Simple modelling of linear and nonlinear mechanical responses to sinusoidal oscillations during muscle contraction

The mechanical responses of muscle to sinusoidal oscillations were analysed using a contraction model based on Huxley's 1957 model. To reproduce the three well-documented exponential processes resolved in the course of sinusoidal analysis, a few modifications had to be made on the original Huxley's model: (1) Each myosin cross-bridge should support substantial force at its position where the rate of detachment (g) abruptly changes. (2) Each cross-bridge should have the capability of stress-relaxation while attached to actin. This stress-relaxation should occur with a rate constant greater than the overall turnover rate of cross-bridges. After these modifications, the model reproduces not only the three exponential processes, but also the nonlinearity in the mechanical response, which is derived from the asymmetrical dependence of the rate constants on the cross-bridge strain. The present study provides a simplest model which reproduces the linear and nonlinear responses to sinusoidal oscillations, and help relate the exponential processes to the underlying attachment/detachment steps in the cross-bridge cycle.