J. Physiol. (1952) ii6, 497-506
THE DUAL EFFECT OF MEMBRANE POTENTIAL
ON SODIUM CONDUCTANCE IN THE GIANT
AXON OF LOLIGO
BY A. L. HODGKIN AND A. F. HUXLEY
From theLaboratory of the MarineBiological Association, Plymouth, and the PhysiologicalLaboratory, University ofCambridge
Thispapercontainsafurtheraccount ofthe electrical properties ofthegiant axon of Loligo. It deals with the 'inactivation' process which gradually reduces sodium permeabilityafterithas undergone the initial rise associated with depolarization. Experimentsdescribed previously (Hodgkin & Huxley, 1952a, b) show thatthe sodium conductance always declinesfrom its initial maximum, but they leave a number of important points unresolved. Thus they giveno information about the rate at whichrepolarization restores the abilityof the membrane torespond withits characteristic increase of sodium conductance. Nor do they provide much quantitative evidence about the influence of membrane potential onthe process responsible for inactivation.
Thesearethemain problems with which thispaperis concerned. The experi- mentalmethodneedsnospecialdescription, since itwasessentiallythe same asthat usedpreviously(Hodgkin,Huiley &Katz, 1952;Hodgkin&Huxley,
The influence of a small change in membrane potential on the abilityofthe membrane to undergo its increase in sodium permeability is illustrated by Fig. 1. Inthisexperiment the membrane potentialwaschangedintwosteps.
Theamplitude of thefirst step was -8 mV. and its durationvariedbetween Oand 50msec. This step will be called the conditioningvoltage (V1). Itwas followedbyasecond step called thetestvoltage (V2)whichwaskeptat a con-
stant amplitude of -44 mV.
RecordAgives thecurrentobserved with thetestvoltagealone. B-Fshow the effect of preceding this by a conditioning pulse of varying duration.
Althoughthedepolarizationof 8 mV.was notassociated withanyappreciable inwardcurrentitgreatlyaltered thesubsequentresponseof thenerve. Thus, ifthe conditioningvoltagelastedlongerthan 20msec., itreduced theinward
current during the test pulse byabout
40%.At intermediate durations the inward current decreased along asmoothexponential curve with a timecon- stant of about 7 msec. The outward current, on the other hand, evidently behaved in a different manner; for it may be seen to approach a final level which was independent of the duration of the conditioning step. This is.
consistent with the observationthatdepolarization is associated withamain- tainedincrease in potassium conductance (Hodgkin & Huxley, 1952a).
Membrane potential Membrane current
0. 3040.50.0 10 20 30 40F5
Fig.1. Development of 'inactivation' during constant depolarization of 8mV. Left-hand column: time course of membranepotential (the numbers show thedisplacement of the membrane potential from its resting value in mV.). Right-hand column: time course of membrane current density. Inwardcurrent is shown as an upward deflexion. (Thevertical linesshowthe'sodium current' expected in the absence of a conditioning step; they vary between 1-03 mA./cm.' in A and 0-87mA./om.' in G). Axon 38; compensatedfeed-back;
Fig. 2 illustrates the converse process of raising the membrane potential beforeapplyingthe testpulse. Inthiscasetheconditioning voltageimproved the state ofthe nerve for theinward currentincreased byabout 70
%ifthe- first step lasted longerthan 15msec.Thisfinding is notaltogether
for the resting potential of isolated squid axons is less than that of other excitable cells (Hodgkin, 1951) and isprobably lowerthanthat intheliving animal.
Aconvenient wayofexpressing these results is to plot theamplitudeof the sodium current during the test pulseagainstthe duration ofthe conditioning
MEMBRANE POTENTIAL AND SODIUM CONDUCTANCE 499 pulse. For this purpose we used the simple method of measurement illustrated by Fig. 3 (inset). This procedure avoids the error introduced by variations of potassiumconductance during the firststep and should give reasonable results for V > -15mV. With larger depolarizations both the method of measure- ment and the interpretation of theresults become somewhat doubtful, since theremay be appreciable sodiumcurrentduring the conditioningperiod. Two
Membrane potential Membrane current
-2 -44 A
Y i... W i
... ...:k k"
0 20 30 4050 0 1020304050
Fig.2. Removal of'inactivation'atmembranepotentialof +31 mV. Experimentaldetailsare asinFig. 1. The vertical lines show the 'sodiumcurrent' with no conditioning step; they varybetween 0-82mA./cm.2inAand0-75mA./cm.2 inG.
ofthecurvesinFig.3wereobtained from the families ofrecordsillustratedin Figs. 1 and 2. The othertwowere determinedfromsimilar families obtained onthe same axon. All four curves showthatinactivation developed or was removedin an approximately exponential manner with a time constant which varied withmembrane potential and had amaximum near V=0. Theyalso indicatethatinactivation tendedto adefinite steadylevelat anyparticular membrane potential. Values of the exponential time-constant (Ti) of the inactivation processaregivenin Table 1.
