Symmetries Uncover the Minimal Regulatory Network for Logical Computations in Bacteria*

The use of symmetries in physics to reduce a complex system to its underlying components and interactions is a widely known useful tool. Recently we have shown¹ that relevant symmetries of biological network systems allow for a systematic reduction of the networks that preserves information flow. Symmetry fibrations, which consists of grouping nodes that share an isomorphic input tree into equivalence relations called fibers, allows for the collapse of the network while preserving information flow. Further reducing the network by the k-core decomposition of the collapsed network gives the minimal network driving the dynamics of the entire network. In gene transcriptional regulatory networks (TRN), where fibers consist of genes that are synchronized for being co-expressed, this gives the minimal transcriptional regulatory network. This minimal structure is understood as a combination of genetic circuits which perform core logical computations from outside inputs and the current state. Hence, symmetry principles unveil the minimal TRN that corresponds to the core computational machinery.
1)Flaviano Morone, Ian Leifer, and Hernán A Makse. Fibration symmetries uncover the building blocks of biological networks. PNSciences, 117(15):8306–8314, 2020.