Bloch oscillations of a soliton in a molecular chain

The paper presents results of numerical experiments simulating Bloch oscillations of solitons in a deformable molecular chain in a constant electric field. By the example of a homogeneous polynucleotide chain it is shown that the system under consideration can demonstrate complicated dynamical regimes when at the field intensities less than a certain critical value, a soliton as a whole exhibits oscillations, while at the field intensities exceeding the threshold, a soliton turns to a breather which oscillates. It is shown that the motion of a charge in a deformable chain is infinite as contrasted to that in a rigid chain.Comment: 3 pages, 3 figure

A new type of localized fast moving electronic excitations in molecular chains

It is shown that in a Holstein molecular chain placed in a strong longitudinal electric field some new types of excitations can arise. This excitations can transfer a charge over large distance (more than 1000 nucleotide pairs) along the chain retaining approximately their shapes. Excitations are formed only when a strong electric field either exists or quickly arises under especially preassigned conditions. These excitations transfer a charge even in the case when Holstein polarons are practically immobile. The results obtained are applied to synthetic homogeneous PolyG/PolyC DNA duplexes. They can be also provide the basis for explanation of famous H.W. Fink and C. Sch\"{o}nenberger experiment on long-range charge transfer in DNA.Comment: 4 pages, 3 figure

Formation of stationary electronic states in finite homogeneous molecular chains

Evolution of an arbitrary initial distribution of a quantummechanical particle in a uniform molecular chain is simulated by a system of coupled quantumclassical dynamical equations with dissipation. Stability of a uniform distribution of the particle over the chain is studied. An asymptotical expression is obtained for the time in which a localized state is formed. The validity of the expression is checked by direct computational experiments. It is shown that the time of soliton and multisoliton type states formation depends strongly on the initial phase of the particle's wave function. It is shown that in multisoliton states objects with a fractional electron charge which can be observed experimentally are realized. The results obtained are applied to synthetic uniform polynucleotide molecular chains.Comment: Published in peer-reviewed open access journal "Mathematical biology and bioinformatics". Supplementary materials can be found there http://www.matbio.org/article.php?journ_id=6&id=56&lang=en

The Virial Theorem and the Ground State Problem in Polaron Theory

The virial theorem for the translation-invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong-coupling limit, which led to the violation of the virial relations. The introduction of an additional variational parameter to the test function reduces the polaron energy and makes it possible to satisfy the relations of the virial theorem for a strong-coupling polaron (the Pekar 1 : 2 : 3 : 4 theorem)

Scaling of Temperature Dependence of Charge Mobility in Molecular Holstein Chains

The temperature dependence of a charge mobility in a model DNA based on Holstein Hamiltonian is calculated for 4 types of homogeneous sequences It has turned out that upon rescaling all 4 types are quite similar. Two types of rescaling, i.e. those for low and intermediate temperatures, are found. The curves obtained are approximated on a logarithmic scale by cubic polynomials. We believe that for model homogeneous biopolymers with parameters close to the designed ones, one can assess the value of the charge mobility without carrying out resource-intensive direct simulation, just by using a suitable approximating function.Comment: 14 pages, 5 figures. Differences from the previous version: part of the text about the second dimensionless system is removed; paragraph about model extensions - dispersion in classical chain and solvating - is adde

Excitation of Bubbles and Breathers in DNA and Their Interaction with the Charge Carriers

The nonlinear excitations induced in DNA by external force are considered on the basis of Peyrard-Bishop-Dauxois model. It is shown that such impact can lead to creation of bubbles which can propogate through the molecule. The interaction of such bubbles with an excess electron or hole is considered. The numerical experiments demonstrate the possibility of charge transfer induced by bubbles. The possible applications of the obtained results in nanobioelectronics are discussed.Comment: 16 pages, 12 figures; in Russian. Published in peer-reviewed open access journal. http://www.matbio.org/journal.php?lang=en

