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NEUROPHARMACOLOGY
Departments of Psychiatry (R.N., D.-R.H., M.S., Y.Hw., Y.Hu., J.E., O.G., E.S., D.M., M.L.) and Radiology (D.-R.H., M.L.), Columbia University College of Physicians and Surgeons and the New York State Psychiatric Institute, New York, New York
Received May 25, 2005; accepted July 7, 2005.
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Abstract |
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). 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 (D2 high) are G protein-coupled, whereas the low-affinity sites (D2 low) are those uncoupled with G protein. In vitro homogenate binding studies suggest that approximately 50% of D2 receptors are configured in the D2 high state (Sibley et al., 1982). However, very little is known about the proportion of D2 receptors that are configured in D2 high state (%Rhigh) 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 D2 high and D2 low receptors, or tend to preferentially bind to the D2 low, they cannot provide information about the D2 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 D2 high and D2 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 D2 high compared with D2 low sites (for references, see Table 1).
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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 (Bmax) and affinity (1/KD):
 | (1) |
 | (2) |
) in Table 1 for Khigh and Klow, the contribution of BPlow to BPNPA would be approximately 9.6 to 2.3%. Further characterization of BPNPA requires in vivo measurement of Khigh, Klow, Rhigh, and Rlow. Because it was anticipated that the low affinity of [11C]NPA for D2 low would preclude the detection of the in vivo binding of [11C]NPA to D2 low, this question was approached by measuring [11C]NPA Khigh and Rhigh, and calculating %Rhigh by comparing Rhigh to the Bmax 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).
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Materials and Methods |
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The aim of this study was to determine the in vivo Bmax and KD 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 Bmax and KD 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 (Kbol, 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, KD 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, 
par, was constrained to the difference between cer (the terminal rate of washout of the cerebellar activity) and 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 [Ca(t); microcurie per milliliter] were fitted to:
 | (3) |
i is the elimination rate constant (minutes) associated with each exponential, f0i is the fraction of zero time intercept associated with each exponential, and CSS 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. CSS is related to clearance (CL; liters per hour) and the rate of infusion Ro (nanomoles per hour) by:
 | (4) |
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 x 1 mm x 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 (VT; milliliters per gram) was defined as the ratio of the ligand concentration in a region (AT; microcurie per milliliter) to the concentration of unmetabolized ligand in arterial plasma (CSS; microcurie per milliliter) at equilibrium:
 | (5) |
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 VT in the cerebellum (VT CER), and VT CER was assumed to be equal to the nondisplaceable distribution volume (V2). The striatal VT (VT 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 VT STR minus VT CER.
Binding Parameters. The primary parameters of interest in this study were Bmax, the concentration of sites (nanomoles per liter of tissue; nanomolar), and KD, 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 Bmax and KD by:
 | (6) |
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 (ACER) and striatum (ASTR) were averaged from 40 to 90 min. VT CER was derived as:
 | (7) |
At equilibrium, the free tracer equilibrates across the blood-brain barrier so that the intracerebral free ligand concentration Fe (nanomolar) is equal to the free ligand concentration in plasma:
 | (8) |
At equilibrium, the bound ligand concentration Be (nanomolar), was derived as:
 | (9) |
For each animal with each ligand, Be and Fe data obtained from the NCA and CA experiments were fitted to the Scatchard plot equation (Scatchard, 1949):
 | (10) |
Method B. Kinetic Analysis. Analysis of NCA experiments. Kinetic estimations of [11C]raclopride and [11C]NPA VT were performed using kinetic analysis and the arterial input function. [11C]Raclopride VT CER and VTSTR were obtained using a one-tissue compartment model (1TCM, two kinetic parameters, K1 and k2). [11C]NPA VT CER and VT 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, VT was derived from kinetic parameters as:
 | (11) |
In the 2TCM, VT was derived from kinetic parameters as:
 | (12) |
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):
 | (13) |
 | (14) |
All the parameters (other than f2, which was derived as f2 = f1/VT 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 VT CER as estimated in that experiment; 2) the total regional distribution volume, K1/k2 x (1 + k3/k4), was constrained to the VT 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. Be was determined as the peak of the specifically bound curve. Fe 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 KD and Bmax 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.
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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 CSS for the NCA and CA conditions for both [11C]raclopride and [11C]NPA. Significant differences were evidenced in CSS 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.
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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.
