The coherent feed-forward loop acts as an efficient information transmitting motif

We present a theoretical formalism to study steady state information transmission in type 1 coherent 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. Utilizing a Gaussian framework, we show that the feed-forward loop motif harnesses the maximum amount of Shannon mutual information fractions constructed between the input signaling species and the final gene product and also between the two downstream gene products. Our findings may explain why a feed-forward loop is naturally selected by the force of evolution as a motif in bacterial transcription control network while the two-step cascade and bifurcation network are not.