Two models for energy and charge transport and storage in biomolecules are considered. A model based on the discrete nonlinear Schrodinger equation with long-range dispersive interactions (LRI's) between base pairs of DNA is offered for the description of nonlinear dynamics of the DNA molecule. We show that LRI's are responsible for the existence of an interval of bistability where two stable stationary states, a narrow, pinned state and a broad, mobile state, coexist at each value of the total energy. The possibility of controlled switching between pinned and mobile states is demonstrated. The mechanism could be important for controlling energy storage and transport in DNA molecules. Another model is offered for the description of nonlinear excitations in proteins and other anharmonic biomolecules. We show that in the highly anharmonic systems a bound state of Davydov and Boussinesq solitons can exist.

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Models for Energy and Charge Transport and Storage in Biomolecules

From polaron to solectron: The addition of nonlinear elasticity to quantum mechanics and its possible effect upon electric transport

Models for energy and charge transport and storage in biomolecules

We study solitonic charge transport in a hydrogen-bonded model system representing a one-dimensional polypeptide chain. Supersonic solitons are constructed for zero temperature in the frame of a Morse lattice model for which an nonlinear electronic system is coupled in a tight-binding approximation to H-bond vibrations of the molecular chain. The latter are of anharmonic nature. Charge transport is realized via the coupling between the electron and the local lattice deformations. This electron-lattice coupling is described by the soliton solutions, assigned to states of a localized charge in association with its local chain deformation. By retaining the discrete nature of the underlying lattice system it is shown that even strongly localized states are mobile. In fact, we illustrate that for nonlinear electron-vibration interaction supersonic solitonic carriers in the lattice assist the transport of narrow electron and lattice solitons. Moreover, by using realistic values from polypeptides for the system parameters we demonstrate that the interaction between the H-bond vibrations and the electron is strong enough to sustain thermal perturbations up to T = 300 K. Most importantly localization is maintained over extended periods of time during which the electron travels directionally over such long distances along the chain exceeding by far those achievable with single-step tunneling. Furthermore, we discuss the role of an applied electric field. It is demonstrated that in a wide range of its values the velocity of the soliton motion and hence the electric current remains unaffected by the electric field. Above this range the velocity of the solitons is proportional to the field strength so that the corresponding current follows Ohm’s law. Then for still higher field strengths above a critical value the coupling between electron and soliton dynamics breaks down.

https://www.ucm.es/data/cont/media/www/pag-40479/2006-HNVE-PR-B.pdf

Effect of anharmonicity on charge transport in hydrogen-bonded systems

From a study of electrical conductivity of protons in the hydrogen-bonded chains in ice we confirm that the magnetization of liquid water is caused by proton transfer in closed hydrogen-bonded chains occurring as a first order phase transition, through which the ice becomes liquid water. We first study the conductive properties of proton transfer along molecular chains in ice crystals in our model. Ice is a typical hydrogen-bonded molecular system, in which the interaction of localized fluctuation of hydrogen ions (H+) with deformation of a structure of hydroxyl group (OH) results in soliton motion of the protons along the molecular chains via ionic and bonded defects. We explain further the quantum conductive properties of proton transfer and determine its mobility and conductivity under constant electric-field using a new theory of proton transfer, which agree with experimental values. From features of first order phase-transition for ice, and some experimental data of pure and magnetized water we confirm further that there are not only free water molecules, but also many linear and closed hydrogen-bonded chains consisting of many polarized water-molecules in the liquid water. Thus a ring proton-current, which resembles to a '' molecular current '' or a '' small magnet '' in solids, can occur in the closed hydrogen-bond chains under action of an externally applied magnetic field. Then the water molecules in the closed chains can be orderly arrayed due to the magnetic interaction among these ring proton currents and the externally applied magnetic field. This is just the magnetized effect of the water. In such a case the optical and electronic properties of the water, including the dielectric constant, magnetoconductivity, refraction index, Raman and Infrared absorption spectra, are changed. We determine experimentally the properties of the magnetized water which agree with the theoretical results of our model. However, the magnetized effect of water is, in general, very small, and vanishes at temperatures above 100 degrees C.

/pdf/the-conductivity-properties-of-protons-in-ice-and-mechanism-3htxq0w0cn.pdf

The conductivity properties of protons in ice and mechanism of magnetization of liquid water

The dynamical theory of a quantum quasiparticle moving in a deformable anharmonic chain is extended into the supersonic region. Besides a supersonic self-trapping mode, which is a direct extension of the well-known subsonic Davydov-Scott mode, two additional dynamically stable transfer mechanisms have been discovered in this region: (i) the capture and transfer of the self-trapping state by a supersonic acoustic (lattice) soliton and (ii) the pairing of two lattice solitons via their interaction with a quasiparticle. \textcopyright{} 1996 The American Physical Society.

Supersonic mechanisms for charge and energy transfers in anharmonic molecular chains

A mechanism based on the peculiar dynamical properties of the hydrogen bond is suggested to describe fast proton transfers in hydrogen-bonded chains with realistic (weak) intersite proton-proton interactions. For this purpose, a two-sublattice model is suggested and studied analytically that admits an exact soliton solution. The solitons, which are topological objects (kinks and antikinks) on the one hand, but dynamical entities (like Boussinesq solitons) on the other hand, are shown to have a sufficiently large width to allow free propagation along the chain.

Collective proton transport with weak proton-proton coupling

Chaotic proton dynamics in the hydrogen bond.

A generalized model for the nonlinear transport of vibrational energy in a molecular chain is derived. It contains the coupling to both the optical and the acoustic modes of the lattice. The model reduces in simplified situations to the Davydov model or the Holstein model. Reductions to two forms of discrete nonlinear Schrodinger equations are discussed, and the corresponding solitary wave solutions are presented. In general, the molecular chain contains some randomness, which is caused by different physical mechanisms: (i) randomly distributed molecules around the chain, (ii) different masses of the side groups, and (iii) random distributions of the intermolecular distances. The various effects are discussed and special attention is given to their influence on the transmission coefficient

Nonlinear transport of vibrational energy in a random molecular chain.

For the free propagation of kinks (antikinks) in the standard Frenkel-Kontorova (FK) model it is necessary that the height of the barrier connecting two adjacent minima of the on-site potentials is sufficiently small as compared with interactions between nearest-neighbor atoms of molecules. Freely propagating kinks are sufficiently extended objects, and their Peierls-Nabarro (PN) relief is neglegible. On the other hand, although the dynamics of chain particles is still collective, narrow kinks are strongly pinned and their transport along the chain can be achieved only by means of some external (regular and/or stochastic) forces.

A. V. Zolotaryuk

Papers

Supersonic mechanisms for charge and energy transfers in anharmonic molecular chains

Collective proton transport with weak proton-proton coupling

Chaotic proton dynamics in the hydrogen bond.

Nonlinear transport of vibrational energy in a random molecular chain.

Narrow Kinks in Nonlinear Lattices: Application to the Proton Transport in Hydrogen-Bonded Systems