Construction and Control of Genetic Regulatory Networks:A Multivariate Markov Chain Approach
- 1 School of Mathematical Sciences, Fudan University, Shanghai,200433, China
- 2 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences
- 3 Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
- 4 Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
- 5 Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Abstract
In the post-genomic era, the construction and control of genetic regulatory networks using gene expression data is a hot research topic. Boolean networks (BNs) and its extension Probabilistic Boolean Networks (PBNs) have been served as an effective tool for this purpose. However, PBNs are difficult to be used in practice when the number of genes is large because of the huge computational cost. In this paper, we propose a simplified multivariate Markov model for approximating a PBN The new model can preserve the strength of PBNs, the ability to capture the inter-dependence of the genes in the network, qnd at the same time reduce the complexity of the network and therefore the computational cost. We then present an optimal control model with hard constraints for the purpose of control/intervention of a genetic regulatory network. Numerical experimental examples based on the yeast data are given to demonstrate the effectiveness of our proposed model and control policy.
- T. Akutsu, S. Miyano and S. Kuhara. Inferring Qualitative Relations in Genetic Networks and Metabolic Arrays. Bioinformatics, 16: 727-734, 2000.
- J. Bower. Computational Modeling of Genetic and Biochemical Networks. MIT Press, Cambridge, M.A. 2001.
- W. Ching, E. Fung and M. Ng. A multivariate Markov Chain Model for Categorical Data Sequences and Its Applications in Demand Predictions. IMA Journal of Management Mathematics, 13: 187-199, 2002.
- W. Ching, E. Fung, M. Ng and T. Akutsu. On Construction of Stochastic Genetic Networks Based on Gene Expression Sequences. International Journal of Neural Systems, 15: 297-310, 2005.
- W. Ching, S. Zhang and M. Ng. On Multi-dimensional Markov Chain Models. Pacific Journal of Optimization, 3: 235-243, 2007.
- W. Ching, S. Zhang, Y. Jiao, T. Akutsu and A. Wong. Optimal Finite-Horizon Control for Probabilistic Boolean Networks with Hard Constraints. The International Symposium on Optimization and Systems Biology (OSB 2007), Lecture Notes in Operations Research, 2007.
- W. Ching, H. Leung, N. Tsing and S. Zhang. Optimal Control for Probabilistic Boolean Networks : Genetic Algorithm Approach. Submitted. 2008.
- E. Dougherty, S. Kim and Y. Chen. Coefficient of Determination in Nonlinear Signal Processing. Signal Processing, 80: 2219-2235, 2000.
- M. Hall, and G. Peters. Genetic Alterations of Cyclins, Cyclin-dependent Kinases, and Cdk Inhibitors in Human Cancer. Adv. Cancer Res., 68: 67-108, 1996.
- S. Huang and D.E. Ingber. Shape-dependent Control of Cell Growth, Differentiation, and Apoptosis: Switching Between Attractors in Cell Regulatory Networks. Exp. Cell Res., 261: 91-103, 2000.
- H. de Jong. Modeling and Simulation of Genetic Regulatory Systems: A Literature Review. J. Comput. Biol., 9: 69-103, 2002.
- S. Kauffman. Metabolic Stability and Epigenesis in Randomly Constructed Gene Nets. J. Theoret. Biol., 22: 437-467, 1969.
- S. Kauffman. Homeostasis and Differentiation in Random Genetic Control Networks. Nature, 224: 177-178, 1969.
- S. Kauffman. The Origin of Orders. Oxford University Press, New York. 1993.
- S. Kim, S. Imoto and S. Miyano. Dynamic Bayesian Network and Nonparametric Regression for Nonlinear Modeling of Gene Networks from time Series Gene Expression Data. Proc. 1st Computational Methods in Systems Biology, Lecture Note in Computer Science, 2602: 104-113, 2003.