# Michel Peyrard, Ecole Normale Supérieure de Lyon

### Professeur de Physique, membre de l' Institut Universitaire de France. Chaire de Physique non linéaire et physique des systèmes biologiques.

e-mail: Michel.Peyrard-at-ens-lyon.fr

### How is information transmitted in a nerve?

 In the last fifteen years a debate emerged about the validity of the famous Hodgkin-Huxley model for nerve impulse. Mechanical models involving solitons have been proposed. This note reviews the experimental properties of the nerve impulse and discusses the proposed alternatives to the Hodgkin-Huxley model. The experimental data, which rule out some of the alternative suggestions, show that, while the Hodgkin-Huxley model may not be complete, it nevertheless includes essential features that should not be overlooked in the attempts made to improve, or supersede, it. Reference: M. Peyrard, Journal of Biological Physics, dx.doi.org/10.1007/s10867-020-09557-2 (2020) (Preprint) - (Read the published paper on-line)

### Earthquakes: understanding subtle differences between the statistics of main shocks, foreshocks and after shocks.

 There are observations which detect differences between the exponents of the Omori law for foreshocks and aftershocks, as well as variations of the b exponent of the Gutenberg-Richter law for main shocks, foreshocks and aftershocks which cannot be accounted for, unless one relies on phenomenological or statistical models with ad-hoc assumptions. The model that we studied with Oleg Braun (Institute of Physics, Kiev) describes all these observations within a framework based on the physics of the rocks, which introduces a natural length scale, the elastic correlation length, and provides quantitative values for most of the the model parameters. The results are robust with respect to large variations of the few parameters which cannot be readily obtained from physical data. Reference: O.M. Braun and M. Peyrard, EPL, 126 49001-1-7 (2019) (Preprint) - (EPL 2019)

### DNA structure: the story is still going on

 In 1953 J.D. Watson and F.H.C. Crick built a three-dimensional model of the famous double helix of DNA, which earned them the Nobel Prize [1]. But this discovery did not end the story of DNA structure. In 1975 F.H.C. Crick and A. Klug proposed a second model, suggesting kinks in DNA. These sharp angles in the helix have nothing to do with the flexible joints due to single strand breaking and base-pair opening. They are well defined structures, connecting two helical segments at an angle of about 95°, in which all base pairs are intact and all bond distances and angles are stereochemically acceptable. Crick and Klug suggested that such kinks could contribute to the folding of DNA in chromatin but they also wondered whether kinks could occur spontaneously in double-stranded DNA in solution. This question remained opened since 1975 because structure determinations for molecules freely moving in solution are very challenging. Our recent study, combining small-angle X-Ray and neutron scattering with a statistical physics analysis of the data [3] showed that kinks can indeed exist in some DNA sequences in solution. This confirms the intuition of Crick and Klug and opens a new view point on DNA structure. The well known image of the rigid double helix has to be completed, and for instance viruses might take advantage of such kinks to pack DNA in their capsides. [1] J.D. Watson and F.H.C. Crick, A Structure for Deoxyribose Nucleic Acid. Nature 171, 737 (1953) [2] F.H.C. Crick and A. Klug, Kinky Helix. Nature 255, 530 (1975) [3] T. Schindler et al., Kinky DNA in solution: Small angle scattering study of a nucleosome positioning sequence. Phys. Rev E 98,042417 (2018) Phys. Rev E 98,042417 (2018)

