Local Control Model of Excitation–Contraction Coupling in Skeletal Muscle

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Abstract
This is a quantitative model of control of Ca2+ release from the sarcoplasmic reticulum in skeletal muscle, based on dual control of release channels (ryanodine receptors), primarily by voltage, secondarily by Ca2+ (Ríos, E., and G. Pizarro. 1988. NIPS. 3:223–227). Channels are positioned in a double row array of between 10 and 60 channels, where exactly half face voltage sensors (dihydropyridine receptors) in the transverse (t) tubule membrane (Block, B.A., T. Imagawa, K.P. Campbell, and C. Franzini-Armstrong. 1988. J. Cell Biol. 107:2587–2600). We calculate the flux of Ca2+ release upon different patterns of pulsed t-tubule depolarization by explicit stochastic simulation of the states of all channels in the array. Channels are initially opened by voltage sensors, according to an allosteric prescription (Ríos, E., M. Karhanek, J. Ma, A. González. 1993. J. Gen. Physiol. 102:449–482). Ca2+ permeating the open channels, diffusing in the junctional gap space, and interacting with fixed and mobile buffers produces defined and changing distributions of Ca2+ concentration. These concentrations interact with activating and inactivating channel sites to determine the propagation of activation and inactivation within the array. The model satisfactorily simulates several whole-cell observations, including kinetics and voltage dependence of release flux, the “paradox of control,” whereby Ca2+-activated release remains under voltage control, and, most surprisingly, the “quantal” aspects of activation and inactivation (Pizarro, G., N. Shirokova, A. Tsugorka, and E. Ríos. 1997. J. Physiol. 501:289–303). Additionally, the model produces discrete events of activation that resemble Ca2+ sparks (Cheng, H., M.B. Cannell, and W.J. Lederer. 1993. Science (Wash. DC). 262:740–744). All these properties result from the intersection of stochastic channel properties, control by local Ca2+, and, most importantly, the one dimensional geometry of the array and its mesoscopic scale. Our calculations support the concept that the release channels associated with one face of one junctional t-tubule segment, with its voltage sensor, constitute a functional unit, termed the “couplon.” This unit is fundamental: the whole cell behavior can be synthesized as that of a set of couplons, rather than a set of independent channels.