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Coarse-grained models have emerged as valuable tools to simulate long DNA molecules while maintaining computational efficiency. These models aim at preserving interactions among coarse-grained variables in a manner that mirrors the underlying atomistic description. We explore here a method for testing coarse-grained vs. all-atom models using stiffness matrices in Fourier space ($q$-stiffnesses), which are particularly suited to probe DNA elasticity at different length scales. We focus on a class of coarse-grained rigid base DNA models known as cgDNA and its most recent version cgDNA+. Our analysis shows that while cgDNA+ follows closely the $q$-stiffnesses of the all-atom model, the original cgDNA shows some deviations for twist and bending variables which are rather strong in the $q \to 0$ (long length scale) limit. The consequence is that while both cgDNA and cgDNA+ give a suitable description of local elastic behavior, the former misses some effects which manifest themselves at longer length scales. In particular, cgDNA performs poorly on the twist stiffness with a value much lower than expected for long DNA molecules. Conversely, the all-atom and cgDNA+ twist is strongly length scale dependent: DNA is torsionally soft at a few base pair distances, but becomes more rigid at distances of a few dozens base pairs. Our analysis shows that the bending persistence length in all-atom and cgDNA+ is somewhat overestimated., Comment: 9 pages, 6 figures

Proteins often regulate their activities via allostery - or action at a distance - in which the binding of a ligand at one binding site influences the affinity for another ligand at a distal site. Although less studied than in proteins, allosteric effects have been observed in experiments with DNA as well. In these experiments two or more proteins bind at distinct DNA sites and interact indirectly with each other, via a mechanism mediated by the linker DNA molecule. We develop a mechanical model of DNA/protein interactions which predicts three distinct mechanisms of allostery. Two of these involve an enthalpy-mediated allostery, while a third mechanism is entropy driven. We analyze experiments of DNA allostery and highlight the distinctive signatures allowing one to identify which of the proposed mechanisms best fits the data.

All-atom simulations have become increasingly popular to study conformational and dynamical properties of nucleic acids as they are accurate and provide high spatial and time resolutions. This high resolution however comes at a heavy computational cost and within the time scales of simulations nucleic acids weakly fluctuate around their ideal structure exploring a limited set of conformations. We introduce the RBB-NA algorithm which is capable of controlling rigid base parameters in all-atom simulations of Nucleic Acids. With suitable biasing potentials this algorithm can "force" a DNA or RNA molecule to assume specific values of the six rotational (tilt, roll, twist, buckle, propeller, opening) and/or the six translational parameters (shift, slide, rise, shear, stretch, stagger). The algorithm enables the use of advanced sampling techniques to probe the structure and dynamics of locally strongly deformed Nucleic Acids. We illustrate its performance showing some examples in which DNA is strongly twisted, bent or locally buckled. In these examples RBB-NA reproduces well the unconstrained simulations data and other known features of DNA mechanics, but it also allows one to explore the anharmonic behavior characterizing the mechanics of nucleic acids in the high deformation regime., Comment: 12 pages, 6 figures

Plectonemes are intertwined helically looped domains which form when a DNA molecule is supercoiled, i.e. over- or under-wounded. They are ubiquitous in cellular DNA and their physical properties have attracted significant interest both from the experimental and modeling side. In this work, we investigate fluctuations of the end-point distance z of supercoiled linear DNA molecules subject to external stretching forces. Our analysis is based on a two-phase model, which describes the supercoiled DNA as composed of a stretched and of a plectonemic phase. Several different mechanisms are found to contribute to extension fluctuations, characterized by the extension variance. We find the dominant contribution to the variance to originate from phase-exchange fluctuations, the transient shrinking and expansion of plectonemes, which is accompanied by an exchange of molecular length between the two phases. We perform Monte Carlo simulations of the Twistable Wormlike Chain and analyze the fluctuation of various quantities, which are found to agree with the two-phase model predictions. Furthermore, we show that the extension and its variance at high forces are very well captured by the two-phase model, provided that one goes beyond quadratic approximations., Comment: 13 pages, 8 figures

