Coherent feed-forward loop acts as an efficient information transmitting motif

We present a theoretical formalism to study steady-state information transmission in a coherent type-1 feed-forward loop motif with an additive signal integration mechanism. Our construct allows a two-step cascade to be slowly transformed into a bifurcation network via a feed-forward loop, which is a prominent network motif. Using a Gaussian framework, we show that among these three network patterns, the feed-forward loop motif harnesses the maximum amount of Shannon mutual information fractions constructed between the final gene-product and each of the master and coregulators of the target gene. We also show that this feed-forward loop motif provides a substantially lower amount of noise in target gene expression, compared with the other two network structures. Our theoretical predictions, which remain invariant for a couple of parametric transformations, point out that the coherent type-1 feed-forward loop motif may qualify as a better decoder of environmental signals when compared with the other two network patterns in perspective.