Dynamic analysis and modeling of biochemical regulatory networks

Abstract

Dynamic analysis and modeling are two of the most active research topics in the study of biochemical networks, and which have a great potential in gene therapy and medicine development. Due to the advances of molecular biology, genomics, computer science, modern control theory, nonlinear dynamics theory and other relevant fields, a system-level understanding of biological systems has become possible. This has thus led to a "new" research field, systems biology, with the goal of unraveling basic dynamic processes, feedback control loops and signal processing mechanisms underlying life at system level. It is worth noting that a molecular event is a noisy process due to significant thermal fluctuations with transcriptional control, alternative splicing, translation, diffusion and chemical modification reaction. Moreover, robustness is generally believed as a fundamental property of biological systems. Complex human diseases such as cancers and diabetes can be classified as failures in robustness mechanisms of biological systems. Furthermore, building a dynamic model for biochemical networks is a key step of systems biology, and there are still many critical issues to be addressed. Therefore, this thesis is focused on dynamic analysis and modeling of biochemical networks. In particular, it will address the issues such as stochastic stability and disturbance attenuation analysis, (constrained) bio-circuits design, entrained collective rhythms and dynamic fuzzy modeling. Firstly, we consider robust stochastic stability for genetic regulatory networks with both intrinsic and extrinsic stochastic noises. A novel delay-dependent robust stability condition with an optimal disturbance attenuation level, in the form of linear matrix inequalities (LMIs), is derived for uncertain stochastic genetic networks with time-varying delays and intrinsic and extrinsic noises. Furthermore, considering structure variations governed by a Markov process, robust stochastic stability and disturbance attenuation analysis are then considered for Markovian genetic networks. These stability conditions can be tested efficiently by available commercial software packages such as Matlab LMI Control Toolbox. Then, attention goes to positive stability analysis and bio-circuits design for nonlinear biochemical networks. A fuzzy interpolation approach is employed to approximate nonlinear biochemical networks. Based on the Lyapunov stability theory, sufficient conditions are developed to guarantee the equilibrium points of nonlinear biochemical networks to be positive and asymptotically stable. In addition, a constrained bio-circuits design with positive control input is also considered. It is shown that these conditions can be formulated as a solution to a convex optimization problem, which can be easily facilitated by using the Matlab LMI control toolbox. Furthermore, it has been widely recognized that a complicated living organism cannot be fully understood by merely analyzing individual components. Thus the next topic of study is the collective rhythms of multicellular systems, which are central to life. The problem of entrained collective rhythms of multicellular systems by using partial impulsive control strategy is addressed. The objective is to design an impulsive controller based only on those partially available cell states so that the entrained collective rhythms are guaranteed for multicellular systems with the cell-to-cell communication mechanism. By using a newly developed impulsive integro-differential inequality, sufficient conditions are derived to achieve the entrained collective rhythms of multicellular systems. Finally, the dynamic fuzzy modeling approach is applied for modeling genetic regulatory networks from gene expression data. The parameters of the dynamic fuzzy model and the optimal number of fuzzy rules for the fuzzy gene network can be obtained via the proposed modeling approach from the measured gene expression data. One of the main features of the proposed approach is that the prior qualitative knowledge on the network structure can be easily incorporated in the proposed identification algorithm so that the faster learning convergence of the algorithm can be achieved. Two sets of data, one the synthetic data, and the other the experimental SOS DNA repair network data with structural knowledge, are used to validate the proposed modeling approach. It is shown that the proposed approach is effective in modeling genetic regulatory networks.

Date of Award	4 Oct 2010
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Gang Gary FENG (Supervisor)