### Physique des Solitons / Physics of Solitons

 Depuis la première observation d'un soliton en 1834, ces ondes solitaires aux caractéristiques exceptionnelles fascinent les scientifiques en raison de leurs propriétés expérimentales très spectaculaires, des développements mathématiques remarquables auxquels leur étude a conduit, mais aussi parce que l'approche en terme de solitons permet de renouveler en profondeur le point de vue sur de nombreux problèmes physiques. Dans cet ouvrage les fondements sont introduits à partir d'exemples de la physique macroscopique (hydrodynamique, ondes de pression sanguine, océanographie, communications par fibres optiques,...). Les principales méthodes théoriques sont ensuite abordées, avant la présentation détaillée de nombreuses applications consacrées à des problèmes microscopiques de la physique des solides (dislocations, chaînes de spins, polymères conducteurs, matériaux ferroélectriques) ou des macromolécules biologiques (transfert de l'énergie dans les protéines, dynamique de la molécule d'ADN). (Erratum) This textbook introduces the basic properties of solitons from examples in macroscopic physics (water waves, blood pressure pulse, optical fiber communications, ...). The main theoretical methods are introduced in a second part. Numerous applications are then discussed in detail in solid state or atomic physics (dislocations, excitations in spin chains, conducting polymers, ferroelectrics, Bose-Einstein condensates) and biological physics (energy transfer in proteins, DNA fluctuations). Physics of Solitons (Cambridge University Press) (Erratum)

### Research interests:

In his famous book "What is life?", addressing the question "how can we explain the basic phenomena of life with physics and chemistry", E. Schrödinger points out that one essential character of life is its ability to show cooperative behaviors. Instead of the incoherent fluctuations of atoms or small molecules in solution, living cells show coherent global dynamics. Cooperativity has also been found to be a very important feature that can deeply affect the behavior of nonlinear systems. While a few nonlinear oscillators can show chaotic dynamics, a nonlinear lattice made of such oscillators coupled to each other, may on the contrary exhibit coherent excitations such as solitons or nonlinear localized modes.

Nonlinear cooperative systems are interesting because they can exhibit spectacular properties, but also because they provide paradigms which are useful to understand many physical observations, from friction at the microscopic scale to the dynamics of biological molecules. My research interests cover both the fundamental properties of nonlinear lattices and their applications in condensed matter and biomolecular physics. Some selected results are presented below.

For further information on the research carried in the Laboratoire de Physique de l'ENS-Lyon, check the laboratory home page

### Dynamics and statistical mechanics of nonlinear lattices.

The design of a thermal rectifier (Europhysics Letters Editorial Board highlights of 2006) While electronics has been able to control the flow of charges in solids for decades, the control of heat flow still seems out of reach, and this is why, when a paper showed for the first time how to build a thermal rectifier'', the thermal analogue of the electrical diode, it attracted a great deal of attention. 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 and may even appear in contradiction with thermodynamics. Actually this is not the case, and 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. Such devices could be useful in nanotechnology, and particularly to control he heat flow in electronic chips.
Reference: M. Peyrard, Europhys. Lett. 76 49-55 (2006) (reprint)

Nonlinear localization in lattices.
Reference: M. Peyrard, Physica D 119, 184-199 (1998). (reprint)

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
Reference: M. Peyrard and I. Daumont, Europhysics Letters 59, 834-840 (2002) (preprint)

Dynamically induced heat rectification: classical or quantum?
The article by Riera-Campeny, Mehboudi, Pons, and Sanpera [Phys. Rev. E 99, 032126 (2019)] studies heat rectification in a network of harmonic oscillators which is periodically driven. Both the title and introduction stress the quantum nature of the system. Here we show that the results are more general and are equally valid for a classical system, which broadens the interest of the paper and may suggest further pathways for a basic understanding of the phenomenon.
Reference: Michel Peyrard, Phys. Rev. E, 101 016101-1-3 (2020)
(reprint)

Solitons and non-dissipative diffusion
Diffusion is in general associated with dissipation. If a test particle is injected in a diffusing medium with a velocity above the thermal velocity, it slows down. This happens because a physical particle constantly exchanges momentum with the medium; momentum exchange however is not a prerequisite for diffusion. Solitons can exhibit non-dissipative diffusion because their interaction with the other components of the medium consists of spatial shifts, jumps'', rather than momentum exchanges. At finite temperatures the sequence of spatial shifts becomes intrinsically stochastic.
Reference: N. Theodorakopoulos and M. Peyrard, Phys. Rev. Lett 83, 2293-2296 (1999) (reprint)

### -- DNA --

#### -- DNA flexibility

The flexibility of DNA has been the object of many studies, but its fundamental understanding is still lacking, and even measurements appear to disagree between each other as they depend in a subtle way on many parameters and experimental methods. How DNA bends is important for biology, but it can also be an indirect marker of the opening fluctuations of the double helix.

