An information-theoretic perspective on feed-forward loop abundances in transcriptional networks

Abstract

Biological networks contain recurring motifs, yet their unequal abundance remains poorly understood. In the transcriptional networks of \textit{Escherichia coli} and \textit{Saccharomyces cerevisiae}, the eight feed-forward loop (FFL) motifs occur at markedly different frequencies. Although previous studies have linked the abundant C1- and I1-FFLs to specific dynamical functions, a common quantitative account of the broader pattern is lacking. An FFL transmits upstream information through direct and indirect paths that share the same input and converge on the same output. Their information contributions therefore need not combine independently. To investigate this, we decompose input-output mutual information (MI) into pathway and interference components, defining the latter as interference mutual information (IMI). IMI can be positive or negative, indicating that pathway coupling can enhance or reduce information transmission. Within physiologically relevant regimes, the IMI hierarchy follows the observed abundance patterns in both FFL classes, whereas total MI and pathway MI do not consistently do so. We further relate this hierarchy to pathway-interference strength and local pathway sensitivities. These results identify pathway interference as an architectural feature of information transmission and provide a quantitative basis for understanding the unequal abundance of FFL motifs.

36 pages, 12 figures