Theory of Biopolymer Stretching at High Forces

We provide a unified theory for the high force entropic elasticity of biopolymers solely in terms of the persistence length, ξ , and the monomer spacing, a. When the force f>ℱ ~ k /a² the biopolymers behave as freely jointed chains (FJCs) while in the range ℱ ~ k <f<ℱ the worm-like chain (WLC) is a better model. We show that ξ can be estimated from the force extension curve (FEC) at the extension x ≈ 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 ≥ 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.