Base Pair Openings and Temperature Dependence of DNA Flexibility
The relationship of base pair openings to DNA flexibility is examined. Published experimental data on the temperature dependence of the persistence length by two different groups are well described in terms of an inhomogeneous Kratky-Porot model with soft and hard joints, corresponding to open and closed base pairs, and sequence-dependent statistical information about the state of each pair provided by a Peyrard-Bishop-Dauxois (PBD) model calculation with no freely adjustable parameters.
Reference: N. Theodorakopoulos and M. Peyrard PRL 108 078104-1-4 (2012)
(reprint)

Temperature Dependence of the DNA Double Helix at the Nanoscale: Structure, Elasticity, and Fluctuations
Biological organisms exist over a broad temperature range of 15°C to 120°C where many molecular processes involving DNA depend on the nanoscale properties of the double helix. Here, we present results of extensive molecular dynamics simulations of DNA oligomers at different temperatures. We show that internal basepair conformations are strongly temperature-dependent, particularly in the stretch and opening degrees of freedom whose harmonic fluctuations can be consid- ered the initial steps of the DNA melting pathway. The basepair step elasticity contains a weaker, but detectable, entropic contri- bution in the roll, tilt, and rise degrees of freedom. To extend the validity of our results to the temperature interval beyond the standard melting transition relevant to extremophiles, we estimate the effects of superhelical stress on the stability of the base- pair steps, as computed from the Benham model. We predict that although the average twist decreases with temperature in vitro, the stabilizing external torque in vivo results in an increase of ~1°/bp (or a superhelical density of 0:03) in the interval 0–100°C. In the final step, we show that the experimentally observed apparent bending persistence length of torsionally uncon- strained DNA can be calculated from a hybrid model that accounts for the softening of the double helix and the presence of tran- sient denaturation bubbles. Although the latter dominate the behavior close to the melting transition, the inclusion of helix softening is important around standard physiological temperatures. Reference: Sam Meyer, Daniel Jost, Nikos Theodorakopoulos, Michel Peyrard, Richard Lavery and Ralf Everaers, Biophys. J. 105 , 1904-1914 (2013)

#### -- DNA fluctuational openings

The famous image of the double helix gives a false image of stability. Actually DNA fluctuates widely. Its base pairs open and close. The lifetime of a closed pair is only of the order of 10 ms. These fluctuations are important for biology, but they also rise many fascinating questions for physics. Theory can describe them but experiments are essential to validate those approaches.

The thermal denaturation of DNA studied with neutron scattering
The melting transition of deoxyribonucleic acid (DNA), whereby the strands of the double helix structure completely separate at a certain temperature, has been characterized using neutron scattering. A Bragg peak from B-form fibre DNA has been measured as a function of temperature, and its widths and integrated intensities have been interpreted using the Peyrard-Bishop-Dauxois (PBD) model with only one free parameter. The experiment is unique, as it gives spatial correlation along the molecule through the melting transition where other techniques cannot.
Reference: Andrew Wildes, Nikos Theodorakopoulos, Jessica Valle-Orero, Santiago Cuesta-Lopez, Jean-Luc Garden, and Michel Peyrard, PRL 106 048101-1-4 (2011) reprint

The Melting of Highly Oriented Fibre DNA Subjected to Osmotic Pressure
A pilot study of the possibility to investigate the temperature-dependent neutron scattering from fibre-DNA in solution is presented. The study aims to establish the feasibility of experiments to probe the influence of spatial confinement on the structural correlation and the formation of denatured bubbles in DNA during the melting transition. Calorimetry and neutron scattering experiments on fibre samples immersed in solutions of polyethylene glycol (PEG) prove that the melting transition occurs in these samples, that the transition is reversible to some degree, and that the transition is broader in temperature than for humidified fibre samples. The PEG solutions apply an osmotic pressure that maintains the fibre orientation, establishing the feasibility of future scattering experiments to study the melting transition in these samples.
Reference: Andrew Wildes, Liya Khadeeva, William Trewby, Jessica Valle-Orero, Andrew Studer, Jean-Luc Garden and Michel Peyrard, J. Phys. Chem. B 119, 4441-4449 (2015) (preprint)

