Fig. 2.

The state diagram and concentration-response relationships for two drugs acting at different sites. (A) A partial state diagram for two drugs (X and Y, each with two sites) acting on a receptor. Inactive receptor states (R) occupy the plane at the bottom [note that some states are obscured (e.g., YRX, Y₂RX)], while active states (A) occupy the plane at the top. The diagram is distorted to show states with only agonist X bound (solid line box at front) and only agonist Y bound (short dash line box at left); the other states have both agonists bound. In the absence of both X and Y, the receptor activates constitutively with L = R/A. Agonist X binds to its site with dissociation constant K_X,R on the resting receptor, and K_X,A on the active receptor, with c_X = K_X,A/K_X,R. Agonist Y binds to a different site, with dissociation constant K_Y,R on the resting receptor and K_Y,A on the active receptor, with c_Y = K_Y,A/K_Y,R. In the scheme, K_X = K_X,R and K_Y = K_Y,R. Note that the presence of bound Y does not affect the binding of X or vice versa. The equilibrium between R and A states is determined by the respective values for c, as dictated by detailed mass action in the coupled cycles. (Panel modified from Akk et al., 2018). (B) The activation curve for drug X at various concentrations of drug Y. (The numbers indicate the background P_A elicited by [Y] present.) (C) shows the decrease in the EC₅₀ value for X as [Y] increases, so L* steadily decreases. (D) shows the same data for the EC₅₀, but now plotted as a function of the increasing background P_A elicited by Y. (B–D) L = 1000, N_X = 2, K_X = 100, c_X = 0.01, and N_Y = 2, K_Y = 30, c_Y = 0.01. For (B), the values for [Y] were 0, 2, 4, 10, and saturating, which produced background P_A values of 0, 0.05, 0.14, 0.40, and 0.91, respectively, and resulted in L* values of 1000, 19.4, 6.25, 1.51, and 0.10. In (C and D), additional points are plotted for values of [Y] of 1 and 30, producing P_A values of 0.02 and 0.72, and L* values of 56.9 and 0.39.