Measurement of the Proportion of D₂ Receptors Configured in State of High Affinity for Agonists in Vivo: A Positron Emission Tomography Study Using [¹¹C]N-Propyl-norapomorphine and [¹¹C]Raclopride in Baboons

The dopamine system plays an important role in the modulation of a large number of neuronal functions, including movement, drive, and reward, and alterations of dopamine transmissions are involved in numerous neuropsychiatric conditions, such as Parkinson's disease, schizophrenia, and substance abuse. Dopamine receptors belong to two families of receptors, D₁-like (including D₁ and D₅ receptors) and D₂-like (including D₂, D₃, and D₄) receptors (Seeman and Van Tol, 1994). Like all G protein-linked receptors, the affinity of D₂-like receptors for agonists is affected by the coupling of the receptors with G proteins. The high-affinity sites (D_{2 high}) are G protein-coupled, whereas the low-affinity sites (D_{2 low}) are those uncoupled with G protein. In vitro homogenate binding studies suggest that approximately 50% of D₂ receptors are configured in the D_{2 high} state (Sibley et al., 1982). However, very little is known about the proportion of D₂ receptors that are configured in D_{2 high} state (%R_high) in vivo.

Over the years, antagonists and inverse agonists such as [¹¹C]raclopride and [¹¹C]N-methyl-spiperone have been developed as radiotracers for imaging D₂-like receptors using positron emission tomography (PET). Because these antagonists and inverse agonists bind with equal affinity to both D_{2 high} and D_{2 low} receptors, or tend to preferentially bind to the D_{2 low}, they cannot provide information about the D_{2 high} receptors (Roberts and Strange, 2005).

(–)-N-Propyl-norapomorphine (NPA) is a full agonist at the D₂ and D₃ receptors (Neumeyer et al., 1973; Gardner and Strange, 1998). The in vitro affinity of NPA for D_{2 high} and D_{2 low} sites have been reported to be in the range of 0.07 to 0.4 nM and 20 to 200 nM, respectively, suggesting a 50- to 200-fold selectivity for D_{2 high} compared with D_{2 low} sites (for references, see Table 1).

Hwang et al. (2000) reported a procedure to radiolabel NPA with C-11 as well as initial imaging experiments in baboons using [¹¹C]NPA. In baboons, [¹¹C]NPA demonstrated a rapid brain uptake with selective accumulation in the striatum. The striatal uptake was decreased to the level of cerebellar uptake after pretreatment with the D₂ receptor antagonist haloperidol, indicating that the striatal uptake of [¹¹C]NPA was saturable and selective for D₂-like receptors. Furthermore, the uptake kinetics of [¹¹C]NPA were fast and amenable to quantitative analysis. In baboons, the binding potential (BP) of [¹¹C]NPA in the striatum was reported as 4.04 ± 1.05 ml g^–1 (Hwang et al., 2004).

Under tracer conditions, the BP of a radiotracer is proportional to the product of the site density (B_max) and affinity (1/K_D): where f₁ is the free fraction of the ligand in plasma. [¹¹C]NPA BP is the sum of the BP for D_{2 high} (BP_high) and D_{2 low} (BP_low). Denoting by R_high and R_low the densities of high- and low-affinity sites, and 1/K_high and 1/K_low the affinities of [¹¹C]NPA for high- and low-affinity states, [¹¹C]NPA BP (BP_NPA) can be expressed as follows: from which it seems that the contribution of BP_low to BP_NPA is likely to be small. For example, if we assume based on in vitro homogenate binding studies that in vivo 20 to 50% of the sites are configured in R_high and use the values reported by (Gardner and Strange, 1998) in Table 1 for K_high and K_low, the contribution of BP_low to BP_NPA would be approximately 9.6 to 2.3%.

Further characterization of BP_NPA requires in vivo measurement of K_high, K_low, R_high, and R_low. Because it was anticipated that the low affinity of [¹¹C]NPA for D_{2 low} would preclude the detection of the in vivo binding of [¹¹C]NPA to D_{2 low}, this question was approached by measuring [¹¹C]NPA K_high and R_high, and calculating %R_high by comparing R_high to the B_max of the antagonist [¹¹C]raclopride measured in vivo in the same animals.

