Introduction

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When characterizing responses mediated through receptors, selective antagonists are usually the drugs of choice. This preference is based on the widespread appreciation of the power of competitive inhibition, which enables the dissociation constants of antagonists (K_B values) to be estimated through functional antagonism. By comparing the K_B values of a handful of selective antagonists with their respective binding affinities (K_D values) measured in cell lines expressing recombinant receptors, it should be possible to identify the receptor subtype mediating a particular response in a tissue with a high degree of certainty.

In contrast, the interaction of agonists with receptors is complex. There are two elements to consider, the affinity and the intrinsic efficacy of the agonist-receptor complex, either of which can provide the basis for discrimination among receptor subtypes. Unfortunately, the estimation of these parameters can be difficult and laborious. Furchgott's method (Furchgott, 1966; Furchgott and Bursztyn, 1967) of partial receptor inactivation is appropriate for estimating the observed dissociation constant of an agonist provided that a single subtype of the receptor elicits the response. Knowing the observed affinities of a group of agonists, it is possible to establish their occupancy-response relationships and, thus, to estimate their relative efficacies. Alternatively, the affinity of an agonist for a G protein-coupled receptor might be deduced from its binding properties measured in the presence of a high concentration of GTP. Such conditions are analogous to those of the intact cell where GTP is abundant in the cytosol. Thus, binding methods in combination with concentration-response measurements can be used to establish the occupancy-response relationship of agonists. This approach has been used to show that the selective muscarinic agonist, McN A-343, has greater relative efficacy at M₄ and M₁ receptors compared with M₂ and M₃ receptors (Ehlert and Yamamura, 1995).

Although plausible, the methods described above are cumbersome and not always readily applicable to various receptor systems. A facile approach for estimating pharmacological activity would be one that only required the concentration-response curve of an agonist. To consider such an approach, it is necessary to account for the variation in the sensitivity of different responses mediated by the same receptor in the same or different tissues. Comparison of the potency of an agonist relative to that of a standard agonist (equipotent molar ratio) should be appropriate in situations where the agonists elicit the same maximal response. However, agonists often differ in their maximal responses, and until recently, there has been no simple means of using the components of potency and maximal response to calculate a quantitative measure of agonist activity. Our laboratory has recently described such a measure termed the "equiactive molar ratio" (EAMR), and we have calculated the EAMR values of the enantiomers of the muscarinic agonist, aceclidine (Ehlert et al., 1996). We found excellent agreement between guinea pig ileum and Chinese hamster ovary (CHO) cells expressing M₃ receptors with regard to the EAMR values of R- and S-aceclidine.

In the present report, we have modified our measure of agonist activity, and we now call it the "intrinsic relative activity " (IRA), which is essentially equal to the reciprocal of our prior EAMR value. We show that, for a group of muscarinic agonists, their IRA values for the phosphoinositide response of CHO cells expressing M₃ receptors are in excellent agreement with those measured for contraction in the guinea pig ileum, an M₃ response. This agreement was observed, although most of the agonists behaved as potent, full agonists in the contractile assay and less potent, partial agonists in the phosphoinositide assay. We also show through modeling techniques that the IRA value of an agonist is equivalent to the product of its affinity (reciprocal of the equilibrium dissociation constant; i.e., 1/K_D) and intrinsic efficacy, expressed relative to a standard agonist. This activity ratio can be envisioned as the theoretical equipotent molar ratio that would be observed in a highly sensitive assay where both the agonist and the standard agonist would behave as full agonists and elicit the same maximal response (100%). Our simple method for estimating IRA values is a powerful technique for characterizing the activity of agonists at different receptor subtypes.

	Materials and Methods

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Cell Culture. CHO cells expressing the human M₃ muscarinic receptor were grown in Dulbecco's modified Eagle's medium supplemented with fetal calf serum and antibiotics as described previously (Ehlert et al., 1996). Experimental assays were conducted in minimum essential medium (MEM) in 24-well culture plates at 37°C and in the presence of 5% CO₂.

