J. Physiol. (1978), 278, pp. 533-557 With 16 text-figures Printed in Great Britain

533

REACTIVATION OF MEMBRANE CHARGE MOVEMENT AND DELAYED POTASSIUM CONDUCTANCE IN SKELETAL MUSCLE FIBRES

BY R. H. ADRIAN AND R. F. RAKOWSKI* From the Physiological Laboratory, Cambridge CB2 3EG

(Received 30 June 1977) SUMMARY

1. Intramembrane charge movement has been measured in striated muscle subjected to prolonged depolarization but repolarized to - 100 mV for up to 100 sec. The method of measurement allows identification of charge or charges which are 'reprimed' by repolarization. 2. Charge 'reprimed' by repolarization appears to differ in its voltage distribution from charge detected in a permanently polarized fibre. The difference is probably due to the different pulse sequences used in the two measurements and to the fact that there appear to be several species of intramembrane charges with different transition potentials and different steepness of voltage distribution (V and k in eqn. (14): see

below). 3. Potassium conductance is reprimed by repolarization following inactivation by depolarization. When the repriming potential is - 100 mV the process appears to be in two stages; repriming to a value rather less than half the final value takes place exponentially with a time constant of 40 see; subsequently repriming to the final value is very slow. At a repriming potential of - 140 mV repriming to the final value (1-2 mmho//,tF) takes place exponentially with a time constant of 17 sec. INTRODUCTION

Schneider & Chandler (1973) measured the voltage distribution of membrane charge in frog striated muscle with a normal resting potential. Similar results were obtained by Chandler, Rakowski & Schneider (1976a) and Adrian & Almers (1976b). Chandler, Rakowski & Schneider (1976b) commented on the similarity of the charge versus potential (Q vs. V) relation to the steady-state voltage relation of the conductance variable n (Hodgkin & Huxley, 1952; Adrian, Chandler & Hodgkin, 1970a). They raised the possibility that the charge movement seen in normally polarized muscle fibres (Charge 1) could represent the movement of gating particles for delayed potassium current. The kinetics of this charge movement appeared to differ slightly from the kinetics of n but neither was sufficiently well determined to exclude a connexion between Charge 1 and potassium current gating. The experiments reported in this paper were designed to test the hypothesis that opening * Present address: Department of Physiology and Biophysics, Washington University School of Medicine, St Louis, Missouri 63110, U.S.A.

R. H. ADRIAN AND R. F. RAKOWSKI of the delayed potassium channel is preceded by movement of a substantial fraction of the membrane charge referred to as Charge 1. We cannot exclude the possibility that some part of Charge 1 is related to the opening of potassium channels: but that part of Charge 1 which reappears (reprimes) and is detected in the present experiments when a depolarized fibre is repolarized to -100 mV for about 100 sec does not have the same voltage distribution as n"". This reprimed charge resembles the charge postulated by Adrian, Chandler & Rakowski (1976) to account for their experiments on repriming contraction in mechanically refractory fibres (Hodgkin & Horowicz, 1960). 534

METHODS

Conventional micro-electrode methods and integrated circuit electronics were used to deliver a constant current to a muscle fibre or to control the potential measured by a micro-electrode in a muscle. The voltage recording electrodes were filled with 3 M-potassium chloride and the current delivery electrodes with 2 M-potassium citrate. Both had resistances of 5-10 MC. Experiments were done on fibres from the sartorius muscle of the frog (Rana temporaria). Three electrodes are inserted into the pelvic end of a muscle fibre with the spacings shown in Fig. 1 A (1 250 jam). Two electrodes record the potentials V1 and V2; a current Io is injected into the fibre by the third electrode. The potential V, is controlled by electronic feed-back and the membrane current can be measured as the potential difference V2- V1 which we call AV (Adrian et al. 1970a). The membrane current is

V(t) Q0-2A312ri(1)

)

where ri is the internal longitudinal resistance of the fibre (a/cm) and 1 is the electrode distance. The steady-state membrane conductance of unit fibre length is then given by

____0)

2AV(oo) 312rV((oo)

g= V1(o)

(2)

The membrane capacity can be measured by 1

00

Ceff = V

[im(t)-gmV1(t)]dt

(3)

10 [A V(t) -A (0) Vl(t)]dt. (4) Eqns. (3) and (4) assume that the membrane conductance g. is constant. The approximate expressions for g. and cf, can be made exact by appropriate correction factors (see below). Provided I/A < 1 both factors are close to 1 0. The estimate of capacity by eqn. (4) is independent of any assumption about the membrane equivalent circuit (Adrian & Almers, 1974). Voltages proportional to 10, V1 and A V were the inputs to three instrumentation amplifiers whose outputs (± 5 V) were sampled by a multiplexer and A/D converter (CED, Cambridge) operating as an interface to a PDP 1I/IOE computer (DEC, Maynard). The amplifier filtered the signals with a 3-pole Butterworth filter (Barr & Stroud, Ltd) at a cut-off frequency of 1 kHz. The multiplexer sampled each of the three voltages at 200 #ssec intervals The sampling period was 256 msec which resulted in arrays (A) for 10, V1 and AV each of 1280 numbers. These arrays were reduced to three arrays (B) each of 256 numbers by the algorithm (Kendall, 1973). B(n) = -35{-3A(5n-4)+12A(5n-3)+17A(5n-2)+12A(5n-1)-3A(5n)}, (5) where B(n) is the nth element in the array B and A(5n) is the 5nth element in the array A. This procedure finds the value at t = n - 0-6 msec of the third order polynomial which is the best fit to each set of five points centred on the (5n- 2)th point of the A array. Step changes in the potential at x = 1 (El) could be imposed by voltage feed-back and began at the beginning of the 11th millisecond of the sampling period and ended at the end of the 139th millisecond. The command pulse for all potential steps was blunted exponentially with a time

=32rgV1(oo)

REACTIVATION OF 9x AND CHARGE MOVEMENT

535

constant of 0-7 msec. This blunting has the advantage of reducing the voltage transient at x = 21 + 1' (the position of the current electrode) which may be larger if a strictly square step of potential is required at x = 1. Blunting the command pulse appears to increase the survival time of fibres. To some extent the choice of blunting time constant (and the rather heavy filtering which it allows) is arbitrary, but if repeated voltage steps are required it is necessary to sacrifice time resolution to get adequate survival. Capacity measurements and measurements of total charge moved are unaffected by blunting the command pulse. The kinetics of membrane charge movement will be affected if the time constants for charge movement are similar to the blunting time constant. But the kinetics of charge movement are likely to be affected by the