Thus, in the present study, PET experiments were conducted in three baboons under noncarrier-added (NCA) conditions (tracer doses) and under carrier-added (CA) conditions (pharmacological doses) to estimate the in vivo affinity and maximal density of binding sites of [¹¹C]NPA and [¹¹C]raclopride. Experiments were conducted using the bolus plus constant infusion paradigm, which produces a state of sustained binding equilibrium at the level of the receptors (Laruelle et al., 1994a,b). Data were analyzed using three methods: simple equilibrium analysis (based on the analysis of the data during the equilibrium interval), kinetic analysis (based on the arterial input function), and a mixed method, denoted modeled equilibrium analysis, with peak equilibrium values estimated from the kinetic fit of the data (Slifstein et al., 2004b).

Materials and Methods

General Design

In total, 12 PET scans were acquired in three male baboons (Papio anubis; 25, 20, and 16 kg denoted A, B, and C, respectively), under two conditions (a NCA added condition followed by a CA condition), using two ligands ([¹¹C]raclopride and [¹¹C]NPA) over a duration of 180 days. The difference between the first scan and the fourth scan was 91, 5, and 62 days for baboons A, B, and C. The animals were not studied using any other radioligands or pharmacological challenges during this period to avoid alterations in D₂ receptor status.

The aim of this study was to determine the in vivo B_max and K_D for both [¹¹C]raclopride and [¹¹C]NPA using the bolus plus constant infusion paradigm (BCI). This method has been successfully used in the past to derive the B_max and K_D of tracers such as [¹²³I]iomazenil and [¹²³I]IBF (Laruelle et al., 1994a,b). Because plasma clearance obeys first-order kinetics, there is a simple relationship between the injected mass of the radioligand and the concentrations at steady state. Assuming both [¹¹C]raclopride and [¹¹C]NPA cross the blood-brain barrier by passive diffusion, the concentration of free radioligand is equal on both sides of the blood-brain barrier at equilibrium, an assumption that has been empirically validated for other radiotracers (Laruelle et al., 1994a). Thus, the BCI paradigm allows the relatively easy control of the concentration of free radioligand within the brain at steady state.

Preliminary experiments with both radiotracers were performed to define the optimal bolus-to-infusion ratio required to attain steady state for each animal. These experiments suggested that the bolus to infusion ratio (K_bol, the time that would be required to inject the bolus at the infusion rate) for [¹¹C]raclopride and [¹¹C]NPA should be 45 to 55 min and 50 to 65 min, respectively.

To determine the optimal doses to use in CA experiments, K_D values of 1.2 and 0.15 nM were assumed for [¹¹C]raclopride and [¹¹C]NPA (Kohler et al., 1985; Narendran et al., 2004). The specific activity of the radioligand was controlled such that the targeted levels of receptor occupancy at steady state would be less than 5% and approximately 60 to 70% for the NCA and CA experiments, respectively. For each animal, the sequence of radiotracers was counterbalanced to prevent bias in the between-radiotracer comparison.

Synthesis of [¹¹C]Raclopride and [¹¹C]NPA

[¹¹C]Raclopride and [¹¹C]NPA were prepared as described previously (Hwang et al., 2000; Mawlawi et al., 2001).

PET Imaging Protocol

Experiments were performed according to protocols approved by the Columbia University Medical Center Institutional Animal Care and Use Committee. Fasted animals were immobilized with ketamine (10 mg kg^–1 i.m.) and anesthetized with 1.8% isoflurane via endotracheal tube. Vital signs were monitored every 10 min, and temperature was kept constant at 37°C with heated water blankets. An i.v. perfusion line was used for the injection of radiotracers and a catheter inserted in a femoral artery was used for arterial blood sampling.

PET imaging was performed with ECAT EXACT HR+ scanner (Siemens/CTI, Knoxville, TN). After a 10-min transmission scan, emission data were collected in 3D mode for 90 min as successive frames (21 frames) of increasing duration for both [¹¹C]raclopride and [¹¹C]NPA.

