Introduction

Top Abstract Introduction Methods Results Discussion References

Adenosine is believed to exert its physiological effects through interactions with at least four receptor subtypes: the A₁, A_2a, A_2b and A₃ receptors (see Fredholm et al., 1994). In the heart, stimulation of adenosine A₁ receptors produces negative dromo-, chrono- and inotropic effects (Olsson and Pearson, 1990) and adenosine itself has been used for the treatment of arrhythmias (Roden, 1996). On the other hand, the pronounced cardiodepressant effects have been a major impediment to the research into the potential of adenosine A₁ receptor agonists as drugs in other therapeutic areas, such as diseases of the central nervous system and lipid metabolism. Until recently, all known adenosine A₁ agonists appeared to behave as full agonists in every experimental system. Because greater organ selectivity can be expected of low-efficacy agonists as opposed to high-efficacy agonists (see Kenakin, 1993a), it has been proposed to design partial agonists for the adenosine A₁ receptor as novel pharmacological tools with less cardiac side effects (IJzerman et al., 1994, 1996).

In the search for partial agonists, several series of adenosine derivatives have been synthesized leading to the identification of analogs of CPA for which the ratio between apparent affinity in the presence and absence of GTP for the adenosine A₁ receptor in radioligand binding studies is lower than for CPA (Van der Wenden et al., 1995; Roelen et al., 1996). Because this ratio, generally referred to as "GTP shift," is considered to be a measure of efficacy (see Cohen et al., 1996; IJzerman et al., 1996; Kenakin, 1993b, 1996), it was concluded that these ligands are partial agonists for the adenosine A₁ receptor. Accordingly, the CPA analogs were tested for their in vivo effect on heart rate in the normotensive rat. By applying an integrated simultaneous pharmacokinetic-pharmacodynamic modeling approach, it was possible to describe the concentration-effect relationships by the three-parameter Hill equation. It was found that ligands with a reduced in vitro GTP shift displayed a lower in vivo intrinsic activity than CPA (Mathôt et al., 1995a; Van Schaick et al., 1997). Furthermore, the in vivo potency (EC₅₀) was correlated with the affinity (K_i) for the adenosine A₁ receptor obtained from radioligand binding studies. These results suggest that the in vivo pharmacodynamics of adenosine A₁ receptor agonists may be explained in mechanistic terms of the drug-receptor interaction, such as affinity and efficacy. However, analysis of concentration-effect data with the empirical Hill equation only provides limited insights in this matter because the potency of an agonist is determined by both affinity and efficacy. Furthermore, the intrinsic activity is a function of both compound (intrinsic efficacy) and system (receptor density and the function relating receptor occupancy to pharmacological effect) characteristics. Therefore, in the present study we have investigated to what extent a model of agonism which explicitly includes parameters for affinity and efficacy can explain differences between the in vivo effects of adenosine A₁ receptor ligands and whether it is possible to obtain meaningful estimates of apparent affinity and efficacy in vivo. It is important to answer these questions, because this will provide quantitative information about the adenosine A₁ receptor agonists and their physiological targets in vivo that was previously unattainable. Furthermore, it will provide a theoretical framework which can serve as a link between in vitro and in vivo studies in future research. Accordingly, we have developed a novel, mechanism-based pharmacokinetic-pharmacodynamic strategy based on the operational model of agonism (Black and Leff, 1983) and reanalyzed datasets of the in vivo effects on heart rate in rats of CPA (Mathôt et al., 1994), the deoxyribose CPA analogs 2dCPA, 3dCPA and 5dCPA (Mathôt et al., 1995a), the C8-amino-substituted analogs 8MCPA, 8ECPA, 8PCPA, 8BCPA and 8CPCPA (Van Schaick et al., 1997) and R-PIA (Mathôt et al., 1995b).

	Methods

Top Abstract Introduction Methods Results Discussion References

In vivo pharmacological experiments. The original data and details of the pharmacokinetic-pharmacodynamic experiments have been published previously (Mathôt et al., 1994, 1995a, b; Van Schaick et al., 1997). Two days before experimentation, the abdominal aortas of male Wistar rats (200-250 g) were cannulated by an approach through the left and right femoral arteries for the measurement of arterial blood pressure and the collection of serial blood samples, respectively, and the right jugular vein was cannulated for administration of drugs. Heart rate was captured from the pressure signal. Conscious, freely moving rats received an intravenous infusion of vehicle (20% dimethyl sulfoxide/water) or compound for 15 min. Continuous hemodynamic recordings started 30 min before the start of the infusion and were continued for at least 5 h. Serial arterial blood samples were hemolyzed immediately and stored at 35°C until high-performance liquid chromatography analysis of blood concentrations.