The influence of membrane potentialonthesteadylevel ofinactivation is illustratedbythe recordsinFig. 4. In thisexperimentthe conditioningstep lastedlongenoughtoallow inactivationtoattain its final levelatallvoltages.
Its amplitude wasvaried between +46 and-29mV., while that ofthe test step was again kept constant at -44mV. The effect ofa small progressive changewas allowedforincalculatingthe verticallinesoneach record. These give the inward current expected in the absence ofa conditioning step and
*.-s°t ,~~ 44mV.
0 5 10 15 20 25msec.
Fig. 3. Timecourseof inactivationatfour different membranepotentials. Abscissa:durationof conditioningstep. Ordinate: circles, sodiumcurrent(measuredasinset)relativetonormal sodiumcurrent; smoothcurve, y=y,0-(yOD-1)exp(-t/Irh),whereye,is theordinateat t=oo
and1histhetime constant(shownbyarrows). ExperimentaldetailsasinFigs. 1 and2.
Membrane potential +46
0- +16 1-4 C
+ 8 D
44 F -14
0 10 20 30 40 S0msec. 0 10 20 30 40 50msec.
Fig.4. Influence of membranepotential on'inactivation' in the steadystate. Experimental
details areasinFig. 1.The verticallinesshow the sodiumcurrentwithnoconditioning step;
they vary between0 74mA./cm.2inA and 0 70mA./cm.2inI.
wereobtainedbyinterpolating betweenrecords made with the test stepalone.
The conditioning voltage clearly had a marked influence on the inward current duringthe second step, for theamplitudeof the sodiumcurrent varied between 1P3mA./cm.2withVJ = +46mV. and about 0-03 mA./cm.2 with V1 =-29 mV.
The quantitative relation between the sodiumcurrentduringthe testpulse andthe membrane potential during the conditioning period is given in Fig. 5.
1-7 -- 10
14 0 8
-02 / 0-7
0-50-40-30 -20 -10 0 10 20 30 40 5OmV.
Fig.5. Influenceof membrane potential on'inactivation' in the steady state. Abscissa:displace- ment ofmembrane potential from its resting value during conditioning step. Ordinate:
circles,sodiumcurrent during test step relative to sodium current inunconditionedtest step (left-handscale) orrelative to maximum sodium current (right-hand scale). The smooth curvewas drawnaccording to equation 1 with a value of -2-5mV.for Vh.Thisgraphis basedon therecords illustrated inFig.4. Sodiumcurrents weredeterminedinthemanner shown inFig. 3.
This shows thatthe twovariablesarerelated by a smoothsymmetricalcurve which hasadefinite limiting value at large membranepotentials. Indiscussing this curve it is convenient to adopt the following nomenclature. We shall denote the ability ofthe nerve to undergo achange in sodiumpermeability bya variable, h, whichcovers a rangefrom0to 1 andisproportionaltothe ordinate inFig. 5. Intheseterms (1-h) isa measure ofinactivation, while h isthe fraction ofthe sodium-carryingsystemwhichis not inactivated and is therefore rapidly available for carrying sodium ions when the membrane is depolarized. Ifthese definitions areadopted we may saythat inactivationis almost complete when V < -20 mV. and is almost absent when V> 30mV.
Atthe resting potentialh is about 0-6 whichimpliesthat inactivationis 40% complete.
The smooth curve inFig. 5 wascalculated from the equation
PH. aXVI. 32
where V is expressed in millivolts and
Vhisthe value of V atwhich h =j in the steadystate. The same equation gave a satisfactory fit inall experiments but therewas somevariation in the value of V,. Fiveexperiments with three fresh fibres gaveresting values ofh between 0Q55and 0-62. In these cases
varied between -1.5 and -3-5mV. On the other hand, two experiments withafibrewhich had been used for some time gave a restinghofonly about 0*25; VAwasthen +7-5 mV. Since the restingpotentialwasfoundtodecline by10-15mV.duringthe course of a long experiment it isreasonabletosuppose that the change in
Vharosesolely from this causeand thattherelation between hand theabsolute membrane potential was independentof the condition of the fibre.
Ina former paper we examined the relationbetween the concentration of sodium ions in the external medium and the sodium current through the membrane (Hodglkn& Huxley, 1952a). Theresultswerereasonably closeto thosepredicted by the 'independence principle'exceptthat thecurrentswere 20-60%toolarge in thesodium-deficient solutions. This effectwasattributed to the small increase in resting potential associated with the substitution of choline ionsforsodium ions. Thisexplanationnow seemsveryreasonable. The restingpotentialprobably increased by about4mV. incholine seawaterand this wouldraise h from0-6 to0 73 in afresh fibre and from 0-25 to 0 37in a fibre which hadbeen used for sometime.
