Mathematics Colloquium: Stochastic Modeling of Biochemical Networks
4:10 Neill Hall
Hye Won Kang
Stochastic effects may play an important role in mathematical modeling of biological and chemical processes in case the copy number of some component involved in the system is small. In this talk, we consider stochastic modeling of biochemical networks with several examples. First, we look at a mathematical model of lung cancer involving microRNAs. MicroRNAs take charge of cellular differentiation, apoptosis, and growth, and they serve as biomarkers in cancer. The model involves an important component of the large signaling pathway in lung cancer. The background noise due to the unknown part of the pathway is modeled in terms of stochastic differential equations. Next, multiscale approximations of stochastic chemical reaction networks are suggested. Evolution of the network is modeled in terms of a continuous-time Markov jump process. Chemical reaction networks are generally large in size and they involve various scales in species numbers and reaction rate constants. The multiscale approximation method is introduced to reduce the network complexity and to derive limiting models with simple structure. Last, we consider stochastic reaction-diffusion systems to model pattern formation in developmental biology. Spatially distributed signals called morphogens influence gene expression that determines phenotype identity of cells. A stochastic model for boundary determination between different cell types is suggested using signaling schemes for patterning.