SODIUM AND POTASSIUM CONDUCTANCE CHANGES DURING A MEMBRANE ACTION POTENTIAL

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SODIUM AND

POTASSIUM CONDUCTANCE CHANGES DURING A

MEMBRANE ACTION POTENTIAL

BYFRANCISCO BEZANILLA,* EDUARDO ROJAS AND

ROBERT E. TAYLOR

Fromthe Faculty of Sciences, UniversityofChile, Clasificador 198, Correo Central, Santiago, Chile and

the Laboratoryof Biophysics, National Institute of Neurological Diseases and Stroke, National Institutes of Health, Bethesda, Maryland, U.S.A.

(Received 29 June 1970) SUMMARY

1. A method for turning a membrane potential control system on and off in less than 10,usec is described. This method was used to record membrane currents in perfused giant axons from Dosidicus

gigas

and

Loligo

forbesi after turning on the voltage clamp system at various times duringthe course ofa membrane action potential.

2. The membrane current measured just after the capacity charging transient was found to have an almost linear relation to the controlled membrane potential.

3. The total membrane conductance taken from these current-voltage curves was found to have a time course during the action potential similar tothat foundby Cole & Curtis (1939).

4. The instantaneous current voltage curves were linear enough to make itpossible to obtain a good estimate of the individual sodium and potassium channel conductances, either algebraically or by clamping to thesodium, orpotassium,reversalpotentials. Good generalagreement was obtained withthe

predictions

oftheHodgkin-Huxley equations.

5. We consider these results to constitute the first direct experimental demonstration of the conductance

changes

to sodium and potassium during the course ofan actionpotential.

* Fellow of the Comision Nacional de

Investigaci6n

Cientifica y Tecnol6gica,

Chile. Present address: Department of Physiology, University of Rochester,

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F. BEZANILLA, E. ROJAS AND B.E. TAYLOR INTRODUCTION

Ourpresent ideasconcerning the ionic nature of the action potential are based on the results of many experiments utilizing a variety of cells, particularly giant nerve fibres (Cole, 1968). The presentation of the sodium-potassium nerve model by Hodgkin & Huxley in 1952 very elegantly accounted for most of theinformation available at that time and provided a challenge to test its predictions. In 1939, Cole & Curtis measured a transientchange in membrane impedance (at 20kc) concomitantwith the actionpotential which wasshown to be mainly due to a change in membrane conductance. Hodgkin & Huxley calculated the time course ofthesodium and potassium conductance change during the courseofanactionpotential and made the total conductance change equal to the sum of these two conductances plus a smallleakage. They showed that the time courseofthe calculated conductance change was very similar to the time course measured by Cole & Curtis(Hodgkin&Huxley, 1952, Fig. 16).However,it has not been possible to measure separately the individual components (sodium and potassium) ofthis total conductance eventhough consider-able attention has been given to thisproblem (Weidmann, 1951; Vassalle,

1966; Morlock, Benamy & Grundfest, 1968; Peper & Trautwein, 1969). This paper presents the resultsof experimentsinwhich the sodium and potassium conductance changes postulated by Hodgkin & Huxley were

measured during the courseofan action potential. Themethodwhich we used to separate these conductances from the total conductance isaccurate only if the instantaneous current-voltage curve at any time during the course ofamembrane actionpotentialislinear. We present evidence that for squid giant axons from Dosidicus

gigas

and from

Loligo

forbesi the departure ofthe instantaneous current-voltagecurvefromlinearityisnot serious overthe relevant potential range.

Apreliminaryreportof this paper has beenpublishedelsewhere (Rojas, Bezanilla & Taylor, 1970).

METHODS

Giantaxonsfrom thesquid Dosidicusgiga8, availableattheLaboratoriode Fisio-logia Celular, Universidad de Chile, Montemar, Chile, and from Loligo forbe8i,

available at the Laboratory of the Marine Biological Association, Plymouth, England, wereused in this work. A description of the arrangement usedfor intra-cellular perfusionhas been presentedbefore (Rojas, Taylor, Atwater & Bezanilla,

1969).

Proper membrane potential control (or membrane current control) implies a

'space clamp' (Cole, 1968). Ideally there would be no variations of membrane

potentialwith distance alongthelengthof the axonin themeasuring regionand in practice this condition is closely approximated (Rojas et al. 1969). A 'membrane actionpotential'isanaction potentialproducedunder these spaceclampconditions

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with no net current flow across the membrane except for a brief shock used to initiate theactivity. During this action potential the properties of the membrane are chang-ing with time. Fig. 1 represents a simplified diagram of the arrangement for mem-branepotentialormembrane current control. If at a given time during the course of the actionpotential (Fig. 1, left side), the membrane potential is suddenly controlled (voltage clamp) the membrane current is not zero and has the time course shown inFig. 1,right side.

