By W. ALMERS* AND S. R. LEVINSON From the Physiological

J. Phyeiol. (1975), 247, pp. 483-509 483With 8 text-figuresPrinted in Great Britain

TETRODOTOXIN BINDING TO NORMALAND DEPOLARIZED FROG MUSCLE AND THE CONDUCTANCE

OF A SINGLE SODIUM CHANNEL

By W. ALMERS* AND S. R. LEVINSONFrom the Physiological Laboratory, Cambridge CB2 3EG,

and the Department of Physiology and Biophysics,University of Washington, Seattle, U.S.A.

(Received 8 October 1974)

SUMMARY

1. We have examined the binding of tritium-labelled and unlabelledtetrodotoxin to frog twitch muscle. Bio-assay as well as radioisotopeexperiments show a saturable component of tetrodotoxin binding witha binding capacity of about 22 p-mole/g wet wt., and a dissociationconstant of about 5 nm.

2. If the observed uptake of tetrodotoxin by muscle represents one-to-one binding of the drug to sodium channels, the channel density is about380 channels//tm2 of a muscle fibre's surface membrane. On the basis ofthis result and electrical measurements of sodium conductance in frogmuscle, we calculate that the conductance of a single sodium channel isofthe order of 10-12 reciprocal ohms. This is one to two orders of magnitudeless than previous estimates.

3. We have looked for an effect ofmembrane depolarization on saturabletetrodotoxin binding, and have found none. This suggests that there islittle molecular interaction between the 'gating' portion of the sodiumchannel molecule, and that which binds tetrodotoxin.

INTRODUCTION

The drug tetrodotoxin blocks sodium currents and action potentialsin nerve and muscle at extremely low concentrations (Hille, 1968; Cuervo& Adelman, 1970; Schwarz, Ulbricht & Wagner, 1973) and has no otherknown effects on excitable membranes. It is therefore reasonable toassume that at sufficiently low concentrations, the drug binds only tosodium channels, and this suggests that one can determine the numberof sodium channels in excitable membranes by examining their capacity

* Present address: Department of Physiology and Biophysics, University ofWashington, Seattle, Washington, U.S.A.

i8-2

W. ALMERS AND S. R. LEVINSON

for binding tetrodotoxin (Moore, Narahashi & Shaw, 1967; Keynes,Ritchie & Rojas, 1971). Due to recent advances in tetrodotoxin assaytechniques (Hafemann, 1972; Levinson & Ellory, 1973) accurate measure-ments of tetrodotoxin uptake are now possible, and experiments on awide variety of intact and homogenized excitable tissues (Barnola,Villegas & Camejo, 1973; Benzer & Raftery, 1972; Colquhoun, Henderson& Ritchie, 1972) have revealed a saturable component of tetrodotoxinbinding with a drug-receptor dissociation constant which is similar oridentical to that found in electrical studies of sodium channel-toxininteraction. The extensive experiments of Colquhoun & Ritchie (1972),Colquhoun et al. (1972) and Henderson, Ritchie & Strichartz (1973) leavelittle doubt that this saturable component of tetrodotoxin uptake doesin fact represent the binding of tetrodotoxin to sodium channels.

Mainly for technical reasons, almost all investigations of tetrodotoxinbinding have been conducted on tissues where electrical data are eitherunavailable or impossible to obtain. This is unfortunate, since most ofour knowledge about sodium channels has so far come from electricalstudies with the voltage-clamp technique. In studying the electricalproperties of the sodium channel and its interaction with tetrodotoxinon the same tissue, one might hope to combine biochemical and bio-physical knowledge.The present paper examines tetrodotoxin binding to frog muscle,

because this preparation has been extensively examined with electricaltechniques (Adrian, Chandler & Hodgkin, 1970). We find that the tetro-dotoxin binding capacity of frog muscle is some 10 times higher thanthat of the various small unmyelinated nerve fibres studied so far. Com-bining our result with the electrical data of Adrian et al. (1970) andIldefonse & Roy (1972) we conclude that the conductance of a singlesodium channel is likely to be of the order of 10-12 reciprocal ohms andtherefore 10 to 100 times less than had previously been supposed. Thedata of Hodgkin & Huxley (1952) in conjunction with those of Levinson& Meves (1975) lead to the same conclusion on squid. Our estimate ofmuscle membrane's sodium channel density also explains why sodium'gating currents' (Armstrong & Bezanilla, 1973, 1974; Keynes & Rojas,1973, 1974) have not so far been observed in muscle (Schneider & Chandler,1973; Almers, 1975).A preliminary account of some of the present results has been included

elsewhere (Almers, 1975).

484

TTX BINDING TO FROG MUSCLE 485

METHODS

Sartorius muscles of the frog Rana temporaria were carefully dissected to avoidfibre damage, and then incubated in media containing various concentrations oftetrodotoxin. Muscles were agitated during the incubation period, which lastedfor between 3 and 6 hr at 40 C, unless otherwise indicated. Before incubation,muscles were drained of as much extracellular fluid as possible by pulling themslowly up the side of a glass beaker and then touching their pelvic tendons tofilter paper for a few seconds. Care was taken to avoid contact between filter paperand the muscle itself. The vial containing the incubate with the toxin was placedon a balance, and the muscles weighed into the vial. The amount of extracellularfluid transferred with the muscle in this way amounted to 20-40% of the muscleweight, in agreement with the results of others who have used this method (Dydynska& Wilkie, 1963).The composition of the incubation media is given in Table 1; all solutions were

buffered to pH 7-2-7 4. Solutions C and D caused the muscles to contract, and inexperiments which involved exposure to these solutions, muscles were dissectedwith their pelvic bones attached and pinned to a plexiglas chamber to preventtheir shortening. After equilibration in solutions C and D for no less than 1 hr, thepelvic bone was cut away and the muscles incubated and processed as those inRinger fluid. All incubations were done at 40 C unless indicated otherwise.

TABLE 1. Composition of solutions

Solution Na+ K+ Cl- CaCl2 CaSO4 Sow Sucrose

Ringer A 115 2-5 117-5 1.8 - -Hypertonic B 115 2-5 117-5 1.8 - - 350Ringer

Depolarizing C 80 - 5 40 113solution

Sulphate D 77-5 2-5 - 5 40 113Ringer

Solutions A, B were buffered to pH 7-4 with 3 mm sodium phosphate buffer,except in bioassay uptake experiments, which instead contained 10 mm Trischloride buffer as well as 1 mM-MgCl2.

Solutions C, D contained 2 mM Tris maleate buffer, unless otherwise indicated.All concentrations in mm.