Phosphoinositide Hydrolysis. Muscarinic receptor stimulated [³H]inositolphosphate accumulation was measured in CHO cells labeled with [³H]inositol as described previously (Ehlert et al., 1996). Briefly, growth media were removed from confluent CHO cell monolayers, and the cells were washed with an aliquot (0.5 ml) of MEM and incubated with MEM (0.5 ml) containing [³H]myo-inositol (0.2 µM; 23 Ci/mmol) for 18 h at 37°C in an incubator gassed with CO₂ (5%). After [³H]inositol incorporation, cells were washed once with MEM (0.5 ml), followed by two 10-min incubations at 37°C with MEM, first in the absence and then in the presence of LiCl (10 mM). Phosphoinositide hydrolysis was initiated with the addition of MEM (0.5 ml) containing LiCl (10 mM) plus various concentrations of muscarinic agonists. The assay was stopped after 30 min by aspirating the media and adding 0.31 ml of methanol. [³H]Inositolphosphates in the methanol extract were collected by a modification of the method of Berridge et al. (1982) as described previously (Ehlert et al., 1996).

Guinea Pig Ileum. Guinea pigs were euthanized with CO₂, and a section of ileum (2-3 cm) ~10 cm rostral to the cecum was removed. The ileum was washed clean with Krebs-Ringer bicarbonate (KRB) buffer (124 mM NaCl, 5 mM KCl, 1.3 mM MgSO₄, 26 mM NaHCO₃, 1.2 mM KH₂PO₄, 1.8 mM CaCl₂, and 10 mM glucose) and mounted longitudinally in an organ bath containing KRB buffer. Isometric contractions were measured with a force-displacement transducer and polygraph. The ileum was allowed to incubate for 40 min, and then three test doses of the muscarinic agonist, oxotremorine-M, were added to ensure that the contractions were reproducible and of sufficient magnitude. The ileum was washed and allowed to rest for 5 min between each test dose. Before measuring the concentration-response curve of an agonist, the KRB buffer was replaced with potassium-deficient KRB buffer (KRB buffer minus 5 mM KCl), and the ileum was allowed to equilibrate for 5 min. To measure the concentration-response curve of an agonist, 7 to 10 concentrations of the agonist were added to the bath in a cumulative fashion, with each concentration being spaced 0.32 log units.

Calculations. The EC₅₀ value (concentration of agonists causing a half-maximal response) and E_max value (maximal response) of an agonist were calculated from the concentration-response data by fitting a logistic equation to the data by nonlinear regression analysis as described previously (Candell et al., 1990). The IRA value of an agonist was calculated relative to carbachol using the following equation:

(1)

in which EC₅₀ and E_max denote the EC₅₀ and E_max values of the agonist, and EC_50  Carb and E_max  Carb denote the EC₅₀ and E_max values of the standard agonist, carbachol. The IRA value is essentially equal to the reciprocal of the EAMR value, the basis of which has been described previously (Ehlert et al., 1996). The IRA value was estimated for each experimental concentration-response curve, and the log mean ± S.E.M. values are reported in Table 7.

Modeling of Concentration-Response Curves. To investigate the validity of our IRA analysis, we constructed theoretical concentration-response curves for agonists of varying affinities and intrinsic efficacies and for responses showing high and low sensitivities. High sensitivity refers to a response for which the EC₅₀ value of the agonist is much lower (i.e., more potent) than its K_D value, whereas low sensitivity refers to a response for which the EC₅₀ value and K_D are approximately the same. Others have used the terms "high" and "low receptor reserve" to denote these situations.

(2)

(3)

(4)

View larger version (16K): [in this window] [in a new window]   Fig. 1.   Simulation of the concentration-response curves of agonists in a noncooperative system. Curves are shown for a standard agonist (), for agonist W with 20-fold lower affinity (), for agonist X with 20-fold lower intrinsic efficacy (), for agonist Y with both 20-fold lower affinity and intrinsic efficacy (), and for agonist Z with 100-fold higher affinity and 20-fold lower intrinsic efficacy (). A, a highly sensitive noncooperative system with K = 0.01 and n = 1. B, a less sensitive noncooperative system with K = 1 and n = 1. For all of the simulations RT = 1, and KD = 1 and  = 10 for the standard agonist. The parameters are defined in eq. 4.

