Discrete and Continuous Models and Applied Computational Science, 2019
We analyzed numerically computed velocity autocorrelation functions and generalized frequency spe... more We analyzed numerically computed velocity autocorrelation functions and generalized frequency spectra of charge distribution in homogeneous DNA sequences at finite temperature. The autocorrelation function and generalized frequency spectrum (frequency-dependent diffusion coefficient) are phenomenologically introduced based on the functional of mean-square displacement of the charge in DNA. The charge transfer in DNA was modeled in the framework of the semi-classical Holstein model. In this model, DNA is represented by a chain of oscillators placed into thermostat at a given temperature that is provided by the additional Langevin term. Correspondence to the real DNA is provided by choice of the force parameters, which are calculated with quantum-chemical methods. We computed the diffusion coefficient for all homogenous DNA chains with respect to the temperature and found a special scaling of independent variables that the temperature dependence of the diffusion coefficient for differ...
... linear dimer, the barrier equals ~0.84 kJ/mol (which is close to the value for the dimer of m... more ... linear dimer, the barrier equals ~0.84 kJ/mol (which is close to the value for the dimer of methane), whereas the forma-tion of a parallel complex requires overcoming a bar-rier whose ... REFERENCES 1. Ben-Naim, A., Hydrophobic Interactions, New York: Plenum, 1980, p. 312. ...
In this paper a statistical analysis of distributions of inter-helical angles in pairs of consecu... more In this paper a statistical analysis of distributions of inter-helical angles in pairs of consecutive and connected α-helices in spatial structures of proteins is presented. A number of rules for selection of the helical pairs from a set of protein structures obtained from the Protein Data Bank (PDB) were developed. The set of helical pairs has been analyzed for the purpose of classification and finding out the features of protein structural organization. All pairs of connected helices were divided into three subsets according to the criterion of crossing of projections of the helices on parallel planes, which pass through the axes of the helices. It is shown that the distribution of all types of helical pairs, whose projections do not cross each others, covers almost the entire range of inter-helical angles. The distribution have a single maximum which is close to right angle. Most pairs in this set constitute helical pairs consisting of α- and 310-helices, and most pairs with the ...
Abstract—This paper demonstrates the effectiveness of the use of the cross-correlation Shannon en... more Abstract—This paper demonstrates the effectiveness of the use of the cross-correlation Shannon entropy; the cross-correlation Shannon entropy is a generalization of spectral entropy, which is widely used in scientific research, as a method of analysis of mutual correlations between plankton abundance fluctuations and temperature variations. In particular, analysis of time series that characterize the dynamics of zooplankton, phytoplankton, and bacterioplankton and water temperature variations shows that mutual correlations are most significant between temperature and bacterioplankton.
Демонстрируется эффективность использования кросс-корреляционной энтропии Шеннона,
представляюще... more Демонстрируется эффективность использования кросс-корреляционной энтропии Шеннона,
представляющей собой обобщение широко применяемой в научных исследованиях спектральной
энтропии, как метода анализа взаимных корреляций между колебаниями планктонного обилия и
вариациями температуры. На примере анализа временных рядов, характеризующих динамику зоопланктона, фитопланктона, бактериопланктона и вариации температуры воды, показывается, в
частности, что наиболее значимыми являются взаимные корреляции между температурой и бактериопланктоном.
The temperature dependence of a charge mobility in a model DNA based on Holstein Hamiltonian is c... more 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.
The statistical analysis of interhelical distances in pairs of connected α-helices found in known... more The statistical analysis of interhelical distances in pairs of connected α-helices found in known proteins has been performed. In accordance with the certain rules, a database of the pairs found in the Protein Data Bank has been compiled. This set was subdivided into three subsets according to criterion of crossing helix projections on the parallel plane passing through the axis of the helix. It was shown that the distribution of distances between the pairs of helices whose projections are not crossed has a more long-range nature than those whose projections are overlapped. Using the regression analysis the nature of distributions is investigated. In particular, it is shown that the distributions of interhelical distances in the subset of pairs of helices without intersections belong to the gamma distributions. It is also shown that the subset of the pairs with crossing projections have a smaller ratio of the minimal distance between the helical axes to the interplanar distance that...
