Inactivation o f the S o d i u m C h a n n e l

I. Sodium Current Experiments FRANCISCO

BEZANILLA

and C L A Y

M. A R M S T R O N G

From the Department of Physiology, University of Pennsylvania, School of Medicine, Philadelphia, Pennsylvania 19174

A B S T R A C T Inactivation o f sodium conductance has been studied in squid axons with voltage clamp techniques and with the enzyme pronase which selectively destroys inactivation. Comparison of the sodium current before and after pronase treatment shows a lag of several h u n d r e d microseconds in the onset o f inactivation after depolarization. This lag can also be demonstrated with double-pulse experiments. When the m e m b r a n e potential is hyperpolarized to - 1 4 0 mV before depolarization, both activation and inactivation are delayed. These findings suggest that inactivation occurs only after activation; i.e. that the channels must open before the}' can inactivate. T h e time constant o f inactivation measured with two pulses (re) is the same as the one measured from the decay of the sodium current d u r i n g a single pulse (rn). For large depolarizations, steady-state inactivation becomes more incomplete as voltage increases; but it is relatively complete and appears i n d e p e n d e n t of voltage when d e t e r m i n e d with a two-pulse method. This result confirms the existence o f a second open state for Na channels, as p r o p o s e d by Chandler and Meves (1970. J. Physiol. [Lond.]. 211:653-678). T h e time constant o f recover}' from inactivation is voltage d e p e n d e n t and decreases as the m e m b r a n e potential is made more negative. A model for Na channels is presented which has voltage-dependent transitions between the closed and open states, and a voltagei n d e p e n d e n t transition between the open and the inactivated state. In this model the voltage d e p e n d e n c e o f inactivation is a consequence o f coupling to the activation process. INTRODUCTION

E a c h s o d i u m c h a n n e l o f t h e s q u i d a x o n m e m b r a n e is c o n t r o l l e d b y two g a t e s , N a a c t i v a t i o n a n d N a i n a c t i v a t i o n , b o t h o f w h i c h m u s t b e o p e n f o r a c h a n n e l to c o n d u c t (14). T h e a c t i v a t i o n g a t e has q u i c k kinetics w h e n b o t h o p e n i n g a n d c l o s i n g . It is c l o s e d at r e s t , b u t o p e n s q u i c k l y a f t e r d e p o l a r i z a t i o n , a n d p r o d u c e s t h e v e r y fast PNa i n c r e a s e t h a t i n i t i a t e s t h e a c t i o n p o t e n t i a l . T h e a c t i v a t i o n g a t e closes q u i c k l y o n r e p o l a r i z a t i o n . T h e i n a c t i v a t i o n g a t e o p e r a t e s m o r e slowly a n d has t h e o p p o s i t e v o l t a g e d e p e n d e n c e : it is o p e n at r e s t , closes slowly o n d e p o l a r i z a t i o n , a n d o p e n s slowly o n r e p o l a r i z a t i o n . T h i s g a t e cuts s h o r t t h e PNa i n c r e a s e t h a t is i n i t i a t e d by o p e n i n g t h e a c t i v a t i o n g a t e , a n d it m a k e s r e p o l a r i z a t i o n to t h e r e s t i n g p o t e n t i a l (by o p e n i n g o f t h e K c h a n n e l s ) e a s i e r . C l o s e d i n a c t i v a t i o n g a t e s a f t e r a d e p o l a r i z a t i o n a r e a n i m p o r t a n t f a c t o r in t h e r e f r a c t o r y period. THE JOURNAL

or

GENERAL

PHYSIOLOGY

• VOLUME

70, 1977

• pages

549-566

549

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T H E .JOURNAL OF GENERAL PHYSIOLOGY • VOLUME 7 0 - 1 9 7 7

Kinetic evidence for the existence o f two gates on each Na channel is strong (13), and has been c o n f i r m e d by internal perfusion o f axons with pronase, which destroys inactivation while leaving activation intact (4). In the H o d g k i n and Huxley formulation, activation and inactivation gates were m a d e (partly for c o m p u t a t i o n a l ease) completely i n d e p e n d e n t . T h a t is, each gate can o p e n and close regardless o f the condition o f the o t h e r gate. Hoyt (15, 16) has pointed out that the gates may be coupled in some way rather than being entirely i n d e p e n d e n t . Subsequent to this investigator's suggestion it has been shown that inactivation after depolarization follows a lag that is not predicted by the H o d g k i n a n d Huxley (14) equations (1, 10; see below). This delay indicates that some c h a n g e must take place in the m e m b r a n e before inactivation begins, but does not establish that there is coupling. O t h e r evidence for coupling has been presented by G o l d m a n and S c h a u f (10) who f o u n d that shifts in the h= curve (14) with test pulse amplitude c o n f o r m e d m o r e closely to the predictions o f a coupled model than to the H o d g k i n and Huxley equations. Clearly, it is i m p o r t a n t to know the time course o f activation and inactivation in o r d e r to decide such questions. We describe in this p a p e r what we think is the most direct d e t e r m i n a t i o n o f the time course of" inactivation on the basis o f the destruction o f inactivation by pronase. It is shown that the results o f pronase experiments are consistent with those derived from less direct measurements, and that all m e a s u r e m e n t s suggest that activation and inactivation are not i n d e p e n d e n t . T h e same conclusion is reached in the following paper, which describes the effect o f inactivation on gating current. MATERIALS

AND

METHODS

Most experiments were performed on segments of giant axons from the squid Loligo pealei (obtained from the Marine Biological Laboratory, Woods Hole, Mass.). A few experiments (indicated in the figure legends) were performed at the Laboratorio de Fisiologia Celular, University of Chile, on Dosidicus gigas obtained off the coast of Chile. To record gating currents the permeant ions must be removed on both sides of the membrane and the linear component of the capacitative current must be subtracted. The methods have been described previousb (2, 3) and in this paper only modifications and improvements of the original procedure will be noted (Fig. 1a). The major improvement to the apparatus was the addition of a computer (PDP8F)connected on-line with the experimental setup. This increased the speed of data collection and allowed us to store data in the magnetic tape unit of the computer for subsequent analysis performed with the same machine. The experimental set-up, including the computer, consisted of two main sections: an analog rack and a digital rack (Fig. la). The digital rack contained the computer with its magnetic tape units, a signal averager, and a programmable time mark generator (Devices Digitimer). The timing of pulses was controlled by the computer in conjunction with the Digitimer, which produced up to five time marks separated by adjustable intervals. The Digitimer marks were used to trigger on and off a series of pulse generators located in the analog rack. Communication between the Digitimer and the pulse generators was by way of optical isolators to prevent ground loops between the two racks. The membrane current signal from the nerve was amplified in the analog rack and then fed into the input of the signal averager, which was under computer control. At the end of an averaging sequence the memor~ contents of the signal averager were

