Genetic Networks with Stochastic Fluctuations

Stochastic fluctuations may not only affect the dynamics of biological systems but also be exploited by living organisms to actively facilitate certain functions. Explicitly considering all variables and chemical reactions in a cell is unrealistic for a gene regulatory network from modeling, analysing and computing viewpoint. However, in a cell, many different time scales characterize the gene regulatory processes, which can be exploited to reduce the complexity of the mathematical models. For instance, the transcription and translation processes generally evolve on a time scale that is much slower than that of phosphorylation, dimerization or binding reactions of transcription factors. In addition, there are also many conservation conditions, such as total DNA number in a cell, which are important in modeling the gene networks. In this paper, we focus to model the gene regulatory networks with stochastic noise by using the property of fast-slow dynamics, and further investigate the biological implications of noise.