  An incoherent feed-forward loop (IFFL) is a network motif known for its
ability to accelerate responses and generate pulses. Though functions of IFFLs
are well studied, most previous computational analysis of IFFLs used ordinary
differential equation (ODE) models where retroactivity, the effect downstream
binding sites exert on the dynamics of an upstream transcription factor (TF),
was not considered. It remains an open question to understand the behavior of
IFFLs in contexts with high levels of retroactivity, e.g., in cells
transformed/transfected with high-copy plasmids, or in eukaryotic cells where a
TF binds to numerous high-affinity binding sites in addition to one or more
functional target sites. Here we study the behavior of IFFLs by simulating and
comparing ODE models with different levels of retroactivity. We find that
increasing retroactivity in an IFFL can increase, decrease, or keep the
network's response time and pulse amplitude constant. This suggests that
increasing retroactivity, traditionally considered as an impediment to
designing robust synthetic systems, could be exploited to improve the
performance of IFFLs. We compare the behaviors of IFFLs to negative
autoregulatory loops, another sign-sensitive response-accelerating network
motif, and find that increasing retroactivity in a negative autoregulated
circuit can only slow the response. The inability of a negative autoregulatory
loop to flexibly handle retroactivity may have contributed to its lower
abundance in eukaryotic relative to bacterial regulatory networks, a sharp
contrast to the significant abundance of IFFLs in both cell types.
