Stability analysis of kinked DNA in $\mathcal{F}(K,\tau)$ model

TL;DR

This paper analyzes the stability of short DNA rings using an extended elastic model, deriving conditions for stability and aligning theoretical results with experimental data.

Contribution

It introduces an extended worm-like rod chain (EWLRC) model incorporating spontaneous curvature to better reflect DNA twist effects and stability.

Findings

Stability conditions derived from Fourier series expansion.

The extended model aligns with experimental observations.

Spontaneous curvature influences DNA ring stability.

Abstract

We phenomenologically analyze short DNA rings' stability by discussing the second variation of its elastic free energy. Through expanding the perturbation functions as Fourier series, we obtain DNA rings' stability condition in a general case. By reviewing the relationship between the Kirchhoff model and the worm-like road chain (WLRC) model, we insert a spontaneous curvature term which can partly reflect the twist angle's contribution to free energy in the WLRC model and name this extended model the EWLRC model. By choosing suitable spontaneous curvature, stability analysis in this model provide us with some useful results which are consistent with the experimental observations.