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Stochastic Simulation of the Cell Cycle Model for Budding Yeast

Published online by Cambridge University Press:  20 August 2015

Di Liu
Di Liu*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
*
*Corresponding author.Email:[email protected]
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Abstract

We use the recently proposed Nested Stochastic Simulation Algorithm (Nested SSA) to simulate the cell cycle model for budding yeast. The results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.

Keywords

65C0560G1774A2592C42Stochastic simulation algorithmstochastic processbio-chemical reacting networksystem biology
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 2 , February 2011 , pp. 390 - 405
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Fedoroff, N. and Fontana, W., Small numbers of big molecules, Science, 297, 1129–1131, 2002.CrossRefGoogle ScholarPubMed
[2]McAdams, H. and Arkin, A., It’s a noisy business! Genetic regulation at the nanomolar scale, Trends. Genet., 15, 65–69, 1999.CrossRefGoogle ScholarPubMed
[3]Gillespie, D., A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comp. Phys., 22, 403–434, 1976.CrossRefGoogle Scholar
[4]Gillespie, D., Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81, 2340–2361, 1977.Google Scholar
[5]Rao, C. and Akin, A., Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm, J. Chem. Phys., 118, 4999–5010, 2003.Google Scholar
[6]Cao, Y., Gillespie, D., Petzold, L., The slow scale stochastic simulation algorithm, J. Chem. Phys., 122, 014116, 2005.Google Scholar
[7]Cao, Y., Gillespie, D., Petzold, L., Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems, J. Comp. Phys., 206, 395–411, 2005.Google Scholar
[8]LiuW. E, D. W. E, D. and Vanden-Eijnden, E., Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates, J. Chem. Phys., 123, 194107, 2005.Google Scholar
[9]LiuW. E, D. W. E, D. and Vanden-Eijnden, E., Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales, J. Comp. Phys., 221, 158–180, 2007.Google Scholar
[10]Salis, H. and Kaznessisa, Y., An equation-free probabilistic steady-state approximation: Dynamic application to the stochastic simulation of biochemical reaction networks, J. Chem. Phys., 123, 214106, 2005.CrossRefGoogle Scholar
[11]Samant, A. and Vlachos, D. G., Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm, J. Chem. Phys., 123, 144114, 2005.CrossRefGoogle ScholarPubMed
[12]Chen, K. C., Calzone, L., Csikasz-Nagy, A., Cross, F. R., Novak, B. and Tyson, J. J., Integrative analysis of cell cycle control in budding yeast, Mol. Biol. Cell, 15, 3841–3862, 2004.Google Scholar
[13]Wang, P., Randhawa, R., Shaffer, C., Cao, Y, and Baumann, W, Converting Macromolecular Regulatory Models from Deterministic to Stochastic Formulation, High Performance Computing and Simulation Symposium (HPCS 2008).Google Scholar
[14]Ahn, T.-H., Watson, L. T., Cao, Y., Shaffer, C. A. and Baumann, W. T., Cell cycle modeling for budding yeast with stochastic simulation algorithms, Computer Modeling in Engineering & Sciences, 51, 27–52, 2009. Also available at http://eprints.cs.vt.edu.Google Scholar
[15]Bortz, A., Kalos, M. and Lebowitz, J., A new algorithm for Monte Carlo simulation of Ising spin systems, J. Comp. Phys., 17, 10–18, 1975.Google Scholar
[16]Gibson, M. A. and Bruck, J., Efficient exact stochastic simulation of chemical systems with many species and many channels, J. Phys. Chem. A, 104, 1876–1889, 2000.Google Scholar
[17]Khasminskii, R. Z., Principle of averaging for parabolic and elliptic differential equations and for Markov processes with small diffusion, Theory Probab. Appl., 8, 1–21, 1963.CrossRefGoogle Scholar
[18]Kurtz, T., A limit theorem for perturbed operator semigroups with applications for random evolutions, J. Funct. Ana., 12, 55–67, 1973.Google Scholar
[19]Papanicolaou, G., Introduction to the asymptotic analysis of stochastic differential equations, Lectures in Applied Mathematics, Diprima, R. C. Edt., 16, 1977.Google Scholar
[20]Srivastava, R., You, L., Summers, J. and Yin, J., Stochastic vs. deterministic modeling of intra-cellular viral kinetics, J. Theor. Biol., 218, 309–321, 2002.Google Scholar
[21]Srivastava, R., Peterson, M. and Bently, W., Stochastic kinetic analysis of the Escherichia coli stress circuit using σ 32-targeted antisens, Biotechnol. Bioeng., 75, 120–129, 2001.Google Scholar
[22]LiuW. E, D. W. E, D. and Vanden-Eijnden, E., Analysis of multiscale methods for stochastic differential equations, Comm. on Pure and Appl. Math., 58, 1544–1585, 2005.Google Scholar
[23]Alberts, B., et al., Essential Cell Biology, 2nd. ed., Garland Science, 2003.Google Scholar
[24]Ghaemmaghami, S., et al., Global analysis of protein expression in yeast, Nature, 425, 737–41, 2003.Google Scholar