View larger version (15K): [in this window] [in a new window]   Fig. 2.   Simulation of the concentration-response curves of agonists in a cooperative system. Curves are shown for a standard agonist (), for agonist W with 20-fold lower affinity (), for agonist X with 20-fold lower intrinsic efficacy (), for agonist Y with both 20-fold lower affinity and intrinsic efficacy (), and for agonist Z with 100-fold higher affinity and 20-fold lower intrinsic efficacy (). A, a highly sensitive cooperative system with K = 0.01 and n = 2. B, a less sensitive cooperative system with K = 1 and n = 2. For all of the simulations RT = 1, and KD = 1 and  = 10 for the standard agonist. The parameters are defined in eq. 4.

	Results

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Theoretical Concentration-Response Curves. To investigate the accuracy of our analysis, we calculated a series of theoretical agonist concentration-response curves and then determined whether our IRA analysis yielded results consistent with the affinities and intrinsic efficacies of the agonists. In this analysis, concentration-response curves are shown for the standard agonist (K_D = 1.0,  = 10), for agonist W having 20-fold lower affinity (K_D = 20,  = 10), for agonist X having 20-lower intrinsic efficacy (K_D = 1.0,  = 0.5), for agonist Y having both 20-fold lower affinity and intrinsic efficacy (K_D = 20,  = 0.5), and for agonist Z having 100-fold higher affinity and 20-fold lower intrinsic efficacy (K_D = 0.01;  = 0.5). The activity of each agonist relative to the standard agonist can be calculated as the product of the relative affinity and relative intrinsic efficacy as shown in the following equation:

(5)

In this equation, RA_A denotes the activity of agonist A relative to the standard agonist, K_A and K_S denote the dissociation constants of A and the standard agonist, and _A and _S denote the intrinsic efficacies of A and the standard agonist. Therefore, the relative activities of agonists W, X, Y, and Z are 0.05, 0.05, 0.0025, and 5.0, respectively. These values are listed in Tables 1 to 4 for comparison with the IRA values of the agonists.

View larger version (18K): [in this window] [in a new window]   Fig. 3.   The effect of changing intrinsic efficacy () on the concentration-response curves of agonists. The concentration-response curves are shown for the standard agonist (;  = 10), for agonist A (;  = 5), for agonist B (;  = 2.5), for agonist C (;  = 1.25), for agonist D (;  = 0.6), for agonist E (;  = 0.3), and for agonist F (;  = 0.15). A, an insensitive, noncooperative system with K = 1 and n = 1. B, an insensitive cooperative system with K = 1 and n = 2. For all of the simulations RT = 1, and KD = 1 and  = 10 for the standard agonist. The parameters are defined in eq. 4.

Phosphoinositide Hydrolysis in CHO Cells. To assess our analysis further, we compared the activity of a group of agonists in two different functional assays that are known to be mediated by the same receptor subtype. The first of these was agonist-stimulated phosphoinositide hydrolysis in CHO cells transfected with the human M₃ subtype of the muscarinic receptor. We measured complete concentration-response curves for arecoline, bethanechol, carbachol, McN-A343, pilocarpine, oxotremorine and oxotremorine-M (see Fig. 4). The data were analyzed by nonlinear regression to estimate the EC₅₀ value, maximal response (E_max) and Hill coefficient of each agonist for eliciting phosphoinositide hydrolysis. EC₅₀ values varied 50-fold from the most potent agonist, oxotremorine-M (EC₅₀, 0.33 µM) to the least potent agonist, bethanechol (EC₅₀, 17.3 µM). E_max values varied from 51-fold stimulation over basal (oxotremorine-M) to 6.8-fold stimulation (McN-A343). Hill coefficients did not differ much from 1 and ranged between 1.06 and 1.25. These data are summarized in Table 7, together with some data published previously from our laboratory on the enantiomers of aceclidine (Ehlert et al., 1996).

