Force fluctuations in stretching a tethered polymer

TL;DR

This paper re-examines a fluctuation relation in polymer unfolding, providing exact solutions and simulations that confirm the relation's form while emphasizing the importance of explicit time dependence in force distributions.

Contribution

It offers an exact solution for force fluctuations in tethered polymer stretching and validates the fluctuation relation through molecular dynamics simulations.

Findings

The ratio of positive to negative force probabilities is exponential in force.

The fluctuation relation's constant depends linearly on average unfolding forces and inverse temperature.

Simulations confirm the theoretical form of the fluctuation relation with proper time dependence.

Abstract

The recently proposed fluctuation relation in unfolding forces [Phys. Rev. E ${\bf 84}$, $060101$(R) $(2011)$] is re-examined taking into account the explicit time dependence of the force distribution. The stretching of a tethered Rouse polymer is exactly solved and the ratio of the probabilities of positive to negative forces is shown to be an exponential in force. Extensive steered molecular dynamics simulations of unfolding of deca alanine peptide confirm the form of fluctuation relation proposed earlier, but with explicit correct time dependence of unfolding forces taken into account. From exact calculations and simulations, a linear dependence of the constant in the exponential of the fluctuation relation on average unfolding forces and inverse temperature is proposed.