A global optimization approach for metabolic flux analysis based on labeling balances

The flux quantification step in metabolic flux analysis (MFA) includes the mathematical modeling of metabolism (based on both metabolite and isotope balancing) and its optimization, which minimizes a weighted distance between measurements and model predictions. When GC–MS is used for assessing the 13C-labeling in intracellular metabolites, the metabolic flux quantification problem originates a non-convex optimization model with bilinear constraints for which the existence of multiple local minima is a special difficulty. In the present work, we propose a global optimization technique that relies on a spatial branch and bound search. A linearization technique is applied on the constraints from labeling balances, in order to obtain a convex relaxed problem that provides a lower bound to the global optimum; due to the nature of the linearization, the initial variable (measured) and parameter (non-measured) bounds strongly affect the model convergence.