Author(s)

Shu-Qin Zhang, Ling-Yun Wu, Wai-Ki Ching, Yue Jiao, Raymond, H. Chan

Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong.
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences.
School of Mathematical Sciences, Fudan University, Shanghai,200433, China.

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.

Gene Expression Sequences, Multivariate Markov Chain, Optimal Control Policy, Probabilistic Boolean Networks.

Zhang, S. , Wu, L. , Ching, W. , Jiao, Y. and Chan, R. (2008) Construction and Control of Genetic Regulatory Networks:A Multivariate Markov Chain Approach. Journal of Biomedical Science and Engineering, 1, 15-21. doi: 10.4236/jbise.2008.11003.