Bio-assay of tetrodotoxinA freshly excised frog sciatic nerve was desheathed for a distance of 1-2 cm in

the thigh region and mounted in a three chamber stimulating-bathing-recordingapparatus as previously described (Levinson & Ellory, 1973; Levinson, 1975),except that the bathing chamber volume was reduced to 0 5 ml. to assay smallervolumes. Stimulating and recording chambers were filled with silicone oil, and therecording of compound action potentials was done from the nerve end in therecording chamber with respect to an indifferent electrode in the bathing chamber.This recording configuration (Bishop, 1937; Brazier, 1960) gave rise to essentiallymonophasic compound action potentials. The nerve was mounted under slighttension, so that replacement of solutions in the bathing chamber could be achieved

486 W. ALMERS AND S. R. LEVINSONwith minimum agitation of the nerve. After mounting, the nerve was allowed tostabilize for 2 to 3 hr in the recording chamber.To assay a sample of tetrodotoxin in Ringer the starting amplitude of the

compound action potential was recorded in toxin-free Ringer, and the solutionin the bathing chamber was replaced with the toxin solution for 4 min. Thisexposure time was sufficient to give greater than 95% of the full effect of any toxinconcentration. At the end of exposure, the height of the action potential wasnoted and the test solution washed out of the bathing chamber with two changesof Ringer solution. After eight minutes the compound action potential had recoveredto its starting value, and the assay could begin again with a different sample. Inthis way, a standard dose-response curve was constructed for each nerve byplotting percent inhibition of the starting action potential versus the concentrationof standard, and connecting the plotted points (which were 3 nm apart on theabscissa) with straight lines. The dose-response curve was usually sigmoid, andthe concentration of toxin giving 50% inhibition of the nerve action potential inthe range 9-15 nM. In order to assay samples of low drug concentrations, thesensitivity of the nerve could be increased either by partially replacing sodiumchloride isosmotically with sucrose and thereby diminishing the safety marginfor nerve impulse conduction, or by exposing the nerve to Ringer solutions ofphospholipase-C (0-2 mg/l., 5 min). -The former method was reversible, the latterwas not, but has yielded nerves which showed 50% inhibition at 3 nM tetrodotoxin.Concentrated samples could be assayed after dilution. By either nerve sensitizationor sample dilution, it was possible to consistently operate on the steepest part ofthe dose-response curve. We bracketed each unknown sample with standardsolutions of similar drug concentration, and estimate the standard error of deter-mining the toxin concentration in a sample as being about 0-25 nM.

Bio-assay experiments on muscle. Two to five muscles were incubated in a smallvolume (about 1 ml./g. tissue) of known initial tetrodotoxin concentration. Theywere then removed from the incubation vial and discarded; the amount of thedrug which remained in the incubate was assayed on a sciatic nerve as described.

Fig. 1. Purity and specific activity determination of labelled tetrodotoxin.Uptakes of radioactivity (A) and tetrodotoxin as determined by bio-assay(B) were obtained from the loss of activity from the supernatant and areexpressed per gram original electric organ weight. Continuous lines areleast-squares fits to eqn. (1); all points were weighted equally. In A andB, points in which both radioassay and bio-assay were performed onthe same sample are represented by A. Samples on which only one or theother assay were performed are shown by 0. In the case where only theradio-assay was performed on samples, the final tetrodotoxin concentration(TTX) was calculated as described in Levinson (1975), based on parallelbio-assay experiments. In addition, several points are included in Brepresenting uptake of unlabeled toxin. These points (V) show that nosignificant difference exists in the bioactivity uptakes of labelled andunlabelled toxin, but they were not included in calculation of the least-squares fit line shown in the Figure. The parameter values of eqn. (1)were, with s.E., M = 17-8 ± 1-2 nc/g, K = 9-1 ± 1 8 nM and b = 0 037 +0-006 nc/g nM in A and M = 148± 4-4 p-mole/g, K = 10-5+ 1-1 nM andb = - 0-074+ 0-023 p-mole/g nm in B. In A, the star (*) marks thevalue of M, the amount of saturable binding at full occupancy. Com-parison of M in A and B yields a specific activity of 17-8 nc/148 p-mole =120-4 c/mole.

TTX BINDING TO FROG MUSCLE

A

0 50 100 200'TTX concentration (nm)

B

0 50 100TTX concentration (nm)

200

Fig. 1. For legend see facing page.

The incubation medium also contained [14C]mannitol as an extracellular spacemarker; aliquots of the incubate were counted at the end of the incubation periodto determine dilution of the incubate by the muscle extracellular space. Toxinuptake by the muscles was then calculated from the drop in incubate toxin con-centration; due allowance was made for dilution of toxin and increase of incubatevolume due to the muscle extracellular space. The pH of the incubates was notaltered by more than 0-5 pH units during the incubation period.

Preparation of tritiated tetrodotoxin

Approximately 3-5 mg of finely powdered, citrate-free tetrodotoxin (Sankyo,Chemical Co.) was submitted to labelling by tritium gas exchange according to themethod of Wilzbach (1957) by the Radiochemical Centre, Amersham. Labiletritium was then removed, yielding about 3 mg solid material incorporating 30 mnc

487

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,, 20'-

0j. 4.D

± t

.2 to 10,10 L.M

5

.054-a ISO

0 5

0.

a

W. ALMERS AND S. R. LEVINSONtritium. This solid was dissolved in 1 ml. 10-2 M acetic acid (pH approx. 3 5) andaliquots removed for bio-assay and purification. Bio-assay of the labelled toxin atthis point showed that most of the original toxin submitted to labelling had beendegraded; of the original 3-5 mg submitted to labelling, only 0-67 mg remainedactive. Thus this crude fraction contained a large amount of radioimpurities.

Purification was performed by high voltage paper electrophoresis (Colquhoun,et al. 1972) at 100 V/cm (using a Pherograph apparatus kindly supplied by DrCaesar Milstein of the M.R.C. Laboratory of Molecular Biology, Cambridge). Theinitial purification was done in 50 mm Tris-acetate buffer at pH 7 9, while thefinal purification was done at pH 6-5 in pyridine-acetate buffer.The final purification resulted in single coincident peaks of radioactivity and

biological activity, as determined by scintillation counting (Packard TriCarbscintillation spectrometer) and bio-assay. The specific activity of the purifiedmaterial was found to be approximately 400 c/mole throughout the activity peak,suggesting a homogeneous product. Consideration of the specific activity of the toxinimmediately after labelling (30 mc/0*67 mg toxin) shows that the toxin had beenpurified thirty-sixfold. In addition, three further analytical runs of this purifiedtoxin at pH 6-5, 7.9 and 8-5 on the high voltage electrophoresis apparatus and thethin layer chromatography system described by Benzer & Raftery (1972) gavesingle symmetrical peaks of radioactivity which were coincident with single peaks ofbiological activity, further demonstrating a high degree of chemical homogeneityof the toxin.However, the purity of the toxin was also checked by an independent method

based on the bio-assay procedure. This method, which has been described in detailelsewhere (Levinson, 1975). compares the uptake of radioactivity and biologicalactivity by a particulate fraction of eel electric organ from an incubate containinglabelled toxin. If the toxin were indeed pure, one should find an exact correspondencebetween the fraction of radioactivity bound from an incubating medium and thefraction of biological activity bound. In practice, it was found that the biologicalfraction was considerably greater than the radioactive fraction bound at concentra-tions below 150 nm, and thus a significant amount of tritium label was not bindingalong with the toxic activity. This demonstrates the existence of radioimpurities inthe labelled tetrodotoxin.

