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. 2011 Jul 19;108(29):12173-8.
doi: 10.1073/pnas.1015616108. Epub 2011 Jul 5.

Quantitative dissection of the simple repression input-output function

Hernan G Garcia  1 , Rob Phillips
Affiliations

Quantitative dissection of the simple repression input-output function

Hernan G Garcia et al. Proc Natl Acad Sci U S A. .

Abstract

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.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
The simple repression motif. (A) States and weights of the thermodynamic model describing this regulatory motif. We assume that Lac repressor sterically excludes RNA polymerase from the promoter, although that assumption is not critical to our analysis. P and R are the numbers of RNA polymerase and Lac repressor molecules inside the cell, respectively. NNS is the number of nonspecific sites, which we assume to be the size of the genome. Δεpd and Δεrd are the difference in energy between being specifically and nonspecifically bound for RNA polymerase and Lac repressor, respectively. The difference in color in the repressor binding site denotes an overlap of the binding site with the promoter. (B) The tuning variables that can be varied in the model and controlled experimentally are the binding strength (by changing the Lac repressor operator sequence) and the number of Lac repressors (by changing its mRNA ribosomal binding site). The effect of tuning these parameters on the fold change in gene expression is shown in the graphs. Note that stronger repressor binding corresponds to a larger fold change. For a detailed derivation of the expression and discussion of the assumptions used see SI Text and Fig. S2.
Fig. 2.
Fig. 2.
Single-site binding energies and prediction of the number of repressors for different strains. (A) The operator binding energies and approximate dissociation constants are deduced from the measurement of the fold change for the different operators in strain RBS1027 combined with our knowledge of its intracellular number of repressors, using Eq. 5. (B) The fold change in gene expression is measured for all four operators in six different strain backgrounds (including RBS1027). Using the binding energies from A, we fit the data to Eq. 5 to make a parameter-free prediction of the number of repressors present in each strain shown in C. Errors in the predictions represent the SE of the corresponding fit. The errors in the binding energies are here denoted as gray shaded regions. Estimated dissociation constants are shown for convenience for comparison with literature values. The basis for these estimates is explained in SI Text.
Fig. 3.
Fig. 3.
Immunoblots for the measurement of the in vivo number of Lac repressors. (A) Typical luminescence image obtained from an immunoblot. (B) Map of the samples loaded on the membrane shown in A. The blank (HG105) and 1I samples are used to create a normalization map by subtracting the blank luminescence from all samples and dividing by 1I. White spots correspond to the cell lysates measured and the blue spots correspond to the different concentrations of purified Lac repressor standard. (C) Normalization map generated by fitting a 2D polynomial to 1I samples scattered around the membrane (black dots) after removing the blank. This map was used to account for nonuniformities in the collection of luminescence from the membrane. (D) Luminescence vs. quantity of LacI loaded. The calibration samples are used to construct a power law fit. The luminescence of the measured samples is shown as well. The unknown amounts of repressor loaded are determined by using the calibration curve. Samples 1I and RBS1 have been diluted 1:8 to match them to the dynamic range of the assay and therefore appear to have less signal within a spot (SI Text).
Fig. 4.
Fig. 4.
Experimental and theoretical characterization of repressor copy number. (A) Immunoblots were used to measure the number of Lac repressors in six strains with different constitutive levels of Lac repressor. Each value corresponds to an average of cultures grown on at least 3 different days. The error bars are the SD of these measurements. (B) The fold-change measurements in Fig. 2B were combined with the binding energies obtained from Fig. 2A (derived from strain RBS1027) to predict the number of Lac repressors per cell in each one of the six strains used in this work. These predictions were examined experimentally by counting the number of Lac repressors using quantitative immunoblots.
Fig. 5.
Fig. 5.
Determination of the in vivo binding energies. For each strain we combine the measurements of the fold change in gene expression with the corresponding number of repressors and solve Eq. 5 to obtain an estimate of the binding energies (dots). The energies obtained from the Oehler et al. data (33) are also shown. The lines correspond to using all measurements of the fold change in gene expression with their corresponding repressor numbers to fit Eq. 5 to obtain the best possible estimate for the binding energies. This fit is shown in Fig. S7B. The results of this approach are shown as horizontal lines and the shaded region captures the uncertainty.
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