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Krylov and steady-state techniques for the solution of the chemical master equation for the mitogen-activated protein kinase cascade

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NUMERICAL algorithmS 2009年第3期51卷 281-307页

作者： MacNamara, Shev Burrage, Kevin Univ Queensland Australian Ctr Bioinformat Brisbane Qld 4072 Australia Univ Queensland Inst Mol Biosci Brisbane Qld 4072 Australia Univ Oxford Comp Lab Oxford OX1 3QD England Univ Oxford Oxford Ctr Integrat Syst Biol Oxford OX1 3QD England

Models of chemical kinetics in which some reactions are much faster than others are often treated by a type of quasi-steady-state approximation (QSSA). The total QSSA (tQSSA) was introduced for models of Michaelis-Menten enzyme kinetics and shown to be valid over a wider parameter regime than the usual QSSA. Here, we extend the tQSSA to the Mitogen-Activated Protein Kinase Cascade, an important signaling system in cell biochemistry. These approximations were first developed in a deterministic setting, but here we also describe how to incorporate this approximation into the discrete and stochastic framework of the Chemical Master Equation (CME). The CME gives rise to a large-scale matrix exponential that can be solved by Krylov methods in combination with operator splitting and the tQSSA.

关键词： Total quasi-steady-state approximation Chemical master equation stochastic simulation algorithm Systems biology Krylov subspace approximations

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A stochastic analysis of actin polymerization in the presence of twinfilin and gelsolin

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JOURNAL OF THEORETICAL BIOLOGY 2007年第4期249卷 723-736页

作者： Matzavinos, Anastasios Othmer, Hans G. Univ Minnesota Sch Math Minneapolis MN 55455 USA Univ Minnesota Digital Technol Ctr Minneapolis MN 55455 USA

We develop an efficient stochastic simulation algorithm for analyzing actin filament growth and decay in the presence of various actin-binding proteins. The evolution of nucleotide profiles of filaments can be tracked and the resulting feedback to actin-binding proteins is incorporated. The Computational efficiency of the new method enables us to focus on experimentally realistic problems, and as one example we use it to analyze the experimental data of Helfer et al. [(2006). Mammalian twinfilin sequesters ADP-G-actin and caps filament barbed ends: implications in motility. EMBO J. 25, 1184 1195] on the capping and G-actin sequestering activity of twinfilin. We show that the binding specificity of twinfilin for ADP-G-actin is crucial for the observed biphasic evolution of the filament length distribution in the presence of twinfilin, and we demonstrate that twinfilin can be an essential part of the molecular machinery for regulating filament lengths after a short burst of polymerization. Significantly, our simulations indicate that the pyrenyl-actin fluorescence experiments would fail to report the emergence of large filaments under certain experimental conditions. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： stochastic simulation algorithm polymerization actin gelsolin twinfilin capping protein

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Evaluating different epidemiological models with the identical basic reproduction number Script capital R0

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JOURNAL OF BIOLOGICAL DYNAMICS 2020年第1期14卷 849-870页

作者： Bai, Fan Univ Bonn Hausdorff Ctr Math Bonn Germany

Epidemiological models with the identical basic reproduction number R-0 may behave differently on both short time scale and long time scale. In this paper, we compare the predicted final sizes for several deterministic epidemic models and estimate the probabilities of a minor/major outbreak for continuous-time Markov chain (CTMC) models, all epidemic models have the identical R-0. It is proved that the final size predicted by the epidemic model with homogeneous mixing is larger than with heterogeneous mixing. For CTMC models with heterogeneous mixing, the probabilities of a minor outbreak initiated by superspreaders and non-superspreaders are calculated and compared. For both deterministic modelling and stochastic modelling, numerical simulations are performed to support the mathematical analysis.

