(A) RNAP (light blue) and a repressor compete for binding to a promoter of interest. There are RA repressors in the active state (red) and RI repressors in the inactive state (purple). The difference in energy between a repressor bound to the promoter of interest versus another non-specific site elsewhere on the DNA equals ΔεRA in the active state and ΔεRI in the inactive state; the P RNAP have a corresponding energy difference ΔεP relative to nonspecific binding on the DNA. NNS represents the number of non-specific binding sites for both RNAP and repressor.
(B) A repressor has an active conformation (red, left column) and an inactive conformation (purple, right column), with the energy difference between these two states given by ΔεAI. The inducer (blue circle) at concentration c is capable of binding to the repressor with dissociation constants KA in the active state and KI in the inactive state. The eight states for a dimer with n = 2 inducer binding sites are shown along with the sums of the statistical weights of the active and inactive states.