Figure 2. The single-locus model and reciprocity.

(A) Linear framework graph for the TF $X$, showing the microstate, b, in which $X$ is specifically bound to DNA and the microstate, nb, in which $X$ is not specifically bound. (B) Graph adapted from Figure 1B for the cell line in which Sox2 is measured and Oct4 is induced and taken to be at thermodynamic equilibrium, with only the ratios of binding to unbinding labels being shown. The subscripts $S$ and $O$ denote Sox2 and Oct4, respectively, the superscript $i$ denotes ‘induced’ and $\omega$ is the cooperativity. (C) As in B for the cell line in which Oct4 is measured and Sox2 is induced. Panels B and C define the single-locus model at thermodynamic equilibrium. (D) Plot of the reciprocity, $\mathrm{\Gamma }$, (orange surface), as defined in Equation 20, against the concentrations, [Sox2${}^i$] and [Oct4${}^i$], of the induced TFs, for the single-locus model with parameter values at thermodynamic equilibrium. The flat blue plane indicates $0$. (E) As in panel D but for parameter values away from thermodynamic equilibrium, calculated as described in the text and the Materials and methods. Only a single off-rate, corresponding to $k_4^{-}$ from so to o in Figure 1B, was increased from the equilibrium value used in panel D, thereby breaking detailed balance. With this change, the reciprocity becomes negative throughout and can equal the reciprocity of $\mathrm{\Gamma }=-0.22$ calculated from the data of Chen et al. (Materials and methods), indicated by the flat brown plane. Numerical parameter values are given in the Materials and methods.