Input Function Measurements

In total, 30 arterial samples were collected per experiment with an automated blood sampling system for the first 4 min followed by manual draws at various intervals. After centrifugation (10 min at 1800g), plasma was collected and activity measured in 0.2-ml aliquots on a gamma counter (Wallac 1480 Wizard 3M automatic gamma counter; PerkinElmer Life and Analytical Sciences, Boston, MA).

For both [¹¹C]raclopride (2, 4, 16, 50, 60, and 80 min) and [¹¹C]NPA (1, 4, 12, 40, 60, and 80 min), six samples were further processed using previously described HPLC procedures (Mawlawi et al., 2001; Hwang et al., 2004) to measure the fraction of plasma activity representing unmetabolized parent compound. The parent fraction was calculated as the ratio of parent to total activity. The parent fractions were fitted to the sum of two exponentials. The smallest exponential of the fraction of the parent curve, λ_par, was constrained to the difference between λ_cer (the terminal rate of washout of the cerebellar activity) and λ_tot (the smallest elimination rate constant of the total plasma) (Abi-Dargham et al., 1999). The input function was then calculated as the product of the total counts and the interpolated fraction parent at each time point.

The measured input function values [C_a(t); microcurie per milliliter] were fitted to: where C_0i is the zero time intercept of each exponential (nanomolar), λ_i is the elimination rate constant (minutes) associated with each exponential, f_0i is the fraction of zero time intercept associated with each exponential, and C_SS the free concentration at steady state (nanomolar). The first term of equation (eq. 3) represents activity due to the bolus and the second term the activity due to the constant infusion. C_SS is related to clearance (C_L; liters per hour) and the rate of infusion R_o (nanomoles per hour) by:

The plasma free fraction (f₁) was measured by ultrafiltration for both tracers using techniques described previously (Narendran et al., 2004).

Image Analysis

The striatum and cerebellum regions of interest were delineated on each baboon's brain MRI (a T1-weighted axial MRI sequence, acquired parallel to the anterior-posterior commissure; TR, 34 ms; TE, 5 ms; flip angle, 45°; slice thickness, 1.5 mm; zero gap, matrix 1.5 mm × 1 mm × 1 mm voxels).

Attenuation-corrected PET emission data were reconstructed with filtered backprojection, using a Shepp filter (cutoff 0.5 cycles/projection rays) and processed using the image analysis software MEDx (Sensor Systems, Inc., Sterling, VA). An image was created by summing all the frames, and this summed image was used to define the registration parameters for use with the MRI, using the between-modality automated image registration algorithm, as described previously (Mawlawi et al., 2001). Registration parameters were then applied to the individual frames for registration to the MRI data set. Regional boundaries were transferred to the individual registered PET frames, and time-activity curves were measured. Right and left striata were averaged. For a given animal, the same regional boundaries were used for both the NCA and CA experiments.

Derivation of Outcome Measures

Distribution Volumes. The regional tissue distribution volume (V_T; milliliters per gram) was defined as the ratio of the ligand concentration in a region (A_T; microcurie per milliliter) to the concentration of unmetabolized ligand in arterial plasma (C_SS; microcurie per milliliter) at equilibrium:

As the concentration of D₂ receptors is negligible in the cerebellum (Mawlawi et al., 2001), only free and nonspecifically bound radiotracer were considered to contribute to V_T in the cerebellum (V_{T CER}), and V_{T CER} was assumed to be equal to the nondisplaceable distribution volume (V₂). The striatal V_T (V_{T STR}) included V₂ and the specific binding distribution volume (V₃). It was assumed that the nondisplaceable distribution volume was equal in both regions. Therefore, V₃ was derived as V_{T STR} minus V_{T CER}.

Binding Parameters. The primary parameters of interest in this study were B_max, the concentration of sites (nanomoles per liter of tissue; nanomolar), and K_D, the in vivo equilibrium dissociation constant of the radiotracer (nanomoles per liter of brain water; nanomolar). Secondary parameters included the BP (milliliters per gram) and the specific-to-nonspecific partition coefficient (V₃″, unit-less). BP and V₃″ are related to B_max and K_D by: where f₁ and f₂ are the free fractions in the plasma and the nondisplaceable compartment, respectively. BP and V₃″ were derived only in NCA experiments. Derivation of B_max and K_D was determined by three analytical methods.

