Three-dimensional Semiflexible Network with Transient Cross-links: A Finite Element Kinetic Monte Carlo Approach
Semiflexible biopolymer networks cross-linked by noncovalent bonds allow the network’s topology to evolve over time and in response to applied stress. We developed a finite element kinetic Monte Carlo simulation approach, which allows cross-links to reorganize in a three-dimensional network, to explore the dynamics of semiflexible networks with transient cross-links. We will first discuss this simulation strategy, and then apply this tool to explore the following aspects of semiflexible networks: The natural bundle formation and the dynamics of bundle growth, especially in density and energy. The stress relaxation of networks with constrained filaments under affine strain field, and we find the linear shear elasticity of these networks mainly arises from the deformation change of the high-energy cross-links orientating in certain directions, and both the number and the elastic energy growth of these cross-links scales linearly with strain. We also find the strain energy dissipates exponentially through the strain-induced cross-link reorganization, and the cross-link configuration is trained during this process in a manner that tends to maintain the current strain on the filaments. Finally we conclude with proposals for new experiments to test these numerical results.