Prestress-dependent Rheology of Semiflexible Polymers of the Cytoskeleton

Abstract

Rheological properties of living cells are essential for their physiological functions. Microrheological measurements have shown that cytoskeletal contractile stress (or prestress) and weak power-law viscoelasticity are governing principles of cell rheology, and that these two properties are closely associated in living cells for reasons that are largely unknown. In this study, we develop a stochastic model of a semiflexible polymer of the cytoskeleton that links the power-law rheology to the prestress. We describe a semiflexible polymer chain as a three-dimensional elastically-jointed chain composed of nonlinearly elastic bonds jointed by linearly elastic torsional springs. Assuming that the chain dynamics is thermally driven, we use a Monte-Carlo-based algorithm to obtain numerical simulations of the chain's creep behavior during uniaxial stretching. We obtain that the creep curves follow a power-law and that this behavior changes with prestress in a manner that is consistent with previously reported data from living cells and reconstituted crosslinked actin gels. We show that the power-law creep results from a finite-speed propagation of free energy from the chain's end points towards the center of the chain in response to externally applied stretching force. We also show that the power-law dependence on the prestress results from the chain's nonlinear, stiffening behavior that originates from both entropic and enthalpic contributions. Based on qualitative similarities between model simulations and experimental data from living cells and actin gels, it is conceivable that the mechanisms embodied in our model may also be key determinants of the overall viscoelastic properties of living cells and actin gels.