Fig. 1.

Model and predictions for one drug. (A) The state diagram for drug X with two sites acting on a receptor after the MWC concerted transition scheme. Inactive receptor states (R) occupy the line at the bottom, whereas active states (A) occupy the line at the top. In the absence of X, the receptor activates with the inverse of the activation equilibrium given as L = R/A. Agonist X binds to its site with dissociation constant K_X,R on the inactive receptor and K_X,A on the active receptor, with c_X = K_X,A/K_X,R. In the scheme, K_X = K_X,_R. The equilibrium between R and A states is determined by c, as dictated by detailed mass action in the coupled cycles. (B) Activation curves (P_A) as a function of [X] for three combinations of parameters. For all the relationships, N_X = 2 and K_X = 100 (K_X = K_X,R). The values for L and c_X were varied as shown in the figure legend. (C) A log-log plot of the normalized EC_50,X against L for three values of N_X with c_X = 0.01 and K_X,R = 100. The lines show slopes of 1/N_X, whereas the filled symbols show the predicted values for the asymptotes. Note that the EC₅₀ value can be less than K_X,A (=1 in the normalized plot) or greater than K_X,R (=100 in the normalized plot). (Panel modified from Akk et al., 2018). (D) The Hill coefficient plotted against L for different values of c_X (0.1, 0.03, 0.01, and 0.001, as indicated) whereas for all plots in the panel N_X = 3, K_X,R = 100. Estimates were made using eq. 1.16.