This study investigated the stability of structural motifs via molecular dynamics, using α-α-corn... more This study investigated the stability of structural motifs via molecular dynamics, using α-α-corners as an example. A molecular dynamics experiment was performed on a sample of α-α-corners selected by the authors from the PDB database. For the first time during a molecular dynamics experiment, we investigated the characteristics of structural motifs by describing their geometry, including the interplanar distance, area of polygon of the helices projections intersection, and torsion angles between axes of helices in helical pairs. The torsion angles for the constriction amino acids in the equilibrium portion of the molecular dynamics trajectory were analyzed. Using the molecular dynamics method, α-α-corners were found to be autonomous structures that are stable in aquatic environments.
The once abstract notions of fractal patterns and processes now appear naturally and inevitably i... more The once abstract notions of fractal patterns and processes now appear naturally and inevitably in various chaotic dynamical systems. The examples range from Brownian motion [15] to the dynamics of social relations [6]. In this paper, after introducing a certain hybrid ...
ABSTRACT 122 This work continues the study of specific features of polar peptides in water [1]. C... more ABSTRACT 122 This work continues the study of specific features of polar peptides in water [1]. Characteristics of selff assembling structures are important for developing approaches to the design of new medical materials, including biomimetics for tissue engineering [2–4]. A characteristic trait of molecules of this type is the presence of a relatively large number of charged atoms alternating with vast hydrophobic segments of the molecular surface. To determine the Gibbs energy of complex strucc tures of selffassembling peptides, a new method of call culation of mean values from a set of configurational states has been used [5]. This method requires solving once the RISM equations [6] with intramolecular corr relation functions calculated from the distributions of interatomic distances of a flexible structure on the basis of molecular dynamics (MD) simulation data. In the present work, we used the repulsive correction to improve the model [7]. It is important that the use of the mean matrix of intermolecular correlations (MMIC) in the RISM equations makes it possible to perform numerical thermodynamic integration and calculate the chemical potential, even without knowll edge of the exact analytical form of this potential. RISM METHODOLOGY RISM Equations with Mean Matrix The RISM equations for an infinitely dilute soluu tion [8], when the partial density of the solute can be,
Демонстрируется эффективность использования кросс-корреляционной энтропии Шеннона, представляющей... more Демонстрируется эффективность использования кросс-корреляционной энтропии Шеннона, представляющей собой обобщение широко применяемой в научных исследованиях спектральной энтропии, как метода анализа взаимных корреляций между колебаниями планктонного обилия и вариациями температуры. На примере анализа временных рядов, характеризующих динамику зоо-планктона, фитопланктона, бактериопланктона и вариации температуры воды, показывается, в частности, что наиболее значимыми являются взаимные корреляции между температурой и бакте-риопланктоном. Ключевые слова: кросс-корреляционная энтропия Шеннона, планктон, температура. Колебания численности популяций в боль-шинстве случаев характеризуются нерегулярно-стью и ограниченной предсказуемостью [1,2]. В качестве причины такой нерегулярности часто рассматривают динамический хаос, т.е. неустой-чивость динамики, независимую от внешних влияний. Подобная неустойчивость во многих математических моделях темпоральных вариаций популяционного обилия проявляется в виде зави-симости нерегулярных временных рядов от на-чальных условий [2-4]. Необходимо, однако, учитывать то, что реальные, а не модельные, по-пуляции связаны между собой, образуя сложные сети трофических взаимодействий (см., напри-мер, [5]), и потому не являются независимыми. Кроме того, все природные популяции подверже-ны воздействию внешних абиотических факто-ров, таких как: температура, солнечная радиация, ветер,-что далеко не всегда учитывается в ходе математического моделирования [6]. Поэтому оценки влияния динамики внешних абиотиче-ских факторов на динамику популяций, наряду с исследованиями межпопуляционных взаимодей-ствий, базирующиеся на данных, полученных в ходе полевых измерений (мониторинга экоси-стем), представляют существенный интерес. Мониторинг экосистем предполагает проведе-ние одновременных измерений биотических и абиотических факторов (см. например, работу [7]), что позволяет сопоставлять между собой cоответствующие временные ряды и, в частности, оценивать степень их сопряженности. Так, в ре-зультате анализа данных полевых исследований экосистемы Нарочанских озер (Белоруссия) бы-ло показано [8], что уровень фазовой синхрониза-ции колебаний температуры воды и колебаний биомассы фитопланктона связан со степенью со-пряжения колебаний популяционного обилия фитопланктона и бактериопланктона. Отметим, что адекватность оценки степени со-пряжения планктонных осцилляций и их синхро-низации с вариациями температуры в значитель-ной мере зависят от объема и качества данных, полученных в ходе полевых наблюдений. В этой связи использование таких методов оценки взаи-мосвязи между колебаниями обилия популяций планктона и связи планктонной динамики с ва-УДК 577.3
