Ca²⁺-force relationship of frog skeletal muscle: A dynamic model for parameter estimation

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.