A stochastic model of gene transcription: An application to L1 retrotransposition events

Grzegorz A. Rempala; Kenneth S. Ramos; Ted Kalbfleisch

doi:10.1016/j.jtbi.2006.02.010

A stochastic model of gene transcription: An application to L1 retrotransposition events

Grzegorz A. Rempala, Kenneth S. Ramos, Ted Kalbfleisch

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19 Scopus citations

Abstract

A simplified mathematical model of gene transcription is presented based on a system of coupled chemical reactions and a corresponding set of stochastic equations similar to those used in enzyme kinetics theory. The quasi-stationary distribution for the model is derived and its usefulness illustrated with an example of model parameters estimation using sparse time course data on L1 retrotransposon expression kinetics. The issue of model validation is also discussed and a simple validation procedure for the estimated model is devised. The procedure compares model predicted values with the laboratory data via the standard Bayesian techniques with the help of modern Markov-Chain Monte-Carlo methodology.

Original language	English (US)
Pages (from-to)	101-116
Number of pages	16
Journal	Journal of Theoretical Biology
Volume	242
Issue number	1
DOIs	https://doi.org/10.1016/j.jtbi.2006.02.010
State	Published - Sep 7 2006

Keywords

Bayesian inference
Chemical reaction kinetics
Gene transcription model
L-retrotransposon
Northern blot
Reaction constants estimation
Stochastic intracellular network

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics

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10.1016/j.jtbi.2006.02.010

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title = "A stochastic model of gene transcription: An application to L1 retrotransposition events",

abstract = "A simplified mathematical model of gene transcription is presented based on a system of coupled chemical reactions and a corresponding set of stochastic equations similar to those used in enzyme kinetics theory. The quasi-stationary distribution for the model is derived and its usefulness illustrated with an example of model parameters estimation using sparse time course data on L1 retrotransposon expression kinetics. The issue of model validation is also discussed and a simple validation procedure for the estimated model is devised. The procedure compares model predicted values with the laboratory data via the standard Bayesian techniques with the help of modern Markov-Chain Monte-Carlo methodology.",

keywords = "Bayesian inference, Chemical reaction kinetics, Gene transcription model, L-retrotransposon, Northern blot, Reaction constants estimation, Stochastic intracellular network",

author = "Rempala, {Grzegorz A.} and Ramos, {Kenneth S.} and Ted Kalbfleisch",

note = "Funding Information: The first author would like to acknowledge the generous research support for this work from the Center for Genetics and Molecular Medicine at the University of Louisville. All authors would like to acknowledge the anonymous referee whose thoughtful comments and suggestions helped improve the original manuscript. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.",

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AU - Ramos, Kenneth S.

AU - Kalbfleisch, Ted

N1 - Funding Information: The first author would like to acknowledge the generous research support for this work from the Center for Genetics and Molecular Medicine at the University of Louisville. All authors would like to acknowledge the anonymous referee whose thoughtful comments and suggestions helped improve the original manuscript. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

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N2 - A simplified mathematical model of gene transcription is presented based on a system of coupled chemical reactions and a corresponding set of stochastic equations similar to those used in enzyme kinetics theory. The quasi-stationary distribution for the model is derived and its usefulness illustrated with an example of model parameters estimation using sparse time course data on L1 retrotransposon expression kinetics. The issue of model validation is also discussed and a simple validation procedure for the estimated model is devised. The procedure compares model predicted values with the laboratory data via the standard Bayesian techniques with the help of modern Markov-Chain Monte-Carlo methodology.

AB - A simplified mathematical model of gene transcription is presented based on a system of coupled chemical reactions and a corresponding set of stochastic equations similar to those used in enzyme kinetics theory. The quasi-stationary distribution for the model is derived and its usefulness illustrated with an example of model parameters estimation using sparse time course data on L1 retrotransposon expression kinetics. The issue of model validation is also discussed and a simple validation procedure for the estimated model is devised. The procedure compares model predicted values with the laboratory data via the standard Bayesian techniques with the help of modern Markov-Chain Monte-Carlo methodology.

KW - Bayesian inference

KW - Chemical reaction kinetics

KW - Gene transcription model

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KW - Northern blot

KW - Reaction constants estimation

KW - Stochastic intracellular network

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A stochastic model of gene transcription: An application to L1 retrotransposition events

Abstract

Keywords

ASJC Scopus subject areas

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