On the geometry of elementary flux modes

Elementary flux modes (EFMs) play a prominent role in the constraint-based analysis of metabolic networks. They correspond to minimal functional units of the metabolic network at steady-state and as such have been studied for almost 30 years. The set of all EFMs in a metabolic network tends to be very large and may have exponential size in the number of reactions. Hence, there is a need to elucidate the structure of this set. Here we focus on geometric properties of EFMs. We analyze the distribution of EFMs in the face lattice of the steady-state flux cone of the metabolic network and show that EFMs in the relative interior of the cone occur only in very special cases. We introduce the concept of degree of an EFM as a measure how elementary it is and study the decomposition of flux vectors and EFMs depending on their degree. Geometric analysis can help to better understand the structure of the set of EFMs, which is important from both the mathematical and the biological viewpoint.

Automated summary

Elementary flux modes (EFMs) are important in the constraint-based analysis of metabolic networks, as they represent minimal functional units at steady-state. The distribution of EFMs in the face lattice of the flux cone of the metabolic network is analyzed, revealing that EFMs in the relative interior of the cone are rare. The concept of EFM degree is introduced to measure their level of elementary nature, providing insights into the decomposition of flux vectors and EFMs.