Dynamical versus statistical mesoscopic models for DNA denaturation

Forward and backward propagating breathers in a DNA model with dipole-dipole long-range interactions

The present study explores the existence and orbital stability of discrete bright breathers through the Joyeux-Buyukdagli DNA model incorporating long-range interactions (LRIs). The nonlinear Schrödinger equation is derived from a semidiscrete approximation and subsequently used to construct the targeted initial condition for numerical computations of the discrete breather. It appears that the interplay between the carrier wave frequency and the LRI induces stationary forward or backward propagating waves. For critical values of the LRI, stationary waves can occur out of the center/edge of the first Brillouin zone. The predicted breathers differ in their robustness and mobility for specific carrier-wave frequency and LRI. In all cases, semianalytical predictions agree with numerical simulations.

Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity

The dynamics of DNA in the presence of uniform damping and periodic force is studied. The damped and driven Joyeux-Buyukdagli model is used to investigate the formation of intrinsic localized modes (ILMs). Branches of ILMs are identified as well as their orbital stabilities. A study of the effect of inhomogeneity introduced into the DNA lattice and its ability to control chaotic behavior is conducted. It is seen that a single defect in the chain can induce synchronized spatiotemporal patterns, despite the fact that the entire set of oscillators and the impurity are chaotic when uncoupled. It is also shown that the periodic excitation applied on a specific site can drive the whole lattice into chaotic or regular spatial and temporal patterns.

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Twist-stretch profiles of DNA chains

Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs configurations. The method selects, for any applied force, the average twist angle which minimizes the molecule's free energy. It is found that the chains generally over-twist under an applied stretching and the over-twisting is physically associated to the contraction of the average helix diameter, i.e. to the damping of the base pair fluctuations. Instead, assuming that the maximum amplitude of the bending fluctuations may decrease against the external load, the DNA molecule first over-twists for weak applied forces and then untwists above a characteristic force value. Our results are discussed in relation to available experimental information albeit for kilo-base long molecules.

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.

Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide

In this paper, we show that the coarse grain model for DNA, which has been proposed recently by Knotts et al. [J. Chem. Phys. 126, 084901 (2007)], can be adapted to describe the thermal and mechanical denaturation of long DNA sequences by adjusting slightly the base pairing contribution. The adjusted model leads to (i) critical temperatures for long homogeneous sequences that are in good agreement with both experimental ones and those obtained from statistical models, (ii) a realistic step-like denaturation behaviour for long inhomogeneous sequences, and (iii) critical forces at ambient temperature of the order of 10 pN, close to measured values. The adjusted model furthermore supports the conclusion that the thermal denaturation of long homogeneous sequences corresponds to a first-order phase transition and yields a critical exponent for the critical force equal to σ = 0.70. This model is both geometrically and energetically realistic, in the sense that the helical structure and the grooves, where most proteins bind, are satisfactorily reproduced, while the energy and the force required to break a base pair lie in the expected range. It therefore represents a promising tool for studying the dynamics of DNA-protein specific interactions at an unprecedented detail level.

Stacking interactions in denaturation of DNA fragments

A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time-dependent paths contributing to the partition function. The size of the paths ensemble, which measures the degree of cooperativity of the system, is computed versus temperature consistently with the model potential physical requirements. It is shown that the ensemble size strongly varies with the molecule backbone stiffness providing a quantitative relation between stacking and features of the melting transition. The latter is an overall smooth crossover which begins from the adenine-thymine-rich portions of the fragment. The harmonic stacking coupling shifts, along the T -axis, the occurrence of the multistep denaturation but it does not change the character of the crossover. The methods to compute the fractions of open base pairs versus temperature are discussed: by averaging the base pair displacements over the path ensemble, we find that such fractions signal the multisteps of the transition in good agreement with the indications provided by the specific heat plots.

Thermal and mechanical properties of a DNA model with solvation barrier

We study the thermal and mechanical behaviors of DNA denaturation in the frame of the mesoscopic Peyrard-Bishop-Dauxois model with the inclusion of solvent interaction. By analyzing the melting transition of a homogeneous A-T sequence, we are able to set suitable values of the parameters of the model and study the formation and stability of bubbles in the system. Then, we focus on the case of the P5 promoter sequence and use the principal component analysis of the trajectories to extract the main information on the dynamical behavior of the system. We find that this analysis method gives an excellent agreement with previous biological results.