  Symmetry principles have proven important in physics, deep learning and
geometry, allowing for the reduction of complicated systems to simpler, more
comprehensible models that preserve the system's features of interest.
Biological systems often show a high level of complexity and consist of a high
number of interacting parts. Using symmetry fibrations, the relevant symmetries
for biological 'message-passing' networks, we reduced the gene regulatory
networks of E. coli and B. subtilis bacteria in a way that preserves
information flow and highlights the computational capabilities of the network.
Nodes that share isomorphic input trees are grouped into equivalence classes
called fibers, whereby genes that receive signals with the same 'history'
belong to one fiber and synchronize. We further reduce the networks to its
computational core by removing 'dangling ends' via k-core decomposition. The
computational core of the network consists of a few strongly connected
components in which signals can cycle while signals are transmitted between
these 'information vortices' in a linear feed-forward manner. These components
are in charge of decision making in the bacterial cell by employing a series of
genetic toggle-switch circuits that store memory, and oscillator circuits.
These circuits act as the central computation machine of the network, whose
output signals then spread to the rest of the network.
