A quantitative description of the voltage-dependent capacitance in frog skeletal muscle in terms of equilibrium statistical mechanics

Reciprocal dihydropyridine and ryanodine receptor interactions in skeletal muscle activation

Dihydropyridine (DHPR) and ryanodine receptors (RyRs) are central to transduction of transverse (T) tubular membrane depolarisation initiated by surface action potentials into release of sarcoplasmic reticular (SR) Ca2+ in skeletal muscle excitation-contraction coupling. Electronmicroscopic methods demonstrate an orderly positioning of such tubular DHPRs relative to RyRs in the SR at triad junctions where their membranes come into close proximity. Biochemical and genetic studies associated expression of specific, DHPR and RyR, isoforms with the particular excitation-contraction coupling processes and related elementary Ca2+ release events found respectively in skeletal and cardiac muscle. Physiological studies of intramembrane charge movements potentially related to voltage triggering of Ca2+ release demonstrated a particular qγ charging species identifiable with DHPRs through its T-tubular localization, pharmacological properties, and steep voltage-dependence paralleling Ca2+ release. Its nonlinear kinetics implicated highly co-operative conformational events in its transitions in response to voltage change. The effects of DHPR and RyR agonists and antagonists upon this intramembrane charge in turn implicated reciprocal rather than merely unidirectional DHPR-RyR interactions in these complex reactions. Thus, following membrane potential depolarization, an orthograde qγ-DHPR-RyR signaling likely initiates conformational alterations in the RyR with which it makes contact. The latter changes could then retrogradely promote further qγ-DHPR transitions through reciprocal co-operative allosteric interactions between receptors. These would relieve the resting constraints on both further, delayed, nonlinear qγ-DHPR charge transfers and on RyR-mediated Ca2+ release. They would also explain the more rapid charging and recovery qγ transients following larger depolarizations and membrane potential repolarization to the resting level.

Charge inactivation in the membrane of intact frog striated muscle fibers

1. Charge movements were compared in normally polarized and depolarized intact frog muscle fibres under voltage clamp. 2. The membrane capacitance was linear through positive control steps made consistently from a holding voltage of -10 mV, in agreement with earlier reports from cut fibres. 3. A shift in holding voltage from -90 to -10 mV reduced both the absolute amount and the voltage dependence of charge movement elicited by voltage steps imposed from a fixed conditioning voltage of -180 mV. The charge transferred by steps from -180 to -20 mV was 43.8 +/- 1.14 nC/microF in fully polarized fibres and 21.7 +/- 1.49 nC/microF in the same depolarized fibres (means +/- S.E. of the mean; four fibres). 4. Charge movement in response to steps from -90 to -20 mV increased from 10.4 +/- 1.60 nC/microF to 28.4 +/- 2.42 nC/microF (five fibres) within 30s of changing the holding voltage from -10 to -90 mV. 5. The same fibres also showed significant charge movement between voltages of -180 and -90 mV. However, shifts in holding voltage did not significantly alter the maximum value of this charge, around 10-11 nC/microF. 6. Membrane capacitance as measured by small steps to a voltage of -90 mV remained constant despite holding potential changes, or lidocaine (10 mM) treatment. 7. The same results were obtained whether the above procedures were applied to fibres exposed to normal extracellular [Ca2+], or in Ca(2+)-free media. In both cases tubular cable corrections did not affect the results. 8. These findings suggest independent charge I and charge II systems in which inactivation of charge I is not associated with its interconversion into charge II.

