How Retroactivity Affects the Behavior of Incoherent Feed-Forward Loops

TL;DR

This paper investigates how retroactivity influences the dynamics of incoherent feed-forward loops (IFFLs), revealing that increased retroactivity can variably affect response time and pulse amplitude, and comparing this to negative autoregulation.

Contribution

It introduces a simulation-based analysis of IFFLs under retroactivity, highlighting their flexible response behavior and contrasting it with negative autoregulation.

Findings

Retroactivity can increase, decrease, or not change IFFL response time.

Increasing retroactivity in negative autoregulation only slows responses.

IFFLs are more prevalent in eukaryotic and bacterial networks, possibly due to their flexible response to retroactivity.

Abstract

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.