J. PhywiOl. (1976), 254, pp. 285-316 With 11 text-ftigurea Printed in Great Britain

285

EFFECTS OF GLYCEROL TREATMENT AND MAINTAINED DEPOLARIZATION ON CHARGE MOVEMENT IN SKELETAL MUSCLE

BY W. K. CHANDLER, R. F. RAKOWSKI* AND M. F. SCHNEIDERt From the Department of Physiology, Yale University School of Medicine, 333 Cedar Street, New Haven, Connecticut, U.S.A.

(Received 13 February 1975) SUMMARY

1. Voltage-clamp experiments were carried out using the techniques described in the preceding paper. 2. In one series of experiments an attempt was made to disrupt the T-system with glycerol treatment. Muscles were soaked in Ringer + 400 mm glycerol for 1 hr at room temperature, transferred to Ringer + 5 mm calcium + 5 mm magnesium for 20-30 min, and then cooled to around 2° C and placed in an isosmotic test solution containing tetrodotoxin for electrical measurements. 3. The density of charge seen in isosmotic tetraethylammonium (TEA) solution with strong depolarizations, normalized according to fibre capacitance, was decreased by glycerol treatment to about one third the amount seen in untreated hypertonic fibres. 4. An analysis of fibre capacitance revealed that only 0 4 of the tubular capacitance was removed by this particular glycerol procedure. If the density of charge with respect to capacitance is corrected for this decrease in capacitance, the results indicate that glycerol treatment removed or immobilized 0-77 of the charge initially present. Thus the effect of glycerol treatment to reduce charge does not depend entirely on disrupting the electrical continuity of the T-system. 5. The effects of maintained depolarization were studied using a TEA Ringer made hypertonic with sucrose. When the voltage was changed from -80 to -21 mV the measurable charge movement declined exponentially to zero with a time constant of 13-24 sec. On repolarization the process recovered exponentially to the initial level with a time constant of 21-53 sec. * Present address: Department of Physiology and Biophysics, Washington University School of Medicine, St Louis, Missouri, U.S.A.

t Present address: Department of Physiology, University of Rochester School of Medicine, Rochester, New York, U.S.A.

286 W. K. CHANDLER AND OTHERS 6. Experiments were also carried out using a sodium Ringer made hypertonic with sucrose. For small depolarizations only charge movement currents were seen, whereas for large depolarizations large delayed ionic currents, presumably carried by potassium, were observed. With moderate depolarizations in the range V = -40 to -30 mV, both components were of comparable magnitude.

7. A plot of the fractional charge movement (Q/Qmax) vs. V fitted at moderate depolarizations is similar to that of n., vs. V fitted at larger depolarizations. Values of n. were obtained by fitting the delayed ionic current to n4( V-VK). For voltages between -40 and -30 mV the time constant for charge TQ was always less than rn; values of Tn/rQ varied from 1-6 to 4-3. 8. Glycerol treatment had little if any effect on the kinetics of delayed rectifier currents. Values of gK measured in isosmotic solution following glycerol were about one third the values obtained in untreated fibres in a hypertonic solution (osmolality three times normal). The threefold difference in k is probably due to a similar difference in internal potassium concentration. 9. These results and others are difficult to reconcile with the idea that the charge movement process acts as a gate for potassium channels. It seems more likely that charge movement is a step in the activation of contraction. INTRODUCTION

In the preceeding paper (Chandler, Rakowski & Schneider, 1976) a general description was given of a voltage dependent charge movement in skeletal muscle. To a first approximation the steady-state properties could be described by assuming that the charge can occupy one of two possible positions with the first being favoured at highly negative membrane potentials. The amount of charge in the second position, Q, follows

Q(V)

Qmax

exp[-(V-V)/lk]'

(1) t+ where Qmax is the total amount of charge, V is the potential at which the charge distributes equally between the two positions, and k is a factor which determines the steepness of the curve. The average values from six fibres were Qmax = 25 nC//tF (normalized for fibre capacitance), V = -44mVandlk = 8mV. The characteristics of the charge movement suggest that its function might be to provide voltage dependence for a physiological process. The process might be turned off at the resting potential, when the charge is in position 1, and turned on with depolarization, when the charge moves to

GLYCEROL TREATMENT AND CHARGE MOVEMENT 287 position 2. Along these lines the kinetics as well as the steady-state properties suggest a role either in activating contraction or in gating potassium channels as the most plausible possibilities. The purpose of the experiments in this paper was to learn more about some qualitative features of the charge in hopes of deciding which of the above possibilities is more likely. The results favour a role in the activation of contraction. A preliminary account of some of the experiments has already been given (Chandler, Schneider, Rakowski & Adrian, 1975). METHODS The experimental techniques and methods of analysis were the same as described in the previous paper. Solutions are given in Table 1. For isosmotic conditions the fibre radius a was calculated from eqn. (2) which applies to a simple cylinder

s~oRri

(2)

The longitudinal resistance, ri, was determined as described in the Methods section ofthe previous paper. Values of Ri, the internal resistivity, were taken from Hodgkin & Nakajima (1972a), namely Ri = 169 n cm at 200 C and Q10 = 0 73. TABLE 1. Solutions

Reference A B C

Na + 117-5 117-5

D E F

120-0 117-5

TEA + 117.5 117-5 -

K+

Rb + 5 5 5 5

Ca ++

1-8 1-8 1.8 18

2-5

1-8

5

1.8

Cl126 126 126 126 126 126

Sucrose 467 467

Solutions also contained tetrodotoxin 10-6 g/ml (except for E) and 1 mm Trismaleate buffer (pH 7-1). RESULTS

Effect of glycerol treatment on charge movement transients An important question at this stage of the investigation was whether the movable charges are located primarily in the surface membrane or in the T-system. A tubular location would be compatible with a role in the activation of contraction, whereas a location predominantly on the surface would suggest some other function such as gating delayed rectifier channels. In an attempt to answer this question experiments were carried out using glycerol treatment which has been reported to sever the electrical continuity of the T-system from the surface (Fujino, Yamaguchi & Suzuki, 1961; Howell & Jenden, 1967; Eisenberg & Eisenberg, 1968; Gage &

288 W. K. CHANDLER AND OTHERS Eisenberg, 1969a; Eisenberg & Gage, 1969; Gage & Eisenberg, 1969b). Muscles were placed in Ringer (solution E) + 400 mM glycerol at room temperature for an hour, then transferred to Ringer + 5 mm calcium + 5 mM magnesium (Eisenberg, Howell & Vaughan, 1971). 20-30 min later the muscles were cooled to around 20 C. At this point propagated action potentials without visible contractions were observed when fibres were A

-60 mV

B

-51

C

-41

D

-31

E

-12

1 mV [

'f l

o0

+17

l

100 msec

Fig. 1. A V(test-control) records from a 'glycerol-treated' fibre. Average of four runs. The fibre contracted slightly in records E and F. Voltage during the test pulse indicated beside each record. Electrode spacing 1 = 186 ,j, 1' = 19 #u. Cable measurements gave A = 0-1371 cm, r, = 3-825 Me/cm, cm = 01322 gF/cm so that 1 mV on AV corresponds to 0 504 IzA/cm or 3-81 ,tA/f#F. Fibre radius estimated to be 50 It. Fibre 6 6, 1.80 C, solution D. Initial resting potential -67 mV, holding potential -80 mV.

