Based On The Adaptive Filtering Of Gene Regulation Network Research

Genetic regulatory network is an important type of biological networks. The regulations among gene expressions are not independent; there are interactions and inter-constrains among them. Study on a single gene expression can not grasp the biology functions and patterns of the living system. Hence, it is necessary to study the regulatory network among gene expressions from the system point of view. It is well known that time delay is ubiquitous in biological, chemical, and electrical dynamical systems, etc. Time delays can derail the stability of the system thereby causing sustained oscillations, bifurcations, and even chaos. So, time delay is one of important aspects in the field of genetic regulatory networks. As well, noise is unavoidable in the process of genetic regulatory networks. So, noise is another important aspect that must be considered.Moreover, in a real genetic regulatory network, it is still not completely understood today as how the genes are expressed in the right time and right place, with the right amount throughout the development of the organism. Studying living organisms requires significant work on observing, collecting, and analyzing data. Because of the limit of technologies, researchers can not obtain all information they need. Thus, theoretical biologists attempt to estimating the missing information from the available data, which gives rise to the following filtering problem:given a genetic regulatory network, how to estimate the unknown products and parameters by using the obtained data from the network. The main results of the thesis are as follows:1. For genetic regulatory networks with time-varying delays and uncertain noise disturbances, some adaptive laws are derived by using adaptive filtering approach and to ensure the stochastic stability by constructing Lyapunov functional. The theoretical results estimate the unknown parameters and states requiring only the output and structure of the underlying network.2. Based on adaptive synchronization setting, a class of uncertain genetic regulatory networks with partial information are investigated from an adaptive filtering approach. A new uncertain model of genetic regulatory network is proposed considering the time delay and noise disturbance. Using this model, uncertain parameters and stated of the network are estimated requiring only network structure and partial output of some nodes(assuming that only some of the concentrations of mRNA and protein could be observed).