Molecular elasticity and the geometric phase
Joseph Samuel, Supurna Sinha
TL;DR
This paper introduces a method to solve the Worm Like Chain model for twisting polymers, revealing a periodic free energy and linking elasticity to geometric phases, with implications for biopolymer mechanics.
Contribution
It develops an accurate solution method for the WLC model and establishes a novel analogy between polymer elasticity and geometric phases.
Findings
WLC free energy is periodic with a 4 pi period.
Elastic response of molecules to torque is graphically demonstrated.
The approach predicts properties of twist-storing biopolymers like DNA.
Abstract
We present a method for solving the Worm Like Chain (WLC) model for twisting semiflexible polymers to any desired accuracy. We show that the WLC free energy is a periodic function of the applied twist with period 4 pi. We develop an analogy between WLC elasticity and the geometric phase of a spin half system. These analogies are used to predict elastic properties of twist-storing polymers. We graphically display the elastic response of a single molecule to an applied torque. This study is relevant to mechanical properties of biopolymers like DNA.
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