Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks

TL;DR

This study investigates the elastic response of cross-linked semiflexible polymer networks, revealing two distinct deformation regimes and identifying a key parameter that determines the transition between them.

Contribution

It introduces a numerical framework to analyze the linear response of 2D cross-linked actin networks and identifies a scalar parameter that predicts deformation regimes.

Findings

Elastic moduli vanish at a rigidity percolation threshold.

Two deformation regimes: affine stretching and bending-dominated.

A scalar parameter predicts the transition between regimes.

Abstract

Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominantly affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.