Departmental Papers (MEAM)

Document Type

Journal Article

Date of this Version

1-1-2009

Comments

Copyright 2008 IEEE. Reprinted from IEEE Transactions on Automatic Control, Special Issue on Systems Biology, Volume 53, January 2008, pages 51-65.

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Abstract

In this paper, we present a comprehensive framework for stochastic modeling, model abstraction, and controller design for a biological system. The first half of the paper concerns modeling and model abstraction of the system. Most models in systems biology are deterministic models with ordinary differential equations in the concentration variables. We present a stochastic hybrid model of the lactose regulation system of E. coli bacteria that capture important phenomena which cannot be described by continuous deterministic models.We then show that the resulting stochastic hybrid model can be abstracted into a much simpler model, a two-state continuous-time Markov chain. The second half of the paper discusses controller design for a specific architecture. The architecture consists of measurement of a global quantity in a colony of bacteria as an output feedback and manipulation of global environmental variables as control actuation. We show that controller design can be performed on the abstracted (Markov chain) model and implementation on the real model yields the desired result.

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Date Posted: 20 March 2008

This document has been peer reviewed.