Mechanics and thermodynamics of contractile entropic biopolymer networks

Contractile biopolymer networks, such as the actomyosin meshwork of animal cells, are ubiquitous in living organisms. The active gel theory, which provides the 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, crosslinked actin network exhibits entropic elasticity. Here we combine an entropic elasticity kinetic theory, in the spirit of the Green and Tobolsky model of transiently crosslinked networks, with an active flux modelling biological activity. We determine this active flux using Onsager reciprocal relations and interpret the corresponding microscopic dynamics. We obtain a closed-form model of the macroscopic mechanical behaviour. We show how this model can be written using the framework of multiplicative strain gradient decomposition, which is convenient for the resolution of such problems.