10

V2

V1

A

B 5-7

-

[

AI

./ 128 msec Fig. 1. A, arrangement of micro-electrodes for voltage clamp experiments. The electrode separation was normally about 250 jtm for 1 and 100 #um for 1'. B, record of the non-linear current (i,,(t)) for a fibre in solutionA (80 mM-rubidium). The current record is obtained by subtracting the currents during two identical steps of potential from -80 to - 10 mV one of which was preceded by 200 msec at - 100 mV (control step) and the other by 108 see at - 100 mV (test step). It therefore represents the currents which were reprimed during the 108 see at - 100 mV. The potential was held at -20 mV apart from repriming and experimental potential steps. The potassium conductance after 128 msec at - 10 mV is 24 1sA/1F - 70 mV = 0-34 mmho/#F. Fibre 1602: 1 = 250jam, r, = 6-8 Me/cm, Rm = 5-7 kO cm2, Cm = 94 fuF/cm2, diam. 80 jam, temp. = 10-2 'C.

delay in charging the tubular membranes and since this delay is probably about a millisecond, blunting of the command pulse should not add much further distortion to the already considerably distorted time course of any rapid charge movement. The membrane current during the potential step (to V,(oo) which is here the average of V,(t)

536

R. H. ADRIAN AND R. F. RAKOWSKI

during the final 10 msec of the step) is proportional to the array A V(t). To convert A V(t) to im(t) we require the internal longitudinal resistance r,. This was obtained from the measured quantities (V,(oo), AfV(oo) and I(oco)) by the following equations which can be derived from eqn. (2) and linear cable theory. A

=171

r i

|12AVI(o)'

VI(oo) exp (21+1'/A) 10(oo)A cosh (I/A)

r= rA2.

(6)

(7) (8)

The membrane capacity for unit length of fibre was obtained by 2h 00 ~ A V(oo) 1(9 V1 1,J(t) dt, JL V(t) 3lrfVf ( A) 31 (10) h A(3-tanh2(l/A)) sinh (1/A)' Almers h is the correction factor referred to above and is derived as eqn. (A 17) in Adrian & (1976a). The integrations were performed by Simpson's rule for the 'on' of the voltage step from the 11th to the 138th msec and for the 'off' of the step from the 139th to the 256th msec. The computer displayed the arrays of V1(t), AV(t) and 10(t) on an oscilloscope for each control and test voltage step. In addition, for each step, values of A, rl and rm were printed. The computer also calculated and printed the fibre diameter and specific membrane resistance (Rm; 0 cm2) and specific membrane capacity (Cm; /.tF/cm2 both for the 'on' transient and for the 'off' transient). For the diameter, Rm and Cm it was necessary to assume a value for the specific resistance of the sarcoplasm (Ri). To calculate the specific membrane resistance and capacities in Table 1 we assumed an R, of 391 Q cm in hypertonic solutions at 2 0C (Hodgkin & Nakajima, 1972) and a Q15 of 1-37. As measurements on a fibre proceed the computer listing of the cable constants and diameter provide a very good guide to the condition of the fibre, and in a 'good' experiment remain remarkably stable. The membrane current during the potential step Qm(t) is given by eqn. (1). We were interested in non-linear currents or in currents which could be made to reappear by hyperpolarizing a depolarized fibre. We therefore compared currents during a control step of potential and during a test step by subtracting control currents from test currents point by point after appropriate scaling for differences in the control and test voltage step size. If we designate the non-linear current or the extra current seen after repolarization by i" (t) then im,(t)

=

im(t)teat -

I

im(t)control

(11)

Fig. 1 B shows a typical record of i'(t) in solution A (Table 1). The initial exponentially decaying current is charge movement, the slowly rising current and the tail current are respectively outward potassium and inward rubidium current through the delayed rectifier channel. The tail current includes a small reverse charge movement. The potassium conductance at the end of the potential step is taken as the change in current divided by the change in potential. If the current through the delayed rectifier is non-linear, the conductance calculated in this way is the chord conductance between two voltages on either side of the zero current potential. In records with potassium current, as in Fig. 1 B, it proved difficult to separate charge movement from ionic current, but when the potassium current was suppressed by tetraethylammonium ion the transient part of i,,(t) appeared to be entirely charge movement. In order to determine the extra charge movement in the test pulse, i,,(t) during the voltage step was fitted by a leastsquares procedure (Chandler et al. 1976a) either by (12) y = c,+c3exp (-t/7-) or by (13) y = C1+ C2t+C3exp (t/) and mutatia mutandi8 for the 'off' of the voltage step. Depending on which function had been fitted either cl or (c, +ct) was subtracted from i (t) and the remaining current was integrated

REACTIVATION OF gE AND CHARGE MOVEMENT

537

between 11 and 138 msec for the 'on' charge movement and between 139 and 256 insec for the 'off' charge movement. The procedure is described in detail in Chandler et al. (1976a, p. 253). The results of the integrations, which represent charge in nC, were normalized to the average of the capacity measured at the 'on' and the 'off' of the control pulse (eqn. (9)). Since the factor 2/3 lr1 is required to determine both fiM(t)dt and cd their ratio, which is the charge movement in nC/sF (= mV), is independent of the value obtained for rj. The conductance at the end of the pulse was also normalized to the measured membrane capacity and so it likewise is independent of the value obtained for r,. The compositions of the experimental solutions are given in Table 1. The solutions are hypertonic to prevent movement; they contain rubidium to linearize the current in the inward rectifier and sulphate to reduce the resting current. Tetrodotoxin (10-7 M) suppresses sodium current; tetraethylammonium (110 mM) suppresses delayed rectifier current.