The Melting Transition of Oriented DNA Fibers Submerged in Polyethylene Glycol Solutions Studied by Neutron Scattering and Calorimetry
Neutron scattering was used to monitor the integrated intensity and width of a Bragg peak from the B-form of DNA immersed in solutions of polyethylene glycol (PEG) as a function of temperature. The data were quantitatively analyzed using the Peyrard-Bishop-Dauxois (PBD) model. The experiments and analysis showed that long segments of double-strand DNA persist until the last stages of melting, and that there appears to be a substantial increase of the DNA dynamics as the melting temperature of the DNA is approached. Reference: Adrián González, Andrew Wildes, Marta Marty-Roda, Santiago Cuesta-López, Estelle Mossou, Andrew Studer, Bruno Demé, Gaël Moiroux, Jean-Luc Garden, Nikos Theodorakopoulos and Michel Peyrard, J. Phys. Chem. B (2018) (preprint)

Guanine radical chemistry reveals the eﬀect of thermal ﬂuctuations in gene promoter regions.
DNA is not the static entity that structural pictures suggest. It has been longly known that it “breathes” and ﬂuctuates by local opening of the bases. Here we show that the eﬀect of structural ﬂuctuations, exhibited by AT-rich low stability regions present in some common transcription initiation regions, inﬂuences the properties of DNA in a distant range of at least 10 base pairs. This observation is conﬁrmed by experiments on genuine gene promoter regions of DNA. The spatial correlations revealed by these experiments throw a new light on the physics of DNA and could have biological implications, for instance by contributing to the cooperative eﬀects needed to assemble the molecular machinery that forms the transcription complex.
Reference: Santiago Cuesta-Lopez, Hervé Menoni, Dimitar Angelov, and Michel Peyrard, Nucleic Acids Research 2011; doi: 10.1093/nar/gkr096
Paper (Nucleic Acid Research)

Modelling DNA at the mesoscale: a challenge for nonlinear science?
(Invited paper for the series "Open Problem" of Nonlinearity
Article (Nonlinearity)
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.
(reprint)

Experimental and theoretical studies of sequence effects on the fluctuation and melting of short DNA molecules
(J. Phys. Condensed Matter 21 034103-1-13 (2009))
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. (preprint)

Nonlinear dynamics and statistical physics of DNA. : a tutorial review
Article (Nonlinearity)
DNA is not only an essential object of study for biologists. it raises very interesting questions for physicists. This paper discuss its nonlinear dynamics, its statistical mechanics, and one of the experiments that one can now perform at the level of a single molecule and which leads to a non-equilibrium transition at the molecular scale.
After a review of experimental facts about DNA, we introduce simple models of the molecule and show how they lead to nonlinear localization phenomena that could describe some of the experimental observations. In a second step we analyze the thermal denaturation of DNA, i.e. the separation of the two strands using standard statistical physics tools as well as an analysis based on the properties of a single nonlinear excitation of the model. The last part discusses the mechanical opening of the DNA double helix, performed in single molecule experiments. We show how transition state theory combined with the knowledge of the equilibrium statistical physics of the system can be used to analyze the results.
(reprint)

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. We introduce a new method that is orders of magnitude faster than MD. Using this method we show that the present evidence is un substantiated, but we are working on improvements of the model could make it possible in the future.
References: Titus S. van Erp, Santiago Cuesta-Lopez, Johannes-Geert Hagmann, Michel Peyrard, Phys. Rev. Lett. 95, 218104 (2005) (reprint) and Titus S. van Erp, Santiago Cuesta-Lopez, and Michel Peyrard, Eur. Phys. J. E 20, 421-434 (2006) (reprint)

