Informational requirements for transcriptional regulation

Abstract

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.

FIG. 1.

Schematic representation of the evolutionary simulator of transcriptional regulatory motifs (ESTReMo). Diagram summarizes the internal organization of an individual organism and its connection with the fitness model. TF, transcription factor.

FIG. 2.

Trace indicators for a complete evolutionary simulation. All values correspond to the fittest organism in the population at any given generation. (A) Organism fitness. Sequence logos illustrate the step-wise evolution of the associated TF-binding motif as new sites are recognized. (B) Free energy of binding for each site in the motif. (C) Information content R_sequence (corrected and uncorrected for small-sample error) of the evolved TF-binding motif. The predicted R_frequency for the system is superimposed. (D) Contributions to the partition function from the sampled background (blue) and the promoter regions (green).

FIG. 3.

Evolution of uniform regulatory systems. Plot shows evolved R_sequence values for simulations on randomly generated backgrounds (solid circles) and on the Escherichia coli genome (squares) as a function of the fraction of total probability mass (α) assigned to target sites. Error bars depict the 95% confidence interval for the mean. Corresponding values of R_frequency, , , and R^† are shown.

FIG. 4.

Evolution of bimodal regulatory systems. The plot shows evolved R_sequence values for different evolutionary simulation scenarios with half of the sites set to higher occupancy (α_high) than the other half (α_low). Error bars depict the 95% confidence interval for the mean. For each R_sequence value, the corresponding R^† values for α_high, α_low, and α_eff values are shown.

FIG. 5.

Evolution of stepwise regulatory ladders. The plot shows evolved R_sequence values for different evolutionary simulation scenarios with sites gradually increasing from low (α_low) to high (α_high) occupancy. Error bars depict the 95% confidence interval for the mean. For each R_sequence value, the corresponding R^† values for α_high, α_low, and α_eff values are shown.

FIG. 6.

Evolution of randomized regulatory scenarios. The plot shows 198 evolved R_sequence values for different evolutionary simulation scenarios. The full dataset is shown instead of summary statistics because of the uniqueness of α values. For each R_sequence value, the corresponding R^† values for α_high and α_low are shown.