivity sequence of alkali ions for Na channels (see third column of Table 1). They applied Eisenman's (22) selectivity theory for glass electrodes to the nerve and suggested that the channel might select by providing sites of high-negative field strength (high concentration of negative charge at small effective radius). Hille (23,24) studied, in nodes of Ranvier, many organic cations in addition. From the size of the excluded ions and their ability to form hydrogen bonds he postulated a selectivity filter as a 3 .1 >< 5.1 A constriction that is lined by eight oxygens as donors of hydrogen bonds, six of them approximately in one plane. Figure 1 (right diagram) gives Hille's (25) molecular interpretation of the filter in a side view showing three of the eight oxygens, with 01 and 01' belonging to a carboxylic group whose protonation leads to block with a pKa of 5.2-5.4 in frog nerve (27-30) and frog muscle (32), and with a IPKa of 4.8 in axons of the sea worm Myxicola (33). 01 could play the role of the anionic site of high field strength. An ion of the crystal size of Na+ is shown advancing from position 1 to 4; one of the accompanying water Table 1

Selectivity of sodium channels expressed as permeability ratio PX/PNa Frog

Frog x+

nerve

Ref.

musclea 1.0

Crayfish

Squid axon

Ref.

1.0

1.0

Sodium

1.0

Hydroxylammonium

0.94

23

0.94

Lithium

0.93

0.94

1.1

20

Hydrazinium

0.59

24

Ammonium

0.16

23

0.11

0.27

36

Guanidinium

0.13

23

0.093

0.25c

0.086

Potassium Aminoguanidinium Cesium Rubidium Choline

23

24

0.06

23

+20 mY. The dependence of inactivation on potential is expressed by the sigmoid relatiolit between h", and membrane potential, whose slope at its steepest point is e-fold Ifor 7-mV potential change in squid axons (57), about 8 mV in toad (58) and Myxicola (56) axons, but 5 mV in frog muscle (51). In formulating equation 6 it has been assumed that activation and inactivation are independent processes. Strict independence has recently been questioned for several reasons, one of which concerns T h' the inactivation time constant. This constant can be determined either from the secondary decrease in PNa during a sustained depolarization or in a two-pulse experiment where IN. is measured during fixed test pulses that follow conditioning pulses of constant amplitude but increasing duration. ft... should thl�n reflect the change in h caused by the conditioning pulses; for moderately depolarizing ones, however, h(t) is found to decrease only after some delay that is not predicted by equation 9. Moreover, Th determined this way is often clearly larger than that obtained during a single pulse of the same amplitude. These deviations have been observed in squid (59), Myxicoia (60, 61), and lobster (62) axons and in the frog node of Ranvier (63) and have given rise to new formal descriptions of Na channel gating (64, 65). Nevertheless, inactivation and activation appear to be separable by pharmacologi cal treatment. Thus, ina.ctivation is very much slowed by internal application of NaF to squid axons (66) and iodate to frog nerve fibers (67), and by external application of venoms of different !;corpion species to frog (68) and squid fibers (69) and of sea anemone toxin to crayfish axons (70). A nearly total abolition of inactivation is achieved by treating squid axons internally with pronase (a mixture of proteolytic enzymes) that does not show this effect on external application (71). After this treatment Na channels open with nearly normal activation kinetics but stay open as long as the membrane is depolarized. This alteration has been interpreted to point =



15

to an inactivation gate that is a readily accessible protein attached to the inner end of the Na channel. However, at least one of the model of coupled activation inactivation kinetics (64) could easily be adopted to simulate the pronase effect (72). It should be mentioned here that normally m 3 h of equation 6 never reaches unity because h decreases before m saturates, so that the maximum observed PNa is only 50-60% of PNa in nerve or even less in frog muscle (32). Therefore, drugs that slow inactivation are expected to increase peak PNa. Except for a slight PNa increase by sea anemone toxin (70) this has not been observed casting some doubt on the physical significance of PNa• Pharmacological modification of activation without major changes of inactivation has also been observed with still another scorpion (Centruroides) venom applied externally to frog nodes of Ranvier (73). Many more drugs affect Na channel gating and the reader is referred to recent reviews for details (12, 13, 74). What is formally described by variable h is not the only type of inactivation reported. Several components of slow inactivation with time constants between 100 msec and minutes have been described for the node of Ranvier (75-77) and for squid (78), Myxicola (78a,b), and lobster axons (79). In some preparations slow inactiva tion is absent in K-free external solutions. POTASSIUM CHANNELS Gating ofK channels is described by equation 7, where the exponent b = 2 in toad fibers (80) and Myxicola axons (56) and b = 4 in frog muscle (51) and squid axons (14). As in Na channels previous strong hyperpolariza tion delays the opening of K channels on a sudden depolarization. This delay can be described by equations 7 to 9 only if b is raised; b = 25 would be required to account for the delay after a hyperpolarization to E ca -200 mV (81). As already mentioned, PK inactivation as expressed by variable k in equation 7 is very much slower than activation (variable n), does not proceed exponentially, and is incomplete, i.e. koo > 0 even at large depolarizations. Obviously k behaves quite differently from h in equation 6. However, after internal treatment of squid axons with certain quaternary ammonium ions, especially nonyl-triethylammonium (C9), a fast and almost complete inactivation of K channels is observed: during a depolarizing pulse IK initially rises as usual but soon decays to very low levels. Armstrong (2, 82, 83) has studied these effects extensively and has developed from these and other experiments a model of the K pore. The basic idea is that the gate is situated near the axoplasmic mouth of the channel. When the gate opens it permits access to a relatively wide (diameter ca 8 A) initial segment that, together with hydrated K+, may also admit quaternary ammonium ions. The latter are too large to fit through the adjacent narrower channel segment (including the selectivity filter) thereby blocking the outward passage of K+. C9 and similar derivatives of tetra ethylammonium (TEA) that possess an apolar chain bind to a hydrophobic group in the internal pore mouth, thus stabilizing the onium ion in the blocking position. Dissociation from the channel site at rest is relatively slow but can be speeded by raising [K+Jo or by hyperpolarizing the membrane. Either measure increases the probability of finding a K+ at a position in the narrow segment of the pore where it can displace a Cg ion by electrostatic repulsion. =