TABi. 1. Solution composition and fibre constants Composition (mm) Solution

Rb2SO, Na2SO4

A 40 55

(TEA)2SO4

CaSO4

B 40 55 8 1.5 350 -

8 1.5 PO buffer pH 7-2 Sucrose 350 Tetracaine All solutions contained 10-7 m-tetrodotoxin Fibre constants at 10 'C (RI = 304 QL cm) 1-24± 004 1-32±0-09 A(umm) 2320 + 190 Rm(fL cm') 2400± 280 17-3 + 2-7 11 5 ± 0'8 Cm(/IF/cm2) 3 No. of fibres 21

C 2*5 98-5 8 1.5

350 2

1-86±0-24 4490± 920

4'1± 0-6 5

RESULTS

Schneider & Chandler (1973) have described the voltage dependence of charge movement in normally polarized fibres by the equation Qmax. Q 4 1 +exp [-(V-V)/k] (14) Without implying any particular mechanism underlying the charge movement the constants V and k obtained by fitting an equation of this form are useful for comparing the charge distribution obtained by various methods. Table 2 summarizes the results already published for charge measurements obtained by several methods. In normally polarized fibres Chandler et al. (1976 a) and Adrian & Almers (1976b) describe a moving charge or charges which they have called Charge 1. The constants obtained by fitting eqn. (14) were similar in the two sets of measurements though the former group did not give great weight to apparent charge movements when the internal potential was positive. A second kind of moving charge, Charge 2, has been described by Adrian et al. (1976) and by Adrian & Almers (1976b) (see also Schneider & Chandler, 1976). Table 2 shows the constants for eqn. (14) which describes the movement of Charge 1, and also of Charge 2. Though Qmax. for Charges 1 and 2 are about the same, the transition potential (V) of Charge 2 is close to the resting

R. H. ADRIAN AND R. F. RAKOWSKI 538 potential and k for Charge 2 is much larger than for Charge 1. The conductance variable n, (Hodgkin & Huxley, 1952; Adrian et al. 1970a) can be approximately fitted by eqn. (14). Table 2 shows, what was already commented on by Chandler et al. (1976b), the steady-state voltage distribution of Charge 1 and ne, are very much alike. Table 2 also shows the constants for the small quantity of charge that can be reprimed without causing a contraction. These measurements were made by Adrian et al. (1976) in isotonic solutions and the apparent differences between Charge 1 and the subthreshold reprimed charge were tentatively attributed to the fact that Charge 1 was measured in hypertonic solutions. TABLE 2. Steady-state distribution constants in eqn. (14). which describe various measured charge movements k V QmAX.

Charge 1 Chandler, Rakowski & Schneider (1976 a) Adrian & Almers (1976 b)

no Charge 2 Subthreshold reprimed charge

(nC/1sF)

(mV)

(mV)

25 32 35

-44 -48 45 -95 -10

7*8 12.6 9 56 22

3'3

Pul8e structures The measurements of Charge 1 were made with control and voltage steps shown in Fig. 2A and B. The reprimed charge measurements used a pulse structure where the control and test potential steps were over the identical range, but because the holding potential was at -20 mV the test pulse was preceded by a period of up to 100 see at or near -90 mV in order to remobilize (reprime) the charge movement. The sequence of pulses was like that in Fig. 2D. We wished to determine in the same fibre whether Charge 1, operationally defined as the charge detected by the pulse sequences in Fig. 2B, has the same characteristics as the charge which disappears on depolarization and reappears (reprimes) on hyperpolarization. A sartorius muscle was put into solution B which minimizes linear and non-linear ionic currents, depolarizes the fibre and provides a tubular length constant, for both hyperpolarization and depolarization, longer than the fibre radius (Schneider & Chandler, 1976). Two separate sequences of control and test voltage steps were imposed. These are shown in Fig. 2 C and D. The first sequence consisted of four small control steps (Cl) and a large test step (TI). CI was + 20 mV from -100 mV, TI was + 80 mV from -80 mV: the periods at -100 mV or -80 mV before and after the steps were about 200 msec and were not long enough to allow significant repriming of charge movement. In the second set of pulses both control (C2) and test (T2) were from the same potential (-80 mV) and were the same size. The test pulse T2 was preceded by a period of 100 see at - 100 mV. The measurements consisted of imposing the first sequence of voltage steps (Cl and T1) followed immediately by the second sequence with both C2 and T2 going to a particular membrane potential. After a 5 min interval to allow full reversal of the repriming in the 100 see period at - 100 mV

539 REACTIVATION OF gE AND CHARGE MOVEMENT the first sequence was repeated followed by the second with C2 and T2 going to some other membrane potential. In this way charge movement was explored in unreprimed and reprimed fibres over the same voltage range and with the two pulse structures. The temperature of the muscle for these measurements was 10 'C. This rather high temperature allows charge repriming in a reasonable time (100 sec) but is too high to allow resolution of the time course of the rapid charge movements. At lower temperature both inactivation and repriming would be slower and this would lengthen the time required for a complete run. Even at 10 'C a complete run required a preparation stable for some 2 hr. B

A

-r-r

-80 ------I

---L

-

x4 C

C

-20

__ n

-80

I

r-*,

Ii!

.

JL

-100

T1

C1 x4 D -20

-80

-100

-----i

o

L_

II ii L

'

A

L----

IL

-s-

T2 100 sec Fig. 2. Pulse structures for detecting intramembrane charge movement, and reprimed charge and current. Continuous lines represent the part of the waveform for which V1, A V and 1 are sampled and stored by the computer. A, as used by Chandler et al. (1976a, b); B, as used by Adrian & Almers (1976b); C and D, used in the present paper to detect 'reprimed', 'total' and 'unreprimed' charge (see pp. 541-2 for definitions).

C2

Capacity measurements Capacities were measured at the 'on' and 'off' of each control and test pulse. Eqn. (9) defines the capacity as the slope of the chord of the QV curve between VH and (VH + Vl (c)). VH was -100 mV for CI and -80 mV for T1, C2 and T2. Fig. 3 shows, for fibre 1701, the capacity measurements as a function of voltage in the unreprimed and reprimed condition. Since there was some change in the control capacity during the course of the experiment the capacities have been normalized to the capacity of the small control pulse. The unreprimed points (open circles) show

R. H. ADRIAN AND R. F. RAKOWSKI the ratio of the capacities measured for C2 and for CI: the reprimed points (filled circles) show the ratio of the capacities measured for T2 and C1. The large open circle on the ordinate is the mean ratio of capacity measurements made with Ti and Cl; its value is 0X82 + 0 01 (mean + S.E. of mean, eleven measurements). Fig. 3 shows that for membrane potentials between -60 and +30 mV the capacity ratio for unreprimed fibres falls and the capacity ratio for reprimed fibres rises for increasingly 540

CT/CC 1 5

0nd

* Repnmed

0

* °

o °.

