Theory of biopolymer stretching at high forces

TL;DR

This paper presents a unified high-force elasticity theory for biopolymers based on persistence length and monomer spacing, validated by simulations and applicable to various biopolymers, explaining when FJC or WLC models are appropriate.

Contribution

It introduces a unified theoretical framework for biopolymer elasticity at high forces, linking force regimes to polymer models and providing a method to estimate persistence length from force extension curves.

Findings

The theory accurately predicts biopolymer behavior across different force regimes.

Validation with simulations confirms the theory's applicability.

Analysis of diverse biopolymers demonstrates the theory's broad relevance.

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.