A combined finite element-Langevin dynamics (FEM-LD) approach for analyzing the mechanical response of bio-polymer networks

A Langevin dynamics based formulation is proposed to describe the shape fluctuations of biopolymer filaments. We derive a set of stochastic partial differential equations (SPDEs) to describe the temporal evolution of the shape of semiflexible filaments and show that the solutions of these equations reduce to predictions from classical modal analysis. A finite element formulation to solve these SPDEs is also developed where, besides entropy, the finite deformation of the filaments has been taken into account. The validity of the proposed finite element-Langevin dynamics (FEM-LD) approach is verified by comparing the simulation results with a variety of theoretical predictions. The method is then applied to study the mechanical behavior of randomly cross-linked F-actin networks. We find that as deformation progresses, the response of such networks undergoes transitions from being entropy dominated to being governed by filament bending and then, eventually, to being dictated by filament stretching. The levels of macroscopic stress at which these transitions take place were found to be around 1% and 10%, respectively, of the initial bulk modulus of the network, in agreement with recent experimental observations.