Cell surface receptors bind their cognate signaling molecules (labeled L) with a

Question

Cell surface receptors bind their cognate signaling molecules (labeled L) with a dissociation
constant KL. There are also antagonists (labeled I) that mimic the signaling molecule
structurally and bind to the same receptor with dissociation constant KI. (Many such antagonists are used as medications to treat a variety of disease states.) Both of these equilibria are shown below. The relative affinities of the signaling molecule and antagonist for the receptor is indicated by the ratio of the concentration of the receptor-signal complex
in the presence ([R.L]I) and the absence ([R.L]O of inhibitor. The value of the antagonistconcentration that produces a value of 0.5 for this ratio is symbolized as [I50]. Show that the above concentration ratio is given by relationship (1) below and that the dissociation constant of the receptor-antagonist complex is given by relationship (2)

Explanation / Answer

tive GPCR activity by Costa and Herz (1989) indicated that receptors could couple to and activate G proteins in the absence of ligand. This necessitated the modification of the original TCM described by De Lean et al. (1980), which did not have the capability of spontaneous formation of the R*G species, into the extended ternary complex model (ETC model; Samama et al., 1993), as is shown in Fig. 2C. From this scheme, it can be seen that the amount of active-state receptor available for subsequent coupling to G protein is given by the isomerization constant L. Therefore, increasing the relative stoichiometry of receptors versus G protein leads to an elevated abundance of R*G, the species responsible for agonist independent response (constitutive receptor activity). For example, for a system containing 1000 receptors and a value for L of 0.001, there will be one single R* species. However, if the receptor number were to be increased by a factor of 1000, then the number of receptors in the signaling R*G form would be 1000. By increasing the number of receptors present in the system, the number of spontaneously active receptors can be increased until a threshold is attained where the resulting response from the spontaneously formed R*G species can be observed. The ETC model was, thus, the first GPCR model to explicitly incorporate allosteric transitions between receptor states (e.g., governed by L and ) and allosteric interactions between multiple binding sites (e.g., governed by and ). Although the ETC model went beyond the original ternary complex model to accommodate experimental findings, it is thermodynamically incomplete. Again, this is directly related to the principle of free energy coupling described above, and has culminated in the development of the more thermodynamically complete, albeit more complex, cubic ternary complex (CTC) model by Weiss et al. (1996a– c; Fig. 2D, left). Although the CTC model is formally more correct than the ETC model, this correctness comes at a price of carrying too many parameters to allow for useful estimation based on experimental observations. In turn, this can make the model less predictive. Therefore, in practical terms, it is worth considering whether the more complex CTC model is worth applying to experimental data instead of the ETC model. The critical issue is the need for the ARG complex, the nonsignaling ternary complex between ligand, receptor, and G protein. here are two approaches that can be used to try to determine which model, ETC or CTC, has greater utility in the receptor pharmacology of GPCR systems. One is the biochemical evaluation of the evidence for the existence of the inactive ARG complex. To date, there is a paucity of such evidence but it is not clear whether this is because of the apparent rarity of this species in biological systems or because of the lack of tools for detecting this species. There are isolated cases where experimental data are consistent with the existence of a nonsignaling ternary complex species. One example involves the inverse agonist ICI-174,864 (N,N-diallyl-TyrAib-Aib-Phe-Leu-OH) acting at the Gi/o -coupled -opioid receptor expressed in HEK 293 cells (Chiu et al., 1996). Whereas the opioid agonist DPDPE mediated an inhibition of forskolin-stimulated cAMP accumulation, ICI- 174,864 caused a further stimulation of the cAMP response above the basal forskolin response, consistent with the inverse agonist properties previously ascribed to ICI-174,864 (Costa and Herz, 1989

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