Bubble coalescence in interacting system of DNA molecules

Abstract

We consider two models of interacting DNA molecules: \textit{First} is (four parametric) bubble coalescence model in interacting DNAs (shortly: BCI-DNA). \textit{Second} is (three parametric) bubble coalescence model in a condensed DNA molecules (shortly BCC-DNA). To study bubble coalescence thermodynamics of BCI-DNA and BCC-DNA models we use methods of statistical physics. Namely, we define Hamiltonian of each model and give their translation-invariant Gibbs measures (TIGMs). For the first model we find parameters such that corresponding Hamiltonian has up to three TIGMs (three phases of system) biologically meaning existence of three states: ``No bubble coalescence'', ``Dominated soft zone'', ``Bubble coalescence''. For the second model we show that for any (admissible) parameters this model has unique TIGM. This is a state where ``No bubble coalescence'' phase dominates.