electrically stimulated with an internal micro-electrode. Finally the muscles were transferred to solution D. A total of 1 2-1-6 hr elapsed from the time of removal from the glycerol solution to the time that experiments began. Voltage-clamp experiments were successfully carried out in twelve fibres from four muscles from Rana temporaria and in two fibres from one

GLYCEROL TREATMENT AND CHARGE MOVEMENT 289 muscle from R. pipiens. The glycerol method was partially successful in that treated fibres could be depolarized without producing visible contraction using pulses which would have produced contraction in untreated fibres. In every case, however, movement occurred if the fibre was sufficiently depolarized with pulses lasting 100 msec, possibly because our recovery time, following glycerol, at room temperature was less than that used by Eisenberg et al. (1971). Fig. 1 shows A V records from a fibre in which it was possible to go as far positive as 17 mV without dislodging the electrodes. In all traces the charge movement transient was much less than that seen in normal fibres 30Il

20

10. 10

-100

-80

-60

0 -40 -20 Test potential (mV)

.20

40

60

Fig. 2. Voltage dependence of charge movement in glycerol treated fibres. Open symbols represent time integrals of charge movement transients in which no visible movement occurred; filled symbols show determinations which were associated with slight contractions. 0, @, fibre 6.6; LI1, U, fibre 7.2; A, A, fibre 8.3. The continuous curve was drawn from eqn. (1) with values obtained in normal fibres in hypertonic solution, namely V = - 44 mV, k

=

8 mV and

Q.. =

25 nC//tsF. The dashed curve was calculated

parameters for charge but assuming a high tubular access resistance. In' this case eqn. (10) was used with p = 0-61, r = 1/7 and

using the

same

E

mV as described in the text. Cable properties of the fibres are

= - 80

given in Table 2.

(Chandler et al. 1976) although it was not entirely absent. Traces E and F show movement artifacts due to slight contractions. Charge, normalized by fibre capacitance, is shown in Fig. 2. The circles are from the experiment in Fig. 1. Two other symbols show data from the only other fibres in which a determination was possible for V > 0 mV.

W. K. CHANDLER AND OTHERS The filled symbols are associated with measurements in which contraction occurred. This usually resulted in movement artifacts, such as seen in E and F in Fig. 1, which introduced small uncertainties into the area measurements. The points in Fig. 2 (as well as the results from all other experiments, Table 3) all lie well below the continuous curve which represents the average Q vs. V curve for normal fibres in hypertonic solution (eqn. (1) this paper and average parameters from Table 1 in the previous paper). Thus glycerol treatment results in a decrease in the average density of charged groups in those membranes which are electrically continuous with the surface. 290

Cable properties of glycerol treated fibres The simplest interpretation of the results in Fig. 2 is to suppose that the charged groups are mainly or entirely located in the tubular membranes and that the effect of the glycerol procedure was to disrupt most of the tubular continuity. An analysis of cable properties, however, reveals that the action of glycerol was somewhat more complicated. Part A of Table 2 shows cable properties tabulated from glycerol treated fibres in solution D. Column (2) gives ri, (3) gives ricm and (4) gives the estimate of fibre radius from eqn. (2). Column (5) gives the measured fibre capacitance expressed in terms of surface membrane area. Column (6) gives the capacitance expected for an untreated fibre of the same radius, calculated as described in the Table. The values in column (7) represent the ratio of measured to untreated tubular capacitance, obtained as the ratio of column (5) to (6) after 0.9 #uF/cm2 was subtracted from each value as the contribution of the surface membrane. The average value, 0-61, indicates that after glycerol treatment 0-61 of the tubules were still electrically continuous with the surface membrane. The three fibres represented in Fig. 1 gave somewhat lower values, 0 49, 0 27 and 0 39. A similar reduction in tubular capacitance following glycerol treatment was also measured using solution C (Table 2, part B). Since electrical shunts around the sites of electrode impalements would produce an error in the estimate of ri, it seemed desirable to analyse the data somewhat differently, using a method which does not depend on experimentally evaluating rt. The determination of the product ricm is only slightly affected by shunt errors (Schneider & Chandler, 1976) and its value is relatively insensitive to the value of fibre radius, so that experimental values of ricm may be compared with values expected on the basis of 0 9 juF/cm2 for surface capacitance and 2-7 x 103 #tF/cm3 for volume (tubular) capacitance (Schneider, 1970; Hodgkin & Nakajima, 1972b).

GLYCEROL TREATMENT AND CHARGE MOVEMENT

291

TABLE 2. Cable properties of glycerol-treated fibres

(1)

(2)

(3)

(4)

(5)

(6)

Total capacitance (,#F/cm2 surface)

(7)

Expected Fraction of for expected Radius untreated tubular ri rrcm Fibre (MD/cm) (sec/cm2) bum) Measured fibres capacitance Part A, TEA solution 58-3 0-579 6.1 2-739 8-77 5.77 0-62 42-5 4.59 0-637 6.2 5-200 6-64 0-64 2-12 27-9 0-446 12-003 6.3 4-67 0-32 46-2 0-657 6.4 4-403 5-14 7-14 0-68 42-9 0-806 6.5 5-147 5-81 6-69 0-85 4-21 50-0 0-506 6.6 3-825 7-65 0-49 36-8 0-942 7-107 5.73 6.7 5-87 0-97 44.4 0-735 4-921 5-35 6.8 6-89 0-74 0-339 2-65 48-9 7.2 4-160 7-50 0-27 35-6 0-489 2-79 5-71 8.3 7-835 0-39 54-5 0-680 3-122 9.2 6-37 8-26 0-74 9.3 2-578 8-07 59-9 0-783 8-99 0-89 0 480 2-51 30-9 9-865 16.2 5-07 0-39 32-2 3-17 0-583 9090 5-25 16.3 0-52 0-61 + 0-06 Average S.E. of mean 0-619 + 0-044 43-6 + 2-7 14.1 14.3 14.4 14.6 Average ± S.E.

Part B, sodium solution 0-584 50-6 4-80 3-832 52-9 4-46 0-516 3-484 6-30 0-627 61-8 2-561 69-2 6-84 0-613 2-061 of mean 0-585 ± 0-025 58-6 + 4.3

7.73 8-04 9-24 10-24

0-57 0-50 0-65 0-64 0-59 + 0-03

Part A gives measurements made in solution D, Table 1. Part B was obtained using solution C. The values for radius in column (4) were calculated from column (2) using eqn. (2). Column (5) was calculated from the values in columns (2)-(4). The values in column (6) were determined using 0 -9 #aF/cm2 for surface capacitance, 2-7 x 103 uF/cm3 for volume (i.e. tubular) capacitance (Schneider, 1970; Hodgkin & Nakajima, 1972b) and values in column (4) for radius. The ratios in column (7) were calculated from columns (5) and (6) after subtracting 0-9 uF/cm2 for surface capacitance. Temperature varied from 0-5 tox2-88 C, electrode spacing from 140 to 233 /tm.

