J. Phyeiol. (1978), 281, pp. 339-358 With 9 text-figure8 Printed in Great Britain

339

REPRIMED CHARGE MOVEMENT IN SKELETAL MUSCLE FIBRES BY R. F. RAKOWSKI From, the Department of Physiology and Biophysics, Washington University School of Medicine, St Louis, Missouri 63110 U.S.A.

(Received 12 October 1977) SUMMARY

1. The three intracellular micro-electrode voltage-clamp technique was used to study the recovery of membrane charge movement in semitendinosus muscles of Rana pipiens. Muscles were placed in a hypertonic depolarizing solution to inactivate voltage dependent charge movement. Tetrodotoxin and tetraethylammonium ions (TEA+) were present to block voltage dependent ionic conductances. Rb+ and S042were present to reduce inward rectification and leakage conductance. 2. The recovery ('repriming') of membrane charge movement was studied following hyperpolarizing pulses from a holding potential of -20 mV to membrane potentials from -30 to - 140 mV for durations of 2-100 sec. The reprimed charge movement measured as the difference in membrane current required for identical voltage steps before and after long duration hyperpolarizing pulses was a linear function of membrane potential and symmetrical in shape. Reprimed charge is, therefore, simply the result of an increase in the linear capacitance of the fibre. 3. The mean value of the percent increase in capacitance for repriming at - 100 mV was 12-3 + 1-7 % (S.E. of mean) for 25 see duration pulses and 27-8 + 290/ for 100 sec duration pulses. If these data are corrected to the steady state and the surface contribution subtracted, the mean increase in 'volume' capacity is 40 3 + 3 60/ (n = 21) for fibres with a mean diameter of .51 + 4 /m. 4. The increase in capacity can arise either by an increase in the transverse tubular length constant (AT) or by gaining electrical access to additional linear capacitance within the fibre volume. If the capacitance arises solely from the transverse tubular system, the value Of AT before repriming can be no larger than 20 ,m in order to explain the observed increase in volume capacity. A value Of AT as small as this seems unlikely. 5. The observation that reprimed charge is simply the result of an increase in linear capacitance is not consistent with the hypothesis that it is a gating mechanism for the activation of contraction. INTRODUCTION

Schneider & Chandler (1973) proposed that membrane charge movements measured in skeletal muscle are related to the process of excitation-contraction coupling. This suggestion was supported by the observation that the steady-state voltage dependence of non-linear membrane charge was comparable to the voltage dependence of mechanical activation. Further suggestive evidence was provided by Chandler, Rakowski & Schneider (1976b) who observed that membrane charge movement

B. F. RAKOWSKI inactivates with maintained depolarization and recovers on hyperpolarization. The slow time constant of this process suggested that it might be the underlying cause of the development of mechanical refractoriness in chronically depolarized fibres. The restoration of the ability to contract ('repriming') would result from recovery of charge movement in fibres that are hyperpolarized. Evidence linking charge movement and contraction was provided by the experiments of Adrian, Chandler & Rakowski (1976). These authors investigated the relationship between repriming duration and the voltage required to elicit a justvisible ('threshold') mechanical response. They found that the voltage dependence of threshold mechanical reprising could be explained by a sigmoid voltage distribution function having the same form as that used to describe membrane charge movement. The parameters used to characterize the voltage distribution function determined by threshold mechanical repriming were similar, but not identical, to the parameters that were used to describe the voltage dependence of membrane charge movement. The discrepancy was tentatively ascribed to differences that might arise because of the hypertonic solution that was used in the charge movement experiments (Chandler, Rakowski & Schneider, 1976a; Adrian & Almers, 1976b). In support of this suggestion an attempt was made to measure the voltage dependence of subthreshold reprimed charge in isotonic solutions. It was found that the voltage distribution function was less steep and was shifted to more positive values in a manner consistent with the threshold mechanical repriming experiments (Figs. 13 and 14, Adrian et al. 1976). Experiments on chronically depolarized fibres had also shown that there was a second type of non-linear membrane charge movement in muscle ('charge 2') (Adrian & Almers, 1976b; Adrian et al. 1976; Schneider & Chandler, 1976). The evidence that is available seems to support the hypothesis that it is the membrane charge movement that inactivates on depolarization and is reprimed by hyperpolarization that is associated with the activation of contraction. It is, therefore, important to investigate the characteristics of reprimed charge movements to provide additional evidence that bears on this hypothesis. The experiments reported here show that reprimed charge movement measured in hypertonic solutions in semitendinosus muscle fibres of Rana pipiens is simply additional symmetrical linear capacity current. The experiments do not rule out the suggestion that some component of the membrane charge movement called 'charge 1' may be associated with contractile activation; however, it is clear that the 'reprimed charge movement' measured in these experiments cannot account for the voltage dependence of contractile activation. 340

