Modeling Enzyme Controlled Metabolic Networks in Rapidly Changing Environments by Robust Optimization

Constraint-based methods, such as the flux balance analysis (FBA), are widely used to model cellular growth processes without relying on knowledge of regulatory features. Regulation is instead substituted by an optimization problem to maximize a biological objective such as biomass accumulation. A recent extension to these methods is called dynamic enzyme-cost FBA (deFBA). This fully dynamic modeling method allows to predict optimal enzyme levels and reaction fluxes under changing environmental conditions. However, this method was designed for well-defined deterministic settings in which dynamics of the environment are exactly known. In this letter, we present a theoretical framework called the robust deFBA which extends the deFBA to handle uncertainty in nutrient availability. We achieve this by combining deFBA with multi-stage model predictive control which explicitly captures the evolution of uncertainty by a scenario tree. The resulting method is capable of predicting robust optimal gene expression levels for rapidly changing environments. We apply these algorithms to a model of the core metabolic process in bacteria under alternating oxygen availability.