In vitro pharmacological experiments. The original data and details of the adenosine A₁ receptor radioligand binding studies have been published previously (Van der Wenden et al., 1995; Roelen et al., 1996). Rat cortical brain membranes were prepared according to the method of Lohse et al. (1984) with the modifications described by Van der Wenden et al. (1995). The binding assay was performed with 0.4 nM [³H]DPCPX as radioligand in the presence and absence of 1 mM GTP. Nonspecific binding was determined in the presence of 10 µM R-PIA.

Data analysis. Pharmacokinetic compartmental analysis was performed by fitting the blood concentration-time profiles to a biexponential function by use of the program Siphar (Simed S.A., Creteil, France) as described before (Mathôt et al., 1994; 1995a, b; Van Schaick et al., 1997). From each individual time-effect profile, 50 data points were sampled at regular intervals between the start of the infusion and the time of the last blood-concentration measurement. The pharmacokinetic fit was then used to calculate agonist blood concentrations at the times of the heart rate sampling. For each agonist, the individual concentration-effect curves thus obtained were fitted simultaneously to the Hill equation:

(1)

to obtain estimates of the upper asymptote (), the midpoint location (EC₅₀, estimated as pEC₅₀, that is logEC₅₀) and the midpoint slope (n_H). E₀ is the no-drug response, which was fixed to the value obtained by averaging data during a period of 30 min at the end of the experiment when the heart-rate had returned to a level not significantly different than that preceding the start of the infusion.

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

	Results

Top Abstract Introduction Methods Results Discussion References

In vivo concentration-effect relationships. With the exception of 8CPCPA, all CPA analogs investigated produced a significant decrease of the heart rate after intravenous infusion in the normotensive rat. Figure 1 shows the concentration-effect relationships that were derived from the concentration-time and effect-time profiles as described before (Mathôt et al., 1994, 1995a, b; Van Schaick et al., 1997). For each compound, all individual concentration-effect data were fitted simultaneously to the Hill equation to provide estimates (mean ± S.E. and ² for interindividual variation) of the concentration-effect curve upper asymptote (), midpoint location (pEC₅₀) and midpoint slope (n_H) after the procedure described under "Methods" (table 1). Parameter estimates for individual concentration-effect curves were then obtained by use of the Bayes estimation procedure implemented in the NONMEM program (see "Methods"). As an example, the results of the model fit for individual 8PCPA curves are illustrated graphically in figure 2. With 8BCPA, no significant effect on heart rate was observed in three of a total of six rats, and the data for these animals were not used for the estimation of the Hill equation parameters shown in table 1.

View larger version (30K): [in this window] [in a new window]   Fig. 1.   Blood concentration-effect relationships for the effect on heart rate in the normotensive rat after intravenous infusion of (A) 0.20 mg/kg CPA, (B) 20 mg/kg 2dCPA, (C) 1.2 mg/kg 3dCPA, (D) 0.80 mg/kg 5dCPA, (E) 4.8 mg/kg 8MCPA, (F) 4.8 mg/kg 8ECPA, (G) 4.8 mg/kg 8PCPA and (H) 8 mg/kg 8BCPA for 15 min. The lines shown superimposed on the experimental data points (n = 6-7) were obtained by simultaneous fitting of the data to the operational model of agonism (equations 2 and 9-11, see text for details and table 2 for parameter estimates). Abscissae, [agonist] (log10 M); ordinates, change in heart rate (beats per minute).

View this table: [in this window] [in a new window]   TABLE 1 Hill equation parameter estimates for the in vivo effects of CPA analogs and R-PIA on heart rate in the rat Parameter estimates (mean ± S.E, n = 6-7) for upper asymptote (), Hill slope (nH) and midpoint location (pEC50) were obtained by nonlinear mixed-effect modeling as described under "Methods." The variances (2) describing the interindividual parameter variation are shown in parentheses.

