Fibration symmetries of integrated bio-network in a hypergraph representation of E.coli.

The multi-layer structure of integrated bio-network in E.coli. spans from transcriptional regulatory networks to metabolic networks where biochemical reactions happen. The interaction between the two networks characterizes the information transfer between metabolites and transcription factors (TF) and helps build coherent cellular states. Previously, fibration symmetries were found in transcriptional regulatory networks and uncovered the building blocks of biological networks. Here, we consider a hypergraph representation to model the integrated network of metabolites, and TFs, where dynamical features of metabolism are retained. We then apply balance coloring algorithm to study the fibration symmetries. We find that strong/weak fibration symmetries propagate from the regulatory networks to the metabolic networks, and, in turn, gene-metabolite complexes carry information from the metabolism to strengthen or weaken the symmetries in regulatory networks. Furthermore, the complexes act as switches controlling the general cellular status.