Присущий математическому моделированию редукционистский подход к анализу природных явле-ний неизб... more Присущий математическому моделированию редукционистский подход к анализу природных явле-ний неизбежно ставит вопрос о соответствии результатов моделирования реальным процессам. Статья посвящена анализу проблем, возникающих при сопоставлении результатов математическо-го моделирования популяционных процессов и данных, полученных в ходе мониторинга природ-ных экосистем. Эти проблемы обусловливаются тем, что далеко не всегда вид зависимостей между переменными, описывающими динамику популяционных процессов, равно как и выбор числен-ных значений параметров математических моделей, удается обосновать, опираясь на результаты мониторинга конкретной экосистемы. В статье предлагается подход, позволяющий в ходе матема-тического моделирования учитывать воздействие всего комплекса биотических и абиотических факторов на динамику популяций. Такой подход базируется на принятии во внимание данных мо-ниторинга экосистем и прямом включении этих данных в математические модели популяционной динамики. Реализация этого подхода позволяет, в частности, оценивать степень влияния отдельных факторов среды обитания как на вариации популяционного обилия, регистрируемые в ходе мони-торинга, так и на такие характеристики популяционных процессов, которые непосредственно не измеряются в ходе мониторинга, но являются результатом математического моделирования. Ключевые слова: популяционная динамика, математическое моделирование, анализ временных рядов. Популяция как динамический объект. Пред-ставление о популяции как о динамическом объ-екте является теоретической идеализацией. В рамках этой идеализации обычно отвлекаются от индивидуальных особенностей отдельных особей (организмов), формирующих популяцию, подоб-но тому, как часто пренебрегают свойствами от-дельных молекул при исследовании динамики жидкостей или газов. Подобно газу и жидкости, популяция может характеризоваться плотностью (популяционным обилием), т.е. числом особей или массой на единицу площади или объема. Плотность природных популяций подвержена изменениям как в пространстве, так и во време-ни. В основе таких изменений лежат биологиче-ские процессы (рост организмов, их размноже-ние и гибель), а наряду с ними-экологические процессы (миграции, межпопуляционные тро-фические взаимодействия, изменения условий обитания). Сложная мозаика факторов, обуслов-ливающих колебания популяционного обилия, во многих случаях нерегулярные, существенно затрудняет попытки выделить основные движу-щие факторы, ответственные за наблюдаемые в природе колебания плотности популяций. Для того чтобы обойти это затруднение, при-бегают к редукции. Такая редукция, в частности, реализуется в механистических моделях, в рамках которых динамика популяций описывается как результат суммирования независимых процессов (например, размножения и смертности). При этом в предположении, что модельная популяция УДК 57.055
In this paper, a statistical analysis of a distribution of interhelical distances in the helical ... more In this paper, a statistical analysis of a distribution of interhelical distances in the helical pairs of known proteins is carried out. A set of helical pairs of the protein molecules which was selected from the Protein Data Bank according to certain rules was subdivided into three subsets according to the criterion of crossing helix projections onto parallel planes passing through the helical axes. It is shown that the distributions of the distances for the helical pairs not having crossing projections have more long-range character than those whose projections cross. Using regression analysis we analyze the character of distributions, in particular, we show that in the subsets which do not have crossing projections, distributions of different distances between helical axes are gamma distributions. It is demonstrated that in the subsets having crossing projections, the ratio between the minimum distance and the interplane one is likely to be small as distinct from the subset not having crossing projections where the opposite is the case. The conclusion is proved that helical pairs having crossing axes projections are additionally stabilized due to internal interactions.
In this paper a statistical analysis of distributions of inter-helical angles in pairs of consequ... more In this paper a statistical analysis of distributions of inter-helical angles in pairs of consequtive and connected α-helices in spatial structures of proteins are presented. A number of rules for selection of the helical pairs from a set of protein structures obtained from Protein Data Bank (PDB) are developed. The set of helical pairs has been analyzed for the purpose of classification and finding out the features of protein structural organization. All the pairs of connected helices are divided into three subsets according to the criterion of crossing of projections of the helices on parallel planes, which pass through the axes of the helices. It is shown that the distribution of all the types of helical pairs, whose projections do not cross each other, covers almost the entire range of inter-helical angles. The distribution has a single minimum which is close to right angle. Most pairs in this set constitute helical pairs consisting of α-and 3 10-helices, and most pairs with the crossing projections of helices are helical pairs formed by two α-helices. It is also shown that a great amount of the pairs of connected α-helices has acute angle (20 60) between the axes of the helices. The distribution of all the types of helical pairs depending on the length of the inter-helical connections is also analyzed. It is shown that the structures with short connections occur most often in all the subsets. Key words: structural motifs of proteins, point model, helical pairs, angle between the axes of the helices.
