Borbely, R.; Tkacik, G.

Cis-regulatory elements (CREs), such as enhancers and promoters, control gene expression by binding regulatory proteins. In contrast to their bacterial counterparts, eukaryotic CREs typically bind transcription factors with short recognition motifs across multiple functional yet often weak binding sites. The evolutionary origin of this genetic architecture remains unclear. Here we study adaptive evolution of entire CREs under selection for controllable gene expression. In a biophysical toy model that recapitulates the essential nonlinearities of eukaryotic regulation, a regulatory phenotype requires a gene to be active when its CRE binds cognate TFs, yet inactive in the presence of noncognate TFs that can cause deleterious crosstalk. We explore CRE evolutionary outcomes utilizing \"optimize-to-adapt\" approach suggested by the theory presented in a companion paper. In this approach, CRE evolution is simulated explicitly at the sequence level, while the parameters of the biophysical model itself -- i.e., the properties of the replicated genotype-phenotype map -- are numerically optimized for CRE evolvability. In the optimal regime, selection navigates the tradeoff between slowly evolving strong and long binding sites (which guarantee low crosstalk), and rapidly evolving multiple short and weak binding sites (which necessitate diffuse selection against excessive noncognate binding across the entire CRE). When we further explore various scenarios for cooperative regulation, we find that the optimal regime predicts a diversity of strong and weak, yet always short, binding sites and favors \"synergistic activation\" of transcription, as reported empirically for eukaryotes. These results showcase how information theory can link evolutionary dynamics with biophysical constraints to rationalize -- and possibly even predict -- optimal regulatory architectures.