The quantitativeresultsobtainedinthis series ofexperimentsaresummarized inTable 1. Most of the experimentsweremade at 347°C. but atemperature of190 C.wasused onone occasion. The results suggestthattemperature has littleeffect on theequilibrium relation betweenhand V, butgreatly alters the rate atwhich thisequilibriumisattained.The
Qlooftherateconstantscannot bestatedwithcertainty but is clearly oftheorder of 3.
This section deals with a single experiment which gave an independent
measurement of the timeconstantof inactivation.
Twopulses of amplitude -44mV. and duration 1 8msec. were applied to themembrane. Fig. 6Aisarecordobtainedwith thesecondpulse alone. The ioniccurrent wasinward and reachedamaximum ofabout 0-25mA./cm.2. As in all other records, the inward current was notmaintained but declined as aresult of inactivation. Restoration of the normal membrane potential was associated with a tail of inward current due to the rapid fall of sodium conductance (see Hodgkin &Huxley, 1952b). When twopulses were applied in quick succession the effect ofthe first was similarto that in A, but the inward current duringthe second wasreducedto about one half(record B).
A gradualrecoverytothenormal level is showninrecords C-G.
The curve inFig.7wasobtained by estimating sodiumcurrentinthemanner
TABLE 1. Experiments with conditioning voltage
Temper- Displacementof membranepotential (mV.)
ature .A_ _ __
Axon (0C.) Variable -29 -22 -14 - 8 - 7 0 9 16 31 46
38 5 A* (steady 0-02 0.04 0*17 - 0*37 059 0-82 0.94 0 99 1 00 39 19 state) 0'02 0'04 0-09 - 0-28 055 0-83 094 0-98 0 99 39t 3 001 0-03 0*04 - 0.11 0.26 0O50 069 0'93 0*99
38 5 h1 (steady 0-02 - - 0.43 0B58 - 0'92 099 -
39 19 state) 0 03 - - 040 0-61 - 094 -
391 3 .- 0-22 0-75 093 -
37 3 004 - 034 0.55 0-81 0-96 -
38 5 h (msew.) 15 - - 7 [8-10] - 8 4
39 19 0 35 - - 15 - [1.7-2.1] - 1*8 - -
39t 3 ..-_ 13 7 -
37 3 3 - 6 [8-10] 9 7 -
38 6 j§(msec.) 1.3 - - 6 [7-9] - 7 3-6
39 6 1-5 - 6 - [7-9] - 8 -
39t 6 ._ - 9 5
37 6 - 22 - 4 - [6-7] 7 5 -
Axon 31 at 45°0. h=18 msec. at V= -44 mV. h=12msec.atV=0 Axon 31at60C. T§=15msec.atV= -44 mV. Th§=10 msec. at V=0
* Measurements made by methodsmustratedin Figs. 4 and5.
t Theaxonhad been used forsometime and wasinpoor conditionwhenthese measurements weremade.
t Methodsillustrated in Figs. 1-3.
§ Calculated from aboveassumingQloof 3.
[ ] Interpolated.
histhefractionofthe sodium system which is rapidly available, (1-h) is the fraction inacti- vated.
vAdetermines the rate at whichhapproaches its steady state.
0 10 20msec.
Fig. 6. Membranecurrentsassociated withtwosquarewavesappliedinsuccession. The amplitude of each squarewave was -44mV. and theduration 1-8msec. Record Ashows thesecond squarewavealone, B-Gboth squarewavesatvariousintervals. Axon31;uncompensated feed-back;temperature4.50C.
shown in Fig. 3 and plotting this against the interval between the two pulses.
Itwill be seen that recovery from inactivation took place in anapproximately exponential manner with a time constant of about 12 msec. A similar curve anda similar time constant were obtained by plotting
This time constant is clearly of the same order as that given by themethod using weak conditioning voltages (see Table 1). An estimate of theinactiva- tion timeconstant at -44 mV.may beobtained by extrapolating the curve in Fig. 7 tozero time. This indicates that the available fraction of the sodium- carrying system wasreduced to 0 37 at the end of a pulse of amplitude -44 mV.
andduration 1'8msec. Hence the inactivationtime constant at -44 mV. is about 1-8msec., which is of the same order as the values obtained withlarge depolarizations by the first method (Table 1). It is also in satisfactory agreement with the time constant obtained by fitting a curve to thevariation of sodium conductance during a maintained depolarization of 40-50 mV.
(Hodgkin& Huxley, 1952c).
0°6 0-7 -
C Cc 0-4
CA 0 10 20 30msec.
