The influences of geometric shape of cross section on equilibrium configuration of DNA in elastic rod model

Ye Xiao,Zaixing Huang

doi:10.1063/1.4936639

Ye Xiao, Zaixing Huang

Open Access

https://doi.org/10.1063/1.4936639

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Abstract

The equilibrium configuration equations of DNA chain with elastic rod model are derived in detail by the variation of the free energy functional, which depends on the curvature, torsion, twisting angle and its derivative with respect to the arc-length of central axis curve of rod. With the different shapes of rod, we obtain the equilibrium equations of DNA with circular and noncircular cross sections, which provide an approach to describe the physical behaviors of A-, B-, Z-DNA. The results show that the elastic rod model with circular cross section can accurately characterize the equilibrium configurations of A-, B-DNA, while the model with elliptical cross sections is more suitable for Z-DNA.

Highlights

Since the structure of the DNA double helix was discovered by James Watson and Francis Crick in 1953,1 the effects of geometric and topological properties on physical behaviors of DNA have always been an important issue in biophysics
The equilibrium configuration equations of DNA chain with elastic rod model are derived in detail by the variation of the free energy functional, which depends on the curvature, torsion, twisting angle and its derivative with respect to the arc-length of central axis curve of rod
The results show that the elastic rod model with circular cross section can accurately characterize the equilibrium configurations of A, B-DNA, while the model with elliptical cross sections is more suitable for Z-DNA

Summary

INTRODUCTION

Since the structure of the DNA double helix was discovered by James Watson and Francis Crick in 1953,1 the effects of geometric and topological properties on physical behaviors of DNA have always been an important issue in biophysics. The geometric configuration of DNA chain is determined by its curvature and torsion. In this model the geometric effects of cross section are taken into account through the bending rigidity and twisting rigidity of DNA chain. The results show that the elastic rod model with circular cross section can accurately characterize the equilibrium configurations of A-, B-DNA, while the model with elliptical cross sections is more suitable for Z-DNA.

THE EQUILIBRIUM EQUATIONS OF DNA CHAIN

FREE ENERGY DENSITY FUNCTIONAL OF DNA CHAIN

CONCLUSIONS