Using DNA to probe nonlinear localized excitations?
We propose an experiment using micro-mechanical stretching of DNA to probe nonlinear energy localization in a lattice. Using numerical simulations and kinetics calculations we estimate the order of magnitude of the expected force fluctuations. They appear to be at the boarder of present experimental possibilities.
Reference: M. Peyrard, Europhysics Letters 44, 271-277 (1998) (reprint)

A Twist Opening Model for DNA.
Reference: Maria Barbi, Simona Cocco, Michel Peyrard and Stefano Ruffo, Journal of Biological Physics, 24, 97-114 (1999) (reprint)
Further work in this direction has been carried by S. Cocco for her PhD and can be found in the reference S. Cocco and R. Monasson, Statistical mechanics of torque induced denaturation of DNA, Phys. Rev. Lett. 83 5178-5181 (1999).

Order of the phase transition in models of DNA thermal denaturation.
We examine the behavior of two types of models which describe the melting of double-stranded DNA chains. Type-I model (with displacement-independent stiffness constants and a Morse on-site potential) is probably the simplest, exactly solvable, one-dimensional lattice model with a true thermodynamic phase transition. Type-II model (with displacement-dependent stiffness constants) is analyzed numerically and shown to have a very sharp transition with finite melting entropy.
Reference: N. Theodorakopoulos, T. Dauxois and M. Peyrard, Order of the phase transition in models of DNA thermal denaturation., Phys. Rev. Lett. 85, 6-9 (2000) (reprint)

#### -- The different forms of DNA

The double helix which is often drawn is only one configuration of DNA, the B-form. But DNA exists also in other configurations, and particularly the A-form, which is a helix with a larger diameter and base pairs inclined with respect to the helix axis. The A-form of DNA played a major role in the early attempts to understand DNA structure. It was actually an X-ray diagram from A-DNA, shown at a conference in 1951 by M. Wilkins, that gave Watson and Crick the key clue to solving the structure of the B-form. Franklin and Gosling worked extensively on A-DNA and with good reason: DNA fibers, which are very convenient to obtain oriented DNA samples, crystallize better and give rise to higher quality X-ray diffraction patterns when in the A-form.
Thermal measurements on A-DNA are important to test the influence of conformational form on melting transition and the universality of models used to describe DNA thermodynamics. DNA adopting the A-form may also be an important part of the gene transcription process in vitro.

Thermal denaturation of A-DNA
The DNA molecule can take various conformational forms. Investigations focus mainly on the so-called B-form", schematically drawn in the famous paper by Watson and Crick. This is the usual form of DNA in a biological environment and is the only form that is stable in an aqueous environment. Other forms, however, can teach us much about DNA. They have the same nucleotide base pairs for building blocks'' as B-DNA, but with different relative positions, and studying these forms gives insight into the interactions between elements under conditions far from equilibrium in the B-form. Studying the thermal denaturation is particularly interesting because it provides a direct probe of those interactions which control the growth of the fluctuations when the melting'' temperature is approached. Here we report such a study on the A-form" using calorimetry and neutron scattering. We show that it can be carried further than a similar study on B-DNA, requiring the improvement of thermodynamic models for DNA.
Reference: J Valle-Orero, A R Wildes, N Theodorakopoulos, S Cuesta-Lopez, J-L Garden, S Danikin, and M Peyrard, New. J. Phys. 16, 113017-1-14 (2014) Journal article (open access)

Glassy behavior of denatured DNA films studied by Differential Scanning Calorimetry
We use differential scanning calorimetry (DSC) to study the properties of DNA films, made of oriented fibers, heated above the thermal denaturation temperature of the double helical form. The films show glassy properties that we investigate in two series of experiments, a slow cooling at different rates followed by a DSC scan upon heating, and aging at a temperature below the glass transition. Introducing the fictive temperature to characterize the glass allows us to derive quantitative information on the relaxations of the DNA films, in particular to evaluate their enthalpy barrier. A comparison with similar aging studies on PVAc highlights some specificities of the DNA samples.
Reference: Jessica Valle-Orero, Jean-Luc Garden, Jacques Richard, Andrew Wildes and Michel Peyrard, J. Phys. Chem. B 116, 4394-4402 (2012) Journal article reprint