Mechanical properties of nucleic acids play an important role in many biological processes which often involve physical deformations of these molecules. At sufficiently long length scales (say above $\sim 20-30$ base pairs) the mechanics of DNA and RNA double helices is described by a homogeneous Twistable Wormlike Chain (TWLC), a semiflexible polymer model characterized by twist and bending stiffnesses. At shorter scales this model breaks down for two reasons: the elastic properties become sequence-dependent and the mechanical deformations at distal sites gets coupled. We discuss in this paper the origin of the latter effect using the framework of a non-local Twistable Wormlike Chain (nlTWLC). We show, by comparing all-atom simulations data for DNA and RNA double helices, that the non-local couplings are of very similar nature in these two molecules: couplings between distal sites are strong for tilt and twist degrees of freedom and weak for roll. We introduce and analyze a simple double-stranded polymer model which clarifies the origin of this universal distal couplings behavior. In this model, referred to as the ladder model, a nlTWLC description emerges from the coarsening of local (atomic) degrees of freedom into angular variables which describe the twist and bending of the molecule. Differently from its local counterpart, the nlTWLC is characterized by a length-scale-dependent elasticity. Our analysis predicts that nucleic acids are mechanically softer at the scale of a few base pairs and are asymptotically stiffer at longer length scales, a behavior which matches experimental data., Comment: 14 pages, 12 figures

While analyzing the persistence length of DNA atomistic simulations Wu et al. [J. Chem. Phys. 142, 125103 (2015)] introduced an empirical formula to account for the observed length-dependence. In particular they found that the persistence length increases with the distance. Here, we derive the formula by Wu et al. using a non-local twistable wormlike chain which introduces couplings between distal sites. Finally, we show that the same formula can account for the length-scale dependence of the torsional persistence length and is, in fact, applicable to any kind of polymer model with non-local couplings., Comment: 3 pages, 1 Figure

The mechanical properties of DNA are typically described by elastic theories with purely local couplings (on-site models). We discuss and analyze coarse-grained (oxDNA) and all-atom simulations, which indicate that in DNA distal sites are coupled. Hence, off-site models provide a more realistic description of the mechanics of the double helix. We show that off-site interactions are responsible for a length scale dependence of the elasticity, and we develop an analytical framework to estimate bending and torsional persistence lengths in models including these interactions. Our simulations indicate that off-site couplings are particularly strong for certain degrees of freedom, while they are very weak for others. If stiffness parameters obtained from DNA data are used, the theory predicts large length scale dependent effects for torsional fluctuations and a modest effect in bending fluctuations, which is in agreement with experiments., Comment: 16 pages, 9 figures; video abstract at https://youtu.be/8FUdFw8IbuY

Biomolecular conformational transitions are usually modeled as barrier crossings in a free energy landscape. The transition paths connect two local free energy minima and transition path times (TPT) are the actual durations of the crossing events. The simplest model employed to analyze TPT and to fit empirical data is that of a stochastic particle crossing a parabolic barrier. Motivated by some disagreement between the value of the barrier height obtained from the TPT distributions as compared to the value obtained from kinetic and thermodynamic analyses, we investigate here TPT for barriers which deviate from the symmetric parabolic shape. We introduce a continuous set of potentials, that starting from a parabolic shape, can be made increasingly asymmetric by tuning a single parameter. The TPT distributions obtained in the asymmetric case are very well-fitted by distributions generated by parabolic barriers. The fits, however, provide values for the barrier heights and diffusion coefficients which deviate from the original input values. We show how these findings can be understood from the analysis of the eigenvalues spectrum of the Fokker-Planck equation and highlight connections with experimental results., Comment: We dedicate this paper to the memory of our dear friend and colleague Carlo Vanderzande

DNA surface-hybridization biosensors utilize the selective hybridization of target sequences in solution to surface-immobilized probes. In this process, the target is usually assumed to be in excess, so that its concentration does not significantly vary while hybridizing to the surface-bound probes. If the target is initially at low concentrations and/or if the number of probes is very large and have high affinity for the target, the DNA in solution may get depleted. In this paper we analyze the equilibrium and kinetics of hybridization of DNA biosensors in the case of strong target depletion, by extending the Langmuir adsorption model. We focus, in particular, on the detection of a small amount of a single-nucleotide "mutant" sequence (concentration $c_2$) in a solution, which differs by one or more nucleotides from an abundant "wild-type" sequence (concentration $c_1 \gg c_2$). We show that depletion can give rise to a strongly-enhanced sensitivity of the biosensors. Using representative values of rate constants and hybridization free energies, we find that in the depletion regime one could detect relative concentrations $c_2/c_1$ that are up to three orders of magnitude smaller than in the conventional approach. The kinetics is surprisingly rich, and exhibits a non-monotonic adsorption with no counterpart in the no-depletion case. Finally, we show that, alongside enhanced detection sensitivity, this approach offers the possibility of sample enrichment, by substantially increasing the relative amount of the mutant over the wild-type sequence., Comment: 27 pages, 4 figures

