Estimation of cross-bridge stiffness from maximum thermodynamic efficiency

In muscle, work is performed by myosin cross-bridges during interactions with actin filaments. The amount of work performed during each interaction can be related to the mechanical properties of the cross-bridge; work is the integral of the force produced with respect to the distance that the cross-bridge moves the actin filament, and force is determined by the stiffness of the attached cross-bridge. In this paper, cross-bridge stiffness in frog sartorius muscle was estimated from thermodynamic efficiency (work/free energy change) using a two-state cross-bridge model, assuming constant stiffness over the working range and tight-coupling between cross- bridge cycles and ATP use. This model accurately predicts mechanical efficiency (work/enthalpy output). A critical review of the literature indicates that a realistic value for maximum thermodynamic efficiency of frog sartorius is 0.45 under conditions commonly used in experiments on isolated muscle. Cross-bridge stiffness was estimated for a range of power stroke amplitudes. For realistic amplitudes (10–15nm), estimated cross-bridge stiffness was between 1 and 2.2pNnm−1. These values are similar to those estimated from quick-release experiments, taking into account compliance arising from structures other than cross-bridges, but are substantially higher than those from isolated protein studies. The effects on stiffness estimates of relaxing the tight-coupling requirement and of incorporating more force-producing cross-bridge states are also considered.