# Mathematical Biology Seminar

### Jae Kyoung Kim

Mathematical Biosciences Institute, The Ohio State University

#### Mathematics for complex and stochastic biochemical networks with disparate timescales

#### Wednesday, December 3, 2014, at 3:05pm

LCB 219

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 reveal the biochemical network architecture with oscillating timecourse data.
Next, I will discuss how to reduce or simplify the stochastic biochemical networks
while preserving the slow timescale dynamics. Specifically, I will show when
macroscopic rate functions (e.g. Hill functions) describing the slow timescale
dynamics of deterministic systems can be used for stochastic simulations. Finally,
I will discuss the role of network topology in determining its function and dynamics with an example of circadian clock.