Informational requirements for transcriptional regulation.

Transcription factors (TFs) regulate transcription by binding to specific sites in promoter regions. Information theory provides a useful mathematical framework to analyze the binding motifs associated with TFs but imposes several assumptions that limit their applicability to specific regulatory scenarios. Explicit simulations of the co-evolution of TFs and their binding motifs allow the study of the evolution of regulatory networks with a high degree of realism. In this work we analyze the impact of differential regulatory demands on the information content of TF-binding motifs by means of evolutionary simulations. We generalize a predictive index based on information theory, and we validate its applicability to regulatory scenarios in which the TF binds significantly to the genomic background. Our results show a logarithmic dependence of the evolved information content on the occupancy of target sites and indicate that TFs may actively exploit pseudo-sites to modulate their occupancy of target sites. In regulatory networks with differentially regulated targets, we observe that information content in TF-binding motifs is dictated primarily by the fraction of total probability mass that the TF assigns to its target sites, and we provide a predictive index to estimate the amount of information associated with arbitrarily complex regulatory systems. We observe that complex regulatory patterns can exert additional demands on evolved information content, but, given a total occupancy for target sites, we do not find conclusive evidence that this effect is because of the range of required binding affinities.