Identifying the sources of noise synergy and redundancy in the gene expression of feed-forward loop motif

Abstract

The propagation of noise through parallel regulatory pathways is a characteristic feature of feed-forward loops in genetic networks. Although the contributions of the direct and indirect regulatory pathways of feed-forward loops to output variability have been well characterized, the impact of their joint action arising from their shared input and output remains poorly understood. Here, we identify an additional component of noise that emerges specifically from this convergent nature of the pathways. Using inter-gene correlations, we reveal the regulatory basis of the cross-interaction noise and interpret it as synergy or redundancy in noise propagation, depending on whether the combined pathways amplify or suppress fluctuations. Synergy typically arises in coherent feed-forward loops, whereas redundancy is common in incoherent ones. This framework not only accounts for previously observed differences in noise behavior across coherent and incoherent structures but also provides a generalizable strategy to connect network structure with stochastic gene regulation. Furthermore, by relating these synergy and redundancy to dynamical properties such as sign-sensitive delay or response acceleration, the framework offers a statistical lens to interpret the functional roles in cellular decision-making.