The tubular contribution to ri cm is independent of fibre radius and is given by the product of R1 and volume capacitance. At 2° C, Ri is estimated to be 298 Q cm making the tubular contribution 0-804 sec/cm2. The surface contribution depends inversely on the first power of radius; for a fibre of radius 40 4am the calculated amount is 0-134 sec/cm2 at 20 C. The average experimental value for ricm is 0-619 sec/cm2 (column 3 of 13

P HY 254

W. K. CHANDLER AND OTHERS Table 2, part A). If 0*134 sec/cm2 is allowed for surface, the difference 0-485 sec/cm2 represents the tubular amount. This value is 0-60 times that expected for an untreated fibre, 0-804 sec/cm2; the factor 0-60 is similar to the average value 0-61 in column (7) of Table 2, part A. The general conclusion is that the glycerol treatment which was used resulted on the average in only 0 4 of the tubular membranes being electrically isolated from the surface. 292

Effect of glycerol treatment on magnitude of charge movement Measurements of the magnitude of the charge are tabulated in Table 3. Column (2) gives the most positive test voltage at which a determination of charge could be made. Measurements were usually attempted at more positive potentials but were not accurate because of fibre movement. Column (3) gives the amount of charge movement which was observed and column (4) gives the amount expected for an untreated fibre at the indicated voltage. The latter value was calculated from eqn. (1) using average values for V, k and Qmax (Table 1, Chandler et al. 1976). Column (5) gives the ratio of charge observed to charge expected. The average value is 0 34. Thus it would appear that the average density of movable charged groups in those membranes which are electrically continuous with the surface was decreased to about one third normal by glycerol treatment. The values for charge movement in columns (3) and (4) of Table 3 have been normalized for fibre capacitance. In order to estimate the fraction of the original charge movement which remained following glycerol treatment it is necessary to determine the fraction of total fibre capacitance which remained (column (6)). The product of columns (5) and (6), given in column (7), represents the fraction of the original amount of movable charge which survived the glycerol procedure. The average value, 0-23, is considerably smaller than the fraction of electrically accessible tubules which survived glycerol, 0-61 (Table 2, column 7). The ratio of the fraction of charge to the fraction of tubular capacitance following glycerol is given in column (8) of Table 3. This ratio would be expected to be 1.0 if the charge were located only in the T-system and if the sole effect of glycerol treatment were tubular disruption. In every fibre the ratio was less than unity, indicating that the charge movement process was disrupted more than tubular continuity. For example, fibre 6-6 in Fig. 1 had about 0 49 times the normal amount of tubular capacitance but only 0-22 times the normal amount of charge, giving a ratio of 0 45. The other fibres in Fig. 2, references 7-2 and 8-3, gave ratios of 0-56 and 0326. The conclusion from the experiments is that glycerol treatment cannot

GLYCEROL TREATMENT AND CHARGE MOVEMENT

293

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W. K. CHANDLER AND OTHERS 294 be used to determine the location, tubular or surface, of the charge movement. This is because the treatment appears to have at least two actions; it exerts a direct effect on the charge movement, tending to remove or immobilize it, in addition to its known effect of severing tubular continuity. The conclusion does not depend critically on the exact value of capacitance assumed for the surface membrane. The calculations in Tables 2 and 3 have been repeated using 2 psF/cm2 for surface membrane and 2-7 x 103 /IF/cm3 for volume capacitance. On this basis ten of the fourteen fibres had more than 0-2 of the tubular capacitance expected for untreated fibres (column (7) of Table 2). The remaining four fibres, with values 0-03-0*16, would be considered to be successfully detubulated and were not included in the remaining steps of the calculations.

RX

CT

Q

ET Fig. 3. Lumped equivalent circuit for the tubular system. R. is the access resistance, RT is the tubular membrane resistance, E is the tubular resting potential, CT is the tubular membrane capacitance and Q refers to the charge movement.

Using 2 #uF/cm2 for surface capacitance the average value of column (7), Table 2A,is 0 53 ± 0-05;ofcolumn(7), Table 3,0-23 + 0-02; of column (8), Table 3,0 49 ± 0 07. Thus the calculations indicate that on the average 0-23 of the charge and 0 53 of the tubular capacitance survived the glycerol treatment. Effect of access resistance on charge movement and tubular capacitance The impedance measurements of Valdiosera, Clausen & Eisenberg (1974) indicate that glycerol treatment may act by increasing the access resistance of the tubular system by a factor of 50-60. If this is the case and if the charge is located in the Tsystem one would expect that measurements of charge movement currents would be distorted. In this section some of the theoretical consequences of this possibility are explored. The general conclusion is that the introduction of an access resistance cannot explain the observation that glycerol treatment appears to reduce charge movement more than tubular capacitance. Fig. 3 shows the lumped equivalent circuit of the T-system used in the calculations. R. is the access resistance in series with the tubular membrane. Tubular resistance

GLYCEROL TREATMENT AND CHARGE MOVEMENT 295 is given by RT, tubular capacitance by CT, and tubular resting potential by E. The element denoted by Q represents the electrical pathway for charge movement. If E is set by the potassium and rubidium gradients, as seems reasonable, then its value would be close to the resting potential or VHp, the holding potential. In this case charge movement transients would not occur with small voltage steps around Vrp. The experimental measurement of tubular capacitance would depend only on CT, RT and RB, giving an apparent value of P2CT (cf. eqn. (15), Adrian & Almers, 1974) where p

=

-RT/(R.+RT)-

(3)

If the only effect of glycerol were to increase R8 and if p were equal to 1 before glycerol treatment, the average value of p2 after glycerol treatment would be 0-61 (column 7 of Table 2, part A). The corresponding value of 0-78 for p would indicate R8 = 0-28 RT. The question is whether this amount of access resistance could explain the large decrease in charge movement which was observed experimentally. If V is used to denote the potential across the circuit and VT is used to denote the potential across the tubular membrane, the tubular current iT is given by

iT= (VT-E)IRT + CT(dVT/dt) + dQ/dt = (V-VT)IR,.

(4) (5)

In the steady state

VT=pV+(1-p)E.

(6)

For a step change in voltage from V. to V the transient component of current is given by tT minus the steady-state current (V - E)/(R, + RT). Combining eqns. (3), (4) and (5) one obtains for the transient component

RT E+R

= PCT t +P de

(7)

Integrating from t = 0 to oo and using eqn. (6) one obtains f (iT-~is+ ) dt = p2CT( V-)+pQ{p+ [1-p]E} -pQ{pV0±[1-p]E}.

(8)

The first term on the right side, P2CT (V -V.), represents the integral of the passive capacitative current which is subtracted by the control record. The remaining terms give the observed charge movement. If V and V. are interchanged, it can be seen that the sign but not the magnitude of the right side of eqn. (8) is changed so that Qoif = - Qo0i. For V. = VHP and for negative values of E, the last term in eqn. (8) is negligible so that the observed charge Q. is given by (9) Q. = pQ{pV+[1-p]E}. Since the purpose of the calculation is to illustrate the effect of access resistance on the measurement of charge movement, the limiting case of placing all the charge in the T-system will be considered. If the capacitance per cm2 of surface or tubular' membrane is given by C., then a length of fibre having 1 cm2 total membrane (surface plus T-system) would have a measured capacitance C of CQ[r + p2(l - r)], where r is the ratio of surface area to total membrane area. Combining this relationship with eqns. (1) and (9) the ratio of observed charge movement to measured capacitance, Q0/C, is given by F P 1 F 1 1 QoIC QMa= + p2(1 (10)

-r)J L1+exp[-(pV+[1-p]E-V!)k]J

which for R. = 0 and p = 1 is identical with eqn. (1) normalized for capacitance.

