Stochastic force generation in an isometric binary mechanical system

Accurate models of muscle contraction are necessary for understanding muscle performance and the molecular modifications that enhance it (e.g., therapeutics, posttranslational modifications, etc.). As a thermal system containing millions of randomly fluctuating atoms that on the thermal scale of a muscle fiber generate unidirectional force and power output, muscle mechanics are constrained by the laws of thermodynamics. According to a thermodynamic muscle model, muscle's power stroke occurs with the shortening of an entropic spring consisting of an ensemble of force-generating myosin motor switches, each induced by actin binding and gated by inorganic phosphate release. This model differs fundamentally from conventional molecular power stroke models that assign springs to myosin motors in that it is physically impossible to describe an entropic spring in terms of the springs of its molecular constituents. A simple two-state thermodynamic model (a binary mechanical system) accurately accounts for muscle force-velocity relationships, force transients following rapid mechanical and chemical perturbations, and a thermodynamic work loop. Because this model transforms our understanding of muscle contraction, it must continue to be tested. Here, we show that a simple stochastic kinetic simulation of isometric muscle force predicts four phases of a force-generating loop that bifurcates between periodic and stochastic beating through mechanisms framed by two thermodynamic equations. We compare these model predictions with experimental data including observations of spontaneous oscillatory contractions (SPOCs) in muscles and periodic force generation in small myosin ensembles.