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Complexity reduction by symmetry: Uncovering the minimal regulatory network for logical computation in bacteria

Fig 2

Canonical fiber building blocks.

These correspond to the canincal fiber building blocks observed in the GRNs of E. coli and B. subtilis, with examples taken from E. coli. The networks can be seen as assemblies of 5 basic classes of fibration building blocks: (i) Trivial fibers. A number of external regulators identically regulate the genes in a fiber, which then show synchronous dynamics. Operons with only one promoter belong to this class, where colored nodes represent genes belonging to the operon (perhaps with more colored nodes in the fibers, depending on the number of genes in the operon). (ii) The feedforward fiber and its sub-classes of -FFF with external regulators. The FF fiber is defined by a feedforward motif with a self-loop in the synchronous set of genes, and the number of external regulators. (iii) The Fibonacci fiber, -FF. A more complex building block, defined by a fractal dimension branching ratio that occurs given the presence of a self-loop and a feedback regulation from the fiber back to the regulator(s). The Fibonacci fibers observed in E. coli have a branching ratio between 1 and 2, placing this building block in between the FFF fibers and the n=2 fibers. (iv) The n=2 fibers, defined by two self-loops in the synchronized genes. When this symmetry is broken it forms the memory and oscillatory logic circuits embedded in the SCCs. And finally (v) composite fibers of the previous ones. By adding different types of the previous 4 building blocks, in a sequential manner, a composite fiber is obtained. An interesting consequence of this is the synchronization of genes that may be far apart from each other and don’t share any regulation.

doi: https://doi.org/10.1371/journal.pcbi.1013005.g002