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The rate of C9 block increases with [ C of inactivation. Hence, ifC9 and K+ enter the channel from the axoplasmic side with equal ease (which is not proven as yet), the rate of K+ entry can be calculated as the rate of C9 entry times [ K+]J[C9];. One finds 2-3 K+ JLsec-1 for a driving force, E - EK, of 150 mV leading to a single channel conductance of 2-3 pS (2). This is less than the value estimated from noise analysis (84). In myelinated frog nerve fibers C9 applied internally by diffusion from a cut internode, i.e. by the technique of Koppenhofer & Vogel (85), has very similar effects, leading to the same conclusions as to the channel structure (86). K channels of frog nodes, in constrast to those of the squid axon, can also be blocked by externally applied TEA. This effect, which does not seem to require open channels, is dealt with in the subsequent section.

SELECTIVE BLOCK OF CHANNELS Block

oj Sodium

Channels

One of the reasons to postulate Na channels separate from K channels was that either channel type can be selectively blocked without influencing the other. The already classical agents to block Na channels without any effect on the gate of the unblocked ones are tetrodotoxin (TTX) and saxitoxin (STX). Of the very many papers on the effects of these toxins (for reviews see 12, 87 88) only those have been selected that may help to determine the structure of the toxin receptor as part of the channel and the number of channels. TTX and STX are of relatively low molecular weight (about 320 and 350, respec tively) and block Na channels by a one-to-one reaction (89-92). The equilibrium dissociation constant, K, of the TTX-channeJ reaction as determined by eJectro physiological measurements is ca 3 nM in squid axons (90), toad and frog nodes of Ranvier (38, 91) and detubulated frog muscle, which is supposed to represent the surface membrane only, whereas K of the reaction with the receptors of the tubule membrane is four times as high (93); if no distinction is made, K"'" 5 nM is observed in muscle (94). K of STX binding in frog nerve and muscle is 1 4 (92) and 0.9 nM (32), respectively. The apparent rates of reaction are rather slow in squid axons (90, 95). Even in frog nodes where TTX has unimpeded access to the membrane the forward rate (at 20°C) is only 2.9 X 106 M-I sec-I and the rate of dissociation is 1.4 X 10-2 sec -I (91); the corresponding rate constants .of STX binding are (at 16°C) 10.1 X 106 M-I sec I afl(� 1.76 X 10-2 sec-I, i.e. clearly higher (92). Likewise, unbinding of [lH]STX than of l [ H]TTX adding STX to a node of Ranvier pretreated with TTX leads to an overshoot in the additional block. Such a transient, however, is expected only if the two toxins compete for the same site (92). A common receptor for STX and TTX has also been deduced from the fact that STX is able to displace PH]TTX from excitable mem branes (97-99). The effect of TTX is reduced both in alkaline and acid solutions. The former effect is most probably caus�:d by a reversible transformation of the active cationic form ,

.

