On the length scale dependence of DNA conformational change under local perturbation

TL;DR

This study investigates how the length of DNA influences its conformational change under local perturbations, revealing length-dependent energy requirements and stability characteristics through analytical and numerical methods.

Contribution

The paper introduces a length-dependent analysis of DNA conformational dynamics using a modified Lindstedt-Poincare method and numerical simulations, highlighting the impact of chain length on stability and energy barriers.

Findings

Minimum energy for conformational change varies with DNA length

Longer DNA chains are less stable against random perturbations

Two distinct length regions affect conformational dynamics

Abstract

Conformational change of a DNA molecule is frequently observed in multiple biological processes and has been modelled using a chain of strongly coupled oscillators with a nonlinear bistable potential. While the mechanism and properties of conformational change in the model have been investigated and several reduced order models developed, the conformational dynamics as a function of the length of the oscillator chain is relatively less clear. To address this, we used a modified Lindstedt-Poincare method and numerical computations. We calculate a perturbation expansion of the frequency of the model's nonzero modes, finding that approximating these modes with their unperturbed dynamics, as in a previous reduced order model, may not hold when the length of the DNA model increases. We investigate the conformational change to local perturbation in models of varying lengths, finding that for chosen input and parameters, there are two regions of DNA length in the model, first where the minimum energy required to undergo the conformational change increases with DNA length; and second, where it is almost independent of the length of the DNA model. We analyze the conformational change in these models by adding randomness to the local perturbation, finding that the tendency of the system to remain in a stable conformation against random perturbation decreases with an increase in the DNA length. These results should help to understand the role of the length of a DNA molecule in influencing its conformational dynamics.