Single and multiple input modules in regulatory networks

Interactions between transcription factors and target genes form regulatory networks that control target gene expression. Regulatory networks contain canonical motifs, including the feed forward loop (FFL), single input module (SIM), and multiple input module (MIM) (Fig. 1). A challenge for network analysis is to identify and enumerate the motifs, required to illuminate their biological significance. Although there is consensus about the definition of the FFL, published definitions of the SIM and MIM are unclear and often used inconsistently. Here, we provide, for the first time, a complete and consistent definition of SIM and MIM, and algorithms for enumerating SIMs and MIMs in any network. From the algorithmic point of view, enumeration of SIMs and MIMs is substantially harder than enumerating FFLs. We compare the distributions of motifs in the Yeast regulatory network under different physiological conditions, reported earlier by the landmark paper of Luscombe et al. (Nature 2004, 431: 308-312). Our reanalysis shows major differences in the number of motifs compared with the results of those authors, requiring significant revision of some of their conclusions.