#### -- The structure of DNA: X-ray and neutron data show hints of structures beyond the familiar double helix --

Kinky DNA in solution: Small angle scattering study of a nucleosome positioning sequence.
DNA is a flexible molecule, but the degree of its flexibility is subject to debate. The commonly-accepted persistence length of about 500 Angstrom is inconsistent with recent studies on short-chain DNA that show much greater flexibility but do not probe its origin. We have performed X-ray and neutron small-angle scattering on a short DNA sequence containing a strong nucleosome positioning element, and analyzed the results using a modified Kratky-Porod model to determine possible conformations. Our results support a hypothesis from Crick and Klug in 1975 that some DNA sequences in solution can have sharp kinks, potentially resolving the discrepancy. Our conclusions are supported by measurements on a radiation-damaged sample, where single-strand breaks lead to increased flexibility and by an analysis of data from another sequence, which does not have kinks, but where our method can detect a locally enhanced flexibility due to an AT-domain.
Reference: Torben Schindler, Adrian Gonzalez Rodriguez, Ramachandran Boopathi, Marta Marty Roda, Lorena Romero-Santacreu, Andrew Wildes, Lionel Porcar, Anne Martel, Nikos Theodorakopoulos, Santiago Cuesta-Lopez, Dimitar Angelov, Tobias Unruh and Michel Peyrard, Phys. Rev. E 98(/B>, 042417-1-10 (2018)
(reprint)

### -- Proteins --

Characterization of the low temperature properties of a simplified protein model.
Prompted by results that showed that a simple protein model, the frustrated Go model, appears to exhibit a transition reminiscent of the protein dynamical transition, we examine the validity of this model to describe the low-temperature properties of proteins. First, we examine equilibrium fluctuations. We calculate its incoherent neutron-scattering structure factor and show that it can be well described by a theory using the one-phonon approximation. By performing an inherent structure analysis, we assess the transitions among energy states at low temperatures. Then, we examine non-equilibrium fluctuations after a sudden cooling of the protein. We investigate the violation of the fluctuation--dissipation theorem in order to analyze the protein glass transition. We find that the effective temperature of the quenched protein deviates from the temperature of the thermostat, however it relaxes towards the actual temperature with an an Arrhenius behavior as the waiting time increases. These results of the equilibrium and non-equilibrium studies converge to the conclusion that the apparent dynamical transition of this coarse-grained model cannot be attributed to a glassy behavior.
Reference: J.-G. Hagmann, N. Nakagawa and M. Peyrard, Phys. Rev. E 89 012705-1-13 (2014)
reprint

Critical examination of the inherent-structure-landscape analysis of two-state folding proteins
Recent studies attracted the attention on the inherent structure landscape (ISL) approach as a reduced description of proteins allowing to map their full thermodynamic properties. However, the analysis has been so far limited to a single topology of a two-state folding protein, and the simplifying assumptions of the method have not been examined. In this work, we construct the thermodynamics of four two-state folding proteins of different sizes and secondary structure by MD simulations using the ISL method, and critically examine possible limitations of the method. Our results show that the ISL approach correctly describes the thermodynamics function, such as the specific heat, on a qualitative level. Using both analytical and numerical methods, we show that some quantitative limitations cannot be overcome with enhanced sampling or the inclusion of harmonic corrections.
Reference: J.-G. Hagmann, N. Nakagawa and M. Peyrard, Phys. Rev. E 80 061907-1-11 (2009)
reprint

