The role of gene regulation in redundant and synergistic information transfers in coherent feed-forward loop

Abstract

For the ubiquitous coherent type-1 feed-forward loop (C1-FFL) motif, the master and co-regulators act as sources of information in decoding the output gene expression state. Using the variance-based definition of information within a Gaussian framework at steady state, we apply the partial information decomposition technique to quantify the redundant (common) and synergistic (complementary) information transfers to the output gene. By enabling the generic C1-FFL motif with complementarily tunable regulatory pathways and fixed gene product abundances, we examine the role of output gene regulation in maintaining the flow of these two multivariate information flavors. We find that the redundant and synergistic information transfers are simultaneously maximized when the direct and indirect output regulatory strengths are nearly balanced. All other manifestations of the generic C1-FFL motif, including the two terminal ones, namely, the two-step cascade and fan-out, transduce lesser amounts of these two types of information. This optimal decoding of the output gene expression state by a nearly balanced C1-FFL motif holds true in an extended repertoire of biologically relevant parametric situations. These realizations involve additional layers of regulation through changing gene product abundances, activation coefficients, and degradation rates. Our analyses underline the regulatory mechanisms through which the C1-FFL motif is able to optimally reduce its output uncertainty concurrently via redundant and synergistic modes of information transfer. We find that these information transfers are guided by fluctuations in the motif. The prevalence of redundancy over synergy in all regulatory implementations is also noteworthy.