Roles of stiffness and excluded volume in DNA denaturation

The nature and the universal properties of DNA thermal denaturation are investigated by Monte Carlo simulations. For suitable lattice models we determine the exponent c describing the decay of the probability distribution of denaturated loops of length l, $P \sim l^{-c}$. If excluded volume effects are fully taken into account, c= 2.10(4) is consistent with a first order transition. The stiffness of the double stranded chain has the effect of sharpening the transition, if it is continuous, but not of changing its order and the value of the exponent c, which is also robust with respect to inclusion of specific base-pair sequence heterogeneities.Comment: RevTeX 4 Pages and 4 PostScript figures included. Final version as publishe

Order of the phase transition in models of DNA thermal denaturation

We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with "nu_perpendicular" = - beta = 1, "nu_parallel" = gamma/2 = 2 (characteristic of short range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents "nu_perpendicular" = - beta = 1/2, "nu_parallel" = gamma/2 = 1.Comment: 4 pages of Latex, including 4 Postscript figures. To be published in Phys. Rev. Let

Force fluctuation in a driven elastic chain

We study the dynamics of an elastic chain driven on a disordered substrate and analyze numerically the statistics of force fluctuations at the depinning transition. The probability distribution function of the amplitude of the slip events for small velocities is a power law with an exponent $+AFw-tau$ depending on the driving velocity. This result is in qualitative agreement with experimental measurements performed on sliding elastic surfaces with macroscopic asperities. We explore the properties of the depinning transition as a function of the driving mode (i.e. constant force or constant velocity) and compute the force-velocity diagram using finite size scaling methods. The scaling exponents are in excellent agreement with the values expected in interface models and, contrary to previous studies, we found no difference in the exponents for periodic and disordered chains.Comment: 8 page

Pinning and Tribology of Tethered Monolayers on Disordered Substrates

We study the statistical mechanics and dynamics of crystalline films with a fixed internal connectivity on a random substrate. Defect free triangular lattices exhibit a sharp transition to a low temperature glassy phase with anomalous phonon fluctuations and a nonlinear force-displacement law with a continuously variable exponent, similar to the vortex glass phase of directed lines in 1+1 dimensions. The periodicity of the tethered monolayer acts like a filter which amplifies particular Fourier components of the disorder. However, the absence of annealed topological defects like dislocations is crucial: the transition is destroyed when the constraint of fixed connectivity is relaxed and dislocations are allowed to proliferate.Comment: revtex, preprint style, 27 pages. This submission is a revision of cond-mat/9607184. The revisions affect only Appendix B, Appendix C, and Eqs. 2.27, 2.28, 2.3

Phase Diagram for Splay Glass Superconductivity

Localization of flux lines to splayed columnar pins is studied. A sine-Gordon type renormalization group study reveals the existence of a Splay glass phase and yields an analytic form for the transition temperature into the glass phase. As an independent test, the $I-V$ characteristics are determined via a Molecular Dynamics code. The glass transition temperature supports the RG results convincingly. The full phase diagram of the model is constructed.Comment: 14 pages, uuencoded compressed tar file with 3 postscript figure

Bubble propagation in a helicoidal molecular chain

We study the propagation of very large amplitude localized excitations in a model of DNA that takes explicitly into account the helicoidal structure. These excitations represent the ``transcription bubble'', where the hydrogen bonds between complementary bases are disrupted, allowing access to the genetic code. We propose these kind of excitations in alternative to kinks and breathers. The model has been introduced by Barbi et al. [Phys. Lett. A 253, 358 (1999)], and up to now it has been used to study on the one hand low amplitude breather solutions, and on the other hand the DNA melting transition. We extend the model to include the case of heterogeneous chains, in order to get closer to a description of real DNA; in fact, the Morse potential representing the interaction between complementary bases has two possible depths, one for A-T and one for G-C base pairs. We first compute the equilibrium configurations of a chain with a degree of uncoiling, and we find that a static bubble is among them; then we show, by molecular dynamics simulations, that these bubbles, once generated, can move along the chain. We find that also in the most unfavourable case, that of a heterogeneous DNA in the presence of thermal noise, the excitation can travel for well more 1000 base pairs.Comment: 25 pages, 7 figures. Submitted to Phys. Rev.

Bubbles, clusters and denaturation in genomic DNA: modeling, parametrization, efficient computation

The paper uses mesoscopic, non-linear lattice dynamics based (Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA below and near the denaturation temperature. Computationally efficient notation is introduced for the relevant statistical mechanics. Computed melting profiles of long and short heterogeneous sequences are presented, using a recently introduced reparametrization of the PBD model, and critically discussed. The statistics of extended open bubbles and bound clusters is formulated and results are presented for selected examples.Comment: to appear in a special issue of the Journal of Nonlinear Mathematical Physics (ed. G. Gaeta

Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach

One-dimensional thermodynamic instabilities are phase transitions not prohibited by Landau's argument, because the energy of the domain wall (DW) which separates the two phases is infinite. Whether they actually occur in a given system of particles must be demonstrated on a case-by-case basis by examining the (non-) analyticity properties of the corresponding transfer integral (TI) equation. The present note deals with the generic Peyrard-Bishop model of DNA denaturation. In the absence of exact statements about the spectrum of the singular TI equation, I use Gauss-Hermite quadratures to achieve a single-parameter-controlled approach to rounding effects; this allows me to employ finite-size scaling concepts in order to demonstrate that a phase transition occurs and to derive the critical exponents.Comment: 5 pages, 6 figures, subm. to Phys. Rev.

Why is the DNA Denaturation Transition First Order?

We study a model for the denaturation transition of DNA in which the molecules are considered as composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d=2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.Comment: Revised version. To appear in Phys. Rev. Let

Statistical Mechanics of Torque Induced Denaturation of DNA

A unifying theory of the denaturation transition of DNA, driven by temperature T or induced by an external mechanical torque Gamma is presented. Our model couples the hydrogen-bond opening and the untwisting of the helicoidal molecular structure. We show that denaturation corresponds to a first-order phase transition from B-DNA to d-DNA phases and that the coexistence region is naturally parametrized by the degree of supercoiling sigma. The denaturation free energy, the temperature dependence of the twist angle, the phase diagram in the T,Gamma plane and isotherms in the sigma, Gamma plane are calculated and show a good agreement with experimental data.Comment: 5 pages, 3 figures, model improve