On the dynamics of a gene regulatory network

Power-rate synchronization of coupled genetic oscillators with unbounded time-varying delay

In this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded time-varying delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having unbounded time-delays. A new concept called power-rate synchronization, which is different from both the asymptotical synchronization and the exponential synchronization, is put forward to facilitate handling the unbounded time-varying delays. By using a combination of the Lyapunov functional method, matrix inequality techniques and properties of Kronecker product, we derive several sufficient conditions that ensure the coupled genetic oscillators to be power-rate synchronized. The criteria obtained in this paper are in the form of matrix inequalities. Illustrative example is presented to show the effectiveness of the obtained results.

Robust stability of genetic regulatory networks with distributed delay

This paper investigates robust stability of genetic regulatory networks with distributed delay. Different from other papers, distributed delay is induced. It says that the concentration of macromolecule depends on an integral of the regulatory function of over a specified range of previous time, which is more realistic. Based on Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions for genetic regulatory networks to be global asymptotic stability and robust stability are derived in terms of LMI. Two numerical examples are given to illustrate the effectiveness of our theoretical results.

[Research on modular organization of gene regulatory network]

Gene regulatory network is very important for researchers to understand biological processes and gene functions. It can deliver complex information about how could large amount of genes be regulated by transcriptional factors and translated into proteins which can carried out biological functions. Generally, knowledge of network topological structure and organization formation can be used to find the regulatory mechanism of genes in the regulatory network. It can illuminate the local characters of the network and reveal the constructing methods of regulatory network; moreover, it can also analyze regulatory pathway completely and systemically. Now, more and more researchers approbate the hierarchy structure of gene regulatory network: regulatory component, Motif, module and the whole network. Here, we discuss the middle two levels: motif and module. We compared various research results of network organization carried out in recent years, explicated their biology signification and pointed out the existing disadvantages and problems. According these problems, we also bring up some possible research trend. And at last, we discuss the prospect of gene regulatory network modular organization researching work.