Simple mechanical models of DNA play an important role in studying the dynamics of its open states. The main requirement when developing a DNA model is the correct selection of its effective potentials and parameters based on experimental data. At the same time, various experiments allow us to "see" different types of DNA open states. Consideration of this feature is one of the most important conditions in the development, optimization, and parameterization of any mechanical model. Violation of this condition, i.e., the comparison of incomparable characteristics, leads to critical errors. The present investigation is devoted to the problem of degrees of freedom of DNA bases taken into account in mechanical models. Using the Peyrard-Bishop-Dauxois model as an example, two types of errors in interpreting experimental data when compared with the model are examined. The first one is a mismatch between the open state types in the model and experiment. The second one is an incorrect specification of the "threshold coordinate" of the open state. The concept of the effective total threshold coordinate of the radial separation of DNA strands for registration of opening is introduced. It is shown that correct interpretation of experimental data can actually eliminate discrepancies with theory.

The temperature dependence of energy, partition function, entropy and free energy, describing a first-order-like phase transition of a DNA molecule is calculated based on the direct method of molecular dynamics for the classical Peyrard-Bishop-Dauxois model. It is shown that without taking into account the quantum freezing of the degrees of freedom at low temperatures, the relationship between these quantities is not determined. The latent heat of DNA melting is calculated for homogeneous PolyA/PolyT and PolyG/PolyC DNA chains. It is shown that this melting transition corresponds to a sharp temperature dependence of the heat capacity.

A modified model of the primary photoreaction in rhodopsin, cis-trans photoisomerization of the chromophore (retinal), is studied. The quantum subsystem of the model includes three vibronic states: the ground state, the excited state, and the ground state of the primary photoproduct. These states correspond to three point masses in the classical subsystem. The modification consists in the exponential dependence of the electronic-vibrational coupling constant on the displacement of point masses. The properties of the optimal loci of the multiparameter space, which characterized by the best agreement with the experimental data, are studied. A rather small “multidimensional volume” of these loci shown in all ranges of the used values of the model parameters. Several ways to optimize the quantum-classical model of rhodopsin photoisomerization have been proposed.

Модифицированная квантово-классическая модель фотоизомеризации хромофора в зрительном пигменте родопсине исследована с точки зрения объёмов локусов многомерного пространства параметров, в пределах которых наблюдается хорошее согласие между результатами расчётов и экспериментальными данными.Квантовая подсистема модели включает основное и возбуждённое состояния хромофора -11-цис ретиналя -а также основное состояние первичного фотопродукта.Каждому состоянию поставлена в соответствие одна материальная точка классической подсистемы, соответствующая той или иной атомной группировке хромофора.В данной работе исследована последняя модификация квантово-классической модели фотореакции с квадратично-экспоненциальной зависимостью электронноколебательной константы связи от смещения точечных масс.Показано, что «многомерный объём» каждого локуса является достаточно малым.Тем не менее, отношение диапазона значений каждого параметра

A modified model of the rhodopsin retinal chromophore cis-trans photoisomerization is developed, where the electron-vibration coupling constant depends exponentially on displacements of mass points. The quantum subsystem of the model includes three electronic states for rhodopsin: (i) the ground state, (ii) the excited state, (iii) the primary photoproduct in the ground state. The classical subsystem includes three mass points. The modifications give sufficient improvement of agreement between computational data and experiments, with all parameters of the model being very close to the most physically realistic values. In particular, improvements concern with data on residual coherent oscillations after photoisomerization is complete.

A variant of the Peyrard-Bishop-Dauxois model is proposed, which takes account of the partially delocalized nature of DNA stacking interactions. It is shown that the nonlocal nature of the inter-site potential can lead to an increase in the local cooperativity of the base pairs' opening an increasing in the number of simultaneously opening adjacent nucleotide pairs during the denaturation bubble's nucleation. The process of the formation and propagation of mobile breathers excited by the initial displacements of a number of nucleotide pairs has been studied. It is revealed that taking account of the non-local coupling in the Peyrard-Bishop-Dauxois model, while maintaining the remaining parameters of the model, leads to a decrease in the speed of the mobile breather and an increase in the probability of nucleation of the denaturation bubble.