BEZANILLA AND ARMSTRONG Sodium Current Inactivation

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transferred to the computer memory a n d from there to magnetic tape. T h e Digitimer and the A-D converter were timed by a single crystal clock. The signal averager is the same machine that was briefly described previously (2) and its design and characteristics have been published elsewhere (5). T h r e e important additions have been made. (a) T h e machine is now able to substract digitally the current produced by the control pulses from the test pulse current. (b) Data can be taken at two

Analog Rack

Digital Rack

Digitimer i i

rl

Optical ~ Isolators I I

Pulse ~ Generators rl Pulse

Dividers1

Command Pulses t Computer I

PDPS-F

r I Voltage =n'~ 1 Clamp

t

J I

P

v.

FIGURE 1. (a) Block diagram of the experimental set-up (for details see text). (b) Pulse sequence for a full cycle of the P/4 procedure. Vn is the holding potential (usually - 7 0 mV). V, was usually -170 mV. Duration of the cycle was normally 0.5 s. In many cases P (test pulse) was a complicated pattern and in these circumstances P/4 (control, or subtracting pulse) was the same pattern but of onefourth the amplitude. different sampling rates on each sweep. T h e first 128 points are taken at a high sampling rate (usually 10 /zs per point) and the second 128 points are taken at a slower rate (usually 50/~s per point). (c) An input stage was placed before the sample and hold amplifier. The input stage is an operational amplifier wired as an integrator, and it integrates the input signal d u r i n g the interval between samples. The period of integration is 1 p.s less than the intersample interval. T h e gain of the integrator changes automatically when the sampling rate is switched. T h e effect of this integration is similar

552

T H E J O U R N A L OF G E N E R A L P H Y S I O L O G Y " V O L U M E 7 0 "

1977

to that of using a low pass filter, and it significantly' improves the signal-to-noise ratio. It can be seen in most of the records (see, for example Fig. 1 of the following paper) that the improvement was greater (up to three times) at the low sampling rate. P/4 Procedure T o subtract the linear portion of capacitative current from the records we used the voltage pattern of Fig. lb. T h e current from four control or subtraction pulses of amplitude P/4 was digitally subtracted from the test pulse current. T h e test pulse was o f amplitude P. T h e complete cycle was repeated 3-10 times to improve the signal-to-noise ratio, with a cycle period (usually) o f 0.5 s. T h e method is similar to that previously described (2) but gives a better signal-to-noise ratio. The Transient Generator Saturation of the A-D converter by large-capacity current transients was prevented by adding in a signal from a "transient generator" (Fig. 1) as described previously (3). As a routine, linearity tests of the apparatus were made by using an analog of the axon u n d e r voltage clamp with the same pulse patterns employed during the experiments. Solutions T h e solutions employed are listed with their composition in Table I. In the text, solutions will be r e f e r r e d as external solution//internal solution. Membrane voltages are not corrected for junction potentials. Analysis of Data Data analysis was p e r f o r m e d with the c o m p u t e r (see above) by means of analysis programs that allowed us to display on an oscilloscope the original sweeps which had been recorded on magnetic tape. A short description of the different curve-fitting and analysis procedures follows. FITTING OF TrtE BASE LINE TWO points of the sweep were marked by cursors and a line of the form y = ax + b (sloping base line) or y = b (flat baseline) was fitted by use of least-squares criteria. T h e c o m p u t e r then redrew the trace relative to the fitted base line. INTEGRATION TWO selected points of the sweep were the limits of the integration, which consisted of summing the product of each data point times the duration of the sampling interval. SINGLE EXPONENTIAL FITTING T o fit a single exponential, the logarithm of each point was c o m p u t e d , and a linear regression was p e r f o r m e d by taking into account the weight imposed by the process of taking logarithms (12). T h e fitted curve was displayed on the oscilloscope and a visual inspection of the quality of the fit was made. DOUBLE EXPONENTIAL FITTING TO fit the function y = A e x p ( - ~ ) + B e x p ( - ~ t ) , a Taylor's expansion of this function with respect to the parameters A, a, B, and /3 was made to linearize the equations and to find the values of these parameters for which the sum of the squares of the deviations was a minimum (12). Initial estimates of the parameters had to be provided and sometimes the convergence to a possible local minimum was tested by changing the initial estimates and observing the final convergence. Again, the goodness o f the fit could be seen directly' by comparing the original data and the calculated curve on the screen o f the oscilloscope. FITTING OF DOUBLE EXPONENTIAL AND BASE LINE In some cases we fitted the general function A exp(-cxt) + B exp(-!3t) + Ct + D. This fitting was done also by

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BEZANILLA AND ARMSTRONG Sodium Current Inactivation

linearization of the general function with respect to the parameters. With this procedure no previous fitting of the base line was performed. CONVENTIONS If one follows the usual conventions, Vm (membrane potential) is the potential inside the axon minus the potential outside. Depolarization makes Vm more positive and hyperpolarization makes it more negative. Membrane current (1) is positive when outward and negative when inward. TABLE

I

COMPOSITION OF SOLUTIONS USED External solutions(mM) Name ASW 10% NaSW 20% NaSW 325 Na 50 Ca 40 Na 50 Ca Tris 60 Na 50 Ca Tris

Na

Tris*

440 44 88 325 40 60

5 401 300

TMA.$

150 447 425

Ca

Mg

CI

10 10 10 50 50 50

50 50 50

570 565 558 575 587 585

Internal solutions§(raM) Name 125 125 200 380

TMA Cs 2 Na TMAFG K 10 Na 20 T E A

K

Na

TMA:~

Cs

TEA-Br§

125 2

125 200

380

10

20

F

Glutamate

50 127 200 75

75 100 315

* Tris ( h y d r o x y m e t h y l ) a m i n o m e t h a n e . T e t r a m e t h y l a m m o n i u m ion. § Sucrose was a d d e d to adjust osmolality to 980 m o s m o l / k g . 1 mM H EP ES or 5 mM Tri s was used as buffer, p H was a d j u s t e d to 7.1. [] T e t r a e t h y l a m m o n i u m b r o m i d e . RESULTS