Fig. 1 compares the radioactivity and biological activity uptakes in eel electroplaqueparticulate fraction as a function of concentration. The lines through the pointsare least-squares fits (see below) assuming these uptakes to be described by alinear unsaturable component superimposed on a saturable Langmuir component(Colquhoun et al. 1972). Both parts A and B of Fig. 1 show a saturable componentof uptake with identical dissociation constant. However, in the radio-assay experi-ment (Fig. 1A) the contribution of the linear component is significant, whereas inthe bio-assay (Fig. 1B) it is not. Thus the linear component in the radioactiveuptake may be attributed to impurities in the fractionated toxin. Concluding thenthat only the saturable component reflects binding of tetrodotoxin, the actualspecific activity of the labelled toxin may be calculated as the ratio of radioactivitybound due to the saturable component at saturation over the amount of toxinbound at saturation as determined by the bioassay. In this way the specific activityof the labelled tetrodotoxin was found to be 120-4 c/mole, and thus the actualpurity of the tetrodotoxin used in these experiments is about 30%.As discussed by Levinson (1975) and Colquhoun, Henderson & Ritchie (1975),

this discrepancy between specific activities and purities calculated from chromato-graphic data and the bioassay procedure is important, since the specific activityof the toxin must be known for calculations of the toxin binding site densities.

488

TTX BINDING TO FROG MUSCLEIn our case, the specific activity from the chromatography is roughly 3 times thatof the actual specific activity found by bio-assay.Radioasay experiments on muscle. Single muscles were incubated in 0-7-2-0 ml.

of media containing [14C]mannitol as a space marker, and various concentrationsof tritiated tetrodotoxin. After incubation, the muscles were removed from theincubate and blotted as previously described; the incubate was discarded. Muscleswere prepared for scintillation counting by one of two methods. The first method(method A) was to denature the muscles at 800 C for 10 min in a sealed vial con-taining 2 ml. distilled water, and let it stand overnight. This was sufficient toallow the radioactivity to be released from the denatured muscle and to distributeitself equally into the distilled water plus the volume occupied by the muscle. In afew experiments, we counted the denatured muscles and found that the concentrationof tritium remaining there was not significantly different from that in the super-natant. The toxin uptake by the muscle was then calculated from the radioactivityof the supernantant. Alternatively (method B) the blotted muscles were digestedin 0 9 ml. NCS (Amersham-Searle) tissue solubilizer and 0 1 ml. distilled waterovernight at 370 C. Toluene scintillator, used because it gave little chemiluminescence(approx. 10-15 cpm), was added to the digests and the samples cooled and counted.Counting was done on a refrigerated Packard Tri-Carb Liquid Scintillation Spectro-meter using standard double-labelling techniques. Blanks, standards and controlswere prepared in parallel with the experimental samples using fresh muscles. Bothmethods A and B of counting gave similar results.

Analy8i8 of uptake data

Following the method of Colquhoun et al. (1972), least-squares estimates of theparameters governing toxin uptake were obtained by minimizing the functionS = Zw(UOb8- U)2 where w is the weight of each data point UOb8, and U thetheoretical uptake given by

M [TTX]K + [TTX] +b[TTX]. (1)

Eqn. (1) described the uptake as consisting of two components, a saturable (firstterm) and an unsaturable portion; the latter is included to allow for any unspecificuptake of the toxin by the tissue and is assumed to depend linearly with slope bon the toxin concentration. The first term is the one of interest here and describeshyperbolic saturable absorption or one-to-one binding of the toxin to its receptor.M is the binding capacity and K the dissociation constant of the saturable com-ponent. Least-squares fitting was done using a Fortran program (NottinghamAlgorithm Group, document E04GAF) based on Marquardt's method (Marquardt,1963). Weighting of data points is discussed in the Results section. Standard errorsof the parameters of (1) were determined from the inverse of the Hessian matrixof the function S.

Electrophysiological experimentsMembrane resting and action potentials were measured differentially between

two micro-electrodes with tip potentials of less than 6 mV and resistances of10-20 mQ. They were filled with 3 M-KCl. Micro-electrodes for current injectionswere filled with 2M potassium citrate. Input stages had impedances in excess of1010 Q and allowed input capacitance neutralization. Rate of voltage change wasrecorded by means of an RC-network connected as an approximate differentiator.Muscles were immobilized by making the medium 2-5 x hypertonic by addition ofsucrose. The entire muscle was stimulated by a pair of external silver wires locatedbetween 5 and 10 mm from the recording site; this allowed clear separation

489

W. ALMERS AND S. R. LEVINSONbetween the stimulus artifact and the propagated action potential. Solution was

flowed continuously over the preparation.

RESULTS

Effect of tetrodotoxin on muscle action potentialFig. 2A shows measurements of the maximal rate of rise (Vmax) of

the propagated action potential before, during and after exposure to-80 _-

E

0

.S

*9 ---A--100 _

ISO _-I0 nM-TTX-I

100 _

X / AS III

so ~ s

I I I I I

0 2 4 6Time (hr)

X 1-0i

0C

t

x

.SE

I.

\0

B

0

no _~~

I I0 5 10

TTX concentration (nM)15

100

0

50

0

Fig. 2. Effect of tetrodotoxin (TTX) on the maximum rate of actionpotential depolarization (1,.J). A: top, membrane potential Vm; bottom,tJn before, during and after exposure to 10 nM tetrodotoxin. Steady-statelevels of V7. are indicated by horizontal lines. Imz = 0 was assumed infibres which failed to give action potentials. B: dose-response curve

obtained from experiments as in A. Right ordinate, PI at the toxinconcentration indicated on the abscissa, relative to the average of valuesmeasured before and after exposure to the drug. The curve was drawnaccording to K/K + [TTX] with K = 4 nm. Average TYa in unpoisonedfibres was 107 V/sec; this defines the right ordinate. Temperature 7-80 C;hypertonic Ringer fluid (solution B).

490

TTX BINDING TO FROG MUSCLE 49110-8 M tetrodotoxin. Our estimates of steady-state levels are indicatedby the three horizontal lines. Every point represents measurements fromeight to fifteen surface fibres; mean resting potentials for each group offibres are also included. Fibres with resting potentials less negative than-80 mV were rejected. Fig. 2B summarizes a number of such experiments.Each point gives the final value of J7max at the indicated concentrationof tetrodotoxin, relative to the mean of the two values measured beforeand after exposure to the drug. It is seen that 4-5 nM tetrodotoxinreduces TJmax to about half. Fig. 2B shows that the action potential offrog muscle is no less sensitive to tetrodotoxin than that of frog myelinatednerve (Schwarz, Ulbricht & Wagner, 1973). However, it is difficult toobtain quantitative information about the interaction between tetrodo-toxin and sodium channels from action potential experiments, since therelationship between J7max and the fraction of blocked sodium channelsis unknown and likely to be non-linear.At higher toxin concentrations, impulse propagation fails in spite

1.0

0 5 IO1 nm-TTX

is 0 2 4 6 8 10

1.00. 00.

05-v ~~~~~Mannitol0~~~~~~~

0 2 4 6 8 10Time (hr)

Fig. 3. Time course of uptake of tritium-labelled tetrodotoxin ([3H]TTX,top) and [14C]mannitol (bottom). Each point represents results from a pairof sartorii from the same animal; one muscle from each pair was incubatedfor the time given on the abscissa, the other for a standard period of 3 hr.The ordinate gives uptake of the former relative to that of the latter.Method A was used to determine radioactivity uptake (see Methods).