Open loop Voltage

currentclamp a clamp

~

I

°VM ; | VM

VM~~~~~~~~

VM

AVC

IM

Fig. 1. Simplified diagram of the experimental procedure. Upper part: a

simplifieddiagram of the system usedtoswitchonthemembrane potential control system. Lower part: the recorded membrane potential and mem-branecurrent. On the left side of theFigurethe membrane is in open loop

current clamp condition because the switchat the output of the control amplifier is connected totheauxiliary feed-backloop. The actionpotential is excitedbyashortpulseofvoltagethroughaveryhighresistor connected

tothe axial wire. On theright side of thefigurethe switchconnectsthe out-put of the control amplifiertothe axial wire and the membrane is under

voltage clamp condition. Thefree course of the action potential is

inter-rupted and the recorded potential is equal to the command potential.

Simultaneouslymembranecurrents arerecordedasshownin thebottom of

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732 F. BEZANILLA, E. ROJAS AND R. E. TAYLOR

At any given time thedirection and the shape of thecurrentrecorddepend upon the timeatwhich thevoltageclampintervalwasinitiatedand uponthe value of the membrane potential duringthe controlperiod.

For the experiment shown inFig. 3, frameb, the control systemwasturned on at the time when the actionpotentialwas atitspeak value. The uppertracesrepresent the recorded membranecurrent and the lower traces represent the recorded mem-brane potential before and during the time at which the membrane potential was under control. Theindividualtraces weretakenatintervals of1sec for depolari-zationsfrom the resting potential (-60mV) to -40 through + 100 mV in 20 mV steps (potentials are referredtothe external solution as zero; depolarizations and outwardcurrents arepositive).Duringthevoltage clampperiod with the membrane potential kept atVcfor

-60mV < Vc < +40mV

there is aninwardcurrent followedby an outwardcurrent.For +40mV < Vc

themembrane current is always outward (although this is not shown in this par-ticularrecord, when

Vc

< -70mV

the membranecurrentisalways inward).From these records it ispossibletomeasure

accurately the changes in membrane potential and the concomitant changes in membrane current. Such records were used to calculate the total membrane

con-ductance just before the interruption and to separate the sodium and potassium conductance at anygiventime duringthecourse ofamembraneaction potential.

Even though the method used to turn on the voltage clamp system is rather

simple, anumber of technical difficulties wereencounteredbefore obtaininga good performance.Fig.2isadiagram of the electrical circuit of the control systemused. The usual switch shown inFig. 1connectingthe output of the controlamplifierto

either the current supplying wire (which is inside the fibre) or to the feed-back resistance wasreplaced by two transistors (a PNP transistor, 2N 3638 andaNPN transistor, 2N 3904). The collectors of these transistors are electrically connected

togethertothe output of the controlamplifier.Theemitterof the NPN transistor is connectedthrough aresistancetotheinputof the controlamplifier. The emitter of

the PNP transistor makes electrical contactwith the current supplying wire. The bases are electrically connected togetherandto a positive constantvoltage source

which resultsin ahighresistancebetweentheemitter and thecollector of thePNP transistor and alow resistance between the emitter and the collector of the NPN transistor; applicationofa negativerectangular voltage pulse tothebasesreverses

thissituation and the membrane potential control system is turned on duringthe

pulse. Thechangeinresistance between theemitterandthe collectorresultingfrom the applicationofanegative voltage pulseiscompletedin less than 3gsecprovided

that thepulseutilizedisestablishedin less than 3/tsec.

Current transients recorded with this system are fast. For example, it is very difficult toseparate the capacitativecurrent transient fromthe ioniccurrent inthe

current transient shown in Fig. 3, second frame. A semilogarithmic plot of these

currents as afunction oftimeshowed that ingeneralthecapacitativecurrentfallsoff

witha time constantof the order of10Itsecand that the ioniccurrentfallsoffwitha

time constantalways greaterthan 100Itsec. Theeffect ofacompensatedfeed-back system (correction for thevoltage errorduetotheresistanceinserieswiththe

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shown inFig. 8A and B. Itcanbeseenthat the current transientsobtained witha

compensatedvoltage clamparefaster than the currenttransients obtained without

compensation.

Compensated feed-back was obtained by feeding a variable fraction, a, of the voltage output of the current amplifier into the summing point of the control

amplifier (see Fig. 2). The degree of series resistance compensation achieved was measured in Q cm2 and was calculated as the ratio voltage difference between the recorded membrane potential with and without compensation/current density measured atthe same time withcompensation.

Fig. 2.Diagram of the voltage clampsystem used. All operational

ampli-fierswerefrom Philbrick. Vx: membrane potential;

I,:

membrane current

duringclamp;

SI:

switch usedtoobtaincompensatedfeed-back; S2:switch utilized to operate the system either as current clamp or voltageclamp.This switch can be replaced by a more sophisticated electronic switch made with FET transistors; NPN transistor: 2N3904; PNP transistor 2N 3638.

VP:rectangularvoltagepulses.

I,,:

rectangular currentpulses.

Vhm:

holding potential. 'hoid: holdingcurrent.

