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Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System of Escherichia Coli
Departmental Papers (MEAM)
  • Agung Julius, University of Pennsylvania
  • Ádám Halász, University of Pennsylvania
  • M Selman Sakar, University of Pennsylvania
  • Harvey Rubin, University of Pennsylvania
  • Vijay Kumar, University of Pennsylvania
  • George J Pappas, University of Pennsylvania
Document Type
Journal Article
Date of this Version
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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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.
Citation Information
Agung Julius, Ádám Halász, M Selman Sakar, Harvey Rubin, et al.. "Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System of Escherichia Coli" (2009)
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