)

Unreprimed

05

-100

-50

0 50 mV Fig. 3. The ratio of the membrane capacity measured with a voltage step from -80 mV to various different membrane potentials (abscissa) to the membrane capacity measured at - 100 mV with a + 20 mV voltage step. Filled circles, variable voltage step follows 100 sec at - 100 mV. Open circles, variable voltage step follows 200 msec at - 100 mv. Fibre 1701: 1 = 250 jrm, ri = 119 MfQ/cm, Rm = 5'9 k! Cm2, Cm = 8-7 #sF/cm2, diam. = 73 #sm, temp. = 10 1 0C.

positive membrane potentials. Taken at its face value this finding means that the QuV curve is non-linear in both unreprimed and reprimed fibres and that its slope decreases in unreprimed fibres but increases in reprimed fibres for increasingly positive internal potentials (Schneider & Chandler, 1976; Adrian & Almers, 1976b). Detailed interpretation of these capacity measurements should be cautious since the scatter is large, and the integration in eqn. (9) was over the entire voltage step (11th to 138th msec of the sampling period) so that small time dependent ionic currents could have affected the capacity measurement. Moreover if the membrane current was not a linear function of the membrane potential for large voltage steps r1 might be incorrectly estimated because it depends on the assumption that the input resistance of the fibre for x > 21+1' is lrmri. Errors of this kind may have affected the points around and positive to 0 mV in Fig. 3.

REACTIVATION OF

AND CHARGE MOVEMENT

gK

541

Charge movement definitions Fig. 4 presents records of charge movement which result from three ways of combining and subtracting the currents from control and test pulses. Formally the left-hand set of records can be defined as iM(t) =

im(t)T2

Vl(CO)C2 .M(t)C2.

In this case V1 (x)C2 is meant to be exactly equal to V1 (O)T2 because the two potential steps were from - 80 mV to the same potential. The ratio will be very nearly equal to 1.0, but is included to take account of small residual differences. We shall call the charge detected by integrating the transient part of i'(t), 'reprimed' charge. i'm(t) 3

i'm(t)2 'total' charge

'reprimed' charge

'unreprimed' charge

-60 -49

_;-

-39

.

-29

^

r

S--

140 8

,

-18

-8

A

2

,-.

12

0;

I1-10,

x

t,*Aftw16-%-,,-A

wq

-W

t

i

23

li

Fig. 4. Computer records of non-linear membrane current in the membrane potential range -60 mV to + 23 mV. Each column represents a different combination of the currents recorded during the voltage steps CI, C2 and T2 (see Fig. 2C, D). For the formal definitions of im(t)01 iM(t), im(t), see text (pp. 541-2). The vertical scale is i

(t)x31 iCm 2

ImV = 2.14 #A//sF.

Each vertical bar is 5 mV. Points are at 1 msec intervals. Fibre 1701: 1 = 250 jsm, r1 = 11-9 MCI/cm, Rm = 5-9 kg cm2, Cm = 8 7 esF/cm2, diam. = 73 jam, temp. = 10.1 C.

R. H. ADRIAN AND R. F. RAKOWSKI 542 The middle set of records can be defined as

'M'(t2 im(t)T2iV(}T2 im(t)CI In this case Vl(oo)cL and im(t)cj were obtained as the sum of four control pulses of =

+ 20 mV from a holding potential of - 100 mV. We shall call the charge detected by integrating the transient part of i (t)2 'total' charge. The right hand set of records is defined as

im(t)3 = im(t)C2

Vi(oO)ci

m(t)

i--iM(t)l. *.IM

Again V1(oo) and im(t)C1 were obtained as the sum of the four control pulses. We call the charge detected 'unreprimed' charge.

Reprimed and total charge It is immediately obvious in Fig. 4 that the situation is complex because there are transient currents, and so presumably charge movements, in all three sets of records. On superficial inspection the 'reprimed' and 'total' charge movements (the two left-hand columns) do not differ obviously. The 'unreprimed' charge is complicated because the transient parts of i (t)3 consist of a small and rapidly decaying positive transient and a slow negative transient at the 'on' of the step and similar movements in the reverse direction at the 'off'. There are rather random shifts of the steady base line during the pulse (non-linear leak current) and though both rapid and slow transients are present for the 'on' and 'off', their on/off symmetry is not exact. The uncertainties in the records of 'unreprimed' charge as well as the apparent presence of two charges makes it unprofitable to attempt to integrate the charge movement in this set of records. We believe that the records in Fig. 4 of 'unreprimed' charge are the result of charge movements, one of which takes place during the control pulse from -80 mV. An alternative explanation of the slow increase in current during the voltage step would be a slowly increasing outward current carried probably by potassium ions. This is certainly sometimes seen. Fig. 5 shows the current records for control and test pulses and records of iV(t)3 from the fibre which gave the records in Fig. 4, and from another fibre which showed more delayed outward current. While one cannot eliminate delayed outward current completely, or in every fibre, Fig. 5 suggests that a slow charge movement takes place during small control pulses (Cl) and this may be proportionately larger than the charge movement during the C2 pulse. In principle the 'unreprimed' charge or charges should be the charges in a depolarized fibre which move in the potential range between the holding potential (-80 mV) and + 20 mV. In practice this will only be true if the currents required during the small control pulse are for linear membrane elements; that is they are not related to any dipole or charge movement which begins to saturate for potentials more positive than -80 mV. The behaviour of the records of unreprimed charge suggests that this is not so. The 'reprimed' charge, because control and test pulses are over the same voltage,

REACTI VATION OF 9 EAND CHARGE MOVEMENT 543 contains only charge which reappears in the 100 see of repriming. If more than one species of charge is affected by the level of polarization of the fibre, the 'repriming' sequence will detect the net appearances of charge in the 100 see at - 100 mV. This could be a change in one charge only but might be a balance of appearances of some A Cl