Delayed Onset of Inactivation in Pronase Experiments After step depolarization o f an axon in a m e d i u m o f low Na c o n c e n t r a t i o n there is an o u t w a r d transient o f gating c u r r e n t (Ig), followed by a slower inward transient o f Na c u r r e n t (INa; Fig. 2a). T h e axon was in 10% NaSW//125 Cs 2 Na, so sodium c u r r e n t is small a n d potassium c u r r e n t (IK) is absent. T r a c e A shows the average o f c u r r e n t for 10 steps to 0 mV, f r o m a holding potential (Vh) o f - 7 0 mV (see figure legend for details), A f t e r the o u t w a r d gating c u r r e n t transient INa increases in m a g n i t u d e as Na activation gates o p e n , and then decays as the inactivation gates close. After trace A was r e c o r d e d , inactivation was destroyed by pronase applied internally for a few minutes a n d trace B was taken. Pronase a p p a r e n t l y destroys some Na channels at the same time as it removes inactivation but it has no effect on the surviving activation gates as j u d g e d f r o m the tails o f s o d i u m c u r r e n t d u r i n g repolarization (4). T o account for destruction o f some channels trace B has been scaled up in amplitude by a factor o f 1.3, which is the factor required to restore the gating c u r r e n t transient to its full amplitude. T h e scaling assumes that in destroying the c o n d u c t a n c e o f a channel, all o f its

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PHYSIOLOGY • VOLUME

70 - 1977

gating c u r r e n t is r e m o v e d . We believe that trace B, after lg has subsided, gives a clear picture o f activation gate o p e n i n g , and that trace A - B , which is the difference between traces A and B, represents the closing o f inactivation gates. T h a t is, trace B shows activation gate o p e n i n g , trace A - B represents inactivation gate closing, and trace A is the result o f the two processes. I f so, inactivation (trace A - B ) follows depolarization with a definite lag. Fig. 2b, c are fits of two models to the e x p e r i m e n t a n d will be discussed below. ¢

B

Pronose(XI.3)

x,(K=O)

~ (h=l)

O.2rnA/cm2

ms

Xl--X~ ..JA-B

Y

FIGURE 2. (a) The time course of inactivation determined with pronase. Trace A is a control record of I, and INa, and B was recorded after 15 min of perfusion with pronase. B has been scaled up by a factor of 1.3. A - B is B subtracted from A, and it gives the time course of inactivation. A and B are sums of current from 10 cycles of the P/4 procedure, divided by 10. 70 mV pulse, from a holding potential of -70 mV. 10% NaSW//125 Cs 2 Na, 10°C. (b, c) A and B are the experimental traces described in part (a). The other curves are the predictions for this experiment of the model in the Discussion (b) or the Hodgkin and Huxley equations for INa (c).

Delayed Onset of Inactivation in Two Pulse Experiments A lag in the onset o f inactivation can also be d e m o n s t r a t e d by the two pulse experiments illustrated in Fig. 3 (cf. reference 1). As shown in the d i a g r a m , a conditioning pulse to - 3 5 , - 3 0 , or - 2 0 mV was followed after a variable interval by a test pulse to 0 mV (cf reference 13). T h e duration o f the interval is given by the n u m b e r s in the top frame. T h e peak amplitude o f the test c u r r e n t reflects the fraction o f the channels that are activatable at the end o f the conditioning pulse. Only two aspects o f the figure need be examined. A n imaginary curve t h r o u g h the heavy dots gives the time course o f INa d u r i n g the conditioning pulse, and an imaginary envelope t h r o u g h the c u r r e n t peaks gives a g o o d a p p r o x i m a t i o n o f the time course o f inactivation d u r i n g the conditioning pulse. T h e envelope has a p r o n o u n c e d sigmoid shape, similar to trace A - B in Fig. 2. T h e delay o f several h u n d r e d microseconds in the onset o f inactivation that is evident in both figures is not predicted by the H o d g k i n and Huxley equations, as discussed below.

555

BEZANILLA AND ARMSTRONG Sodium Current Inactivation

CP:V=-20 k

. -

,:l;iliii , . ! : i ; ~ ~.. l' '~ I~' ,

._

t~.t /

-35 :7,

"

•

'

on~.

v w v UINIIIiiV ~'r

"

,o.

OA rnalcm2

FIGURE 3. T h e delayed onset of inactivation demonstrated with a two-pulse procedure. T h e activatable fraction of the sodium conductance was determined by a test pulse to 0 mV, after conditioning pulses (CP) of different durations and amplitudes. CP duration is given by the n u m b e r s in the u p p e r frame for which Vm d u r i n g CP was - 2 0 mV. T h e envelope of the test peaks gives the time course of inactivation (on the 1.6-ms time scale) and is distinctly sigmoid in shape. The heavy dots give Isa at the end of each conditioning pulse, and d u r i n g CP (1.6-ms time scale). It can be seen that inactivation is fastest when 1Na in the conditioning pulse is well developed. Details of the procedure are as follows. Each family of traces was generated by many repetitions of the pulse pattern shown in the inset, with a different CP duration each time. I n making each photograph, a control record was first taken (no CP, trace labeled 0) at a sweep speed given by the 10-ms scale. CP duration was then increased to 0.2 ms, and the origin of the trace was shifted to the right to prevent overlap with the previous test peak. T h e a m o u n t of the shift was proportional to CP duration, and the appropiate time calibration is given in parentheses. Currents d u r i n g the longest conditioning pulse are labeled in the u p p e r and lower frame. Conditioning pulse current is thus shown at expanded time scale by the envelope of dots, and at compressed time scale by the labeled curves. Dosidicus axon injected with TEA + in artificial seawater. 9°C.