By combining analytical results and simulations of various coarse-grained models we investigate the minimal energy shape of DNA minicircles which are torsionally constrained by an imposed over or undertwist. We show that twist-bend coupling, a cross interaction term discussed in the recent DNA literature, induces minimal energy shapes with a periodic alternance of parts with high and low curvature resembling rounded polygons. We briefly discuss the possible experimental relevance of these findings. We finally show that the twist and bending energies of minicircles are governed by renormalized stiffness constants, not the bare ones. This has important consequences for the analysis of experiments involving circular DNA meant to determine DNA elastic constants., Comment: 11 pages, 7 figures

The simplest model of DNA mechanics describes the double helix as a continuous rod with twist and bend elasticity. Recent work has discussed the relevance of a little-studied coupling $G$ between twisting and bending, known to arise from the groove asymmetry of the DNA double helix. Here, the effect of $G$ on the statistical mechanics of long DNA molecules subject to applied forces and torques is investigated. We present a perturbative calculation of the effective torsional stiffness $C_\text{eff}$ for small twist-bend coupling. We find that the "bare" $G$ is "screened" by thermal fluctuations, in the sense that the low-force, long-molecule effective free energy is that of a model with $G=0$, but with long-wavelength bending and twisting rigidities that are shifted by $G$-dependent amounts. Using results for torsional and bending rigidities for freely-fluctuating DNA, we show how our perturbative results can be extended to a non-perturbative regime. These results are in excellent agreement with numerical calculations for Monte Carlo "triad" and molecular dynamics "oxDNA" models, characterized by different degrees of coarse-graining, validating the perturbative and non-perturbative analyses. While our theory is in generally-good quantitative agreement with experiment, the predicted torsional stiffness does systematically deviate from experimental data, suggesting that there are as-yet-uncharacterized aspects of DNA twisting-stretching mechanics relevant to low-force, long-molecule mechanical response, which are not captured by widely-used coarse-grained models., Comment: 16 pages, 6 figures

We derive an analytical expression for the transition path time (TPT) distribution for a one-dimensional particle crossing a parabolic barrier. The solution is expressed in terms of the eigenfunctions and eigenvalues of the associated Fokker-Planck equation. The particle performs an anomalous dynamics generated by a power-law memory kernel, which includes memoryless Markovian dynamics as a limiting case. Our result takes into account absorbing boundary conditions, extending existing results obtained for free boundaries. We show that TPT distributions obtained from numerical simulations are in excellent agreement with analytical results, while the typically employed free boundary conditions lead to a systematic overestimation of the barrier height. These findings may be useful in the analysis of experimental results on transition path times. A web tool to perform this analysis is freely available., Comment: 7 pages; 6 figures

The capture and translocation of biomolecules through nanometer-scale pores are processes with a potential large number of applications, and hence they have been intensively studied in the recent years. The aim of this paper is to review existing models of the capture process by a nanopore, together with some recent experimental data of short single- and double-stranded DNA captured by Cytolysin A (ClyA) nanopore. ClyA is a transmembrane protein of bacterial origin which has been recently engineered through site-specific mutations, to allow the translocation of double- and single-stranded DNA. A comparison between theoretical estimations and experiments suggests that for both cases the capture is a reaction-limited process. This is corroborated by the observed salt dependence of the capture rate, which we find to be in quantitative agreement with the theoretical predictions., Comment: Published in JPCM Special Issue "Transport in Narrow Channels"

Recent work indicates that twist-bend coupling plays an important role in DNA micromechanics. Here we investigate its effect on bent DNA. We provide an analytical solution of the minimum-energy shape of circular DNA, showing that twist-bend coupling induces sinusoidal twist waves. This solution is in excellent agreement with both coarse-grained simulations of minicircles and nucleosomal DNA data, which is bent and wrapped around histone proteins in a superhelical conformation. Our analysis shows that the observed twist oscillation in nucleosomal DNA, so far attributed to the interaction with the histone proteins, is an intrinsic feature of free bent DNA, and should be observable in other protein-DNA complexes.

