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Stochastic chemical kinetics : A review of the modelling and simulation approaches.

ABSTRACT: A review of the physical principles that are the ground of the stochastic formulation of chemical kinetics is presented along with a survey of the algorithms currently used to simulate it. This review covers the main literature of the last decade and focuses on the mathematical models describing the characteristics and the behavior of systems of chemical reactions at the nano- and micro-scale. Advantages and limitations of the models are also discussed in the light of the more and more frequent use of these models and algorithms in modeling and simulating biochemical and even biological processes.

SUBMITTER: Lecca P

PROVIDER: S-EPMC5425731 | biostudies-literature | 2013 Dec

REPOSITORIES: biostudies-literature

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Stochastic chemical kinetics : A review of the modelling and simulation approaches.

Lecca Paola P

Biophysical reviews 20130730 4

A review of the physical principles that are the ground of the stochastic formulation of chemical kinetics is presented along with a survey of the algorithms currently used to simulate it. This review covers the main literature of the last decade and focuses on the mathematical models describing the characteristics and the behavior of systems of chemical reactions at the nano- and micro-scale. Advantages and limitations of the models are also discussed in the light of the more and more frequent ...[more]

PMID: 28510113

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Project description:BackgroundThe yeast Saccharomyces cerevisiae responds to amino acid starvation by inducing the transcription factor Gcn4. This is mainly mediated via a translational control mechanism dependent upon the translation initiation eIF2·GTP·Met-tRNAiMet ternary complex, and the four short upstream open reading frames (uORFs) in its 5' mRNA leader. These uORFs act to attenuate GCN4 mRNA translation under normal conditions. During amino acid starvation, levels of ternary complex are reduced. This overcomes the GCN4 translation attenuation effect via a scanning/reinitiation control mechanism dependent upon uORF spacing.ResultsUsing published experimental data, we have developed and validated a probabilistic formulation of GCN4 translation using the Chemical Master Equation (Model 1). Model 1 explains GCN4 translation's nonlinear dependency upon uORF placements, and predicts that an as yet unidentified factor, which was proposed to regulate GCN4 translation under some conditions, only has pronounced effects upon GCN4 translation when intercistronic distances are unnaturally short. A simpler Model 2 that does not include this unidentified factor could well represent the regulation of a natural GCN4 mRNA. Using parameter values optimised for this algebraic Model 2, we performed stochastic simulations by Gillespie algorithm to investigate the distribution of ribosomes in different sections of GCN4 mRNA under distinct conditions. Our simulations demonstrated that ribosomal loading in the 5'-untranslated region is mainly determined by the ratio between the rates of 5'-initiation and ribosome scanning, but was not significantly affected by rate of ternary complex binding. Importantly, the translation rate for codons starved of cognate tRNAs is predicted to be the most significant contributor to the changes in ribosomal loading in the coding region under repressing and derepressing conditions.ConclusionsOur integrated probabilistic Models 1 and 2 explained GCN4 translation and helped to elucidate the role of a yet unidentified factor. The ensuing stochastic simulations evaluated different factors that may impact on the translation of GCN4 mRNA, and integrated translation status with ribosomal density.

Project description:The master probability equation captures the dynamic behavior of a variety of stochastic phenomena that can be modeled as Markov processes. Analytical solutions to the master equation are hard to come by though because they require the enumeration of all possible states and the determination of the transition probabilities between any two states. These two tasks quickly become intractable for all but the simplest of systems. Instead of determining how the probability distribution changes in time, we can express the master probability distribution as a function of its moments, and, we can then write transient equations for the probability distribution moments. In 1949, Moyal defined the derivative, or jump, moments of the master probability distribution. These are measures of the rate of change in the probability distribution moment values, i.e. what the impact is of any given transition between states on the moment values. In this paper we present a general scheme for deriving analytical moment equations for any N-dimensional Markov process as a function of the jump moments. Importantly, we propose a scheme to derive analytical expressions for the jump moments for any N-dimensional Markov process. To better illustrate the concepts, we focus on stochastic chemical kinetics models for which we derive analytical relations for jump moments of arbitrary order. Chemical kinetics models are widely used to capture the dynamic behavior of biological systems. The elements in the jump moment expressions are a function of the stoichiometric matrix and the reaction propensities, i.e the probabilistic reaction rates. We use two toy examples, a linear and a non-linear set of reactions, to demonstrate the applicability and limitations of the scheme. Finally, we provide an estimate on the minimum number of moments necessary to obtain statistical significant data that would uniquely determine the dynamics of the underlying stochastic chemical kinetic system. The first two moments only provide limited information, especially when complex, non-linear dynamics are involved.

Dataset Information

Stochastic chemical kinetics : A review of the modelling and simulation approaches.

Publications

Stochastic chemical kinetics : A review of the modelling and simulation approaches.

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