Method A. Simple Equilibrium Analysis. Equilibrium analysis was applied to the PET frames obtained from 40 to 90 min. The slope of the cerebellum and striatum activity over time expressed as a percentage of the mean value obtained from 40 to 90 min was used as a measure of the degree of equilibrium attained. The activity microcurie per milliliter) in the cerebellum (A_CER) and striatum (A_STR) were averaged from 40 to 90 min. V_{T CER} was derived as:

At equilibrium, the free tracer equilibrates across the blood-brain barrier so that the intracerebral free ligand concentration F_e (nanomolar) is equal to the free ligand concentration in plasma:

At equilibrium, the bound ligand concentration B_e (nanomolar), was derived as:

For each animal with each ligand, B_e and F_e data obtained from the NCA and CA experiments were fitted to the Scatchard plot equation (Scatchard, 1949): with K_D and B_max determined by linear regression. BP and V₃″ were derived in NCA experiments as V_{T STR} – V_{T CER} and BP/V_{T CER}, respectively.

Method B. Kinetic Analysis.Analysis of NCA experiments. Kinetic estimations of [¹¹C]raclopride and [¹¹C]NPA V_T were performed using kinetic analysis and the arterial input function. [¹¹C]Raclopride V_{T CER} and V_TSTR were obtained using a one-tissue compartment model (1TCM, two kinetic parameters, K₁ and k₂). [¹¹C]NPA V_{T CER} and V_{T STR} were obtained using a two-tissue compartments model (2TCM, four kinetic parameters, K₁ to k₄). The choice of 1TCM for [¹¹C]raclopride and 2TCM for [¹¹C]NPA was based on the goodness of fit.

In the 1TCM, V_T was derived from kinetic parameters as:

In the 2TCM, V_T was derived from kinetic parameters as:

Kinetic rate constants were estimated by nonlinear regression using a Levenberg-Marquardt least-squares minimization procedure implemented in MATLAB (Mathworks Inc., Natick, MA). BP and V₃″ were derived as described above.

Analysis of CA experiments. Data were fitted to the following nonlinear system of differential equations (Sadzot et al., 1991; Slifstein et al., 2004a): where C_a, C₂, and C₃ are the concentration in the arterial, nondisplaceable, and specific compartments, respectively, and k₊ = f₂k_on. K_D and B_max were determined as:

All the parameters (other than f₂, which was derived as f₂ = f₁/V_{T CER}) were estimated by nonlinear least-squares regression of the data onto the numerical solution of the differential equations with two constraints as described previously (Slifstein et al., 2004b): 1) the ratio K₁/k₂ in each experiment was constrained to V_{T CER} as estimated in that experiment; 2) the total regional distribution volume, K₁/k₂ × (1 + k₃/k₄), was constrained to the V_{T STR} measured in NCA experiments. All kinetic analysis was performed in the Matlab (Mathworks Inc.) software environment.

Method C. Modeled Equilibrium Analysis. The modeled equilibrium method was adapted from peak equilibrium analysis (Farde et al., 1986) and modified as described previously (Slifstein et al., 2004b). Data from each experiment were fitted by kinetic modeling as described above to yield modeled specifically bound and free plus nonspecifically bound curves. B_e was determined as the peak of the specifically bound curve. F_e was determined as f₂ times the value of the free plus nonspecifically bound curve at the time of peak specific binding. In other words, bound and free were both estimated from the values of these parameters that were determined from the kinetic fit within the region of interest itself and not from the difference between the region of interest and the reference region. Because the f₂ used in method C was obtained from the same kinetic fit outlined in method B, these methods were not truly independent of each other. For all three animals, data were fitted to the Scatchard plot equation (eq. 10), and K_D and B_max were determined as described above.

Statistical Analysis

Statistical analysis was performed with paired t tests to test differences between conditions (NCA and CA) unless otherwise specified. A two-tailed probability value of p ≤ 0.05 was selected as significant.

