DNA Twist Elasticity: Mechanics and Thermal Fluctuations

Abstract: The elastic properties of semiflexible polymers are of great importance in biology. There are experiments on biopolymers like double stranded DNA, which twist and stretch single molecules to probe their elastic properties. It is known that thermal fluctuations play an important role in determining molecular elastic properties, but a full theoretical treatment of the problem of twist elasticity of fluctuating ribbons using the simplest worm like chain model (WLC) remains elusive. In this paper, we approach this problem by taking first a mechanical approach and then incorporating thermal effects in a quadratic approximation applying the Gelfand-Yaglom (GY) method for computing fluctuation determinants. Our study interpolates between mechanics and statistical mechanics in a controlled way and shows how profoundly thermal fluctuations affect the elasticity of semiflexible polymers. The new results contained here are: 1) a detailed study of the minimum energy configurations with explicit expressions for their energy and writhe and plots of the extension versus Link for these configurations. 2) a study of fluctuations around the local minima of energy and approximate analytical formulae for the free energy of stretched twisted polymers derived by the Gelfand Yaglom method. We use insights derived from our mechanical approach to suggest calculational schemes that lead to an improved treatment of thermal fluctuations. From the derived formulae, predictions of the WLC model for molecular elasticity can be worked out for comparison against numerical simulations and experiments.