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Constraint based methods, such as the Flux Balance Analysis, are widely usedto model cellular growth processes without relying on extensive information onthe regulatory features. The regulation is instead substituted by anoptimization problem usually aiming at maximal biomass accumulation. A recentextension to these methods called the dynamic enzyme-cost Flux Balance Analysis(deFBA) is a fully dynamic modeling method allowing for the prediction ofnecessary enzyme levels under changing environmental conditions. However, thismethod was designed for deterministic settings in which all dynamics,parameters, etc. are exactly known. In this work, we present a theoreticalframework extending the deFBA to handle uncertainties and provide a robustsolution. We use the ideas from multi-stage nonlinear Model Predictive Control(MPC) and its feature to represent the evolution of uncertainties by anexponentially growing scenario tree. While this representation is able toconstruct a deterministic optimization problem in the presence ofuncertainties, the computational cost also increases exponentially. We counterthis by using a receding prediction horizon and reshape the standard deFBA tothe short-time deFBA (sdeFBA). This leads us, along with further simplificationof the scenario tree, to the robust deFBA (rdeFBA). This framework is capableof handling the uncertainties in the model itself as well as uncertaintiesexperienced by the modeled system. We applied these algorithms to twocase-studies: a minimal enzymatic nutrient uptake network, and the abstractionof the core metabolic process in bacteria.

Modeling metabolic networks including gene expression and uncertainties