Results

Injected Dose and Mass

The mean injected dose for [¹¹C]raclopride was 2.07 ± 0.56 and 4.03 ± 1.45 mCi for the NCA (n = 3) and CA (n = 3) conditions, respectively. The mean injected mass for [¹¹C]raclopride was 1.05 ± 0.15 μg (3.0 ± 0.4 nmol) and 336 ± 87 μg (969 ± 250 nmol) for the NCA and CA conditions, respectively.

The mean injected dose for [¹¹C]NPA was 2.96 ± 1.25 and 3.60 ± 0.65 mCi for the NCA (n = 3) and CA (n = 3) conditions, respectively. The mean injected mass for [¹¹C]NPA was 1.24 ± 0.19 μg (4.2 ± 0.6 nmol) and 180 ± 7 μg (611 ± 22 nmol) for the NCA and CA conditions, respectively.

Plasma Parameters

Table 2 lists the plasma clearance, f₁, and C_SS for the NCA and CA conditions for both [¹¹C]raclopride and [¹¹C]NPA. Significant differences were evidenced in C_SS but not in clearance and f₁ between CA and NCA conditions for both tracers, demonstrating that the mass dose does not affect plasma clearance and nonspecific binding in plasma.

Brain Activity

Figure 1 displays the MRI and coregistered PET [¹¹C]raclopride and [¹¹C]NPA images in NCA experiments in the same baboon. Both [¹¹C]raclopride (Fig. 2) and [¹¹C]NPA (Fig. 3) reached an acceptable equilibrium level (as defined above) by 40 min in both the striatum and cerebellum. For [¹¹C]raclopride, changes over this interval were –2 ± 5%/h in the striatum and –8 ± 5%/h in the cerebellum. For [¹¹C]NPA, these changes were –1 ± 10%/h and –3 ± 10%/h in striatum and cerebellum.

Binding Parameters

Method A. Simple Equilibrium Analysis.Table 2 lists V₂ and f₂ for the NCA and CA conditions for both [¹¹C]raclopride and [¹¹C]NPA. No significant differences were noted in V₂ and f₂ between CA and NCA conditions for both tracers, demonstrating that the mass dose does not affect cerebellum distribution volume for both tracers. Table 3 lists the F_e, B_e, BP, and V₃″ for [¹¹C]raclopride and [¹¹C]NPA in all three baboons.

Table 4 lists the B_max and K_D of [¹¹C]raclopride and [¹¹C]NPA and the %R_high derived in all three baboons with the simple equilibrium analysis (Fig. 4).

Method B. Kinetic Analysis. The mean kinetic V₂ for [¹¹C]raclopride was 0.91 ± 0.34 and 0.75 ± 0.27 ml g^–1 for the NCA (n = 3) and CA (n = 3) conditions, respectively (paired t test, p = 0.15). The mean kinetic BP and V₃″ was 2.53 ± 1.25 and 2.71 ± 0.36 for the [¹¹C]raclopride NCA condition.

The mean kinetic V₂ for [¹¹C]NPA was 6.30 ± 0.56 and 5.40 ± 1.03 ml g^–1 for the NCA (n = 3) and CA (n = 3) conditions, respectively (paired t test, p = 0.38). The mean ¹ and 0.96 ± 0.33 for kinetic BP and V₃″ was 6.08 ± 2.45 ml g^– the [¹¹C]NPA NCA condition.

Table 4 lists the B_max and K_D of [¹¹C]raclopride and [¹¹C]NPA and the %R_high derived in all three baboons with the kinetic analysis. None of the outcome measures derived by kinetic analysis were significantly different from the outcome measures by simple equilibrium analysis.

Method C. Modeled Equilibrium Analysis.Table 4 lists the B_max and K_D of [¹¹C]raclopride and [¹¹C]NPA and the %R_high derived in all three baboons with the modeled equilibrium analysis. None of the outcome measures derived by the modeled equilibrium analysis were significantly different from the outcome measures derived by simple equilibrium and kinetic analysis.

Discussion

The two main findings of this study are 1) the in vivo affinity of [¹¹C]NPA is 0.16 nM and 2) the number of binding sites available to [¹¹C]NPA at this affinity is 21.6 ± 2.8 nM, corresponding to 79 ± 2% of the sites available to [¹¹C]raclopride (27.3 ± 3.9 nM). The technical strengths and weaknesses of the study design and the implications of these findings are discussed.