A reconstruction of charge movement during the action potential in frog skeletal muscle

The transfer of intramembrane charge during an action potential at 4 degrees C was reconstructed for a model representing the electrical properties of frog skeletal muscle by a cylindrical surface membrane and 16 concentric annuli ("shells") of transverse tubular membrane of equal radial thickness. The lumina of the transverse tubules were separated from extracellular fluid by a fixed series resistance. The quantity, geometrical distribution and steady-state and kinetic properties of charge movement components were described by equations incorporating earlier experimental results. Introducing such nonlinear charge into the distributed model for muscle membrane diminished the maximum amplitude of the action potential within the transverse tubules by 2 mV but increased the maximum size of the after-depolarization by 3-5 mV and also its duration. However, these changes were small in comparison to the 135-mV deflection represented by the action potential. They therefore did not justify altering the values of the electrical parameters adopted by Adrian R.H., and L.D. Peachey (1973. J. Physiol. [Lond.]. 235:103-131.) and used in the present calculations. Cable properties significantly affected the time course and extent of charge movement in each shell during action potential propagation into the tubular system. Q beta charge moved relatively rapidly in all annuli, and did so without significant latency (approximately 0.3 ms) after the surface action potential upstroke. Its peak displacement varied between 53 and 58% (the range representing the difference fiber edge/fiber axis) of the total Q beta charge. This was attained at 5.4-7.3 ms after the stimulus, depending on depth within the tubules. In contrast, q gamma moved after a 1.7-2.9 ms latency and achieved a peak displacement of up to 22-34% of available charge. Both charge movement species could be driven by repetitive (47.7 Hz) action potentials without buildup of charge transfer. Such stimulus frequencies would normally cause tetanus. Latencies in q gamma charge movement in response to an action potential were resolved into (a) propagation of tubular depolarization required to gain the "threshold" of q gamma charge (0.8-1.5 ms) and (b) dielectric loss processes. The latter took consistently around 1.5 ms throughout the tubular system. Taken with (c) the earlier reports of a minimal latency in delta [Ca2+] signals attributed to tubulo-cisternal coupling following voltage sensing (approximately 2 ms: Zhu, P.H., I. Parker, and R. Miledi., 1986. Proc. R. Soc. Lond. B. Biol. Sci. 229:39-46.). these times can be reconciled to the latency (~ 4-5 ms) reported between the onset of the surface action potential and that of delta [Ca2+] signals (Vergara, J., and M. Delay. 1986. Proc. R. Soc. Lond. B. Biol. Sci. 229:97-110.). This is consistent with a relationship between the q gamma system and excitation-contraction coupling whether as an independent event (e.g.,Adrian, R.H., and C.L.-H. Huang. 1984. J. Physiol. (Lond.). 353:419-434.) or as an end reaction following earlier (q beta) transfers of charge (e.g., Horowicz, P., and M.F. Schneider. 1981. J. Physiol. (Lond.). 314:565-593.; Melzer, W., M.F. Schneider, B.J. Simon,and G. Szucs. 1986. J. Physiol. (Lond.). 373:481-512.)

Intramembrane charge movements in frog skeletal muscle in strongly hypertonic solutions

Intramembrane charge movements were studied in intact, voltage-clamped frog (Rana temporaria) skeletal muscle fibers in external solutions made increasingly hypertonic by addition of sucrose. The marked dependence of membrane capacitance on test potential persisted with increases in extracellular sucrose concentration between 350 and 500 mM. Charge movements continued to show distinguishable early monotonic (q beta) decays and the strongly voltage-dependent delayed (q gamma) charging phases reported on earlier occasions. In contrast, a further increase to 600 mM sucrose abolished the most steeply voltage-sensitive part of the membrane capacitance. It left a more gradual variation with potential that closely resembled the function that resulted when q gamma charge was abolished by tetracaine in the presence of 500 mM sucrose. Charging transients were now simple monotonic (q beta) decays and lacked delayed (q gamma) transients. Furthermore, tetracaine (2 mM) altered neither the kinetic nor the steady-state features of the charge left in 600 mM sucrose. However, Ca2+ current activation in the same fibers persisted through such tonicity increases under identical conditions of temperature, external solution, and holding voltage. Tonicity changes thus accomplish an independent separation of q gamma and q beta charge as defined hitherto through their tetracaine sensitivity. Their effects on q gamma charge correlate with earlier observations of osmotic conditions on delta[Ca2+] signals (1987. J. Physiol. (Lond.) 383:615-627.) and the parallel effects of other agents on excitation-contraction coupling and q gamma charge. In contrast, they suggest that Ca2+ current activation does not require q gamma charge transfer whether by itself or as part of the excitation-contraction coupling process.

