Figure 2.

Statistical mechanics of recruitment (a) Schematic showing the relationship between the various states of the promoter and its regulatory region, and their corresponding weights within the statistical mechanics framework. (b) Fold-change in promoter activity as a function of the number of activated (inducer-bound) CRP molecules, according to Equations 5 and 8, for different values of the adhesive interaction energy between activator and RNAP. As in Figure 1, $\mathrm{\Delta }{\epsilon }_{ad}=k_{B}Tln(K_{ad}^S/K_{ad}^{NS})$, with $K_{ad}^{NS}=10000\text{nM}$ [40] and $K_{ad}^S=0.02\text{nM}$ [41]. These in vitro numbers are chosen as a representative example to provide intuition for the action of activators. Applications to in vivo experiments are given in the accompanying paper [1^••]. Several different representative values of the adhesive interaction ε_ad that are consistent with measured activation are chosen to illustrate how activation depends upon this parameter.