RESULTS

Instantaneous

current-voltage

relations

during

the

course

ofamembrane actionpotential

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734 F. BEZANILLA, E. ROJAS AND R. E. TAYLOR

before and during the time in which the membrane

potential

was under control. The individual traces were taken at intervals of 1 sec for de-polarizationsfrom the restingpotential(of -60

mV)

to + 80, +100mVor +120mV in 20mV steps. Frame a shows the results obtained when the control systemwas turnedon abitafter (1.0 msec) the

application

ofthe stimulating current (see stimulus artifact) and frame d illustrates the

K

J___J

a b

c d

Fig. 3.Superimposedoscilloscopetracesof membranepotentialsand

mem-branecurrentsbefore andduringthevoltageclamp period.Uppertracesin each frame represent the recorded membrane currents and lower traces

represent the recorded membranepotentials. (These records are not flat becausecompensated feed-backwasused.)Calibrations:current: 2-68mA/ cm2; voltage: 100mV; time: 2msec. Do8idicus axon. Resting potential

-60mV;Temperature: 8° C.

results obtained when the control systemwasturnedon almostatthe end ofthe action

potential

(4.5

msec). The

voltage

traces are notflat because the controlled membrane potential was corrected for the

voltage drop

across 4Qcm2 of series resistance. The

following

is apparent from these records:

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(II) Steady-state currents are quite independent of the time at which the control system is turned on. The shape of the inward current, onthe otherhand, dependsonthe timeatwhich the controlsystemis turnedon.

This point is best illustrated

by

the results

presented

in

Fig.

4 where the membranepotential was controlled at -40 mV and the

resting

potential was -60 mV. Upper traces show the membrane currents and lower traces show the recorded membranepotential. The inward currents

change

from

a b c d

I)

J-

J

I

e f g h

i j k I

Fig. 4. Action potential interruption to -40mV. At a given controlled potential,theshapeof the earlycurrentdependsuponthe timeatwhichthe

voltage clamp interval wasinitiated. Uppertraces representthe recorded membranecurrents.Lowertracesrepresenttherecorded membrane

poten-tial. Resting potential was -60mV. Calibrations: current: 3mA/cm2;

voltage: 100 mV; time: 2 msec.Dosiiu8 axonat 12°C.

their usual shape (frame a) to that of a 'tail' of inward current

(from

framed toframek). Thecharacteristic ofthe recorded membrane currents suggests that as in the case ofa

regular

voltage

clamp

pulse

the inward currents are carried by sodium ions and that the

delayed

outward currents arecarriedby potassium ions,which isthe

only

cation present in the

perfusing

solution

(Atwater,

Bezanilla &

Rojas,

1969;

Bezanilla,

Rojas & Taylor, 1970).

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736 F. BEZANILLA, E. ROJAS AND R. E. TAYLOR

charged and that themeasured currentis ionic current. Theresults ofsix experiments are shown inFig. 5A and B. The time (afterthe

beginning

of the stimulating current pulse) during the course ofthe membrane action potential at which each curve was measured is given next to the corres-ponding current-voltagecurve.It isapparent from thesecurvesthat there

1

A-,

E

V

E

C 01

01

C .0

E

V

100

I 1

50 100

1 100 -50

-1

I15

o

.

-3. Expt. API-3 A Membrane potential (mV)

Fig.5.Instantaneouscurrent-voltage relations during the course of a mem-brane actionpotential.I-Vcurveswereobtained from frames similar to those shown inFig. 3. The time at which themembrane potential control was turnedonisgivennexttoeachI-Vcurve.This time is measured from the initiationof therectangular pulse of stimulating current. A. Instantaneous I-Vcurves forDosidicu8 axons. The time at which the action potentials reached theirpeakvalueswere 1-1msecforAPI-9-2; 09 msecfor API-8;

1-13 for API-9-1 and 1-3 for API-3. B. Instantaneous I-V curves for

Loligo axon. Timesatthepeak of the action potentials were 1-0 msec for

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is an almost linear relationship between current and membrane potential at different times during the action potential.

The usual procedure to obtain an instantaneouscurrent-voltage relation is toplot the logarithm of the current as a function of time andextrapolate backtozero time. We show in the Discussion section ofthispaperthat the

4

I -100

E

-c

DC

.0

E

0)

6

4

2

-2

Expt. API-11

-10

B Membranepotential (mV)

Fig. 5B. For legend see opposite page.

errorintroducedby measuring the current 30 ptsec after the step change in potential is smaller than 10

%.

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F. BEZANILLA, E. ROJAS AND R. E. TAYLOR

quantitative comparisonbetween different actionpotentialsit isnecessary totake into account thevariable stimulus response times. Forthisreason the timeofthepeak for each action potential is given inthe Figurelegend. About 22% ofthe curvesshown in Fig. 5A and Bwhere taken beforethe peak of the action potential.

