Fig. 6

Illustration of a sufficient cyclic subgraph that corresponds to a stable motif. In the ABCDE subgraph the target node E has two necessary regulators, C and D, ABC is a sufficient path and A→D is a sufficient edge, making the entire subgraph sufficient. In the ABCDEGF subgraph the target node F has two regulators, E and G; the A to E subgraph is sufficient while the A to G path is sufficient inhibitory. Using the subgraph chaining function at node E, we chain the sufficient subgraph ABCDE with the necessary inhibitory edge E⊣F, giving us a sufficient inhibitory relationship (check Table 2). Similarly, at node G, we chain the sufficient inhibitory path ADG with the sufficient edge G→F which gives sufficient inhibitory (check Table 1). Since the subgraph chaining for both regulators of the target node F gives the same result, we have a sufficient inhibitory subgraph from A to F. FHI is a necessary inhibitory path. Combining subgraph ABCDEGF and path FHI, we have a sufficient subgraph ABCDEGFHI with the source node A and target node I. Node A has two necessary regulators, E and I and we know that A is sufficient for both of these regulators, hence making A sufficient for itself. We thus have a sufficient cyclic subgraph (i.e. a sufficient subgraph starting as well as ending at the same node, A) which in effect is a stable motif. Nodes with white background are in the ON state, while those with gray background are in the OFF state in the stabilized state of the motif. Node names marked in bold indicate driver nodes