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Ca(2+)-force Relationship Of Frog Skeletal Muscle: A Dynamic Model For Parameter Estimation

D. M. Shames, A. J. Baker, M. W. Weiner, S. A. Camacho

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A simple mathematical model describing the dynamic connection between Ca2+ and force generation in intact skeletal muscle from the frog has been developed from isometric force responses to cytosolic Ca2+ concentration ([Ca2+]c) transients during tetanic and twitch contractions. The main element of the model is a two-state cross-bridge cycle characterized by the fractional rate of cross-bridge attachment (f(app)) and the fractional rate of cross-bridge detachment (g*). While g* is constant, f(app) is time varying and regulated by both [Ca2+]c and force. Having only four adjustable parameters, the model is mathematically unique, thereby allowing precise parameter estimation from the dynamic Ca2+ and force data. The model should be useful for developing insights into the relative importance for force generation and relaxation of 1) the size and shape of the Ca2+ transient, 2) the sensitivity of the fractional rate of cross-bridge attachment to both the [Ca2+]c and the force responses, and 3) the fractional rate of cross-bridge detachment, which is insensitive to both Ca2+ and force.