Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise

We develop a null model of the evolution of transcriptional regulatory networks, and use it to support an adaptive origin for a canonical "motif", a 3-node feed-forward loop (FFL) hypothesized to filter out short spurious signals by integrating information from a fast and a slow pathway. Our mutational model captures the intrinsically high prevalence of weak affinity transcription factor binding sites. We also capture stochasticity and delays in gene expression that distort external signals and intrinsically generate noise. Functional FFLs evolve readily under selection for the hypothesized function, but not in negative controls. Interestingly, a 4-node "diamond" motif also emerged as a short spurious signal filter. The diamond uses expression dynamics rather than path length to provide fast and slow pathways. When there is no external spurious signal to filter out, but only internally generated noise, only the diamond and not the FFL evolves.