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70

• 1977

T o a first a p p r o x i m a t i o n the rate o f inactivation, which is given by the slope o f the i m a g i n a r y e n v e l o p e curve, is p r o p o r t i o n a l to INa (or GNa) in the conditioning pulse. T h i s suggests that the activation gate o f a channel must o p e n b e f o r e inactivation can occur; the inactivation rate is r o u g h l y p r o p o r t i o n a l to the n u m b e r o f o p e n channels. F u r t h e r details o f Fig. 3 are in the legend. T h e suggestion that activation m u s t p r e c e d e inactivation is s u p p o r t e d by Fig. 4. It has b e e n shown that h y p e r p o l a r i z i n g the m e m b r a n e delays the t u r n - o n o f GNa (2), a n d Fig. 4 d e m o n s t r a t e s that inactivation is also delayed. T h e two curves in the figure give the a m p l i t u d e s o f the test currents for an e x p e r i m e n t like that in Fig. 3, starting f r o m Vm = - 5 5 m V in one case a n d - 140 mV in the other. ( T h e fiber was held at - 6 5 m V a n d pulsed to these values 10 ms b e f o r e Time, ms 0 0.7

0.4 ~

0.8 ~

1.2

"o .N m tip

0.8

E O Z m

o z

0.9

¢1 ¢1 O.

1.0

F1GURE 4. Effect of hyperpolarization on the delayed onset of inactivation. Pulse schedule as in Fig. 3. Each point is peak 1Na in the second pulse, normalized relative to control INa for which there was no prepulse. Circles: starting Vm = -55 mV. Squares: starting Vm = - 140 mV. Axon injected with 450 CsF and 100 TEABr and bathed in ASW. 2°C. the b e g i n n i n g o f a conditioning pulse to - 3 0 m V . Inactivation, like activation [not illustrated] is delayed by h y p e r p o l a r i z a t i o n , which again suggests that activation m u s t p r e c e d e inactivation. It m u s t be noted, however, that the delay for activation a n d that for inactivation have not b e e n m e a s u r e d at the same potential.)

Other Measures of Inactivation Time Course In the p r e c e d i n g sections we e x a m i n e d the time course o f inactivation by using a one-pulse m e t h o d (the p r o n a s e e x p e r i m e n t s o f Fig. 2) a n d a two-pulse m e t h o d (Fig. 3). It has been stated, however, that the one-pulse a n d two-pulse m e t h o d s give d i f f e r e n t results for the time course o f inactivation. G o l d m a n a n d Schauf (11), using Myxicola axons, r e p o r t e d that 7h, the time constant o f inactivation m e a s u r e d f r o m the decay o f INa after a single pulse, differs f r o m that m e a s u r e d with a two-pulse m e t h o d . T h e latter time constant they called ~'e. T h e y f o u n d the d i f f e r e n c e to be most p r o n o u n c e d f r o m - 3 0 to - 5 0 m V . As

BEZANILLA AND ARMSTRONG

557

Sodium Current Inactivation

Vm is m a d e negative in this r a n g e , re increases steeply but Ch is, in Myxicola, m u c h less voltage d e p e n d e n t t h a n re. H o d g k i n a n d H u x l e y (using squid axons) originally r e p o r t e d that re a n d ¢n have the s a m e value, a n d that ~'h is j u s t as voltage d e p e n d e n t n e a r - 4 0 m V as ¢c- This is clearly a question o f i m p o r t a n c e , a n d we consequently r e p e a t e d these e x p e r i m e n t s a n d o b t a i n e d the results shown in Fig. 5, which are in g o o d a g r e e m e n t with those o f H o d g k i n a n d H u x l e y . T h e axons r e p r e s e n t e d were b a t h e d in solutions with low Na c o n c e n t r a t i o n , a n d I s was eliminated by replacing internal K + with T M A +. T h e falling p h a s e o f each INa transient was fitted with a single e x p o n e n t i a l (sometimes two exponentials would have b e e n a better fit, cf. r e f e r e n c e 8) by a least-squares

10

0 @~ one pulse •

t w o pulse

8

¢n

E

6

2 I

AO

t -~

I

0

I

I

~

Vm, m V

FIGURE 5. Time constant of inactivation. For the one-pulse method (see inset for symbols), the time constant of decay oflNa (¢h) (see text) is plotted as a function of Vm during the test pulse (open symbols). In the two-pulse method (see inset, Fig. 3) peak INa during the second pulse (to Vm = 20 mV) was plotted semilogarithmically as a function of the duration of the first pulse and a time constant rc was obtained. ¢.~ is given by the filled triangles. Axons were in 40 Na 50 Ca//200 TMA. Each symbol represents a different axon. Holding potential was - 7 0 mV for circles and -100 mV for triangles. P/4 procedure. 8°C. m e t h o d , a n d the results are given in Fig. 5. In all t h r e e e x p e r i m e n t s rh is a steep function o f voltage n e a r --30 to --40 inV. In two e x p e r i m e n t s , both 7e a n d ~'h were m e a s u r e d a n d c o m p a r e d in the voltage r a n g e n e a r - 4 0 m V , a n d the results are shown in Fig. 5 a n d T a b l e II. I f anything, ~'h tends to be slightly slower than rc but the d i f f e r e n c e is p r o b a b l y not significant. T h e m a j o r d i f f e r e n c e between the Myxicola a n d squid results is, as n o t e d , in the time course OflNa for depolarizations to a b o u t - 4 0 mV; in squid, inactivation after a single pulse is quite slow in this voltage range. This is illustrated in Fig. 6, for an a x o n in 325 Na 50 Ca//380 K 10 Na 20 T E A . At - 4 0 m V , inactivation is so slow that it is not a p p a r e n t by the e n d o f the trace. Inactivation as a Function of Vm Steady-state inactivation o f the Na channels increases with m e m b r a n e voltage in the r a n g e - 7 0 to 0 mV (13, 14), but it then decreases again at large positive

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THE JOURNAL OF GENERAL PHYSIOLOGY • VOLUME 70 ' 1977

voltages (6). This p h e n o m e n o n is illustrated in Fig. 6 for an axon with 10 mM Na inside: for the depolarization to +80 mV, steady-state IN, is a p p r o x i m a t e l y one-third o f the peak value. T h e findings o f C h a n d l e r and Meves (6) suggested to us that inactivation might be affected by c u r r e n t flow t h r o u g h the channel and be less complete for large o u t w a r d currents. We investigated this question by d e t e r m i n i n g steady-state inactivqtion in axons with no Na + inside. T o do TABLE INACTIVATION

TIME

I I

CONSTANTS

FOR

TWO

METHODS

Time constant, (ms) Vm

one pulse

two pulse

Temperature oC

-45 -40 -35 -45

9.0 6.9 5.3 3.1

8.3 6.5 4.9 2.5

- 40

2.6

2.1

15

-35

1.9

1.8

15

o

b

' ~"'---~

FIGURE 6.

