Optimal control of microbial cells by natural and synthetic strategies – Maximic

The growth of microorganisms is fundamentally an optimization problem which consists in dynamically allocating resources to cellular functions so as to maximize growth rate or another fitness criterion. Simple ordinary differential equation models, called self-replicators, have been used to formulate this problem in the framework of optimal and feedback control theory, allowing observations in microbial physiology to be explained. The resulting control problems are very challenging due to the nonlinearity of the models, parameter uncertainty, the coexistence of different time-scales, a dynamically changing environment, and various other physical and chemical constraints. Maximic aims at developing novel theoretical approaches for addressing these challenges in order to (i) study natural resource allocation strategies in microorganisms and (ii) propose new synthetic control strategies for biotechnological applications.

In order to address (i), we will develop extended self-replicator models accounting for the cost of regulation and energy metabolism in bacterial cells. We will study these models by a combination of analytical and numerical approaches to derive optimal control solutions and a control synthesis, dealing with the bang-bang-singular structure of the solutions. Moreover, we define quasi-optimal feedback control strategies inspired by known regulatory mechanisms in the cell. To test whether bacteria follow the predicted optimal strategies, we will quantify dynamic resource allocation in the bacterium Escherichia coli by monitoring, by means of time-lapse fluorescent microscopy, the expression of selected genes in single cells growing in a microfluidics device.

In order to address (ii), we will build self-replicator models that include a pathway for the production of a metabolite of interest. We also add a mechanism to turn off microbial growth by means of an external input signal, at the profit of the production of the metabolite. We will formulate the maximization of the amount of metabolite produced as an optimal control problem, and derive optimal solutions and a control synthesis, as well as quasi-optimal feedback strategies satisfying chemical and physical design constraints. The proposed synthetic control strategies will be tested experimentally by growing E. coli strains capable of producing glycerol from glucose in a mini-bioreactor system. We will quantify the amount of glucose consumed and glycerol produced, in the case of a predefined input signal (open-loop control) or adaptive regulation of the input signal based on on-line measurements of the growth rate and the expression of fluorescent reporters of selected genes (closed-loop control).

The Maximic project proposes fundamental research on system theory, mathematical modeling, control, and optimization, directly related to challenging applications in the life sciences. It will be carried out by a strong and complementary consortium of researchers covering the areas of control theory, mathematical and computational biology, microbiology, and biophysics. The participants have a long-standing collaborative history, necessary for addressing the ambitious challenges of the proposal. The results of the project are expected to have an impact in mathematical modeling and control theory. We will notably contribute new modeling approaches and methods to address exciting questions in an emerging research domain: the development of control strategies to better understand and reengineer living cells by implementing feedback controllers on the molecular level with the help of synthetic biology techniques and experimental devices. In addition, Maximic will have an impact in microbiology and, in the longer run, in biotechnology, by providing new insights into natural resource allocation strategies and by preparing the way for the transfer of control theory approaches to new metabolic engineering strategies.