Denaturation of Circular DNA: Supercoil Mechanism

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.