Juan F. R. Archilla

Moving breathers in a DNA model with competing short- and long-range dispersive interactions

Abstract Moving breathers is a means of transmitting information in DNA. We study the existence and properties of moving breathers in a DNA model with short-range interaction, due to the stacking of the base pairs, and long-range interaction, due to the finite dipole moment of the bond within each base pair. In our study, we have found that mobile breathers exist for a wide range of the parameter values, and the mobility of these breathers is hindered by the long-range interaction. This fact is manifested by: (a) an increase of the effective mass of the breather with the dipole–dipole coupling parameter; (b) a poor quality of the movement when the dipole–dipole interaction increases; (c) the existence of a threshold value of the dipole–dipole coupling above which the breather is not movable. An analytical formula for the boundaries of the regions where breathers are movable is calculated. Concretely, for each value of the breather frequency, one can obtain the maximum value of the dipole–dipole coupling parameter and the maximum and minimum values of the stacking coupling parameter where breathers are movable. Numerical simulations show that, although the necessary conditions for the mobility are fulfilled, breathers are not always movable. Finally, the value of the dipole–dipole coupling constant is obtained through quantum chemical calculations. They show that the value of the coupling constant is small enough to allow a good mobility of breathers.

Nonlinear charge transport mechanism in periodic and disordered DNA

We study a model for polaron-like charge transport mechanism along DNA molecules with emphasis on the impact of parametrical and structural disorder. Our model Hamiltonian takes into account the coupling of the charge carrier to two different kinds of modes representing fluctuating twist motions of the base pairs and H-bond distortions within the double helix structure of λ-DNA. Localized stationary states are constructed with the help of a nonlinear map approach for a periodic double helix and in the presence of intrinsic static parametrical and/or structural disorder reflecting the impact of ambient solvent coordinates. It is demonstrated that charge transport is mediated by moving polarons and breather compounds carrying not only the charge but also causing local temporal deformations of the helix structure through the traveling torsion and bond breather components illustrating the interplay of structure and function in biomolecules.

Charge Transport in Poly(dG)-Poly(dC) and Poly(dA)-Poly(dT) DNA Polymers.

We investigate the charge transport in synthetic DNA polymers built up from single type of base pairs. In the context of a polaronlike model, for which an electronic tight-binding system and bond vibrations of the double helix are coupled, we present estimates for the electron-vibration coupling strengths utilizing a quantum-chemical procedure. Subsequent studies concerning the mobility of polaron solutions, representing the state of a localized charge in unison with its associated helix deformation, show that the system for poly(dG)–poly(dC) and poly(dA)–poly(dT) DNA polymers, respectively possess quantitatively distinct transport properties. While the former supports unidirectionally moving electron breathers attributed to highly efficient long-range conductivity, the breather mobility in the latter case is comparatively restrained, inhibiting charge transport. Our results are in agreement with recent experimental results demonstrating that poly(dG)–poly(dC) DNA molecules acts as a semiconducting nanowire and exhibit better conductance than poly(dA)–poly(dT) ones.

Moving discrete breathers in a Klein?Gordon chain with an impurity

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein?Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.

Discrete breathers and Anderson modes: two faces of the same phenomenon?

Abstract Time-periodic localized oscillations occur in a variety of contexts, in particular in weakly coupled anharmonic lattices and in disordered harmonic networks of oscillators, where they are known respectively as discrete breathers and Anderson modes. It is shown numerically in some examples of systems which interpolate between these two limits that discrete breathers can be continued to Anderson modes, modulo small jumps associated with resonance with Anderson modes on other parts of the network.

Demonstration of the stability or instability of multibreathers at low coupling

Abstract Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrodinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.

Influence of moving breathers on vacancies migration

A vacancy defect is described by a Frenkel–Kontorova model with a discommensuration. This vacancy can migrate when interacts with a moving breather. We establish that the width of the interaction potential must be larger than a threshold value in order that the vacancy can move forward. This value is related to the existence of a breather centred at the particles adjacent to the vacancy.

Bright and dark breathers in Fermi-Pasta-Ulam lattices

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, {\em C. R. Acad. Sci. Paris}, 332, Ser. 1, pp. 581 (2001)] using numerical computations. Approximate analytical expressions for small amplitude bright and dark breathers are found to fit very well exact numerical solutions even far from the top of the phonon band. On the other hand, we study numerically large amplitude breathers non predicted in the above cited reference. In particular, for a class of asymmetric FPU potentials we find an energy threshold for the existence of exact discrete breathers, which is a relatively unexplored phenomenon in one-dimensional lattices. Bright and dark breathers superposed on a uniformly stressed static configuration are also investigated.

Effect of base-pair inhomogeneities on charge transport along the DNA molecule, mediated by twist and radial polarons

Some recent results for a three-dimensional, semi-classical, tight-binding model for DNA show that there are two types of polarons, namely radial and twist polarons, which can transport charge along the DNA molecule. However, the existence of two types of base pairs in real DNA makes it crucial to find out if charge transport also exists in DNA chains with different base pairs. In this paper, we address this problem in its simple case, a homogeneous chain except for a single different base pair, which we call a base-pair inhomogeneity, and its effect on charge transport. Radial polarons experience either reflection or trapping. However, twist polarons are good candidates for charge transport along real DNA. This transport is also very robust with respect to weak parametric and diagonal disorder.

Moving breathers in a bent DNA model

We study the properties of moving breathers in a bent DNA model with short range interaction, due to the stacking of the base pairs, and long range interaction, due to the finite dipole moment of the bonds within each base pair. We show that the movement of a breather is hindered by the bending of the chain analogously to a particle in a potential barrier.