Jae Kyoung Kim
BIOMATHEMATICS SEMINAR
Speaker: Jae Kyoung Kim Abstract. The functions of living cells are regulated by the complex biochemical network, which consists of stochastic interactions among genes and proteins. However, due to the complexity of biochemical networks and the limit of experimental techniques, identifying entire biochemical interaction network is still far from complete. On the other hand, output of the networks, timecourses of genes and proteins can be easily acquired with advances in technology. I will describe how to use oscillating timecourse data to reveal biochemical network structure by using a fixed-point criteria. Moreover, I will describe how mathematical modeling can be used to understand the dynamics and functions of complex biochemical networks with an example of circadian clock. Finally, in biochemical networks, reactions occur on disparate timescale. This timescale separation has been used to project deterministic models of biochemical networks onto lower-dimensional slow manifolds with quasi-steady state approximation (QSSA). I will discuss whether this reduction technique for deterministic systems can be used for stochastic systems. Specifically, I will show when macroscopic rate functions derived with QSSA (e.g. Hill functions) can be used to derive the propensity functions for microscopic rates. |