Three topological features of regulatory networks control life-essential and specialized subsystems

Gene regulatory networks (GRNs) play key roles in development, phenotype plasticity, and evolution. Although graph theory has been used to explore GRNs, associations amongst topological features, transcription factors (TFs), and systems essentiality are poorly understood. Here we sought the relationship amongst the main GRN topological features that influence the control of essential and specific subsystems. We found that the K_nn, page rank, and degree are the most relevant GRN features: the ones are conserved along the evolution and are also relevant in pluripotent cells. Interestingly, life-essential subsystems are governed mainly by TFs with intermediary K_nn and high page rank or degree, whereas specialized subsystems are mainly regulated by TFs with low K_nn. Hence, we suggest that the high probability of TFs be toured by a random signal, and the high probability of the signal propagation to target genes ensures the life-essential subsystems' robustness. Gene/genome duplication is the main evolutionary process to rise K_nn as the most relevant feature. Herein, we shed light on unexplored topological GRN features to assess how they are related to subsystems and how the duplications shaped the regulatory systems along the evolution. The classification model generated can be found here: https://github.com/ivanrwolf/NoC/ .