Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli
Copyright 2006 IEEE. Reprinted from Proceedings of the 45th IEEE Conference on Decision & Control 2006.
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to email@example.com. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
This paper focuses on the lactose regulation system in Escherichia coli bacteria, one of the most extensively studied examples of positive feedback in a naturally occurring gene network. State-of-the-art nonlinear dynamical system models predict a bi-stability phenomenon that is confirmed in experiments. However, such deterministic models fail to explain experimental observations of spontaneous transition between the two stable states in the system and the simultaneous occurrence of both steady states in a population of cells. In this paper, we propose a stochastic model that explains this phenomenon. Furthermore, we also extract a coarser two-state continuous-time Markov chain as a higher level abstraction of this model, and show that macroscopic properties are retained in the abstraction.
Agung Julius, Ádám Halász, R. Vijay Kumar, and George J. Pappas. "Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli" Departmental Papers (MEAM) (2006).
Available at: http://works.bepress.com/george_pappas/16