Stimulus amplification, efficacy, and the operational model. Part II--ternary complex occupancy mechanisms

To understand how deviations from simple binary occupancy affect measures of efficacy, the generalized stimulus function developed in Part I was used to examine the actions of drugs in systems where occupation of the receptor was modeled using a two-state, ternary complex, or combination of mechanisms. Amplification of drug responses can occur during formation of an active agonist-receptor complex, during generation of the initial stimulus, and during signal transduction. Expressions were derived to characterize the separate contributions of these three phases. Ideally, comparison of relative intrinsic efficacy measures differences in the ability of the agonists to convert active complex into an active stimulus. In practice, differences in the ability of the drugs to form the stimulus-generating complex may also contribute to the efficacy ratio and must be taken into consideration. Failure to adequately account for differences in occupancy can result in overestimation of the efficacy ratio. The magnitude of the difference between true and experimental measures of intrinsic efficacy may be affected by G protein concentration, by the affinity between the G protein and receptor, and (in some models) by the receptor activation constant. Provided that the dissociation constant between the G protein and receptor is of the same order of magnitude as, or lower than the receptor concentration, however, experimental estimates should provide reasonably accurate estimates of the true efficacy ratio. In agreement with previously published experimental data, total G protein level was found capable of influencing agonist maximal response, Emax, and EC50 values in all four ternary complex models. The magnitude of the changes in Emax and EC50 appear to be dependent upon the efficacy of the agonist as well as characteristics of the post-receptor stimulus sequence.Additionally, the concentration-response relations for all four ternary complex models could be reduced to a modified operational format in which the apparent dissociation constant Kapp replaced the true KA, and an apparent operational efficacy, tauapp, replaced tau. tauapp can be estimated experimentally from measurements of the Kapp and EC50, while the operational maximum, Em, may be found from the calculated tauapp and the measured Emax of the response curve. These findings support the use of direct operational model-fitting in a variety of systems, regardless of the mechanisms underlying occupancy. Values of Kapp calculated using the exact formula for [ARG] displayed an anomalous rise or discontinuity where the concentrations of total G protein equaled that of the receptor protein. This discontinuity is not observed in the estimates based on approximations to [ARG], and may explain practical difficulties in evaluating the dissociation constant under these conditions.