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Abstract
A system for the quantitative analysis of ligand-receptor interactions is presented, based on models of different levels of complexity. For two pools of receptors, binding of a radioactive ligand is described by b = [(Bml x A(nl))/(K(nl)dl + A(nl))] + [(Bm2 x A(n2))/(Kn2(d2) + A(n2))], (1) where b is the number of bound receptors at a ligand concentration [A], Bml and Bm2 are the receptor concentrations. Kdl and Kd2 are dissociation constants for the ligand-receptor complex, and n1 and n2 are Hill coefficients. The magnitude of the physiological response for a system consisting of two discrete pools of receptors with different affinities is given by p = [(Pm x A(nl))/(EC50(nl) + A(nl))] + [(Pm2 x A(n2)/(EC50(n2)2 + A(n2))], (2) where p is the magnitude of the response to an agonist (or antagonist) at concentration [A], Pml and Pm2 are the maximal magnitudes of the responses for the individual pools of receptors, EC50(1) and EC50(2) are the agonist concentrations giving responses of magnitudes Pm1/2 and Pm2/2, and n1 and n2 are Hill coefficients. The parameters of these equations show: the number of pools of receptors with different affinities for the ligand (Kd or EC50), the number of active receptors (Bmax) or the magnitudes of the maximal response (Pmax), and the numbers of ligand molecules binding with the receptor (n, the Hill coefficient). E is the efficiency (E = Bmax/2Kd, or E = Pmax/2EC50) and gives the overall characteristics of the activity of the effector system. This method of analysis can be applied to any biological reactions whose results can be presented quantitatively.