METHODS

Experimental procedure The three-intracellular micro-electrode voltage clamp technique (Adrian, Chandler & Hodgkin, 1970) was used to control the membrane potential and measure the membrane current density in skeletal muscle fibres of the semitendinosus muscle of the frog, Rana pipien8 (Vermont). Experiments were performed during the months of March through June. Frogs were decapitated and pithed and the semitendinosus muscle dissected in normal frog Ringer solution. At least 1 hr before to the beginning of an experiment the muscle was pinned out at approx. 1-4 times its in situ length and the solution changed to the experimental solution. Electrodes were inserted in fibres that terminated on the ventral side of the distal tendon. The fibre terminations could be easily visualized using a dissecting microscope at a magnification of 80 x . The V1 electrode

REPRIMED CHARGE MOVEMENT

341 was inserted at a distance of 250 sum (1) and the V2 electrode inserted at a distance of 500 jun (21) from the end of the fibre. The current electrode was inserted as close as practical to the V2 electrode, usually at a separation of 1o00 jm (l'). An external reference electrode (V0) was placed in the bath and positioned to within about 2 mm of the fibre under study. The membrane potential at the two recording sites was recorded differentially as (VI'l 1- ) and (V2 -O) but will be simply referred to here as V1 and V2. The potential difference V2 - V1 is referred to as A V and is proportional to the membrane current density at the position of the V1 electrode. The voltage signal to the feed-back circuit was V- V0. The membrane current per unit length of fibre at the point of voltage control is given by eqn (1), jm (t)

=

3l2r1'

(1)

where l (mm) is the spacing of the voltage electrodes and r1(n/cm) is the internal longitudinal resistance of the fibre (Adrian et al. 1970).

Voltage clamp The voltage-clamp circuit used in these studies was based on a circuit designed by Almers (1971). The gain of the final stage amplifier (Analog Devices, model 170) was adjusted so that its output did not saturate when the control amplifier (Philbrick Nexus, 140701) reached its maximum output. The maximum output voltage of the clamp circuit was ± 80 V. Before making measurements on each fibre the clamp circuit was 'tuned' to give an optimally square response to a brief 20 mV hyperpolarizing voltage pulse, using command pulses with a rise time of less than 20 flsec. The voltage step recorded at the V1 electrode typically attained its final value within 0-2 msec. Subsequently all command voltage steps were intentionally exponentially blunted with a time constant of 0 9 msec.

Electrodes and shielding Electrodes were prepared from 1 0 mm diameter glass tubing containing a fine fibre glass filament. The electrodes were filled immediately before use. Intracellular voltage electrodes had resistances from 5 to 15 Mn. The external reference electrodes had resistances between 1 and 7 Mn. Voltage electrodes were filled with 3 im-KCI and were coated with colloidal silver paint to within less than 1 mm of their tip. The painted silver shield of each electrode was driven by the output of its electrometer. Current passing electrodes were filled with 231-K citrate and were enclosed in a grounded metal shield. The resistances of the current electrodes were not routinely measured. Temperature control The bath temperature was controlled by a feed-back circuit that maintained the bath within + 02 'C of the desired temperature. The variation of temperature throughout the volumne of the chamber (approx. 5 ml.) was less than 1 0 'C. The temperature in all of the experiments reported here was between 3 and 4 'C. Data collection and filtering Three channels were sampled during each sweep. These were (1) ATV, (2) V' - V0 and (3) It, the total current applied to the preparation. These analoguie voltages were led to conventional instrumentation amplifiers (Teledyne Philbrick 4252) followed by low pass active filters with a cut-off frequency of 1 1 kHz (Frequency Devices, model 736-LT4, 6 pole, Bessel response). Each channel was sampled in sequence at intervals of 200 #usec by a 12 bit analogue to digital (A-D) converter, multiplexer and sample and hold circuit (DEC, LPS-11). The A-D converter was under the control of a real time crystal clock that was also used to time and trigger the command voltage pulses using a 12 bit digital to analogue converter (Datel, DAC-69-12B). Pulse generation and data collection were under the control of a PDP 11-40 computer. The subroutine used during the data collection episode was written in machine language. Tile computer was equipped with a display processor (DEC, VT-11) so that the individual sweeps arid subtracted records could be viewed at the time of the experiment and during subsequent analysis.