Total conductance change during the courseofa membrane actionpotential

Let us first consider the electrical equivalent circuit forthe axon mem-brane under conditions of space clamp as shown in Fig. 6A (Cole, 1968). The equivalent circuit consists of two impedances in series. The first one represents the series resistance and it is generally considered as a pure ohmic component (Hodgkin et al. 1952). The second impedance corres-ponds to the axolemma. This impedance is representedby a capacitor in parallel with several ionic conductive paths, each one ofthemhaving its own electromotiveforce (Hodgkin & Huxley, 1952).

Themodel can be simplified byreplacingallthe electricalelements repre-senting different conductive paths by a single conductive path (provided thatthe instantaneousI-V curves arelinear)with only one electromotive force (Condon & Odishaw, 1958; Cole, 1968) as shown in Fig. 6B. It can nowbe shown that it is possible to measure the membrane conductance,

GM,

andthe open circuit potential,

VT,

from the data presented in Fig. 3. The net current through the axolemma is givenby

IM

= M

Cm

dt +

Ii

(1)

whereIM ismeasured in

mA/cm2,

CA,

isthecapacity ofthe axolemma mea-sured in

#uF/cm2

and

Ii

istheioniccurrentmeasured inmA/cm2.The current through the axon membrane can be given in terms of conductances and

potentials as follows:

I

(Vt

- VT)

GM

(2)

dVM

(V

~

V)G~

(3)

ITM

=

CM

dt +

(nM- TIT

,

where GM is the total membrane conductance measured in mmho/cm2. Duringamembrane actionpotentialthe net currentthroughthe axolemma is zero, i.e.

IM=°=

CM

dt +Ii.

(LA)

When the control system is turned on

then,

for a controlled potential of

Vc

(seeFig. 6) and a total current

Ic,

measuredafter the capacity transient, themembrane potential during the control period is

VNrc =

VC

-ICR.

(4)

(11)

The total membrane conductance, GM, is thus given

by

the ratio of the change in ionic current

(Ic-Ii

where

Ii

is calculated with eqn.

(1A))

divided by the

change

in membrane

potential

(Vmc-VM

where VMC is given by eqn. (4)) as

NM =

(C7MdVM/dt+IC)I(VC-VM-ICs)

(5)

'Cl

Rs

IC~

R5

C

I/Na

K IL CM GM

I

~~VNa

VK VL VT

A B

Fig. 6.Equivalentcircuitsfortheaxonmembrane.Equivalentcircuit

pro-posedby Hodgkin&Huxley.R8 represents the series resistance measured

in Ccm2. Ic represents the current during the voltage clamp andVcthe

controlledpotential duringthe clamp.All other symbolshavetheir usual meanings. B. For thisequivalentcircuitall conductances andelectromotive forces have beenreplacedbyoneconductance,

G.,

inseries withone electro-motive force,VT.

where again VM and

dVM/dt

are measured from the action

potential just

beforethecontrolsystem isturnedonand

IC

isthe totalcurrentmeasured after thecapacitativecurrenttransient.This

expression

isvalid

only

ifGM (i) is not a function ofthe membrane

potential,

and

(ii)

does not

change

from the moment in which VM is measured to the moment when

IC

is measured. The first

assumption

wastested andthe resultswere discussed in theprevious section of Results. The second

assumption

was tested

by

Hodgkin & Huxley (1952) when

they

showed that the sodium and the potassium conductanceswere continuous functions over astep

change

in membrane

potential.

When the

potential

during

the control

period

takestwodifferent

values,

V.,

and

Vc2,

and the

corresponding

currents

IC1

and

IC2

are

measured,

then from eqn. (4) we obtain

GM

=

IVcg-Rs(ICSIc1

(6)

Clearly

independent

measurements of

RR

are

required

to calculate GM witheither

expression

(5) or

(6).

When

compensated

feed-backisusedthe determination ofGM witheqn.

(6)

is immediate.

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740 F.BEZANILLA, E. ROJAS AND R. E. TAYLOR

mmho/cm2

50

0

mV 100 __

0 1 2 3 4 5

A msec

mmho/cm2

150

100

50

0

100 _

0

0 1 2 3 4

B msec

Fig. 7. Total conductance change. A. Conductance change calculated with eqn. (5) assuming that

C.

is 1*OflF/cm2 and that

R,

is equalto 8Q2 cm2.

ExperimentAPI-il,Loligo axon at10.50C. B.Conductance change

calcu-latedwith eqn. (6).R.was taken to be 8Q2cm2.Experiment API-12 Loligo

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Fig. 7 AshowsGM ascalculatedwith eqn. (5) assumingaseries resistance of 8 Q cm2 and a membrane capacity equal to 1

,uF/cm2.

Fig. 7B shows GM as calculated with eqn. (6) assuming the same value for

Rs.

In both experiments uncompensated feed-back was used.

