DNA thermal denaturation by polymer field theory approach: effects of the environment

Yu Holovatch,Yu Honchar,C Von Ferber

doi:10.5488/cmp.24.33603

Abstract

We analyse the effects of the environment (solvent quality, presence of extended structures - crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the d = 3 case, the corresponding diverging ε = 4-d expansions are evaluated by restoring their convergence via the resummation technique. For the space dimension d = 2, the exponents are deduced from mapping the polymer model onto a two-dimensional random lattice, i.e., in the presence of quantum gravity. We also show that the first order transition is further strengthened by the presence of extended impenetrable regions in a solvent that restrict the number of the macromolecule configurations.

Highlights

Poland-Scheraga model: scaling relations and ε-expansionThe model suggested by Poland and Scheraga in middle-sixties [2, 3] describes the DNA thermal denaturation by a proper account of energy-entropy interplay: at low temperatures T, the bound state, figure 1 a, is favoured by energy whereas at high T the unbound state, figure 1 b, is favoured by entropy as the one having more configurations
We analyse the effects of the environment that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands
The DNA thermal denaturation is described in terms of the Poland-Scheraga model [2,3,4] that allows its treatment in terms of phase transition theory

Summary

Poland-Scheraga model: scaling relations and ε-expansion

The model suggested by Poland and Scheraga in middle-sixties [2, 3] describes the DNA thermal denaturation by a proper account of energy-entropy interplay: at low temperatures T, the bound state, figure 1 a, is favoured by energy whereas at high T the unbound state, figure 1 b, is favoured by entropy as the one having more configurations. A more general approach to analyze scaling properties of the macromolecule configurations shown in figure 1 was based on polymer network theory, as interaction between the loop and the chain was taken into account [17,18,19,20,21, 26, 27] Considering both the side chains and the loop as self-avoiding walks (SAWs), it was shown that the phase transition is of. Substituting expressions (1.6)-(1.11) into the scaling relations (1.5) one can evaluate loop exponents ci at any value of d It is well known, that ε-expansions of the field theory are asymptotic at best and proper resummation technique is required to get a reliable numerical information on their basis [37, 38]. The first order ε-expansion provides the so-called optimal truncation [38] for the ci(ε) series

Crowded environment

Conclusions