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Michel Peyrard

Publications and source records attributed to Michel Peyrard.

At least 37 records · Page 2Linked to original sources
arXiv2009

Adding a New Dimension to DNA Melting Curves

Standard DNA melting curves record the separation of the two strands versus temperature, but they do not provide any information on the location of the opening. We introduce an experimental method which adds a new dimension to the melting curves of short DNA sequences by allowing us to record the degree of opening in several positions along the molecule all at once. This adds the spatial dimension to the melting curves and allows a precise investigation of the role of the base-pair sequence on the fluctuations and denaturation of the DNA double helix. We illustrate the power of the method by investigating the influence of an AT rich region on the fluctuations of neighboring domains.

cond-mat.stat-mech↗
arXiv2009

On 4-point correlation functions in simple polymer models

We derive an exact formula for the covariance of cartesian distances in two simple polymer models, the freely-jointed chain and a discrete flexible model with nearest-neighbor interaction. We show that even in the interaction-free case correlations exist as long as the two distances at least partially share the same segments. For the interacting case, we demonstrate that the naive expectation of increasing correlations with increasing interaction strength only holds in a finite range of values. Some suggestions for future single-molecule experiments are made.

cond-mat.soft↗
arXiv2008

Modelling DNA at the mesoscale: a challenge for nonlinear science?

When it is viewed at the scale of a base pair, DNA appears as a nonlinear lattice. Modelling its properties is a fascinating goal. The detailed experiments that can be performed on this system impose constraints on the models and can be used as a guide to improve them. There are nevertheless many open problems, particularly to describe DNA at the scale of a few tens of base pairs, which is relevant for many biological phenomena.

cond-mat.stat-mech↗
arXiv2008

Experimental and theoretical studies of sequence effects on the fluctuation and melting of short DNA molecules

Understanding the melting of short DNA sequences probes DNA at the scale of the genetic code and raises questions which are very different from those posed by very long sequences, which have been extensively studied. We investigate this problem by combining experiments and theory. A new experimental method allows us to make a mapping of the opening of the guanines along the sequence as a function of temperature. The results indicate that non-local effects may be important in DNA because an AT-rich region is able to influence the opening of a base pair which is about 10 base pairs away. An earlier mesoscopic model of DNA is modified to correctly describe the time scales associated to the opening of individual base pairs well below melting, and to properly take into account the sequence. Using this model to analyze some characteristic sequences for which detailed experimental data on the melting is available [Montrichok et al. 2003 Europhys. Lett. {\bf 62} 452], we show that we have to introduce non-local effects of AT-rich regions to get acceptable results. This brings a second indication that the influence of these highly fluctuating regions of DNA on their neighborhood can extend to some distance.

cond-mat.stat-mech↗
arXiv2008

Modeling friction on a mesoscale: Master equation for the earthquake-like model

The earthquake-like model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach naturally describes stick-slip and smooth sliding regimes of tribological systems within a framework which separates the calculation of the friction force from the studies of the properties of the contacts.

cond-mat.stat-mech↗
arXiv2007

Modeling DNA beacons at the mesoscopic scale

We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer models; alternative calculations performed using the freely rotating chain and the discrete Kratky-Porod models are reported. Stem formation is modeled according to the Peyrard-Bishop-Dauxois Hamiltonian. The kinetics of opening and closing is described in terms of a diffusion-controlled motion in an effective free energy landscape. Melting profiles, dependence of melting temperature on loop length, and kinetic time scales are in semiquantitative agreement with experimental data obtained from fluorescent DNA beacons forming poly(T) loops. Variation in strand rigidity is not sufficient to account for the large activation enthalpy of closing and the strong loop length dependence observed in hairpins forming poly(A) loops. Implications for modeling single strands of DNA or RNA are discussed.

cond-mat.soft↗
arXiv2006

Bubbles and denaturation in DNA

The local opening of DNA is an intriguing phenomenon from a statistical physics point of view, but is also essential for its biological function. For instance, the transcription and replication of our genetic code can not take place without the unwinding of the DNA double helix. Although these biological processes are driven by proteins, there might well be a relation between these biological openings and the spontaneous bubble formation due to thermal fluctuations. Mesoscopic models, like the Peyrard-Bishop-Dauxois model, have fairly accurately reproduced some experimental denaturation curves and the sharp phase transition in the thermodynamic limit. It is, hence, tempting to see whether these models could be used to predict the biological activity of DNA. In a previous study, we introduced a method that allows to obtain very accurate results on this subject, which showed that some previous claims in this direction, based on molecular dynamics studies, were premature. This could either imply that the present PBD should be improved or that biological activity can only be predicted in a more complex frame work that involves interactions with proteins and super helical stresses. In this article, we give detailed description of the statistical method introduced before. Moreover, for several DNA sequences, we give a thorough analysis of the bubble-statistics as function of position and bubble size and the so-called $l$-denaturation curves that can be measured experimentally. These show that some important experimental observations are missing in the present model. We discuss how the present model could be improved.

physics.bio-ph↗
arXiv2006

The design of a thermal rectifier

The idea that one can build a solid-state device that lets heat flow more easily in one way than in the other, forming a heat valve, is counter-intuitive. However the design of a thermal rectifier can be easily understood from the basic laws of heat conduction. Here we show how it can be done. This analysis exhibits several ideas that could in principle be implemented to design a thermal rectifier, by selecting materials with the proper properties. In order to show the feasibility of the concept, we complete this study by introducing a simple model system that meets the requirements of the design.

cond-mat.mtrl-sci↗
arXiv2005

Can one predict DNA Transcription Start Sites by studying bubbles?