296

W. K. CHANDLER AND OTHERS

The three effects of introducing an access resistance are (1) to increase the plateau value obtained with large depolarizations, (2) to broaden the curve and (3) to shift the midpoint. The factor by which the plateau is increased is given by the first term in brackets in eqn. (10). The steepness factor for the curve, k, is replaced by k/p and the midpoint is shifted from V to V/p - E( 1- p)/p. Cable analyses for the three fibres in Fig. 2 gave values of 0 70, 0-52 and 0*62 for p (square root of column 7 of Table 2A). The dashed curve in Fig. 2 was calculated from eqn. (10) using the average of these three values for p, 0-61, a value of 1/7 for r (appropriate for a fibre radius of 40 #u) and E = -80 mV. Once p and r are determined the increase in plateau is smallest for the case in which all the charge is located in the T-system, an assumption used in deriving eqn. (10). If some of the charge is located on the surface the increase in plateau is even larger, approaching Qmax/[r + p2(l - r)] for the limiting case in which all the charge is on the surface. The failure of the theory to provide a fit shows that the ability of glycerol treatment to reduce the measured movable charge density cannot be explained simply by introducing an access resistance.

Effect of maintained depolarization on charge movement One question which naturally arises is whether the properties of the charge movement are altered during prolonged depolarization when a muscle becomes mechanically refractory (Hodgkin & Horowicz, 1960) and delayed rectification is inactivated (Nakajima, Iwasaki & Obata, 1962; Adrian, Chandler & Hodgkin, 1970). Fig. 4 shows results from an experiment designed to examine this point. Trace a in Fig. 4A shows a record of A V(test-control) obtained with a 59 mV pulse from the holding potential -80 mV. This record, as well as the others in the Figure, represents the difference between single test and control traces, not signal averaged, with ionic currents subtracted. A diagram of the voltage pulses for the control and test sequences for determinations from VHP = -80 mV and VHP = -21 mV is shown in the lower part of the Figure. At t = 0 the holding potential was changed from -80 to -21 mV. Traces b-f in Fig. 4A show current records obtained at different times, indicated at the left, following the change to -21 mV. The direction of the transient is inverted from that shown in trace 4Aa because the direction of the voltage pulses has been reversed. The 'on' of traces b-f should be compared with the 'off' of trace a, and the 'off' of b-f should be compared with the 'on' of a. It is clear from the records that the magnitude of the charge movement gradually declined after the holding potential was changed; after 2 min it was virtually absent. Trace a, Fig. 4B, was taken just before the holding potential was returned to -80 mV. Traces b-f show the recovery of the charge movement at different times following the change in VHP. Recovery was complete as indicated by the similarity of traces Aa and Bf. During both the dis-

GLYCEROL TREATMENT AND CHARGE MOVEMENT 297 appearance and the recovery of the charge movement the 'on' and 'off' areas were equal as shown in Fig. 5. Fig. 6 shows a plot of charge movement as a function of time. The time courses of the disappearance, shown by the filled circles, and of the recovery, open circles, were exponential. The fitted curves in Fig. 6 give time constants of 23-5 sec for the inactivation at -21 mV and 38-2 sec for the recovery at -80 mV. Table 4 gives values of time constants in this and three other experiments. A

VHP=-21 mV ~~~~~~~~~~~~a

a

VHP

~-130

-80 MV

VHP=-80 mV b

=-21 mV b s a sec W--W

14 __

sec

_

6 sec

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13

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d

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Voltage steps for VHP =-21 mV

-21 mV -139

-

U

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1lI-00msec Voltage steps for VHP = -80 mV

Fig. 4. Effect of maintained depolarization on charge movement. Each record is the difference of a single test and control A V record with base lines subtracted. 4Aa, record taken from holding potential VHP = -8.0 mV. 4A, b-f and 4 Ba, records taken after VHp was changed to -21 mV. Time after the change is indicated to the left of each record. Total duration at VHP= -21 mV was 136 sec. 4 B, b-f, records taken following return of VHp to -80 mV; time given at left. The lower part of the Figure shows the pattern of voltage pulses for the, control (C) and test (T) sequence for VHP = -21 mV (left) and VHp= -80 mV (right). The pulses were designed so that for VHP = -21 mV the period of hyperpolarization was as short as possible, and for VHp = -80 mV the depolarization was as short as possible. Electrode spacing I = 186 sum, I' = 28 j#m. Cable measurements gave A = 0 1038 cm, r1 = 10.596 MW/cm, cm = 0.1879 #uF/cm so that 1 mV on the A V trace corresponds to 0 182 #A/cm or 0 968 ,sA/IF. Fibre 11.8, 1.40 C, solution A.

W. K. CHANDLER AND OTHERS

298

-20 r-

0

-15

F

-

U

-10 F

0'1 0

-5

F

0

0 -

15 20 (nC/#F) Fig. 5. Equality of 'on' and 'off' areas during and after a period of maintained depolarization. Abscissa, charge measured for depolarizing steps from -80 to -21 mV; ordinate, charge measured for hyperpolarizing steps from -21 to -80 mV. *, initial measurements at VHP = -80 mV. *, measurements during inactivation at Vp = -21 mV. 0O measurements during recovery at V.H = -80 mV. The straight line drawn at 450 represents perfect agreement between 'on' and 'off' areas. Same experiment as Fig. 4. 20 r

0

5

10

Qdepol.

15-

I

U-~

U_

C*

10

5

A

-100

300 200 0 100 Time after depolarizing step (sec)

400

Fig. 6. Time course of slow inactivation and recovery of charge movement. Ordinate, average of 'on' and 'off' measurements. Abscissa, time with t = 0 corresponding to changing the holding potential to -21 mV. The times of this change and of the return to -80 mV are marked by arrows. Symbol description given in Fig. 5. The continuous curves are best fit exponential functions. The time constants are given in Table 4. Same experiment as Fig. 4.

GLYCEROL TREATMENT AND CHARGE MOVEMENT 299

Comparison of the steady-state properties of charge movement and delayed rectifier currents Measurements of charge movement are also possible using solutions which contain sodium rather than TEA (solution B), so that the delayed rectifier currents are not blocked. Fig. 7A shows A V(test-control) records for a series of depolarizing pulses. The traces are shown at three different gains as indicated in the legend. Records of voltage during the test pulse are shown in Fig. 7B. TABLE 4. Time constants associated with slow inactivation of charge movement

(1)

(2)

Time at-21 mV Fibre (see) 11.6 239 11.7 262 11.8 136 11.9 178 Average ± S.E. of mean

(3)

Time constant

-80 to-21 mV (see) 12.9 17-0 23 5 17.6 17 8 + 2.2

(4)

-21 to-80 mV (see) 42.5 52-8 38-2 20-9

38-6± 6-6

Column (3) gives the time constant at which inactivation occurred when the potential was switched from -80 to -21 mV, duration in column (2). Column (4) gives the time constant for recovery when the potential was switched back. Temperature 1.2-1-50 C.

The first three traces in Fig. 7A show charge transients very similar to those seen with TEA (Chandler et al. 1976). There is no evidence of a conductance change associated with the depolarizing pulse. The record taken at -32 mV shows an initial charge transient followed by a small delayed outward current which developed along a sigmoid time course. The next records, -23 mV and more positive, show progressively larger delayed currents which turn on more and more rapidly as V is increased. Estimates of the magnitude of the charge movement in the first three traces can be made in the. usual way, subtracting ionic currents and integrating. The fourth trace, -32 mV, was fitted for both charge movement and potassium currents simultaneously, as will be described in connexion with Fig. 9. Values of charge determined from the first four traces in Fig. 7A are plotted as filled circles in Fig. 8, normalized using Qmrax = 25 nC/,uF (Chandler et al. 1976). Charge movement transients for V > -23 mV were obscured by the potassium currents so that accurate measurements of the magnitudes were not possible.

