Abstract
It is well known that the presence of an incoherent feedforward loop (IFFL) in a network may give rise to a steady state non-monotonic dose response. This note shows that the converse implication does not hold. It gives an example of a three-dimensional system that has no IFFLs, yet its dose response is bell-shaped. It also studies under what conditions the result is true for two-dimensional systems, in the process recovering, in far more generality, a result given in the T-cell activation literature.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
There was an error in the previous version. The paper had incorrectly stated that there were no IFFLs in the counterexample. The new example has no IFFLs. Thanks to David Angeli (Imperial College) for noticing the error. I used the opportunity to add some more material to the introduction.