Stochastic Modeling and Control of Biological Systems: The Lactose Regulation System of Escherichia Coli

• Published in: IEEE transactions on automatic control 2008-01, Vol.53 (Special Issue), p.51-65
• Main Authors: Julius, A.A., Halasz, A., Sakar, M.S., Rubin, H., Kumar, V., Pappas, G.J.
• Format: Article
• Language: English
• Subjects: Abstraction; Biological control systems; Biological system modeling; Biological systems; Control system synthesis; Differential equations; E coli; Escherichia coli; Lactose; Markov analysis; Microorganisms; Ordinary differential equations; Output feedback; simulation; stochastic hybrid system; Stochastic processes; Stochastic systems; Studies; Systems biology
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2007.911346

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.