Periodically driven DNA: Theory and simulation

TL;DR

This paper models driven DNA under oscillatory force, revealing a dynamical transition, scaling behaviors of hysteresis loop area, and new force-dependent exponents, supported by analytical and numerical methods.

Contribution

It introduces a generic driven DNA model, identifies a dynamical transition, and uncovers new scaling exponents related to force and frequency.

Findings

Hysteresis loop area scales with frequency and force, matching previous detailed models.

A new force scaling exponent of 2.5 was identified and validated.

Scaling exponents are robust against temperature and friction variations.

Abstract

We propose a generic model of driven DNA under the influence of an oscillatory force of amplitude $F$ and frequency $\nu$ and show the existence of a dynamical transition for a chain of finite length. We find that the area of the hysteresis loop, $A_{\rm loop}$, scales with the same exponents as observed in a recent study based on a much more detailed model. However, towards the true thermodynamic limit, the high-frequency scaling regime extends to lower frequencies for larger chain length $L$ and the system has only one scaling ($A_{\rm loop} \approx \nu^{-1}F^2)$. Expansion of an analytical expression for $A_{\rm loop}$ obtained for the model system in the low-force regime revealed that there is a new scaling exponent associated with force ($A_{\rm loop} \approx \nu^{-1}F^{2.5}$), which has been validated by high-precision numerical calculation. By a combination of analytical and numerical arguments, we also deduce that for large but finite $L$, the exponents are robust and independent of temperature and friction coefficient.