View larger version (22K): [in this window] [in a new window]   Fig. 2.   Model fitting of individual blood concentration-effect relationships for the effect on heart rate in six individual rats (A to F) after intravenous infusion of 4.8 mg/kg 8PCPA for 15 min. The dashed lines were simulated by use of the Hill model (equation 8) with the following NONMEM empirical Bayes estimates: (A) = 166, nH = 1.1, pEC50 = 6.0; (B)  = 189, nH = 1.2, pEC50 = 5.8; (C)  = 171, nH = 2.5, pEC50 = 6.3; (D)  = 87, nH = 1.9, pEC50 = 6.7; (E)  = 93, nH = 2.1, pEC50 = 6.0; (F)  = 21, nH = 3.7, pEC50 = 5.8. The solid lines were simulated by use of the operational model of agonism (equations 2 and 9-11) with pKA constrained to 5.53 (table 2) and with the following NONMEM empirical Bayes estimates: (A) Emax = 293, n = 1.0, log  = 0.19; (B) Emax = 306, n = 1.4, log  = 0.19; (C) Emax = 176, n = 2.7, log  = 0.87; (D) Emax = 219, n = 0.3, log  = 0.2; (E) Emax = 253, n = 1.1, log  = 0.004; (F) Emax = 266, n = 1.9, log  = 0.3. Abscissae, [agonist] (log10 M); ordinates, change in heart rate (bpm).

Estimation of apparent affinity and efficacy. Subsequently, an attempt was made to fit the individual concentration-effect curve data for each agonist to the operational model of agonism (equations 2 and 9-11). The values of E_max and n and the associated variances (²) describing the interindividual variation were constrained to the estimates of  (273 bpm, ² = 1920) and n_H (1.18, ² = 0.89), respectively, obtained with the agonist that displayed the highest intrinsic activity, 5dCPA (table 1). In all cases, the model converged and estimates of apparent affinity (pK_A) and efficacy () were obtained (table 2). For the sake of clarity, only the fits with the mean population parameter estimates are shown in figure 1 for each compound. However, by use of empirical Bayes estimation (see "Methods"), the model could also provide adequate descriptions of each individual curve, as illustrated in figure 2 for 8PCPA.

View this table: [in this window] [in a new window]   TABLE 2 Estimates of in vivo and in vitro affinity and efficacy for CPA analogs and R-PIA In vivo estimates of affinity (pKA) and efficacy (log ) were obtained by fitting the data to the operational model of agonism as described under "Methods." The variances (2) describing the interindividual log  variation are shown in parentheses. The values of Emax and n and the associated 2 values were constrained to the estimates for  and nH, respectively, obtained with 5dCPA (table 1). In vitro estimates of affinity (pKi) and efficacy (GTP shift) were taken from Van der Wenden et al. (1995) and Roelen et al. (1996). All estimates are shown as mean ± S.E.

View larger version (21K): [in this window] [in a new window]   Fig. 3.   Blood concentration-effect relationships for the effect on heart rate in the normotensive rat after intravenous infusion of 0.18 mg/kg R-PIA for 15 min. The dashed and solid lines shown superimposed on the experimental data points (n = 6) were obtained by simultaneous fitting of the data to the Hill equation (see table 1 for parameter estimates) and the operational model of agonism (see table 2 for parameter estimates), respectively.

View larger version (13K): [in this window] [in a new window]   Fig. 4.   Relationship between apparent in vivo pKA estimates for the heart rate effect in the rat based on (A) whole blood and (B) free plasma concentrations and pKi values for the adenosine A1 receptor in rat brain homogenates in the presence of GTP (table 2). The solid line was obtained by linear regression; the dashed line represents the line of identity.

View larger version (12K): [in this window] [in a new window]   Fig. 5.   Relationship between in vivo log  estimates obtained for the heart rate effect in the rat and GTP shifts (the ratio between apparent affinity in the presence and absence of GTP) found for the adenosine A1 receptor in radioligand binding studies (table 2). The line was obtained by linear regression (r = 0.92; P < .001) which yielded the following relation: log  = (0.32 × GTP shift)  1.30.

