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Professeur de Physique,
e-mail: Michel.Peyrard-at-ens-lyon.fr
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Physique des Solitons / Physics of Solitons
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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).
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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
La physique de la matière condensée va-t-elle redécouvrir
l'espace?
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.
Nonlinear localization in lattices.
Statistical properties of one dimensional ``turbulence''.
Controlling the energy flow in nonlinear lattices:
a model for a thermal rectifier.
Solitons and non-dissipative diffusion
Modelling DNA at the mesoscale: a challenge for nonlinear
science?
Experimental
and theoretical studies of sequence
effects on the fluctuation and melting of short DNA molecules
Nonlinear dynamics and statistical physics of DNA.
: a tutorial review
Can one predict DNA Transcription Start Sites by studying
bubbles?
Using DNA to probe nonlinear localized excitations?
A Twist Opening Model for DNA.
Order of the phase transition in models of DNA thermal
denaturation.
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.
Hydration water, charge transport and protein dynamics.
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.
While we are more and more used to fast communications across the
world, the publication of scientific results has not followed this
trend. The number of papers rises, putting a heavy load on
journals and referees, which has often increased the delay between the
submission of a paper and its actual publication. It is therefore
tempting to bypass the journals and simply post papers on the
Internet, for instance in a preprint database. This is not fully
satisfactory and this is why JBP
is launching a new type of publications, the Short
Notes, which answers the
requirement for fast dissemination while maintaining a peer review
system to guarantee the quality of the papers and a paper printed
version which is still the only way to ensure long term
availability.
For further information, check the
journal web page.
Les Houches School: Physics of DNA assembly, and
applications
Les Houches School: Physics of Molecular Machines
5th International Conference on Biological Physics, Gothenburg, Sweden
August 23 - 27, 2004
Dynamics and statistical mechanics of nonlinear lattices.
Conférence présentée à l'assemblée générale de l'Institut
Universitaire de France, Toulouse, 1999
(Texte de la conférence)
Reference: M. Peyrard, Europhys. Lett. 76 49-55 (2006)
(reprint)
Reference: M. Peyrard, Physica D 119, 184-199 (1998).
(reprint)
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)
We address the problem of heat conduction in 1-D nonlinear chains; we
show that, acting on the parameter which controls the strength of the
on site potential inside a segment of the chain, we induce a
transition from conducting to insulating behavior in the whole
system. Quite remarkably, the same transition can be observed by
increasing the temperatures of the thermal baths at
both ends of the chain by the same amount.
The control of heat conduction by nonlinearity
opens the possibility to propose new devices such as a thermal
rectifier.
Reference: M. Terraneo, M. Peyrard, and G. Casati,
Phys. Rev. Lett., 88 094302-1-4 (2002)
(preprint)
Nature Science Update
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)
Physics of biological molecules.
-- DNA --
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
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)
(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)
(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)
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)
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)
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)
Reference: Maria Barbi, Simona Cocco, Michel Peyrard and Stefano
Ruffo, Journal of Biological Physics, 24, 358-369 (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).
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)
-- Proteins --
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
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)
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)
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.
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.
A Short Note , which cannot exceed 6 pages,
is a first
report of an important result that the authors intend to
submit as a full paper in JBP within 4 months. Short
Notes are handled fully electronically and examined by one referee,
often a member of the Editorial Board, who agrees to send a fast
report. The author is informed of the decision by e-mail, and, if the
Short Note is accepted it appears in a special section in the
next issue of JBP and, moreover, it is immediately posted, in
its final form, on the web site of the journal where it is available
freely to any scientist, including of course the authors who
can print a copy of their paper which is exactly identical to the one
that will appear in the journal.