-



17

of the toxin into the inactive zwitterion (38, 89, 100, 101). The effect of low pH, on the other hand, is best described by a competition between TTX and H+ for the same receptor (38). A similar effect of low pH is seen with STX (92) in agreement with diminished [3H]STX also reduced in acid solution (98, 102, 103) and both STX and TTX bind less in the presence of various cations, suggesting that the toxin receptor is a metal cation binding site (102) that could correspond to well 2 in the energy profile of Figure 1 (left). These and other results and a recent revision of the STX structure (104) have led Hille (105) to propose that the toxins block by sticking a guanidinium group in the selectivity filter, extending an idea of Kao & Nishiyama (106). Stabilization would be achieved by five hydrogen bonds between the toxin molecule and the oxygen ring of the filter and by the electrostatic attraction between the guanidinium group and the negative charge on the filter; its protonation would prevent binding of the toxin. TTX derivatives are usually inactive and whatever trace activity is observed may be due to contamination with unreacted TTX (107). Inactivity could result from removing hydrogen bond donors but this idea cannot consistently be carried through (105). In this connection it should be mentioned that changes at the group farthest from the guanidinium group leads to a derivative that is only three to nine times less active than TTX (108). TTX and stx, even at very large concentrations, are ineffective if applied from inside the axon (85, 109, 110), another point in favor of the externally situated selectivity filter to be involved in the block. Interestingly, local anesthetics like procaine or lidocaine that assumably act from the axoplasmic side of the membrane do not interfere with toxin binding, as shown in voltage clamp (111) and radioactive tracer studies (96, 98, 103). Finally, as expected of a drug acting on the selectivity filter, TTX does not seem to immobilize the gate and hence does not block the putative gating current, as discussed in detail in the next section. Independence of gate and TTX receptor may also be inferred from the fact that Na channels whose kinetics have been enormously slowed by treatment with the alkaloid veratridine are nevertheless blocked by TTX in quantitatively the same way as unmodified channels (13, 112). By the same token the alkaloid mixture veratrine does not affect 3 [ H]STX binding to garfish nerve membranes (96). Titration of Sodium Channels

Because of their high affinity for the Na channel, STX and TTX have been used to titrate channels. The first attempts (113, 114) were made by equilibrating nerve preparations of known surface area successively in a small volume of TTX solutions, whereby its concentration gradually decreased. Loss of toxin was determined as loss of blocking potency, i.e. by bioassay. After allowing for the (measured) extracellular space,and on the assumption that the toxin binds only to its receptors (channels), an upper limit of their density was obtained. It was between 36 and 75 sit es p.m-2 for thin, unmyelinated nerve fibers of lobster, crab, and rabbit (vagus), prep arations that yield a large membrane area per weight (114). These and similar prep arations have also preferably been tested when tritium-labeled toxins became avail able. Uptake of3H-labeled toxin"typically has two components, a saturable Lang-


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muir component, whose equilibrium constant is comparable to K of block experi ments, and a linear nonspecific component, whose origin has been much discussed, whether it is caused by radioactive impurities (99, 115) or represents toxin bind ing to sites other than specific blocking receptors (116). Of course, the presence of appreciable amounts of radio-impurities in a chromatographically homogeneous 3H-labeled toxin preparation would lead to an overestimation of its specific activity and hence to an underestimation of the number of saturable binding sites. Thus Levinson & Meves (117) considered, by comparison with a bioassay, the specific activity of their [3H1TTX at 553 sites /-tm-2 for squid axons, the highest channel density so far determined by 3H-labeled toxin binding. This value, however, is comparable to recent estimates from block kinetics (95), gating currents (53, 118, 119), and noise analysis (84). Other preparations yield much lower channel densities, e.g. about 20 sites /-tm-2 in lobster nerve (98, 120) and even only 3 sites /-tm-2 in garfish olfactory nerve (98). In a square array this latter density would correspond to a distance of 0.6 /-tm, i.e. more than twice the diameter of these small fibers! In membrane homogenates from garfish olfactory the binding is only little higher (103, 121). 3 [ H]TTX homogenates of lobster nerve was comparable to that of intact nerves corresponding to 28 sites /-tm-2 (99). Future determinations with purer and highly radioactive 3H-Iabeled toxins that begin to become available may yield higher densities; at least the figure for rabbit vagus, 22-27 sites /-tm-2 (96, 98), had to be increased fourfold on re-determination (122). It should be mentioned here that Henderson & Wang (97) and Benzer & Raftery (123) have succeeded in solubilizing a membrane compo nent that very specifically binds [3H]TTX of 500, 000. Interestingly, from the loss of TTX binding power on irradiation with high-voltage electrons Levinson & Ellory (124) arrived at a similar value of 230,000 daltons for the Na channel. Binding to fibers of frog sartorius muscle has been studied both by bioassay and with 3 [ H]TTX, (122). On the assumption that the tubules contain one-quarter of all Na channels (125) and that the ratio of tubule to surface membrane is about six (126),one arrives at 280 sites /-tm-2 on the surface and 16 sites /-tm-2 in the tubules (94). A more direct approach is to compare binding to normal fibers with that to fibers detubulated by osmotic shock on the assumption that in the latter the tubules are inaccessible to TTX. Bioassay experiments of this kind have led to 175 sites /-tm-2 on the surface and 41-52 sites /-tm-2 in the tubules (93). These results are of particular interest since frog muscle and squid axons are the only preparations in which channel density can be compared with membrane sodium conductance, as measured in voltage clamp experiments, to estimate single channel conductances of about 1 and 3 pS, respec tively (94). The conductance of single channels is discussed in detail in this volume (IS). Block of Potassium Channels

