Composition structures and biologically meaningful logics: plausibility and relevance in bipartite models of gene regulation

Boolean network models have widely been used to study the dynamics of gene regulatory networks. However, such models are coarse-grained to an extent that they abstract away molecular specificities of gene regulation. In contrast, bipartite Boolean network models of gene regulation explicitly distinguish genes from transcription factors (TFs). In such models, multiple TFs may simultaneously contribute to the regulation of a gene by forming heteromeric complexes. The formation of heteromeric complexes gives rise to composition structures in the corresponding bipartite network. Remarkably, composition structures can severely restrict the number of Boolean functions (BFs) that can be assigned to a gene. The introduction of bipartite Boolean network models is relatively recent, and so far an empirical investigation of their biological plausibility is lacking. Here, we estimate the prevalence of composition structures arising through heteromeric complexes in Homo sapiens . Moreover, we present an additional mechanism by which composition structures arise as a result of multiple TFs binding to the cis -regulatory regions of a gene and we provide empirical support for this mechanism. Next, we compare the restriction in BFs imposed by composition structures and by biologically meaningful properties. We find that two types of minimally complex BFs, namely nested canalyzing functions (NCFs) and read-once functions (RoFs), are more restrictive than composition structures. Finally, using a compiled dataset of 2687 BFs from published models, we find that composition structures are highly enriched in real biological networks, but that this enrichment is most likely driven by NCFs and RoFs. ### Competing Interest Statement The authors have declared no competing interest.