A coherent feedforward loop design principle to sustain robustness of biological networks

Many studies have investigated the relationship between structural properties and dynamic behaviors in biological networks. In particular, feedback loop (FBL) and feedforward loop (FFL) structures have received a great deal of attention. One interesting and common property of FBL and FFL structures is their coherency of coupling. However, the role of coherent FFLs in relation to network robustness is not fully known, whereas that of coherent FBLs has been well established.

To establish that coherent FFLs are abundant in biological networks, we examined gene regulatory and signaling networks and found that FFLs are ubiquitous, and are in a coherently coupled form. This result was also observed in the species-based signaling networks that are integrated from KEGG database. By using a random Boolean network model, we demonstrated that these coherent FFLs can improve network robustness against update-rule perturbations. In particular, we found that coherent FFLs increase robustness because these structures induce downstream nodes to be robust against update-rule perturbations. Therefore, coherent FFLs can be considered as a design principle of human signaling networks that improve network robustness against update-rule perturbations.