So far no blocking agent for the K channel has been found that is quite comparable to the action of TTX or STX on the Na channel. TEA comes closest to it but only



19

where it acts on external application as, for example, in myelinated nerve fibers of frog and toad. Like the toxins, TEA seems to block by a reversible one-to-one reaction, however with an equilibrium constant K = 0.4 mM (127), i.e. 105 times higher than that of the toxin-Na channel reaction. Also,opening of the unblocked channels is somewhat slowed and there seems to be some slight effect on Na channel kinetics (128). Unlike squid, in which TEA acts only from inside the axon and in which it blocks outward IK more than inward IK (129, 130), TEA applied externally to nodes of Ranvier blocks both inward and outward IK about equally (128). Internal TEA also blocks K channels of Ranvier nodes (85) but in this case the (outward) IK shows some slight inactivation of the kind seen much more clearly with C9 (86). It could well be that there are different receptors on either side of the nodal membrane. The ones accessible to external application seem to discriminate on the basis of size: K increases from 0.4 to 15 mM if one ethyl group of TEA is substituted by a methyl group. K of tetramethylammonium (TMA) is estimated to be greater than 500 mM so that TMA may serve as an excellent Na+ substitute (131). The TEA-channel reaction is too fast to be resolved by the present technique; the rate of dissociation of the TEA-receptor complex is at least 2 X 102 sec-I but possibly is much larger (13, 132). TEA also acts on external application to frog skeletal muscle by blocking the delayed K channel; the block is prompt (133), K 8 mM, and channel kinetics are slowed (134). The inward rectifier is less susceptible with K = 20 mM (135). In view of the labile TEA-channel complex, binding experiments with labeled TEA do not seem to be feasible unless one succeeds in binding the label covalently. Promising steps in this direction have recently been done with a photoaffinity label derived from TEA (136). This derivative acts as a reversible PK inhibitor in frog nodes of Ranvier,both on external and internal application,however with different effects on PK kinetics. Additional irradiation with UV light leads to irreversible block of K channels but only after external drug treatment. Finally another simple compound, 4-aminopyridine (4-AP),should be mentioned that very selectively blocks K channels. It has so far been tested on cockroach giant axons (137), frog nerve (138, 139), frog muscle (140), and Myxicola ( l40a) and squid axons, where it acts both from outside and inside (141, 142). Block by 4-AP is independent of IK direction but partially removed on sustained depolarization. There is reason to assume that it acts from inside even on external application (139). =

GATING CURRENTS Hypothetical Gating Current

Nothing has been said so far about the current ideas of the mechanism by which membrane potential controls channel gates. CaH has been favored for a long time to play an essential role,possibly by serving as voltage-sensitive plugs. This hypothe sis and others involving dissolved ions or molecules have been reviewed and refuted in a recent article on Na channel gating by Hille (74). Thus, it seems that the voltage-sensing and gating structures are intrinsic components of the membrane. This notion is also contained in the physical basis that Hodgkin & Huxley (14)


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suggested for their mathematical description of ionic permeability (see equations 6 through 9). These authors assumed that on depolarization charged particles move within the membrane, thereby opening channels, or in the case of inactivation closing them. Thus the sigmoid onset of INa in squid axons could be explained if the movement of three (=0 in mOh of equation 6) independent charged particles to a certain region within the membrane is necessary to open a channel. The total charge on these t4ree particles can be estimated from the maximum slope of the PNa-E relation with Boltzmann 's principle that predicts for a single charge an e-fold change for R TIF, i.e. 2:5 mY at room temperature. Clearly, similar models can be . developed involving the: orientation of dipoles (e.g. 143). In either case movement of this charge should, in principle, become detectable as gating current. Ther modynamically speaking, since metabolism and ionic gradients seem to be ruled out as directly contributing energy to open and close the gate (74), the electrical field must do the necessary work on the gate or some potential sensor by moving charge through the intramembrane field, thus creating a gating current. The size of this current must be small (;ompared to the ionic current carried by hundreds of Na+ that pass each channel during an action potential. Hence, only if the ionic current is suppressed is there a chance to measure gating current. Before recent attempts in this direction are described it may be helpful to list some of the features of hypothetical gating current carried by particles that behave in strict accordance with the variable m of Hodgkin & Huxley. Since these particles are confined to the membrane, the gating charge moved through a depolarizing pulse (Qon) in one direction should be quantitatively moved back (Qoff) on repolari zation. Also, there should exist a maximum value, Qma.. of the charge that can be moved equivalent to a change of m from zero to unity. Since the gating current, Ig,m, carried by m particles is Qmax dmldt, its time course can be obtained by differentiating equation 9 (see also 119) for the case of y = m: Ig. m = Qm ax

I

-:;:(m., - mo) exp(-tIT m), m

10.