C2-C1

C2

e;MS ^; v

B

mv [X

-

*-I

r

C' C2-C1

C2

Fig. 5. The pairs of records on the left are records of A V for CI and C2 steps. These records have been scaled for display approximately according to the voltages of the two steps (see eqn. (11)). The records on the right are i (t) calculated by eqn. (11) for a fibre (A) which showed little or no delayed rectification, and (B) for a fibre in which some delayed rectification remained. Both fibres were in solution B containing 110 mMTEA+. A, fibre 1701: 1 = 250 ,um, r1 = 119 MO/cm, Rm = 5 9 kO cm2, Cm = 87 ,uF/cm2, diam. = 73 um, temp. = 10-1 C. 1 mV = 2-14 #uA/hF. B, fibre 1703: 1 = 250 jam, ri = 53 MO/cm, R,,J = 3 5 kO cm2, Cm = 24 #F/cm2, temp. = 10 3 'C. I mV = 3.00 uA/ItF.

charges and disappearances of others. Until we have evidence to the contrary we shall assume that 'reprimed' charge is one charge species which is inactivated by depolarization and reprimed by repolarization. If non-linear elements contribute to the charge movements in the small control pulses (Cl) the measurements of 'total'

R. H. ADRIAN AND R. F. RAKOWSKI charge cill not necessarily be identical with 'reprimed' charge. The records of ' unreprimed' charge suggest that 'total' charge will be less than 'reprimed' charge. In three fibres with reasonably complete results 'reprimed' Qmax was 29 ± 3 nC/4uF and 'total' Qmax was 14 + 3 nC/1sF. Fig. 6A and B plot Q/Qmax on linear and logarithmic ordinates for 'total' and 'reprimed' charge from three fibres of muscle 17. The results in Fig. 6 do not establish unequivocally that 'reprimed' charge shows 544

o (nC//iF) 30

A

00 0

0

-20 0

* 0O

0

o *

0

-10

I .

p

.

0

I 0I50

-50

50

0 mV

0/0 max

B 1

be

S

F01 0*1

0y

I I I~~~~~~

-50

50 0 mV Fig. 6. 'Reprimed' charge (open circles) and 'total' charge (filled circles) plotted against the membrane potential. A, the charge (Q in nC//uF) is plotted on a linear scale against V. B, the charge normalized to a saturating value (Q/Qmax) is plotted on a logarithmic scale. Fibre 1701: 1 = 250 jsm, ri = 11-9 MC/cm, Rm = 5-9kQ cm2, Cm = 8-7 juF/cm2, diam. = 73,um, temp. = 10-1 C. Fibre 1702: 1 = 250 /zm, r, = 12-8 MfI/cm, Rm = 4-3 kf cm2, Cm = 10-7 sF/cm2, diam. = 71 sum, temp. 10-3 0C. Fibre 1703: 1 = 250 jum, ri = 5 3 Mfl/cm, Rm = 3.5 kQ cm2, Cm = 24 #sF/cm2, temp. = 10.3 'C.

545 REACTIVATION OF gE AND CHARGE MOVEMENT a saturating sigmoid behaviour. In order to compare these results with others we have arbitrarily fitted eqn. (14) to the results in Fig. 6. Subsequent experiments (R. F. Rakowski, unpublished) suggest that 'reprimed' charge is more nearly linear

than appears in Fig. 6. Insofar as eqn. (14) is a valid description of these results, one can say that the transition potential (V) for 'total' charge is some 20 mV negative to V for 'reprimed' charges. It is not however as far negative as V for Charge 1 or n~o (approx. -45 mV; see Table 2). The different pulse structures clearly recover different apparent charge movements. 'Total' charge, defined as the integral of the transient part of i'(t)3, employs the same pulse structure as Charge 1 of Adrian & Almers (1976b). However, the constants in eqn. (14) which describe 'total' charge and Charge 1 are not the same. Nonetheless it is probable that Charge 1 like 'total' charge represents the net effect of the movements of several species of charge, some moving more in the test pulse and some moving, in proportion, more in the control pulse. Indeed this must be so if we admit that there is no a prior reason why only one charged species should be moving in any one voltage range. TABLE 3. Comparison of 'reprimed' charge with threshold mechanical repriming

QWuay. (nC/uF) 'Reprimed' charge Subthreshold reprised charge* Repriming contraction experiments* *

29 3.3 -

V

k

(mV)

(mV)

-4 -10

-23

28 22 19

From Adrian et al. (1976).

The differences between Charge 1 and 'total' charge may reflect differences between depolarized and normally polarized fibres which are additional to the presence of the charge which we have called 'reprimed' charge. It may be that there is a charge normally present in polarized fibres which is reprimed so slowly after depolarization that 100 sec at - 100 mV is inadequate for its reappearance. 'Reprimed' charge, defined as the integral of the transient part of i (t)1, is substantially larger than, but has much the same voltage distribution as the subthreshold reprised charge described by Adrian et al. (1976). 'Reprimed' charge therefore has a voltage distribution not unlike the one required to fit the repriming of contraction experiments also described by Adrian et al. (1976). Table 3 gives V and k for eqn. (14) for 'reprimed' charge, subthreshold reprimed charge, and for the charge postulated from the contraction experiments. In the determination of 'reprimed' charges the test and control voltage steps cover the same potential range. Only charge movements that are affected by the steady level of polarization will be detected by the 'reprimed' charge protocol. Charge movements and ionic leakage currents that are unchanged during the repriming pulse will be subtracted no matter how non-linear they may be. We believe therefore that 'reprimed' charge has a higher probability of being a single species of mobile charge than either Charge 1 or 'total' charge. The similarity of 'reprimed' charge to subthreshold reprimed charge (Adrian et al. 1976) makes us think that i8

PH Y

278

R. H. ADRIAN AND R. F. RAKOWSKI 546 'reprimed' charge represents the most reliable measurements of the charge movement to be associated with activation of contraction. Repriming of potassium conductance The repriming period in the experiments on charge movement was 100 see at - 100 mV and the charge reprimed during that period was 29+3 nC/,uF. This represents a large fraction of the charge detected in normally polarized fibres. To what extent is the maximum available potassium conductance (9K) restored by 100 sec at -100 mV at 10 'C? This question was investigated in two ways: the -10

-20 mV

-80

-100

-T T=6 sec A

.t

13 B

_.

