Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli

Abstract

, "Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli" (2006). Departmental Papers (MEAM). 151. http://repository.upenn.edu/meam_papers/151Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli AbstractThis 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. Comments 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 pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/151 Abstract-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.

Controlling biological systems: the lactose regulation system of Escherichia coli

“…The model (1) qualitatively reproduces the observed experimental behavior. The higher-dimensional version defined in [9] and discussed in [1], very closely approximates that behavior. However, that model (with its original parameter set) is correct only as a description of the average behavior of a large number of cells described as a single "reactor".…”

“…The first part corresponds to the lower half of the hourglass in Figure 1, that discusses modeling of the lac regulation system as a stochastic hybrid system. The model presented in this paper is a slight modification of the one presented in our earlier work [1]. We also discuss how the stochastic hybrid model can be abstracted into a two-state continuous time Markov chain, and demonstrate how this abstraction is consistent with the macroscopic behavior of a colony of bacteria.…”

“…Following the discussion in [1], we identify the necessity of introducing stochasticity in the model to bridge the gap between the macroscopic behavior (population average) and microscopic behavior.…”

“…the number of molecules in the reaction. We develop a hybrid stochastic model for the system, where only a subset of the species is treated stochastically and the remainder are treated as continuous variables that obey traditional ODEs [1]. This computationally less expensive approach allows us to perform quasi-simultaneous simulations for many cells.…”

“…Our starting point is a model of the lactose system due to Yildirim and Mackey [1], [9], adapted to the use of thiomethyl galactosidase (TMG) as inducer. Briefly, the mRNA (M ) transcribed from the lactose operon is translated into three different gene products, among them permease (P ) and β-galactosidase (B).…”