Micromechanical model for elasticity of the cell cytoskeleton

Semiflexible polymer networks, such as cell cytoskeleton, differ significantly from their flexible counterparts in their deformation energy storage mechanism. As a result, the network elasticity is governed by both enthalpic and entropic variations. In addition, the enthalpic effect shows two distinct regimes of energy storage mechanism, the affine and nonaffine regimes. In the past, computation-based modeling on random networks, such as the Mikado model, was used to demonstrate the physical mechanism of mechanical deformation of semiflexible networks. These models are computationally intensive and hence are difficult to apply to studying whole cells. In this paper, we develop a micromechanical model to predict the average macroscopic elastic properties of a random, semiflexible, biopolymer network. The model employs a unit cell consisting of four semiflexible chains and four equivalent axial-bending springs. The proposed unit-cell-based micromechanical model represents a statistically average realization of the actual network and gives the average mechanical properties, such as the shear modulus. Comparisons between the model predictions and Mikado model results confirm that this micromechanical model captures the essential deformation physics revealed from previous studies on the actual network and is capable of predicting the transition between nonaffine and affine deformations. This model can be used to develop efficient continuum constitutive models of the cytoskeleton in the future.