28 C

62 D

5-7

.,_

or'A pFF

E

108

E '*^/

_

* I

I

~~~~~~~~~~~I

128 msec Fig. 7 Records of i' (t) from an experiment to measure the rates at which charge moveTnent and potassium conductance are reprimed. The fibre was in solution A. The records of im(t) are made by subtracting A V records from two voltage steps from -80 to -10 mV, one of which was preceded by a variable repriming period at - 100 mV. The times (from 6 to 108 sec) are given against each record. Fibre 1602: 1 = 250 #sm, r1 = 6-8 Me/cm, Rm = 5.7 kQ cm2, Cm = 94 ,uF/cm2, diam. = 80 pm, temp. = 10-2 'C.

REACTIVATION OF gE AND CHARGE MOVEMENT 547 repriming time was varied at a fixed repriming potential; the repriming potential was varied at a fixed repriming time (100 see). Because it was necessary to leave 5 min between successive reprimings it was seldom possible to make both sets of measurements on the same fibre. An experiment of the first kind is shown in Fig. 7. The muscle was in a solution with a rubidium concentration of 80 mm (solution A, Table 1) in order to make the current through the delayed rectifier small in the voltage range -40 to 0 mV. We hoped by this method to make it possible to separate charge movement and potassium current. Fig. 7 shows that as the repriming time is increased both charge movement and potassium current increase. However it did not prove possible to separate clearly the charge movement and potassium current in order to see whether their rates of reappearance were identical. Fig. 7 suggests that they are certainly similar. For this fibre the maximum conductance after 108 see 1-0 U-

0

E E 10 C

05 r0-5

(0

-

o

0

C.,&

0

100

50

150

Repriming pulse duration (sec.)

Fig. 8. The time course of recovery of delayed potassium conductance. O. repriming voltage - 100 mnV; *, - 140 mV. Following each hyperpolarizing pulse, the amount of delayed conductance reactivated was measured by a test pulse to + 2 mV. The fibre was allowed to inactivate by maintaining the holding potential of -20 mV for 5 min after each determination. Fibre no. 1601, solution A, I = 240,um, ri Cm = 8 7 #uF/CM2, diam. = 88 jzm, temp. = 9 -8 'C.

=

5-6

Mf2/cm, R,,,

=

4-5 kf Cm2,

repriming at - 100 mV is about 0 4 mmho/#F which is substantially less than gK in a fibre in hypertonic solution with a normal resting potential (1-2 mmho//,tF). However, Almers, (1976) has reported values as low as 2 mmho/cm2 in isotonic solutions.

Although substantial conductance changes occur in Fig. 7 their kinetics are slower than those of the ordinary delayed rectification of striated muscle. The onset of the current in Fig. 7E is not strikingly sigmoid and it has an approximate halftime of 40 msec. The tail current is not a single exponential. This must raise the i8-2

548 R. H. ADRIAN AND R. F. RAKOWTSKI question of whether the conductance charge seen after 100 see repriming is a fast or slow potassium current (Adrian, Chandler & Hodgkin, 1970b). Fig. 8 shows the time course of reactivation of delayed potassium conductance in a fibre in which it was possible to do a series of determinations for two different repriming voltages. The pulse protocol was the same as that used in Fig. 7. The data can be adequately described by a single exponential recovery process. The time constant of reactivation was 40 see for repriming at- 100 mV and 17 see for -140 mV. 0 12

0-10 0

c 008

(3)

C\ O 0 06\ (1) i

.°

, 004

-

C.,

(7))

0.02

(1) -160

-140

-100 -120 Repriming voltage (mV)

-80

-60

Fig. 9. The dependence of the rate constant for the reactivation of potassium conductance on the repriming voltage. The numbers in parentheses indicate the number of determinations at that repriming voltage. The data were taken from nine different fibres. The error bars indicate the standard error of the mean. The line is the least squares fit to eqn. (15) with each point weighted according to the number of determinations. The temperature ranged from 6-7 to 10-2 'C and was corrected to 10° before averaging by assuming a Q10 of 2-5. The best-fit parameters were V' = -86 mV, k = 5 mV and a = 0-00756 sec'. Unweighted and uncorrected data gave values of V = 87 mVr, k = 5 mV and a = 0-00765 sec-1.

Measurements similar to those in Figs. 7 and 8 were made on nine different fibres. The mean values of the repriming rate constant as a function of the repriming potential is illustrated in Fig. 9. It is clear that the relationship between the repriming rate constant and repriming voltage is U-shaped with a minimum value in the region of -90 mV. The line in Fig. 9 is drawn according to the best-fit to eqn. (15). NW -

coth

L(V-)i

(15)

Eqn. (15) may be derived in a manner analogous to that used to describe the kinetics of charge movement activation by Chandler et al. (1 976 a) and Almers & Best

549 REACTIVATION OF ye; AND CHARGE MOVEMENT (1976). The parameters used to fit the data in Fig. 9 were V =-86 mV, k = 5 mV and a = 0-00756 sec-'. Measurements of the reactivation of potassium conductance were also made for a fixed repriming duration of 100 see at various repriming voltages. These data can be corrected to give the steady-state value by using the correction factor 1/(1 -exp (- 100/T(V))) where r( V) is derived from the data in Fig. 9. This method assumes that the steadystate condition is attained by a single exponential recovery process and does not TABLE 4. Best fit parameters for the reactivation of delayed potassium conductance

V k Fibre Temp. Cm OK 9K (mV) (mV) (OC) no. (rnmho/,uF) (,uF/cm2) (mrnho/cm2) 13-1 22-9 11-2 1-75 -108 8-8 0608 10-3 18-6 1-81 15-4 -105 8-6 0609 1-3 6-3 0-20 9-1 -86 8-8 0702 8-3 1-03 12-5 8-0 -93 12-9 0703 5-6 12-7 0-44 16-8 -99 13-3 0802 11-3 .10X1 1-05 12-9 -98 Mean + 1-3 + 4-1 + 1-4 +0-33 +4 S.E. of mean Solution A. Holding potential -20 mV, repolarized for 100 sec. Test pulse potential -18 mY. The data were corrected to give the steady-state value as described in the text. The uncorrected data gave the following mean values: V = -99 ± 4 mV, k = 12-5 + 1-3 mV and9K = 1-02 ± 0-32 mmho/,uF. Specific membrane capacitance was calculated from 20 mV control pulses from - 100 mV as described in Methods.

2-0 r U-

0

E 1 5H E CC

c

-o0

101-

~0

05 H

CD) cc

