Mechanism for conversion between twist and writhe of DNA based on chiral gauge potential

Abstract

It is well known that the linking number is the sum of the writhing number and twisting number based on white’s formula. In this work, we reveal the underlying physics of the transformation between the twist and the writhe of deoxyribonucleic acid (DNA). In the framework of the Landau model, we describe the local interaction between the base pairs by using the chiral gauge potential. With the chiral gauge potential, we develop a geometrical model where the free energy density is given by the geometrical parameters, including the normal curvature, the geodesic curvature, and the geodesic torsion. It is shown that the chiral gauge potential plays a crucial role in the conversion between the twist and the writhe of DNA. By using the invariance of the self-linking number, we find that when the total twisting number is changed by −Δ Q, the writhing number is changed by Δ Q. Our findings not only deepen the understanding of the topological nature of DNA, but also provide a physical model for the research of the conformation of DNA.