Sodium and potassium conductance change during the course of a membrane actionpotential

The total membrane conductance can be split into its 'sodium' and 'potassium 'components bythefollowingmethod. Ifthepotentialisswitched tothe potassium reversalpotentialthereis no potassium currentand the current is almost entirely inthe sodium channel

(neglecting

asmall com-ponentofleakagecurrent). The initial valuesofthe ioniccurrenttransients are proportional to the sodium conductance change.

Similarly, by switchingthe membranepotentialtothe reversalpotential of the sodium currents the current is almost entirely in the potassium channel.The initial values ofthe ionic current transients are proportional tothe potassium conductance.

It can be shown that this separation ofthe sodium and potassium con-ductances from the total conductance is alsopossibleevenif thepotential duringthe voltage clampperiod is not thetruereversal

potential

foreither the fast or slow channel (see Appendix). After the capacitative current transient is completed the total current is

IC

=

INa+IK+IL,

(7)

where I'a' IK andIL are the sodium,potassium andleakagecurrent com-ponents respectively. This can be expressed in terms of conductances (see Fig. 6A):

IC

= GNa(VC -Na-ICRS)+GK (VC-VK-ICRs)+GL(VC-VL-ICRs), where

1Na,

VK

and VL arethe reversal potentials for the

Na+,

and K+and leakagechannelsrespectively (Chandler&Meves, 1965). When

Vc

takesthe value ofeitherVNaor

VK

andthe series resistance effect is

completely

com-pensated, the individual Na+ and K+ conductances are

immediately

calculatedprovidedthatGL and

VL

areknown. Inpractice itis difficultto removethe effect of the series resistancecompletely.Thismeansthatwhen

Vc

takes the values of either

V1,a

or

VK

the calculated conductances havetobe corrected. When Vctakes values

V~a

or

V*,

nearVNaor

VK respectively,

the conductances G*a orGE calculated as

C*

IC(VK*)

GNa

=

Vf

( va'

(8A)

V*

-V*

GK = V

CV*'

(8B)

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742 F. BEZANILLA, E. ROJAS AND R. E. TAYLOR

approximately represent the sodium and potassium conductance changes (seeAppendix).Inthese calculations the contribution of the leakage channel and themembrane potential error due to an incomplete compensation are not taken into account. Fig. 8A and B show results obtained oninternally

I

IJ

J

a b

A

re

A e

a

B e

f

J111

b

f

-r~

J

)J_

C

g

d

-I

d

h

Fig. 8. Action potential interruption to V1*. Results obtained with a

Do8idicw axon. ExperimentAPI-8: Resting potential -65mV.

Tempera-ture8°C. A.Partially compensated feed-back.Calibrations:current:2-5mnA/ cm2;voltage: lOOmV;time: 2 msec. B.Uncompensated feed-back. The cali-brations are the same as for A.

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off is much less dependent on the time at which the voltage clamp was turnedon.

Fig. 9 shows the current and membranepotential records when

Vc

=

VNa

for perfused axonsfrom

Loligo.

Fig. 10 shows

GNa

and GEobtained utilizingthe instantaneous current measured from current records similar to those shown in Figs. 8 and 9. The sodium conductance increases rapidly and reaches its maximum

a b c

I

-d e f

I _ _ __ _ ____

- g - h

-Fig. 9. Action potential interruption to VNa. Results obtained with a

Loligoaxon.Unretouchedrecords from experiment API-12. Resting poten-tial -78mV. Temperature 9.50C. Calibrations: current 10mA/cm2; voltage:100mV;time: 1 msec. Uncompensated feed-back. Reversal poten-tial

VN.

= +79mV. Notice that there is no underswing in this action potential.

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F. BEZANILLA, E. ROJAS AND R. E. TAYLOR Comparison with the

Hodgkin

& Huxley modelnerve

The individual ionic conductancesshowninFig. 10which were calculated utilizing eqn. (8) can be corrected for the effects of the small leakage conductance and of the series resistance (see Appendix). The absolute value ofthe peaksodium conductance shown in Fig. 10 is slightlylarger than the value of 53-4 mmho/cm2 calculated by Hodgkin & Huxley (see Table 4, Hodgkin & Huxley, 1952).

60 1 So

E 2°t2°E

40 - 100

20 - 50

E

0 1 2 3 4

Fig. 10. Temporal course ofG*8 andG*during a membrane action

poten-tial. Upper part of this Figure

showsE

the temporal course of (open circles) and G* (filled circles) calculated with the uncorrected data from experimentAPI-12. Temperature9.50C. Resting potential-78 mY. Lower part of this Figure shows G7*calculated with thedata obtained on aLotigo

axon. Resting potential -64mY. Notice the underswing in the action

potential.

Sodiumandpotassiumconductanceschangewith thedifferentconditions taken into account during the calculation. In comparing the time course and the sizeof the potassium conductance relative to the size of the sodium conductance it is convenient to normalize both calculated and measured conductances. Accordingly the data shown in Fig. 10 were normalized after corrections forleakage conductance and series resistance. The calcu-lated conductance at 100C have been normalized and they are compared with the experimental results in Fig. 11. For these calculations only the initial conditions were changed to take into account the high resting potential measured in thisparticular fibre.