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 worm-like 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 coarse-grained 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 $G=30\pm1$~nm. The groove asymmetry induces a novel twist length scale and an associated renormalized twist stiffness $\kappa_{\rm t} \approx 80$~nm, which is different from the intrinsic torsional stiffness $C \approx 110$~nm. This naturally explains the large variations on experimental estimates of the intrinsic stiffness performed in the past., Comment: 20 pages, 8 figures

We develop a theoretical description of the critical zipping dynamics of a self-folding polymer. We use tension propagation theory and the formalism of the generalized Langevin equation applied to a polymer that contains two complementary parts which can bind to each other. At the critical temperature, the (un)zipping is unbiased and the two strands open and close as a zipper. The number of closed base pairs $n(t)$ displays a subdiffusive motion characterized by a variance growing as $\langle \Delta n^2(t) \rangle \sim t^\alpha$ with $\alpha < 1$ at long times. Our theory provides an estimate of both the asymptotic anomalous exponent $\alpha$ and of the subleading correction term, which are both in excellent agreement with numerical simulations. The results indicate that the tension propagation theory captures the relevant features of the dynamics and shed some new insights on related polymer problems characterized by anomalous dynamical behavior., Comment: 8 pages, 3 figures, submitted

By using the blob theory and computer simulations, we investigate the properties of a linear polymer performing a stationary rotational motion around a long impenetrable rod. In particular, in the simulations the rotation is induced by a torque applied to the end of the polymer that is tethered to the rod. Three different regimes are found, in close analogy with the case of polymers pulled by a constant force at one end. For low torques the polymer rotates maintaining its equilibrium conformation. At intermediate torques the polymer assumes a trumpet shape, being composed by blobs of increasing size. At even larger torques the polymer is partially wrapped around the rod. We derive several scaling relations between various quantities as angular velocity, elongation and torque. The analytical predictions match the simulation data well. Interestingly, we find a "thinning" regime where the torque has a very weak (logarithmic) dependence on the angular velocity. We discuss the origin of this behavior, which has no counterpart in polymers pulled by an applied force., Comment: 30 pages, 8 figures, 1 TOC figure; video abstract at https://youtu.be/LwicoSkh3mI

Some recent results on the rotational dynamics of polymers are reviewed and extended. We focus here on the relaxation of a polymer, either flexible or semiflexible, initially wrapped around a rigid rod. We also study the steady polymer rotation generated by a constant torque on the rod. The interplay of frictional and entropic forces leads to a complex dynamical behavior characterized by non-trivial universal exponents. The results are based on extensive simulations of polymers undergoing Rouse dynamics and on an analytical approach using force balance and scaling arguments. The analytical results are in general in good agreement with the simulations, showing how a simplified approach can correctly capture the complex dynamical behavior of rotating polymers., Comment: 13 pages; 7 figures; proceedings of the International Workshop on "Brownian Motion in Confined Geometries", Max Planck Institute for the Physics of Complex Systems in Dresden from 17 - 21 March 2014; to appear in EPJ-ST

We study the rotational dynamics of a flexible polymer initially wrapped around a rigid rod and unwinding from it. This dynamics is of interest in several problems in biology and constitutes a fundamental instance of polymer relaxation from a state of minimal entropy. We investigate the dynamics of several quantities such as the total and local winding angles and metric quantities. The results of simulations performed in two and three dimensions, with and without self-avoidance, are explained by a theory based on scaling arguments and on a balance between frictional and entropic forces. The early stage of the dynamics is particularly rich, being characterized by three coexisting phases., Comment: 9 pages, 9 figures

We briefly review some of the models used to describe DNA denaturation dynamics, focusing on the value of the dynamical exponent $z$, which governs the scaling of the characteristic time $\tau\sim L^z$ as a function of the sequence length $L$. The models contain different degrees of simplifications, in particular sometimes they do not include a description for helical entanglement: we discuss how this aspect influences the value of $z$, which ranges from $z=0$ to $z \approx 3.3$. Connections with experiments are also mentioned.

The relaxation dynamics of a polymer wound around a fixed obstacle constitutes a fundamental instance of polymer with twist and torque and it is of relevance also for DNA denaturation dynamics. We investigate it by simulations and Langevin equation analysis. The latter predicts a relaxation time scaling as a power of the polymer length times a logarithmic correction related to the equilibrium fluctuations of the winding angle. The numerical data support this result and show that at short times the winding angle decreases as a power-law. This is also in agreement with the Langevin equation provided a winding-dependent friction is used, suggesting that such reduced description of the system captures the basic features of the problem., Comment: 4 pages, 5 figures. Accepted for publication in Phys. Rev. Lett

In this article it is shown how optimized and dedicated microarray experiments can be used to study the thermodynamics of DNA hybridization for a large number of different conformations in a highly parallel fashion. In particular, free energy penalties for mismatches are obtained in two independent ways and are shown to be correlated with values from melting experiments in solution reported in the literature. The additivity principle, which is at the basis of the nearest-neighbor model, and according to which the penalty for two isolated mismatches is equal to the sum of the independent penalties, is thoroughly tested. Additivity is shown to break down for a mismatch distance below 5 nt. The behavior of mismatches in the vicinity of the helix edges, and the behavior of tandem mismatches are also investigated. Finally, some thermodynamic outlying sequences are observed and highlighted. These sequences contain combinations of GA mismatches. The analysis of the microarray data reported in this article provides new insights on the DNA hybridization parameters and can help to increase the accuracy of hybridization-based technologies., Comment: 13 pages, 11 figures, 1 table, Supplementary Data available in Appendix

