Rate constant of muscle force redevelopment reflects cooperative activation as well as cross-bridge kinetics

The rate of muscle force redevelopment after release-restretch protocols has previously been interpreted using a simple two-state cross-bridge cycling model with rate constants for transitions between non-force-bearing and force-bearing states, f, and between force-bearing and non-force-bearing states, g. Changes in the rate constant of force redevelopment, as with varying levels of Ca2+ activation, have traditionally been attributed to Ca2+-dependent f. The current work adds to this original model a state of unactivated, noncycling cross-bridges, The resulting differential equation for activated, force-bearing cross-bridges, N-cf, was N-cf=[g+f(K/(K+1))]1N(cf)+f(K/(K+1))N-T, where K is an equilibrium constant defining the distribution between cycling and noncycling cross-bridges and N-T is the total number of cross-bridges. Cooperativity by which force-bearing cross-bridges participate in their own activation was introduced by making K dependence N-cf. Model results demonstrated that such cooperativity, which tends to enhance force generation at low levels of Ca2+ activation, has a counter-intuitive effect of slowing force redevelopment. These dynamic effects of cooperativity are most pronounced at low Ca2+ activation. As Ca2+ activation increases, the cooperative effects become less important to the dynamics of force redevelopment and, at the highest levels of Ca2+ activation, the dynamics of force redevelopment reflect factors other than cooperative mechanisms. These results expand on earlier interpretations of Ca2+ dependence of force redevelopment; rather than Ca2+-dependent f, Ca2+-dependent force redevelopment arises from changing expressions of cooperativity between force-bearing cross-bridges and activation.