540 research outputs found
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.Comment: To be published in J. Phys. Condensed Matte
Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain
We consider the continuum version of an elastic chain supporting topological
and non-topological degrees of freedom; this generalizes a model for the
dynamics of DNA recently proposed and investigated by ourselves. In a certain
limit, the non-topological degrees of freedom are frozen, and the model reduces
to the sine-Gordon equations and thus supports well-known topological soliton
solutions. We consider a (singular) perturbative expansion around this limit
and study in particular how the non-topological field assume the role of an
auxiliary field. This provides a more general framework for the slaving of this
degree of freedom on the topological one, already observed elsewhere in the
context of the mentioned DNA model; in this framework one expects such
phenomenon to arise in a quite large class of field-theoretical models.Comment: 18 pages, 2 figure
Nonintegrable Schrodinger Discrete Breathers
In an extensive numerical investigation of nonintegrable translational motion
of discrete breathers in nonlinear Schrodinger lattices, we have used a
regularized Newton algorithm to continue these solutions from the limit of the
integrable Ablowitz-Ladik lattice. These solutions are shown to be a
superposition of a localized moving core and an excited extended state
(background) to which the localized moving pulse is spatially asymptotic. The
background is a linear combination of small amplitude nonlinear resonant plane
waves and it plays an essential role in the energy balance governing the
translational motion of the localized core. Perturbative collective variable
theory predictions are critically analyzed in the light of the numerical
results.Comment: 42 pages, 28 figures. to be published in CHAOS (December 2004
Anharmonic stacking in supercoiled DNA
Multistep denaturation in a short circular DNA molecule is analyzed by a
mesoscopic Hamiltonian model which accounts for the helicoidal geometry.
Computation of melting profiles by the path integral method suggests that
stacking anharmonicity stabilizes the double helix against thermal disruption
of the hydrogen bonds. Twisting is essential in the model to capture the
importance of nonlinear effects on the thermodynamical properties. In a ladder
model with zero twist, anharmonic stacking scarcely affects the thermodynamics.
Moderately untwisted helices, with respect to the equilibrium conformation,
show an energetic advantage against the overtwisted ones. Accordingly
moderately untwisted helices better sustain local fluctuational openings and
make more unlikely the thermally driven complete strand separation.Comment: In pres
Modelling DNA at the mesoscale: a challenge for nonlinear science?
Invited paper, in the series "Open Problems" of NonlinearityInternational audienceWhen 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
Weierstrass's criterion and compact solitary waves
Weierstrass's theory is a standard qualitative tool for single degree of
freedom equations, used in classical mechanics and in many textbooks. In this
Brief Report we show how a simple generalization of this tool makes it possible
to identify some differential equations for which compact and even semicompact
traveling solitary waves exist. In the framework of continuum mechanics, these
differential equations correspond to bulk shear waves for a special class of
constitutive laws.Comment: 4 page
Dynamical transitions in incommensurate systems
In the dynamics of the undamped Frenkel-Kontorova model with kinetic terms,
we find a transition between two regimes, a floating incommensurate and a
pinned incommensurate phase. This behavior is compared to the static version of
the model. A remarkable difference is that, while in the static case the two
regimes are separated by a single transition (the Aubry transition), in the
dynamical case the transition is characterized by a critical region, in which
different phenomena take place at different times. In this paper, the
generalized angular momentum we have previously introduced, and the dynamical
modulation function are used to begin a characterization of this critical
region. We further elucidate the relation between these two quantities, and
present preliminary results about the order of the dynamical transition.Comment: 7 pages, 6 figures, file 'epl.cls' necessary for compilation
provided; subm. to Europhysics Letter
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