Numerical study of the disordered Poland-Scheraga model of DNA denaturation

Abstract

We numerically study the binary disordered Poland-Scheraga model of DNA denaturation, in the regime where the pure model displays a first order transition (loop exponent $c=2.15>2$). We use a Fixman-Freire scheme for the entropy of loops and consider chain length up to $N=4\cdot 10^5$, with averages over $10^4$ samples. We present in parallel the results of various observables for two boundary conditions, namely bound-bound (bb) and bound-unbound (bu), because they present very different finite-size behaviors, both in the pure case and in the disordered case. Our main conclusion is that the transition remains first order in the disordered case: in the (bu) case, the disorder averaged energy and contact densities present crossings for different values of $N$ without rescaling. In addition, we obtain that these disorder averaged observables do not satisfy finite size scaling, as a consequence of strong sample to sample fluctuations of the pseudo-critical temperature. For a given sample, we propose a procedure to identify its pseudo-critical temperature, and show that this sample then obeys first order transition finite size scaling behavior. Finally, we obtain that the disorder averaged critical loop distribution is still governed by $P(l)\sim 1/l^c$ in the regime $l\ll N$, as in the pure case.

arXiv comment12 pages, 13 figures. Revised version

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• Random walks and polymers in the presence of quenched disorder
• Dynamical versus statistical mesoscopic models for DNA denaturation
• Numerical evidence for relevance of disorder in a Poland-Scheraga DNA denaturation model with self-avoidance: Scaling behavior of average quantities
• Bubble statistics and positioning in superhelically stressed DNA
• The free energy in the Derrida--Retaux recursive model
• Random copolymer adsorption: Morita approximation compared to exact numerical simulations
• Numerical study of DNA denaturation with self-avoidance: pseudo-critical temperatures and finite size behaviour
• Random wetting transition on the Cayley tree : a disordered first-order transition with two correlation length exponents