We consider two complementary polymer strands of length $L$ attached by a common end monomer. The two strands bind through complementary monomers and at low temperatures form a double stranded conformation (zipping), while at high temperature they dissociate (unzipping). This is a simple model of DNA (or RNA) hairpin formation. Here we investigate the dynamics of the strands at the equilibrium critical temperature $T=T_c$ using Monte Carlo Rouse dynamics. We find that the dynamics is anomalous, with a characteristic time scaling as $\tau \sim L^{2.26(2)}$, exceeding the Rouse time $\sim L^{2.18}$. We investigate the probability distribution function, the velocity autocorrelation function, the survival probability and boundary behaviour of the underlying stochastic process. These quantities scale as expected from a fractional Brownian motion with a Hurst exponent $H=0.44(1)$. We discuss similarities and differences with unbiased polymer translocation., Comment: 7 pages, 8 figures

The winding angle probability distribution of a planar self-avoiding walk has been known exactly since a long time: it has a gaussian shape with a variance growing as $<\theta^2>\sim \ln L$. For the three-dimensional case of a walk winding around a bar, the same scaling is suggested, based on a first-order epsilon-expansion. We tested this three-dimensional case by means of Monte Carlo simulations up to length $L\approx25\,000$ and using exact enumeration data for sizes $L\le20$. We find that the variance of the winding angle scales as $<\theta^2>\sim (\ln L)^{2\alpha}$, with $\alpha=0.75(1)$. The ratio $\gamma = <\theta^4>/<\theta^2>^2=3.74(5)$ is incompatible with the gaussian value $\gamma =3$, but consistent with the observation that the tail of the probability distribution function $p(\theta)$ is found to decrease slower than a gaussian function. These findings are at odds with the existing first-order $\epsilon$-expansion results., Comment: 18 pages, 12 figures, 1 table

It has recently been shown that in some DNA microarrays the time needed to reach thermal equilibrium may largely exceed the typical experimental time, which is about 15h in standard protocols (Hooyberghs et al. Phys. Rev. E 81, 012901 (2010)). In this paper we discuss how this breakdown of thermodynamic equilibrium could be detected in microarray experiments without resorting to real time hybridization data, which are difficult to implement in standard experimental conditions. The method is based on the analysis of the distribution of fluorescence intensities I from different spots for probes carrying base mismatches. In thermal equilibrium and at sufficiently low concentrations, log I is expected to be linearly related to the hybridization free energy $\Delta G$ with a slope equal to $1/RT_{exp}$, where $T_{exp}$ is the experimental temperature and R is the gas constant. The breakdown of equilibrium results in the deviation from this law. A model for hybridization kinetics explaining the observed experimental behavior is discussed, the so-called 3-state model. It predicts that deviations from equilibrium yield a proportionality of $\log I$ to $\Delta G/RT_{eff}$. Here, $T_{eff}$ is an effective temperature, higher than the experimental one. This behavior is indeed observed in some experiments on Agilent arrays. We analyze experimental data from two other microarray platforms and discuss, on the basis of the results, the attainment of equilibrium in these cases. Interestingly, the same 3-state model predicts a (dynamical) saturation of the signal at values below the expected one at equilibrium., Comment: 27 pages, 9 figures, 1 table

We investigate by Monte Carlo simulations the zipping and unzipping dynamics of two polymers connected by one end and subject to an attractive interaction between complementary monomers. In zipping, the polymers are quenched from a high temperature equilibrium configuration to a low temperature state, so that the two strands zip up by closing up a "Y"-fork. In unzipping, the polymers are brought from a low temperature double stranded configuration to high temperatures, so that the two strands separate. Simulations show that the unzipping time, $\tau_u$, scales as a function of the polymer length as $\tau_u \sim L$, while the zipping is characterized by anomalous dynamics $\tau_z \sim L^\alpha$ with $\alpha = 1.37(2)$. This exponent is in good agreement with simulation results and theoretical predictions for the scaling of the translocation time of a forced polymer passing through a narrow pore. We find that the exponent $\alpha$ is robust against variations of parameters and temperature, whereas the scaling of $\tau_z$ as a function of the driving force shows the existence of two different regimes: the weak forcing ($\tau_z \sim 1/F$) and strong forcing ($\tau_z$ independent of $F$) regimes. The crossover region is possibly characterized by a non-trivial scaling in $F$, matching the prediction of recent theories of polymer translocation. Although the geometrical setup is different, zipping and translocation share thus the same type of anomalous dynamics. Systems where this dynamics could be experimentally investigated are DNA (or RNA) hairpins: our results imply an anomalous dynamics for the hairpins closing times, but not for the opening times., Comment: 15 pages, 9 figures