	Discussion

Top Abstract Introduction Methods Results Discussion References

To date, most pharmacokinetic-pharmacodynamic studies have used empirical models, such as the Hill equation, to describe concentration-effect relationships in vivo. Levy (1994), however, has pointed out the limitations of empirical models and called for a more mechanism-based approach in pharmacokinetic-pharmacodynamic modeling (see also Breimer and Danhof, 1997). Kenakin (1992) has suggested that by combining pharmacokinetic factors and drug-receptor theory in vivo studies can provide critical information about drug potency, efficacy and selectivity, although such information may be difficult to obtain because of the inherent complexity and heterogeneity of in vivo systems. The need for a mechanistic model has become particularly apparent during the course of our search for partial adenosine A₁ receptor agonists, because the expression of efficacy is not only a function of the intrinsic efficacy of a ligand but is also highly dependent on the system in which the receptor operates. Thus, to be able to predict whether a ligand will behave as a "full," "partial" or "silent" agonist for a particular pharmacological effect, a model is required which explicitly recognizes the protean nature of agonists in different systems expressing the same receptor. Therefore, in this paper, we have applied the operational model of agonism (Black and Leff, 1983) to obtain estimates of in vivo apparent affinity and efficacy at the rat cardiac adenosine A₁ receptor for a series of CPA analogs. Because the operational model of agonism contains an assumption about the algebraic form of the relation between response and concentration of agonist-receptor complex, it provides an explicit equation that describes agonist concentration-effect curves under different experimental situations and can account for tissue dependence of partial agonists (see Black and Leff, 1983; Black, 1996). Various groups have shown that the operational model of agonism can adequately describe experimental concentration-effect curves obtained in in vitro bioassays and yield consistent affinity and efficacy estimates for a variety of different agonist-receptor interactions (see Leff, 1988; Leff et al., 1990; Zernig et al., 1996). However, as far as we know, the operational model of agonism has been applied in only two in vivo studies of mu opioid receptor-mediated antinociception by Zernig et al. (1994, 1995). In contrast to the present study, however, these authors did not use an integrated pharmacokinetic-pharmacodynamic approach for their analysis and fitted agonist doses, rather than concentrations, to the model.

The main finding of the present study is that the operational model of agonism can account for the effects on heart rate of a series of CPA analogs (figs. 1 and 2) and provides estimates of in vivo apparent affinity and efficacy that are highly consistent with results obtained from in vitro radioligand binding studies at adenosine A₁ receptors (figs. 4 and 5). Therefore, the present approach allows for a meaningful integration of concepts of receptor theory into pharmacokinetic-pharmacodynamic modeling of the effects of adenosine A₁ receptor agonists and the mechanistic model provides a theoretical framework that can be used for quantitative analysis and for prediction of in vivo effects from data obtained in pharmacological in vitro experiments. Black and Leff (1983) have shown that intrinsic activity () can be defined in terms of E_max,  and n as follows:

(12)

Thus, without prejudice to mechanism, by combining this equation with the observed linear relation between log  and GTP shift (log  = (0.32 × GTP shift)  1.30, see fig. 5) a direct relation can be made between intrinsic activity in vivo and results from radioligand binding experiments. Notwithstanding the relatively large variability in the GTP shift measurements (table 2), figure 6 shows that at least in a qualitative manner the model provides a consistent description of the experimentally observed intrinsic activities. Only with 2dCPA a ~2-fold higher intrinsic activity would have been expected on the basis of the model. At present we have no explanation for this discrepancy, but it might be indicative for a difference in the mechanism of action of 2dCPA compared with the other CPA analogs. Note that the predicted intrinsic activity for 8CPCPA (~20 bpm, fig. 6) falls within the range of S.E. values estimated for the intrinsic activities of the other agonists (table 1), consistent with the fact that no significant effect was observed with this ligand. The validity of the model-based predictions is not confined to CPA analogs, because it was shown that the operational model could also account for the effects of a reference adenosine A₁ receptor agonist from a different chemical class, R-PIA (fig. 3).

View larger version (15K): [in this window] [in a new window]   Fig. 6.   Relationship between GTP shift at the adenosine A1 receptor and intrinsic activity for the in vivo effect on heart rate in rats. The solid line shows the predicted relationship that was derived from the operational model of agonism fitting results (equation 12). The filled circles correspond to the observed GTP shifts (table 2) and observed intrinsic activities in vivo (table 1) for each agonist.

It is interesting to note that in our in vitro rat brain membrane assay, the GTP shifts for a full (5dCPA) and practically "silent" (8CPCPA) adenosine A₁ receptor agonist differ less than 6-fold (table 2 and fig. 6). This relatively small range of GTP shifts is consistent with the observation that high-affinity agonist binding to adenosine A₁ receptors in rat brain membranes is relatively insensitive to guanine nucleotides (see Nanoff et al., 1995; Kenakin, 1996). Recently, Nanoff et al. (1995) have provided evidence that this phenomenon, referred to as "tight coupling mode," is caused by the presence of a distinct membrane protein ("coupling cofactor"), which traps the ternary agonist/G-protein complex in a stable conformation and thereby inhibits signaling of adenosine A₁ receptors.