W. ALMERS AND S. R. LEVINSONof normal resting potentials. The failure rate was already 13 % out oftwenty-four fibres at 10 nm in the experiment of Fig. 2 A. Working inisotonic Ringer at room temperature we have tested impulse propagationat a higher concentration of 50 nm tetrodotoxin as follows. Three elec-trodes were inserted into a fibre, one to inject current, the other two torecord the membrane potential close by (100-200 1am) and further away(2.1-4.1 mm from the point of current injection). The potential near thecurrent electrode was then depolarized beyond - 12 mV. In none of tenfibres tested (two muscles, average resting potential + S.E. of mean 85-3 +0-8 mV) did an action potential result at the far electrode. The experi-ment shows that at 50 nm tetrodotoxin, muscles at room temperature(240 C) cannot conduct action potentials.

Time course of tetrodotoxin uptakeSince the aim of this study was to examine the binding at equilibrium

of tetrodotoxin to frog muscle, it was important to get an idea of theincubation time required to reach equilibrium. The experiment in Fig. 3was carried out on muscle pairs; one muscle was exposed to the incubationmedium for the time shown on the abscissa, the other for a standardperiod of 3 hr. The ratio of uptakes under the two conditions is plottedon the ordinate. [14C]mannitol uptake ratios are also plotted. It is clearthat there is little net uptake of mannitol after 30 min incubation, whichis the earliest time tested; uptake of tetrodotoxin, on the other hand,continues for several hours.The difference in time course between [14C]mannitol and tetrodotoxin

uptakes is far too large to be due only to the difference in molecularsize of the two substances. Most likely, the deep fibres within the sartoriusmuscle and their associated membranes constitute a large 'sink' for thetoxin, which has to be filled by toxin molecules diffusing through thefibre interspaces. The slowing of diffusion-limited processes by simul-taneous chemical reactions has been analysed mathematically (Crank,1956) and experimentally by several authors (Colquhoun & Ritchie, 1972;Colquhoun et al. 1972; Rang, 1966). The problem will be given no furtherconsideration at this stage, except to point out that equilibrium is notattained until several hours, and that the theoretical treatments referredto above lead one to expect equilibration to proceed more quickly athigher, and more slowly at lower concentrations.

Bio-assay measurements of tetrodotoxin uptakeOur bio-assay experiments are summarized in Fig. 4. Tetrodotoxin

uptake is plotted against the toxin concentration in the incubation

492


medium at the end of the soaking period. The continuous line is a least-squares fit to the data of eqn. (1) with the parameters

M = 18-6+ 4-4p-mole/g wet,K = 5-t + 1-7 nM,b = 0O04+013p-mole/nmgwet.

The parameter b is not significantly different from zero. K is similar tothe concentration at which the rate of rise of the action potential isreduced to half (see Fig. 1). The extremely close agreement may to someextent be fortuitous, since the relation between Tmax and the fractionof blocked sodium channels is probably non-linear. Nevertheless, it isreasonable to suppose that Fig. 4 represents the binding of tetrodotoxinto sodium channels.

Weighting for statistical analysis. In practice, the uptake U (p-molelg wet) wascalculated from the incubation volume 8 (ml.), the muscle weight w (g), the initial(xi) and final (Xe) toxin concentrations in the incubation medium, and the mannitolspace of the muscle f (ml./g tissue) by

U = (xi-X,)SWl-xff.

30

0bw 20

0

0.x1 10

0.

(2)

00

0

* 0

0

0 00

0

0

00 0

0 50 100TTX concentration (nM)

Fig. 4. Tetrodotoxin uptake at various concentrations of the toxin. Abscissagives final tetrodotoxin concentration in the incubation medium after4 hr incubation. Bio-assay method. Continuous line is eqn. (1) with theparameters: M = 18-6 p-mole/n-mole g wet, K = 5*1 nm, b = 004 p-mole/nM g wet.

493

W. ALMERS AND S. R. LEVINSONThe reciprocal of the variance of U, o-2, is the desired weighting factor. Assumingany error in U to be mainly due to errors in the measurements of xi and f, andassuming that any statistical correlation between these variables can be neglected,one has approximately

2 ]2 F +12 (3)

and from (2)

W7u#-[x(+f) [of Xf]2, (4)

where olaf and Of are the standard deviations of measurements of xf and f, respec-tively. We estimate Of = 20 pulg and aof = 0-25 nm. In some experiments at low(< 32 nM) drug concentrations the extracellular space was not measured, and weassumed it to equal the average from other experiments done at the same time;the standard deviation of f in these experiments was orf = 40 #ul./g. This valuepresumably included measurement uncertainty as well as genuine variation. Whenxf was too high to allow direct bio-assay of the incubation medium, dilution wasnecessary, and in that case we took 0,2 = (0.25d)2 nM2 where d is the dilution factor.The average value for (8w+1)2 was 1-96 g2 ml.-2 in our experiments. With thesevalues, eqn. (4) predicts that in experiments where f is known, measurements ofU should scatter with standard deviations ofo.u = 0-354 p-mole/g wet at xf = 1*5 nM,and oU = 2-80p-mole/g wet at xf = 110nM. Pooling all measurements between107 and 122 nm, we obtain an uptake of 20-6 p-mole/g wet with a standard deviationof 3.9 p-mole/g wet. This standard deviation is slightly higher than the predictedvalue, possibly because in addition to measurement uncertainty, there is somebiological variation of toxin uptake.

Uptake of tritium-labelled tetrodotoxin in Ringer fluidFig. 5 and 6 show uptake of radioactivity from Ringer fluid with

varying concentrations of the toxin. Fig. 5 was obtained with radioassaymethod A, Fig. 6 with method B (see Methods section). As in similarexperiments on other tissues (Colquhoun et al. 1972) there is clear evidencenot only for a component of uptake which saturates in the nanomolarrange and which we believe to represent binding of [3H]tetrodotoxin tosodium channels, but also for a second component which shows noevidence of saturation over the concentration range explored here. Thecontinuous line represents a least-squares fit of eqn. (1) to the data (seeMethods) with the parameters given in the figure legends. Given thespecific activity of 26641 dpm/p-mole (120.4 c/mole) obtained by simul-taneous bio-assay and radio-assay experiments on eel electroplaquehomogenate (see Methods), one obtains for the saturable component fromFig. 5 the parameters, with 5.E.,

I = 19.7 + 2.4 p-mole/g wet,K = 3*1+07nM,

and from Fig. 6M = 23-1 + 3.9 p-mole/g wet,K = 5-5+114nM.

494

TTX BINDING TO FROG MUSCLE49If the non-saturable component were entirely due to tetrodotoxin, it

would be equivalent to b = 0-26 + O'08 p-mole/nm g wet in Fig. 5 and0*32 + 0-07 p-mole/nm g wet in Fig. 6. However, our sample of tritiatedtetrodotoxin contained impurities, and at least some of the non-saturablybound radioactivity in Figs. 5 and 6 is almost certainly not tetrodotoxin.Our experiments therefore give only an upper limit to the non-saturable

60

15

EO 0

10 0a4U

0: 20 4 0 8 100

TTX concentration (nm )

Fig. 5. Uptake of tritium at different external concentrations of [3H]TTX.Incubation in 0-7 ml. per muscle lasted 6 hr for the points below 10 nmiand 3 hr for all others. Abscissa gives incubate toxin concentration at theend of the incubation period; it was obtained from the initial concentrationby correcting for uptake by the tissue. Continuous line is eqn. (1) withM = 5244 dpm/g wet, K = 3-1 nm and b = 69 dpm/nm g wet. Dashed lineis the linear, dotted line the saturable uptake of radioactivity. The leftordinate applies to the saturable component and is based on the specificactivity of 266-1 dpm/p-mole tetrodotoxin. Method A.

uptake of the toxin. Nevertheless, as long as the radioimpurities arebound 'non-saturably', i.e. with an affinity which is sufficiently lowerthan that for the toxin, the saturable component of tritium uptake canbe extracted unambiguously from experiments as in Figs. 5 and 6, andits parameters should not be influenced by radioimpurities. The excellentagreement between the parameters in radio-assay and bio-assay experi-ments indicate that the saturable tritium uptakes in Figs. 5 and 6represent, in fact, tritiated tetrodotoxin.