Recommended form of bibliographic references: Tikhonov D.A., Sobolev E.V., Lakhno V.D. Charge dif... more Recommended form of bibliographic references: Tikhonov D.A., Sobolev E.V., Lakhno V.D. Charge diffusion in homogeneous molecular chains based on the analysis of generalized frequency spectra in the framework of the Holstein model // Keldysh Institute Preprints.
The temperature dependence of a charge mobility in a model DNA based on a Holstein Hamiltonian is... more The temperature dependence of a charge mobility in a model DNA based on a Holstein Hamiltonian is calculated for four types of homogeneous sequences It has turned out that upon rescaling all four 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.
This paper demonstrates the effectiveness of the use of the cross-correlation Shannon entropy; th... more This paper demonstrates the effectiveness of the use of the cross-correlation Shannon entropy; the cross-correlation Shannon entropy is a generalization of spectral entropy, which is widely used in scientific research, as a method of analysis of mutual correlations between plankton abundance fluctuations and temperature variations. In particular, analysis of time series that characterize the dynamics of zooplankton, phy-toplankton, and bacterioplankton and water temperature variations shows that mutual correlations are most significant between temperature and bacterioplankton. Fluctuations in population abundance are mostly characterized by irregularity and limited predictability [1, 2]. Dynamical chaos, i.e., dynamical instability that does not depend on external effects, is often considered as a cause of this irregularity. In many mathematical models of temporal variations in the population abundance, this instability is expressed as the dependence of an irregular time series on initial conditions [2-4]. However, one should take the fact into account that real, rather than model populations are interrelated and form complex networks of trophic interactions (see, e.g., [5]); therefore, they are not independent. In addition, all natural populations are exposed to the effect of external abiotic factors, such as temperature, solar radiation, and wind, which is far from always taken into account in mathematical mod-eling [6]. Therefore, along with studies of between-population interactions, estimates of the influence of the dynamics of external abiotic factors on the population dynamics using the data of field studies (ecosys-tem monitoring) are of considerable interest. Ecosystem monitoring assumes simultaneous measurements of biotic and abiotic factors (see, e.g., [7]), which makes it possible to compare the respective time series with each other and, in particular, assess the degree of their conjugacy. Thus, analysis of the data of field studies of the Naroch lake ecosystem (Belorussia) has shown [8] that the level of phase synchronization of water temperature fluctuations and phytoplankton biomass fluctuations is related to the degree of coupling of fluctuations in the population abundance of phytoplankton and bacterioplankton. It should be noted that the adequacy of the estimate of the degree of coupling between plankton oscillations and their synchronization with temperature variations significantly depends on the volume and quality of field survey data. Therefore, it is reasonable to use the methods of estimating the intercou-pling between fluctuations in plankton population abundance and relation between the plankton dynamics and temperature variations, which differ from methods previously used in [8] and do not depend on them. The purpose of this research is to establish correlations between power spectra that characterize the population dynamics of phytoplankton, zooplankton, and bacterioplankton and temperature fluctuations in the group of the Naroch Lakes. MATERIALS AND METHODS The Naroch Lakes are located in the northwestern part of Belorussia; they are a system of three water bodies connected by branches with each other: Lake Naroch (which is, in turn, composed of two parts: the large stretch and small stretch), Lake Myastro, and Lake Batorino. The main characteristics of these water bodies (area, water volume, mean and maximum COMPLEX SYSTEMS BIOPHYSICS
Discrete and Continuous Models and Applied Computational Science, 2019
We analyzed numerically computed velocity autocorrelation functions and generalized frequency spe... more We analyzed numerically computed velocity autocorrelation functions and generalized frequency spectra of charge distribution in homogeneous DNA sequences at finite temperature. The autocorrelation function and generalized frequency spectrum (frequency-dependent diffusion coefficient) are phenomenologically introduced based on the functional of mean-square displacement of the charge in DNA. The charge transfer in DNA was modeled in the framework of the semi-classical Holstein model. In this model, DNA is represented by a chain of oscillators placed into thermostat at a given temperature that is provided by the additional Langevin term. Correspondence to the real DNA is provided by choice of the force parameters, which are calculated with quantum-chemical methods. We computed the diffusion coefficient for all homogenous DNA chains with respect to the temperature and found a special scaling of independent variables that the temperature dependence of the diffusion coefficient for differ...