View larger version (22K): [in this window] [in a new window]   Fig. 4.   Effects of muscarinic agonists on phosphoinositide hydrolysis in CHO cells. , Oxotremorine-M; , oxotremorine; , carbachol; , arecoline; , S-aceclidine; ×, R-aceclidine; , pilocarpine; , bethanechol; , McN-A343. The data points represent the mean values of four experiments, each done in triplicate. The data for the enantiomers of aceclidine are from Ehlert et al. (1996). The average S.E.M. was 1.05-fold.

Guinea Pig Ileum. The second functional assay that we examined was the muscarinic contractile response of the guinea pig ileum, which is known to be mediated by the M₃ receptor (Eltze et al., 1993; Eglen, 1997; Ehlert et al., 1997). Complete concentration-response curves were measured for the agonists described above, and these are shown in Fig. 5. The data were analyzed by nonlinear regression to estimate the EC₅₀ value, maximal response (E_max), and Hill coefficient of each agonist. The EC₅₀ values varied 172-fold from a low value of 31.6 nM (oxotremorine-M) to a high value of 5.42 µM (McN-A343). Most of the agonists behaved as full agonists and exhibited similar maximal responses ranging from 85 to 126% that of carbachol. In contrast, the maximum responses for pilocarpine (75%) and McN-A343 (57%) were systematically lower. The Hill coefficients of all of the agonists except McN-A343 were similar, ranging from 1.74 to 2.14. The average Hill coefficient of McN-A343 was lower (1.65); however, it exhibited a relatively large standard error (0.31). This variation was due primarily to one large value of 2.96. When this latter value was omitted from the analysis, the average Hill coefficient of McN-A343 was 1.32 with a standard error of 0.10. Thus, compared with the phosphoinositide response of CHO cells, the guinea pig ileum behaves like a more sensitive response with a cooperative stimulus response relationship (n = 2; eq. 3) like that shown in Fig. 2. For such a system, full agonists exhibit Hill coefficients close to 2, whereas partial agonists, like McN-A343, exhibit lower Hill coefficients. The data for the guinea pig ileum are summarized in Table 7, together with some data published previously for the enantiomers of aceclidine (Ringdahl et al., 1982).

View larger version (17K): [in this window] [in a new window]   Fig. 5.   Effects of muscarinic agonists on the contractile response of the guinea pig ileum. , Oxotremorine-M; , oxotremorine; , carbachol; , arecoline; , pilocarpine; , bethanechol; , McN-A343. The data points represent the mean values of 21 experiments for carbachol, 5 experiments for McN-A343, and 6 experiments for the other agonists. The average S.E.M. was 5.7%.

IRA Calculations. We calculated the IRA values of the agonists from their EC₅₀ and E_max values for the phosphoinositide response and the contractile response using eq. 1. These values are expressed relative to carbachol and are listed in Table 7. It can be seen that there is excellent agreement between the CHO cells and the guinea pig ileum with regard to agonist IRA values, despite the large difference in the sensitivities of the two assays. All of the concentration-response curves in the CHO cells had Hill coefficients close to 1, indicating a lack of cooperativity in the stimulus-response function. This situation is analogous to the model shown in Fig. 1, where it was observed that the IRA value, calculated according to eq. 1, gave a reliable estimate of the relative activity of the agonist. As described in the preceding paragraph, the contractile response behaved like the cooperative system described in Figs. 2B and 3B. In such a system, the IRA value underestimates the activity of partial agonists, like pilocarpine and McN A343. Inspection of the IRA values for pilocarpine and McN-A343 shows that the values obtained in the guinea pig ileum are 2- to 3-fold lower than those measured in CHO cells, suggesting that the ileal values are erroneously low. Consequently, we used the method outlined in the Appendix to estimate the IRA values of pilocarpine and McN-A343 relative to carbachol in the guinea pig ileum. These new estimates are listed as "corrected IRA values" in Table 7. These corrected values in the guinea pig ileum for pilocarpine and McN-A343 (0.138 and 0.0174) are in good agreement with those calculated in CHO cells (0.150 and 0.0194). The excellent agreement between CHO cells and guinea pig ileum with regard to IRA values is shown in Fig. 6.