495


30_

100

80

20 10 200E0. 6

40

6. 10 7rcx

-~~~~~~~~20

0 100 200TTX concentration (nm)

Fig. 6. Uptake oftritium at different concentrations of[3H-]TTX. Incubation6 hr in 0-7 ml. per muscle; average muscle weight 70 mg. Filled circles giveuptake in the absence, open squares that in the presence of 1-2 pmunlabelled tetrodotoxin. Continuous line is eqn. (1) with M = 6149 dpm/gwet, K = 5-5 nm, b = 72 dpm/nM g wet. For further details see legendon Fig. 5. Method B.

Weighting for 8tati8tical analysis. We have aimed at weighting each point inFigs. 5 and 6 by the reciprocal of its variance. The square-root of the variance wasestimated from pooled data points from Fig. 6 and then plotted against tetrodotoxinconcentration. A least-squares second-order polynomial was then fitted to theplot, and the weight for each point in Figs. 5 and 6 obtained from the resultingcurve. In fact, the three parameters in eqn. (1) are not very sensitive to the methodof weighting. Weighting each point in Fig. 6 equally, for instance, would haveyielded the following parameters: M = 25-32 + 4.5 p-mole/g wet, K = 7-7 ± 3 0 nmand b equivalent to 0 33 + 0 03 p-mole/nM g wet. None of these estimates aresignificantly different from those given above.

In the above experiments, saturable and non-saturable componentswere separated by least-squares analysis of the uptake-concentrationcurve. An alternative way is to compare uptake at the same concentrationof [3H]tetrodotoxin in the absence and presence of an excess of theunlabelled drug. In the latter case, only the non-saturable componentshould bind radioactivity, and the difference between the two measure-ments can serve to estimate the binding capacity of the saturable com-ponent. Three experiments of this kind on paired muscles are summarizedin Table 2. The results are also included in Fig. 6; open squares wereobtained in the presence of 1 or 2 tUm unlabelled tetrodotoxin and agree

496

TTX BINDING TO FROG MUSCLEwell with the curve for non-saturable binding (dashed line) predicted onthe basis of least-squares analysis. The total saturable binding capacityM = 24*2 p-mole/g wet found by assuming an association constant of55 mM, fits well with the other results. The experiment of Table 2confirms our view that the saturable uptake of radioactivity is tritium-labelled tetrodotoxin, since unlabelled toxin clearly competes with oursaturably bound radioactive substance for the same site.

TABLE 2. Competition between 8H-labelled and unlabeled tetrodotoxin

UB[3H]TTX p-mole/g

Muscles [nM] UA wet UA-UB M

1 A, B 26, 29 27*0 5-5 21*5 25.82 A, B 27, 29 30*3 10.1 20*2 24*83 A, B 72 43-6 22*2 21'4 22*7

Mean + s.E. of mean 24-2±1+6

Muscles A, B were pairs from the same animal; muscle A was incubated in theabsence, B in the presence of either 1000 no& (IB, 2B) or 2000 nM (3B) unlabelledtetrodotoxin. UA and UB uptakes of muscles A and B, respectively. M was calculatedassuming K = 5-5 nx and using the average of the values given under the columnfor [3H]TTX. Incubation time 6 hr, method B.

Uptake of [3H]tetrodotoxin by depolarized fibresWhen excitable membranes are depolarized, their sodium channel mole-

cules undergo a sequence of changes which result first in an increase ofsodium permeability and then in 'inactivation' or shutting-off of sodiumchannels. Clearly, sodium channels in polarized and depolarized mem-branes are in different states, and it seemed of interest to see whetherdepolarized and therefore 'inactivated' sodium channels still bindtetrodotoxin.

Fig. 7 shows tetrodotoxin uptake at different concentrations from asolution which contained 80 mm potassium (solution C). This solutionhas the same ionic strength and tonicity as Ringer fluid, but fibresimmersedin it have membrane potentials ofaround -16 mV (16.6 + 1 3 S.E.of mean, eight observations, see also Hodgkin & Horowicz, 1959). Atthat potential, sodium channels are fully inactivated; the Hodgkin-Huxleyvariables h and m are zero and virtually unity respectively (Adrian et al.1970). Although the results in Fig. 7 were obtained in a relatively shortperiod (14 May to 25th, twenty-six observations) and on what shouldhave been a homogeneous population of frogs, there is a great deal morescatter than in Ringer fluid, and data at each concentration were pooledand averaged in order to give a clearer visual impression of the concen-tration-uptake relation. It is nevertheless clear that depolarized fibres

497

P H Y 247I9


show saturable uptake of tetrodotoxin similar to that in Ringer fluid.The continuous line represents a least-squares fit to the single, unpooleddata points, which were weighted in the manner discussed in connexionwith Fig. 6. The resulting parameters were

M = 23.8 + 5.4p-mole/g wet,K = 10.0 + 2-9 nm.

4010

0~~~~~~~~~~~~~E 0

. ree 20 E

10

TTX concentration (nm)

Fig. 7. Uptake of [3H]TTX by depolarized fibres (solution C). Filledcircles, mean ± S.E. of mean of two to four pooled observations at theindicated concentration; open circles are single observations. The con-tinuous line is a least-squares fit of eqn. (1) to the unpooled single datapoints with the parameters M = 23-8 p-molelg wet, K = 10t0 nX andb = -0O046 p-mole/nm g wet. Non-saturable uptake (dashed line) is notsignificantly different from zero. Left and right ordinates as in Figs. 5and 6. Incubation time 6 hr. Method B.

Non-specific uptake of radioactivity was equivalent to b = - 0-046 + 0-064p-mole/nM g wet; this is not significantly different from zero. However,as is evident from Table 3 (muscles 3A, 4A and 5A), some muscles clearlydo show evidence of unsaturable tritium uptake. We have no explanationfor the apparent large variability ofnon-saturable uptake between muscles;it is our impression that it accounts for most of the scatter in Fig. 7.

Table 3 compares uptake by paired depolarized muscles in the presenceand absence of an excess of unlabelled tetrodotoxin. As before (seeTable 2), the saturable binding capacity for tritium-labelled tetrodotoxincan be calculated from the difference between uptakes under the twoconditions. An association constant of 10 nM between the receptor andthe toxin was taken from Fig. 7 and used to calculate the binding capacityM. The mean value for M from these experiments was 19-6 p-mole/g wet.