Fig.7. Recovery frominactivation. Abscissa: interval between end offirstpulse andbeginning ofsecondpulse. Ordinate: sodiumcurrentin secondpulsemeasuredasshown inFig. 3 and expressed asafraction ofthe sodium currentin anunconditioned pulse.The circles are
experimental pointsderived from the records inFig.6. The smoothcurveis drawnaccording totheexpression1-463exp(-tlva),whereTrh%=12msec.
Thetwo-pulseexperimentisinterestingbecause itemphasizesthedifference between therapid fall of sodium conductance associated with repolarization and theslower declineduring amaintained depolarization. Botheventslead to a decrease in sodium current, but the underlying mechanisms are clearly different. In the first case it must be supposed that repolarization converts active membrane into resting membrane; in the second that prolonged depolarization turnsit into arefractory orinactivated condition from which it recoversat arelativelyslowratewhen the fibre isrepolarized. It cannotbe arguedthatrepolarizationreduces sodium conductanceby making the active
MEMBRANE POTENTIAL AND SODIUM CONDUCTANCE 505 membrane refractory. If this were so, one would expect that the inward current during the second pulse would be reduced to zero at short intervals, instead of to 37%as in Fig. 7. Thereduction to 37
%is clearlyassociated with the incomplete decline ofsodium conductance during the first pulse and not with the rapid and complete decline due to repolarization at the end of the first pulse.
The experimental evidence in this paper and in those which precede it (Hodgkin &Huxley, 1952 a, b) suggests that the membrane potential has two distinct influencesonthe system which allows sodium ions to flow through the membrane. The early effects of changes in membrane potential are a rapid increase in sodium conductance when the fibre is depolarized and a rapid decrease when it is repolarized. The late effects are a slow onset of a refractory orinactivecondition during a maintained depolarization and a slow recovery followingrepolarization. A membrane in the refractory or inactive condition resembles one in the resting state in having a low sodium conductance. It differs in that it cannot undergo an increase in sodium conductance if the fibre is depolarized. The difference allows inactivation to be measured by methods suchasthose describedinthis paper. The results show thatboththe final level ofinactivation andthe rate at which this level is approached are greatly influenced by membrane potential. At high membrane potentials inactivation appears tobeabsent, atlow membrane potentialsitapproaches completion withatimeconstantof about 1V5 msec. at 6° C. This conclusion is' clearly consistent withformer evidence which suggests that the sodium con- ductance declines to a low level with a time constant of1-2msec. during a large and maintaineddepolarization (Hodgkin & Huxley, 1952a). Bothsets ofexperiments may be summarized by statingthat changes in sodium con- ductance are transient over a wide range of membrane potentials.
The persistence of inactivation after a depolarization is clearly connected with the existenceof a refractory state and withaccommodation. Itisnotthe only factor concerned, since the persistence of the raisedpotassium conduc- tance will also help to holdthe membrane potential at a positive value and will therefore tendto makethe fibre inexcitable. The relative importance of the two processes can only be judged by numerical analysis of the type described inthe finalpaperof this series (Hodgkin & Huxley, 1952c).
1. Smallchanges inthe membranepotential ofthegiantaxonof
Loligoare associated with large alterations in the ability ofthe surface membrane to undergo itscharacteristic increase insodium conductance.
2. Asteadydepolarization of10mV.reduces thesodium currentassociated withasudden depolarization of 45 mV. by about 60%. Asteadyriseof10mV.
A. L. HODGKIN AND A. F. HUXLEY
increases the sodium current associated with subsequent depolarization by about 50
3. These effects are described by stating that depolarization gradually inactivates the system which enables sodium ions to cross the membrane.
4. In the steady state, inactivation appears to be almost complete ifthe membrane potential is reduced by 30mV. and is almost absent if it is increased by 30mV. Between these limits the amount of inactivation is determinedby asmooth symmetrical curve and is about 40
%complete in a resting fibreat the beginning of an experiment.
5. At 60 C. the time constant of the inactivation process is about 10 msec.
with V=0, about 1*5 msec. with V= -30 mV. and about 5 msec. at V= +30mV.
HODGKIN, A. L. (1951). The ionic basis of electrical activity in nerve andmuscle. Biol.Rev.26, 339-409.
HODGKIN,A. L.&HUXLEY, A. F. (1952a). Currents carried bysodiumandpotassium ions through themembrane of the giant axon of Loligo. J.Phy8iol. 116, 449-472.
HODGKN, A. L.&HUXLEY, A. F. (1952b). The componentsofmembraneconductanceinthegiant axonofLoligo. J.Physiol. 116, 473-496.
HODGKI,A. L. &HuxLEY, A. F. (1952c). A quantitative description of membranecurrent and its application to conduction and excitation in nerve. J. Physiol. (in the press).
HODGKIN,A. L.,HuxLEY,A. F. & KATZ,B. (1952). Measurement of current-voltage relations in the membrane of the giant axon ofLoligo. J.Physiol. 116, 424-448.