Implementation Considerations, Not Topological Differences, Are the Main Determinants of Noise Suppression Properties in Feedback and Incoherent Feedforward Circuits

Biological systems use a variety of mechanisms to deal with the uncertain nature of their external and internal environments. Two of the most common motifs employed for this purpose are the incoherent feedforward (IFF) and feedback (FB) topologies. Many theoretical and experimental studies suggest that these circuits play very different roles in providing robustness to uncertainty in the cellular environment. Here, we use a control theoretic approach to analyze two common FB and IFF architectures that make use of an intermediary species to achieve regulation. We show the equivalence of both circuits topologies in suppressing static cell-to-cell variations. While both circuits can suppress variations due to input noise, they are ineffective in suppressing inherent chemical reaction stochasticity. Indeed, these circuits realize comparable improvements limited to a modest 25% variance reduction in best case scenarios. Such limitations are attributed to the use of intermediary species in regulation, and as such, they persist even for circuit architectures that combine both IFF and FB features. Intriguingly, while the FB circuits are better suited in dealing with dynamic input variability, the most significant difference between the two topologies lies not in the structural features of the circuits, but in their practical implementation considerations.