From MFA to FBA: Defining linear constraints accounting for overflow metabolism in a macroscopic FBA-based dynamical model of cell cultures in bioreactor

Macroscopic dynamical models of cell cultures in bioreactor are made of sets of ODEs representing the mass balances of the main macroscopic species (biomass, main substrates and metabolites). They can be coupled to a Flux Balance Analysis (FBA) linear program whose solution gives metabolic flux values at each time instant. The linear constraints used in this linear program are made of positivity constraints for the fluxes, equalities which link the fluxes to simple macroscopic models of the substrate uptake rates and a set of equalities and inequalities corresponding to some biological assumptions. In this paper, a methodology is proposed to help defining this latter set of linear constraints, with a special focus on overflow metabolism description. It is shown how these linear constraints, together with the objective cost function to be used in the linear program, can be derived from a preliminary Metabolic Flux Analysis (MFA) and a careful comparison of the admissible metabolic flux intervals obtained either using both input and output flux measurements or using only input flux measurements. Finally, a method is proposed for estimating the dynamical model output uncertainties resulting from the intervals of admissible fluxes. In a case study made of hybridoma cell batch and fed-batch cultures, it is shown how to model overflow metabolism on both glucose and glutamine thanks to inequality constraints. The linear program corresponding to a FBA problem is then used in a macroscopic dynamical model which is able to reproduce biomass, substrates and metabolites concentration time profiles in direct and cross validation.