498

TTX BINDING TO FROG MUSCLE49Within experimental and statistical error, the agreement with the resultfrom Fig. 7 is satisfactory.

TABLE 3. Competition between -3H-labelled and unlabelledtetrodotoxin in depolarized muscles

UB[3H]TTX (p-molefg)

Muscles (n-M) UA wet UA7UB M

25 May1 A, B 27, 29 14.3 -3-1 17-4 23*62 A, B 27, 29 17-5 - 1-4 18-9 25*6

14 June3 A, B 39, 41 30*4 15.1 15*3 19-24 A, B 67, 69 47*9 33*3 14-6 16-85 A, B 70, 72 56*4 45*0 11-3 12*9

Mean s.iE. of mean 19-6±2-6

Muscles A, B from the same animal; A was incubated in the absence and B inthe presence of either 1000 nm (B, 2B) or 2000 nm~(3B, 4B, 5B) unlabelledtetrodotoxin. U. and UB are uptakes of muscles A and B, respectively. M wascalculated assuming K = 10-0 nm (Fig. 7) and using the average concentrationsgiven under column [3H]TTX. Incubation time 6 hr, method B.

Binding constant and membrane potentialWhile depolarization makes no significant difference to muscle's

capacity for saturable binding of tetrodotoxin, the above results mightsuggest a small effect on the dissociation constant K (10 IIm in solution Cversus 3-1-5-5 nm in Ringer). Further experiments to examine this pointare shown in Fig. 8 and Table 4. Uptakes were compared on pairedmuscles, one of which was incubated in the depolarizing fluid (solutionD) the other in a sulphate Ringer (solution D) identical to solution Cexcept that all but 2-5 mm of the potassium was replaced with sodium.Fresh fibres in this polarizing solution have membrane potentials ofabout 90 mY (91.6 + 0-7 mY S.E. of mean; ten observations). We havealso measured membrane potentials in one muscle at the end of 6 hrincubation by transferring the muscle into a dry recording chamber andpouring the 2 ml. incubate over it. The mean value + s.E. of mean was82-41 + 1 mV in twenty surface fibres impaled at random, indicating thatthe incubation had no substantial effect on the membrane potential.

Fig. 8 shows tetrodotoxin uptake at concentrations which are toolow to result in appreciable non-saturable tritium binding. Open circleswere obtained from polarized fibres (solution D), filled circles from de-polarized fibres (solution C). The curve was drawn according to eqn. 1with b = 0-0 M = 23 p-mole/g wet and K = 9 nm. A more quantitative

499

500 W. ALMERS AND S. R. LEVINSON

comparison between the two conditions is given in Table 4. Bindingconstants were calculated byK = (M/U -1) [TTX] whereM was assumedto be 23 p-mole/g wet. The ratio of binding constants in polarized anddepolarized fibres is indistinguishable from unity (1.06 + 0.16). The bindingconstant was on the average around 9 nm in these experiments. If real,the difference between this value and those obtained from our experimentsin Ringer fluid could probably be explainedby the difference in temperaturebetween the two sets of experiments (Schwarz et al. 1973).We conclude that within experimental error, a tetrodotoxin molecule

cannot distinguish between polarized and depolarized sodium channels.

10 _10~~~~~~~~~~

to /40

E5_

X/0.

0 /

0 2 4 6TTX concentration (nm)

Fig. 8. Comparison of uptake at low toxin concentrations between polarized(solution D, filled circles) and depolarized fibres (solution C, open circles).Incubation 6 hr in 2 ml. volume at 240 C. In this experiment, the incubatewas buffered with 3 mm sodium phosphate buffer of pH 7-3; after theexperiment, the pH of the pooled incubates was measured and found tobe 6-7 in solution D and 7-1 in solution C. Method B. Continuous lines iseqn. (1) with b = 00, K = 9 nm and M = 22 p-mole/g wet.

DISCUSSION

Tetrodotoxin binding to normal and depolarized muscleThe bio-assay and radioisotope experiments reported in this paper

demonstrate that frog twitch muscle shows saturable binding of tetro-dotoxin with a binding capacity of about 22 p-mole/g wet weight.Assuming one-to-one interaction between drug and receptor, our experi-


TABLE 4. Dissociation constant and membrane potential

Muscle A (polarized) Muscle B (depolarized)A -1- _k AU

UA UB(p-mole/g KA (p-mole/g KB KA

Muscles wet) (nM) wet) (nM) KB

[3H]TTX = 2-1 nM1 A, B 5-10 7-35 500 7-51 0982 A, B 5-43 6.91 3*53 12*25 0563 A, B 4*75 8*14 5-15 7*32 1.11

[3H]TTX = 4.5 nM4 A, B 4-85 16-97 6-84 10*52 1-615 A, B 8-40 7-80 9 49 6*36 1-236 A, B 8-43 7-71 7*74 8*85 0-87

Mean 9415 8-80 1-06+s.E. of mean 1-72 099 0.16

Muscles A, B were from the same animal and were incubated for 6 hr at thetetrodotoxin concentration indicated. UA and KA are uptake and dissociationconstant for muscle A, UB and KB are the corresponding values for muscle B.Values for K were calculated from K = (MIU-i ) [3H-TTX] withM = 23 p-mole/gwet. Same experiment as Fig. 8. Temperature 24° C. The experiment shows thatmembrane potential in sulphate media does not affect the dissociation constant.

ments suggest an affinity constant K of 3-6 nm at a temperature of 40 C.This agrees well with the pharmacological effect of tetrodotoxin on themuscle action potential. Tetrodotoxin reduces the maximum rate of actionpotential depolarization to 50% at concentrations of 4-5 nm (presentresults in hypertonic Ringer, 80 C) or 10 nm (results of Colquhoun, Rang& Ritchie, 1974, in isotonic Ringer at 200 C). Furthermore, Schwarz et al.(1973) obtained a dissociation constant of about K = 3 nm at 120 C frommeasurements of sodium currents and action potentials on frog myelinatednerve. Considering the difference in method and given the experimentaluncertainties, the agreement between their value of K and ours is satis-factory. We cannot rule out the presence in the membrane of electricallysilent sites which bind the drug with the same affinity as sodium channels,such as, for example, metabolic precursors of the channel molecule.However, as long as there is no evidence in this direction, we concludethat the saturable uptake of tetrodotoxin by muscle represents thebinding of the drug to sodium channels.We have tested whether membrane depolarization has any effect on

the saturable uptake of the toxin, and have found none. Since the openingand closing ('gating') of sodium channels is very steeply dependent onthe membrane potential, our result would suggest a considerable degree

19-3

501

W. ALMERS AND S. R. LEVINSONof independence between the 'gating' portion of the channel moleculeand the part which binds the toxin. This notion of independence isstrengthened by the finding that tetrodotoxin does not interfere withwhat are thought to be currents related to the opening and closing ofsodium channels (Armstrong & Bezanilla, 1974; Keynes & Rojas, 1974).Perhaps the toxin binding site (which may be close to or identical to theion 'selectivity filter' as suggested by Hille, 1971) is located at theoutward facing end of the sodium channel molecule, and the 'gating'machinery on the other.

