A strain-dependent ratchet model for [phosphate]- and [ATP]-dependent muscle contraction

A minimal strain-dependent ratchet model of muscle cross-bridge action is proposed which is broadly compatible with structural and kinetic constraints. Its essential features are: (1) dynamic binding of the S1-products complex to actin through a disorder-order transition coupled to the release of inorganic phosphate; (2) the absence of a force-generating rotation of the myosin head between the two force-holding states A.M.ADP and A.M; (3) strain-control of ADP release and ATP binding, giving net isometric tension and directed motility by the selective dissociation of negatively strained bound states. With a disordered pre-force state, the binding rate to state A.M.ADP need not be symmetric in x, the actin site displacement. With faster binding at positive x, the model predicts many steady-state and transient properties of striated muscle observed experimentally, including phases 2-4 of tension recovery from length changes and their dependence on excess phosphate (which enhances and accelerates phase 3) and reduced ATP (which gives a bimodal phase 2 and slows one mode). The response to large perturbations is often sensitive to the number of actin sites used, and to the inclusion of a 1 nm displacement of the neck region on release of ADP. The latter stabilizes the periodic tension behaviour produced by repeated releases.