W. K. CHANDLER AND OTHERS 300 The continuous curve in Fig. 8 was calculated from eqn. (1). In this and eight other experiments least-squares fits were made and the values for V and k are given in Table 5. The average value for V, -31 mV, is 13 mV B

A A

, -.

W- -M

-60

-

-50

-

_-40

r__

2mV[

-32

-

100mV[ -

8mV[

-23

*-

~~-16-8

+9

80 mV[Im

V[.

.__________

100 msec

±27 100 msec

Fig. 7. Records of charge movement and delayed potassium currents.

A, A V(test-control). The 2 mV vertical calibration bar applies to traces V -16lmV. The final voltage V1 during the pulse is given beside each trace. B, traces of V1 during the test pulse. The first six traces were signal averaged four times, after which the last three traces were obtained once. Electrode spacing 1 = 205 /tm, I' = 9 ,sm. Cable measurements gave A = 0-0965 cm, r, = 7 034 MQ/cm, cm- 0O3544 ,uF/cm so that 1 mV on AV corresponds

#uA/cm or 0-639 j1A/1tF. Fibre 15.4, solution B, 0.90 C. Initial resting potential -77 mV, holding potential -80 mV.

to 0 226

more positive than the value of -44 mV obtained with TEA (solution A, Chandler et al. 1976). This difference is statistically significant, 0 001 < P < 0 01; on the other hand the value for k, 9-6 mV, is not significantly different from 7-8 mV, the value obtained using TEA.

GLYCEROL TREATMENT AND CHARGE MOVEMENT 301 1-0 r

0-8 I-

E

061-

0' 0 8:

0-F~ 0-2

-

I

I

-100

-80

I -60

I

I

I

I

-20

0

I

I

-40

I

I

20

I

I

40

V (mV)

Fig. 8. Comparison of steady-state values of charge and na,. *, values of QIQmax on the assumption that Qma. = 25 nC/,uF. The solid line was calculated using eqn. (1) with V = -32 mV and k = 9 mV. 0O values of noo from eqn. (11), using VK = -80 mV and gK = 156 mmho//zF. The dashed curve represents nOO vs. V as given by Adrian et al. (1970), but shifted 12 mV to the right. Same experiment as Fig. 7. TABLE 5. Parameters for fitting charge (1)

Fibre reference 13.1 13.4 13.5 13.6 13.8 15.1 15.2 15.3 15.4 Average + S.E. of mean

vs.

potential in sodium solution

(2) V (mV) - 27-4 - 37-2 - 31-2 - 36-8 37-8 - 27-2 - 27-0 23-6 32-3 31-2 + 1-7 -

-

-

-

(3) k

(mV) 14-2 7.4

14X8 9-0 5*0 6-2 9.4 12-4 8-0 9-6 ± 1-2

Columns (2) and (3) give best fit parameters for eqn. (1) assuming Q, Temperature ranged from 0-2 to 1-60 C, solution B.

=

25 nC//cIF.

302 W. K. CHANDLER AND OTHERS Potassium currents in the last six traces in Fig. 7 A, V > -32 mV, were fitted according to (11) ,K = 9Kn4(V-VK), where n obeys first order kinetics (Hodgkin & Huxley, 1952; Adrian et at. 1970). The value of n was taken to be zero at the holding potential, -80 mV, and VK was rather arbitrarily assumed to be -80 mV. Values of no0 are plotted as open circles in Fig. 8. It is clear from the data in Fig. 8 that the steady-state distribution for charge resembles that for n,. The theoretical curves, the continuous one for Q vs. V based on eqn. (1) and the dashed one representing n0 vs. V, taken from Adrian et al. (1970) but shifted 12 mV positive, are also similar. These similarities provide support for the possibility that the charge movement might gate potassium channels, functioning in a manner analogous to the gating particles for sodium channels in the squid axon (Armstrong & Bezanilla, 1973; Keynes & Rojas, 1973; Armstrong & Bezanilla, 1974; Keynes & Rojas, 1974). This possibility would be difficult to distinguish from a role in the activation of contraction since contractile activation and the turning-on of potassium conductance have many similar properties. For example, the threshold voltage for contraction is about the same as the voltage at which delayed rectification is first apparent (Costantin, 1968). Both processes become refractory with maintained depolarization and the curves which relate the degree of refractoriness to voltage are similar (Hodgkin & Horowicz, 1960; Adrian et al. 1970).

Comparison of the kinetics of charge movement and delayed rectification Since the curve relating Q vs. V is almost indistinguishable from the one for n0 vs. V it was of interest to compare the kinetics of the two processes. Fig. 9 A shows the A V record for -32 mV from Fig. 7 A. At this voltage the current due to rearrangement of charge can be adequately resolved from that carried by potassium ions. The points during the pulse in Fig. 9 A can be fitted by AV = AVQ + AVK where AVQ is the charge movement component and AVK is the potassium current component; AVQ = AVQ(O)exp(-t/TQ) and AVK = AVK(oo)[ 1- exp(- t/rn)]4. The four parameters were varied to give a best fit; rQ, the time constant for the exponential decay of the charge movement; AVQ(O), the initial magnitude of the exponential; Tn, the time constant for n; and AVK( X), the final value for potassium current. Fig. 9 B shows a comparison of the data points with the AVK component of the fitted curve. During the last half of the depolarizing pulse the curve and data are in good agreement. Fig. 9C shows the same data as 9 A except that the curve for A VK, given

GLYCEROL TREATMENT AND CHARGE MOVEMENT 303

t.

I

vV

100 Msec

Fig. 9. Theoretical fit to the charge movement transient and I. A, same A V(test-control) record as shown in Fig. 7A, - 32 mV. The points during the pulse were fitted by A V = AJ'Q + Al/K where AV, is the charge movement component and Al/K is the potassium current component; TQ = 12-5 msec and 'r. = 33-3 mseq, The initial rounding in the A V trace was excluded from the fit by not using the first seven points. B, data points during the pulse from part A. After the first 30 msec only every fifth point is plotted. The curve represents the Al/K component of the fit. C, Al/K has been subtracted from the data points during the pulse in A, leaving the charge movement transient. D, data points from C and AT'Q from the fit. Every fifth point is plotted during the pulse starting with the sixth point. See text for additional details.

304 W. K. CHANDLER AND OTHERS in 9 B, has been subtracted from the points during the pulse. The 'off' points have been left unchanged. The trace in 9C, then, represents the current resulting from charge movement. The agreement between these points and the exponential part of the fitted curve, AVQ, is shown in 9 D. TABLE 6. Comparison of time constants for Charge and n Part A; hypertonic sodium 8olution

(1) Fibre reference 13.1 13.4 13.5 13.6 13.8 15.1 15.2 15.3 15.4 Average ± s.E. of mean

(2)

Voltage (mV) -41 -42 -32 -32 -31 -24 -31 -31 -32

(3)

(4)

(5)

TQ

Tn (msec) 28-9

2*29

30 3 28-8 27-1 308 40*7 33.3 31-8 + 1*3

1-86 2-42 1-58 2-50 4*11 2-66 2'84 + 033

(msec) 12-6 8-7 7.7 16-3 11.9

17-2

12*5 9.9 12-5 12-1 + 1.1

33.5 33*0

Part B; glycerol treated, iso8motic 8odium solution -22 26*8 7.7 19.1 -14 3-0 21-7 -21 14.3 853 14-9 -12 4-0 - 31 14.4 34-8 3-7 - 31 32-7 14-6 14.6 - 21 6-7 21-8 Average ± s.E. of mean 14.1

3*85 4*29

3*48 6-37 2-61

3.73

9-41 2-24 3-25 4-44+ 0 97

Column (2) gives the voltage at which rQ (column 3) and r. (column 4) were determined. The measurements in Part A were carried out in solution B; those in part B were done using solution C following glycerol treatment. Temperature varied from 02 to 1.6° C.

