Fig. 3.
Nine state model of the specific site (e.g. a promoter) for binding of a TF (green square) and a competitor (blue star). On the promoter, the TF and the competitor can bind to the unspecific site (white boxes) and the specific target site (red boxes). Both species occupy these sites exclusively. Since each site can have three states, empty, competitor or TF bound, there are 32 = 9 states of the promoter. The equilibrium constants are written in terms of the ratios bind/unbind with the rates Kl = λl/μl; Hl = Λl/ζ l = 1,2. The equilibrium constants H2,K2 are chosen such that the law of detailed balance is fulfilled. The direct arrival at the specific target site with 3D diffusion of the protein is K = λ/μ for the TF and H = Λ/ζ for the competitor. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)