8 8 8 15

Time

....

course

i

~'~-"'~.__._

OflNa as a function

of potential.

i

(a) Experimental

traces.

The numbers indicate the potential during the test pulse. Each trace isthe result of the current obtained in 325 Na 50 Ca//380 K 10 Na 20 TEA minus the current obtained in the same solutions with TTX added. P/4 procedure. Series resistance compensation 4 llcm 2. 2°C. (b) Sodium currents predicted by the model presented in the Discussion. Each trace has been calculated for the corresponding membrane potential indicated in part (a) and with the parameters listed in Table IV. this, Vm was r e t u r n e d to - 6 0 mV after a long pulse and tail c u r r e n t was m e a s u r e d just after the step b a c k a n d plotted as a function o f V m d u r i n g the p r e c e d i n g pulse. For c o m p a r i s o n a n d normalization purposes, tail c u r r e n t was also m e a s u r e d when the step was i n t e r r u p t e d at the peak o f the INa transient, and these currents are plotted in Fig. 7, normalized relative to the largest tail current. This curve shows the usual behavior of peak GNa as a function o f Vm: it rises along a sigmoid curve, and saturates at a b o u t +20 mV. C u r r e n t s after long pulses were normalized in the same way and are given by the curve with filled circles in the figure. This curve rises relatively slowly to about + 10 mV a n d then m o r e steeply. At +90 mV, steady s t a t e G N a is 43% o f its m a x i m u m value. We conclude that inactivation can be incomplete in the absence o f internal Na a n d o u t w a r d INa, a n d that C h a n d l e r a n d Meves were correct in

B E Z A N I L L A AND A R M S T R O N G

559

Sodium Current Inactivation

a s c r i b i n g i n c o m p l e t e i n a c t i v a t i o n to a v o l t a g e - d e p e n d e n t r a t h e r t h a n a c u r r e n t dependent process. S t e a d y - s t a t e i n a c t i v a t i o n was also s t u d i e d b y a t w o - p u l s e m e t h o d (Fig. 8,

1.0

o

~

so ms

~ 0.8 Z --~

0.4

J

0.2

d~J

-40

0

I

I

40

80

V m,mV FIGURE 7. Inactivation as a function of Vm as measured with tails. T h e pulse p r o c e d u r e is shown in the inset. I1 was d e t e r m i n e d at the peak o f IRa and 12 at the end o f a 50 ms pulse. TTX-insensitive currents were subtracted off before 11 and 12 were d e t e r m i n e d . Both I1 and 12 have been normalized relative to the maximum tail c u r r e n t obtained at peak INa. Axon in 60 Na 50 Ca//200 T M A . Holding potential, - 7 0 mV. P/4 procedure. 8°C.

1.o "O 0.8 ._N

E o.s

6

z ,._.-

0.4 0.2 I -120

I

I

I

-40

0

40

I

Vm, mV FIGURE 8. Inactivation as a function o f Vm as d e t e r m i n e d with a double-pulse method. T h e pulse p r o c e d u r e is indicated in the inset. I is plotted as a function o f V m d u r i n g the first pulse (see inset), and it has been normalized relative to Isa for which there was no first pulse (filled circle). TTX-insensitive currents were subtracted off before 1 was measured. Holding potential, - 7 0 mV. T h e first pulse was 40 ms long and at the end Vm was r e t u r n e d to - 7 0 mV for 0.7 ms. T h e second pulse took Vm to 30 mV. Axon in 60 Na 50 Ca//200 T M A . P/4 procedure. 8°C.

inset), w h i c h g a v e a n initially s u r p r i s i n g r e s u l t . T h e s e c o n d p u l s e was o f f i x e d a m p l i t u d e , w h i l e t h e first was v a r i a b l e . T h e p l o t in Fig. 8 gives t h e p e a k a m p l i t u d e o f INa d u r i n g t h e s e c o n d p u l s e as a f u n c t i o n o f Vm d u r i n g t h e first. T h e p o i n t s h a v e b e e n n o r m a l i z e d r e l a t i v e to I s a f o r w h i c h t h e r e was n o first

560

T H E J O U R N A L OF G E N E R A L P H Y S I O L O G Y • V O L U M E 7 0 • 1 9 7 7

pulse, the filled circle. Between - 7 0 a n d 0 m V the points follow the usual sigmoid curve, with a m i d p o i n t at a b o u t - 3 0 inV. B e y o n d 0 m V the curve is almost flat, with a slight u p w a r d t u r n n e a r +60 m V . M e a s u r e d in this way, steady-state inactivation is a b o u t 80% and is almost i n d e p e n d e n t o f Vm above 0 mV, quite unlike the results f r o m Figs. 6 a n d 7. T h e difference in the two m e t h o d s can be reconciled by the C h a n d l e r a n d Meves (6) model for a second a~ztivated state, as discussed below. 1.0

/--

7. -130

~

-70

.__N 0.8

E

~- 0.6 O Z ._~ 0.4 _,¢ {o

0.2 I

I

I

I

2

4

6

8

Recovery Interval,

1

ms

FIGURE 9. Time course of recover}' from inactivation. These curves represent peak lNa (plotted as the fraction of peak INn without prepulse) as a function of the recover}' interval between the prepulse and the test pulse (see inset). Prepulse and test pulses took Vm to 10 mV. Solid symbols: recover}' at -70 mV. Open symbols: recover}' at -130 mV. Prepulse duration: 10 ms. P/4 procedure. The axon was in 20% NaSW//125 TMA. 8°C.

