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Showing 1 to 11 of 11 for “"Chemical Master Equation"”.
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Numerical Methods for the Chemical Master Equation
The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene …
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Inexact methods for the chemical master equation with constant or time-varying propensities, and application to parameter inference
… to modeling such problems is to find their master equation. In systems biology, the equation is called the chemical master equation (CME), and solving the CME is a difficult task, because of the curse of dimensionality. The goal of this dissertation is to alleviate this curse via the use of …
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Tensors and Stochastic Automata Networks with Application to Chemical Kinetics
Often, given a system of biochemical reactions, it is useful to be able to predict the system’s future state from the initial quantities of the involved molecules. There are many methodologies for developing such predictions, ranging from simple approaches such as Monte Carlo simulations to more …
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Accelerating Finite State Projection through General Purpose Graphics Processing
… modelers a new way of directly solving the chemical master equation. The algorithm utilizes the matrix exponential function, and so the algorithm’s performance suffers when it is applied to large problems. Other work has been done to reduce the size of the exponentiation through mathematical …
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A Stochastic Model for The Transmission Dynamics of Toxoplasma Gondii
… algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the …
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Mass fluctuation kinetics : analysis and computation of equilibria and local dynamics
… is a set of coupled first-order differential equations describing the temporal evolution of means, variances and covariances of species concentrations in systems of chemical reactions. It generalizes classical mass action kinetics (MAK) in which fluctuations around the mean are ignored. This …
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Advances in the stochastic and deterministic analysis of multistable biochemical networks
… concentrations in the cell that can arise in biochemical networks. That is, situations where one, or a family of, proteins may sit at one of two or more different steady state concentrations in otherwise identical cells, and in spite of them being in the same environment. Models of multisite …
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Analysis and Application of Haseltine and Rawlings's Hybrid Stochastic Simulation Algorithm
… follows the same theoretical derivation as the chemical master equation (CME), but the low efficiency of SSA limits its application to large chemical networks. To improve efficiency of stochastic simulations, Haseltine and Rawlings proposed a hybrid of ODE and SSA algorithm, which combines …
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A tale of two microbes: Computational investigations of biological processes in escherichia and methanosarcina at multiple scales
… to a single electron density, bond vibration or chemical reaction. Rather, the processes inherent to living organisms---adaptation, growth, homeostasis, metabolism, replication, and response to stimuli---result from concerted function of the physical and chemical interactions of thousands to …
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Stochastic and physical modeling of fundamental biological processes
… model, described in terms of reaction-diffusion master equations, contains 1336 reactions and 251 species that dynamically couple transcription and translation to ribosome assembly. We use the Lattice Microbes software package to simulate the stochastic production of mRNA, proteins, and ribosome …
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Computational investigations of evolutionary transitions during development of the cellular translation and transcription machinery
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