The relationship between Q gamma and Ca release from the sarcoplasmic reticulum in skeletal muscle

Asymmetric membrane currents and fluxes of Ca2+ release were determined in skeletal muscle fibers voltage clamped in a Vaseline-gap chamber. The conditioning pulse protocol 1 for suppressing Ca2+ release and the "hump" component of charge movement current (I gamma), described in the first paper of this series, was applied at different test pulse voltages. The amplitude of the current suppressed during the ON transient reached a maximum at slightly suprathreshold test voltages (-50 to -40 mV) and decayed at higher voltages. The component of charge movement current suppressed by 20 microM tetracaine also went through a maximum at low pulse voltages. This anomalous voltage dependence is thus a property of I gamma, defined by either the conditioning protocol or the tetracaine effect. A negative (inward-going) phase was often observed in the asymmetric current during the ON of depolarizing pulses. This inward phase was shown to be an intramembranous charge movement based on (a) its presence in the records of total membrane current, (b) its voltage dependence, with a maximum at slightly suprathreshold voltages, (c) its association with a "hump" in the asymmetric current, (d) its inhibition by interventions that reduce the "hump", (e) equality of ON and OFF areas in the records of asymmetric current presenting this inward phase, and (f) its kinetic relationship with the time derivative of Ca release flux. The nonmonotonic voltage dependence of the amplitude of the hump and the possibility of an inward phase of intramembranous charge movement are used as the main criteria in the quantitative testing of a specific model. According to this model, released Ca2+ binds to negatively charged sites on the myoplasmic face of the voltage sensor and increases the local transmembrane potential, thus driving additional charge movement (the hump). This model successfully predicts the anomalous voltage dependence and all the kinetic properties of I gamma described in the previous papers. It also accounts for the inward phase in total asymmetric current and in the current suppressed by protocol 1. According to this model, I gamma accompanies activating transitions at the same set of voltage sensors as I beta. Therefore it should open additional release channels, which in turn should cause more I gamma, providing a positive feedback mechanism in the regulation of calcium release.

Anatomical distribution of voltage-dependent membrane capacitance in frog skeletal muscle fibers

Components of nonlinear capacitance, or charge movement, were localized in the membranes of frog skeletal muscle fibers by studying the effect of 'detubulation' resulting from sudden withdrawal of glycerol from a glycerol-hypertonic solution in which the muscles had been immersed. Linear capacitance was evaluated from the integral of the transient current elicited by imposed voltage clamp steps near the holding potential using bathing solutions that minimized tubular voltage attenuation. The dependence of linear membrane capacitance on fiber diameter in intact fibers was consistent with surface and tubular capacitances and a term attributable to the capacitance of the fiber end. A reduction in this dependence in detubulated fibers suggested that sudden glycerol withdrawal isolated between 75 and 100% of the transverse tubules from the fiber surface. Glycerol withdrawal in two stages did not cause appreciable detubulation. Such glycerol-treated but not detubulated fibers were used as controls. Detubulation reduced delayed (q gamma) charging currents to an extent not explicable simply in terms of tubular conduction delays. Nonlinear membrane capacitance measured at different voltages was expressed normalized to accessible linear fiber membrane capacitance. In control fibers it was strongly voltage dependent. Both the magnitude and steepness of the function were markedly reduced by adding tetracaine, which removed a component in agreement with earlier reports for q gamma charge. In contrast, detubulated fibers had nonlinear capacitances resembling those of q beta charge, and were not affected by adding tetracaine. These findings are discussed in terms of a preferential localization of tetracaine-sensitive (q gamma) charge in transverse tubule membrane, in contrast to a more even distribution of the tetracaine-resistant (q beta) charge in both transverse tubule and surface membranes. These results suggest that q beta and q gamma are due to different molecules and that the movement of q gamma in the transverse tubule membrane is the voltage-sensing step in excitation-contraction coupling.

