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An Algorithm for the Stochastic Simulation of Gene Expression and Heterogeneous Population Dynamics

Published online by Cambridge University Press:  20 August 2015

Daniel A. Charlebois ,
Jukka Intosalmi ,
Dawn Fraser  and
Mads Kærn
Daniel A. Charlebois*
Affiliation:
Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada Ottawa Institute of Systems Biology, University of Ottawa, 451 Symth Road, Ottawa, Ontario, K1H 8M5, Canada
Jukka Intosalmi
Affiliation:
Department of Mathematics, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland Department of Signal Processing, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland
Dawn Fraser
Affiliation:
Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada Ottawa Institute of Systems Biology, University of Ottawa, 451 Symth Road, Ottawa, Ontario, K1H 8M5, Canada
Mads Kærn*
Affiliation:
Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada Ottawa Institute of Systems Biology, University of Ottawa, 451 Symth Road, Ottawa, Ontario, K1H 8M5, Canada Department of Cellular and Molecular Medicine, University of Ottawa, 451 Symth Road, Ottawa, Ontario, K1H 8M5, Canada
*
Corresponding author.Email:daniel.charlebois@uottawa.ca
Corresponding author.Email:mkaern@uottawa.ca
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Abstract

We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations. To benchmark performance, we compare simulation results with steady-state and time-dependent analytical solutions for several scenarios, including steady-state and time-dependent gene expression, and the effects on population heterogeneity of cell growth, division, and DNA replication. This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression. We also use the algorithm to model gene expression dynamics within “bet-hedging” cell populations during their adaption to environmental stress. These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics, relevant physiological details and phenotypic variability.

Keywords

87.10.Mn87.10.Rt87.16.Yc87.17.EeConstant-number Monte Carlostochastic simulation algorithmgene expressionheterogeneous population dynamics