关键词： Deterministic modelling continuous-time Markov chain models final epidemic size probability of a minor outbreak stochastic simulation algorithm

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Fokker-Planck approximation of the master equation in molecular biology

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COMPUTING AND VISUALIZATION IN SCIENCE 2009年第1期12卷 37-50页

作者： Sjoberg, Paul Lotstedt, Per Elf, Johan Uppsala Univ Dept Informat Technol Div Comp Sci POB 337 S-75105 Uppsala Sweden Uppsala Univ Dept Cell & Mol Biol S-75124 Uppsala Sweden Harvard Univ Dept Biol & Chem Cambridge MA 02138 USA

The master equation of chemical reactions is solved by first approximating it by the Fokker-Planck equation. Then this equation is discretized in the state space and time by a finite volume method. The difference between the solution of the master equation and the discretized Fokker-Planck equation is analyzed. The solution of the Fokker-Planck equation is compared to the solution of the master equation obtained with Gillespie's stochastic simulation algorithm (SSA) for problems of interest in the regulation of cell processes. The time dependent and steady state solutions are computed and for equal accuracy in the solutions, the Fokker-Planck approach is more efficient than SSA for low dimensional problems and high accuracy.

关键词： Master equation Fokker-Planck equation Numerical solution stochastic simulation algorithm

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Effects of Demographic stochasticity on Population Persistence in Advective Media

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BULLETIN OF MATHEMATICAL BIOLOGY 2010年第5期72卷 1254-1270页

作者： Kolpas, Allison Nisbet, Roger M. Univ Calif Santa Barbara Dept Ecol Evolut & Marine Biol Santa Barbara CA 93106 USA

Many populations live and disperse in advective media. A fundamental question, known as the "drift paradox" in stream ecology, is how a closed population can survive when it is constantly being transported downstream by the flow. Recent population-level models have focused on the role of diffusive movement in balancing the effects of advection, predicting critical conditions for persistence. Here, we formulate an individual-based stochastic analog of the model described in (Lutscher et al., SIAM Rev. 47(4):749-772, 2005) to quantify the effects of demographic stochasticity on persistence. Population dynamics are modeled as a logistic growth process and dispersal as a position-jump process on a finite domain divided into patches. When there is no correlation in the interpatch movement of residents, stochasticity simply smooths the persistence-extinction boundary. However, when individuals disperse in "packets" from one patch to another and the flow field is memoryless on the timescale of packet transport, the probability of persistence is greatly enhanced. The latter transport mechanism may be characteristic of larval dispersal in the coastal ocean or wind-dispersed seed pods.

关键词： Population dynamics Drift paradox Demographic stochasticity stochastic simulation algorithm

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An efficient finite-difference strategy for sensitivity analysis of stochastic models of biochemical systems

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BIOSYSTEMS 2017年 151卷 43-52页

作者： Morshed, Monjur Ingalls, Brian Ilie, Silvana Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada Ryerson Univ Dept Math Toronto ON M5B 2K3 Canada

Sensitivity analysis characterizes the dependence of a model's behaviour on system parameters. It is a critical tool in the formulation, characterization, and verification of models of biochemical reaction networks, for which confident estimates of parameter values are often lacking. In this paper, we propose a novel method for sensitivity analysis of discrete stochastic models of biochemical reaction systems whose dynamics occur over a range of timescales. This method combines finite-difference approximations and adaptive tau-leaping strategies to efficiently estimate parametric sensitivities for stiff stochastic biochemical kinetics models, with negligible loss in accuracy compared with previously published approaches. We analyze several models of interest to illustrate the advantages of our method. (C) 2016 Elsevier Ireland Ltd. All rights reserved.

关键词： stochastic simulation algorithm stochastic models of biochemical kinetics tau-Leaping method Sensitivity analysis Adaptive time-stepping Chemical Master Equation

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A hybrid multiscale kinetic Monte Carlo method for simulation of copper electrodeposition

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JOURNAL OF COMPUTATIONAL PHYSICS 2008年第10期227卷 5184-5199页

作者： Zheng, Zheming Stephens, Ryan M. Braatz, Richard D. Alkire, Richard C. Petzold, Linda R. Univ Calif Santa Barbara Dept Mech Engn Santa Barbara CA 93106 USA Univ Illinois Dept Chem & Biomol Engn Urbana IL 61801 USA

A hybrid multiscale kinetic Monte Carlo (HMKMC) method for speeding up the simulation of copper electrodeposition is presented. The fast diffusion events are simulated deterministically with a heterogeneous diffusion model which considers site-blocking effects of additives. Chemical reactions are simulated by an accelerated (tau-leaping) method for discrete stochastic simulation which adaptively selects exact discrete stochastic simulation for the appropriate reaction whenever that is necessary. The HMKMC method is seen to be accurate and highly efficient. (C) 2008 Elsevier Inc. All rights reserved.