View larger version (32K): [in this window] [in a new window]   Fig. 6.   Comparison of the IRA values of agonists estimated from the phosphoinositide response in CHO cells () and the contractile response of the guinea pig ileum (). The IRA values were estimated from the data shown in Figs. 4 and 5. The IRA values are listed in Table 7.

	Discussion

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We contend that the product of affinity (1/K_D) and intrinsic efficacy () is a useful means of characterizing the activity of an agonist at a receptor. We now show that the IRA value of an agonist is equivalent to the product of its affinity and intrinsic activity expressed relative to the that of a standard agonist. We also show this parameter can be calculated from the agonist concentration-response curve. In most instances, estimates of EC₅₀ and maximal response (E_max) are all that is necessary.

The foregoing implies that the product of affinity and intrinsic efficacy is related to the graphical parameters of an agonist concentration-response curve. This interesting relationship is outlined in Fig. 7, which shows the concentration-response relationships for two agonists, A and B. Responses are plotted against the agonist concentration on a linear scale instead of the usual log scale. Assuming an operation model (i.e., eq. 4), it can be shown that the ratio of the initial slope of the concentration-response curve of agonist B divided by that of agonist A is equal to (_BK_A/_AK_B)ⁿ, where K_A and K_B denote the dissociation constants of A and B, and n denotes the exponent the in stimulus-response relationship (see eq. 3). Thus, the ratio of initial slopes is equivalent to IRAⁿ.

View larger version (15K): [in this window] [in a new window]   Fig. 7.   Relationship between the initial slopes of two concentration-response curves and the dissociation constants (Ka and Kb) and intrinsic efficacies (a and b) of two agonists (A and B). The parameters are defined in eq. 4.

It is not possible to dissect out the individual components of affinity and intrinsic efficacy from the IRA value; it is only possible to measure their product. However, this limitation is mitigated by two significant points: 1) whereas measurements of affinity and intrinsic efficacy are somewhat cumbersome and not widely tackled, the estimation of IRA only requires the measurement of a concentration-response curve; and 2) a considerable amount of pharmacology occurs at low levels of stimulus, and under these conditions, the behavior of an agonist is governed entirely by the product of its affinity and intrinsic efficacy. This concept can be appreciated by taking the limit of the stimulus function as the agonist concentration approaches zero (see eq. 2). It can be shown that this limit is equal to the product of the agonist concentration and the expression R_T/K_D. This latter expression is equivalent to the initial slope of the stimulus function for the agonist. When this slope is normalized with respect to the corresponding value of another agonist, the IRA value is obtained. The initial slope of an output function is a common means of assessing the sensitivity of a variety of transducers in electronics. Accordingly, the IRA value is a useful means of assessing the sensitivities of agonists. For a highly sensitive response, where most of the agonists behave as full agonists, differences in pharmacological activity are measured entirely by the EC₅₀ values of agonists. Under these conditions, the EC₅₀ value of an agonist divided by that of the standard agonist is equal to the IRA value. The same IRA value would be obtained in a less sensitive system, even if the agonist exhibited a lower maximal response than that of the standard agonist. In contrast, the potency ratio of the agonist (agonist EC₅₀ value divided by that of the standard) may change with the sensitivity of the system (e.g., see Fig. 1). The constancy of the agonist IRA value across systems of different sensitivities (i.e., different Ks, see eq. 3) illustrates its advantage over the agonist potency ratio.

