Dirk Hennig

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.

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.

ELECTRON TRAPPING BY SOLITONS. CLASSICAL VERSUS QUANTUM MECHANICAL APPROACH

Assuming either classical electrodynamics or the quantum mechanical tight-binding of an electron to a nonlinear lattice with exponentially repulsive potential interactions we show how in both cases electron trapping can be mediated by solitons thus forming similar robust bound states (solectrons).

Localization properties of electronic states in a polaron model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers

Abstract.We numerically investigate localization properties of electronic states in a static model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with realistic parameters obtained by quantum-chemical calculation. The randomness in the on-site energies caused by the electron-phonon coupling is completely correlated to the off-diagonal parts. In the single electron model, the effect of the hydrogen-bond stretchings, the twist angles between the base pairs and the finite system size effects on the energy dependence of the localization length and on the Lyapunov exponent are given. The localization length is reduced by the influence of the fluctuations in the hydrogen bond stretchings. It is also shown that the helical twist angle affects the localization length in the poly(dG)-poly(dC) DNA polymer more strongly than in the poly(dA)-poly(dT) one. Furthermore, we show resonance structures in the energy dependence of the localization length when the system size is relatively small.

Directed transport of an inertial particle in a washboard potential induced by delayed feedback

We consider motion of an underdamped Brownian particle in a washboard potential that is subjected to an unbiased time-periodic external field. While in the limiting deterministic system in dependence of the strength and phase of the external field directed net motion can exist, for a finite temperature the net motion averages to zero. Strikingly, with the application of an additional time-delayed feedback term directed particle motion can be accomplished persisting up to fairly high levels of the thermal noise. In detail, there exist values of the feedback strength and delay time for which the feedback term performs oscillations that are phase locked to the time-periodic external field. This yields an effective biasing rocking force promoting periods of forward and backward motion of distinct duration, and thus directed motion. In terms of phase space dynamics we demonstrate that with applied feedback desymmetrization of coexisting attractors takes place leaving the ones supporting either positive or negative velocities as the only surviving ones. Moreover, we found parameter ranges for which in the presence of thermal noise the directed transport is enhanced compared to the noise-less case.

ON THE MATHEMATICAL MODELING OF SOLITON-MEDIATED LONG-RANGE ELECTRON TRANSFER

We discuss here possible models for long-range electron transfer (ET) between a donor (D) and an acceptor (A) along an anharmonic (Morse–Toda) one-dimensional (1d)-lattice. First, it is shown that the electron may form bound states (solectrons) with externally, mechanically excited solitons in the lattice thus leading to one form of soliton-mediated transport. These solectrons generally move with supersonic velocity. Then, in a thermally excited lattice, it is shown that solitons can also trap electrons, forming similar solectron bound states; here, we find that ET based on hopping can be modeled as a diffusion-like process involving not just one but several solitons. It is shown that either of these two soliton-assisted modes of transport can facilitate ET over quite long distances.

Current control in a tilted washboard potential via time-delayed feedback

We consider the motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e., a current. It is demonstrated that with an additional time-delayed feedback term, the particle current can be reversed against the direction of the bias. The control function induces a ratchetlike effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to the current control in a wide temperature range.

Moving breathers in bent DNA with realistic parameters

Recent papers have considered moving breathers (MB) in DNA models including long range interaction due to the dipole moments of the hydrogen bonds. We have recalculated the value of the charge transfer when hydrogen bonds stretch using quantum chemical methods which takes into account the whole nucleoside pairs. We explore the consequences of this value on the properties of MBs, including the range of frequencies for which they exist and their effective masses. They are able to travel through bending points with fairly large curvatures, provided that their kinetic energy is larger than a minimum energy which depends on the curvature. These energies and the corresponding velocities are also calculated in function of the curvature.

Breather solutions of a nonlinear DNA model including a longitudinal degree of freedom

We present a model of the DNA double helix assigning three degrees of freedom to each pair of nucleotides. The model is an extension of the Barbi–Cocco–Peyrard (BCP) model in the sense that the current model allows for longitudinal motions of the nucleotides parallel to the helix axis. The molecular structure of the double helix is modelled by a system of coupled oscillators. The nucleotides are represented by point masses and coupled via point–point interaction potentials. The latter describe the covalent and hydrogen bonds responsible for the secondary structure of DNA. We obtain breather solutions using an established method for the construction of breathers on nonlinear lattices starting from the anti-coupling limit. In order to apply this method we analyse the phonon spectrum of the linearised system corresponding to our model. The obtained breathing motion consists of a local opening and re-closing of base pairs combined with a local untwist of the helix. The motions in longitudinal direction are of much lower amplitudes than the radial and angular elongations.