关键词： multiscale simulation kinetic Monte Carlo stochastic simulation algorithm copper electrodeposition

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Propensity of a circadian clock to adjust to the 24 h day-night light cycle and its sensitivity to molecular noise

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JOURNAL OF THEORETICAL BIOLOGY 2006年第4期241卷 716-724页

作者： Calander, Nils Chalmers Univ Technol Dept Phys SE-41296 Gothenburg Sweden

The circadian clock of Drosophila melanogaster and its tendency to adjust to the day-night light cycle is simulated by deterministic and stochastic methods. The robustness of the locking to the light-cycle with respect to molecular noise is studied. It is found that within the model studied, the molecular noise in the stochastic simulation erases the finer injection-locking structures, stronger injection signals are needed and the locking has the character of prolonged locked time intervals with cycle slips in between. The simulations are compared to a simple injection-locking model with noise that seems to describe the overall behavior well. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： circadian clock molecular noise phase-locking stochastic simulation algorithm

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Accounting for environmental change in continuous-time stochastic population models

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THEORETICAL ECOLOGY 2019年第1期12卷 31-48页

作者： Legault, Geoffrey Melbourne, Brett A. Univ Colorado Dept Ecol & Evolutionary Biol Boulder CO 80309 USA Univ N Carolina Dept Biol Chapel Hill NC 27515 USA

The demographic rates (e.g., birth, death, migration) of many organisms have been shown to respond strongly to short- and long-term environmental change, including variation in temperature and precipitation. While ecologists have long accounted for such nonhomogeneous demography in deterministic population models, nonhomogeneous stochastic population models are largely absent from the literature. This is especially the case for models that use exact stochastic methods, such as Gillespie's stochastic simulation algorithm (SSA), which commonly assumes that demographic rates do not respond to external environmental change (i.e., assumes homogeneous demography). In other words, ecologists are currently accounting for the effects of demographic stochasticity or environmental variability, but not both. In this paper, we describe an extension of Gillespie's SSA (SSA + ) that allows for nonhomogeneous demography and examine how its predictions differ from a method that is partly naive to environmental change (SSAn) for two fundamental ecological models (exponential and logistic growth). We find important differences in the predicted population sizes of SSA + versus SSAn simulations, particularly when demography responds to fluctuating and irregularly changing environments. Further, we outline a computationally inexpensive approach for estimating when and under what circumstances it can be important to fully account for nonhomogeneous demography for any class of model.

关键词： Demographic stochasticity Environmental change Stationary Non-stationary Homogeneous Nonhomogeneous Environment-dependent demography stochastic simulation algorithm Poisson process

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Simulating vacuum residue hydroconversion by means of Monte-Carlo techniques

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CATALYSIS TODAY 2014年 220卷 208-220页

作者： de Oliveira, Luis Pereira Verstraete, Jan J. Kolb, Max IFP Energies Nouvelles Rond Point Echangeur Solaize F-69360 Solaize France Ecole Normale Super Lyon Chim Lab F-69364 Lyon 07 France

The present work focuses on the development of a novel methodology for the kinetic modeling of heavy oil conversion processes. The methodology models both the feedstock composition and the process reactions at a molecular level. The composition modeling consists of generating a set of molecules whose properties are close to those of the process feedstock analyses. This synthetic mixture of molecules is generated by a two-step molecular reconstruction algorithm. In its first step, an equimolar set of molecules is built by assembling structural blocks in a stochastic manner. In the second step, the mole fractions of the molecules are adjusted by maximizing an information entropy criterion. Once the composition of the feedstock is represented, the conversion process is simulated by applying, event by event, its main reactions to the set of molecules by means of a kinetic Monte Carlo (kMC) method. The methodology has been applied to hydroconversion of Ural vacuum residue and both the feed and the predicted effluents were favorably compared to the experimental yield pattern. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Composition modeling Kinetic modeling Information entropy maximization Vacuum residue hydrocracking stochastic simulation algorithm Kinetic Monte-Carlo

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