OL 0 -50 -100 Repriming voltage (mV) Fig. 10. The reactivation of potassium conductance as a function of the repriming voltage. 0O uncorrected data for 100 sec recovery; *, data corrected to the steady state as described in the text. The line is drawn according to eqn. (16) with the following constants determined by the least-squares fit to the data: V = - 105 mV, k = 15-4 mV and g. = 1-81 nmho/sF. The uncorrected data gave the following values: V = -105 mV, k = 13-8 mV and 9K = 1-75 mmho/,ueF. Fibre 0609, solution A, 1 = 240 jzm, r, = 2-6 MQ/cm, Rm = 1-4 k0 cm2, Cm = 10-3 uF/c1,12, diam. = 124 jm, temp. = 8-6 'C. -200

-150

R. H. ADRIAN AND R. F. RAKOWSKI account for changes that may require more than 1 or 2 min. Both the 'steady-state' and uncorrected data from one fibre are shown in Fig. 10. The line is drawn according to eqn. (16).

550

(16) 9K= 1 +exp [(V-V)/l] The constants derived from the least square fit to the data in Fig. 10 and that from four other fibres are given in Table 4. The mean value of V (-98+ 4 mV) and k (12.9 + 1*4 mV) is substantially different from that derived from the kinetic data alone (Fig. 9). The reason for this discrepancy is not clear. Both measurements,

Fig. 11. Collected results of measurements of reprising of potassium conductance. Large points (means ± s.E. of mean) are from experiments with fixed repriming time (100 sec) and variable repriming potential. The small points are individual measurements of conductance for variable reprising time and fixed repriming voltage (as in Fig. 7).

however, give values of V for the reactivation of potassium conductance that are substantially more negative than the value of -40 mV that was determined by Adrian et al. (1970a, b) as the mid-point of the steady-state relationship for the inactivation of potassium conductance. In these previous experiments fibres were initially held at -100 mV in hypertonic Ringer with 2-5 mM-potassium and the extent of inactivation was measured following conditioning depolarizations of 2-3 sec duration at 20 'C. Although there are several factors that may partially account for the difference in the observations, such as the difference in rubidium or potassium concentration, the discrepancy is strikingly large. Since the maximum value of

REACTIVATION OF gli AND CHARGE MOVEMENT

551 reprimed conductance in the present experiments (113 + 4*1 mmho/cm2) is within the range of the maximum potassium conductance reported in normally polarized fibres by Adrian et al. (1970a) (8-5-20 mmho/cm2) and comparable to the range reported by Almers (1976) (2-10 mmho/cm2), the data suggest that the potassium conductance that is reprimed in 100 sec at - 140 mV is comparable in magnitude to the delayed potassium conductance seen in normally polarized fibres. It is possible

2*0

0

E E

0

10

@8_0

I -80I

p

-60

aoo -20 tX 20 0

-40

40

60

mV Fig 12. Potassium conductance activated in the presence of 2 mm-tetracaine by a voltage step to the voltage indicated by the abscissa from a holding potential of -80 mV (open circles) or -20 mV (filled circles). Fibre constants Cm Diam. Temp. RM Fibre (0c) (Pm) (MC cm-1) (kQ cm2) (flF cm-2) (um) 1.4 6.2 7-2 250 73 10.0 1801 1.3 7.3 7.6 70 250 1902 10.6 30 5.3 6.5 76 2001 250 10.5 8-5 2003 250 66 10X5 6X8 3X3 4.9 87 2004 250 10X5 2X9 4X2 42 1*6 50 15 2 250 20C5 10.5 2006 250 48 9-8 4-4 89 10.5 Muscles 18 and 19 were in solution C. Muscle 20 was in solution C with rubidium concentration = 80 mm, sodium being omitted for the added rubidium.

that the recovery of delayed potassium conductance takes place in two stages, an initial approximately exponential recovery for repriming times up to about 100 sec followed by an even slower shift in the position of the steady-state inactivation curve to more positive potentials. Alternatively we may be looking at two potassium

R. H. ADRIAN AND R. F. RAKOWSKI 552 currents repriming at different rates. Occasionally fibres were seen in which the recovery of potassium conductance did not seem to be strictly exponential, but instead, increased slowly with time rather than achieving a constant value. This process was not studied in detail because of its extreme slowness. The measurements of reprimed potassium conductance from nineteen fibres are collected in Fig. 11 which plots on isometric coordinates the surface ofYK as a function V

-20 V=+10 mV A_

20 B

/,

25

C /

30 D

_

20ff [ 35 E

I

128 msec

Fig. 13. Records of i. (t) obtained in the presence of 2 mm-tetracaine by subtracting the A V records after scaling for voltage steps from -40 to -20 mV and from -20 mV to the voltages indicated against each record. Fibre 2006: 1 = 250 jum, r, = 4-8 Me/cm, Rm = 9 8 kf cm2, Cm = 4.4 fuF/cm2, diam. 89 #um, temp. 10-5 'C.

of repriming time and repriming voltage. It is clear from Figs. 10 and 11 that after repriming for 110 see at -100 mV (10 TC) the reprimed potassium conductance is only about one third to one half of its normal value. Under the same conditions the charge movement detected in muscle 17 appears to have approached its normal value.

REACTIVATION OF YK AND CHARGE MOVEMENT

553

Effects of tetracaine Almers (1976) has shown that 2 mM-tetracaine displaces the activation curve of the potassium current by about + 25 mV and the charge distribution function by only about + 5 mV. Using 2 mM-tetracaine in a sulphate solution with 5mM-rubidium (solution C, Table 1) the rise in potassium conductance was displaced beyond 0 mV to positive internal potentials. Fig. 12 plots maximum potassium conductance against membrane potential for two groups of fibres, one held at -80 mV (open circles), the other held at -20 mV. The former group showed charge movement preceding the development of potassium current, as in the results of Almers (1976); the latter group showed no detectable charge movement preceding the potassium

mV 2 on ordinate. Points are from Adrian et al. (1976, 14. Fig. Charge plotted logarithmic Fig. 16). The line is defined by eqn. (14) and the parameters in Table 2.