342

R. F. RAKOWSKI

Experimental records were photographed from the computer display terminal. The photographic records reproduced here have been slightly retouched for clarity after reduction. The data collected during a sweep consisted of 1280 points sampled at intervals of 0-2 msec on each of the three channels. Prior to storage on magnetic disk the data were reduced to three arrays of 256 points representing 1 msec intervals of time using a 5 point filter algorithm (Kendall, 1973; Adrian & Rakowski, 1978). All computations are based on the values of the digitally filtered data. The records presented here are the results of the subtraction of a single pair of control and test records. The linearity of the data collection system was tested by voltage clamping a linear cable model of a muscle fibre. Subtraction of test and control pulses gave a flat response for all pulse magnitudes tested, with the exception that when the scaled response to four small (20 mV) control pulses was subtracted from a test pulse greater than 80 mV, the first point of the AV trace after the 'on' and 'off' of the step did not subtract exactly. Accordingly provision was made in the analysis program to exclude the first point at the 'on' and 'off' from the data analysis. In the determination of the areas of charge movement transients the first point was set equal to the second as described by Chandler et al. (1976a).

Calculation of cable parameters The method used to calculate passive cable parameters and the 'electrical diameter' of the fibre was identical to the method described in detail by Adrian & Rakowski (1978). The magnitude of the voltage step, length constant (A), internal resistance per unit length (ri), electrical diameter (d), membrane resistance (RBI) and membrane capacitance (Cm,) were calculated for each sweep and printed out during the experiment. These parameters, particularly the membrane resistance, gave a good index to the condition and stability of a fibre. Except where noted the parameters that have been normalized to the total membrane capacitance use the value of Cm determined in the control pulse that immediately preceded the test pulse. Throughout this paper the standard error is reported as the confidence interval.

Determination of charge movement areas and time constants Methods used to calculate charge movement areas and time constants are given by Adrian & Rakowski (1978). Solution The composition of the experimental solution was as follows: 40 mM-Rb2SO4, 55 mx-(TEA)2 SO,, 8 mM CaSO4, 350 mM-sucrose, 2 x 10-7 M tetrodotoxin, 1-5 mM-Na phosphate buffer, pH = 7-1 Tetrodotoxin was present to eliminate ionic current through the Na+ channel and TEA was present to block delayed outward ionic currents. Rb+ was used rather than K+ in order to reduce the current through the inward rectifier. The solution was made hypertonic by the addition of sucrose so that contraction did not occur. Muscles placed in this solution shrink, lose internal K+ and Cl-, and are depolarized to a resting potential of about -20 mV. (TEA)2S04 was prepared from an aqueous solution of TEA OH (Aldrich) by titration with 1N-H2SO4 to neutral pH. RESULTS

Reprimed charge movement The pulse protocol used in these experiments was designed to examine the recovery of membrane charge movement following long duration hyperpolarizing (repriming) pulses. The procedure is illustrated in Fig. 1. The diagram in Fig. 1A indicates the voltage pattern used to obtain a 'control' capacity current transient. In all experiments the muscle fibres were maintained at a holding potential of -20 mV. A 200 msec hyperpolarizing prepulse to - 100 mV was applied before beginning the data collection interval. The 256 msec long data collection period is indicated by the bold lines in Fig. 1A and B. This data collection interval consisted of 10 msec of baseline sampling at the prepulse potential of -100 mV followed by a pulse

343 REPRIMED CHARGE MO VEMENT 128 msec in duration to the desired membrane potential, Vt,,t, and finally a 118 msec long period sampled after the return to - 100 mV. Subsequent to the data sampling interval the membrane potential was returned to the holding potential. Integration of the capacity transient that results from such a pulse sequence gives a measure Vtest

-20

A

-20

B

P > 0 1) and for the 'off' data (0.5 > P > 0.2). The slope of the lines in Fig. 4 was 0*139 + 0 011 for the 'on' data and 0 204 + 0 018 for the 'off' data. The units of the slope are ,sF of additional

;

,-..m.~

at

~

+22

A

,,,,. ,.__..

_

-

~ ,o~?S~~IeJMVE

_

+

-20

59.St4,P.,A.% -40

_ s~~~~~~ ~~~-1 _ _ 20 26 -140 128 msec

Fig. 3. Records of reprimed charge for various test pulse voltages. Reprimed charge was determined following 100 sec repriming at - 100 mY. The test pulse voltage is indicated besides each trace. Same fibre as in Figs. 1 and 2.

'reprimed' capacitance per uF of total capacitance before repriming. In other words the 'on' data correspond to an increase of the effective capacitance of 13.9 % and the 'off' data correspond to a 20 4 % increase after repriming.