Agreement between the Methods

In this study, K_D and B_max were derived using three methods. The simple equilibrium analysis requires the establishment of a sustained equilibrium state. Because [¹¹C]raclopride and [¹¹C]NPA both have relatively fast kinetics, they achieved reasonable and comparable equilibria within the duration of the study. The agreement in the derivation of B_max and K_D between the kinetic analysis, which does not require attainment of equilibrium during the scan, and simple equilibrium analysis acted as an internal control. The agreement between these methods was strengthened by the modeled equilibrium analysis that integrates elements of each.

Opposite Effects of Raclopride and NPA on Endogenous Dopamine

The acute administration of D₂ antagonists and D₂ agonists at pharmacological doses during the CA condition induces an increase or decrease of dopamine concentration relative to that under tracer conditions (Bunney et al., 1973a,b). Because this change in endogenous dopamine could present a source of potential artifact, the effect of such changes on the measured in vivo B_max and K_D for the antagonist [¹¹C]raclopride and agonist [¹¹C]NPA as determined by a two-point Scatchard plot was assessed (see Appendix). This analysis shows that depending on the magnitude of change in endogenous dopamine concentrations after a pharmacological CA dose, both the B_max and K_D are underestimated for the antagonist [¹¹C]raclopride and overestimated for the agonist [¹¹C]NPA. The effect of this artifact would be to underestimate differences between [¹¹C]raclopride and [¹¹C]NPA maximal density of available sites (i.e., %R_high might be lower, but not greater than the 79% estimated by our data).

Effects of Anesthesia on Fraction of R_high

Another potential confound for this study is the effect of anesthesia (isoflurane and ketamine) on the binding parameters of both radiotracers. In vitro homogenate binding studies using anesthetic doses of ketamine and isoflurane have been shown to inhibit the high-affinity state of D₂ receptors (Seeman and Kapur, 2003). It is possible that under unanesthetized conditions the in vivo [¹¹C]NPA B_max and [¹¹C]raclopride K_D may be higher than reported here due to a higher proportion of R_high and the resultant increased endogenous competition by dopamine. This is unlikely to change the [¹¹C]raclopride B_max and [¹¹C]NPA K_D. Future experiments in unanesthetized animals are necessary to address these issues.

[¹¹C]Raclopride Binding Parameters

The in vivo K_D of [¹¹C]raclopride measured in this study (1.59 ± 0.28 nM) was in agreement with in vitro values (Table 5) reported to be in the 1 to 2 nM range. In contrast, the [¹¹C]raclopride in vivo K_D reported in this study is lower than in vivo values reported using PET (Table 6), which range between 8 and 12 nM. As noted previously (Laruelle et al., 1994b), this discrepancy results from the use of total cerebellum activity to represent free ligand in the previous PET studies. Taking into account that only 14.6 ± 2.1% of the cerebellum concentration is free (f₂, Table 2), the previously reported values of [¹¹C]raclopride K_D would be revised to approximately 1.5 nM after f₂ adjustment, consistent with the reported in vitro values as well as our in vivo [¹¹C]raclopride estimate of K_D.

This discrepancy in the definition of the free parameter does not affect the B_max estimate. The striatum [¹¹C]raclopride D₂B_max (27.3 ± 3.9 nM) measured in this study is consistent with the range for striatum D₂B_max reported in the PET literature (Table 6). Of note, two of the three animals used in this study were also included in a previous PET study measuring the B_max of another D₂ receptor antagonist of the benzamide family ([¹⁸F]fallypride) (Slifstein et al., 2004b). The [¹⁸F]fallypride B_max (28.0 ± 10.9 nM) measured in these two animals (baboon A and B) was very close to their [¹¹C]raclopride B_max measured here (27.0 ± 5.4 nM), highlighting the consistency of the B_max measurements with antagonist radioligands.

