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An Accelerated Method for Simulating Population Dynamics

  • Daniel A. Charlebois (a1) (a2) and Mads Kærn (a1) (a2) (a3)
Abstract
Abstract

We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations. The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations. To benchmark accuracy and performance, we compare simulation results with those generated from a previously validated population dynamics algorithm. The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions. Considering the increasing complexity of cell population models, the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient, coarse-grained exploration of parameter space.

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Corresponding author.Email:daniel.charlebois@uottawa.ca
Email:mkaern@uottawa.ca
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[1] M. Acar , J. T. Mettetal and A. van Oudenaarden , Stochastic switching as a survival strategy in fluctuating environments, Nat. Genet., 40 (2008), 471475.

[2] W. Blake , G. Balazsi , M. Kohanski , F. Isaacs , K. Murphy , Y. Kuang , C. Cantor , D. Walt and J. Collins , Phenotypic consequences of promoter-mediated transcriptional noise, Mol. Cell, 24 (2006), 853865.

[3] B. M. Boman , M. S. Wicha , J. Z. Fields and O. A. Runquist , Symmetric division of cancer stem cells - a key mechanism in tumor growth that should be targeted in future therapeutic approaches, Clinical Pharmacology and Therapeutics, 81 (2007), 893898.

[5] D. A Charlebois , N. Abdennur and M. Kaern , Gene expression noise facilitates adaptation and drug resistance independently of mutation, Phys. Rev. Lett., 107 (2011), doi: 10.1103/Phys-RevLett.107.218101.

[6] A. S. Ribeiro , D. A. Charlebois and J. Lyold-Price , CellLine, a stochastic cell lineage simulator, Bioinformatics, 23 (2007), 34093411.

[7] A. Eldar and M. Elowitz , Functional roles for noise in genetic circuits, Nature, 467 (2010), 167173.

[9] D. Fraser and M. Kaern , A chance at survival: gene expression noise and phenotypic diversification strategies, Molec. Microbiol., 71 (2009), 13331340.

[10] D. T. Gillespie , A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys., 22 (1976), 403434.

[11] D. T. Gillespie , Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81 (1977), 23402361.

[13] D. Volfson , J. Marciniak 1, W. J. Blake , N. Ostroff 1, L. S. Tsimring and J. Hasty , Origins of extrinsic variability in eukaryotic gene expression, Nature, 439 (2006), 861864.

[14] W. B. Huttner and Y. Kosodo , Symmetric versus asymmetric cell division during neurogenesis in the developing vertebrate central nervous system, Curr. Opin. Cell. Biol., 17 (2005), 648657.

[15] M. Kaern , T. C. Elston , W. J. Blake and J. J. Collins , Stochasticity in gene expression, Nat. Rev. Genet., 6 (2005), 451464.

[16] B. B. Kaufmann and A. van Oudenaarden , Stochastic gene expression: from single molecules to the proteome, Curr. Opin. Genet. Dev., 17 (2007), 107112.

[17] Y. Lin , K. Lee and T. Matsoukas , Solution of the population balance equation using constant-number Monte Carlo, Chem. Eng. Sci., 57 (2002), 22412252.

[18] T. Lu , D. Volfson , L. Tsimring and J. Hasty , Cellular growth and division in the Gillespie algorithm, Syst. Biol., 1 (2004), 121128.

[19] D. Nevozhay , R. M. Adams , E. V. Itallie , M. R. Bennett and G. Balazsi , Mapping the environmental fitness landscape of a synthetic gene circuit, PLoS Comput. Biol., 8 (2012), doi:10.1371/journal.pcbi.1002480.

[20] N. Maheshri and E. K. O’Shea , Living with noisy genes: how cells function reliably with inherent variability in gene expression, Annu. Rev. BioPhys. Biomol. Struct., 36 (2007), 413434.

[21] N. V. Mantzaris , Stochastic and deterministic simulations of heterogeneous cell population dynamics, J. Theor. Biol., 241 (2006), 690706.

[22] N. V. Mantzaris , 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), 42714288.

[23] M. D. McKay , R. J. Beckman and W. J. Conover , A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 (1979), 239245.

[25] R. Murugan , Multiple stochastic point processes in gene expression, J. Stat. Phys., 131 (2008), 153165.

[26] J. Paulsson , Summing up the noise in gene networks, Nature, 427 (2004), 415418.

[27] J. M. Raser and E. K. O’Shea , Control of stochasticity in eukaryotic gene expression, Science, 304 (2004), 18111814.

[30] M. Scott , B. Ingalls and M. Kaern , Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks, Chaos, 16 (2006), 026107.

[31] V. Shahrezaei and P. S. Swain , Analytical distributions for stochastic gene expression, PNAS, 105 (2008), 1725617261.

[32] V. Shahrezaei , J. Ollivier and P. Swain Colored extrinsic fluctuations and stochastic gene expression, Mol. Syst. Biol., 4 (2008), 196.

[33] A. Sigal , R. Milo , A. Cohen , N. Geva-Zatorsky , Y. Klein , Y. Liron , N. Rosenfeld , T. Danon , N. Perzov and U. Alon , Variability and memory of protein levels in human cells, Nature, 444 (2006), 643646.

[34] M. Smith and T. Matsoukas , Constant-number Monte Carlo simulation of population balances, Chem. Eng. Sci., 53 (1998), 17771786.

[35] J. L. Spudich and D. E. Koshland , Non-genetic individuality: chance in the single cell, Nature, 262 (1976), 467471.

[36] P. S. Swain , M. B. Elowits and E. D. Siggia , Intrinsic and extrinsic contributions to stochasticity in gene expression, PNAS, 99 (2002), 1279512800.

[37] M. Thattai and A. van Oudenaarden , Attenuation of noise in ultrasensitive signaling cascades, BioPhys. J., 82 (2002), 29432950.

[38] G. Uhlenbeck and L. Ornstein , On the theory of Brownian motion, Phys. Rev., 36 (2008), 823841.

[39] S. Woolner and N. Papalopulu , Spindle position in symmetric cell divisions during epiboly is controlled by opposing and dynamic apicobasal forces, Dev. Cell, 22 (2009), 775787.

[40] R. Zadrag-Tecza , M. Kwolek-Mirek , G. Bartosz and T. Bilinski , Cell volume as a factor limiting the replicative lifespan of the yeast Saccharomyces cerevisiae, Biogerontology, 10 (2009), 481488.

[41] Z. Zhang , W. Qian and J. Zhang , Positive selection for elevated gene expression noise in yeast, Mol. Syst. Biol., (2009), doi:10.1038/msb.2009.58.

[42] D. Zhuravel , D. Fraser , S. St-Pierre , L. Tepliakova , W. Pang , J. Hasty and M. Kaern , Phenotypic impact of regulatory noise in cellular stress-response pathways, Syst. Synth. Biol., 4 (2010), doi:10.1007/s11693-010-9055-2.

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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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