Modeling spatial inhomogeneities in a crossbridge ensemble reveals where mean-field estimates of sarcomere stiffness break down.

Abstract

How actomyosin crossbridges share and transmit loads between the thick and thin filaments in a sarcomere underlies the emergence of muscle's stimulus-dependent material properties. In particular, stiffness, the resistance to external length perturbations, is of interest because of its importance to muscle's in vivo function. Following A.F. Huxley's original work, many sarcomere models treat the thick and thin filaments as rigid and lump their compliance into a single series elastic element. Under this approximation, the crossbridges act as parallel elastic force generators. So their stiffnesses are thought to add linearly and their collective dynamics are captured by the ensemble mean. In this work, we investigate the accuracy of this approximation by exactly deriving the stiffness of a spring network that accounts for the spatially distributed filament and crossbridge compliances. We show that even the small degree of measured filament compliance in a sarcomere leads to a profound deviation of the mechanical behavior from the ensemble mean. Unlike the lumped compliance approximation, the exact accounting finds that the emergent stiffness depends on the spatial distribution of crossbridges; a property that cannot be captured by a mean model. Moreover, under physiologically relevant crossbridge numbers, the lumped compliance approximation underestimates the net stiffness of a pair of filaments by over two-fold. Further analyses show that crossbridge clusters may be thermodynamically favored because they lower the total system strain energy that arises from externally applied loads at the filament boundaries and the internal forces applied by the myosin powerstroke. We speculate that the dependence of stiffness and strain energy on the spatial inhomogeneity of crossbridges has mechanochemical consequences that affect the development and cycling of crossbridges in actomyosin networks.