## Applied Mathematics Colloquium: Dr. Hye-Won Kang

#### UMBC

**Title:** Quasi-steady-state approximations of the stochastic
enzyme kinetics model

**Speaker: **Hye-Won Kang, UMBC

**Abstract: **Quasi-steady-state
approximations (QSSAs) are useful tools to reduce complex biochemical networks
and to derive their approximate models with the simpler structure. However, we
need to be careful to apply these approximations to general biochemical
networks, since the approximations are
valid for specific parameter ranges. QSSAs
have been widely studied in the deterministic setting by multiple authors, and
several conditions for their validity have been proposed. In this talk, we
consider the stochastic Michaelis-Menten enzyme kinetics model and derive
several quasi-steady-state approximations. In particular, we consider the
standard QSSA (sQSSA), the total QSSA (tQSSA), and the reverse QSSA (rQSSA). We
use multiscaling techniques and derive a simple set of conditions under which
these QSSA systems are exact large-volume limits of the underlying stochastic
kinetic network. This is joint work with Wasiur KhudaBukhsh, Heinz Koeppl, and
Grzegorz Rempala.