Rheology of crossbridge ensembles

Abstract

How skeletal muscle responds to mechanical perturbations, its rheology, is important for animal movement control. The molecular machinery of myosin II-actin crossbridge cycling is a crucial part of muscles rheological properties, and multiple models have been proposed for this mechanochemical process. But current understanding of the scale-connection from individual molecular motors to ensemble rheology is limited. Here we present computational and mathematical analyses of several different hypotheses of crossbridge dynamics, from 2-state to 5-state myosin II motor models, and show that an ensemble of actomyosin crossbridges exhibits surprisingly simple rheological behavior in all cases. The ensemble rheology is captured by a sum of at most three linear viscoelastic sub-processes, and as few as one for some crossbridge models. This simplification lends itself to computationally efficient phenomenological muscle models with experimentally measurable parameters, while still remaining grounded in crossbridge theory. However, the collapse of the ensemble behavior to few linear sub-processes identifies major limitations of crossbridge models that cannot be resolved by adding complexity to the crossbridge cycle and point to the roles of inter-crossbridge interactions and non-crossbridge elements.