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Transient Dynamics of Reduced-Order Models of Genetic Regulatory Networks
July-Aug. 2012 (vol. 9 no. 4)
pp. 1230-1244
R. Pal, Dept. of Electr. & Comput. Eng., Texas Tech Univ., Lubbock, TX, USA
S. Bhattacharya, Dept. of Electr. & Comput. Eng., Texas Tech Univ., Lubbock, TX, USA
In systems biology, a number of detailed genetic regulatory networks models have been proposed that are capable of modeling the fine-scale dynamics of gene expression. However, limitations on the type and sampling frequency of experimental data often prevent the parameter estimation of the detailed models. Furthermore, the high computational complexity involved in the simulation of a detailed model restricts its use. In such a scenario, reduced-order models capturing the coarse-scale behavior of the network are frequently applied. In this paper, we analyze the dynamics of a reduced-order Markov Chain model approximating a detailed Stochastic Master Equation model. Utilizing a reduction mapping that maintains the aggregated steady-state probability distribution of stochastic master equation models, we provide bounds on the deviation of the Markov Chain transient distribution from the transient aggregated distributions of the stochastic master equation model.

[1] N. Wiener, Cybernetics: Or the Control and Communication in the Animal and the Machine. MIT Press, 1948.
[2] A. Arkin, J. Ross, and H.H. McAdams, "Stochastic Kinetic Analysis of Developmental Pathway Bifurcation in Phage-Infected Escherichia Coli Cells," Genetics, vol. 149, pp. 1633-1648, 1998.
[3] H.H. McAdams and A. Arkin, "Stochastic Mechanisms in Gene Expression," Proc. Nat'l Academy of Sciences USA, vol. 94, pp. 814-819, 1997.
[4] D.T. Gillespie, "A Rigorous Derivation of the Chemical Master Equation," Physica A, vol. 188, pp. 404-425, 1992.
[5] J. Goutsias, "A Hidden Markov Model for Transcriptional Regulation in Single Cells," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 3, no. 1, pp. 57-71, Jan.-Mar. 2006.
[6] J. Goutsias, "Classical versus Stochastic Kinetics Modeling of Biochemical Reaction Systems," Biophysical J., vol. 92, no. 7, pp. 2350-2365, Apr. 2007.
[7] C.A Gomez-Uribe and G.C. Verghese, "Mass Fluctuation Kinetics: Capturing Stochastic Effects in Systems of Chemical Reactions through Coupled Mean-Variance Computations," J. Chemical Physics, vol. 126, no. 2, pp. 024109-1-024109-12, 2007.
[8] H.C. Lee, H.K. Kim, and P. Kim, "A Moment Closure Method for Stochastic Reaction Networks," J. Chemical Physics, vol. 130, no. 13, pp. 134107-134121, 2009.
[9] R. Pal and M.U. Caglar, "Control of Stochastic Master Equation Models of Genetic Regulatory Networks by Approximating Their Average Behavior," Proc. IEEE Int'l Workshop Genomic Signal Processing and Statistics, 2010.
[10] A.T. Weeraratna, Y. Jiang, G. Hostetter, K. Rosenblatt, P. Duray, M. Bittner, and J.M. Trent, "Wnt5a Signalling Directly Affects Cell Motility and Invasion of Metastatic Melanoma," Cancer Cell, vol. 1, pp. 279-288, 2002.
[11] R. Pal, A. Datta, and E.R. Dougherty, "Optimal Infinite Horizon Control for Probabilistic Boolean Networks," IEEE Trans. Signal Processing, vol. 54, no. 6, pp. 2375-2387, June 2006.
[12] E. Yzerman, J. DenBoer, M. Caspers, A. Almal, B. Worzel, W. Vander Meer, R. Montijn, and F. Schuren, "Comparative Genome Analysis of a Large Dutch Legionella Pneumophila Strain Collection Identifies Five Markers Highly Correlated with Clinical Strains," BMC Genomics, vol. 11, article 433, 2010.
[13] R. Pal and S. Bhattacharya, "Characterizing the Effect of Coarse-Scale Pbn Modeling on Dynamics and Intervention Performance of Genetic Regulatory Networks Represented by Stochastic Master Equation Models," IEEE Trans. Signal Processing, vol. 58, no. 6, pp. 3341-3351, June 2010.
[14] B. Munsky and M. Khammash, "The Finite State Projection Algorithm for the Solution of the Chemical Master Equation," J. Chemical Physics, vol. 124, no. 4,article 044104, 2006.
[15] S. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution. Oxford Univ. Press, 1993.
[16] I. Shmulevich, E.R. Dougherty, S. Kim, and W. Zhang, "Probabilistic Boolean Networks: A Rule-Based Uncertainty Model for Gene Regulatory Networks," Bioinformatics, vol. 18, pp. 261-274, 2002.
[17] N. Friedman, M. Linial, I. Nachman, and D. Peer, "Bayesian Networks to Analyze Expression Data," Proc. Fourth Ann. Int'l Conf. Computational Molecular Biology, pp. 127-135, 2000.
[18] H. Lahdesmaki, S. Hautaniemi, I. Shmulevich, and O. Yli-Harja, "Relationships between Probabilistic Boolean Networks and Dynamic Bayesian Networks as Models of Gene Regulatory Networks," Signal Processing, vol. 86, pp. 814-834, 2006.
[19] D.P. Bertsekas and J.N. Tsitsikilis, Introduction to Probability, second ed. Athena Scientific, 2008.
[20] T.L. Lai and H. Robbins, "Maximally Dependent Random Variables," Proc. Nat'l Academy Sciences USA, vol. 73, pp. 286-288, 1976.
[21] J.W. Clark, "Molecular Targeted Drugs," Harrison's Manual of Oncology, ch. 1.10, pp. 67-75, McGraw-Hill Professional, 2007.
[22] R.A. Science, "Integrated Solutions for Gene Knockdown," Biochemica, no. 4, pp. 18-20, 2004.
[23] R. Pal, A. Datta, M.L. Bittner, and E.R. Dougherty, "Intervention in Context-Sensitive Probabilistic Boolean Networks," Bioinformatics, vol. 21, pp. 1211-1218, 2005.
[24] M. Hegland, C. Burden, L. Santoso, S. MacNamara, and H. Booth, "A Solver for the Stochastic Master Equation Applied to Gene Regulatory Networks," J. Computational and Applied Math., vol. 205, no. 2, pp. 708-724, 2007.
[25] T. Jahnke and W. Huisinga, "A Dynamical Low-Rank Approach to the Chemical Master Equation," Bull. Math. Biology, vol. 70, pp. 2283-2302, 2008.

Index Terms:
transient analysis,computational complexity,genetics,Markov processes,master equation,physiological models,probability,transient aggregated distributions,transient dynamics,genetic regulatory network model,reduced-order Markov chain model,gene expression,fine-scale dynamics,sampling frequency,parameter estimation,computational complexity,coarse-scale behavior,reduction mapping,aggregated steady-state probability distribution,stochastic master equation model,Markov chain transient distribution,Mathematical model,Computational modeling,Biological system modeling,Steady-state,Markov processes,Transient analysis,Markov chains.,Genetic regulatory network modeling robustness,transient analysis
Citation:
R. Pal, S. Bhattacharya, "Transient Dynamics of Reduced-Order Models of Genetic Regulatory Networks," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. 4, pp. 1230-1244, July-Aug. 2012, doi:10.1109/TCBB.2012.37
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