Beam theory of cellular microfilaments based on coarse-grained molecular force field

Abstract

Microfilaments are the main component of the cell cytoskeleton and have a crucial influence on the morphology of living cells. The microfilaments provide mechanical support against applied loads and overcome competing forces that arise from various mechanisms, such as the elasticity of the cell membrane, binding reactions, and surface tension. However, modeling the mechanical properties of microfilaments is an open problem. In the present paper, we proposed a new continuum deformation energy density of microfilaments using the coarse-grained molecular force field and the local differential geometry of curves. In the new theory, the deformation energy density is a function of the microfilament’s strain and the curvature. This theory also unfolded the connections between the mechanical parameters and the coarse-grained force field. We found that the stretching stiffness and the bending stiffness are independent of the section of microfilaments. Microfilaments have a nonlinear stretching-bending term different from the classical beam theory. This means the classical beam theory cannot be directly applied to microfilaments with large deformations. Our theory provides the basis that the modified classical beam theory applies to the nonlinear mechanical behavior of cellular microfilaments.