Macroscopic Dynamics for Nonequilibrium Biochemical Reactions from A Hamiltonian Viewpoint
Speaker

Jianguo Liu, Duke University
Time

2021-12-13 10:00 ~ 11:00, 3 hours ago (Asia/Shanghai Time)
Venue

Online-ZOOM
ZOOM Info

Conference ID: 382-175-6853

Password: 2177

ZOOM Link: https://zoom.com.cn/j/3821756853
Abstract

Most biochemical reactions in living cells are open system interacting with environment through chemostats. At a mesoscopic scale, the concentration of each species in those biochemical reactions can be modeled by the random time-changed Poisson processes. To characterize the macroscopic behaviors in the large volume limit, the law of large number in path space determines a mean-field limit nonlinear Kurtz ODE, while the WKB expansion yields a Hamilton-Jacobi equation and the convex conjugate L of the corresponding Hamiltonian H gives the good rate function (action functional) in the large deviation principle.

In this talk, we propose a gauge-symmetry criteria for a new class of nonequilibrium chemical reactions including many enzyme reactions and this gives rise a new concept of balance within same reaction vector. With this idea, we (i) formulate a Onsager-type gradient flow structure in terms of the energy landscape psi, i.e., the steady solution to HJE; (ii) find the transition path between multiple nonequilibrium steady states (rare events in biochemical reactions). We illustrate this idea through a bistable enzyme reaction and show the energy barrier for the rare transitions is computed via energy landscape psi, which is different from the barrier computed from the drift-diffusion approximation at the central limit scale. This is a joint work with Yuan Gao of Purdue University.
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