  The denaturation transition of circular DNA is studied within a
Poland-Scheraga type approach, generalized to account for the fact that the
total linking number (LK), which measures the number of windings of one strand
around the other, is conserved. In the model the LK conservation is maintained
by invoking both overtwisting and writhing (supercoiling) mechanisms. This
generalizes previous studies which considered each mechanism separately. The
phase diagram of the model is analyzed as a function of the temperature and the
elastic constant $\kappa$ associated with the overtwisting energy for any given
loop entropy exponent, $c$. As is the case where the two mechanisms apply
separately, the model exhibits no denaturation transition for $c \le 2$. For
$c>2$ and $\kappa=0$ we find that the model exhibits a first order transition.
The transition becomes of higher order for any $\kappa>0$. We also calculate
the contribution of the two mechanisms separately in maintaining the
conservation of the linking number and find that it is weakly dependent on the
loop exponent $c$.
