Dr. Hong Qian
Department of Applied Mathematics
University of Washington
Seattle, WA
TCB / CPLC sponsored seminar

Friday, April 9, 2010
2:00 pm (CT)
4269 Beckman Institute

Abstract

We consider a small driven biochemical network, the phosphorylation-dephosphorylation cycle (or GTPase), with a positive feedback. We investigate its bistability, with fluctuations, in terms of a nonequilibrium phase transition. We show that the nonequilibrium phase transition has many of the characteristics of classic equilibrium phase transition: Maxwell construction, discontinuous first-derivative of the “free energy function”, Lee-Yang's zero for the generating function, and a critical point that matches the cusp in nonlinear bifurcation theory. As for the biochemical system, we establish mathematically an emergent “landscape” for the system. The landscape suggests three different time scales in the dynamics: (i) molecular signaling, (ii) biochemical network dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. We suggest that the mesoscopic signature of the nonequilibrium phase transition is the biochemical basis of epi-genetic inheritance.