Hybrid model predictive control of induction of Escherichia coli

The lactose regulation system of Escherichia coli is known to exhibit a bistable behavior. The stable states correspond to the phenotypical states of the system, induced and uninduced. Stochastic modeling of the system enables us to reproduce an experimentally observed phenomenon of spontaneous transitions between the induced and uninduced states. The average behavior of a colony of a large number of cells can be accurately described by an abstract model of the system, which is a two state Markov chain. In this paper, we consider a control problem that involves regulating the fraction of induction of a colony of Escherichia coli. We use the abstract model to design a feedback controller based on model predictive control strategy. Upon simulation, we show that the model predictive control is superior to other control strategies that we have designed before, in terms of less fluctuation in the control input and less tracking error.