Evolvability of feed-forward loop architecture biases its abundance in transcription networks

Background: Transcription networks define the core of the regulatory machinery of cellular life and are largely responsible for information processing and decision making. At the small scale, interaction motifs have been characterized based on their abundance and some seemingly general patterns have been described. In particular, the abundance of different feed-forward loop motifs in gene regulatory networks displays systematic biases towards some particular topologies, which are much more common than others. The causative process of this pattern is still matter of debate. Results: We analyzed the entire motif-function landscape of the feed-forward loop using the formalism developed in a previous work. We evaluated the probabilities to implement possible functions for each motif and found that the kurtosis of these distributions correlate well with the natural abundance pattern. Kurtosis is a standard measure for the peakedness of probability distributions. Furthermore, we examined the functional robustness of the motifs facing mutational pressure in silico and observed that the abundance pattern is biased by the degree of their evolvability. Conclusions: The natural abundance pattern of the feed-forward loop can be reconstructed concerning its intrinsic plasticity. Intrinsic plasticity is associated to each motif in terms of its capacity of implementing a repertoire of possible functions and it is directly linked to the motif's evolvability. Since evolvability is defined as the potential phenotypic variation of the motif upon mutation, the link plausibly explains the abundance pattern.