Flux balance analysis (FBA) is a key method for the constraint-based analysis of metabolic networks. A technical problem may occur in FBA when known (e.g., measured) fluxes of certain reactions are integrated into an FBA scenario rendering the underlying linear program (LP) infeasible, for example, due to inconsistencies between some of the measured fluxes causing a violation of the steady-state or other constraints. Here, we present and compare two methods, one based on an LP and one on a quadratic program (QP), to find minimal corrections for the given flux values so that the FBA problem becomes feasible. We provide a general guide on how to treat infeasible FBA systems in practice and discuss relevant examples of potentially infeasible scenarios in core and genome-scale metabolic models. Finally, we also highlight and clarify the relationships to classical metabolic flux analysis, where solely algebraic approaches are used to compute unknown metabolic rates from measured fluxes and to balance infeasible flux scenarios.
Keywords: Escherichia coli; constraint-based modeling; mass balances; metabolic flux analysis; quadratic programming; weighted least-squares.