The First and Second Variation of the Total Energy of Closed Duplex DNA in Planar Case

TL;DR

This paper derives the first and second variations of the total energy of planar closed duplex DNA, providing new shape equations and correcting a previous mistake in the literature.

Contribution

It presents the first and second energy variations for planar DNA and corrects an error in prior research, advancing understanding of DNA shape energetics.

Findings

Derived the first and second energy variations for planar DNA.

Obtained general shape equations of DNA.

Corrected a previous mistake in the literature.

Abstract

DNA's shape mostly lies on its total energy $F$. Its corresponding equilibrium shape equations can be got by classical variation method: letting the first energy variation $\delta^{(1)}F=0$. Here we not only provide the first variation $\delta^{(1)}F$ but also give the second variation $\delta^{(2)}F$ in planar case. Moreover, the general shape equations of DNA are obtained and a mistake in [Zhang, \emph{et al}. {\it Phys. Rev. E} {\bf 70} 051902 (2004)] is pointed out.