We study a model of "elastic" lattice polymer in which a fixed number of monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We show that the stored length density $\rho_m = 1 - /m$ scales asymptotically for large $m$ as $\rho_m=\rho_\infty(1-\theta/m + ...)$, where $\theta$ is the polymer entropic exponent, so that $\theta$ can be determined from the analysis of $\rho_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure $\rho_m$. The resulting estimates support the hypothesis that the exponent $\theta$ is determined only by the number of prime knots and not by their type. However, if knots are present, we observe strong corrections to scaling, which help to understand how an entropic competition between knots is affected by the finite length of the chain., Comment: 10 pages

One important preprocessing step in the analysis of microarray data is background subtraction. In high-density oligonucleotide arrays this is recognized as a crucial step for the global performance of the data analysis from raw intensities to expression values. We propose here an algorithm for background estimation based on a model in which the cost function is quadratic in a set of fitting parameters such that minimization can be performed through linear algebra. The model incorporates two effects: 1) Correlated intensities between neighboring features in the chip and 2) sequence-dependent affinities for non-specific hybridization fitted by an extended nearest-neighbor model. The algorithm has been tested on 360 GeneChips from publicly available data of recent expression experiments. The algorithm is fast and accurate. Strong correlations between the fitted values for different experiments as well as between the free-energy parameters and their counterparts in aqueous solution indicate that the model captures a significant part of the underlying physical chemistry., Comment: 21 pages, 5 figures

We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S=1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function, and the string order parameter. For this distribution at weak disorder, the systems is in the gapless Haldane phase with a disorder dependent dynamical exponent, z, and z=1 signals, the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point., Comment: 8 pages, 5 figures

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., Comment: 11 pages, 16 figures - final version as published

The genes of eukaryotes are characterized by protein coding fragments, the exons, interrupted by introns, i.e. stretches of DNA which do not carry any useful information for the protein synthesis. We have analyzed the melting behavior of randomly selected human cDNA sequences obtained from the genomic DNA by removing all introns. A clear correspondence is observed between exons and melting domains. This finding may provide new insights in the physical mechanisms underlying the evolution of genes., Comment: 4 pages, 8 figures - Final version as published. See also Phys. Rev. Focus 15, story 17

We analyze the unbinding transition for a two dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated to denaturated loops and end-segments distributions show sharp differences at the transition point and in the high temperature phase. Their values can be deduced from some exact arguments relying on a conformal mapping of copolymer networks into a fluctuating geometry, i.e. in the presence of quantum gravity. An excellent agreement between analytical and numerical estimates is observed for all cases analized., Comment: 9 pages, 11 figures, revtex4

Extensive DMRG calculations for spin S=1/2 and S=3/2 disordered antiferromagnetic Heisenberg chains show a rather distinct behavior in the two cases. While at sufficiently strong disorder both systems are in a random singlet phase, we show that weak disorder is an irrelevant perturbation for the S=3/2 chain, contrary to what expected from a naive application of the Harris criterion. The observed irrelevance is attributed to the presence of a new correlation length due to enhanced end-to-end correlations. This phenomenon is expected to occur for all half-integer S > 1/2 chains. A possible phase diagram of the chain for generic S is also discussed., Comment: 6 Pages and 6 figures. Final version as published

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., Comment: 8 Pages, 9 Figures, substantially extended version

Recently Garel, Monthus and Orland (Europhys. Lett. v 55, 132 (2001)) considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition., Comment: 7 Pages, RevTeX, 8 Figures

For a model of DNA denaturation, exponents describing the distributions of denaturated loops and unzipped end-segments are determined by exact enumeration and by Monte Carlo simulations in two and three dimensions. The loop distributions are consistent with first order thermal denaturation in both cases. Results for end-segments show a coexistence of two distinct power laws in the relative distributions, which is not foreseen by a recent approach in which DNA is treated as a homogeneous network of linear polymer segments. This unexpected feature, and the discrepancies with such an approach, are explained in terms of a refined scaling picture in which a precise distinction is made between network branches representing single stranded and effective double stranded segments., Comment: 8 pages, 8 figures

