Bubble coalescence in interacting system of DNA molecules

TL;DR

This paper models bubble coalescence in DNA molecules using statistical physics, identifying multiple phases in one model and a single dominant phase in another, enhancing understanding of DNA bubble dynamics.

Contribution

It introduces two parametric models of DNA bubble coalescence and analyzes their phase behavior using Gibbs measures, revealing multiple phases in one model and uniqueness in the other.

Findings

First model exhibits up to three phases, including bubble coalescence.

Second model has a unique phase with no bubble coalescence.

Thermodynamic analysis clarifies conditions for different DNA bubble states.

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.