Resource constrained flux balance analysis predicts selective pressure on the global structure of metabolic networks

Nima Abedpour, Markus Kollmann

A universal feature of metabolic networks is their hourglass or bow-tie structure on cellular level. This architecture reflects the conversion of multiple input nutrients into multiple biomass components via a small set of precursor metabolites. However, it is yet unclear to what extent this structural feature is the result of natural selection. We extend flux balance analysis to account for limited cellular resources. Using this model, optimal structure of metabolic networks can be calculated for different environmental conditions. We observe a significant structural reshaping of metabolic networks for a toy-network and E. coli core metabolism if we increase the share of invested resources for switching between different nutrient conditions. Here, hub nodes emerge and the optimal network structure becomes bow-tie-like as a consequence of limited cellular resource constraint. We confirm this theoretical finding by comparing the reconstructed metabolic networks of bacterial species with respect to their lifestyle. We show that bow-tie structure can give a system-level fitness advantage to organisms that live in highly competitive and fluctuating environments. Here, limitation of cellular resources can lead to an efficiency-flexibility tradeoff where it pays off for the organism to shorten catabolic pathways if they are frequently activated and deactivated. As a consequence, generalists that shuttle between diverse environmental conditions should have a more predominant bow-tie structure than specialists that visit just a few isomorphic habitats during their life cycle.