Evolution of hierarchy in bacterial metabolic networks

Flow hierarchy is a useful way to characterize the movement of information and matter throughout a network. Hierarchical network organizations are shown to arise when there is a cost of maintaining links in the network. A similar constraint exists in metabolic networks, where costs come from reduced efficiency of nonspecific enzymes or from producing unnecessary enzymes. Previous analyses of bacterial metabolic networks have been used to predict the minimal nutrients that a bacterium needs to grow, its mutualistic relationships with other bacteria, and its major ecological niche. We use metabolic network inference to obtain metabolite flow graphs of 2935 bacterial metabolic networks and find that flow hierarchy evolves independently of modularity and other network properties. By inferring the ancestral metabolic networks and estimating the hierarchical character of the inferred network, we show that hierarchical structure first increased and later decreased over evolutionary history. Furthermore, hierarchical structure in the network is associated with slower growth rates; bacteria with hierarchy scores above the median grow on average 2.25 times faster than those with hierarchy scores below the median.