Although du Souich et al. (1993) have pointed out that the relation between drug binding to plasma proteins and pharmacological response can be complex, intuitively it would be expected that estimates based on free plasma concentrations are a better reflection of the agonist dissociation equilibrium constant than estimates based on whole blood concentrations. However, in our analysis the pK_A estimates based on whole blood concentrations were virtually identical with the pK_i values (fig. 4A) whereas the pK_A estimates based on free plasma concentrations were ~0.5 log-unit higher than the pK_i values (fig. 4B). At present we have no explanation for this.

In the "comparative method" (Barlow et al., 1967; Leff et al., 1990) used in the present study, a reference full agonist is required to provide values of the system parameters, E_max and n, so that K_A and  for the partial agonist can be estimated. Obviously, the outcome of this method relies on the validity of the assumption that the reference agonist indeed behaves as a full agonist. Ideally, this assumption should be tested with the use of an irreversible antagonist, but such a ligand has not yet been available for the adenosine A₁ receptor. However, we have not yet encountered an adenosine A₁ receptor ligand which displays a higher intrinsic activity in vivo or yields a higher GTP shift in our radioligand binding assay than the ligand that was used as the reference full agonist in the present study, 5dCPA. Furthermore, a hypothetical E_max value higher than the maximum response elicited by 5dCPA (273 bpm) would not be physiologically meaningful, because this would imply the possibility of the occurrence of heart rate values of less than ~100 bpm, which would lead to complete cardiovascular failure in most animals. Therefore, the assumption that 5dCPA behaves as a full agonist at cardiac adenosine A₁ receptors in vivo seems to be valid, a conclusion that is supported by the excellent correlations between the outcomes of the operational model fitting and the results from radioligand binding studies. It is of interest to note that the present analysis indicates that CPA and R-PIA, which are generally considered to be reference full agonists for the adenosine A₁ receptor, behave as partial agonists in our model system. This finding, however, is not unprecedented because Fozard and Milavec-Krizman (1993) found that CPA and R-PIA produced smaller contractile responses in rat isolated spleen than another selective adenosine A₁ receptor agonist, CHA. In a preliminary study we have found evidence that CHA also behaves as a full agonist at the cardiac A₁ receptor in vivo (maximum reduction in heart rate after 15 min infusion of 0.3 mg/kg CHA: 268-277 bpm, n = 2).

Leff et al. (1990) and Van der Graaf and Danhof (1997) have pointed out that large between-tissue variation in E_max and/or the slope parameter (n) may result in erroneous estimates of affinity and efficacy and that in such cases the simultaneous operational fitting method should not be applied. However, although it has been shown that E_max can vary significantly between animals even under carefully controlled in vitro conditions (Leff and Dougall, 1989), this issue has been largely ignored in other accounts in the literature concerning applications of the direct operational model fitting approach. In the present paper, we have developed a method, based on nonlinear mixed effect modeling algorithms that were originally developed for the analysis of pharmacokinetic data (see Schoemaker and Cohen, 1996), that explicitly takes into account the interindividual variation in E_max and n and is thus more robust than the simultaneous fitting procedures proposed by Leff et al. (1990) and Zernig et al. (1996). Furthermore, this method may yield more insight in the factors that determine between-animal variation in concentration-effect profiles. Thus, the small values found for the variances (²) describing the interindividual variation of the efficacy parameter (, table 2) suggest that the two factors that determine , the total receptor concentration and the efficiency of the coupling between agonist-receptor complex and effect, are relatively constant between animals and that the variation in intrinsic activity seen with the same agonist is mainly caused by differences in E_max and n. This finding could be relevant with respect to the feasibility of the therapeutic strategy to obtain tissue selectivity based on efficacy. However, at present we do not know to what extent data obtained in our animal model can be extrapolated to humans.

In general, analysis of drug-receptor interactions is best quantified in isolated-organ or cellular in vitro bioassays because the concentration of drug at the receptor site and the effect of interfering regulatory mechanisms can be controlled more easily than under in vivo conditions. However, in the present study we have shown that it is possible to obtain meaningful measures of agonist affinity and efficacy at cardiac adenosine A₁ receptors in vivo by applying a simple operational model of agonism. The model may serve as a practical guide for future development of partial adenosine A₁ receptor agonists and help to elucidate the mechanisms underlying adenosine A₁ receptor-mediated responses in vivo.