Networks of interactions between feed-forward loop transcriptional motifs in gene-regulatory networks

Transcriptional motifs are smaller subnetworks found within the gene-regulatory networks of many organisms in larger abundance. The feed-forward loop (FFL) is one such three-node motif, wherein one top-level protein regulates the expression of a target gene either directly, or indirectly through an intermediate regulator protein. However, no systematic effort has yet been made to understand how individual FFLs interconnect. Here, we address this problem by examining embedded transcriptional motifs that interact topologically by sharing one (vertex-share graphs), two (edge-share graphs), or three (triad-share graphs) nodes. Using transcriptional networks of the bacterium E. coli and the yeast S. cerevisiae, we constructed networks of FFLs based on these interaction patterns, and termed them "motif networks". In view of these motif networks we show that on average FFLs connect primarily to others similarly connected - a phenomenon termed assortativity and often attributed to social networks. We fit these correlations to a power-law equation, which exhibits a sublinear exponent indicative of an "economy of scale" in the FFL connectivity. We show that connectivity distributions of the motif networks (similar to degree distributions in complex networks) appear approximately uniform, but with a large variance. Although assortative mixing may arise from a scale-free degree distribution, we conclude that assortativity observed here arises by alternative means.