Helix-coil Transition in Closed Circular DNA
  A simplified model for the closed circular DNA (ccDNA) is proposed to describe some specific features of the helix-coil transition in such molecule. The Hamiltonian of ccDNA is related to the one introduced earlier for the linear DNA. The basic assumption is that the reduced energy of the hydrogen bond is not constant through the transition process but depends effectively on the fraction of already broken bonds. A transformation formula is obtained which relates the temperature of ccDNA at a given degree of helicity during the transition to the temperature of the corresponding linear chain at the same degree of helicity. The formula provides a simple method to calculate the melting curve for the ccDNA from the experimental melting curve of the linear DNA with the same nucleotide sequence. 
V.F. Morozov, Shura Hayryan, E.Sh. Mamasakhlisov, A.V. Grigoryan, A.V.   Badasyan, Chin-Kun Hu