The Inherent Structure Landscape of a Protein.
We use an extended Go model to study the energy landscape and the fluctuations of a model protein. The model exhibits two transitions, folding and dynamical transitions, when changing the temperature. The inherent structures corresponding to the minima of the landscape are analyzed and we show how their energy density can be obtained from simulations around the folding temperature. The scaling of this energy density is found to reflect the folding transition. Moreover, this approach allows us to build a reduced thermodynamics in the Inherent Structure Landscape. Equilibrium studies, from full MD simulations and from the reduced thermodynamics, detect the features of a dynamical transition at low temperature and we analyze the location and timescale of the fluctuations of the protein, showing the need of some frustration in the model to get realistic results. The frustrated model also shows the presence of a kinetic trap which strongly affects the dynamics of folding.
References: Naoko Nakagawa and Michel Peyrard, Proc. Natl. Acad. Sci. USA (PNAS) 103, 5279-5284 (2006) (reprint) and Naoko Nakagawa and Michel Peyrard, Phys. Rev. E 74 041916-1-17 (2006) (reprint)

Hydration water, charge transport and protein dynamics.
The hydration water of proteins is essential to biological activity but its properties are not yet fully understood. A recent study of dielectric relaxation of hydrated proteins [A. Levstik et al., Phys. Rev E. {\bf 60} 7604 (1999)] has found a behavior typical of a proton glass, with a glass transition of about 268K. In order to analyze these results, we investigate the statistical mechanics and dynamics of a model of two-dimensional water'' which describes the hydrogen bonding scheme of bounded water molecules. We discuss the connection between the dynamics of bound water and charge transport on the protein surface as observed in the dielectric measurements.
Reference: M. Peyrard, Hydration water, charge transport and protein dynamics. J. of Biological Physics 27, 217-228 (2001) (preprint)

### -- Understanding friction at the mesoscale --

In spite of its crucial practical importance, friction is still far from being fully explained. Besides a proper explanation of the static friction laws, the dynamical aspects of friction are even less understood. This is exemplified by the problem posed by the lack of a well established mechanism for the familiar stick-slip phenomenon that one perceives with a door's creak or the playing of a violin with a bow. Many phenomena in nature, where one part of a system moves in contact with another part, exhibit such a stick-slip motion which changes to smooth sliding with the increase of the driving velocity. One of the difficulties is that friction involves many length scales. We feel it at macroscopic scale, but it arises from numerous tiny contacts at the micron scale.
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.
References: O.M. Braun and M. Peyrard, PRL 100, 125501-1-4 (2008)
(reprint) O.M. Braun and M. Peyrard, Phys. Rev. E 82, 036117-1-19 (2010) (reprint)
Dependence of kinetic friction on velocity: Master equation approach
We investigate the velocity dependence of kinetic friction with a model which makes minimal assumptions on the actual mechanism of friction so that it can be applied at many scales provided the system involves multi-contact friction. Using a recently developed master equation approach we investigate the influence of two concurrent processes. First, at a nonzero temperature thermal fluctuations allow an activated breaking of contacts which are still below the threshold. As a result, the friction force monotonically increases with velocity. Second, the aging of contacts leads to a decrease of the friction force with velocity. Aging effects include two aspects: the delay in contact formation and aging of a contact itself, i.e., the change of its characteristics with the duration of stationary contact. All these processes are considered simultaneously with the master equation approach, giving a complete dependence of the kinetic friction force on the driving velocity and system temperature, provided the interface parameters are known.
Reference: O.M. Braun and M. Peyrard, Phys. Rev. E 83, 046129-1-9 (2011) (reprint)
Role of aging in a minimal model of earthquakes
Reference: O.M. Braun and M. Peyrard, Phys. Rev. E 87, 032808-1-7 (2013) (reprint)
Seismic quiescence in a frictional earthquake model
Many earthquakes are preceded by foreshocks, but their frequency can nevertheless vary widely depending on the type of earthquake. Moreover, some earthquakes are preceded by an unexpected calm period, lasting for several hours or more. It is such a period of quiescence, viewed as a characteristic feature of the imminence of the main shock that allowed the only successful prediction of an earthquake, which saved a large number of lives in China in 1975. The existence of some activity before a major earthquake does not seem surprising, but the fact that a quiescence period could be a characteristic announcement of an earthquake looks more surprising. Various mechanisms have been considered to explain seismic quiescence but its generic origin was still an open question. In this article we propose a generic mechanism related to the distribution of the threshold for the breaking of the contacts along a fault and illustrate it by simulations of a simple earthquake model. Our model shows that seismic quiescence may emerge from what could, at first glance, be considered as a secondary effect, the aging of the contacts, which in turn may strongly alter the distribution of the thresholds at which contacts break and qualiatively change the pattern of foreschocks.
Reference: O.M. Braun and M. Peyrard, Geophys. J. Int. 213, 676-683 (2018) (article)

