Mechanics of biopolymer networks from the thermodynamics of molecular motors

Contractile biopolymer networks, such as the actomyosin meshwork of animal cells, are ubiquitous in living organisms. The active gel theory, which provides a thermodynamic framework for these materials, has been mostly used in conjunction with the assumption that the microstructure of the biopolymer network is based on rigid rods.  However, experimentally, crossed-linked actin networks exhibit entropic elasticity.  Here we combine an entropic elasticity kinetic theory with an active flux modelling biological activity.  We determine this active flux using Onsager reciprocal relations applied at the microscopic scale of individual motors. We derive the macroscopic active stress that arises from the resulting dynamics and obtain a closed-form model of the macroscopic mechanical behaviour.