current. Fig. 13 shows records of non-linear current for positive potential steps from a fibre in 2 mM-tetracaine where potential was held at -20 mV. Tetracaine shifts the activation potential for potassium current but it does not greatly affect the activation or inactivation potentials for the charge movement which precedes the potassium current. Presumably this charge movement was inactivated when the fibre was held at -20 mV. In the absence of such charge movement the potassium conductance can still increase by the same amount as in a normal fibre.

R. H. ADRIAN AND R. F. RAKOWSKI

554

DISCUSSION

The main conclusion from these experiments is that charge movement measured in normally polarized fibres is the result of several species of moving charges or dipoles. A component of this charge movement appears to be related to the initiation of contraction. The other moving charges or dipoles are, almost certainly, the Charge 2 described by Adrian & Almers (1976b) and Adrian et at. (1976), probably a small charge associated with gating of the sodium channel (Armstrong & Bezanilla, 1974; 0 (nC/pF)

_ 40

30

-

100

50

m+Q2+ reprimed charge

0

50

mV

Fig. 15. Q V8. V curves for sodium gating current (m taken from Adrian et al. 1970a); Charge 2 see Fig. 14; the sum of m and Charge 2, and the sum of m, Charge 2 and 'reprimed' charge with the parameters in Table 3. The straight line is the linear extrapolation of charge moved by a small potential step at - 100 mV.

Keynes & Rojas, 1974), and possibly a charge movement associated with the potassium channels. It is however possible, under some conditions, to get opening of potassium channels without detected charge movements (Fig. 13). If Adrian & Peres (1977) are right in suggesting that the potassium gating current is proportional to d(gK)/dt it would be very difficult to detect that gating current in the presence of

55 555 REACTIVATION OF g .K AND CHARGE MO VEMENT potassium current, and the results of Fig. 13 would be explained by inactivation of the exponentially decaying charge movement seen in Fig. 7, and tentatively associated with contraction. It is useful to see how far existing knowledge about charge movements in striated muscle explains the present results. Fig. 14 plots on a semilogarithmic scale Q vs. V for Charge 2 taken from Adrian et at. (1967, Fig. 16). The line is drawn according to 0

A

(nC//iF) Reprimed

'Totar 10

B

Reprimed

'Totar 01

-50

50

mV Fig. 16. Charge movements which would be measured as 'reprimed' and 'total' charge in a membrane with three charges as in Fig. 15. A, charges plotted on a linear scale; arrows are the values of V for reprisedd' and 'total' charge. B, charges plotted on a logarithmic ordinate. Dotted line in both is Charge 1 described by Chandler et al. 1976a (Table 2).

R. H. ADRIAN AND R. F. RAKOWSKI eqn. (14) with the constants given in Table 2. Since the measurements reported here were in the potential range - 100 to + 20 mV it is only the upper part of the Charge 2 curve that is relevant. This is redrawn in Fig. 15 on a linear scale. The curve marked Q2, with its origin at - 100 mV and saturating at 17-5 nC/,tF, represents the actual quantity of Charge 2 which would move when the potential changes from -100 mV to some other value between - 100 and + 50 mV. Likewise the curve marked m is drawn by supposing that the sodium gating charge movement has the same voltage relation as mr in muscle (Adrian et al. 1970 a) and that the total quantity represents a Qmax. of 5 niC//uF (Almers, Adrian & Levinson, 1975; Adrian & Almers, 1976b). The sum of these two curves is shown as m + Q2. The straight line is tangent to the Q2 curve at V = 100 mV. The uppermost curve is the m+ Q2 curve to which 'reprimed' charge has been added (see Table 3 for the constants). If we suppose that the 200 msec which precedes either control pulse in Fig. 2 (Cl or C2) is sufficient to reactivate ml charge movement, we can use Fig. 15 to predict the Q vs. V curves which will be recovered by the pulse structures in Fig. 2. C1 vs. T2, which we have called 'total' charge will be the difference between the uppermost curve and the straight line: C2 vs. T2 which we have called 'reprimed' charge will be ex hypothesi the difference between the uppermost curve and the curve labelledM + Q2. If m charge is not reactivated in the 200 msec, 'reprimed' charge will be unaltered, but 'total' charge will always be less than 'reprimed' charge. Fig. 16 plots on linear and logarithmic scales the 'reprimed' and 'total' charges predicted from Fig. 15 on the assumption that rn is reactivated. The dotted line on the logarithmic plot is Charge 1 using the constants of Chandler et al. (1976a) (see Table 2). It is clear that the presence of other charges goes some way to explain the differences between Charge 1 and ' reprimed' charge. It does not go all the way and the possibility remains that Charge 1 includes more charges than the three charges allowed for in Fig. 15. 556

a

We are grateful to WV. Smith for expert assistance. This work was done during the tenure of research fellowship granted by the Muscular Dystrophy Association of America to R.F.R. REFERENCES

ADRIAN, R. H. & ALMERS, WV. (1974). Membrane capacity measurements on frog skeletal muscle in media of low ion content. J. Physiol. 237, 573-605. ADRIAN, R. H. & ALMERS, WV. (1976a). The voltage dependence of membrane capacity. J. Physiol. 254, 317-338. ADRIAN, R. H. & ALMERS, WV. (1976b). Charge movement in the membrane of striated muscle. J. Physiol. 254, 339-360. ADRIAN, R. H., CHANDLER, W. K. & HODGKIN, A. L. (1970a). Voltage clamp experiments in striated muscle fibres. J. Physiol. 208, 607-644. ADRIAN, R. H., CHANDLER, WX. K. & HODGKIN, A. L. (1970b). Slow changes in potassium permeability in skeletal muscle. J. Physiol. 208, 645-668. ADRIAN, R. H., CHANDLER, W. K. & RAKOWSKI, R. F. (1976). Charge movement and mechanical repriming in striated muscle. J. Physiol. 254, 361-388. ADRIAN, R. H. & PERES, A. R. (1977). A gating signal for the potassium channel? Nature, Lond. 267, 800-803. ALMERS, WV. (1976). Differential effects of tetracaine on delayed potassium channels and displacement currents in frog skeletal muscle. J. Physiol. 262, 613-637. ALMERS, W., ADRIAN, R. H. & LEVINSON, S. R. (1975). Some dielectric properties of muscle membrane and their possible importance for excitation-contraction coupling. Ann. N.Y. Acad. Sci. 264, 278-292.

REACTIVATION OF

9K

AND CHARGE MOVEMENT

557

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