Because affinity and intrinsic efficacy are probably unique properties of a given agonist-receptor complex, then the IRA value is also probably diagnostic of the particular agonist-receptor complex. Thus, the IRA value of an agonist is most likely constant when estimated from different responses mediated by the same receptor subtype. It should be possible to estimate the IRA values of agonists by examining their ability to trigger second messenger response in cell lines transfected with a specific receptor subtype. By comparing their respective IRA values in the cell line with those measured in a native tissue, it should be possible to deduce which receptor mediates the response of the tissue, provided that sufficiently selective agonists are used. In the present study, we noted exceptional agreement between IRA values calculated for M₃ receptors in CHO cells and guinea pig ileum (see Fig. 6). Just as we are comfortable assuming that the pA₂ value of an antagonist is a reliable measure of its affinity for a particular receptor subtype, we might also consider that the IRA value of an agonist is an equally reliable measure of agonist activity at a particular receptor subtype. In other words, the IRA value is a powerful tool for characterizing the activity of agonists at different receptor subtypes. An exception to this rule could occur if there are different active states of the agonist receptor complex that show different selectivities for different G proteins. Under such conditions, the pharmacological profile of an agonist could change depending upon the G protein with which it interacts (Leff et al., 1997). Regardless, our IRA analysis would be a useful means of determining whether such a phenomenon occurs. For example, the IRA values of agonists for eliciting responses in different cell lines expressing the same receptor but different G proteins could be calculated to determine whether receptor-G protein coupling affects agonist activity.

If the IRA value of an agonist is dependent mainly on the receptor subtype, then it should be relatively constant for all responses mediated through the same receptor. To get some idea of the how well this hypothesis holds true, we calculated the IRA values of selected agonists relative to carbachol from a variety of published studies in which the EC₅₀ values and maximal responses were measured in functional assays for the M₁, M₂, and M₃ subtypes of the muscarinic receptor. The most complete sets of data that we examined were those of Eltze et al. (1993), Lazareno et al. (1993), and Richards and van Giersbergen (1995). Eltze et al. (1993) measured the ability of agonists to stimulate contractions of the guinea pig ileum (M₃) and to inhibit the electrically stimulated rabbit vas deferens (M₁) and guinea pig atria (M₂). The other investigators measured responses in cell lines transfected with subtypes of the muscarinic receptor. These responses were agonist-stimulated GTPase activity [Lazareno et al. (1993)] and agonist-mediated phosphoinositide hydrolysis and inhibition of cAMP accumulation [Richards and van Giersbergen (1995)]. We also examined the data of Mei et al. (1991) on the phosphoinositide response in fibroblasts transfected with the M₁ receptor, those of Schwartz et al. (1993) on the phosphoinositide response in CHO cells transfected with the M₁ receptor, and those of McKinney et al. (1991) on inhibition of cAMP accumulation in CHO cells transfected with the M₂ receptor. Figure 8 shows the results of these calculations plotted as a scatter graph. Also included are the data from the present report. The average standard deviation for the IRA values of an agonist at a receptor subtype represented a 1.9-fold variation. The average IRA values at the M₁, M₂, and M₃ receptors were 0.98, 0.84, and 0.71 for arecoline; 10.2, 8.8, and 3.0 for oxotremorine; and 0.61, 0.24, and 0.24 for pilocarpine. Therefore, these agonists did not discriminate markedly among the M₁, M₂, and M₃ subtypes of the muscarinic receptor. In contrast, the IRA value of McN-A343 at M₁ receptors (0.70) was 43-fold greater than that observed at M₂ receptors (0.016) and 46-fold greater than that measured at M₃ receptors (0.015). This M₁ selectivity can account for the ability of McN-A343 to activate ganglionic muscarinic receptors (M₁) while having little action on muscarinic receptors in the heart (M₂) or smooth muscle (M₃) (Roszkowski, 1961; Jones, 1963). It has been shown that the selective action of McN-A343 is due to its greater intrinsic efficacy at M₄ and M₁ receptors as compared with M₂ and M₃ receptors (Ehlert and Yamamura, 1995).

View larger version (20K): [in this window] [in a new window]   Fig. 8.   Comparison of the IRA values of selected agonists estimated from published EC50 and Emax values. The IRA values relative to carbachol were calculated using eq. 1 and the published EC50 and Emax values of the agonists in a variety of different studies. The data are from Eltze et al. (1993) (), Lazareno et al. (1993) (), Richards and van Giersbergen (1995) (), Mei et al. (1991) (), Schwartz et al. (1993) (), McKinney et al. (1991) (), and the present study, CHO cells () and guinea pig ileum (). The details of the assays for M1, M2, and M3 muscarinic receptors are given in the text.

