Numerical evidence for relevance of disorder in a Poland-Scheraga DNA denaturation model with self-avoidance: Scaling behavior of average quantities

TL;DR

This study numerically investigates how sequence heterogeneity affects DNA denaturation in a Poland-Scheraga model with self-avoidance, revealing finite size effects and disorder relevance through off-lattice simulations.

Contribution

It provides the first off-lattice numerical analysis of disorder effects in a self-avoiding Poland-Scheraga DNA model for large sequences, highlighting finite size effects and disorder relevance.

Findings

Finite size effects depend on an intrinsic length scale x.

Disorder effects become significant only for exponentially large sequence lengths.

Crossover observed from pure-like to disorder-dominated behavior at large sizes.

Abstract

We study numerically the effect of sequence heterogeneity on the thermodynamic properties of a Poland-Scheraga model for DNA denaturation taking into account self-avoidance, i.e. with exponent c_p=2.15 for the loop length probability distribution. In complement to previous on-lattice Monte Carlo like studies, we consider here off-lattice numerical calculations for large sequence lengths, relying on efficient algorithmic methods. We investigate finite size effects with the definition of an appropriate intrinsic length scale x, depending on the parameters of the model. Based on the occurrence of large enough rare regions, for a given sequence length N, this study provides a qualitative picture for the finite size behavior, suggesting that the effect of disorder could be sensed only with sequence lengths diverging exponentially with x. We further look in detail at average quantities for the particular case x=1.3, ensuring through this parameter choice the correspondence between the off-lattice and the on-lattice studies. Taken together, the various results can be cast in a coherent picture with a crossover between a nearly pure system like behavior for small sizes N < 1000, as observed in the on-lattice simulations, and the apparent asymptotic behavior indicative of disorder relevance, with an (average) correlation length exponent \nu_r >= 2/d (=2).