where the initial valu(�, mo, should be practically zero for starting or holding potentials, EH, sufficiently negative, say -100 mY. From equation 10 we expect, on a depolarizing step, Ig.m to rise instantaneously in the positive (outward) direction and to decay exponentially with T m' which is determined solely by the mem brane potential during the current flow. Moreover, since mo "'" 0 for EH < -100 mY, we expect Qon for various pulse potentials Ep (where Ep > EH) to be Ig.m (t=O)T m = Qmax m�, so that QonlQmax as a function of Ep should reflect m� (Ep). Observations Agreeing with the Model

The first experiments to reveal a current component comparable to the hypothetical gating current were done on squid axons (144, 145), as a rule internally perfused with virtually impermeant Cs+ and externally bathed in a solution in which Na+ and K+ had been substituted by impermeant Tris ions. Usually TTX was also added, which does not interf(�re with the gating mechanism (54, 146). To improve the


21

signal-to-noise ratio the results of many identical pulses were averaged by a c om puter; to eliminate the linear (symmetrical) component of the capacitative current on each potential step, an equal number of pulses of exactly the same amplitude but opposite sign were added. In Figure 2 the middle pair of traces give, on a high gain, the current patterns observed during a single positive and negative pulse of 80 mV, starting from EH -60 mY. The lowermost record shows the summed response to 300 of such pairs of impulses where the on response is an outward and the off response is an inward current. The on response, after a short rising phase, reaches its maximum before the ionic current has turned on (Figure 2, uppermost trace) and subsequently declines with a single time constant, Ton' often to a small, steady outwar d curre n t that is most likely due to leakage rectification. The off response, too, often decays with a single time constant, Toff' The rising phase is interpreted as the result of a fast inward-directed component of gating current during the start


=

N

E u

�I 6

I

� -60 -(

-140

( -60

1·0

Figure 2

msec

Sodium current (upper trace), single-sweep displacement currents (middle traces),

and averaged record of 300 pairs of such displacement currents (lower trace). For the upper trace a squid fiber was perfused internally with high cesium and bathed in sea water with 25%

the normal Na+ content. For the other records the

fiber was subsequently bathed in Na-free

(Tris) sea water containing also 300 nM rrx. The figures against the traces show the mem

brane potentials during and between pulses in millivolts. From Keynes & Rojas (53). Reprinted with permission.

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of each hyperpolarizing pulse as one might expect from equation 10 if m a is finite and, of course, m� = 0 and if Tm (-140) < Tm (+20). Hence, starting from a very negative E H (where ma 0) should eliminate the rising phase, as has indeed often (but not always) been observed (146). Other interpretations of this phase have been suggested (147, 148). On the other hand there should exist a more positive value of E H for which the charge distribution is halfway 'between two extremes (i.e. for m� = 0.5) so that the effects of positive and negative pulses may cancel each other. Figure 3 b shows for pulses of ±90 mV that this is the case if they start from E H ca -60 mV. For �!ven more positive E H the responses reverse, i.e. the on re sponse becomes inward and the off response outward (Figure 3c). In squid axons reversal has been reported for EH between ca -75 and -55 mV (118, 146, 149). The areas under on response and off response correspond to the total charge, Qon and Qoff' that is moved. For short pulses Qon Qoffas required by the hypotheti cal [g. m (118,119, 146,. sumptive gating currents have also been measured in myelinated nerve fibers treated with TTX and TEA (151-153) and in Myxicola giant axons treated with TTX and


=

=

=

HP-94·5 mV

a

20 :

'-

o -20

.........."" . ... ........ .. .. ,"Io ___

>�

,;

b

HP-60 mV

20 o

)•. ... �.-....... .. ..

-20 HP

c

20 o -20

Figure 3

-

35 · 5

.-\ -"..-."";: \.... f

i

...",.J",..,-,;- . ... .. ........ . .....�

Averaged gating current response to ±90-mV pulses (32 each. 2.5-msec duration)

as a function of holding potential (HP) as indicated against traces. Note reversal of on and

off response as HP becomf>S -60 mV or more positive. Squid axon perfused with high rubidium and TEA and bathed in Tris sea water; 3.5°C. From Meves (1 1 8). Reprinted with permission.

