Activation in a Skeletal Muscle Contraction Model with a Modification for Insect Fibrillar Muscle

Abstract

A sliding filament model for muscle contraction is extended by including an activation mechanism based on the hypothesis that the binding of calcium by a regulating protein in the myofibrils must occur before the rate constant governing the making of interactions between cross-bridges and thin filament sites can take on nonzero values. The magnitude of the rate constant is proportional to the amount of bound calcium. The model's isometric twitch and rise of force in an isometric tetanus are similar to the curves produced by real muscles. It redevelops force after a quick release in an isometric tetanus faster than the initial rise. Quick release experiments on the model during an isometric twitch show that the "active state" curve produced is different from the postulated calcium binding curve. The force developed by the model can be increased by a small quick stretch delivered soon after activation to values near the maximum generated in an isometric tetanus. Following the quick stretch, the force remains near the tetanic maximum for a long time even though the calcium binding curve rises to a peak and subsequently decays by about 50%. The model satisfies the constraint of shortening with a constant velocity under a constant load. Modifications can be made in the model so that it produces the delayed force changes following step length changes characteristic of insect fibrillar muscle.