Fig. 4

Non-trivial circuits leading to synchronization: FFF (AR loop with regulon and external regulator). a purR and its target gene pyrC regulated by fur form a FFF. FFF has one loop and one external regulator and therefore is classified as \(|n = 1, \ell = 1 \rangle\). purR and pyrC belong to the same fiber (will be shown in b) and therefore are “collapsed” under fibration \(\psi\), while fur is left untouched. b purR receives an input from itself creating an infinite chain and regulator fur, that doesn’t have any inputs. Therefore, infinite chain with additional input on each layer represents an input tree of purR. Similarly, pyrC receives input from purR that leads to the infinite chain and fur that creates an additional input. fur doesn’t receive any inputs and therefore has an input tree of height 0. Input trees of purR and pyrC are isomorphic, therefore purR and pyrC belong to the same fiber and synchronize their activity