R. F. RAKOWSKI

348

Linear reprimed charge vs. voltage relationship for different repriming durations Data similar to that shown in Figs. 3 and 4 were obtained at two different repriming durations in the fibre illustrated in Fig. 5. The mean of the 'on' and 'off' reprimed charge movement is plotted for 25 see repriming at - 100 mV and for 100 see 50 40

°, Off

3030~~~~~~~~~~~~ -

_,1

C

20

,

On

-

0~~~~~~~~~~~~~~~~~~0 -10

E 0. 10)

-20 L -150

-100

-50 Test pulse voltage (mV)

0

50

Fig. 4. Linearity of reprimed charge. Charge movement areas from the data in Fig. 3 are plotted as a function of the test pulse voltage (Vtet). *, 'on' transient area; Q, 'off' transient area. See text for additional information. Note particularly that the negative charge movement determinations fall on or near the lines rather than showing the saturating behaviour of a non-linear membrane charge movement. Fibre 6-3.

repriming at -100 mV. Once again there was a statistically significant linear correlation of the data for both 25 and 100 see repriming (P < 0.01). The slope of the linear regression line for 25 see repriming was 0-109 + 0-011 and the slope for 100 see repriming in this fibre was 0-384 + 0-024. Data of this kind were obtained in a total of ten fibres. The mean value of the linear regression slope for 25 see repriming at - 100 mV was 0-176 + 0-027 (n = 3). The mean value of the slope for 100 see repriming at - 100 mV was 0-333 + 0-037 (n = 8). The one fibre on which determinations were made for both 25 and 100 see repriming durations is illustrated in Fig. 5. There was a statistically significant linear correlation in all ten fibres on which measurements were made (P < 0.01). It is also interesting to note that the mean value of the y intercept of the 100 see repriming data, that is, the magnitude of the reprimed charge movement expected for a depolarizing pulse from-100 to 0 mV, was 25-8 + 2-5 nC/jtF. This value is similar to the value of 24-5 + 1-7 nC/utF reported as the maximum value of 'charge 1' measured in normally polarized fibres by Chandler et al. (1976a).

REPRIMED CHARGE MOVEMENT

349

The kinetic of reprimed charge movements The reprimed charge movement transients shown in Fig. 3 are apparently symmetrical and do not appear to depend on the test pulse voltage. These observations are examined more quantitatively in Fig. 6. The time constants of the 'on' and 'off' charge movement transient were determined by a least squares fit to a single exponential. The time constants determined in three fibres from the same muscle are plotted 50

40

1 00 sec

30 U.

20

to) 20

sec ~~~~~~~~~~~25

/

10 0/

.210 *20 *~~~

-30 -150

-100

-50 Test pulse voltage (mV)

_

0

_

_

_

_

__~~~~~~~~~

___ _

50

Fig. 5. Linear reprimed charge movement for 25 and 100 see repriming durations. Records of reprimed charge were determined in a fibre after repriming at - 100 mV. *, 25 see; 0O 100 sec repriming duration. See text for additional information. Fibre 8-2. Electrode spacing, I = 250 jum, 1' = 125,um. Temp. 3*8 0C. A = 0-92 mm, ri = 34.9 MO/cm, rm = 301 kQ cm, d =36*4jum,C0 = 4.17,uF/cm2.

as a function of the membrane potential in Fig. 6A. The error bars indicate the range of values observed for the 'off' transients at -100 mV. The time constants are more rapid than those reported for charge 1 and are comparable to the magnitude of the delay expected to charge the capacitance of the transverse tubular system (Chandler et al. 1976a; Chandler & Schneider, 1976). The data in Fig. 6A do not show any obvious dependence of the reprimed charge movement kinetics on the membrane potential. The correlation coefficient calculated for these data indicated that there was not a statistically significant linear releationship between the measured time constants and membrane potential (0-2 > P > 0.1). On the other hand, the statement that the 'on' and 'off' transients are symmetrical is supported by the data replotted as shown in Fig. 6B. In this instance the 'on' time constant for a particular reprimed charge movement trace is plotted against the 'off' time constant of the same trace. The straight line drawn on the figure is the line of equality.

R. F. RAKOWSKI 350 Linear regression analysis of the data showed a statistically significant linear correlation of 'on' and 'off' time constants (P < 0 01 ) and a Student's t test of the slope of the regression line indicated that it is not significantly different from 1 0 (0 10 > P > 0.05).

6

A

5 .)

A

0

A

0 A

0

A

E4

I

I .-

*0 0

1

o

a

-1 5()

100 -50 Membrane potential (mV)

-j

50

0

6 B

5 0 CA

E

4

A 0

CU

CA

I A 0

A

3 .