Theoretical and Experimental Investigations of DNA Open States

Literature data on the properties of DNA open states are reviewed and analyzed. These states are formed as a result of strong DNA fluctuations and have a great impact on a number of biochemical processes; among them is charge transfer in DNA, for example. A comparative analysis of experimental data on the kinetics and thermodynamics of DNA open states for a wide temperature range was carried out. Discrepancies between the results of various experiments have been explained. Three types of DNA open states are recognized based on their differences in thermodynamic properties and other characteristics. Besides, an up-to-date definition of the term "open state" is given. A review is carried out for simple mathematical models of DNA in most of which the state of one pair is described by one or two variables. The main problems arising in theoretical investigations of heterogeneous DNA in the framework of models of this level are considered. The role of each group of models in interpretation of experimental data is discussed. Special consideration is given to the studies of the transfer and localization of the nucleotide pairs oscillations' energy by mechanical models. These processes are shown to play a key role in the dynamics of a heterogeneous duplex. Their theoretical interpretation is proven to be very important for the development of modern molecular biology and biophysics. The main features of the theoretical approaches are considered which enabled describing various experimental data. Prospects of the models' development are described, particular details of their optimization are suggested, and possible ways of modernization of some experimental techniques are discussed.Comment: Translation into English of a revised version of the original article (v.1) published in Russian. Review paper, 106 page

A new approach to microscopic modeling of a hole transfer in heteropolymer DNA

Thermal oscillations of base pairs in the Peyrard-Bishop-Holstein model are simulated by stochastic fluctuations of base overlap integrals. Numerical investigation of the model is carried out for a hole transfer in $G_1A_2G_3G_4$ sequence which was previously studied experimentally by F. Lewis et al. A hole migration between $G_1$ and $G_3G_4$ is determined by the matrix elements of the charge transition, but presence and amplitude of their stochastic fluctuations proved to play a key role in reproduction of the experimental kinetics. Good agreement with the experimental data was obtained for a wide range of the model parameters' combinations.Comment: 14 pages, 1 figure, 1 tabl

Hole Conductivity in Heterogeneous DNA Fragments

The characteristics of cation radical (hole) migration in heterogeneous DNA were investigated on the basis of Kubo formula, in which correlation functions were obtained from solutions of systems of Bogoliubov hierarchy. The cutting of Bogoliubov hierarchy was carried out by excepting correlations of the third and higher order. The obtained system of non-linear differential equations was investigated both analytically and numerically. The environment polarization, caused by interaction of holes with base pairs vibrations, was shown to play the key role in transport processes. The energy of the interaction can ten-fold exceed vibration energy. The transfer rate between adjacent DNA bases in one-dimensional case was shown to be almost independent of the nature and behavior of more distant pairs. The charge probability amplitude oscillates in the picosecond timescale. Nonetheless, the rates of hole transfer, obtained by averaging over these oscillations, turned out to be very close to the experimental data. The calculated dependence of the hole transfer rate between two guanine bases on the number of intervening adenine bases was also in good agreement with the experimental data. Besides, the temperature dependence of the transfer rate was investigated. Hopping mechanism was shown to make the main contribution to the hole transport process at 300 K.Comment: 26 pages, 5 figures, 4 tables; in Russian. Published in peer-reviewed open access journal. http://www.matbio.org/about.php?lang=en

New insight into the dynamics of rhodopsin photoisomerization from one-dimensional quantum-classical modeling

Characterization of the primary events involved in the $cis-trans$ photoisomerization of the rhodopsin retinal chromophore was approximated by a minimum one-dimensional quantum-classical model. The developed mathematical model is identical to that obtained using conventional quantum-classical approaches, and multiparametric quantum-chemical or molecular dynamics (MD) computations were not required. The quantum subsystem of the model includes three electronic states for rhodopsin: (i) the ground state, (ii) the excited state, and (iii) the primary photoproduct in the ground state. The resultant model is in perfect agreement with experimental data in terms of the quantum yield, the time required to reach the conical intersection and to complete the quantum evolution, the range of the characteristic low frequencies active within the primary events of the $11-cis$ retinal isomerization, and the coherent character of the photoreaction. An effective redistribution of excess energy between the vibration modes of rhodopsin was revealed by analysis of the dissipation process. The results confirm the validity of the minimal model, despite its one-dimensional character. The fundamental nature of the photoreaction was therefore demonstrated using a minimum mathematical model for the first time.Comment: 30 pages, 5 figure