Mesoscopic Open Biochemical Reaction Systems and Delbruck-Gillespie Processes for Stochastic Biochemical Population Dynamics
We advance a theory, and computational framework, for cellular biology based on stochastic, nonlinear dynamics based on the Delbrück-Gillespie processes for mesoscopic biochemical reaction systems. In the limit of infinite population size, the stochastic dynamics recovers the traditional nonlinear ordinary differential equation system based on the Law of Mass Action. We show there are three distinct time scales in the stochastic dynamcis: elementary biochemical reactions, intra-attractoral dynamics for a network self-organization, and inter-attractoral dynamics on an evolutionary time scale. Issues of complex systems dynamics such as bistability, rupture, and nonequilibrium thermodynamics will be discussed.
Hong Qian is Professor of Applied Mathematics at the University of Washingtson. For more information, please visit: http://www.amath.washington.edu/people/faculty/qian/.