The kinetics relating calcium and force in skeletal muscle.

The kinetics relating Ca2+ transients and muscle force were examined using data obtained with the photoprotein aequorin in skeletal muscles of the rat, barnacle, and frog. These data were fitted by various models using nonlinear methods for minimizing the least mean square errors. Models in which Ca2+ binding to troponin was rate limiting for force production did not produce good agreement with the observed data, except for a small twitch of the barnacle muscle. Models in which cross-bridge kinetics were rate limiting also did not produce good agreement with the observed data, unless the detachment rate constant was allowed to increase sharply on the falling phase of tension production. Increasing the number of cross-bridge states did not dramatically improve the agreement between predicted and observed force. We conclude that the dynamic relationship between Ca2+ transients and force production in intact muscle fibers under physiological conditions can be approximated by a model in which (a) two Ca2+ ions bind rapidly to each troponin molecule, (b) force production is limited by the rate of formation of tightly bound cross-bridges, and (c) the rate of cross-bridge detachment increases rapidly once tension begins to decline and free Ca2+ levels have fallen to low values after the last stimulus. Such a model can account not only for the pattern of force production during a twitch and tetanus, but also the complex, nonlinear pattern of summation which is observed during an unfused tetanus at intermediate rates of stimulation.