Effects of feedback and feedforward loops on dynamics of transcriptional regulatory model networks

We demonstrate the advantages of feedforward loops using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical behaviors of network embedded feedback and feedforward loops, we found that feedforward loops can provide higher temporal order (coherence) with lower entropy (randomness) in a temporal program of gene expression. In addition, complexity of the state space that increases with longer length of attractors and greater number of attractors is also reduced for networks with more feedforward loops. Feedback loops show opposite effects on dynamics of the networks. These results suggest that feedforward loops are one of the favorable local structures in biomolecular and neuronal networks.