Sodium channel density in frog muscleGiven an average extracellular space of 0-3 ml/g muscle in our experi-

ments, the present results indicate that 0 7 g of fibres bind about 22 p-moletetrodotoxin. Assuming the average muscle fibre to be a cylinder of80 ,tm diameter (Mayeda, 1890; Hodgkin & Nakajima, 1972) and to havea density of 1P0, it appears that there are about 378 sites/m2 of cylindersurface.

There is as yet no experimental evidence concerning the distributionof sodium channels between the membrane of fibre surface and transversetubules, though it has been shown (Costantin, 1970) that full contractileactivation of a muscle fibre depends on the activity of tetrodotoxin-sensitive sodium channels in the tubules. Later work (Bezanilla, Caputo,Gonzales-Serratos & Venosa, 1972; Bastian & Nakajima, 1974) hasconfirmed this. If one follows the suggestion of Adrian & Peachey (1973)that one quarter of all sodium channels sit in the tubules, and takes theratio of tubule to surface membrane area as about 6 (Peachey, 1965),channel densities would be about 280 sites/4um2 on the surface and16 sites//tm2 in the tubules. Alternatively, with a tubular surface/volumeratio of 106/cm (Peachey, 1965) these values would suggest a tubularsodium channel concentration of 2-3 /tM.

Tetrodotoxin diffusion delay8 in the tran8verae tubules. Bastian & Nakajima (1974)have made the puzzling observation that after rapid removal of tetrodotoxin fromthe medium, the twitch recovery in an isolated single fibre showed a slow phasewith a half-time of several minutes. This is a great deal longer than would beexpected from the rate of dissociation of the receptor-drug complex (Schwartz etal. 1973). A tubular sodium channel concentration of the suggested magnitudecould explain the effect. Even if toxin removal and the drug-receptor dissociationproceeded instantaneously, the toxin concentration in the tubules would fall onlyslowly because it remains 'buffered' by toxin molecules which dissociate fromtubular binding sites.

Diffusion in the presence of saturable binding or un-binding of the diffusingspecies can be described by the differential equation

-c IV2C-M-,- DTTX ata~t& (5)

502

TTX BINDING TO FROG MUSCLEwhere DTTX is the effective diffusion constant for the toxin, p the fraction ofoccupied sites, and c and m the concentrations of toxin and binding sites, respec-tively, both normalized by dividing by the dissociation constant K. FollowingColquhoun et al. (1972), one can write aplat = (1 +C)-2 &c/8t, and eqn. (2) thenbecomes

& ~ 12At 1+m/(1 +c)2DTTXVC (6)

From (3) it appears that the effect of binding sites on the diffusing species will bean apparent reduction of the diffusion constant by the factor [1+m/(1+c)2]. InBastian and Nakajima's experiments (1974), the concentration c will have variedboth locally in the tubules as well as with time, and an exact treatment of thiscase has been given by Adrian (unpublished). However, one can gain a rough ideaof the magnitude of the effect by neglecting radial concentration gradients withinthe tubular network, and by looking at a short moment in time during whichthe tubular toxin concentration should not vary significantly. At a toxin concen-tration of 5 nm, for instance, c = 1; with the concentration of binding sites sug-gested above, m becomes about 400. Thus, dissociation of toxin molecules wouldslow washout of the drug about hundredfold.

Almers (1972a) has described an electrical method for measuring the time courseof potassium diffusion into muscle tubules, and his data (e.g. Fig. 4 in Almers,1972b or Fig. 1A in Almers, 1972a) show that the mean tubular potassium con-centration equilibrates with an average half-time of 0-4-0-5 sec. Considering thediffusion coefficient of sucrose (5-21 x 10-6 cm2/sec; Weast, Selby & Hodgman, 1965)which has a molecular weight similar to that of tetrodotoxin, it is probable thatthe toxin diffuses about 3-6 times more slowly than potassium (DK = 18-9 x 10-6cm2/sec; Weast et al. 1965). This would suggest a half-time of toxin equilibrationof about 0-5 x 3-6 x 100 = 181 sec. This is close to the average half-time of 6 minreported by Bastian & Nakajima (1974) which included a delay of some threeminutes resulting from dead spaces in their apparatus, and whose experimentswere probably done on larger fibres than those of Almers (1972a, b).

Our figure for the sodium channel density of frog muscle is about tentimes higher than the value reported by Colquhoun et al. (1974) for ratdiaphragm. The significance of this large difference is unclear, and itwould be of considerable interest to compare sodium currents undervoltage-clamp conditions in the two tissues. If rat diaphragm and frogmuscle had identical sodium channels, it would be difficult to see howrat diaphragm could conduct impulses; in frog muscle impulse propagationcertainly requires more than 21 sites//Im2 since it fails at a drug con-centration of 50 nm. Several possibilities can be discussed to account forthe difference between the two tissues. (A) the conductance of a singlerat sodium channel might be more than 10 times higher than that infrog; Colquhoun et al. (1974) suggest a value of 10-10 mho for rat diaphragm.In the absence of experimental proof, this seems unlikely to us, since wefind it difficult to imagine how a rather selective ionic channel can havea conductance 10 times higher than that of a virtually non-selective,water-filled pore such as the channel formed by gramicidin A (Hladky &Haydon, 1972; for further discussion, see below). (B) Sodium channels

503


in the rat might inactivate more slowly than in the frog, and remainconducting for a longer duration during an action potential. (C) Thereare two types of ionic channels in rat diaphragm which can cause mem-brane depolarization, one with the usual and high sensitivity to tetro-dotoxin, the other with little or none. This is clearly the case in denervatedrat diaphragm, and the results of Colquhoun et al. (1974, their Fig. 6)suggest to us that it may also apply to some extent to the innervatedpreparation. The concentration needed to halve the maximum rate ofaction potential depolarization (Pmax) in the rat is some ten times higherthan in frog muscle. Their Fig. 6 also shows that between 0 and 50 nM,J'max depends steeply on drug concentration, whereas at higher con-centrations, the drug sensitivity becomes much less.

The conductance of a single sodium channelSince it is highly probable that tetrodotoxin molecules bind to sodium

channels on a one-to-one basis, tetrodotoxin binding studies can be usedto measure the sodium channel density in excitable membranes. Oncethis has been done, it is possible to estimate the conductance of a singlesodium channel by simply dividing the electrically measured 'maximal'sodium membrane conductance by the number of tetrodotoxin bindingsites. Several authors have used this approach (Hille, 1970; Keynes,Ritchie & Rojas, 1971; Colquhoun et al. 1974) and have obtained valuesof the order of 10-10 mho. This is substantially higher than valuesobtained by direct measurement (Hladky & Haydon, 1972) or noiseanalysis (Anderson & Stevens, 1973) on some ionic channels which, unlikethe sodium channel, show little or no selectivity.A serious disadvantage of the above estimates of single sodium channel

conductances is that they rely on tissues where it is relatively easy tomeasure tetrodotoxin binding, but as yet impossible to measure themembrane sodium conductance. Instead, one had to assume that thesodium conductance of small fibres is the same as that of nerves whichappear to be highly specialized for fast impulse conduction, such as thesquid giant axon. In frog skeletal muscle, one is more fortunate, sincemaximal sodium conductances have been measured by Adrian et al.(1970) and Ildefonse & Rougier (Ildefonse & Roy, 1972). Adjusting thevalues given by these authors to apply to a muscle at 1-3° C in isotonicRinger fluid, a density of 380 sodium channels per /,m2 would suggestsingle channel conductances of about 1 pmho. One can obtain comparablevalues for the squid giant axon either by using the electrical data ofHodgkin & Huxley (1952) in conjunction with the sodium channel densityof 553/,um2 measured by Levinson & Meves (1975), or by comparing'gating charge' and maximal sodium conductance (Keynes & Rojas,