The analysis in Fig. 9 shows that AVQ and AVK components can be fitted simultaneously if the voltage is sufficiently positive to turn-on the potassium conductance but is not so positive that the potassium currents swamp the charge transient. The comparison of TQ and Tn in a total of nine fibres is summarized in Table 6, part A. In all cases Tn was larger than TQ; values of Tn/TQ from individual fibres ranged from 1-6 to 4-3 with an average value of 2-8 as given in column (5) of the table. Although the steady-state distribution of Q vs. V resembles n. vs. V, the inequality of Tn and TQ shows that the charge movement transient does not correspond

GLYCEROL TREATMENT AND CHARGE MOVEMENT 305 B

A -61 -51 -

-41 -

~~~~~~-32-

_

-22100 mV[

lmV[

-14

\./

-'.--.---

, -

5

.

mV[I....

-______

+3

__

./O*. 100 msec

-5

-

+ 12

+ 29

100 msec

Fig. 10. Effect of glycerol treatment on charge movement and IK. A, A V (test-control) records with test voltage indicated. The first six records, V < -14 mV, were signal averaged 4 times and are plotted at high vertical gain (1 mV calibration bar). Then the next four records were obtained from single traces and are plotted at lower gain (5 mV calibration bar). Note movement artifact on the last trace, + 29 mV. The final voltage during the pulse is indicated beside each record. B. records of V1 during the test pulse. Electrode spacing 1 = 186 jsm, I' = 19 jsm. Cable measurements gave A = 0-2064 cm, r, = 3-832 MO/cm, cm = 0-1523 ,uF/cm so that 1 mV on AV corresponds to 0-503 4aA/cm or 3-30 ,#A/,#F. Fibre 14.1, solution C following glycerol treatment, 1.00 C. Initial resting potential - 61 mV, holding potential -80 mV.

306 W. K. CHANDLER AND OTHERS kinetically to dn/dt. The discrepancy between TQ and mn is little affected if the potassium current is assumed to be proportional to nW where x is greater than 4 (Cole & Moore, 1960).

Effect of glycerol treatment on charge movement and delayed rectification Fig. 10 shows AV and V1 records obtained from a fibre in an isosmotic sodium solution (solution C) following glycerol treatment carried out as described earlier. The kinetics of the potassium currents were similar to those seen in a hypertonic Na solution (Fig. 7) but the magnitude of the iA V signal was considerably smaller. Part of the increase in A V seen with hypertonicity can be attributed to the increase in R1 (Hodgkin & Nakajima, 1972 a) and the other part to an apparent increase in "K probably related to the increase in internal potassium concentration. TABLE 7. Estimates of PK (1)

(2)

(3)

(4)

Measured . expected capacitance

(mmho per /%F expected capacitance)

#K

gK

Fibre 13.1 13.5 13.6 13.8 15.1 15.2 15.3 15.4 Average + s.E. of mean

(mmho per 1tF measured capacitance)

Part A; hypertonic sodium solution 2'42 047 078 1-53 066 1-02 1*04 1-56 1 19 + 0-22

Part B; glycerol treated, isosmotic sodium solution 14.1 052 0-62 14.3 097 055 14.4 0-61 068 14.6 044 067 0-64+0-12 Average ±s.E. of mean

0-32 0*53 0-41 0-29 039 ± 0*05

Column (2) gives values of 9 normalized for the measured capacitance, assuming = -80 mV. Column (3) gives the ratio of the measured capacitance to the capacitance expected for a normal fibre of the same radius. Table 2 B column (5) +. column (6). Column (4) is the product of (2) and (3). Other details as in Table 6.

VK

As with hypertonic solutions (Table 6, part A) the discrepancy between TQ and Tn is also seen with glycerol treated fibres immersed in isosmotic solutions (Table 6, part B).

GLYCEROL TREATMENT AND CHARGE MOVEMENT 307 Table 7 shows values of gK measured in hypertonic sodium solution (part A) and in isosmotic sodium solution following glycerol treatment (part B). The average value of 1P19 mmho/c#F in hypertonic solution (column 2, part A) would correspond to 5-10 nunho/cm2 referred to surface membrane, in agreement with Adrian et al. (1970). The corresponding value in isosmotic solution following glycerol treatment was 0*64 mmho/ #F. Since the measured fibre capacitance is reduced by glycerol treatment k has also been expressed relative to the capacitance expected for an untreated fibre having the same radius. Column (3) of Table 7 B gives the ratio of measured capacitance to that expected and column (4) gives gK normalized according to the expected original value of capacitance. Since most of the potassium conductance is located on the surface (Adrian et al. 1970; Adrian & Peachey, 1973) the corrected 9K, column (4) part B, should be compared with column (2) part A. The two average values, 1*19 in part A and 0 39 mmho//,tF in part B, indicate that either the number of conducting sites or the conductance per site is different by a factor of three in the two conditions. The most reasonable explanation is to suppose that IK is proportional to the internal potassium concentration [K]1, as is the case for perfused squid axons (Chandler, Hodgkin & Meves, 1965). The hypertonic solution B is about three times the tonicity of C and so should elevate [K]1 threefold, an amount in agreement with the elevation of gE. If this explanation is correct it indicates that the glycerol treatment which we used is effective in removing or immobilizing 0-7-0'8 of the charge movement but does not affect the potassium channels.

Contraction threshold In one muscle experiments were carried out to determine the effects of TEA on the contraction threshold for a 200 msec pulse. Contraction thresholds were measured first in solution F (containing sodium and potassium), then in solution D (TEA and rubidium), and finally again in solution F. The results were - 42-4 + 1-6 mV (mean + S.E. of mean) in F, - 48.3 + 1-7 mV in D, - 39-4 + 0-8 mV in F for five, six and five fibres respectively (0.5- 2.00 C). The reason for the differences in our value in sodium solution (F), -41 mV, and values reported by others, -52 mV (Adrian, Chandler & Hodgkin, .1969) and - 48-5 mV (Costantin, 1968), is not clear but may be related to the fact that we used Tris buffer instead of phosphate. A similar shift was found when we compared our n. vs. V curves with the theoretical relation used by Adrian et al. (1970), as illustrated in Fig. 8. The shift of contraction threshold of- 7.4 mV seen with TEA, solution D vs. F, is statistically significant (P < 0.005) and is consistent with the results of Costantin (1968) who found a shift of - 8'6 mV under similar conditions (see also Kao & Stanfield, 1970).

308

W. K. CHANDLER AND OTHERS DISCUSSION

The most straightforward experimental result is the finding that changing the holding potential from -80 to -21 mV caused a slow exponential decline of the measurable charge movement. On repolarization the charge movement returned to the initial level, again along an exponential time course. The reversible disappearance provides a control for the experimental technique. It rules out the possibility that the charge movement is an artifact of the instrumentation. The results of the preceding paper require .that there be at least two configurations for the charge. These were called 1 and 2 but will now be denoted by 'resting' and 'activating'. The inactivation experiment requires a third refractory configuration. These three states can be represented Qresting

Qactivating

Qrefractory

The value of the rate constant (a +,f) is of order of magnitude 0 1 msec-1 at 00 C whereas (y + d) is order of magnitude 0a 1 sec1. There may also be direct connexions between the resting and refractory configurations, as indicated by the dashed lines, but the experiments to date do not require it. On depolarization from the resting potential Q would distribute rapidly between resting and activating positions, then slowly between activating and refractory positions. On a time scale of units (y + 6)-1 the distribution at any moment between resting and activating would be essentially the steady-state distribution. Recovery from the refractory position would involve a slow change from refractory to activating. Once a particle reached the activating position it would rapidly move to the resting position so that only a minute fraction would be activating at a given moment. The slow inactivation, unfortunately, does not help decide whether the charge plays a role in excitation-contraction coupling or in gating potassium channels. It is consistent with either possibility since both mechanical activation and potassium currents are inactivated by maintained depolarization. Furthermore, the kinetics of the charge inactivation seem consistent with either possibility. The time constant of the charge inactivation, 10-25 sec at V = -21 mV (10 C), is similar to that associated with the