We investigate the Rubinstein-Duke model for polymer reptation by means of density-matrix renormalization group techniques both in absence and presence of a driving field. In the former case the renewal time \tau and the diffusion coefficient D are calculated for chains up to N=150 reptons and their scaling behavior in N is analyzed. Both quantities scale as powers of N: $\tau \sim N^z$ and $D \sim 1/N^x$ with the asymptotic exponents z=3 and x=2, in agreement with the reptation theory. For an intermediate range of lengths, however, the data are well-fitted by some effective exponents whose values are quite sensitive to the dynamics of the end reptons. We find 2.7

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 published

Critical properties of quantum spin chains with varying degrees of disorder are studied at zero temperature by analytical and extensive density matrix renormalization methods. Generally the phase diagram is found to contain three phases. The weak disorder regime, where the critical behavior is controlled by the fixed points of the pure system and the strong disorder regime, which is attracted by an infinite randomness fixed point, are separated by an intermediate disorder regime, where dynamical scaling is anisotropic and the static and dynamical exponents are disorder dependent., Comment: 4 pages, 3 figures

We investigate the critical properties of a one dimensional stochastic lattice model with n (permutation symmetric) absorbing states. We analyze the cases with $n \leq 4$ by means of the non-hermitian density matrix renormalization group. For n=1 and n=2 we find that the model is respectively in the directed percolation and parity conserving universality class, consistent with previous studies. For n=3 and n=4, the model is in the active phase in the whole parameter space and the critical point is shifted to the limit of one infinite reaction rate. We show that in this limit the dynamics of the model can be mapped onto that of a zero temperature n-state Potts model. On the basis of our numerical and analytical results we conjecture that the model is in the same universality class for all $n \geq 3$ with exponents $z = \nu_\|/\nu_\perp = 2$, $\nu_\perp = 1$ and $\beta = 1$. These exponents coincide with those of the multispecies (bosonic) branching annihilating random walks. For n=3 we also show that, upon breaking the symmetry to a lower one ($Z_2$), one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters., Comment: 10 pages, RevTeX, and 10 PostScript figures included

We analyze the Rubinstein-Duke model for polymer reptation by means of density matrix renormalization techniques. We find a crossover behavior for a series of quantities as function of the polymer length. The crossover length may become very large if the mobility of end groups is small compared to that of the internal reptons. Our results offer an explanation to a controversy between theory, experiments and simulations on the leading and subleading scaling behavior of the polymer renewal time and diffusion constant., Comment: 4 Pages, RevTeX, and 4 PostScript figures included

Using exact enumeration methods and Monte Carlo simulations we study the phase diagram relative to the conformational transitions of a two dimensional diblock copolymer. The polymer is made of two homogeneous strands of monomers of different species which are joined to each other at one end. We find that depending on the values of the energy parameters in the model, there is either a first order collapse from a swollen to a compact phase of spiral type, or a continuous transition to an intermediate zipped phase followed by a first order collapse at lower temperatures. Critical exponents of the zipping transition are computed and their exact values are conjectured on the basis of a mapping onto percolation geometry, thanks to recent results on path-crossing probabilities., Comment: 12 pages, RevTeX and 14 PostScript figures included

A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals with nearest neighbor attractions and next nearest neighbor repulsions. The mean field free energy is calculated by expressing the model in terms of interacting directed walks on a lattice. The resulting equilibrium shape is very rich with facet boundaries and boundaries between reconstructed and unreconstructed regions which can be either sharp (first order) or smooth (continuous). In addition there are tricritical points where a smooth boundary changes into a sharp one and triple points where three sharp boundaries meet. Finally our numerical results strongly suggest the existence of conical points, at which tangent planes of a finite range of orientations all intersect each other. The thermal evolution of the equilibrium shape in this model shows strong similarity to that seen experimentally for ionic crystals., Comment: 14 Pages, Revtex and 10 PostScript figures included

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 two and the model does not show DP critical behaviour anymore. The exponents $\theta=\nu_{\|}/\nu_{\perp}$ and $\beta/\nu_{\perp}$ are calculated numerically. The value of $\beta/\nu_{\perp}$ is close to the value of the Parity Conserving universality class, in spite of the absence of local conservation laws., Comment: Substantially revised version, RevTeX, 10 Pages and 5 PostScript figures included