Recovery from Inactivation Inactivation gates o p e n w h e n m e m b r a n e potential is r e s t o r e d to a negative value a f t e r a depolarization. This process has been called recovery f r o m inactivation and its time course can be studied with two d e p o l a r i z i n g pulses s e p a r a t e d by a variable interval, as d r a w n in the inset o f Fig. 9. T h e first pulse must be long e n o u g h to d e v e l o p inactivation, a n d the second pulse is given to test the a m o u n t o f Na c o n d u c t a n c e available after the recovery interval which is a variable. Fig. 9 shows that inactivation recovery has an a p p r o x i m a t e l y e x p o n e n t i a l time course that is voltage d e p e n d e n t . At - 7 0 m V the time constant o f recovery is 2.7 ms and it decreases to 0.6 ms at Vm = - 1 3 0 m V . Voltage d e p e n d e n c e o f the recovery rate is not a new finding but we know o f no r e p o r t e d observations at very negative voltages. DISCUSSION

T h e m a j o r findings o f this p a p e r are that inactivation begins with a lag a f t e r depolarization, a n d that the time course o f inactivation is the s a m e w h e t h e r m e a s u r e d with a one-pulse or a two-pulse m e t h o d . T h e lag, which has been detected b e f o r e (1, 10), has now b e e n d e m o n s t r a t e d by two methods: by the conditioning pulse e x p e r i m e n t (Fig. 3); a n d by destroying inactivation with p r o n a s e (Fig. 2). With the two-pulse m e t h o d , the lag is evident only for

Sodium Current

BEZANILLA AND ARMSTRONG

Inactivation

561

conditioning pulses o f very short duration. It is t h e r e f o r e not surprising that a lag was not observed by H o d g k i n and H u x l e y (13) in their original description o f inactivation, for the shortest prepulse they used was 2 ms. R a t h e r surprisingly, the time course o f inactivation is not well known in spite o f considerable theoretical work r e g a r d i n g the mechanism o f the p h e n o m e n o n . T h e p r o b l e m , o f course, is that the kinetics o f l s a are d e t e r m i n e d by two gating factors, and the behavior o f neither is known in detail. In o u r view, the pronase e x p e r i m e n t o f Fig. 2 provides the most straightforward measure o f the time course o f inactivation, despite the uncertainty i n t r o d u c e d by the necessity to scale the post-pronase r e c o r d to make u p for destruction o f some Na channels. In addition to c o n f i r m i n g the existence o f a lag, the pronase e x p e r i m e n t shows (if the scaling is correct) that a large fraction o f the Na channels can be simultaneously active after a large depolarization. In the H o d g k i n and H u x l e y equations, there is considerable overlap between activation and inactivation a n d , in consequence, the n u m b e r o f c o n d u c t i n g channels after depolarization is a r a t h e r small fraction o f the total. For H o d g k i n and Huxley's axon 17, for e x a m p l e , only 43% o f the channels are o p e n at the peak o f the transient even for a very large pulse with h0 = 1 (14). T h e e x p e r i m e n t o f Fig. 2 suggests that Na channels are used m u c h m o r e efficiently than the H o d g k i n and H u x l e y equations predict, and that 70% or 80% o f them can be o p e n at the peak o f the Isa transient. In o u r hands, the time course o f inactivation is the same w h e t h e r m e a s u r e d with a o n e pulse or a two pulse m e t h o d , and this is in a g r e e m e n t with previous results f r o m squid (14) and myelinated frog fibers (Chiu, personal communication). In these preparations t h e r e is no distinction between rh and Tc, unlike the situation in Myxicola (11) and lobster (18). T h e lag in the onset o f inactivation and the accentuation o f this lag by hyperpolarization (Fig. 4) suggest that the activation gates o f an Na channel must o p e n b e f o r e the inactivation gate can close. Gating c u r r e n t e x p e r i m e n t s r e p o r t e d in the next p a p e r strongly s u p p o r t this idea, and provide the main impetus for the following model, which describes the possible states o f a sodium channel, ~24 X 5

.

a 3 ~ X 4

b4

.

a 2 •

ba

X 3

.

a I •

b2

X 2 .

K • X 1 .

bl

E ., ~. X I Z .

J~

•

hR.

,~

T h e model is e x p a n d e d in the next p a p e r to account for gating c u r r e n t p h e n o m e n a . T h e r e are f o u r closed states, xs-x2; two o p e n states xl, h2; and one inactivated state x~z. T h e conductance o f the closed and inactivated states is zero. Both open states are postulated to have the same c o n d u c t a n c e , roughly 10-11 S per channel (9, 17, 18). F o u r sets o f calculations have been p e r f o r m e d to match the model to e x p e r i m e n t a l findings. T h e computations must be r e g a r d e d as preliminary, for inactivation is linked to activation in the model and c a n n o t be described accurately without m o r e knowledge r e g a r d i n g activation than is presently at hand. Specifically, in the terms o f this model, it is necessary to specify the rate constants al---a4 and bl-b4, and this was d o n e as follows:

562

THE JOURNAL OF GENERAL PHYSIOLOGY " VOLUME 70 " 1977 a X 4

.

a • X 3 .

b

a ~ X 2 .

b

K ~ X 1 .

• XlZ

b

.

k

•

h2

7r

T h a t is, it was assumed that all o f the f o r w a r d rate constants for the activation process are equal, and similarly for the backward rate constants. State x5 is populated only at very negative voltages and was omitted. No attempt was made to simulate gating c u r r e n t . T h e main purposes o f the calculations are to show, by the simplest model possible, that activation and inactivation may be coupled and that the inactivation step need not be significantly voltage d e p e n d ent. Both points are s u p p o r t e d by evidence f r o m gating c u r r e n t studies that are r e p o r t e d in the next paper. TABLE PARAMETERS Curve

a ms - l

OF

THE

I I I CURVES

b ms -1

IN

FIG.

2b, c

K

h

]

ms i

ms-t

mA/¢m =

y*

8

0

0.65

0.12

-0.42

y (K = 0)*

8

0

0

0

--0.42

Curve

am

/3=

ah

~

)

ms- i

ms- t

ms-1

ms- t

m A /cm 2

mah

5

0

0.108

0.692

-0.53

m3

5

0

1

0

-0.53

* F o r t h e s e c a l c u l a t i o n s , ~ = ¢r = O.