GLYCEROL TREATMENT AND CHARGE MOVEMENT 309 relaxation from a potassium contracture, about 10sec at 0 mV (30 C; Caputo, 1972b). The time constant of potassium inactivation, 1-2 see at 10 mV (30 C; Adrian et al. 1970), is several times smaller than the value for charge inactivation, but this could be explained by assuming that the n particles are inactivated with a time constant of 10-25 sec and that IK follows a high power of n. The time constant for removal of charge inactivation, 20-60 sec at -80 mV (10 C), may be less than the recovery time for tension following a potassium contracture observed by Caputo (1972a). In the latter case, however, membrane repolarization was produced by lowering external potassium and full repolarization required some tens of seconds. The time course of removal of potassium inactivation, exponential following a short period of depolarization and sigmoid following a long period (Heistracher & Hunt, 1969; Adrian et al. 1970), would be consistent with an exponential recovery of the n particles similar to that observed for the charge movement. The experimental findings from glycerol treatment were less straightforward than those associated with maintained depolarization. Rather disappointingly the procedure cannot be used to decide the location of charge, surface or tubular, since its action is more complicated than simply to disrupt tubular continuity. Under the conditions of our experiments glycerol resulted in the disruption of 0'7-0'8 of the charge movement but of only 0 4 of the tubules. If these were the only two actions of glycerol treatment, the experiments of Dulhunty & Gage (1973) would provide evidence that charge movement is a step in the activation of contraction. In their experiments the conditions of the glycerol treatment were adjusted so that the twitch disappeared while tubular capacitance remained normal. The explanation would be that their relatively mild procedures selectively disrupted charge but left the electrical continuity of the tubules intact, a rather attractive idea. The difficulty is that there is no evidence to indicate that the effects of glycerol are only twofold; the removal of the twitch in the Dulhunty & Gage experiments may be due to a third, unrelated action.

Difficulties with equating charge movement and potassium gating current Although the experiments do not conclusively rule out the possibility that the charge movement gates potassium channels, several properties of the charge movement are somewhat difficult to reconcile with this view. A. The time constants for charge movement and for dn/dt are different. This lack of agreement is shown in Fig. 9 and Table 6 and, as mentioned earlier, is not improved by using an nx formulation where x is greater than 4. An alternative would be to suppose that, unlike squid sodium channels

310 W. K. CHANDLER AND OTHERS (Armstrong & Bezanilla, 1973; Keynes & Rojas, 1973; Armstrong & Bezanilla, 1974; Keynes & Rojas, 1974), the 'on' transient of the charge movement does not correspond to the rate of change of a Hodgkin-Huxley (1952) activation variable. In fibre 15.4, Fig. 9, rQ = 12-5 msec and tn = 33-3 msec at V = -32 mV. The difference, 20-8 msec, would reflect a delay between Q and n. Although it is possible to construct a model consistent with such a delay, three additional complications impose restrictions. Firstly, the delay is voltage dependent; at + 27 mV, Fig. 7A, it must be less than 5-3 msec, the value of Tn. Secondly, the delay, measured in a rather narrow voltage range, varies from fibre to fibre, not giving a fixed relationship between TQ and Tn; values in columns (3) and (4) of Table 6 show no apparent correlation and the ratio Tn/TQ in column (5) varies almost threefold, 1-58 to 4-29. Thirdly, the 'on' transient is initially rounded and the degree of roundedness varies among fibres, appearing to be in rough proportion to the tubular time constant (compare Figs. 6 and 14, Chandler et al. 1976). This is suggestive of a tubular location for the charge movement (Chandler et al. 1976) whereas the potassium channels are mainly on the surface (Adrian et al. 1970; Adrian & Peachey, 1973). B. Glycerol treatment affects charge movement, not potassium channels. Glycerol treatment sufficient to remove or immobilize 0-7-0-8 of the charge does not appreciably alter the kinetics of IK nor does it seem to decrease the number of conducting channels. The second statement depends on the reasonable assumption that IK at strong depolarizations is proportional to [ K+]i and this has not been tested directly in muscle. C. Qmax can increase while IK disappears. In squid axons the magnitude of the sodium current usually declines during the course of an experiment. In a 'dead axon', incapable of producing sodium current, the gating currents are absent (Armstrong & Bezanilla, 1974). A similar situation has not been found in our experiments. To the contrary, in fibre 10.2 small potassium currents, not blocked by the TEA solution, were present during run no. 1 (trace g, Fig. 6 B in Chandler et al. 1976.), then disappeared by run no. 4. At the same time Qmax increased from 19-1 to 32-9 nC//uF (Table 1, Chandler et al. 1976). D. Potassium gating currents similar in magnitude to charge movements in muscle have not been found in squid nerve. The value of gK in an intact squid axon is about 36 mmho/cm2 (Hodgkin & Huxley, 1952) or 36 mmho/ ,uF assuming C = 1 #F/cm2. The average value in our experiments in hypertonic solutions was 1-2 mmho/,uF, 30 times less. In this case [K+]i would be about 420 mM, three times normal (140 mM), comparable to [K+]1 in an intact axon. If potassium channels in squid axons and in frog muscles have a similar conductance per channel, the density of channels

GLYCEROL TREATMENT AND CHARGE MOVEMENT 311 in the nerve (surface) membrane would be about 30 times the density in muscle (surface + tubular) membrane. If the two kinds of potassium channels are gated similarly, the identification of muscle charge movement with potassium gating would require currents in squid 30 times larger than those in muscle. At V = 0 mV the peak values of the 'on' and 'off' transients in muscle are 2-4 1A/1tF (Fig. 6A, Chandler et al. 1976). Currents with similar kinetics but 30 times larger have not been seen in squid axons. They are probably not present for they would have been revealed by experiments such as those illustrated in Figs. 4 and 5 in Armstrong & Bezanilla (1974). Some consequences which would follow if the charge were located in the T-system and played a role in excitation-contraction coupling Reasons (A) to (D) above and the results of repriming experiments (Adrian, Chandler & Rakowski, 1976) make it more likely that the charge movement is involved in mechanical activation rather than in gating gK. The fact that mechanical activity is blocked in hypertonic solutions is not an objection to this suggestion since calcium release appears to be largely unaffected judging from measurements of activation heat (Smith, 1972). The rest of the discussion is based on the assumption that charge movement is a step in excitation-contraction coupling and that accordingly the process is located in the tubules. The density of charged groups in tubular membrane, 500-600/,um2 (Chandler et al. 1976), is about the same as the density of the electron dense 'feet' which extend between the tubular and S-R membranes (Franzini-Armstrong, 1970). Thus it is possible that charged groups and feet are associated on a one-to-one basis. The number of groups, or feet, per cm3 of muscle is equal to 1 -5-1 8 x 1014 groups/cm3, given by 5-6 x 1010 groups/cm2 tubular membrane times 3 x 103 (cm2 membrane)/(cm3 muscle) (Peachey, 1965). Full activation of muscle requires a release of calcium equivalent to a concentration of roughly 100 ItM (M. Endo & L. L. Costantin, personal communication), corresponding to 6 x 1016 ions/cm3. If the 'feet' or the charged groups are part of the mechanism involved with calcium release, then about 300 ions need to be released per foot. The next question is whether the rates of calcium movement are compatible with known rates of ionic movements in excitable membranes. For relatively short pulses the potential for a threshold contraction shifts to more positive values, so that for a 4 msec pulse the voltage needs to be 0 mV for contraction to occur (Adrian et al. 1969). Using a HodgkinHuxley (1952) parameter to describe changes in charge distribution, and eqns. (8)-(12) of the previous paper, we calculate for -90 mV that