We study the critical behavior of the random q-state Potts quantum chain by density matrix renormalization techniques. Critical exponents are calculated by scaling analysis of finite lattice data of short chains ($L \leq 16$) averaging over all possible realizations of disorder configurations chosen according to a binary distribution. Our numerical results show that the critical properties of the model are independent of q in agreement with a renormalization group analysis of Senthil and Majumdar (Phys. Rev. Lett.{\bf 76}, 3001 (1996)). We show how an accurate analysis of moments of the distribution of magnetizations allows a precise determination of critical exponents, circumventing some problems related to binary disorder. Multiscaling properties of the model and dynamical correlation functions are also investigated., Comment: LaTeX2e file with Revtex, 9 pages, 8 eps figures, 4 tables; typos corrected

The density matrix renormalization group (DMRG) is applied to some one-dimensional reaction-diffusion models in the vicinity of and at their critical point. The stochastic time evolution for these models is given in terms of a non-symmetric ``quantum Hamiltonian'', which is diagonalized using the DMRG method for open chains of moderate lengths (up to about 60 sites). The numerical diagonalization methods for non-symmetric matrices are reviewed. Different choices for an appropriate density matrix in the non-symmetric DMRG are discussed. Accurate estimates of the steady-state critical points and exponents can then be found from finite-size scaling through standard finite-lattice extrapolation methods. This is exemplified by studying the leading relaxation time and the density profiles of diffusion-annihilation and of a branching-fusing model in the directed percolation universality class., Comment: 16 pages, latex, 5 PostScript figures included

The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q \to \infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point., Comment: 11 pages, RevTeX, 6 PostScript figures included. Manuscript substantially extended, details on the analytical and numerical calculations added. To appear in Phys. Rev. B

We consider an Ising model confined in an $L \times \infty$ geometry with identical surface fields at the boundaries. According to the Kelvin equation the bulk coexistence field scales as 1/L for large L; thermodynamics and scaling arguments predict higher order corrections of the type $1/L^2$ and $1/L^{5/3}$ at partial and complete wetting respectively. Our numerical results, obtained by density-matrix renormalization techniques for systems of widths up to L = 144, are in agreement with a $1/L^2$ correction in the partial wet regime. However at complete wetting we find a large range of surface fields and temperatures with a correction to scaling of type $1/L^{4/3}$. We show that this term is generated by a {\it thin} wetting layer whose free energy is dominated by the contacts with the wall. For $L$ sufficiently large we expect a crossover to a $1/L^{5/3}$ correction as predicted by the theory for a {\it thick} wetting layer. This crossover is indeed found in a solid-on-solid model which provides a simplified description of the wetting layer and allows the study of much larger systems than those available in a density-matrix renormalization calculation., Comment: 9 pages, RevTeX, 7 PostScript figures included. Some misprints corrected. Final version as published

We use the density matrix renormalization group (DMRG) to perform a detailed study of the critical properties of the two dimensional Q state Potts model, including the magnetization and energy-density profiles, bulk and surface critical exponents and the Casimir amplitudes. We apply symmetry breaking boundary conditions to a $L \times \infty$ strip and diagonalize the corresponding transfer matrix for a series of moderately large systems ($L \le 64$) by the DMRG method. The numerically very accurate finite lattice results are then extrapolated by efficient sequence extrapolation techniques. The critical density profiles and the Casimir amplitudes are found to follow precisely the conformal predictions for Q=2 and 3. Similarly, the bulk and surface critical exponents of the models are in very good agreement with the conformal and exact values: their accuracy has reached or even exceeded the accuracy of other available numerical methods. For the Q=4 model both the profiles and the critical exponents show strong logarithmic corrections, which are also studied., Comment: 12 pages, RevTeX, 14 PostScript figures included

The properties of a fluid, or Ising magnet, confined in a $L \times \infty$ geometry with opposing surface fields at the walls are studied by density matrix renormalization techniques. In particular we focus on the effect of gravity on the system, which is modeled by a bulk field whose strength varies linearly with the distance from the walls. It is well known that in the absence of gravity phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores phase coexistence up to the bulk critical temperature, in agreement with previous mean field results. A detailed study of the scaling to the critical point, as $L \to \infty$, is performed. The temperature shift scales as $1/L^{y_T}$, while the gravitational constant scales as $1/L^{1+y_H}$, with $y_T$ and $y_H$ the bulk thermal and magnetic exponents respectively. For weak surface fields and $L$ not too large, we also observe a regime where the gravitational constant scales as $1/L^{1+y_H - \Delta_1 y_T}$ ($\Delta_1$ is the surface gap exponent) with a crossover, for sufficiently large $L$, to a scaling of type $1/L^{1+y_H}$., Comment: 9 pages, RevTeX, 11 PostScript figures included. Minor corrections. Final version as published