M e m b r a n e c u r r e n t was calculated f r o m the equation Im = XlJ,

where ? = Gsa (V--VNa). i is the c u r r e n t that would flow for a given driving force (V--VNa) if all channels were open simultaneously; and ~;N~ (14) is the c o n d u c t a n c e o f an o p e n channel times the total n u m b e r o f channels. T h e first calculation is a fitting o f the model to the e x p e r i m e n t o f Fig. 2, and the rate constants and o t h e r p a r a m e t e r s d e t e r m i n e d are given in Table I I I . T r a c e A was fitted first (less the gating current), yielding the theoretical curve labeled xl. Rate constant K was then set to zero to stimulate removal o f inactivation by pronase, a n d curve xl (K = 0) was calculated. Finally, the two c o m p u t e d curves were subtracted f r o m each o t h e r to give the lower curve, x i - x t (K - 0). Overall, the fits are reasonably good. T h e r e is a p r o m i n e n t lag in the onset o f inactivation (that is, x ~ - x t (K = 0) is sigmoid), and the peak value o f curve Xl is 73% o f the final level o f c u r r e n t in the curve x~ (K = 0); i.e. a rather large fraction o f the channels are open at the peak o f curve xi. A somewhat better fit can be obtained with the m o r e complex model o f the next p a p e r which predicts a longer lag in activation a n d a larger o p e n fraction of channels at the peak o f the n o r m a l c u r r e n t transient. T h e H o d g k i n and Huxley equations give a relatively poor fit to this experiment as shown in Fig. 2c (parameters are given in Table III). T h e mah curve

BEZAr~ILL~t ANY ARMSTSONG

Sodium

Current

563

Inactivation

c o n f o r m s closely to trace A, b u t fixing h at 1.0 to simulate r e m o v a l o f inactivation by p r o n a s e yields a c u r v e (m 3) that is far l a r g e r in a m p l i t u d e t h a n trace B. T h e c u r v e m 3 h - m 3 is also a p o o r fit to trace A - B , a n d has an initial lag that is m u c h smaller than that e x p e r i m e n t a l l y observed. T h e second calculation fits the m o d e l to the INa transients in Fig. 6 a . T h e results o f the fit are given in Fig. 6b, a n d the p a r a m e t e r s are in T a b l e IV. ] was set by a s s u m i n g a linear instantaneous c u r r e n t voltage c u r v e below the s o d i u m equilibrium potential a n d a c u r v e with lesser slope (by a factor o f 0.72) above Vr~a. T h e time constant o f the step x l z ~ h2 was taken f r o m C h a n d l e r a n d Meves (7) a n d scaled to 8°C by using a Q10 o f 3. A point o f particular interest is that g o o d fits are o b t a i n e d even t h o u g h the rate constant o f inactivation (K) shows no systematic variation with voltage. T h e overall rate o f inactivation is strongly affected by voltage, as is rh (14); but it is quite possible that most or all o f this voltage d e p e n d e n c e arises f r o m c o u p l i n g to the activation process (x4 TABLE

I V

PARAMETERS OF T H E T H E O R E T I C A L CURVES IN FIG. 6b V~

a

b

x

X

•

~r

ra V

m s -1

rns -1

rt~ -1

ms -I

ms -!

m s -1

mA/ cm ~

-40 -30 -20 + 80

0.5 1.0 1.67 9.0

0.88 0.4 0.4 0

0.8 1.1 0.8 0.83

0 0 0 0

0 0 0.075 0.35

0 0 1.9 1.4

-4.15 -3.74 -3.32 0.60

xl), as Fig. 6b shows. Gating c u r r e n t m e a s u r e m e n t s in the next p a p e r also suggest that the f o r w a r d rate constant o f inactivation is not significantly voltage dependent. T h e third calculation shows that the m o d e l predicts a reasonable facsimile o f the h= curve (14). T h e values o f a a n d b were selected to r e p r o d u c e the m~ that is implied by Fig. 8 o f H o d g k i n a n d H u x l e y (14). This curve (labeled m~, x 0 is plotted in Fig. 10, t o g e t h e r with the h® curve f r o m Fig. 9 o f H o d g k i n a n d H u x l e y (14) on the a s s u m p t i o n that the resting potential in their e x p e r i m e n t s was - 6 0 inV. T h e calculation was p e r f o r m e d by setting x4+xs+x2+xl+xlz

= 1, x s = h2 = O,

a n d d e t e r m i n i n g the distribution a m o n g the various states for the selected values o f a a n d b. Curves o f 1-xtz are plotted for t h r e e values o f K/k. T h e curve for K/h = 1,000 is the best fit to the h= curve a l t h o u g h it is s o m e w h a t too steep, particularly in the r a n g e - 6 0 to - 7 0 m V , a n d it saturates n e a r - 7 0 r a t h e r t h a n - 1 0 0 m V . N e i t h e r o f these defects seems very serious since the calculated c u r v e d e p e n d s on the ratio o f a to b, a n d this ratio, like m~ f r o m which it is derived, c a n n o t be accurately d e t e r m i n e d in the voltage r a n g e negative to - 5 0 or - 6 0 m V . T h e c u r v e also d e p e n d s on the activation rate constants, which m a y not have the values that have b e e n a s s u m e d . T h e f o u r t h c o m p u t a t i o n , which is not illustrated, shows that rc a n d ~'h are the same for this model, as would be e x p e c t e d , since by either o f the e x p e r i m e n t a l p r o c e d u r e s inactivation rate is p r o p o r t i o n a l to the n u m b e r o f channels in state X I •

564

THE JOURNAL

OF GENERAL

PHYSIOLOGY

• VOLUME

70 " 1977

T w o o t h e r attributes o f the m o d e l can be a p p r e c i a t e d without the n e e d for calculation, a n d these are the effects o f states Xs a n d h2. State Xs is included to account for the increased lag in b o t h activation a n d inactivation caused by h y p e r p o l a r i z a t i o n . I f most o f the channels are in state x4 at - 7 0 m V a n d in state x5 at - 150 m V , the lag will be longer for a step b e g i n n i n g f r o m , t h e m o r e negative voltage. ( I t is likely that state Xs should in fact be several states to p r o v i d e the necessary lag.) State h, is the second activated state postulated by C h a n d l e r a n d Meves (6) a n d is included h e r e to explain the high steady-state value o f G~a (sodium conductance) for large voltages. State h2 is f a v o r e d at large positive Vm. It was shown above that steady-state inactivation at large Vm seems i n c o m p l e t e w h e n

0 00 / /

/

5000~.

xI

0.4

o.z

o qO0 -80 I

I

!

|

,

I

-60 -40 -20 Vm.mV

!