0

CA A

0

2

C

0

1 L

0

1 4 2 3 5 6 Off time constant (msec) Fig. 6. Reprimed charge movement time constants. A, time constant of the decline of the reprimed charge transient is plotted as a function of the test pulse potential. Repriming potential -100 mY, repriming duration 100 sec. The error bars indicate the range of values observed for the 'off' transients at 100 mV. Data from three fibres, 0, fibre 8 1; A, fibre 8 2; *, fibre 8 3. B, the 'on' time constant for reprimed charge is plotted against the 'off' time constant. Same data as in A. The line is the line of equality. Additional information in text. Cable parameters: fibre 8- 1,1 = 250 /Sm, 1' = 125 jum, temp. 3.9 A = 0-83 mm, r, = 40-9 MO/cm, r0 = 280 kO cm, d = 33 7 jm, C=, = 6.83 #tF/cm2; fibre 8-2 given in Fig. 5; fibre 8-3, 1 250 jim, 1' = 125 jm, temp. 38 TC, A = 0 93 mm, ri = 18-8 MC/cm, r. = 162 kK2 cm, d = 50 3 jnm, Cm = 5 59 #sF/cm2. -

00,

=

The mean value of the 'on' and 'off' time constant for the reprimed charge data shown in Fig. 6 is 2-72 + 0-14 msec. A similar analysis was performed to determine the time constants of the control A V transients that were measured prior to repriming

REPRIMED CHARGE MOVEMENT 351 in these same fibres. The mean value of the time constants of the control A V transients is 1*63 + 0.05 msec. There is a statistically significant difference (P < 0-01) between the time constant of reprimed charge and the A V transient of the control pulse. This is consistent with the interpretation that reprimed charge represents an additional contribution of capacity within the fibre volume that would be expected to have a somewhat slower timecourse than the capacity transient measured under the control conditions. 2 sec 4 ~~~~~~ ~~~~~

Ao_

8

.1 6

64

#AF 2.6~~~

1~~~00

128 msec

Fig. 7. Records of reprimed charge for various repriming durations at - 100 mV. The reprimed charge records were determined for the repriming durations indicated besides each trace. The repriming potential was -100 mV. Fibre 7-2, 1 = 250,/srn it = 100 /sm, temp. 3-3 00, A = P-02 mm, rj 27-3 MCI/cm, r. = 282 kfl cm, d = 41-3 ,um, C. = 5-74 Mfl/CM2. The vertical current scale corresponds to 5 mV, A V magnitude.

R. F. RAKOWSKI

352

The time course of the increase in capacity Data from a fibre in which reprimed charge was determined for various repriming durations are shown in Fig. 7. The repriming voltage was - 100 mV and the test pulse voltage was + 1 mV. The repriming duration is indicated beside each trace. The mean value of each pair of 'on' and 'off' charge movement transients from the data in Fig. 7 is plotted as a function of the repriming pulse duration in Fig. 8. The data can be adequately described by a single exponential recovery process. The steady-state value of reprimed charge determined by a least-squares fit procedure 30 r

U-

-4.20

0

C

0) 0, a)

~0 0) EC

.

0. a)

10

.-

0 0

50 100 150 Repriming pulse duration (sec)

-20 200

Fig. 8. The time course of reprimed charge recovery. The mean value of the 'on' and 'off' reprimed charge movement areas from the traces shown in Fig. 7 are plotted as a fiction of the repriming time at - 100 mV.

is 25*9 nC/4ttF and the exponential time constant is 52 sec. Since the magnitude of the test pulse was 101 mV this steady-state value pf reprimed charge is equivalent to a 25 6 % increase in the effective capacity of the fibre. A similar experiment in another fibre gave a time constant of 39 5 see and a steady-state value of reprimed charge of 42-9 nC//tF.

Dependence of reprised charge on the repriming voltage Determinations of reprimed charge were made on a fibre at various repriming voltages. The mean values of each 'on' and 'off' charge transient are plotted in Fig. 9. The repriming duration was 100 see and the test pulse voltage was + 1 mV. The data clearly show that reprimed charge increases as the repriming voltage is made more negative. For convenience of comparison with steady-state inactivation curves

REPRIMED CHARGE MOVEMENT 353 determined in other experiments (for example, Fig. 10 of Adrian & Rakowski, 1978), the data have been fitted to the following equation: (2) Q = Q/(1 + exp ((V-V)/k)), where Q is reprimed charge (nC//LF), V is the repriming voltage (mV) and Q. V and k are arbitrary constants corresponding to the maximum value of Q, the mid point of the curve and a steepness factor. Such an equation might be appropriate to decribe the steady-state inactivation of a voltage dependent charge movement, but its use here is without theoretical basis. The parameters determined by a least squares fit to the data in Fig. 8 are Q = 44 3 nC/,tF, V = -93 mV and k = 204 mV. 60 50

-

U-

ZC 40 30 E

8. 20

-

10 10~~~~~~ 0 -150

-100

-50 Repriming voltage (mV)

0

50

Fig. 9. The effect of repriming voltage on reprimed charge. Reprimed charge was measured following 100 sec repriming at various repriming potentials more negative than the holding potential of -20 mV. Test pulse potential, + 1 mV. The points are the mean value of the 'on' and 'off' transient determined at each repriming voltage. See text for additional information. Fibre 7-5, 1 = 250 pm, I' = 100 pm, temp. 3.4 OC, A = 1*17 mm, r, = 13.3 MD/cm, rm = 189 kf2 cm, d = 59 5 jAm, Cm = 7 78 UF/cm2.