The variance of our simple IRA estimate appears to be similar to that of the more commonly used potency ratio. In fact, we found that the average standard deviation of the log IRA value (0.0778; i.e., 1.20-fold) was a little less than that of the log potency ratio (0.0959; i.e., 1.25-fold). It is interesting to compare the source of variation in the estimate of IRA and potency ratio. This variance includes the variation within the population (s_p²) and the error in estimation (s_e²), so that the total variance (s²) of each parameter is equal to the sum of its s_p² and s_e² (i.e., s² = s_p² + s_e²). Because the simple IRA calculation (eq. 1) includes four parameters (EC₅₀, EC_50  Carb, E_max, and E_max  Carb), whereas the potency ratio only includes two (EC₅₀ and EC_50  Carb), then the population variation of the IRA (IRA-s_p²) should be greater than that of the potency ratio (potency ratio-s_p²). This conclusion is based on the assumption that each parameter contributes to the total s_p². However, the greater IRA-s_p² is offset by the lower error in the estimation of IRA (i.e., smaller s_e²). In considering the source of the error in estimation (s_e²), it is useful to express the log potency ratio as log EC_50  Carb  log EC₅₀ and the log IRA as log (E_max/EC₅₀)  log (EC_50  Carb/E_max  Carb). Because errors in the estimation of EC₅₀ and E_max are correlated, there should be less error in the estimation of the ratio EC₅₀/E_max compared with the error in EC₅₀ alone. For example, if EC₅₀ is overestimated, so will be E_max such that the ratio (EC₅₀/E_max) will have less error than that of EC₅₀ alone. Consequently, the error in the estimation of IRA (IRA-s_e²) should be less than that of the potency ratio (potency ratio-s_e²). In summary, the IRA value should exhibit greater variation within the population as compared with the potency ratio; however, the error in the estimation of IRA should be less than that of the potency ratio. As a result, we would expect little difference in the variances of IRA and potency ratio. As described above, we actually observed a slightly lower variance for IRA as compared with the potency ratio.

Our IRA value also provides the basis for calculation of the relative efficacy of an agonist provided that the dissociation constants of the agonist and the standard agonist are known. Because the IRA value represents the product of the affinity and efficacy of an agonist expressed relative to that of a standard agonist, it should be possible to factor out the affinity component to estimate relative efficacy. A simple method for doing so is described in the Appendix (see eqs. A11 and A12).

In summary, we have described a simple and novel means of calculating the product of the affinity and intrinsic efficacy of an agonist expressed relative to that of a standard agonist. This product (IRA) can be estimated from a single concentration-response curve of an agonist. The simplicity of the IRA calculation contrasts with the more tedious, conventional means of estimating affinity and relative efficacy, which require measuring responses before and after partial receptor inactivation or measuring binding properties in addition to the functional response. Although more tedious, the latter approach does provide separate estimates of affinity and relative efficacy, whereas our IRA value only provides an estimate of their product. Nevertheless, the IRA value is superior to the potency ratio when full and partial agonists are compared with one another (see Tables 1B and 5-7). The IRA calculation can be applied to previously published EC₅₀ and E_max values so that the product of affinity and intrinsic efficacy can be extracted from literature already published (see Fig. 8). Most importantly, the IRA value can be used to address a variety questions that depend on knowledge of the affinity and intrinsic efficacy of an agonist. Some of these applications include: 1) the potency ratios of agonists in a highly sensitive system can be predicted from their IRA values in a less sensitive system (e.g., the phosphoinositide response of a cloned receptor in a cell line). Because a recombinant receptor is totally defined and the physiological responses of intact tissues are often highly sensitive, the IRA calculation provides a powerful means of predicting the activity of agonists from their behavior in cell lines transfected with recombinant receptors; 2) the IRA value can be used to determine what receptor mediates a given response; and 3) the IRA value can be used to determine whether agonist receptor activity is altered by the nature of the G protein with which the receptor interacts. In each of these applications, all that is required are the concentration response curves of agonists.