The engineering principles of combining a transcriptional incoherent feedforward loop with negative feedback

Regulation of gene expression is of paramount importance in all living systems. In the past two decades, it has been discovered that certain motifs, such as the feedforward motif, are overrepresented in gene regulatory circuits. Feedforward loops are also ubiquitous in process control engineering, and are nearly always structured so that one branch has the opposite effect of the other, which is a structure known as an "incoherent" feedforward loop in biology. In engineered systems, feedforward control loops are subject to several engineering constraints, including that (1) they are finely-tuned so that the system returns to the original steady state after a disturbance occurs (perfect adaptation), (2) they are typically only implemented in the combination with negative feedback, and (3) they can greatly improve the stability and dynamical characteristics of the conjoined negative feedback loop. On the other hand, in biology, incoherent feedforward loops can serve many purposes, one of which may be perfect adaptation. It is an open question as to whether those that achieve perfect adaptation are subject to the above engineering principles.

We analyzed an incoherent feedforward gene regulatory motif from the standpoint of the above engineering principles. In particular, we showed that an incoherent feedforward loop Type 1 (I1-FFL), from within a gene regulatory circuit, can be finely-tuned for perfect adaptation after a stimulus, and that the robustness of this behavior is increased by the presence of moderate negative feedback. In addition, we analyzed the advantages of adding a feedforward loop to a system that already operated under negative feedback, and found that the dynamical properties of the combined feedforward/feedback system were superior.

Our analysis shows that many of the engineering principles used in engineering design of feedforward control are also applicable to feedforward loops in biological systems. We speculate that principles found in other domains of engineering may also be applicable to analogous structures in biology.