Therapidriseof both the calculated and measured sodium conductance isalmostidentical and occurs almostat the sametime. The fall off of the experimental sodium conductance, however, is faster than the calculated falloff.

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The time course of both potassium conductances is very similar and the ratiopeak

GK/peak

GNaforthe experimental curve compares well with the sameratioforthe calculated data. After thepeak of the sodium conductance thepotassium conductance takes a progressively larger share. The interval

10r

05

I-150 _

100

-so

...

L

0 2

msec

3 4

I

Fig.11. Comparisonwith theGNaandGKascalculated with theHodgkin& Huxley equations. Upperfiguresrepresent normalized sodium and potas-sium conductances. The maximum sodium conductance in each case was considered as one. Dashed lines: normalized G* and G* for experiment API-12. Dotted lines: normalized sodium and potassium conductances correctedfor a leakage conductance of 5mmho/cm2and a series resistance of 8 fl cm2 following eqns. (3) and (4) in the Appendix. The continuous lines are the Hodgkin & Huxley correspondingGNaandGK. These were com-puted increasing the resting potential 20 mV by having a constant 9-21tA/ cm2 hyperpolarizing current. Temperature 100C. Lower curves represent the tracings of the measured membranepotential (dottedcurve) and the calculated one(continuous curve). The measured actionpotentialhasbeen displaced towards the left sothat thepeaksof both actionpotentialsoccur

at thesame time.

between the sodium andpotassiumconductance

peaks

is

dependent

onthe initial conditions, particularlytherestingpotential

(Cole

& Moore, 1960). Thus the onset of the potassium conductance is delayed as the resting potential increases. For a 20mV hyperpolarization theequations predict an increase ofthe interval between the sodium and potassium peak of

1

0 L

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F. BEZANILLA, E. ROJAS AND R. E. TAYLOR

about 250pasec. This same increase was measured utilizing the potassium conductance curves shown in Fig. 10 which were obtained on two fibres withdifferent resting potentials (-78 mV and -64 mV).

DISCUSSION

Validity of the method

First, it is necessary toclarifywhat is meantbyseparationofindividual ion conductances from the total membrane conductance. Then we may ask about the propertiesofthe system which may introduce errors in the determinationofrelevantquantities.Wehave used theapproach ofHodgkin, Huxley & Katz (1952) where it is first assumed that the different ions flow throughthemembraneindependently. Exceptfor active transport (Baker, Blaustein, Keynes, Manil, Shaw & Steinhardt, 1969) no experimental evidence for interactions have appeared. We may take the equivalent circuitshown inFig. 6asbeing generallyvalid asakindofspatialaverage, since it isdifficult to believe that the membrane is a uniform structure. The mosaic nature of the membrane also leads to the uncertainty that the resistance inseries withthemembranecapacitance isthe sameatdifferent points orfordifferentionicpathways. Difficulties arise not with the equiva-lent circuit but with the questionof the dependence of the parameters on voltage, time and current flow. In the Hodgkin-Huxley equations the individual ion conductance terms do not vary with membrane potential for times shortcomparedtothedelaysassociated withtheir equations. This is an experimentally approachable question of some importance. The results which we have presented give very strong support to the conclu-sion that for axons of Dosidicus or

Loligo

the 'instantaneous' current-voltagerelations arelinear. The methodfor separatingtheseconductances presented here depends on this linearity. If for other excitable mem-branes the curves were not linear new definitions would be needed (cf. Frankenhaeuser, 1960;Dodge & Frankenhaeuser, 1959). Forexample, the slope conductanceatzero current mightbe used as aparameter and ifthe current-voltage curves atvarioustimeshad the sameshapethe quantities measured bysuddenly controllingthe membrane potentialto

VK

or

VN.,

essentially chord conductances, would be proportional tothis parameter. Itis not appropriate to discuss the matter at length here but it should bementioned that the 'sodium conductance' referstothe conductance for ions passing through a channel with certain properties whether or not sodium happens tobe the ion carryingthe current. For the experiments presented here the axons were perfused with potassium fluoride. It is knownthatpotassium flowsthroughthe sodium channel with about 1/10 to1/25theeaseofsodium ions

(Chandler

&

Meves,

1965;Rojas&

Atwater,

(19)

1967). Thusforthese measurements the situation for thesodium channels isequivalentto aninternal sodium concentration which is some fractionof the existingpotassium concentration. Similar considerations applytothe potassium conductance.

Effects ofseries resistance

Asmentioned above it isnotknown iftheseries resistance asshownin Fig. 6 is the same for the sodium and potassium channels but this is a refinement which we cannotconsider here. We may ask about the effects of this series resistance or we may attempt to compensate for itby elec-tronic means or try tocorrectthe databy computation(whichis notalways uniquelypossible; see Taylor, Moore & Cole, 1960).