... linear dimer, the barrier equals ~0.84 kJ/mol (which is close to the value for the dimer of m... more ... linear dimer, the barrier equals ~0.84 kJ/mol (which is close to the value for the dimer of methane), whereas the forma-tion of a parallel complex requires overcoming a bar-rier whose ... REFERENCES 1. Ben-Naim, A., Hydrophobic Interactions, New York: Plenum, 1980, p. 312. ...
In this paper a statistical analysis of distributions of inter-helical angles in pairs of consecu... more In this paper a statistical analysis of distributions of inter-helical angles in pairs of consecutive and connected α-helices in spatial structures of proteins is presented. A number of rules for selection of the helical pairs from a set of protein structures obtained from the Protein Data Bank (PDB) were developed. The set of helical pairs has been analyzed for the purpose of classification and finding out the features of protein structural organization. All pairs of connected helices were divided into three subsets according to the criterion of crossing of projections of the helices on parallel planes, which pass through the axes of the helices. It is shown that the distribution of all types of helical pairs, whose projections do not cross each others, covers almost the entire range of inter-helical angles. The distribution have a single maximum which is close to right angle. Most pairs in this set constitute helical pairs consisting of α- and 310-helices, and most pairs with the ...
Abstract—This paper demonstrates the effectiveness of the use of the cross-correlation Shannon en... more Abstract—This paper demonstrates the effectiveness of the use of the cross-correlation Shannon entropy; the cross-correlation Shannon entropy is a generalization of spectral entropy, which is widely used in scientific research, as a method of analysis of mutual correlations between plankton abundance fluctuations and temperature variations. In particular, analysis of time series that characterize the dynamics of zooplankton, phytoplankton, and bacterioplankton and water temperature variations shows that mutual correlations are most significant between temperature and bacterioplankton.
Демонстрируется эффективность использования кросс-корреляционной энтропии Шеннона,
представляюще... more Демонстрируется эффективность использования кросс-корреляционной энтропии Шеннона,
представляющей собой обобщение широко применяемой в научных исследованиях спектральной
энтропии, как метода анализа взаимных корреляций между колебаниями планктонного обилия и
вариациями температуры. На примере анализа временных рядов, характеризующих динамику зоопланктона, фитопланктона, бактериопланктона и вариации температуры воды, показывается, в
частности, что наиболее значимыми являются взаимные корреляции между температурой и бактериопланктоном.
The temperature dependence of a charge mobility in a model DNA based on Holstein Hamiltonian is c... more 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.
The statistical analysis of interhelical distances in pairs of connected α-helices found in known... more The statistical analysis of interhelical distances in pairs of connected α-helices found in known proteins has been performed. In accordance with the certain rules, a database of the pairs found in the Protein Data Bank has been compiled. This set was subdivided into three subsets according to criterion of crossing helix projections on the parallel plane passing through the axis of the helix. It was shown that the distribution of distances between the pairs of helices whose projections are not crossed has a more long-range nature than those whose projections are overlapped. Using the regression analysis the nature of distributions is investigated. In particular, it is shown that the distributions of interhelical distances in the subset of pairs of helices without intersections belong to the gamma distributions. It is also shown that the subset of the pairs with crossing projections have a smaller ratio of the minimal distance between the helical axes to the interplanar distance that...
This study investigated the stability of structural motifs via molecular dynamics, using α-α-corn... more This study investigated the stability of structural motifs via molecular dynamics, using α-α-corners as an example. A molecular dynamics experiment was performed on a sample of α-α-corners selected by the authors from the PDB database. For the first time during a molecular dynamics experiment, we investigated the characteristics of structural motifs by describing their geometry, including the interplanar distance, area of polygon of the helices projections intersection, and torsion angles between axes of helices in helical pairs. The torsion angles for the constriction amino acids in the equilibrium portion of the molecular dynamics trajectory were analyzed. Using the molecular dynamics method, α-α-corners were found to be autonomous structures that are stable in aquatic environments.
