Modeling and simulation of the mechanical response of biopolymer networks / y Wei Xi

Abstract

The mechanical response of live cells is largely determined by the cytoskeleton, a network composed of different types of biopolymers. In addition to maintain structural integrity and stability of cells, cytoskeleton also plays important roles in the processes like intracellular transport, cell division and locomotion. Although extensive effort has been spent in the past few decades trying to study the nonlinear and viscoelastic properties of bio-filament networks both experimentally and theoretically, fundamental questions such as how thermal fluctuations of biopolymers and the deformability as well as the association/dissociation kinetics of crosslinking molecules, “gluing” individual filaments together, dictate the bulk response of a network remain unsettled.

To address these important issues, a computational framework for analyzing the mechanical behavior of biopolymer networks was developed in this thesis on the basis of continuum mechanics. Specifically, a combined finite element-Langevin dynamics(FEM-LD)method was first established to capture the influence of thermal undulations of biopolymers. The validity of this new approach was verified by comparing its results with a variety of theoretical predications. In addition, strategies for the implementation of this method in simulating the dynamic response of realistic filamentous networks have also been developed. Interestingly, it was found that entropic effect will be important when the macroscopic strain level is below ~1%,beyond which the network response will be dominated by filament elasticity.

After that, formulations taking into account the deformability and failure of crosslinking molecules, along with large deflections of individual filaments, were added to the model. It was shown that the stress-strain relationship of random biopolymer networks typically undergoes linear increase –strain hardening –stress serration –total fracture transitions due to the interplay between the bending and stretching of individual filaments and the deformation and breakage of cross-linkers. Furthermore, the network fracture energy was found to reach its minimum when the crosslinking molecules possess intermediate rotational stiffness, reflecting the fact that most of the strain energy will be stored in the distorted filaments with rigid cross-linkers while the imposed deformation will be “evenly” distributed among significantly more crosslinking molecules with high rotational compliance.

Finally, the influence of binding/unbinding kinetics of cross-linkers on the rheological response biopolymer networks was examined and three distinct regimes were identified. At high driving frequencies, the bulk network response will be governed by the mechanics of individual filaments, leading to a 3/4 exponent scaling behavior, while stress relaxation induced by the unbinding of crosslinking molecules will dominate the process at intermediate frequencies. In comparison, the collective effect of multiple dissociation of cross-linkers will result in a power-law rheology behavior (with an exponent of ~0.5) when the driving frequency is very low, in broad agreement with experimental observations.