Predictions of the effects of agonists with differing efficacies. (A) Concentration–response curves calculated using Eq. 1 for the high-efficacy agonist X (K_X = 20 µM, c_X = 0.004, N_X = 2) and the low-efficacy agonist Y (K_Y = 20 µM, c_Y = 0.02, N_Y = 2). The curves show calculated P_A in the presence of X or Y applied alone (solid blue and red lines, respectively) or X applied in the presence of 2 µM (EC₅), 35 µM (EC₅₀), or 500 µM (EC₉₅) agonist Y (dotted, dashed, or dash-dotted lines, respectively). (B) Response ratios (RR), calculated as a response to X + Y over the response to X alone, as a function of the concentration of agonist X. At low concentrations of X, coapplication of Y increases the current response, manifesting as RR > 1. Coapplication of the low-efficacy agonist Y reduces the response to intermediate concentrations of X (RR < 1). RR approaches 1 at high concentrations of X where the latter outcompetes Y. (C) Response ratios as a function of the P_A of the response to X. In the co-agonist model (Appendix), the coapplication of Y has no effect on the response to X (i.e., RR = 1) when P_A,X = P_A,max,Y. The calculations for three concentrations of Y (EC₅, EC₅₀, and EC₉₅) indicate different slopes but identical RR = 1 intercepts. The solid lines show linear fits to RR > 1 values. The fits are improved (lower residual sums of squares) at higher concentrations of Y. Note, that the value of P_A,max,Y from the high-concentration asymptote for the red line in panel A is identical to the value of the intercept in panel C (shown with arrow).