Controlling biological systems: the lactose regulation system of Escherichia coli

Abstract

In this paper we present a comprehensive framework for 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. Abstract-In this paper we present a comprehensive framework for 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. Disciplines Engineering | Mechanical EngineeringThe 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. I. INTRODUCTIONIn this paper we present a framework that consists of modeling, abstraction and control of a biological system, namely, the lactose regulation system of the Escherichia coli bacteria. The conceptual idea behind the paper is captured in Figure 1. Roughly speaking, the paper can be divided into two parts. 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.The second part of the paper pertains to the upper half of the ...

Hybrid model predictive control of induction of Escherichia coli

“…ODE model Yildirim and Mackey [5] proposed a biochemically founded ordinary differential model of the lactose-induced network shown in the upper panel of Figure 1. In our earlier work [15], [16], we adopted the structure of this model and applied it to the TMG-induced network (lower panel of the same figure). The equations of motion for induction by TMG (T ) are:…”

“…These results underline the necessity of expressing stochasticity in the model, if we want to capture these phenomena. In our earlier work, we expressed the stochasticity of the system by constructing a stochastic hybrid system model of the system [15], [16]. This stochastic hybrid model is based on a modified Gillespie's explicit τ -leaping algorithm [23].…”

“…In our earlier work [15], [16], we also proposed an abstraction for the stochastic hybrid model described in the previous subsection. The fact that the cells can spontaneously switch between the two phenotypical states (induced and uninduced) is captured by modeling the system as a two-state continuous time Markov chain, whose states are induced and uninduced (see Figure 3).…”

“…In [15], [16], we have proven that the design of a feedback controller for such a control problem can be cast as the following problem.…”

“…In this paper, we study the problem of controlling a colony of E. coli by means of global sensing and actuation [15], [16]. In this problem, we assume that we do not have access to the state of individual cells.…”