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