W. K. CHANDLER AND OTHERS 312 a = 0-001 msec-1, ,3 = 0-306 msec-1 and for 0 mV that ac = 0-293 msec-1, ,f = 0-001 msec-1. The Hodgkin-Huxley parameter starts from a value near zero at the beginning of the pulse, rises to a value of 0-69 in 4 msec, then decays back to zero on repolarization. The average dwell time of a particle in the activating position would be 1-65 msec during the pulse and 2-25 msec following the pulse. If the number of activated calcium release sites is equal to the number of particles in the activating position, each calcium release site would be activated, on the average, for 3-9 msec during which time no more than 300 calcium ions must be released. This corresponds to a flux of at most 0-8 x 105 ions/sec through each site, a rate that is not unreasonably high compared to ionic movements through sodium channels in nerve membranes (Hille, 1970). If the function of each charged group is to control one calcium release site, it is possible to make a crude estimate of how many sites must be open at the mechanical threshold for a long lasting pulse. The threshold which was measured for the TEA solution (D) was - 48-3 mV. Using V = -44mV, k = 8mVeqn. (1) givesQ = 0-37Qmax. There is good reason, however, to suppose that the hypertonic solutions which were used for charge measurements shifted the threshold to the left by 10-20 mV (Gordon & Godt, 1970). If the sarcoplasmic side of the tubular membrane were covered with a layer of fixed negative charges having a density of 1-4 x 1013 electronic charges/cm2, as suggested for the squid axon (Chandler et al. 1965), a change from isosmotic (solution D) to hypertonic (solution A) conditions should decrease the magnitude of the double layer potential by about 10 mV. Shifting V from - 48-3 to -58 mV and using the same values for V and k, eqn. (1) gives for threshold Q = 0 15 Qmax. It seems clear that any detailed description of how movement of a charged group leads to calcium release would be highly speculative. One mechanism which is not plausible is to suppose that a significant change in the double layer potential is produced when the charge moves from one side of the tubular membrane to the other and that somehow this is sensed by the S-R. The double layer potential which would be produced by all the groups, about 2 x 103 electronic charges/IZm2, is less than 1 mV (cf. Chandler et al. 1965). A more reasonable approach would be to assume that there is some kind of mechanical linkage which extends from the charge in the tubular membrane to a site in the S-R membrane. The diagrams in Fig. 11 show a rather hypothetical way in which this could happen. Each charged group is assumed to control one calcium channel in the S-R membrane. Two separate models are pictured, A and B, which have the same mechanical linkage but differ in the design of the charged complex. In each case part

GLYCEROL TREATMENT AND CHARGE MOVEMENT 313 of the complex is connected by a rigid rod to a plug. The channel is closed by the plug when the charge is in the resting position (a). In the activating position (b) the plug is removed so that calcium ions can flow from the lumen of the S-R into the sarcoplasm and activate contraction. In the refractory condition (e) the channel is again plugged. A Tubular membrane

B S-R membrane

Tubular membrane

S-R membrane

III

IIIl a

b

b

Fig. 11.- Hypothetical examples of how a charged complex might regulate S-R calcium release. I denotes the lumen of the T tubules, the space labelled II is continuous with the sarcoplasm and III indicates the inside of the lateral cistern of the S-R where calcium is thought to be stored. InA 2is greater than Z1, by about 3. In B Z' is 3; the other charged complex consists of two groups of valence Z2' connected by a basket which can move Z' to the right; 2Z' > Z'. Configuration (a) corresponds to resting, (b) to activating and (c) to refractory. See text for further details.

The charged complex in model A of Fig. I1 is a dipole with charged Z1 at the end connected to the plug and charge Z2 at the free end. If we require that the angle between the dipole and the rod cannot be less than 900,) the complex will be in position a at the resting potential if Z2 > Z . To account for the value ic = 8 mV in eqn. (1) Z2 should exceed Z1 by about 3. -

314

W. K. CHANDLER AND OTHERS If the angle between the dipole and connecting rod were rigid, on depolarization the complex would move to the left, position b, removing the plug from the calcium channel. In the model it is assumed that motion of Z1 is restricted to a direction perpendicular to the plane of the membrane. If the angle between the dipole and the connecting rod were not fixed, but could freely assume values greater than 900, depolarization would result in a transition from position a to c, i.e. only the Z2 portion of the complex would cross the membrane. By requiring that changes in angle from b to c can occur only very slowly compared with movements of the complex from a to b, it is possible for state b to be favoured immediately following depolarization and for state c to be favoured at later times. This is the case which would allow activation of contraction to develop rapidly, then be inactivated. Model B can achieve the same results if movements of Z", which equals about 3, are rapid compared to movements of the Z' complex. On depolarization Z' moves to the left, from position a to b. Then if 2Z' > Z', the Z' complex slowly moves to the right, from b to c, taking Z' with it. With either model if the depolarization were interrupted by a return to the resting potential, any charge in position b would return to a. During recovery from the refractory state (c), the charge could by-pass position (b) and proceed directly from c to a. These models are entirely hypothetical and are only two of the many possibilities which one might imagine. Their value arises mainly because they emphasize (1) that depolarization of the tubular membrane can turn on calcium flux across the adjacent S-R membrane, (2) that repolarization can rapidly shut off calcium release (Hodgkin & Horowicz, 1960; Caputo, 1972b) and (3) that inactivation affects both charge movement and calcium release. The notion that activation occurs by unplugging a channel specific for calcium or a calcium complex may be entirely wrong. The mechanism could involve an electrically neutral exchange, such as one calcium ion for two potassium ions, or an increase in the permeability of the S-R membrane to an ion other than calcium, a process which in turn might facilitate calcium release. It is also possible that the coupling between the charge particle and the S-R is not mechanical in nature but involves some other mechanism, such as chemical diffusion. We thank Mr H. Fein and staff for help with design and construction of equipment and Dr R. W. Tsien for helpful discussion. Financial support was provided by the U.S. National Institutes of Health, grant NB-07474, and by the Muscular Dystrophy Association of America, research fellowship to R.F.R.

GLYCEROL TREATMENT AND CHARGE MOVEMENT 315 REFERENCES

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Effects of glycerol treatment and maintained depolarization on charge movement in skeletal muscle.

1. Voltage-clamp experiments were carried out using the techniques described in the preceding paper. 2. In one series of experiments an attempt was ma...
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