Fig. 3.

Classification of building blocks in E. coli. (A) Basic fiber building blocks. These building blocks are characterized by a fiber that does not send back information to its regulator. They are characterized by two integer fiber numbers: $\left|n,\ell \right.⟩$. We show selected examples of circuits and input trees and bases. The full list of fibers appears in SI Appendix, Table VI and Dataset S1. The statistical count of every class is in SI Appendix, Table I. Bottom example shows a generic building block for a general n-ary tree $\left|n,\ell \right.⟩$ with $\ell$ regulators. (B) Complex Fibonacci and multilayer building blocks. These building blocks are more complex and characterized by an autoregulated fiber that sends back information to its regulator. This creates a fractal input tree that encodes a Fibonacci sequence with golden branching ratio in the number of paths $a_i$ versus path length, $i-1$. When the information is sent to the connected component that includes the regulator, then a cycle of length $d$ is formed and the topology is a generalized Fibonacci block with golden ratio ${\phi }_d$ as indicated. We find three such building blocks: 2-FF, 3-FF, and 4-FF. Bottom panel shows a multilayer composite fiber with a feedforward structure.