Negative resistance compensation. It is possible partially to compensate for a series resistance (see Hodgkinet al. 1952) electronically as shown in the circuit diagram in Fig. 2. Analyis of the stability properties ofthe systemshown in Fig. 2 hasnotbeen done to ourknowledge and the best we candoatthe present istocompare the measuredcurrent

(Ic)

withthe deviation ofthe time course of theclamped potential

(VC).

IfRB is apure resistance andthe system isworking properlythey shouldbeproportional. Let usconsidertheresults when thepotential duringthevoltage clamp period is equal to the reversal potential for the potassium channels. Fig. 8A and B show the results obtained with incomplete compensation and without compensation. Uncompensated series resistance reduces the magnitudeof the initial transientofsodiumcurrent and also decreases the rate atwhichthe sodiumcurrent turnsoff. Somerecords even showadelay of this sodiumcurrent turnoff. Thisdelayseems tobedifferentdepending on the initial magnitude ofthe currents.

Theeffects ofthe series resistance uponthe membrane current transients were studied by solvingthe Hodgkin-Huxley equations under conditions similar to the experimental situations. It is assumed that the change in membrane potential from its value before the voltage clamp system is turned on follows an exponential time course with a time constant rc.

Fig. 12 shows some of the results. rc was chosenequal to 1

/Isec

and the series resistance was varied from 0 to 50Q cm2. The usual analytical solutions of the Hodgkin-Huxley equations would correspond to a fully compensated system and an instantaneous membrane potential change. The case labelled 0 Q cm2 in Fig. 12 for the membrane potential change with time constant of1

,u0

psec is closeto this.

(20)

F. BEZANILLA, E. ROJASAND R. E. TAYLOR

may exhibit ahump as demonstratedbythecurvefor50Qcm2inFig. 12. Although such large series resistances have not been reported for squid giant axons similar effects could arise for axons with very large con-ductances.

If in Fig. 12 we take the curves representing ionic currents and we extrapolate them to the time zero and these extrapolated currents are

-20

-1 5

-1*0

-0.5

0 -266

.-83

0 02 04 06 0*8

50

0 msec

Fig. 12.Ic-t-R8diagramshowing the effects of the series resistance on

current transients as computed using the Hodgkin & Huxley equations. Conditions usedtosolve theequations aregiven in the insert. The action potentialwasinterrupted1 1 msecafter theapplication of the stimulating

current. (Dotted line shows uninterrupted action potential.) Lower part of insert is expanded time scale around moment of interruption. Response characteristic ofvoltage clamping system is represented by an exponential

time constant of 1.0

/tsec

for Vc after interruption. Maximum inward

current given bynumbers of the top of first three transients.

(21)

compared with the initial currents obtained with the equations for a perfect step in membrane potential, no serious discrepancies areobserved for a series resistance of less than 6 Q cm2. Thus our measurements should be close to the instantaneous ionic currents even without complete series resistance compensation.

Comparisonwith earlier results and predictions

Our results concerning the total conductance change during the action potential agreefairlywell with the measured conductance change demon-strated by Cole & Curtis in 1939. We did not try to make quantitative comparisons between their results and ours because we measured the conductance change during a membrane action potential and theCole & Curtis measurements were made during a propagated action potential. However, theshapeofthe conductance curve as a functionoftime in our measurements shows the same features and approximately the same time relationship with the membrane potential as their results.

The temporal course of the sodium and potassium conductances are very similar to those predicted by the H-H equations (see Fig. 11). The major differences are that the experimental sodium conductance decreases faster and that the experimental potassium conductance recovers slower than predicted by the equations. We have seen better agreement in the sodium conductancefall off in other axons but the potassium decay was slower in all cases. Considering that the major features of the experimental con-ductance changesareverywellreproducedbythe equationswe concluded that they are a very good description ofthe membranebehaviour during excitation.

Wewishtothank Professor A. L.Hodgkinand Dr KennethS. Cole forreadingand

commentingonthis paper. This workwassupported bytheUniversityof Chile and by theU.S. National Institutes of Health under grant NB-06503-03.Computations

werecarried outwhile F. B. was avisiting FellowattheU.S.A. National Institutes of Health.

APPENDIX Separation ofthe conduotances

When the

potential during

the control

period

is differentfrom the true reversal potentials (either VNa or VK) it is still possibleto split the total conductance into its components.

Forinterruptions of the membrane actionpotentialto

VNa

and

VK

then using eqn. (8) of thetextwe canwrite:

GNa(VN~a-IRs

-Va)

+

GK(VN~a-IR.-VK)

=

11-GL(VN~a-IRs-VL),

(1)

(22)

F. BEZANILLA, E.ROJAS AND R. E. TAYLOR

where

I,

and I2 arethe instantaneous ionic currents duringthe potential control period at

V*a

and

V*

respectively. Tosolve eqns. (1) and (2) it is necessary to know the values OfGL,VNa,

VK,

VL and RJ. These five para-metersmay bedetermined in regular voltage clamp and currentclampruns.

