Theoretical and Experimental Dissection of DNA Loop-Mediated Repression

Transcriptional networks across all domains of life feature a wide range of regulatory architectures. Theoretical models now make clear predictions about how key parameters describing those architectures modulate gene expression, and the ability to construct genetic circuits with tunable parameters enables precise tests of such models. We dissect gene regulation through DNA looping by tuning network parameters such as repressor copy number, DNA binding strengths, and loop length in both thermodynamic models and experiments. Our results help clarify the short-length mechanical properties of DNA.

Figure 1

Loop-mediated gene regulation is tuned by parameters incorporated into a thermodynamic model. (a) Lac repressor reduces gene expression by binding its operators, including binding to both operators and looping the intervening DNA. (b) A thermodynamic model of gene regulation contains the states of the two operator constructs, their associated weights, and the rates of transcription from each state. (c) The model predicts the influence of each parameter on gene expression, as captured in the experimentally measurable quantity repression defined in Eq. (1). (d) 3D plot of repression as a function of number of repressors per cell and the main operator binding energy for $\Delta F_{\mathrm{loop}}(L)=9k_{\mathrm{B}}T$ and $r_2=r_3$. YFP, yellow fluorescent protein; RNAP, RNA polymerase.

Figure 2

Titrating the number of repressors per cell resulted in repression levels similar to predicted values. (a) To predict how repression scales with number of repressors, we first measured repression for a strain with the wild type number of repressors per cell ($11\pm 2$) and used the equation from Fig. 1c to calculate the looping energy. The prediction, as depicted by the dashed black line with the shaded region defining the 95% confidence interval, was compared to other experimental measurements. Global fits of all data points in the figure to the main operator binding energy and the looping energy are shown with the blue solid line and green dotted line respectively. (b) Repression as a function of loop length for two different values of the repressor number per cell. The black dashed line and shaded region show the parameter-free prediction for 130 repressors per cell using the best fit main operator binding energy calculated in (a). The blue solid line shows the global fit to the main operator binding energy for the 130 repressors per cell data. Error bars are standard error.

Figure 3

The looping energy is independent of operator binding energies. (a) Repression measurements for constructs in which the main operator was O2 and the auxiliary operator was Oid (black circles) were used to predict how repression scales with the main operator binding energy. The family of curves illustrates how repression responds to $0.5k_{\mathrm{B}}T$ shifts in the binding energy of the main operator. The red line shows the prediction using the previously reported binding energy to operator O1 [22], in close agreement with measurements of Oid-O1 constructs (blue diamonds). (b) The looping energies extracted from both operator combinations are within error. Error bars represent standard error.

Figure 4

Correcting for direct upstream repression when calculating looping energies. (a) Regulatory interactions occur between RNA polymerase and the Lac repressor bound to a nearby upstream operator, skewing in vivo measurements of looping based on gene expression. (b) To account for direct auxiliary repression in looping constructs, we measure $r_3/r_2$, at each operator distance. (c) Correcting the two operator model from Fig. 1b to account for direct auxiliary repression reveals increased looping energies for the shortest loops and restores a uniform periodicity of repression with length at short operator distances. Error bars represent standard error.