New mathematical tools help understand cell functions, adaptability, and evolvability to discover hidden variables to predict phenotypes that could be tested in wet labs in the future. Different models have been successfully used to discover the properties of the protein-protein interaction networks or interactomes. We found that in the hyperbolic Popularity-Similarity model, cellular proteins with the highest contents of structural intrinsic disorder cluster together in many different eukaryotic interactomes and not the prokaryotic E. coli, where proteins with high levels of intrinsic disorder are very low. We also found that the normalized theta variable from the Popularity-Similarity model for a protein family correlate to the seniority of the organisms under analysis.