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 1 , January 2011 , pp. 89 - 112
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Acar, M., Mettetal, J. T. and van Oudenaarden, A., Stochastic switching as a survival strategy in fluctuating environments, Nat. Genet., 40 (2008), 471–475.Google Scholar
[2]Adalsteinsson, D., McMillen, D. and Elston, T. C., Biochemical network stochastic simulator (BioNetS): software for stochastic modeling of biochemical networks, BMC Bioinfo., 5 (2004), 24.Google Scholar
[3]Brewer, B. J., Chlebowicz-Sledziewska, E. and Fangman, W. L., Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces cerevisiae, Mol. Cell. Biol., 4 (1984), 2529–2531.Google Scholar
[4]Cohen, D., Optimizing reproduction in a randomly varying environment, J. Theor. Biol., 12 (1966), 119–129.Google Scholar
[5]Eager, D. L., Zahorjan, J. and Lazowska, E. D., Speedup versus efficiency in parallel systems, IEEE Trans. Comput., 38 (1989), 408–423.Google Scholar
[6]Fraser, D. and Kaern, M., A chance at survival: gene expression noise and phenotypic diversification strategies, Molec. Microbiol., 71 (2009), 1333–1340.Google Scholar
[7]Gillespie, D. T., A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys., 22 (1976), 403–434.Google Scholar
[8]Gillespie, D. T., Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81 (1977), 2340–2361.Google Scholar
[9]Gillespie, D. T., Stochastic simulation of chemical kinetics, Annu. Rev. Phys . Chem., 58 (2007), 35–55.Google Scholar
[10]Gillespie, D. T., Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys., 115 (2001), 1716–1733.Google Scholar
[11]Kaern, M., Elston, T. C., Blake, W. J. and Collins, J. J., Stochasticity in gene expression, Nat. Rev. Genet., 6 (2005), 451–464.Google Scholar
[12]Kaufmann, B. B. and van Oudenaarden, A., Stochastic gene expression: from single molecules to the proteome, Curr. Opin. Genet. Dev., 17 (2007), 107–112.Google Scholar
[13]Kepler, T. B. and Elston, T. C., Stochasticity in transcriptional regulation, Biophys. J., 81 (2001), 3116–3136.Google Scholar
[14]Kierzek, A. M., Stocks: Stochastic kinetic simulations of biochemical systems with Gillespie algorithm, Bioinf., 18 (2002), 470–481.Google Scholar
[15]Kostoglou, M. and Karabelas, A. J., Evaluation of zero-order methods for simulation particle coagulation, J. Colloid. Interface. Sci., 163 (1994), 420–431.Google Scholar
[16]Lee, K. and Matsoukas, T., Simultaneous coagulation and break-up using constant-N Monte Carlo, Powder. Technol., 110 (2000), 82–89.Google Scholar
[17]Levins, R., Evolution in Changing Environments: Some Theoretical Explorations, Princeton University Press, Princeton, 1968.Google Scholar
[18]Lin, Y., Lee, K. and Matsoukas, T., Solution of the population balance equation using constant-number Monte Carlo, Chem. Eng. Sci., 57 (2002), 2241–2252.Google Scholar
[19]Lu, T., Volfson, D., Tsimring, L. and Hasty, J., Cellular growth and division in the Gillespie algorithm, Syst. Biol., 1 (2004), 121–128.Google Scholar
[20]Maheshri, N. and O’Shea, E. K., Living with noisy genes: how cells function reliably with inherent variability in gene expression, Annu. Rev. Biophys. Biomol. Struct., 36 (2007), 413–434.Google Scholar
[21]Mantzaris, N. V., Stochastic and deterministic simulations of heterogeneous cell population dynamics, J. Theor. Biol., 241 (2006), 690–706.Google Scholar
[22]Mantzaris, N. V., From single-cell genetic architecture to cell population dynamics: quantitatively decomposing the effects of different population heterogeneity sources for a genetic network with positive feedback architecture, Biophys. J., 92 (2007), 4271–4288.Google Scholar
[23]Paulsson, J., Summing up the noise in gene networks, Nature, 427 (2004), 415–418.CrossRefGoogle ScholarPubMed
[24]Ramkrishna, D., The status of population balances, Rev. Chem. Engng., 3 (1985), 49–95.Google Scholar
[25]Ribeiro, A. S, Charlebois, D. A and Lloyd-Price, J., Cellline, a stochastic cell lineage simulator, Bioinf., 23 (2007), 3409–3411.Google Scholar
[26]Roussel, M. and Zhu, R., Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression, Phys. Biol., 3 (2006), 274–284.Google Scholar
[27]Rosenfeld, N., Perkins, T. J., Alon, U., Elowitz, M. B. and Swain, P. S., A fluctuation method to quantify in vivo fluorescence data, Biophys. J., 91 (2006), 759–766.Google Scholar
[28]Samoilov, M. S., Price, G. and Arkin, A. P., From fluctuations to phenotypes: the physiology of noise, Sci. STKE, 366 (2006), re17.Google Scholar
[29]Schaffer, W. M., Optimal efforts in fluctuating environments, Am. Nat., 108 (1974), 783–790.Google Scholar
[30]Shahrezaei, V. and Swain, P. S., Analytical distributions for stochastic gene expression, PNAS, 105 (2008), 17256–17261.Google Scholar
[31]Smith, M. and Matsoukas, T., Constant-number Monte Carlo simulation of population balances, Chem. Eng. Sci., 53 (1998), 1777–1786.Google Scholar
[32]Stearns, S. C., Life-history tactics: a review of the ideas, Q. Rev. Biol., 51 (1976), 3–47.Google Scholar
[33]Swain, P. S., Elowitz, M. B. and Siggia, E. D., Intrinsic and extrinsic contributions to stochas-ticity in gene expression, PNAS, 99 (2002), 12795–12800.Google Scholar
[34]Tyson, J. J. and Diekmann, O. J., Sloppy size control of the cell division cycle, Theor. Biol., 118 (1986), 405–426.Google Scholar
[35]Volfson, D., Marciniak, J., Blake, W. J., Ostroff, N., Tsimring, L. S. and Hasty, J., Origins of extrinsic variability in eukaryotic gene expression, Nature, 439 (2006), 861–864.CrossRefGoogle ScholarPubMed