'Off' tails of intramembrane charge movements in frog skeletal muscle in perchlorate-containing solutions

1. Charge movements in response to hyperpolarizing ('off') voltage-clamp steps were examined in frog skeletal muscle fibres in the presence of 8 mM-perchlorate. 2. The appearance of prolonged 'off' decays, of duration 50-100 ms coincided with those of slow 'q gamma' charge transfers in preceding 'on' transients. 3. Charge was conserved in the presence of perchlorate whether testing or pre-pulse voltages were varied. Additionally, steady-state charge as a function of voltage was independent of the direction from which the voltage was reached. 4. 'Off' recoveries were most prolonged at voltages around -90 to -100 mV and became less marked with depolarization. 5. Charging currents in response to hyperpolarizing steps that intercepted prolonged ('q gamma') 'on' decays showed reduced slow 'off' tails but intact 'off' decays at early times. 6. Transients elicited by depolarizing steps that intercepted 'off' tail currents showed decreased slow 'on' components. By varying the time at which 'off' responses were so intercepted, it was shown that 'off' tails can require well over 100 ms to attain a steady state in perchlorate. 7. Prolonged depolarization to a holding potential of -30 mV inactivated delayed ('q gamma') components in both 'on' and 'off' responses but left the more rapid ('q beta') decays intact. 8. These observations are easier to reconcile with parallel systems responsible for independent early ('q beta') and delayed ('q gamma') transients in both 'on' and 'off' steps than with the existence of 'q beta' and 'q gamma' transitions in a causal sequence.

Analysis of 'off' tails of intramembrane charge movements in skeletal muscle of Rana temporaria

Components of non-linear charge were isolated in transients obtained in response to hyperpolarizing ('off') voltage-clamp steps in frog muscle fibres. 'Off' currents of the q gamma charge were isolated by comparing records obtained from long depolarizing steps with those resulting from short steps which intercepted the 'on' currents of the q gamma charge. The 'off' transients of the q gamma component so deduced were rapid decays lasting 10-15 ms, in contrast with their prolonged time course in the preceding 'on' steps. 'Off' responses were rapid even at voltages when the 'on' current, obtained from imposed 10 mV steps made at a series of closely incremented conditioning voltages, was delayed and prolonged. Such slow transfers of charge could not be demonstrated in 'off' tails. Large depolarizing steps resulted in rapid q gamma transients in 'on' currents not distinguishable from the rest of the charge movement. Nevertheless, by separating the q gamma component through its inactivation by prolonged depolarization, it was possible to show that q gamma currents in the 'off' tails were still rapid decays. It is concluded that in contrast to the varied pattern shown by q gamma in 'on' transients, its 'off' responses are everywhere relatively fast decays. These features can be predicted by a simple two-state model in which the forward and backward rate constants depend upon the amount of charge moved, as well as the membrane voltage.

Experimental analysis of the relationship between charge movement components in skeletal muscle of Rana temporaria

Experiments were performed to ascertain whether the monotonic (q beta) and delayed (q gamma) components of non-linear charge in skeletal muscle membranes form a sequential system, or are the result of separate, independent processes. The non-linear capacitance studied in a large number of fibres increased with fibre diameter. This dependence was attributable to tetracaine-sensitive (q gamma) but not to tetracaine-resistant (q beta and q alpha) charge. The kinetics and total quantity of q gamma charge moving in response to voltage steps from varying pre-pulse potentials to a fixed probe potential remained constant despite variations in the size of the early q beta decay. The kinetics of the delayed (q gamma) charging current obtained from a single 20 mV depolarizing step were compared with the sum of the responses to two 10 mV steps adding to the same voltage excursion. The respective transients superimposed only if one of the 10 mV steps did not reach the voltage at which q gamma first appears. In the two preceding experiments, total charge was conserved. These results are consistent with separate and functionally independent q beta and q gamma systems of potential-dependent charge, with q gamma residing in the transverse tubules and q beta on surface membrane. The findings can be discussed in terms of a contractile 'activator' with a steep sensitivity to voltage that begins only with depolarization beyond a level close to the actual mechanical threshold.

