On the Bending and Stretching Elasticity of Biopolymer Filaments

Elastic filaments play an important role in the behaviour of cells and biological tissues. In this paper a two-dimensional nonlinear elastic framework, incorporating both bending and stretching, for the behaviour of biopolymer filaments treated as one-dimensional continua is developed. Explicit formulas for the extension-force relationship are obtained which include dependence on the initial end-to-end distance of the filament, unlike some existing models in the literature of, for example, the worm-like chain. The approach adopted allows treatment of both flexible and semi-flexible filaments and has the flexibility to accommodate different degrees of approximation. A key ingredient in the application of the model is inclusion of a body force term in the equilibrium equation. This is essential for finding non-trivial solutions of the governing equations and boundary conditions for filaments under tension. This highlights certain inconsistencies in the mechanics evident in the biophysics literature. Since the behaviour of individual filaments has a strong influence on the behaviour of networks of filaments the theory developed here can serve as a basis for analyzing the elasticity of networks such as actin and other filamentous biopolymer networks.