The once abstract notions of fractal patterns and processes now appear naturally and inevitably i... more The once abstract notions of fractal patterns and processes now appear naturally and inevitably in various chaotic dynamical systems. The examples range from Brownian motion [15] to the dynamics of social relations [6]. In this paper, after introducing a certain hybrid ...
ABSTRACT 122 This work continues the study of specific features of polar peptides in water [1]. C... more ABSTRACT 122 This work continues the study of specific features of polar peptides in water [1]. Characteristics of selff assembling structures are important for developing approaches to the design of new medical materials, including biomimetics for tissue engineering [2–4]. A characteristic trait of molecules of this type is the presence of a relatively large number of charged atoms alternating with vast hydrophobic segments of the molecular surface. To determine the Gibbs energy of complex strucc tures of selffassembling peptides, a new method of call culation of mean values from a set of configurational states has been used [5]. This method requires solving once the RISM equations [6] with intramolecular corr relation functions calculated from the distributions of interatomic distances of a flexible structure on the basis of molecular dynamics (MD) simulation data. In the present work, we used the repulsive correction to improve the model [7]. It is important that the use of the mean matrix of intermolecular correlations (MMIC) in the RISM equations makes it possible to perform numerical thermodynamic integration and calculate the chemical potential, even without knowll edge of the exact analytical form of this potential. RISM METHODOLOGY RISM Equations with Mean Matrix The RISM equations for an infinitely dilute soluu tion [8], when the partial density of the solute can be,
Демонстрируется эффективность использования кросс-корреляционной энтропии Шеннона, представляющей... more Демонстрируется эффективность использования кросс-корреляционной энтропии Шеннона, представляющей собой обобщение широко применяемой в научных исследованиях спектральной энтропии, как метода анализа взаимных корреляций между колебаниями планктонного обилия и вариациями температуры. На примере анализа временных рядов, характеризующих динамику зоо-планктона, фитопланктона, бактериопланктона и вариации температуры воды, показывается, в частности, что наиболее значимыми являются взаимные корреляции между температурой и бакте-риопланктоном. Ключевые слова: кросс-корреляционная энтропия Шеннона, планктон, температура. Колебания численности популяций в боль-шинстве случаев характеризуются нерегулярно-стью и ограниченной предсказуемостью [1,2]. В качестве причины такой нерегулярности часто рассматривают динамический хаос, т.е. неустой-чивость динамики, независимую от внешних влияний. Подобная неустойчивость во многих математических моделях темпоральных вариаций популяционного обилия проявляется в виде зави-симости нерегулярных временных рядов от на-чальных условий [2-4]. Необходимо, однако, учитывать то, что реальные, а не модельные, по-пуляции связаны между собой, образуя сложные сети трофических взаимодействий (см., напри-мер, [5]), и потому не являются независимыми. Кроме того, все природные популяции подверже-ны воздействию внешних абиотических факто-ров, таких как: температура, солнечная радиация, ветер,-что далеко не всегда учитывается в ходе математического моделирования [6]. Поэтому оценки влияния динамики внешних абиотиче-ских факторов на динамику популяций, наряду с исследованиями межпопуляционных взаимодей-ствий, базирующиеся на данных, полученных в ходе полевых измерений (мониторинга экоси-стем), представляют существенный интерес. Мониторинг экосистем предполагает проведе-ние одновременных измерений биотических и абиотических факторов (см. например, работу [7]), что позволяет сопоставлять между собой cоответствующие временные ряды и, в частности, оценивать степень их сопряженности. Так, в ре-зультате анализа данных полевых исследований экосистемы Нарочанских озер (Белоруссия) бы-ло показано [8], что уровень фазовой синхрониза-ции колебаний температуры воды и колебаний биомассы фитопланктона связан со степенью со-пряжения колебаний популяционного обилия фитопланктона и бактериопланктона. Отметим, что адекватность оценки степени со-пряжения планктонных осцилляций и их синхро-низации с вариациями температуры в значитель-ной мере зависят от объема и качества данных, полученных в ходе полевых наблюдений. В этой связи использование таких методов оценки взаи-мосвязи между колебаниями обилия популяций планктона и связи планктонной динамики с ва-УДК 577.3
