Stabilizing and Destabilizing Effects of Embedding 3-Node Subgraphs on the State Space of Boolean Networks

We demonstrate the effects of embedding subgraphs in a Boolean network, which is one of the discrete dynamic models for transcriptional regulatory networks. After comparing the dynamic properties of networks embedded with seven different subgraphs including feedback and feedforward subgraphs, we found that complexity of the state space increases with longer lengths of attractors, and the number of attractors is reduced for networks with more feedforward subgraphs. In addition, feedforward subgraphs can provide higher mutual information with lower entropy in a temporal program of gene expression. Networks with the other six subgraphs show opposite effects on network dynamics. This is roughly consistent with Thomas's conjecture. These results suggest that feedforward subgraph is favorable local structure in complex biological networks.