Solving eqns. (1) and (2) for GNa and

OK

we get

G~a

=

(V*

-VNa)

(K1

-

I)

+

(ha

-

V*

a) (K2

-'2)

+Rs

(K21-K112)

(VNa-VK) [Rs

(I2h-)+(VNa-VK)] (3)

a_ -

(V

-VNa) (K,-I,)

+

(VNa

-Va)

(K2-12)+R5

(K211-K112)

(4

a(Va

VK)

[Rs(I2

- )+

(VNja-VK)]

where K1 and K2 are defined as follows:

K1

=

GL(VNa-I1RsVL),

(5)

K2

=

GL(VE-I2RS-VL).

(6)

When

V*a

= VNa, VE =

VK

and the series resistance has been

fully

com-pensated, neglecting the leakage conductance eqns. (3) and (4) give

G*a

= GNa and GE = GK where

G*a

and GE have been defined in eqns. (8A) and (8B)of the text.

REFERENCES

ATWATER, I., BEZANILLA, F. & ROJAS, E. (1969). Sodium influxes in internally perfusedsquid giantaxonduringvoltageclamp.J.Physiol. 201,657-664. BAKER, P. F.,BLAUsTEIN, M. P., KEYNES, R. D., MANIL, J., SHAW, T. I. &

STEIN-HARDT, R. A. (1969). The ouabain-sensitive fluxes of sodium and potassium in squidgiantaxon. J.Physiol. 200, 459-496.

BEZANILLA, F.,ROJAS, E. & TAYLOR, R. E. (1970). Time course of the sodium influx insquid giantaxonduringasingle voltageclamp pulse. J.Physiol.207, 151-164.

CHANDLER, W.K. & MEvES, H. (1965). Voltage clamp experiments on internally perfused giantaxons.J.Physiol. 180, 788-820.

COLE, K. S. (1968).Membrane,Ion8 andImpulses. BerkeleyCalifornia:Universityof California Press.

COLE, K. S. & CURTIS, H.J. (1939). Electric impedance of the squid giant axon

duringactivity. J.gen. Physiol.22, 649-670.

COLE,K. S.&MOORE,J.W. (1960). Potassium ioncurrentinthesquidgiant axon: Dynamic characteristic. Biophys. J. 1, 1-14.

CONDON, E.V. &ODISHAW, H. (1958). Handbook ofPhysic8. NewYork:

McGraw-HillBook CompanyInc.

DODGE, F. A. & FRANKENHAEUSER, B. (1959). Sodium currentsin the myelinated

nerve fibre of Xenopus laevis investigated with the voltage clamp technique. J.Physiol. 148, 188-200.

FRANKENHAEUSER, B. (1960). Sodium permeability in toad nerve and in squid

nerve.J. Physiol. 152, 159-166.

HODGKIN, A.L. &HUXLEY, A.F. (1952). A quantitative descriptionofmembrane

currentand itsapplication toconduction andexcitation in nerve. J.Physiol.117, 500-544.

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HODGKIN,A.L. &HuxiAY,A. F.(1952).Thecomponentsof membraneconductance

inthe giantaxonofLoligo. J. Phy8iol. 116, 473-496.

HODGKIN, A.L., HuxLEY, A. F. & KATZ, B. (1952). Measurement of current-voltagerelations in the membrane of the giant axonof Loligo. J. Phy8iol. 116,

424-448.

MORLOCK,N.L.,BENAMy,D.A. &GRuINDFEST,H. (1968).Analysisofspike

electro-genesis of eel electroplaques withphase plane andimpedancemeasurements. J.

gen.Phy8iol. 52, 22-45.

PEPER, K. &TRAUTWEIN, W. (1969). A note on thepacemakercurrentinpurkinje fibers. Pfluger8Arch. ge8. Phy8iol.309, 356-361.

ROJAS, E. & ATWATER, I. (1967). Effect of tetrodotoxin on the early outward currents inperfused giant axons. Proc. natn. Acad. Sci. U.S.A. 57, 1350-1355.

ROJAS, E., BEZANILLA, F. & TAYLOR, R.E. (1970). Demonstration of sodium and potassium conductance changes during a nerve action potential. Nature, Lond.

225, 747-748.

ROJAS, E., TAYLOR, R.E., ATWATER, I. & BEZANILLA, F. (1969). Analysis of the effects of calcium or magnesium on voltage-clamp currents in perfused squid axonsbathed in solutions ofhighpotassium. J.gen. Phy8iol. 54, 532-552. TAYLOR, R. E., MOORE, J. W. & CoLE, K.S. (1960). Analysis of certainerrors in

squidaxonvoltage clampmeasurements. Biophy8.J. 1, 161-202.

VASAIJLE, M. (1966). Analysis of cardiac pacemaker potential using a 'voltage clamp' technique. Am. J.Phy8iol.210, 1335-1341.

Figure

Updating...

References