23


4-AP ( l s 3a). If Qon or Qoff is plotted as a function of pulse potential (at E H -90 to - 1 00 mY) in squid, frog, and Myxicola fibers, a sigmoid curve is obtained that saturates for E > ca +40, mY. The saturating value, Q rnax > is between 26 and 34 nC ).t m-2 , corresponding to 1 600 and 2 1 00 esu ).tm-2 in squid ( 1 1 8, 1 1 9); if started at EH = - I SO mV the Q-Ep curve shows another relatively flat limb for E < -100 mV ( 1 48). Qrnax in Myxicola axons is 750-900 esu ).tm-2 ( I 53a); in p frog fibers it is much larger: 1 7,200 esu ).t m-2 ( 1 5 1 ). The pulse potential for which Qon or Qoff reaches half-saturation seems to vary; values between - 1 6 ( 1 1 8) and -26 mV (5 3) have been reported for squid axons, -36 mV for nodes of Ranvier ( 1 5 1), and ca -20 mV for Myxicola axons ( l 53a). For the hypothetical Ig.m at very negative E H, half-saturation should be attained at a pulse potential, E', at which moo = 0.5; the same criterion has been mentioned in connection with E H at which reversal occurs. Since the latter potential is defi nitely more negative, the simple Ig.m model does not seem to be adequate ( 1 1 8). In a more general approach one can assume that the mobile charges within the membrane follow a Boltzmann distribution with two allowed configurations whose energies are 10 , and 10 2, respectively. It can be shown (53, 1 1 9) that for large negative EH the energy difference t.€ = € , - €2 = kT In [q/( \ - q)], where q = Qon / Q rna x is the normalized charge. k Boltzmann constant. and T absolute temperature. A plot of observed q values in the form of In [q/(l - q)] vs E yields a straight l ine inte rceptin g the potential axis at E = Eo where q = 0.5. Writing t.E a. (Eo - E) the slope of the line becomes a.1 kT, where a. effective valency of each particle, i.e. the number of electronic charges it carries times the fraction of the total field acting on it. In squid axons the mean Eo -26 mV and the mean slope is (-18.5 mVyl, yielding a = -1.3 esu at 5°C whereas E' (Moo = 0.5) = -29 mV after some corrections (53). The corresponding values for the frog node are Eo -3 3 . 7 mY, slope of (-14.9 mV)-' so that a = -1 . 65 esu at 1 2°C ( 1 5 1 ) whereas E' in toad fibers is ca -35 mV (55). If a Na channel is controlled by a particles each carrying a charge of a.. the channel density can be obtained from Qmax/(-a a.); in squid axons this would be 2 100 esu ).tm-2/(3 X 1 . 3 esu) = ca 530 /A-m-2 (53), close to 533 ).t m-2 as obtained from PH]TTX binding ( 1 1 7). For the frog this calculation yields 1 7,200 esu ).tm-2/(2 X 1 . 65 esu) = 52 12 ).tm-2, i.e. a density nearly ten times as high ( 1 5.1). A different physical basis has been given to the Q-E relation in squid axons by fitting the function fix) = tanh x for the orientation of permanent dipoles in the case that they can take up only two positions, parallel or anti parallel; x = (p, U/kT), where p, = dipole moment and U potential gradient across the membrane, assumed to be 70 A thick ; k and T have their usual meaning. A good fit is obtained for p, = 270 D units ( 1 1 8; see also 143).


=

=

=

=

=

=

=

=

Deviating Results Most of the results described so far could give the impression of a fairly close correspondence between the observed small currents and the hypothetical Ig.m as derived from the formal Hodgkin-Huxley description of ionic currents. The results presented in this section will show that the relationship between intramembrane

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charge movement and channel gating is more complicated. This may have many reasons, one being that what is termed gating current may only partially be involved in opening and closing channels. This is expressed by the more noncommittal terms displacement current or asymmetry current that are often used. Another reason for discrepancies may be that the classical Hodgkin-Huxley equations may not ade quately describe ionic currents under all circumstances.


TIME CONSTANTS

The first set of results that cannot readily be reconciled with the Ig.m model concerns the time constants, Ton and Toff, of the gating current that should, for large negative EH, correspond to Tm(Ep) and Tm(EH), respectively. Therefore, Tolf should be independent of Ep; however, in squid axons, but not in frog fibers (54, 15 1), Tolf lengthens, at constant EH, when the pulse amplitude is increased from ±40 to ca ± 140 mV (53, 118). This complicates the comparison of Tolf with TNa> the time constant with which INa declines on repolarization. Early studies claimed Tolf "'" TNa (119, 146, 154); this finding is in direct contlict with the simple Ig.m model. Hence TNa was carefully reexamined for several E p and E H and was found, in agreement with the Hodgkin-Huxley description, to be independent of Epo However, since Tolf in the same preparations was not, Toft/TNa varied, at constant EH = -60 mY, between ca \.6 and 2.2 with pulse height; for EH < -90 mY, Tolf/TNa was ca 3 or even slightly larger (53). Clear deviations from Toff/TNa = 3 would invalidate the idea thatNa channels close as three independent particles move back to their resting position at equal speed. If one of the three particles moves much faster than the other two an off response with two time constants would ensue, one of which could be comparable to TNa (154). A second slower component of the off response has indeed been observed but its significance remains unclear (118, 146). To explain Totr -50 mV appears to correspond nevertheless to Tm(E) with the possible exception of T m values between E = -40 and -70 mV . The latter curve has its maximum at E = -36 mV whereas the former curve peaks near E =-4 1 mV (53). In earlier squid experiments Ton(Ep) had its maximum near E = - 1 2 mV ( 1 1 8), i.e. ca 25 mV more positive than T m (E) as calculated from the equations of Hodgkin & Huxley ( 1 4). CHEMICAL TREATMENT

