Biopolymer elasticity: Mechanics and thermal fluctuations

Abstract

We present an analytical study of the role of thermal fluctuations in shaping molecular elastic properties of semiflexible polymers. Our study interpolates between mechanics and statistical mechanics in a controlled way and shows how thermal fluctuations modify the elastic properties of biopolymers. We present a study of the minimum-energy configurations with explicit expressions for their energy and writhe and plots of the extension versus link for these configurations and a study of fluctuations around the local minima of energy and approximate analytical formulas for the free energy of stretched twisted polymers. The central result of our study is a closed-form expression for the leading thermal fluctuation correction to the free energy around the nonperturbative writhing family solution for the configuration of a biopolymer. From the derived formulas, the predictions of the wormlike chain model for molecular elasticity can be worked out for a comparison against numerical simulations and experiments.