### -- Thermodynamics of out-of-equilibrium systems --

Memory effects in glasses: Insights into the thermodynamics of out-of-equilibrium systems revealed by a simple model of the Kovacs effect
Glasses are interesting materials because they allow us to explore the puzzling properties of out-of-equilibrium systems. One of them is the Kovacs effect in which a glass, brought to an out-of-equilibrium state in which all its thermodynamic variables are identical to those of an equilibrium state, nevertheless evolves, showing a hump in some global variable before the thermodynamic variables come back to their starting point. We show that a simple three-state system is sufficient to study this phenomenon using numerical integrations and exact analytical calculations. It also brings some light on the concept of fictive temperature, often used to extend standard thermodynamics to the out-of-equilibrium properties of glasses. We confirm that the concept of a unique fictive temperature is not valid, an show it can be extended to make a connection with the various relaxation processes in the system. The model also brings further insights on the thermodynamics of out-of-equilibrium systems. Moreover, we show that the three-state model is able to describe various effects observed in glasses such as the asymmetric relaxation to equilibrium discussed by Kovacs, or the reverse crossover measured on B 2 O 3 .
Reference: M. Peyrard and J.-L. Garden, Phys. Rev. E 102, 052122 (13p) (2020)
(PRE paper)

Besides its fundamental interest, the model that we investigate in this article is simple enough to be used as a basis for courses or tutorials on the thermodynamics of out of equilibrium systems. It allows simple numerical calculations and analytical analysis which highlight important concepts with an easily workable example. (This version) includes studies of fast cooling and heating, exhibiting cases with negative heat capacity, and further discussions on the entropy which are not presented in the Physical Review E paper.

### Teaching:

Research at the boundary between physics and biology is currently expanding very fast. It requires a good understanding of both physics and biology, and, in addition, a good knowledge of the chemical aspects. This is why ENS-Lyon has introduced a special program on Physique et chimie des systèmes biologiques as part of the Master de Sciences de la Matière.
Further information can be obtained from the Site of the Master de Sciences de la Matière.

### The Journal of Biological Physics:

Many physicists are now turning their attention to domains which were not traditionally part of physics and are applying the sophisticated tools of theoretical and experimental physics to investigate new fields, such as biological processes. The Journal of Biological Physics (JBP) provides a medium where this growing community of physicists can publish its results and discuss its aims and methods.

The journal welcomes papers which use the tools of physics, both experimental and theoretical, in an innovative way, to study biological problems, as well as research aimed at providing a better understanding of the physical principles underlying biological processes.
All areas of biological physics can be addressed, from the molecular level, through the mesoscale of membranes and cells, up to the macroscopic level of a population of living organisms - the main criteria of acceptance being the physical content of the research and its relevance to biological systems. In order to increase the links between physics and biology and among the various fields of biological physics, authors are advised to include a first section that introduces the basic issues addressed and the primary achievements to a non-specialist reader.
In addition to original research papers, JBP welcomes review papers which call the attention of physicists to interesting unresolved biological problems that deserve investigation by physical methods. Special issues, published under the supervision of a guest editor, containing a series of papers devoted to a particular topic in addition to the regular papers, can also be published. They may be invited by the board but suggestions for a topical issue can also be accepted. They will be discussed with the editor. Book reviews are also welcome. Moreover, as a link between physicists interested in biological problems, JBP can also publish information such as meeting announcements or conference proceedings.

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