0

FIGURE 10. Inactivation as predicted by the coupled model. Curve labeled h~ is from Fig. 9 of Hodgkin and Huxley (1952 b). Steady-state inactivation curves were calculated with the model presented in the discussion and represent 1 - XxZ for K/ = 500, 1,000, and 5,000. m~, xl is the mg curve of Hodgkin and Huxley (1952b). This curve was fitted with the model to give the ratio a/b, which was used in calculating 1 - xxz. m e a s u r e d f r o m the INa tail a f t e r a large pulse (Fig. 7), but is m u c h m o r e c o m p l e t e w h e n d e t e r m i n e d by a two-pulse m e t h o d (Fig. 8). T h i s can be e x p l a i n e d as follows. At the e n d o f a very large pulse, a b o u t o n e - t h i r d o f the channels are in state h2, a n d they contribute to steady-state INa a n d the INa tail at pulse e n d . A f t e r a fraction o f 1 ms at - 6 0 or - 7 0 m V , all o f these channels have r e v e r t e d f r o m state h2 to the inactivated state xxz, a n d they can c o n d u c t again w h e n V m is pulsed to 30 m V (as in Fig. 8) only after recovery f r o m inactivation..So after ~0.5 ms at - 7 0 m V , most o f the channels are in state xxz regardless o f w h e t h e r the first pulse was large or very large. Steady-state inactivation thus seems i n d e p e n d e n t o f pulse size (for large pulses) w h e n d e t e r m i n e d with a two-pulse m e t h o d . T h e c o m m o n impression that inactivation can occur without p r e c e d i n g activation seems to speak against the m o d e l p r o p o s e d here. This i m p r e s s i o n

BEZANILLA AND ARMSTRONG Sodium Current Inactivation

565

must be based more on a literal interpretation of the Hodgkin and Huxley e q u a t i o n s t h a n o n o b s e r v a t i o n , f o r we a r e a w a r e o f n o e v i d e n c e to s u p p o r t it. I n Fig. 3 i n a c t i v a t i o n is p r e c e d e d b y easily m e a s u r a b l e a c t i v a t i o n d u r i n g t h e c o n d i t i o n i n g p u l s e . A t m o r e n e g a t i v e v o l t a g e s it is c l e a r t h a t s i g n i f i c a n t a c t i v a t i o n m u s t also o c c u r , as is e v i d e n t f r o m t h e p h e n o m e n o n o f a n o d a l b r e a k e x c i t a t i o n : a f i b e r t h a t is h y p e r p o l a r i z e d by a l o n g p u l s e o f c u r r e n t m a y g e n e r a t e a n a c t i o n p o t e n t i a l w h e n t h e c u r r e n t is t u r n e d off. I n s u c h a case e n o u g h N a c h a n n e l s o p e n to i n i t i a t e t h e a c t i o n p o t e n t i a l e v e n w h e n Vm is n e g a t i v e to t h e n o r m a l threshold. The model given here predicts a small sodium current during recovery from i n a c t i v a t i o n , as c h a n n e l s r e f l u x t h r o u g h state xtz b e f o r e c l o s i n g . T h i s c u r r e n t has n o t b e e n o b s e r v e d , a n d is n o t p r e d i c t e d b y t h e m o r e c o m p l e x m o d e l o f t h e next paper. This work was s u p p o r t e d by United States Public Health Service grant no. NS 08951.

Received for publication 24 January 1977. REFERENCES 1. ARMSTRONG, C. M.

2.

3. 4.

5. 6.

7.

8. 9. 10.

11.

12.

1970. Comparison o f gk inactivation caused by quaternary a m m o n i u m ion with gNa inactivation. Biophys. J. 10(2, Pt. 2):185a. (Abstr.). ARMSTRONG, C. M., and F. BEZANILL^. 1974. Charge movement associated with the o p e n i n g and closing o f the activation gates of the Na channels. J. Gen. Physiol. 63:533-552. ARMSTRONG, C. M., and F. BEZANILLA 1975. Currents associated with the ionic gating structures in nerve m e m b r a n e . Ann. N. Y. Acad. Sci. 264:265-277. ARMSTRONG, C. M., F. BEZANILLA, and E. RojAs. 1973. Destruction o f sodium conductance inactivation in squid axons perfused with pronase. J. Gen. Physiol. 62:375-391. BEZ^mLLA, F., and C. M. ARMSTRONG. 1977. A low cost signal averager and data acquisition device. Am. J. Physiol.: Cell Physiol. 1(3):C211-C215. CHANDLER, W. K., and H. MEVES. 1970. Evidence for two types o f sodium conductance in axons perfused with sodium fluoride solution. J. Physiol. (Lond.). 211:653-678. CHANDLER, W. K., and H. MErEs. 1970. Rate constants associated with changes in sodium conductance in axons perfused with sodium fluoride. J. Physiol. (Lond.). 211:679-705. Cnlu, S. Y. 1976. Observations on sodium channel inactivation in frog nerve. Biophys. J. 16(2, Pt. 2):25a. (Abstr.). CONTI, F., L. J. DEFELmE, and E. WANKE. 1975. Potassium and sodium c u r r e n t noise in the m e m b r a n e of the squid giant a x o n . J . Physiol. (Lond.). 248:45-82. GOLDMAN, L., and C. L. SCH^UF. 1972. Inactivation o f the sodium c u r r e n t in Myxiola giant axons. Evidence o f coupling to the activation process.J. Gen. Physiol. 59:659-675. GOLDMAN, L., and C. L. SCHAUV. 1973. Quantitative description o f sodium and potassium currents and c o m p u t e d action potentials in Myxicola giant axons. J. Gen. Physiol. 61:361-384. GUEST, P. B. 1961. Numerical methods o f curve fitting. Cambridge University Press, Cambridge.

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THE JOURNAL OF GENERAL PHYSIOLOGY • VOLUME 70 " 1977

13. HODGKIN, A. L., and A. F. HUXLEY. 1952. T h e dual effect of m e m b r a n e potential

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