Low-degree decompositions of flux vectors in faces of the flux cone

Decomposing a flux vector into elementary flux modes (EFMs) is a well-known task in the constraint-based analysis of metabolic networks. Using geometric insights into the facial structure of the flux cone, we develop a new method for decomposition. To illustrate our approach, we consider a variety of genome-scale metabolic networks from the BiGG database. We decompose the optimal solutions to flux balance analysis problems into EFMs and compare different possible decompositions. Taking into account their degree allows understanding the interplay of the different EFMs that can participate in the decomposition of a given flux vector and highlights the particular importance of low-degree decompositions. The new method can be applied to genome-scale metabolic networks, where the whole set of EFMs is often too large to be computed in practice. The special properties of low-degree decompositions make them an interesting subject for future biological studies.