Optimal Regulatory Circuit Topologies for Fold-Change Detection

Evolution repeatedly converges on only a few regulatory circuit designs that achieve a given function. This simplicity helps us understand biological networks. However, why so few circuits are rediscovered by evolution is unclear. We address this question for the case of fold-change detection (FCD): a response to relative changes of input rather than absolute changes. Two types of FCD circuits recur in biological systems-the incoherent feed-forward and non-linear integral-feedback loops. We performed an analytical screen of all three-node circuits in a class comprising similar to 500,000 topologies. We find that FCD is rare, but still there are hundreds of FCD topologies. The two experimentally observed circuits are among the very few minimal circuits that optimally trade off speed, noise resistance, and response amplitude. This suggests a way to understand why evolution converges on only few topologies for a given function and provides FCD designs for synthetic construction and future discovery.