Denaturation of Circular DNA: Supercoil Mechanism

Abstract

The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double stranded helix, released by a loop denaturation, is absorbed by \emph{supercoils}. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent \(c\). However the first order transition displayed by the PS model for \(c>2\) in linear DNA is replaced by a continuous transition with arbitrarily high order as \(c\) approaches 2, while the second-order transition found in the linear case in the regime \(1<c\le2\) disappears. In addition, our analysis reveals that melting under fixed linking number is a \emph{condensation transition}, where the condensate is a macroscopic loop which appears above the critical temperature.