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 C-13-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. The global optimization algorithm estimates fluxes in the central metabolism of Saccharomyces cerevisiae, based on experimental data previously reported [Gombert, A. K., dos Santos, M. M., Christensen, B., Nielsen, J. (2001). Network identification and flux quantification in the central metabolism of Saccharomyces cerevisiae under different conditions of glucose repression. Journal of Bacteriology, 183(4), 1441-1451]. To attain global convergence, a detailed bound tightening procedure is developed. Measured labelings and non-measured net fluxes are the branching variables, and the branching is performed on the one that has the largest difference between its values in the convex and non-convex models. Results were compared to the ones obtained using an evolutionary algorithm that requires extensive computational effort to achieve a feasible solution. We found that there are local solutions with important differences on the central pathways. In the global optimum, the calculated fluxes for the central pathways are similar to the best result obtained by evolutionary search, whereas the quadratic errors for both variable sets, measured labelings and fluxes, are smaller. (c) 2004 Elsevier Ltd. All rights reserved.