Models of stochastic gene expression

Gene expression is an inherently stochastic process: Genes are activated and inactivated by random association and dissociation events, transcription is typically rare, and many proteins are present in low numbers per cell. The last few years have seen an explosion in the stochastic modeling of these processes, predicting protein fluctuations in terms of the frequencies of the probabilistic events. Here I discuss commonalities between theoretical descriptions, focusing on a gene-mRNA-protein model that includes most published studies as special cases. I also show how expression bursts can be explained as simplistic time-averaging, and how generic approximations can allow for concrete interpretations without requiring concrete assumptions. Measures and nomenclature are discussed to some extent and the modeling literature is briefly reviewed.  2005 Elsevier B.V. All rights reserved.

[1]  Jeffrey Mervis.  Big Facilities Account Is Big Headache for NSF , 2002, Science.

[2]  M. Savageau.  Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. , 1969, Journal of theoretical biology.

[3]  T. Kepler,et al.  Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. , 2001, Biophysical journal.

[4]  M. Savageau.  Comparison of classical and autogenous systems of regulation in inducible operons , 1974, Nature.

[5]  L. Serrano,et al.  Engineering stability in gene networks by autoregulation , 2000, Nature.

[6]  M. Thattai,et al.  Attenuation of noise in ultrasensitive signaling cascades. , 2002, Biophysical journal.

[7]  M. Thattai,et al.  Intrinsic noise in gene regulatory networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Johan Paulsson,et al.  Near-critical phenomena in intracellular metabolite pools. , 2003, Biophysical journal.

[9]  X. Xie,et al.  Single-molecule approach to dispersed kinetics and dynamic disorder: Probing conformational fluctuation and enzymatic dynamics , 2002 .

[10]  Melvin Lax,et al.  Fluctuations from the Nonequilibrium Steady State , 1960 .

[11]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[12]  Mads Kærn,et al.  Noise in eukaryotic gene expression , 2003, Nature.

[13]  J. Raser,et al.  Control of Stochasticity in Eukaryotic Gene Expression , 2004, Science.

[14]  M. Savageau,et al.  Parameter Sensitivity as a Criterion for Evaluating and Comparing the Performance of Biochemical Systems , 1971, Nature.

[15]  M. Ehrenberg,et al.  Noise in a minimal regulatory network: plasmid copy number control , 2001, Quarterly Reviews of Biophysics.

[16]  D R Rigney,et al.  Stochastic model of constitutive protein levels in growing and dividing bacterial cells. , 1979, Journal of theoretical biology.

[17]  J. Peccoud,et al.  Markovian Modeling of Gene-Product Synthesis , 1995 .

[18]  P. Swain,et al.  Intrinsic and extrinsic contributions to stochasticity in gene expression , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Joel Keizer,et al.  Statistical Thermodynamics of Nonequilibrium Processes , 1987 .

[20]  D R Rigney,et al.  Note on the kinetics and stochastics of induced protein synthesis as influenced by various models for messenger RNA degradation. , 1979, Journal of theoretical biology.

[21]  David R. Rigney,et al.  Stochastic Models of Cellular Variability , 1979 .

[22]  Johan Paulsson,et al.  Multiple homeostatic mechanisms in the control of P1 plasmid replication. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[23]  R. Zwanzig.  Nonequilibrium statistical mechanics , 2001, Physics Subject Headings (PhySH).

[24]  Ertugrul M. Ozbudak,et al.  Regulation of noise in the expression of a single gene , 2002, Nature Genetics.

[25]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[26]  A. Løbner-Olesen,et al.  Distribution of minichromosomes in individual Escherichia coli cells: implications for replication control , 1999, The EMBO journal.

[27]  A. Arkin,et al.  Stochastic mechanisms in gene expression. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[28]  M. Savageau.  Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology , 1976 .

[29]  Peter G Wolynes,et al.  Stochastic gene expression as a many-body problem , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[30]  J. Elf,et al.  Selective Charging of tRNA Isoacceptors Explains Patterns of Codon Usage , 2003, Science.

[31]  K. Vahala.  Handbook of stochastic methods for physics, chemistry and the natural sciences , 1986, IEEE Journal of Quantum Electronics.

[32]  O. Berg.  A model for the statistical fluctuations of protein numbers in a microbial population. , 1978, Journal of theoretical biology.

[33]  M. Ehrenberg,et al.  Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[34]  W. Schieve,et al.  Stochastic model of linear, continuous protein synthesis in bacterial populations. , 1977, Journal of theoretical biology.

[35]  H. Kacser,et al.  The control of flux. , 1995, Biochemical Society transactions.

[36]  J. Paulsson.  Summing up the noise in gene networks , 2004, Nature.