It has been speculated that bubble formation of several base-pairs due to thermal fluctuations is indicatory for biological active sites. Recent evidence, based on experiments and molecular dynamics (MD) simulations using the Peyrard-Bishop-Dauxois model, seems to point in this direction. However, sufficiently large bubbles appear only seldom which makes an accurate calculation difficult even for minimal models. In this letter, we introduce a new method that is orders of magnitude faster than MD. Using this method we show that the present evidence is unsubstantiated.

physics.bio-ph↗
arXiv2005

The Fermi-Pasta-Ulam "numerical experiment": history and pedagogical perspectives

The Fermi-Pasta-Ulam (FPU) pioneering numerical experiment played a major role in the history of computer simulation because it introduced this concept for the first time. Moreover, it raised a puzzling question which was answered more than 10 years later. After an introduction to this problem, we briefly review its history and then suggest some simple numerical experiments, with a provided Matlab code, to study various aspects of the ``FPU'' problem.

nlin.PS↗
arXiv2004

Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system

The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one end fixed are computed exactly from the two-dimensional nonlinear Morse map. These exact nonlinear structures are interpreted as domain walls (DW), interpolating between bound and unbound segments of the chain. The free energy of the DWs is calculated to leading order beyond the Gaussian approximation. Thermodynamic instabilities (e.g. DNA unzipping and/or thermal denaturation) can be understood in terms of DW formation.

cond-mat.stat-mech↗
arXiv2003

Thermal denaturation of an helicoidal DNA model

We study the static and dynamical properties of DNA in the vicinity of its melting transition, i.e. the separation of the two strands upon heating. The investigation is based on a simple mechanical model which includes the helicoidal geometry of the molecule and allows an exact numerical evaluation of its thermodynamical properties. Dynamical simulations of long-enough molecular segments allow the study of the structure factors and of the properties of the denaturated regions. Simulations of finite chains display the hallmarks of a first order transition for sufficiently long-ranged stacking forces although a study of the model's ``universality class'' strongly suggests the presence of an ``underlying'' continuous transition.

cond-mat.stat-mech↗
arXiv2002

Statistical properties of one dimensional "turbulence"

We study a one-dimensional discrete analog of the von Karman flow, widely investigated in turbulence. A lattice of anharmonic oscillators is excited by both ends in order to create a large scale structure in a highly nonlinear medium, in the presence of a dissipative term similar to the viscous term in a fluid. This system shows a striking similarity with a turbulent flow both at local and global scales. The properties of the nonlinear excitations of the lattice provide a partial understanding of this behavior.

cond-mat.stat-mech↗
arXiv2001

Thermodynamic instabilities in one dimension: correlations, scaling and solitons

Many thermodynamic instabilities in one dimension (e.g. DNA thermal denaturation, wetting of interfaces) can be described in terms of simple models involving harmonic coupling between nearest neighbors and an asymmetric on-site potential with a repulsive core, a stable minimum and a flat top. The paper deals with the case of the Morse on-site potential, which can be treated exactly in the continuum limit. Analytical expressions for correlation functions are derived; they are shown to obey scaling; numerical transfer-integral values obtained for a discrete version of the model exhibit the same critical behavior. Furthermore, it is shown in detail that the onset of the transition can be characterized by an entropic stabilization of an -otherwise unstable-, nonlinear field configuration, a soliton-like domain wall (DW) with macroscopic energy content. The statistical mechanics of the DW provides an exact estimate of the critical temperature for a wide range of the discretization parameter; this suggests that the transition can be accurately viewed as being "driven" by a nonlinear entity.

cond-mat.stat-mech↗
arXiv2000

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.

cond-mat.stat-mech↗
arXiv2000

Discreteness effects on soliton dynamics: a simple experiment

We present a simple laboratory experiment to illustrate some aspects of the soliton theory in discrete lattices with a system that models the dynamics of dislocations in a crystal or the properties of adsorbed atomic layers. The apparatus not only shows the role of the Peierls-Nabarro potential but also illustrates the hierarchy of depinning transitions and the importance of the collective motion in mass transport.

nlin.PS↗
arXiv1999

Vector Nonlinear Klein-Gordon Lattices: General Derivation of Small Amplitude Envelope Soliton Solutions

Group velocity and group velocity dispersion for a wave packet in vectorial discrete Klein-Gordon models are obtained by an expansion, based on perturbation theory, of the linear system giving the dispersion relation and the normal modes. We show how to map this expansion on the Multiple Scale Expansion in the real space and how to find Non Linear Schrödinger small amplitude solutions when a nonlinear one site potential balances the group velocity dispersion effect.

chao-dyn↗