Models of calcium activation account for differences between skeletal and cardiac force redevelopment kinetics

To explain observed differences in the activation dependence of force redevelopment kinetics between cardiac and skeletal muscle, two numerical models of contractile regulation by Ca2+ were investigated. Ca2+ binding and force production were each modelled as two-state processes with forward and reverse rate constants taken from the literature. The first model incorporates four possible thin-filament states. In the second model Ca2+ is assumed not to dissociate from a thin-filament unit in the force-generating state, resulting in three states. The four-state model can account for the activation dependence of the rate constant of tension redevelopment (ktr) seen in skeletal muscle, without requiring that Ca2+ directly modulates the kinetics of any step in the cross-bridge cycle. Using identical kinetic parameters, the three-state model shows no activation dependence of ktr, consistent with our results in cardiac muscle. Following a step increase in [Ca2+], the rate of rise in tension (as described by the rate constant kCa) varies with the final [Ca2+] for both models, consistent with experimental results from skeletal and cardiac muscle. These numerical models demonstrate that experimental measurements thought to reveal changes in kinetic parameters may simply reflect coupling between the two kinetic processes of Ca2+ binding and force generation. Furthermore, the models present possible differences in the Ca2+ activation scheme between cardiac and skeletal muscle which can account for the contrasting activation dependencies of force redevelopment kinetics.