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Fig. 6 | BMC Bioinformatics

Fig. 6

From: Identification, visualization, statistical analysis and mathematical modeling of high-feedback loops in gene regulatory networks

Fig. 6

Data structures, procedures, and challenges in high-feedback topology enumeration. a Cycle intersection and cycle edge intersection graphs for an example network. Cycles are named for their nodes in the order visited. b Summary of Type-I and mixed-sign high-feedback identification. c Identification of candidate Type-I topologies by examining triangles in the cycle intersection graph. d Elimination of duplicate or nonminimal Type-I topologies by detecting emergent cycles. Selected cycles ACDB and AD both have ACD and ADB as neighbors in the cycle edge intersection graph. All edges in ACD or ADB are in the union of ACDB and AD, so they are emergent cycles (gradients in cycle edge intersection graph). If cycles are ordered lexicographically, the emergent cycle ACD is before selected cycle D, so the selected triangle (thick lines) cannot be canonical. Even if the order was correct, removing the D self-loop leaves at least 3 interconnected cycles, so this topology is not minimal. Example shown is based on a subnetwork of a core T cell regulatory network [6]. e The previous network without the self-loop. Gradients indicate edges involved in multiple selected cycles. This topology is minimal because removing any edge leaves fewer than 3 cycles. If cycles are ordered lexicographically, the selected triangle is the canonical representation of this topology because the only emergent cycle ADB is ordered after all the selected triangle’s cycles. f Summary of Type-II identification. g Identification of candidate Type-II topologies by examining pairs of neighbors in the cycle intersection graph. The callout on each potential bridge cycle lists all possible pairs of neighbor cycles and whether they are independent. h Elimination of nonminimal Type-I topologies from Type-II candidates. Cycle AD combined with bridge cycle ACDB creates emergent cycles ACD and ADB, so this topology is not minimal. Example shown is a different subnetwork of the network used in d

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