|
BIOMATHEMATICS SEMINAR
Speaker: Jae Kyoung Kim
Title: Mathematics for Complex and Stochastic Biochemical
Networks with Disparate Timescales
Affiliation: Mathematical Biosciences Institute
Date: Wednesday, October 22, 2014
Place and Time: Room 200, Love Building, 3:35 pm
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.
|