Another group of experimental results that are difficult to explain in terms of the Ig.m model was obtained by chemical treatment of the axons. Thus internal perfusion of squid axons with Zn2+ reversibly reduces PNa ( 1 5 5) and reversibly abolishes the gating current (146, 1 56). A more detailed study, however, revealed that ZnH treatment did not affect the reversed response for EH > -60 mY. One possible explanation would be that there exist Zn-insensitive as well as Zn-sensitive mobile charges, with only the latter related to channel gating ( 1 47). Heavy water is known to increase the time constants of the ionic currents in squid axons by a factor of about 1 .4 ( 1 57). In a recent study this was confirmed for TNa but T off was unchanged by D20 ( 1 1 8). For an explanation it has been proposed that the hypothetical conformational change of gating particles (after their move ment that actually opens the channel) involves hydrogen bonding (9). Procaine (0. 1 mM) depresses peak PNa and slows its onset in squid axons (158) and was shown, however at a very high concentration (37 mM), to reduce both Qoff and T off ( 1 1 9). In toad nerve fibers where 0. 1 mM procaine reduces peak PNa by ca 40% and increases T m(Ep + 10 mV), the initial current value of the on response is reduced by ca 1 5% whereas Ton and Toff do not seem to be changed ( 1 53). Hence in either preparation the time constants of ionic and gating current are differently affected by the local anesthetic. =

INACTIVATION A last group of experiments whose results cannot readily be explained by the Ig, m model concerns PNa inactivation. Hodgkin & Huxley ( 1 4) described inactivation by the independent variable h (see equation 6), which slowly decreases on depolarization. Hence, in a simple consistent model of gating current one would ascribe to this variable another (single) particle whose effective charge can be estimated from the h� -E relation to be ca 3.6 in squid axons ( 1 59), i.e. comparable to the combined charges of 3 X 1 .3 = 3.9 on the m particles. Since for Ep 0 mV, Th = 4.5 T m and hoo = 0, we can calculate for very negative EH (where ho = 1 .0) the hypothetical Ig, h in analogy to Ig. m (equation 1 0). Ig. h would ini tially be about one-quarter of Ig, m and would decline 4.5 times more slowly. No such gating current component has so far been identified. Incidentally, by a similar calculation the hypothetical gating current of K channels, Ig. must be very small because of the low channel density (70 )1m-2 at most; 84) that reduces Qrnax and because T n = ca 10 Tm ' On the other hand. the observed Qoff decreases with =

n,

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increasing pulse length, as does PNa due to inactivation, so that at SoC QOff/Qon is about 0.33 in 5-msec pulses, Ep = +50 mY (1 4S, 150), and about 0.5 in 20-msec pulses, Ep +20 mY (160); a comparable effect appears to exist in nodes of Ranvier (161). These observations could mean that charges become immobilized during long lasting pulses, with their movement back to the resting position so slow that it escapes detection. A current component, however, has been seen on returning to very negative En where recovery from inactivation is relatively fast (162). In Myx icola , where repetitive pulsing at a rate of 10 Hz decreases INa by half, Qon remains equal to Qoff., but both are reduced by ca 15% (153a). Internal treatment of squid axons with pronase, which abolishes PNa inactivation (71), seems to prevent im mobilization (14S). It is not clear at the moment to what extent this temporary loss of charge is connected to PNa inactivation, which should proceed faster and to lower levels of PNa ( 1 60). Interpretation of these experiments is further complicated by the fact that Toff decreases with pulse duration (148) and that single-sweep current records after very long positive and negative pulses intersect (crossing over), leading to an apparent charge deficit (161). A closer correspondence between decrease of PNa and gating current has been demonstrated in squid experiments when the external solution contained 5% of the normal [Na+lo (95% Tris) and no TTX. In this solution averaged current records are diphasic, i.e. after an early phase of the outward on response an inward INa component is seen. If the test pulses follow conditioning depolarizing prepulses (e.g. to +10 mY for 5 msec at 2°C) at an interval of 2 msec, at least half of the early gating current (14S) and most of INa are absent. With increasing pulse interval the two components re,:over together (156). Interestingly, internal treatment with pronase abolishes the d/!pressing effect of prepulses on the early on response (154, 156). Sodium and gating current can also be abolished by holding the squid axon membrane at +56 mY for 2 min (2°C). Both current components recover slowly at E H = -70 mY with a half-time of ca 50 sec (146). Whatever happens to the mobile charges during sustained depolarization is but slowly restored on repolarization. This is also true for the reversal of the gating current response for EH > -60 mY (l I S). If at EH = -32 mY each test pulse is preceded by a O.4-sec hyperpolarization to -92 mY, no normal gating response is observed and INa is still very much depressed. On the other hand, at EH -96 mY very short depolarizing prepulses are sufficient to obtain reversed responses during and after the test pulses (162a).