Присущий математическому моделированию редукционистский подход к анализу природных явле-ний неизб... more Присущий математическому моделированию редукционистский подход к анализу природных явле-ний неизбежно ставит вопрос о соответствии результатов моделирования реальным процессам. Статья посвящена анализу проблем, возникающих при сопоставлении результатов математическо-го моделирования популяционных процессов и данных, полученных в ходе мониторинга природ-ных экосистем. Эти проблемы обусловливаются тем, что далеко не всегда вид зависимостей между переменными, описывающими динамику популяционных процессов, равно как и выбор числен-ных значений параметров математических моделей, удается обосновать, опираясь на результаты мониторинга конкретной экосистемы. В статье предлагается подход, позволяющий в ходе матема-тического моделирования учитывать воздействие всего комплекса биотических и абиотических факторов на динамику популяций. Такой подход базируется на принятии во внимание данных мо-ниторинга экосистем и прямом включении этих данных в математические модели популяционной динамики. Реализация этого подхода позволяет, в частности, оценивать степень влияния отдельных факторов среды обитания как на вариации популяционного обилия, регистрируемые в ходе мони-торинга, так и на такие характеристики популяционных процессов, которые непосредственно не измеряются в ходе мониторинга, но являются результатом математического моделирования. Ключевые слова: популяционная динамика, математическое моделирование, анализ временных рядов. Популяция как динамический объект. Пред-ставление о популяции как о динамическом объ-екте является теоретической идеализацией. В рамках этой идеализации обычно отвлекаются от индивидуальных особенностей отдельных особей (организмов), формирующих популяцию, подоб-но тому, как часто пренебрегают свойствами от-дельных молекул при исследовании динамики жидкостей или газов. Подобно газу и жидкости, популяция может характеризоваться плотностью (популяционным обилием), т.е. числом особей или массой на единицу площади или объема. Плотность природных популяций подвержена изменениям как в пространстве, так и во време-ни. В основе таких изменений лежат биологиче-ские процессы (рост организмов, их размноже-ние и гибель), а наряду с ними-экологические процессы (миграции, межпопуляционные тро-фические взаимодействия, изменения условий обитания). Сложная мозаика факторов, обуслов-ливающих колебания популяционного обилия, во многих случаях нерегулярные, существенно затрудняет попытки выделить основные движу-щие факторы, ответственные за наблюдаемые в природе колебания плотности популяций. Для того чтобы обойти это затруднение, при-бегают к редукции. Такая редукция, в частности, реализуется в механистических моделях, в рамках которых динамика популяций описывается как результат суммирования независимых процессов (например, размножения и смертности). При этом в предположении, что модельная популяция УДК 57.055
In this paper, a statistical analysis of a distribution of interhelical distances in the helical ... more In this paper, a statistical analysis of a distribution of interhelical distances in the helical pairs of known proteins is carried out. A set of helical pairs of the protein molecules which was selected from the Protein Data Bank according to certain rules was subdivided into three subsets according to the criterion of crossing helix projections onto parallel planes passing through the helical axes. It is shown that the distributions of the distances for the helical pairs not having crossing projections have more long-range character than those whose projections cross. Using regression analysis we analyze the character of distributions, in particular, we show that in the subsets which do not have crossing projections, distributions of different distances between helical axes are gamma distributions. It is demonstrated that in the subsets having crossing projections, the ratio between the minimum distance and the interplane one is likely to be small as distinct from the subset not having crossing projections where the opposite is the case. The conclusion is proved that helical pairs having crossing axes projections are additionally stabilized due to internal interactions.
In this paper a statistical analysis of distributions of inter-helical angles in pairs of consequ... more In this paper a statistical analysis of distributions of inter-helical angles in pairs of consequtive and connected α-helices in spatial structures of proteins are presented. A number of rules for selection of the helical pairs from a set of protein structures obtained from Protein Data Bank (PDB) are developed. The set of helical pairs has been analyzed for the purpose of classification and finding out the features of protein structural organization. All the pairs of connected helices are divided into three subsets according to the criterion of crossing of projections of the helices on parallel planes, which pass through the axes of the helices. It is shown that the distribution of all the types of helical pairs, whose projections do not cross each other, covers almost the entire range of inter-helical angles. The distribution has a single minimum which is close to right angle. Most pairs in this set constitute helical pairs consisting of α-and 3 10-helices, and most pairs with the crossing projections of helices are helical pairs formed by two α-helices. It is also shown that a great amount of the pairs of connected α-helices has acute angle (20 60) between the axes of the helices. The distribution of all the types of helical pairs depending on the length of the inter-helical connections is also analyzed. It is shown that the structures with short connections occur most often in all the subsets. Key words: structural motifs of proteins, point model, helical pairs, angle between the axes of the helices.
