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

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 ν_r >= 2/d (=2).

Latex, 33 pages with 15 postscript figures

References in corpus (10)

• Smoothing effect of quenched disorder on polymer depinning transitions
• Sequence sensitivity of breathing dynamics in heteropolymer DNA
• Loop Dynamics in DNA Denaturation
• Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents
• Statistical mechanics of base stacking and pairing in DNA melting
• Master equation approach to DNA-breathing in heteropolymer DNA
• Numerical study of the disordered Poland-Scheraga model of DNA denaturation
• Critical properties and finite--size estimates for the depinning transition of directed random polymers
• On scaling laws at the phase transition of systems with divergent order parameter and/or internal length : the example of DNA denaturation
• Two-dimensional wetting with binary disorder: a numerical study of the loop statistics

Cited by in corpus (12)

• Fractional moment bounds and disorder relevance for pinning models
• The depinning transition in presence of disorder: a toy model
• Exact extreme value statistics at mixed order transitions
• Statistical physics of the melting of inhomogeneous DNA
• Dependence on temperature and GC content of bubble length distributions in DNA
• Dynamical versus statistical mesoscopic models for DNA denaturation
• Bubble statistics and positioning in superhelically stressed DNA
• DNA breathing dynamics: Analytic results for distribution functions of relevant Brownian functionals
• Denaturation of Circular DNA: Supercoil Mechanism
• Strong Disorder Renewal Approach to DNA denaturation and wetting : typical and large deviation properties of the free energy
• Mapping between the order of thermal denaturation and the shape of the critical line of mechanical unzipping in 1-dimensional DNA models
• Numerical study of DNA denaturation with self-avoidance: pseudo-critical temperatures and finite size behaviour