The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A-->3A, 2A-->0 is studied through the non-Hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the pair-contact process, which has a phase transition in the universality class of directed percolation (DP) and an infinite number of absorbing steady states. When single-particle diffusion is added, the number of absorbing steady states is reduced to 2 and the model no longer shows DP critical behavior. The exponents theta=nu(parallel)/nu(perpendicular) and beta/nu(perpendicular) are calculated numerically. The value of beta/nu(perpendicular) is close to the value of the parity conserving universality class, in spite of the absence of local conservation laws.

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 approximately 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.

Recent magnetic tweezers experiments have reported systematic deviations of the twist response of double-stranded DNA from the predictions of the twistable worm-like chain model. Here we show, by means of analytical results and computer simulations, that these discrepancies can be resolved if a coupling between twist and bend is introduced. We obtain an estimate of 40 ± 10 nm for the twist-bend coupling constant. Our simulations are in good agreement with high-resolution, magnetic-tweezers torque data. Although the existence of twist-bend coupling was predicted long ago (Marko and Siggia, Macromolecules 27, 981 (1994)), its effects on the mechanical properties of DNA have been so far largely unexplored. We expect that this coupling plays an important role in several aspects of DNA statics and dynamics.Introduction The mechanical properties of doublestranded DNA (dsDNA) are critical for both its structure and function within the cell. The stretching of ds-DNA under applied forces has been measured by single molecule techniques [1, 2] and is accurately reproduced by a simple polymer model, containing the bending stiffness as the only parameter [1]. Elastic polymer models were also successfully employed to study the torsional properties of dsDNA [4] and compared to single-molecule experiments, such as magnetic tweezers (MT) [2] (Fig. 1, right). The currently accepted elastic model for dsDNA is the twistable worm-like chain (TWLC) [6]. Although the TWLC correctly describes the overall response of ds-DNA to applied forces and torques, it fails to quantitatively explain the force-dependence of the effective torsional stiffness [3, 4]. Here, we show that an alternative elastic model proposed by Marko and Siggia (MS) [5], quantitatively describes the force-dependence of the effective torsional stiffness, by taking into account a direct coupling between twist and bend deformations. Furthermore, we demonstrate that the MS model explains an unresolved discrepancy in the measured intrinsic torsional stiffness, obtained from different techniques. Finally, we show that the MS model provides a better description of the pre-buckling torque response of dsDNA, determined in high-resolution magnetic torque tweezers (MTT) experiments, than the TWLC.TWLC and MS models Both the TWLC and MS models describe dsDNA as a continuous, twistable curve by associating an orthonormal frame { e 1 , e 2 , e 3 } with each base pair (Fig. 1) [5]. We choose e 3 tangent to the helical axis and e 1 and e 2 oriented as in Fig. 1. In the continuum limit these vectors are functions of the arc-length variable s. For the stretching forces considered here (f < 10 pN) dsDNA is inextensible, hence 0 ≤ s ≤ L, with L the contour length. A local dsDNA conformation is given by a vector Ω(s) which describes the infinitesimal rotation connecting { e 1 (s), e 2 (s), e 3 (s)} to { e 1 (s + ds), e 2 (s + ds), e 3 (s + ds)}. The direction of Ω(s) identifies the rotation axis, and |Ω(s)|ds the infinitesimal rotation angle. In particular, if Ω(s) is parallel to e 3...

We analyze a series of publicly available controlled experiments (Latin square) on Affymetrix high density oligonucleotide microarrays using a simple physical model of the hybridization process. We plot for each gene the signal intensity versus the hybridization free energy of RNA/DNA duplexes in solution, for perfect matching and mismatching probes. Both values tend to align on a single master curve in good agreement with Langmuir adsorption theory, provided one takes into account the decrease of the effective target concentration due to target-target hybridization in solution. We give an example of a deviation from the expected thermodynamical behavior for the probe set 1091 at due to annotation problems, i.e. the surface-bound probe is not the exact complement of the target RNA sequence, because of errors present in public databases at the time when the array was designed. We show that the parametrization of the experimental data with RNA/DNA free energy improves the quality of the fits and enhances the stability of the fitting parameters compared to previous studies.

Recent advances in the understanding of the melting behavior of double-stranded DNA with statistical mechanics methods lead to improved estimates of the weight factors for the dissociation events of the chains, in particular for interior loop melting. So far, in the modeling of DNA melting, the entropy of denaturated loops has been estimated from the number of configurations of a closed self-avoiding walk. It is well understood now that a loop embedded in a chain is characterized by a loop closure exponent c which is higher than that of an isolated loop. Here we report an analysis of DNA melting curves for sequences of a broad range of lengths (from 10 to 10 6 base pairs) calculated with a program based on the algorithms underlying MELTSIM. Using the embedded loop exponent we find that the cooperativity parameter is one order of magnitude bigger than current estimates. We argue that in the melting region the double helix persistence length is greatly reduced compared to its room temperature value, so that the use of the embedded loop closure exponent for real DNA sequences is justified.

It is well-established that many physical properties of DNA at sufficiently long length scales can be understood by means of simple polymer models. One of the most widely used elasticity models for DNA is the twistable wormlike chain (TWLC), which describes the double helix as a continuous elastic rod with bending and torsional stiffness. An extension of the TWLC, which has recently received some attention, is the model by Marko and Siggia, who introduced an additional twist-bend coupling, expected to arise from the groove asymmetry. By performing computer simulations of two available versions of oxDNA, a coarsegrained model of nucleic acids, we investigate the microscopic origin of twist-bend coupling. We show that this interaction is negligible in the oxDNA version with symmetric grooves, while it appears in the oxDNA version with asymmetric grooves. Our analysis is based on the calculation of the covariance matrix of equilibrium deformations, from which the stiffness parameters are obtained. The estimated twist-bend coupling coefficient from oxDNA simulations is G = 30 ± 1 nm. The groove asymmetry induces a novel twist length scale and an associated renormalized twist stiffness κ t ≈ 80 nm, which is different from the intrinsic torsional stiffness C ≈ 110 nm. This naturally explains the large variations on experimental estimates of the intrinsic stiffness performed in the past.

PACS. 64.60.Ht Dynamic critical phenomena - 02.70.-c Computational techniques - 02.60.Dc Numerical linear algebra,

Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the barrier. Average transition path times and, recently, their full probability distribution have been measured for several biomolecular systems, e.g., in the folding of nucleic acids or proteins. Motivated by these experiments, we have calculated the full transition path time distribution for a single stochastic particle crossing a parabolic barrier, including inertial terms which were neglected in previous studies. These terms influence the short time scale dynamics of a stochastic system and can be of experimental relevance in view of the short duration of transition paths. We derive the full transition path time distribution as well as the average transition path times and discuss the similarities and differences with the high friction limit.