Exploring patterns in modularity of protein interaction networks across the tree of life using Spectral Entropy

Modularity and organizational hierarchy are important concepts in understanding the 1 structure and evolution of interactions in complex biological systems. In this work, we introduce 2 and use a spectral characterization measure (Spectral Entropy) to quantify modularity in protein3 to-protein interaction (PPI) networks in species across the tree of life. We evaluated the relation 4 between the size of a PPI network and its (Spectral Entropy-based) modularity, and found a 5 sigmoidal response between the two. We also found significant differences in the distribution 6 of Spectral Entropy values among the three domains of life (Bacteria, Archaea, Eukaryotes). To 7 explore further correlations with biological traits, we focused solely on bacterial PPI networks, 8 which are the most numerous among the three domains and had associated trait metadata, and 9 investigated how modularity impacts or is impacted by growth, aerobicity, selection and location 10 on the tree of life. We found no relation between maximal growth rate and Spectral Entropy, but 11 a strong dependence between G-C content (a proxy for selection) and Spectral Entropy. We also 12 discovered that Spectral Entropy is negatively affected by phylogenetic placement (evolutionary 13 distance from the last universal common ancestor). The general nature of the Spectral Entropy 14 measure of hierarchical modularity in networks suggests that it will be useful in other settings 15 where structural properties of real-world networks are being compared. 16