Quantitative dissection of the simple repression input-output function.

We present a quantitative case study of transcriptional regulation in which we carry out a systematic dialogue between theory and measurement for an important and ubiquitous regulatory motif in bacteria, namely, that of simple repression. This architecture is realized by a single repressor binding site overlapping the promoter. From the theory point of view, this motif is described by a single gene regulation function based upon only a few parameters that are convenient theoretically and accessible experimentally. The usual approach is turned on its side by using the mathematical description of these regulatory motifs as a predictive tool to determine the number of repressors in a collection of strains with a large variation in repressor copy number. The predictions and corresponding measurements are carried out over a large dynamic range in both expression fold change (spanning nearly four orders of magnitude) and repressor copy number (spanning about two orders of magnitude). The predictions are tested by measuring the resulting level of gene expression and are then validated by using quantitative immunoblots. The key outcomes of this study include a systematic quantitative analysis of the limits and validity of the input-output relation for simple repression, a precise determination of the in vivo binding energies for DNA-repressor interactions for several distinct repressor binding sites, and a repressor census for Lac repressor in Escherichia coli.