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

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.