Similar data were obtained in two other fibres reprimed for only 25 sec. The parameter values in these two fibres are Q = 13 8 nC/,zF, V = -85 mV, k = 9.4 mV and Q = 15 4 nC//uF, V = - 110 mV, k = 32-8 mV. It was not possible to correct these data to the steady-state since data are not available that give the voltage dependence of the repriming rate constant. The effect of changes in tubular length constant on capacity measurements The data shown in Figs. 4, 5 and 6 support the suggestion that reprimed charge results simply from an increase in the effective capacity measured following a long duration hyperpolarizing pulse. Eqn. (3) given in Hodgkin & Nakajima (1972a) and derived by Schneider & Chandler (1976) can be used to calculate the 'effective 12

PH Y

28i

354 B. F. RA KO WSKI capacity' of a muscle fibre. The applicability of this equation is also discussed by Adrian & Almers (1974). a

=

s+

dCW(

Il(d/2AT) 2

(3)

4sIo~/4 where Cett is the effective capacity of a muscle fibre (,uF/cm2), C. is the capacity of the surface membrane (/tF/cm2), d is the fibre diameter (cm), Cw is the tubular wall capacity per unit volume of a fibre (#F/cm3). I, and Io are modified Bessel functions of order 1 and 0 and AT is the tubular length constant (cm). The constant Cw can be calculated from the specific membrane capacitance of the tubular wall Cw(,UF/cm2) using eqn. (4).

VW

awSt

(4)

where St/ Vi is the ratio of the tubular membrane surface area to the volume of the fibre. Theoretical values of effective capacity can be calculated by assuming AT = 100 #m, C. = Cw = 0-9 gF/cm2 and St/Vf = 3xlO3cm-' (Hodgkin & Nakajima, 1972b). Mobley & Eisenberg (1975) give a slightly different estimate for the ratio St/Vt, 2*2 x 103 cm-'. In order to predict the effective capacity that would be measured in fibres that have been shrunk in volume in the hypertonic solutions used in the present experiments the ratio St/Vi was increased by a factor of 2-2 which is the ratio of the osmolarity of the solution used in these experiments to the normal osmolarity of frog Ringer solution. Although there is considerable scatter in the data, the experimentally measured capacities before repriming are in general agreement with this prediction. The average increase in the measured capacity following 100 sec repriming was 27-8 + 2-9 % and 12-3 + 1-7 % for 25 sec repriming (data from twenty-one fibres having a mean diameter of 51 + 4 Itm). These values are comparable to the fractional increase in effective capacity calculated from the slope of reprimed charge vs. membrane potential data such as that shown in Figs. 4 and 5. Since it is not the surface capacity that is altered if a change in tubular length constant occurs, but only the volume capacity as predicted by the right hand term in eqn (3), it is more appropriate to calculate the average increase in volume capacity. This may be done by subtracting the surface contribution from the data. Assuming a specific surface capacitance of 0 9 #F/cm2 the average increase in volume capacitance is 33 0 + 3 6 % for 100 see repriming and 15 9 + 3.3 0/ for 25 see repriming at - 100 mV. If all of the data is corrected to the steady-state, the result gives a calculated increase in volume capacity of 40 3 + 3-6 0/ for repriming at - 100 mV. Using eqn (3) it is possible to estimate the maximum value of the tubular length constant that would be sufficient to explain the observed increase in effective capacity. That is, assuming that AT became infinite in the steady state, what value Of AT prior to reprising is required to produce a 40-3 % increase in volume capacity in a 51 jum diameter fibre? This result is obtained for d/2AT = 1-27, that is, the calculated maximum value of AT before repriming required to produce the observed increase in capacity is only 20,um. As discussed by Adrian & Almers (1976a) the tubular length constant in this experimental solution is expected to be longer than the fibre diameter. It is, therefore, possible that repriming has unmasked some reservoir of membrane capacity other than that associated with the T-tubular system.