Recommended form of bibliographic references: Tikhonov D.A., Sobolev E.V., Lakhno V.D. Charge dif... more Recommended form of bibliographic references: Tikhonov D.A., Sobolev E.V., Lakhno V.D. Charge diffusion in homogeneous molecular chains based on the analysis of generalized frequency spectra in the framework of the Holstein model // Keldysh Institute Preprints.
The temperature dependence of a charge mobility in a model DNA based on a Holstein Hamiltonian is... more The temperature dependence of a charge mobility in a model DNA based on a Holstein Hamiltonian is calculated for four types of homogeneous sequences It has turned out that upon rescaling all four 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.
This paper demonstrates the effectiveness of the use of the cross-correlation Shannon entropy; th... more This paper demonstrates the effectiveness of the use of the cross-correlation Shannon entropy; the cross-correlation Shannon entropy is a generalization of spectral entropy, which is widely used in scientific research, as a method of analysis of mutual correlations between plankton abundance fluctuations and temperature variations. In particular, analysis of time series that characterize the dynamics of zooplankton, phy-toplankton, and bacterioplankton and water temperature variations shows that mutual correlations are most significant between temperature and bacterioplankton. Fluctuations in population abundance are mostly characterized by irregularity and limited predictability [1, 2]. Dynamical chaos, i.e., dynamical instability that does not depend on external effects, is often considered as a cause of this irregularity. In many mathematical models of temporal variations in the population abundance, this instability is expressed as the dependence of an irregular time series on initial conditions [2-4]. However, one should take the fact into account that real, rather than model populations are interrelated and form complex networks of trophic interactions (see, e.g., [5]); therefore, they are not independent. In addition, all natural populations are exposed to the effect of external abiotic factors, such as temperature, solar radiation, and wind, which is far from always taken into account in mathematical mod-eling [6]. Therefore, along with studies of between-population interactions, estimates of the influence of the dynamics of external abiotic factors on the population dynamics using the data of field studies (ecosys-tem monitoring) are of considerable interest. Ecosystem monitoring assumes simultaneous measurements of biotic and abiotic factors (see, e.g., [7]), which makes it possible to compare the respective time series with each other and, in particular, assess the degree of their conjugacy. Thus, analysis of the data of field studies of the Naroch lake ecosystem (Belorussia) has shown [8] that the level of phase synchronization of water temperature fluctuations and phytoplankton biomass fluctuations is related to the degree of coupling of fluctuations in the population abundance of phytoplankton and bacterioplankton. It should be noted that the adequacy of the estimate of the degree of coupling between plankton oscillations and their synchronization with temperature variations significantly depends on the volume and quality of field survey data. Therefore, it is reasonable to use the methods of estimating the intercou-pling between fluctuations in plankton population abundance and relation between the plankton dynamics and temperature variations, which differ from methods previously used in [8] and do not depend on them. The purpose of this research is to establish correlations between power spectra that characterize the population dynamics of phytoplankton, zooplankton, and bacterioplankton and temperature fluctuations in the group of the Naroch Lakes. MATERIALS AND METHODS The Naroch Lakes are located in the northwestern part of Belorussia; they are a system of three water bodies connected by branches with each other: Lake Naroch (which is, in turn, composed of two parts: the large stretch and small stretch), Lake Myastro, and Lake Batorino. The main characteristics of these water bodies (area, water volume, mean and maximum COMPLEX SYSTEMS BIOPHYSICS
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Papers by D. Tikhonov
представляющей собой обобщение широко применяемой в научных исследованиях спектральной
энтропии, как метода анализа взаимных корреляций между колебаниями планктонного обилия и
вариациями температуры. На примере анализа временных рядов, характеризующих динамику зоопланктона, фитопланктона, бактериопланктона и вариации температуры воды, показывается, в
частности, что наиболее значимыми являются взаимные корреляции между температурой и бактериопланктоном.
представляющей собой обобщение широко применяемой в научных исследованиях спектральной
энтропии, как метода анализа взаимных корреляций между колебаниями планктонного обилия и
вариациями температуры. На примере анализа временных рядов, характеризующих динамику зоопланктона, фитопланктона, бактериопланктона и вариации температуры воды, показывается, в
частности, что наиболее значимыми являются взаимные корреляции между температурой и бактериопланктоном.