Meeting Abstract
Muscles act as agonist-antagonist pairs at joints to move them and to also provide mechanical stiffness. The antagonist provides minimal resistance when stretched during motion to reduce energy consumption and mitigate the risk of tissue damage. This implies a fluid-like behavior, where the antagonist freely yields under external loads without building up stresses in the crossbridges. For providing stability or rejecting external pertubations, i.e. for mechanical stiffness, the agonist and antagonist behave like an elastic solid by resisting external loads and stressing the crossbridges. Here, we use an ensemble crossbridge model of the sarcomere to understand how muscle may accomplish these seemingly opposing demands of an elastic solid vs. viscous fluid. Actomyosin crossbridges elastically resist stretching on times shorter than the detachment timescale of myosin. Thus, the sarcomere resembles an elastic solid against fast perturbations (high frequencies). Over longer times (low frequencies), myosin motors cycle between bound/unbound states, thus releasing any stored elastic energy and the sarcomere yields in response to exteral loads. We show analytically that the mechanical response in the limit of infinite molecular bonds is a generalized linear viscoelastic model (Maxwell material) with multiple timescales over which stress relaxes at the crossbridges. The timescales emerge from the binding/unbinding rates, as well as the spread of crossbridge strains. Therefore, the sarcomere under stretching is not simply a linear spring and damper in series. Our analyses illustrate that slowing of the unbinding rate with load is central to the functional properties of the sarcomere, namely to yield freely against light loads and yet resist large loads.