REPRIMED CHARGE MOVEMENT

355

Changes in cable properties after repriming The tubular length constant AT can be altered by changes in a number of different parameters. If the increase in capacity is a result of an increase in AT we may gain some further insight into the mechanism of the apparent increase in AT by comparing the values of the cable parameters determined before and after the repriming pulse. The mean values of the cable parameters measured before repriming for all twentyone fibres are as follows: fibre length constant, A = 1-09 + 0-08 mm; internal longitudinal resistance, ri = 24-3 + 3 0 MCI/cm; membrane resistance, rm = 235 + 22 kil cm; mean fibre diameter, d = 51 + 4 ,tm. In the seven fibres reprimed for 25 sec at - 100 mV the cable parameters measured after the repriming pulse are A = 0 91 + 0-15 mm; rj = 26-2 + 5 9 MK/cm; rm = 164+ 30 kQ cm; d = 55+ 14,sm. After 100 sec repriming at - 100 mV the cable parameters measured in fourteen fibres are A = 1-21+0d15mm; ri = 16.0+2-9MQ/cm,rm = 192+33kQcm; d = 66+7 um. The fibre length constant does not change appreciably, but the fibre diameter increases and the internal resistance and membrane resistance decrease after repriming. This pattern can be seen more clearly by calculating the ratio of each parameter after reprising to the control value observed before repriming for each individual fibre. Using the data from the fibres reprimed for 100 sec and expressing these ratios as a percentage, A was 103+6%; fibre diameter, 130+10%; ri, 70+8% and rm, 69 + 7 % of the control value measured before repriming in the same fibre. The change in length constant is not statistically significant (P > 0.5), but the increase in fibre diameter and decrease in ri and rm are statistically significant (P < 0.01). Bracketed cable measurements The cable measurements made following long duration repriming pulses suggest that the fibres swell and that the membrane resistance is decreased. However, this result may arise as an artifact of increased current leakage around the microelectrodes. In order to examine this possibility cable measurements were made on fibres (1) initially held at -20 mV (2) hyperpolarized by changing the holding potential to - 100 mV for 5 min and (3) restored to the original holding potential of -20 mV for 5 min. In each case the membrane capacity was measured for + 20 mV voltage steps from a prepulse potential of - 100 mV. At this voltage there should be little or no contribution to membrane capacity from the non-linear charge known as 'charge 1' (Chandler et al. 1976a). In the five fibres on which measurements were made there was an increase in the capacitance measured after 5 min of hyperpolarization to a value that averaged 1-5 times greater than the measurement at the -20 mV holding potential. This is consistent with the previous observations that there is an increase in linear capacitance following a long duration repriming pulse. In two fibres it was possible to complete the protocol and bracket the measurement of cable parameters by returning to the -20 mV holding potential. In one fibre there was a decline in Rm from 4 05 kQ cm2 initially to a final value of 1-91 kQ cm2 at the end of the experiment. This is consistent with the interpretation that an 12-2

3566

P. P. RAKOWSKI

increase in leakage around the impalement sites was occurring during the course of the experiment. This fibre showed an apparent increase in fibre diameter from 58 to 97 ,tm and a decrease in the measured value of ri from 13-7 to 4-9 Mfl/cm when it was hyperpolarized. It appears, therefore, that a fibre that is damaged at the impalement sites will give artifactual changes in cable parameters that are comparable to the magnitude and direction of the changes measured in the repriming experiments. A second fibre returned to very nearly the same value of Rm at the end of the experiment (4.64 kQ cm2 initially and 4*32 kQ cm2 finally). In this instance neither the fibre diameter (66 jsm) nor rj (10.6 MQ/cm) changed significantly when the fibre was hyperpolarized. This suggests that the apparent swelling and decrease in rj and rm that was measured in the cable determinations in repriming experiments is an artifact of current leakage around the electrode impalement sites. This means that it is not possible to choose between various alternative explanations for the observed increase in capacity based on these cable measurements. It should be noted, however, that an increase in capacity is observed in all instances whether or not there is a decline in Rm during the course of an experiment. DISCUSSION

The principal result of these experiments is the observation that reprimed charge movement measured following long duration hyperpolarizing pulses is simply an increase in linear capacity. A major question is whether the reservoir of capacitance within the transverse tubular system is sufficient to account for the observed increase. The experimental results can be quantitatively explained by tubular capacity alone only if the tubular length constant increases from an initial value of 20 ,tm or less prior to repriming to a value that is sufficiently long to measure the total membrane capacity without significant voltage decrement in the tubular system. Schneider & Chandler (1976) have estimated the length constant of the transverse tubular system from the capacitance change observed by fully activating the inwardly rectifying K+ conductance system. They found that in 100 mM-K+ when the inward rectifier was fully activated the mean value of the tubular length constant was 31 + 4 ,um. In Rb-containing solutions inward rectification should be markedly reduced, the membrane conductance very low and consequently AT should be much larger than the value of AT calculated for the condition in which the inward rectifier is fully activated. Adrian & Almers (1976a) have also argued that in a hypertonic Rb sulphate solution the tubular length constant should be sufficiently large so that there will be essentially no radial variation in the steady-state voltage across the fibre. If this is correct the capacity increase seen after repriming cannot result solely from an increase of AT within the transverse tubular system. It is important to note that the mean specific membrane resistance (Rm) measured in the twenty-one fibres of this study prior to repriming was found to be 3-6 + 0-4 kn/cm2, a value that is even larger than the value of Rm determined by Adrian & Almers (1976a) at comparable electrode spacing (2.1 + 0 4 kQ/cm2). These observations are consistent with the speculative but plausible hypothesis that the increase in capacitance following repriming results from gaining electrical

