Statistical physics of the melting of inhomogeneous DNA

TL;DR

This study investigates how sequence heterogeneity influences DNA melting, revealing that different regions open at slightly different temperatures but exhibit similar local opening behaviors, with implications for understanding phase transition order.

Contribution

It provides a detailed analysis of local DNA melting transitions in inhomogeneous sequences using two dynamical models, highlighting the effects of heterogeneity and sequence length on melting behavior.

Findings

Heterogeneity causes different sequence portions to open at different temperatures.

Local opening behavior resembles that of homogeneous sequences of the same length.

Sequence length influences the applicability of thermodynamic limit assumptions.

Abstract

We studied how the inhomogeneity of a sequence affects the phase transition that takes place at DNA melting. Unlike previous works, which considered thermodynamic quantities averaged over many different inhomogeneous sequences, we focused on precise sequences and investigated the succession of local openings that lead to their dissociation. For this purpose, we performed Transfer Integral type calculations with two different dynamical models, namely the heterogeneous Dauxois-Peyrard-Bishop model and the model based on finite stacking enthalpies we recently proposed. It appears that, for both models, the essential effect of heterogeneity is to let different portions of the investigated sequences open at slightly different temperatures. Besides this macroscopic effect, the local aperture of each portion indeed turns out to be very similar to that of a homogeneous sequence with the same length. Rounding of each local opening transition is therefore merely a size effect. For the Dauxois-Peyrard-Bishop model, sequences with a few thousands base pairs are still far from the thermodynamic limit, so that it is inappropriate, for this model, to discuss the order of the transition associated with each local opening. In contrast, sequences with several hundreds to a few thousands base pairs are pretty close to the thermodynamic limit for the model we proposed. The temperature interval where power laws holds is consequently broad enough to enable the estimation of critical exponents. On the basis of the few examples we investigated, it seems that, for our model, disorder does not necessarily induce a decrease of the order of the transition.