Charge movements near the mechanical threshold in skeletal muscle of Rana temporaria

Charge movement was investigated over a range of potentials close to the mechanical threshold in voltage-clamped frog skeletal muscle. The delayed (q gamma) component of the charging currents appeared with a time course lasting well over 100 ms at around -50 to -40 mV, but the currents became larger and faster with further depolarization. The slow charging current was investigated using a 10 mV probe step intercepting the time course of these currents. This procedure showed that the charging currents could last as long as 100-300 ms. The total charge was conserved when the charging current was small and prolonged. The results can be related directly to earlier findings concerning contractile activation of muscle by applied voltage steps to potentials near threshold ( Adrian , Chandler & Hodgkin, 1969).

Time domain spectroscopy of the membrane capacitance in frog skeletal muscle

Dielectric spectra representing the frequency dependence of the complex permitivity at a range of depolarizations were obtained from voltage-clamped frog skeletal muscle membranes. This employed an analysis that derived the Fourier coefficients defining the capacitative transients to 10 mV steps as continuous functions of frequency, and so could examine closely the relevant frequencies at which non-linear components occurred. Non-linear capacitative components were identified through their appearance at lower frequencies than those of the linear components as obtained at the -85 mV control voltage, from spectra representing a logarithmic scale of frequencies. Permitivities from small depolarizing steps between about -75 and -50 mV gave single q beta dielectric loss peaks; the real permitivities declined monotonically with increasing frequency. Simple arc loci were obtained in the complex plane. With further depolarization, an additional q gamma loss peak at low frequencies and a resonant frequency in the real spectra occurred over a narrow voltage range around -45 mV. The complex loci then showed features implying an increased movement of charge not explicable through the simple effect of an electric field on a dielectric species. Spectra from small hyperpolarizing steps possessed only single dielectric loss peaks and real permitivities that declined monotonically with increasing frequency. However, in the complex plane, the loss tangents at the higher frequencies implied a population of two or more dielectric relaxations. The potential dependence of the frequency at maximum dielectric loss obtained from depolarizing steps showed a discontinuity at the onset of q gamma. In contrast, in hyperpolarizing responses, this dependence was smooth. The q beta relaxations obtained after q gamma was abolished by 1 mM-tetracaine gave dielectric spectra that were similar whether to depolarizing or hyperpolarizing potential steps. They gave single dielectric loss peaks and semicircular complex plane loci. The singularities in the dielectric spectra thus result from the q gamma charge movement component. They may reflect co-operative mechanisms that might also produce its steep voltage dependence and kinetics, and consequently those of the physiological processes it may control. These are discussed in terms of the mechanisms expected in allosteric proteins.

Experimental analysis of alternative models of charge movement in frog skeletal muscle

A series of pulse procedures was used to distinguish experimentally between a 'capacitative' (Schneider & Chandler, 1973) and a 'resistive' (Matthias, Levis & Eisenberg, 1980) model of 'charge movements' in skeletal muscle. A general condition describing the conservation of charge in a non-linear capacitor that was used as the basis for the experiments is derived in the Appendix. It was shown that earlier criteria concerning equality of 'on' and 'off' charge in response to large steps are insufficient to exclude resistive models. However, the capacitative, but not the resistive model successfully explained results bearing on charge conservation assessed through pulse procedures involving: (i) small, 10 mV voltage steps from a series of prepulse voltages, (ii) voltage steps to a fixed potential from a series of hyperpolarized voltages, (iii) pulse sequences incorporating a 'staircase' of voltage steps. It is concluded that the earlier use of 'on' and 'off' equality in response to large voltage steps is insufficient to exclude a resistive basis for the non-linear transient. However pulse procedures explicitly designed to distinguish the two models give results consistent with a capacitative model for the non-linear charge and at variance with a resistive one.