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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 Fe, Be, BP, and V3'' for [11C]raclopride and [11C]NPA in all three baboons.
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Table 4 lists the Bmax and KD of [11C]raclopride and [11C]NPA and the %Rhigh derived in all three baboons with the simple equilibrium analysis (Fig. 4).
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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 Bmax and KD of [11C]raclopride and [11C]NPA and the %Rhigh 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 Bmax and KD of [11C]raclopride and [11C]NPA and the %Rhigh 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.
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Agreement between the Methods
In this study, KD and Bmax 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 Bmax and KD 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 Bmax and KD 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 Bmax and KD 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., %Rhigh might be lower, but not greater than the 79% estimated by our data).
Effects of Anesthesia on Fraction of Rhigh
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 Bmax and [11C]raclopride KD may be higher than reported here due to a higher proportion of Rhigh and the resultant increased endogenous competition by dopamine. This is unlikely to change the [11C]raclopride Bmax and [11C]NPA KD. Future experiments in unanesthetized animals are necessary to address these issues.
[11C]Raclopride Binding Parameters
The in vivo KD 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 KD 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 KD 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 KD.
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This discrepancy in the definition of the free parameter does not affect the Bmax estimate. The striatum [11C]raclopride D2 Bmax (27.3 ± 3.9 nM) measured in this study is consistent with the range for striatum D2 Bmax 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 Bmax of another D2 receptor antagonist of the benzamide family ([18F]fallypride) (Slifstein et al., 2004b). The [18F]fallypride Bmax (28.0 ± 10.9 nM) measured in these two animals (baboon A and B) was very close to their [11C]raclopride Bmax measured here (27.0 ± 5.4 nM), highlighting the consistency of the Bmax 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 D2 high measured in vitro (Table 1). This agreement between the in vivo and in vitro values for KD strongly suggest that the in vivo binding of [11C]NPA measured with PET corresponds to binding to D2 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 Rhigh/Rlow (Narendran et al., 2004) and the likely 100 fold difference between the Khigh and Klow (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.
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The fundamental result of this study (Rhigh = 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 (
BP) 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 %Rhigh to be 79% (see Fig. 7 in Narendran et al., 2004), consistent with the direct measurement of %Rhigh 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 D2 high and D2 low with autoradiography (Richfield et al., 1989), a setting in which endogenous receptor coupling is more likely to be preserved than in homogenates (where %Rhigh 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 %Rhigh 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, %Rhigh was only 21%. The difference in %Rhigh 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 D2 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 D2 high sites. Thus [11C]NPA seems to be an appropriate tool to study D2 high in health and disease.
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Appendix |
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, 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:
 | (A1) |
= 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 (BH/FH – BL/FL)/(BH – BL), the measured Scatchard slope –1/KD is seen to equal:
 | (A2) |
D. Note first that f always exceeds 1 because the expression (Bmax – BL)/(BH – BL) 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 is effectively unbounded. As becomes infinitely large, f approaches (Bmax – BL)/(BH – BL). Making the realistic assumption that BL << BH < Bmax, the limiting value of f is approximately Bmax/BH. In other words, 
exceeds 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:
 | (A3) |
.
For this case, the Scatchard slope is:
 | (A4) |
 | (A5) |
 | (A6) |
are 
.
Effect of Pharmacological Dose of Antagonist versus Agonist on in Vivo Bmax as Determined by Scatchard Plot
Rearrangement of the Scatchard equation to isolate the Bmax estimator leads to:
 | (A7) |
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:
 | (A8) |
Making the same tracer dose approximation as mentioned above, such that 
, this is approximately:
 | (A9) |
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Acknowledgements |
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Footnotes |
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ABBREVIATIONS: PET, positron emission tomography; NPA, N-propyl-norapomorphine; NCA, noncarrier-added; CA, carrier-added; BCI, bolus plus constant infusion paradigm; MRI, magnetic resonance imaging; (+)-PD 128907, (S)-(+)-(4aR,10bR)-3,4,4a,10b-tetrahydro-4-propyl-2H,5H-[1]benzopyrano-[4,3-b]-1,4-oxazin-9-ol hydrochloride; TCM, tissue compartment model.
Address correspondence to: Dr. R. Narendran, New York State Psychiatric Institute, 1051 Riverside Dr., Box #31, New York, NY 10032. E-mail: rn2012{at}columbia.edu
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