Determining a Unique Solution to Underdetermined Metabolic Networks Via a Systematic Path through the Most Accurate Fluxes

Abstract

Metabolic Flux Analysis (MFA) and Flux Balance Analysis (FBA) often lead to underdetermined problems in the sense that there are more unknown fluxes in the metabolic network than the number of available equations which represent balanced metabolites and measured fluxes. Even the additional inequality constraints, e.g. flux positivity, and/or the use of an objective function in FBA do not allow obtaining a unique solution in many cases. This contribution aims at determining a simple, systematic and computationally efficient algorithm for obtaining a unique solution based on the iterative determination of the Most Accurate Fluxes (MAF). A measure of accuracy is introduced and the systematic algorithm is proposed and illustrated on a case study aiming at the determination of unique dynamic flux values within hybridoma cells. It is also shown that the MAF distribution is similar to the mean values obtained from a uniform sampling of admissible solutions.