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Anharmonic vibrational resonances in small water clusters
Computer Research and Modeling, 2009, v. 1, no. 3, pp. 321-336Views (last year): 1. Citations: 4 (RSCI).Numerical calculations of structures and vibrational spectra of small water clusters are performed by solution of the molecular Schrodinger equation in the density functional theory framework using B3LYP and X3LYP hybrid functionals. Spectral features and evolution of hydrogen bond properties in clusters with their size increasing are discussed. The vibrotational Hamiltonian parameters and Fermi and Darling-Dennison anharmonic resonances in small water oligomers are determined. Obtained results may be used in quantum mechanics/molecular dynamics simulations of water and processes in active site of enzyme.
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Permeability of lipid membranes. A molecular dynamic study
Computer Research and Modeling, 2009, v. 1, no. 4, pp. 423-436Views (last year): 20. Citations: 2 (RSCI).A correct model of lipid molecule (distearoylphosphatidylcholine, DSPC) and lipid membrane in water was constructed. Model lipid membrane is stable and has a reliable energy distribution among degrees of freedom. Also after equilibration model system has spatial parameters very similar to those of real DSPC membrane in liquid-crystalline phase. This model was used for studying of lipid membrane permeability to oxygen and water molecules and sodium ion. We obtained the values for transmembrane mobility and diffusion coefficients profiles, which we used for effective permeability coefficients calculation. We found lipid membranes to have significant diffusional resistance to penetration not only by charged particles, such as ions, but also by nonpolar molecules, such as oxygen molecule. We propose theoretical approach for calculation of particle flow across a membrane, as well as methods for estimation of distribution coefficients between bilayer and water phase.
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Mixed algorithm for modeling of charge transfer in DNA on long time intervals
Computer Research and Modeling, 2010, v. 2, no. 1, pp. 63-72Views (last year): 2. Citations: 2 (RSCI).Charge transfer in DNA is simulated by a discrete Holstein model «quantum particle + classical site chain + interaction». Thermostat temperature is taken into account as stochastic force, which acts on classical sites (Langevin equation). Thus dynamics of charge migration along the chain is described by ODE system with stochastic right-hand side. To integrate the system numerically, algorithms of order 1 or 2 are usually applied. We developed «mixed» algorithm having 4th order of accuracy for fast «quantum» variables (note that in quantum subsystem the condition «sum of probabilities of charge being on site is time-constant» must be held), and 2nd order for slow classical variables, which are affecting by stochastic force. The algorithm allows us to calculate trajectories on longer time intervals as compared to standard algorithms. Model calculations of polaron disruption in homogeneous chain caused by temperature fluctuations are given as an example.
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Modelling spatio-temporal dynamics of circadian rythms in Neurospora crassa
Computer Research and Modeling, 2011, v. 3, no. 2, pp. 191-213Views (last year): 6. Citations: 20 (RSCI).We derive a new model of circadian oscillations in Neurospora crassa, which is suitable to analyze both temporal and spatial dynamics of proteins responsible for mechanism of rythms. The model is based on the non-linear interplay between proteins FRQ and WCC which are products of transcription of frequency and white collar genes forming a feedback loop comprised both positive and negative elements. The main component of oscillations mechanism is supposed to be time-delay in biochemical reactions of transcription. We show that the model accounts for various features observed in Neurospora’s experiments such as entrainment by light cycles, phase shift under light pulse, robustness to action of fluctuations and so on. Wave patterns excited during spatial development of the system are studied. It is shown that the wave of synchronization of biorythms arises under basal transcription factors.
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Efficient Pseudorandom number generators for biomolecular simulations on graphics processors
Computer Research and Modeling, 2011, v. 3, no. 3, pp. 287-308Views (last year): 11. Citations: 2 (RSCI).Langevin Dynamics, Monte Carlo, and all-atom Molecular Dynamics simulations in implicit solvent require a reliable source of pseudorandom numbers generated at each step of calculation. We present the two main approaches for implementation of pseudorandom number generators on a GPU. In the first approach, inherent in CPU-based calculations, one PRNG produces a stream of pseudorandom numbers in each thread of execution, whereas the second approach builds on the ability of different threads to communicate, thus, sharing random seeds across the entire device. We exemplify the use of these approaches through the development of Ran2, Hybrid Taus, and Lagged Fibonacci algorithms. As an application-based test of randomness, we carry out LD simulations of N independent harmonic oscillators coupled to a stochastic thermostat. This model allows us to assess statistical quality of pseudorandom numbers. We also profile performance of these generators in terms of the computational time, memory usage, and the speedup factor (CPU/GPU time).
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Mathematical modeling of stochastic equilibria and business cycles of Goodwin model
Computer Research and Modeling, 2013, v. 5, no. 1, pp. 107-118Views (last year): 5. Citations: 4 (RSCI).The Goodwin dynamical model under the random external disturbances is considered. A full parametrical analysis for equlibria and cycles of deterministic model is developed. We study probabilistic properties of stochastic attractors using stochastic sensitivity functions technique and numerical methods. A phenomenon of the generation of stochastic business cycles in the zones of stable equilibria is discussed.
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Propagation of Rayleigh waves at oblique impact of the meteorite about the earth’s surface and their effects on buildings and structures
Computer Research and Modeling, 2013, v. 5, no. 6, pp. 981-992Views (last year): 3. Citations: 2 (RSCI).In this paper the dynamic elasticity problem of the simultaneous normal and tangential impact on the half-space is solved. This problem simulates the oblique incidence of meteorite on the Earth’s surface. The surface Rayleigh wave is investigated. The resulting solution is used as an external effect on the high-rise building, located at some distance from the spot of falling for the safety and stability assessment of its structure. Numerical experiments were made based on the finite element software package STARK ES. Upper floors amplitudes of the selected object were calculated under such dynamic effects. Also a systematic comparison with the results at the foundation vibrations, relevant to standard a 8-point earthquake accelerograms, was made.
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Cluster models of molecular motors: kinesin and myosin V
Computer Research and Modeling, 2014, v. 6, no. 5, pp. 747-760Views (last year): 2. Citations: 1 (RSCI).We present a semiphenomenological model of the two molecular motors: kinesin and myosin V, which play a great role in intracellular transport. The temporal dynamics of changes in the characteristic geometric parameters and the elastic stresses generated during the movement of motors is studied. The rates of movement of kinesin and myosin V, and their dependence on the concentration of ATP are discussed.
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Exact evolutionary dynamics on multi dimensional fitness landscape
Computer Research and Modeling, 2015, v. 7, no. 6, pp. 1269-1277Views (last year): 4.Crow–Kimura model is one of the famous models of population genetics. Last decade models with low-dimensional fitness landscape have been investigated. We consider the Crow–Kimura model of evolutionary dynamics on multi-dimensional fitness landscape with a single peak. We deduce exact solution for the dynamics, confirmed well by the numerics.
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Modeling the impact of mobility of individuals on space-time dynamics of a population by means of a computer model
Computer Research and Modeling, 2016, v. 8, no. 2, pp. 297-305Views (last year): 2. Citations: 3 (RSCI).A computer model describing the spatial-temporal dynamics of populations of interacting with renewable resource is proposed. The life cycle of the individual is described. The algorithm for spatial mobility of individuals within an area is proposed, which takes into account nutritional and social activity. The paper presents the computational experiments with the model that mimic the movement of herds of animals in the area, and describes the model experiment when the group type of animal behavior due to changes in the characteristics of the environment and animal behavior the herd animals is formed, which later goes again in the group type of animal behavior.
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International Interdisciplinary Conference "Mathematics. Computing. Education"