504


1974). Various estimates of sodium channel conductances are given inTable 5. Their values are 0-6 or 1-4 pmho/channel for muscle; the difference

TABLE 5. Conductance of single sodium channels

Sodiumchannels

Muscle

Squid nerve

Gramicidin Achannel

Acetylcholinechannel(muscle)

(n

Condition 1

2-5 x hypertonic1-30 C

isotonic, 200 C

60C

0 5 M-NaCl,30C

Ringer, 80 C

AnCu

DiI

9Naamho/em2)citedralue

9Na(mmho/cm2)

adjusted

Con-ductanceof singlechannel

10-12 mho Reference

70 53 1-4 Adrian et at. (1970)This paper

50 22 0-6 Ildefonse & Roy(1972)

This paper160 160 2-9 Hodgkin & Huxley

(1952)Levinson & Meves(1975)

alysis of 'gating 2-5 Keynes & RojasLrrents' (1974)-ect measurement 9-4 Hladky & Haydon

(1972)Noise analysis 20-30 Anderson &

Stevens (1973)

The first three rows apply to tissues where both gNa and tetrodotoxin bindingwere measured; single channel conductances were obtained by dividing the maxi-mal sodium conductance 9Na (Hodgkin & Huxley, 1952) by the number of tetro-dotoxin binding sites per unit area. The first column for gNa gives the value foundin the literature; for muscle, these values were adjusted to apply to isotonicRinger fluid at 0-3° C. The value given by Adrian et al. (1970) was obtained inhypertonic medium on fibres which were shrunken to probably about 0-57 timestheir isotonic volume (Blinks, 1965); in order to refer their value to the surfacearea of a cylinder of diameter similar to that of an unshrunken fibre, it wasmultiplied by (0-57)'. The value of Ildefonse & Roy (1972) was corrected to applyto 00 C by assuming a temperature coefficient of 1-5 (Moore, 1958). The squid axonvalue applies to fresh axons (Hodgkin & Huxley, 1952).

reflects experimental uncertainty. The corresponding value for squidnerve should be greater, since the activity of permeant electrolyte thereis about 4 times higher than in muscle. Estimating channel conductancesin the way discussed here is too crude a method to decide whether thisis so. Nevertheless, the value of 2-5 pmho/channel for squid given inTable 5 is not inconsistent with this prediction.

Included for comparison in Table 5 are the conductances of thechannels formed by the antibiotic gramicidin A, and of the acetylcholine

505

W. ALMERS AND S. R. LEVINSONchannel at the neuromuscular junction. These channels, too, are permeableto sodium, but have appreciably larger conductances than the tetrodo-toxin-sensitive channel. This makes good sense, since neither gramicidinnor acetylcholine channels show much selectivity for univalent cations.A channel which does not discriminate between univalent cations mightbe expected to permit higher transit rates than a relatively selective chan-nel, which has first to 'test' the identity of each approaching ion beforeallowing its passage.When calculating the single sodium channel conductance from site densities, one

needs to know the 'maximal' membrane sodium conductance, which correspondsto the state where all sodium channels are conducting. Sodium channels, onceopen, inactivate, and one has to allow for this effect. Usually, this is done asdescribed by Hodgkin & Huxley (1952) by a kinetic analysis which assumes thatchannel opening and inactivation are independent processes. Experiments onpronase-treated axons where sodium currents do not inactivate (Armstrong,Bezanilla & Rojas, 1973) tend to confirm the notion that peak sodium currentsunder a voltage clamp give a good estimate of the maximal sodium conductance.

In summary, one can say that the conductance of a single sodiumchannel is probably one or two orders of magnitude smaller than waspreviously thought. This illustrates the importance of measuring sodiumchannel density and maximal sodium conductance on the same tissue.Conversely, it now appears likely that the sodium conductance per unitmembrane area in the large variety of small non-myelinated nerve fibresstudied by Colquhoun et al. (1972b) is substantially lower than that ofsquid axons and frog twitch muscle.

Sodium channels and muscle 'gating currents'Recently, Armstrong & Bezanilla (1973, 1974) and Keynes & Rojas

(1973, 1974) have observed membrane currents in squid giant axons,which probably represent the re-orientation of charged molecule or dipolesinside the membrane. These 'gating currents' are thought to accompanythe opening and closing of sodium channels. Intramembrane chargemovements have also been observed in muscle (Schneider & Chandler,1973; Almers, 1975). If referred to unit membrane capacity, they are ofsimilar magnitude to those in squid nerve; however, their times courseis much slower than the kinetics of muscle sodium currents, and theyare thought to be related to contractile activation. Muscle, like squidnerve, has sodium channels, and it is of interest to ask why sodium'gating currents' which are so prominent in squid nerve, have so farfailed to appear in experiments on frog muscle. The present results givea straightforward answer. In an average fibre of 7 #uF/cm2 membranecapacity, the sodium channel density per unit capacity is 380/7 x 108 or5.4 x 109 channels/,uF. From Levinson & Meves' data (1975), the corre-

506


sponding figure for a squid nerve of 0-9 #F/cm2 membrane capacity(Hodgkin, Huxley & Katz, 1952) is 533/0.9 x 108 or 61 x 109 channels/ItIF.If the maximal 'gating charge' of 33 nC/jtF (30 nC/cm2; Keynes & Rojas,1974) in squid axons is entirely due to sodium channels, one wouldexpect the sodium gating charge in muscle to be no larger than about3 nC/gF of membrane capacity. Given the limited time resolution ofmuscle voltage-clamp experiments, a charge movement of this magnitudecould easily have gone unnoticed next to the much larger charge move-ments of 20-35 nC/,tF (Schneider & Chandler, 1973; Almers, 1975) whichare thought to be unrelated to sodium channel gating.

We thank Mr Roger Y Tsien and Dr D. Colquhoun for helpful discussion, criticalreading of the manuscript and advice on statistical analysis, Mr Tsien and DrJ. E. A. McIntosh for help with computer programmes, and Drs R. H. Adrian,D. A. Haydon and R. D. Keynes for providing laboratory facilities. Part of thiswork was carried out while one of us (W.A.) held a post-doctoral fellowship ofMuscular Dystrophy Associations of America, Inc. Supported in part by USPHSgrant AM-17803.

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ADRIAN, R. H. & PEACHEY, L. D. (1973). Reconstruction of the action potentialof frog sartorius muscle. J. Phy8iol. 235, 122-144.

ALMERS, W. (1972a). The decline of potassium permeability during extreme hyper-polarization in frog skeletal muscle. J. Phy8iol. 225, 57-83.

ALMERS, W. (1972b). Potassium conductance changes in skeletal muscle and thepotassium concentration in the transverse tubules. J. Phy8iol. 225, 35-56.

ALMERS, W. (1975). Observations on intramembrane charge movements in skeletalmuscle. Phil. Tran8. R. Soc. (in the Press).

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By W. ALMERS* AND S. R. LEVINSON From the Physiological