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