Theory of biopolymer stretching at high forces

Abstract

We provide a unified theory for the high force elasticity of biopolymers solely in terms of the persistence length, $\xi_p$, and the monomer spacing, $a$. When the force $f>\fh \sim k_BT\xi_p/a^2$ the biopolymers behave as Freely Jointed Chains (FJCs) while in the range $\fl \sim k_BT/\xi_p < f < \fh$ the Worm-like Chain (WLC) is a better model. We show that $\xi_p$ can be estimated from the force extension curve (FEC) at the extension $x\approx 1/2$ (normalized by the contour length of the biopolymer). After validating the theory using simulations, we provide a quantitative analysis of the FECs for a diverse set of biopolymers (dsDNA, ssRNA, ssDNA, polysaccharides, and unstructured PEVK domain of titin) for $x \ge 1/2$. The success of a specific polymer model (FJC or WLC) to describe the FEC of a given biopolymer is naturally explained by the theory. Only by probing the response of biopolymers over a wide range of forces can the $f$-dependent elasticity be fully described.