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

Abstract

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.)