REPRIMED CHARGE MOVEMENT 357 access to the sarcoplasmic reticulum. Stereological measurements of the membrane area of the sarcoplasmic reticulum by Mobley & Eisenberg (1975) indicate that the total area of the sarcoplasmic reticulum is about 35 times that of the surface membrane. If there was no steady-state potential decrement along the sarcoplasmic reticulum we would expect a six- or sevenfold increase in capacity if the transverse tubular system were to become electrically continuous with the sarcoplasmic reticulum. A more realistic view, however, is that there will be substantial potential nonuniformity along the membranes of the reticulum and a voltage decrement across any access resistance across the junction between it and the tubular system. It is possible, therefore, that repriming may produce a condition in which electrical continuity is established between the sarcoplasmic reticulum and tubular system. The result originally expected for these experiments, namely that hyperpolarization restores a non-linear membrane charge movement, seems to be ruled out by the observations in Figs. 4 and 5. The majority of reprimed charge movement, as measured by this pulse protocol, is linear. The observation that the reprimed charge movement time constant does not depend on membrane potential (Fig. 6) supports this conclusion. If we accept the conclusion that the majority of reprimed charge movement is linear, a serious question is raised about the viability of the proposal that the inactivation and repriming of non-linear membrane charge movement accounts for the threshold mechanical repriming behaviour of muscle (Adrian et al. 1976). There are a number of differences between these experiments and previous work that may account for the failure to observe the repriming of a significant quantity of nonlinear membrane charge. The present experiments were done on the semitendinosus muscle of Rana pipiens in hypertonic solutions, while the mechanical repriming experiments of Adrian et al. (1976) were done on the sartorius muscle of Rana temporaria in isotonic solutions. A major discrepancy rests on resolving the voltage dependence of subthreshold reprimed charge. This measurement is a difficult one to make since the magnitude of charge movement observed below the mechanical threshold is quite small. Considering the uncertainty of the individual measurements, the data in Fig. 13 of Adrian et al. (1976) might be described just as well by a straight line rather than the non-linear Q vs. V relationship used. The initial observation of charge inactivation and recovery was made by Chandler et al. (1976b) who observed that the magnitude of the charge transient declined exponentially if the holding potential was changed from -80 to -20 mV. Charge recovered exponentially when the holding potential was restored to -80 mV. It was not determined whether the charge that declined and recovered was, in fact, non-linear. It is possible that a decrease in linear capacitance could explain the observed decrease in charge, but this is not very likely since the time course of linear and non-linear components would have had to coincide exactly to produce a completely flat trace. A second possibility is that non-linear charge is immobilized by relatively brief depolarizations (minutes) and that it becomes irreversibly immobilized after chronic depolarization (hours). Irreversible immobilization would explain why repriming of charge was observed by Chandler et al. (1976b) in normally polarized fibres, but not observed in these experiments on chronically depolarized fibres. On the other hand, if charge is irreversibly immobilized it cannot explain mechanical

358 R. F..RK RAKOWSKI 358 B WK repriming. Repriming of contraction can occur even after a chronic depolarization of more than 1 hr. The results, therefore, are not consistent with the suggestion that reprimed charge accounts for mechanical repriming. The present results do not rule out the suggestion that non-linear membrane charge movements in muscle are related to the activation of contraction. Indeed, it is clear that the voltage-dependent activation of contraction must be accompanied by a gating signal of some kind. These results do suggest, however, that a simple increase in the linear capacity of muscle fibres following prolonged hyperpolarizing pulses accounts for the observed 'reprimed charge movement'. It may be that this results from an increase in tubular length constant or other mechanism that unmasks additional linear capacity within the fibre volume, however, it is also clear that such a linear mechanism cannot by itself explain the voltage dependence of mechanical

activation. I thank Dr Wolf Almers and Dr R. H. Adrian for helpful criticism of the manuscript. This work was supported by a grant from the Muscular Dystrophy Associations of America and by the U.S. National Institutes of Health, grant no. AM-16528. REFERENCES

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