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The Finite State Projection Approach for the Solution of the Master Equation and its Application to Stochastic Gene Regulatory Networks. (2008)

by B Munsky
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Stochastic Gene Expression: Modeling, Analysis, and Identification *

by Mustafa Khammash , Brian Munsky
"... Abstract Gene networks arise due to the interaction of genes through their protein products. Modeling such networks is key to understanding life at the most basic level. One of the emerging challenges to the analysis of genetic networks is that the cellular environment in which these genetic circui ..."
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Abstract Gene networks arise due to the interaction of genes through their protein products. Modeling such networks is key to understanding life at the most basic level. One of the emerging challenges to the analysis of genetic networks is that the cellular environment in which these genetic circuits function is abuzz with noise. The main source of this noise is the randomness that characterizes the motion of cellular constituents at the molecular level. Cellular noise not only results in random fluctuations (over time) within individual cells, but it is also a source of phenotypic variability among clonal cellular populations. In some instances fluctuations are suppressed downstream through intricate dynamical networks that act as noise filters. Yet in other important instances, noise induced fluctuations are exploited to the cell's advantage. The richness of stochastic phenomena in biology depends directly upon the interactions of dynamics and noise and upon the mechanisms through which these interactions occur. In this article, we explore the origins and impact of cellular noise, drawing examples from endogenous and synthetic biological networks. We motivate the need for stochastic models and outline the key tools for the modeling and analysis of stochasticity inside living cells. We show that tools from system theory can be effectively utilized for modeling, analysis, and identification of gene networks. * This article is an expanded version of a conference paper that appeared in the proceedings of IFAC 2009 SYSID
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...distributions of X allows for negative values of X, which clearly does not reflect the positive nature of the populations represented by X(t). In these cases, a lognormal or other positive distribution closure may be preferred, but at the cost of more complicated closure expressions for the higher order moments. 3.4 Density Computations Another approach to analyze models described by the CME aims to compute the probability density functions for the random variable X. This is achieved by approximate solutions of the CME, using a new analytical approach called the Finite State Projection (FSP) ([23, 32, 24, 21]). The FSP approach relies on a projection that preserves an important subset of the state space (e.g. that supporting the bulk of the probability distribution), while projecting the remaining large or infinite states onto a single ’absorbing’ state. See Figure 4. Probabilities for the resulting finite state Markov chain can be computed exactly, and can be shown to give a lower bound for the corresponding probability for the original full system. The FSP algorithm provides a means of systematically choosing a projection of the CME, which satisfies any prespecified accuracy requirement. The bas...

Analyzing Large Network Dynamics with

by Courtney Chancellor, Maxime Folschette, Morgan Magnin, Olivier Roux , 2014
"... HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Guidelines for the Identification of a Stochastic Model for the Genetic Toggle Switch∗

by Brian Munsky, Mustafa Khammash , 2010
"... Issue in Quantitative Biology and is subject to IET copyright. When the final version is published, the copy of record will be available at ..."
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Issue in Quantitative Biology and is subject to IET copyright. When the final version is published, the copy of record will be available at
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