[¹¹C]NPA Binding Parameters. In vitro, the binding of NPA to D₂ receptors is best fitted by a two site model (Table 1), and the high-affinity state is converted to low-affinity state in the presence of GTP (Grigoriadis and Seeman, 1985). In this study, the two-point Scatchard plots of [¹¹C]NPA fitted to a one-site model estimated an affinity of 0.16 ± 0.01 nM, values that are consistent with the affinity of NPA for D_{2 high} measured in vitro (Table 1). This agreement between the in vivo and in vitro values for K_D strongly suggest that the in vivo binding of [¹¹C]NPA measured with PET corresponds to binding to D_{2 high} receptors. In theory, an in vivo multiple point Scatchard plot of [¹¹C]NPA could be fitted to a two site model. However, given the 70:30 ratio of R_high/R_low (Narendran et al., 2004) and the likely 100 fold difference between the K_high and K_low (Sibley et al., 1982) this procedure would be problematic. This is because the inflection of the curve due to low affinity site binding would only become apparent at saturation levels greater than 80%, where the signal to noise ratio of PET is too low to provide useful data (see simulation in Fig. 5). Therefore, a two-point fit was chosen based on the assumption that it would be representative of high-affinity site binding.

The in vivo [¹¹C]NPA site density was significantly smaller than that of [¹¹C]raclopride, suggesting a difference in the nature of sites labeled by both compounds. Assuming this difference is because [¹¹C]NPA binds only to D_{2 high} and [¹¹C]raclopride binds to both D_{2 high} and D_{2 low}, 79 ± 2% of D₂ receptors are D_{2 high}. This also implies that, under tracer conditions, the contribution of D_{2 low} to [¹¹C]NPA BP is truly negligible. Using eq. 2 and the results of the present study (%R_high of 79%), the contribution of D2 low to [¹¹C]NPA BP would be only 0.26%.

The fundamental result of this study (R_high = 79 ± 2%) is in agreement with the results of a previous study comparing the vulnerability of [¹¹C]raclopride and [¹¹C]NPA to endogenous competition by DA (Narendran et al., 2004). Three male baboons were studied with [¹¹C]raclopride and [¹¹C]NPA under baseline conditions and after administration of amphetamine. The amphetamine-induced decrease in binding potential (ΔBP) of [¹¹C]NPA was on average 1.42 times greater that of [¹¹C]raclopride at each dose tested. Assuming a 30% occupancy of D₂ receptors by DA in anesthetized baboons (Laruelle et al., 1997), the results of that study predicted the %R_high to be 79% (see Fig. 7 in Narendran et al., 2004), consistent with the direct measurement of %R_high in the current study (79 ± 2%).

This result is also consistent with a recent PET study conducted in rhesus monkey by Kortekaas et al. (2004). In that study, the authors demonstrated the ability of another D₂/D₃ agonist (+)-PD 128907 (which in vitro demonstrates a relatively higher preference to bind to D₃ receptors) to displace striatal [¹¹C]raclopride binding in an orderly dose-dependent manner that followed a one-site fit to a maximum of 85%. This led the authors to conclude that in vivo there was no evidence in favor of a multiple sight model representing the high- and low-affinity receptors or the D₂ and D₃ subtype. Alternatively, these results could be interpreted as evidence for a majority of D₂/D₃ receptors to be configured in a state of high affinity for agonists (Kortekaas et al., 2004).

The results of this study are also consistent with an in vitro study measuring D_{2 high} and D_{2 low} with autoradiography (Richfield et al., 1989), a setting in which endogenous receptor coupling is more likely to be preserved than in homogenates (where %R_high has been reported in the range of 12 to 50%; Sibley et al., 1982; Seeman et al., 2002). Competition studies of [³H]spiperone with dopamine revealed biphasic competition curves, and %R_high was 77%, a value in the range of our in vivo estimate (79%). Guanine nucleotides completely converted the high-affinity site to a low-affinity site. In contrast, for D₁ receptors, %R_high was only 21%. The difference in %R_high between D₁ and D₂ receptors might explain why the in vivo binding of D₂ and not D₁ receptor antagonist radioligands are decreased by challenges that increase endogenous DA (Abi-Dargham et al., 1999)

In conclusion, results of in vivo PET saturation experiments conducted in three baboons with the D₂ antagonist [¹¹C]raclopride and the D₂ agonist [¹¹C]NPA demonstrated a large proportion (70–80%) of D₂ receptors configured in D_{2 high} state in vivo. This is likely to contribute to the potency of endogenous dopamine to affect the binding of D₂ receptor radiotracers. This also indicates that at tracer dose, [¹¹C]NPA BP is almost exclusively associated with D_{2 high} sites. Thus [¹¹C]NPA seems to be an appropriate tool to study D_{2 high} in health and disease.