The article is analyzed Jimak S.S. et al. “Mathematical modeling of open state accounting as a function of 2 H/ 1 H ratio in a double-stranded DNA molecule”, appeared in “Mathematical Biology and Bioinformatics”. The values of H-bond energies used in the simulation as a parameter are estimated. A new mechanism for the effect of DNA deuteration on biological function of DNA described by authors is proposed.

A modified Peyrard-Bishop-Dauxios model with non-local nature of the inter-site potential was studied in a collisional thermostat with a Maxwell velocity distribution of short-lived virtual particles at a temperature of 310 K. Introduction of non-locality to the inter-site potential was found to reduce significantly the equilibrium constants for the denaturation bubble formation reaction. This property improves the agreement of calculated data with experiments. The effect is especially pronounced for large bubbles. The end effects in the new version of the model are investigated. The significant contribution of entropy and the important role of the processes of transfer and localization of mechanical energy at the end sections of DNA are shown.

Сформулированы модифицированные уравнения нелинейной модели ДНК с Морзе on-site и inter-site потенциалами взаимодействия. Проведено моделирование динамики ДНК на их основе. Такая модель рассматривается как альтернативная модели Пейрарда–Бишопа–Доксуа. Исследован простейший случай с пузырьком в виде полупериода синусоиды. Показано, что оптимальная нуклеационная длина пузырька денатурации зависит от ряда параметров модели, в отличие от случая модели Пейярда–Дишопа–Доксуа, где нуклеационная длина всегда равна 1–2 парам оснований. В общем случае, для любого сочетания параметров модифицированной модели существует оптимальная нуклеационная длина пузырька денатурации, которая, характеризуется соответствующей минимальной энергией нуклеации; при этом энергия нуклеации более коротких пузырьков получается значительно выше.

Сравнение квантово-классической модели фотоизомеризации родопсина с квантовомеханическим подходом Хан-СтокаШигаев А

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.

A quantum-classical model of photoisomerization of the visual pigment rhodopsin chromophore is proposed. At certain (and more realistic) parameter value combinations, the model is shown to accurately reproduce a number of independent experimental data on the photoreaction dynamics: the quantum yield, the time to reach the point of conical intersection of potential energy surfaces, the termination time of the evolution of quantum subsystem, as well as the characteristic low frequencies of retinal molecular lattice fluctuations during photoisomerization. In addition, the model behavior is in good accordance with experimental data about coherence and local character of quantum transition.

A quantum-classical model of cis-trans photoisomerization of the visual pigment rhodopsin chromophore was investigated in wide ranges of parameters. The quantum subsystem of the model includes three electronic states for rhodopsin: the ground state, the excited state, and the ground state of primary photoproduct. The local temperature of the mass points of the classical subsystem was used as a main reference quantity. The best agreement with experimental data was shown to be in the range of moderate temperatures in agreement with the Raman spectroscopy data. The essential role of a quick transfer of the photoexcitation excess energy into apoprotein part in photoproduct stabilization process was illustrated. Also, the fundamental nature and the local character of the photoreaction were shown in the numerical investigations.

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.

A closed system of nonlinear differential equations is proposed for current correlation functions of the Kubo expression for conductivity. The chain of equations is closed by dropping the correlations of higher order. The approach allows estimating an error of the dropped correlations. A successive approximation technique can take account of the corrections and allow for subtle effects caused by DNA structure and identifies areas, where these corrections are significant. The local conductivity in one-dimensional case was shown to be defined by adjacent sites. Zone conductivity takes place for small electron-vibrational interactions. The conductivity decreases with temperature rise, but it may increase or decrease at low temperatures because of finiteness of polymer fragment. At low temperatures the zone conductivity persists for large electron-vibrational interactions, however the possibility of hopping appears, and hopping conductivity increases with temperature rise and becomes determinant at some temperature but starts decreasing with temperature rise at high temperatures. (C) 2017 Elsevier B.V. All rights reserved.

It is shown that in DNA-like molecules containing added, excess charges, such as electrons and holes (cation-radicals), it is possible by highly energetic, local, mechanical excitation at definite places of the chain to control the creation of breathers/bubbles and hence to control the long-range transfer of charges moving along the chain in a definite given direction with no external electric field needed.

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.