=

=

FINAL REMARKS Lack of a unifying theory of gating prevents a consistent pre sentation of gating current results. Measurement of these tiny currents is difficult and prone to considerable errors, which may lead to conflicting results among investigators. There is also considerable variation in the acceptance of these currents as significant expression of the gating process, from downright rejection (163) to literal identification with the Hodgkin-Huxley variable m much in the way of the Ig. m model presented here for the sake of understanding. Future experiments hope fully will teach us to distinguish between specific and unspecific gating current



27

components, possibly with the help of the various drugs that modify channel kinet ics. There is also a clear tendency to pay more attention to the total capacitative current and not just to the asymmetrical component of its slow phase. At any rate, the results described in the last paragraphs seem to suggest, as do the INa measure ments discussed earlier, that inactivation is a consequence of activation and not an independent process. This sequence of events is also incorporated in a recent model of Na channel gating (9), which in addition suggests a different mechanism for inactivation by sustained strong depolarization from which recovery is very slow (76, 79, 85, 146). Existence of different types of inactivation may be the reason for some of the inconsistencies in the gating current results. CONCLUSIONS

Research of the last years has firmly established the existence of several types of ionic channels in excitable membranes. These types differ in their selectivity and their kinetic response to changes in membrane potential. Distinction between chan nel types has been greatly helped by the use of highly selective blocking agents, and at least in Na channels selectivity and selective block (by TTX and STX) have a common structural basis: the selectivity filter acts as part of the toxin receptor. These toxins block a Na channel regardless of the ion species passing through it, they do not interfere with the kinetics of the channels left unblocked, and there is overwhelming evidence that the toxins do not jam the gates of the blocked channels either. Evidence of this kind suggests that filter and gate are separate structures, and although fairly detailed ideas of the filter structure have been developed, the molecu lar basis of the voltage-sensitive gate is still completely unknown. Great efforts in unraveling the gate mystery are presently done by measuring the movement of the small intramembrane charge that seems to accompany the opening and closing of the channel passage. Of course, one can hardly imagine a field-sensor that is not charged and whose reaction to changes in the field does not involve movement of the charge. Hence identification of the relevant gating current component is but a first step in clarifying the nature of the charged groups and eventually the gating mechanism. Since a channel appears to be an assembly of proteins stretching from one side of the membrane to the other, conformational changes may well play a decisive role in gating. However vague our present picture of the ionic channel is, it undeniably resembles that of certain ionophores in lipid bilayers. The resem blance, also of functional details, is surprising. In some of these artificial excitable membranes complete channels do not seem to be pre-existent but are formed only under the influence of the electrical field from subunits, so that the assembly is equivalent to gating. Baumann & Mueller ( 164) have based a complete model of membrane excitability on this mechanism. Even if it should turn out to be of no relevance to the function of natural membranes, the formation of channels from subunits, e.g. during the ontogenetic emergence of excitability, may be a principle worth keeping in mind for future research.

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ACKNOWLEDGMENTS

I wish to thank K.-D. Knitlki for valuable discussions and L. Vosgerau and E. Dieter for secretarial hdp. I gratefully acknowledge support by the Deutsche For schungsgemeinschaft.


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Trans.

1 1 8. 1 1 9. 120. 121. 122. 123. 1 24. 125. 126. 127. 1 28.

R.

Soc.

London

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Biochemical investigations of ionic channels in excitable membranes.

Evidence for ionic pores in excitable membranes.

Similarities between sodium channels in excitable membranes and in epithelia.

Currents associated with the ionic gating structures in nerve membrane.

Mechanism for channel gating in excitable bilayers.

A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon.

Polyphosphonium-based bipolar membranes for rectification of ionic currents.

Ionic channels induced by surfactin in planar lipid bilayer membranes.

Single-channel, macroscopic, and gating currents from sodium channels in the squid giant axon.

Kinetic properties and inactivation of the gating currents of sodium channels in squid axon.

Gating currents in Shaker K+ channels. Implications for activation and inactivation models.

Gating currents associated with Na channels in canine cardiac Purkinje cells.

The metabolism of phosphatidylinositol in excitable membranes.

A description of adaptation in excitable membranes.

Electromagnetic gating in ion channels.

Artificial ion channels regulating light-induced ionic currents in photoelectrical conversion systems.

Asymmetric electrostatic effects on the gating of rat brain sodium channels in planar lipid membranes.

Ionic thermoelectric gating organic transistors.

Sodium and calcium gating currents in an Aplysia neurone.

The extracellular patch clamp: a method for resolving currents through individual open channels in biological membranes.

Cooperative gating between ion channels.

Genes, channels and membrane currents in Paramecium.

Asymmetric displacement currents in giant axons and macromolecular gating processes.

Voltage-dependent ion channels and their gating.