Appendix

Effect of Pharmacological Dose of Antagonist versus Agonist on in Vivo Affinity as Determined by Scatchard Plot

We examine the effect on K_D determined by two-point Scatchard plot when the high-occupancy dose has pharmacological effects. We look at two cases: increased extracellular endogenous neurotransmitter during the high-mass dose (antagonist) and decreased endogenous neurotransmitter (agonist) during the high-mass dose. In each case, we assume that there is baseline occupancy by endogenous transmitter, so that the reference value is not K_D, but , where R is the baseline ratio of the extracellular concentration of endogenous ligand to its inhibition constant.

Case 1: Antagonist. In this case, the equilibrium equations for the low mass and high mass doses are: where B_L, F_L, B_H, and F_H are bound and free radiotracer under low- and high-mass dose conditions, K_D′ is as described above, and γ = R₂/(1 + R), where R₂ is the increase in the ratio R after the high-mass dose.

By dividing these expressions by F to obtain B/F and rearranging to obtain the slope (B_H/F_H – B_L/F_L)/(B_H – B_L), the measured Scatchard slope –1/K_D is seen to equal: where the factor f is the expression in parentheses. From this, it follows that K_D′ is f times as large as K̂_D. Note first that f always exceeds 1 because the expression (B_max – B_L)/(B_H – B_L) always exceeds 1. Because, lacking evidence to the contrary, the endogenous neurotransmitter level during the high-mass measurement is potentially orders of magnitude larger than the baseline level, the range of the term γ is effectively unbounded. As γ becomes infinitely large, f approaches (B_max – B_L)/(B_H – B_L). Making the realistic assumption that B_L << B_H < B_max, the limiting value of f is approximately B_max/B_H. In other words, exceeds K̂_D at most by the reciprocal of the radioligand occupancy of the high-mass scan. If, for example, during the high mass measurement there is 70% occupancy by radioligand, then the bounds on are .

Case 2: Agonist. For clarity, we make the simplifying assumption that, after the high-mass dose, the extracellular concentration of endogenous neurotransmitter is 0. In this case, the conditions are: where the K_D in the denominator of the high-mass expression is the true in vivo K_D, not .

For this case, the Scatchard slope is: The term occ_EN is the baseline occupancy by endogenous neurotransmitter. Making the same assumption as mentioned above that B_L << B_H and defining occ_RL as the occupancy by radioligand during the high-mass measurement, this becomes: With the further assumption as stated above that B_H = 0.7 B_max, this reduces to: For occ_EN in the literature range of 10 to 30%, the bounds on are .

Effect of Pharmacological Dose of Antagonist versus Agonist on in Vivo B_max as Determined by Scatchard Plot

Rearrangement of the Scatchard equation to isolate the B_max estimator leads to: where f refers to the factor by which K_D′ is changed, as described in the two cases mentioned above. For the present case, where there are two points (high and low mass), both points are on the regression line, so these equations are an identity; either the low- or high-mass observed values can be substituted into the equation and equality will be preserved.

When the low-mass values are substituted into the equation, the formula is the same for both the agonist and antagonist cases, although the meaning of the factor f is different in the two cases, as described above. The result is:

Making the same tracer dose approximation as mentioned above, such that , this is approximately: i.e., the B_max estimate will be altered in the same direction and to approximately the same extent as the affinity estimate. This result has the intuitive interpretation that if the low-mass scan is performed under truly tracer dose conditions, then the datum (B_L, B_L/F_L) will be very close to the y-axis, so that rotations of a line about this point will cause little change in the y-axis intercept; i.e., true binding potential (B_max/K_D without reference to any free fraction) will be nearly preserved. Because the ratio of the two factors remains relatively unchanged, the factors themselves will be altered to the same extent.