Hunting for the high‐affinity state of G‐protein‐coupled receptors with agonist tracers: Theoretical and practical considerations for positron emission tomography imaging

Abstract The concept of the high‐affinity state postulates that a certain subset of G‐protein‐coupled receptors is primarily responsible for receptor signaling in the living brain. Assessing the abundance of this subset is thus potentially highly relevant for studies concerning the responses of neurotransmission to pharmacological or physiological stimuli and the dysregulation of neurotransmission in neurological or psychiatric disorders. The high‐affinity state is preferentially recognized by agonists in vitro. For this reason, agonist tracers have been developed as tools for the noninvasive imaging of the high‐affinity state with positron emission tomography (PET). This review provides an overview of agonist tracers that have been developed for PET imaging of the brain, and the experimental paradigms that have been developed for the estimation of the relative abundance of receptors configured in the high‐affinity state. Agonist tracers appear to be more sensitive to endogenous neurotransmitter challenge than antagonists, as was originally expected. However, other expectations regarding agonist tracers have not been fulfilled. Potential reasons for difficulties in detecting the high‐affinity state in vivo are discussed.


| Oligomerization-dependent high-affinity state
The growing amount of evidence on GPCR oligomerization in cultured cells and living tissues 25 and on the pharmacological relevance of such oligomerization (see Ferre et al 26 for review) has given rise to the concept of oligomerization-dependent high-affinity state. When the agonist interacts with a receptor oligomer, occupying and activating a single receptor unit within it, conformational changes in this receptor influence the conformation of other receptors within the same oligomer and decrease their affinity for other agonist molecules ( Figure 3). In other words, separation into high-and low-affinity states is caused by negative cooperativity effects of the agonist binding to oligomerized receptors. 27 Receptor oligomerization is arguably mainly relevant for the explanation of the interplay between signaling pathways of different receptors 26 : interaction between oligomer subunits is conceptually simpler than interference of downstream cascades. However, among data from radioligand binding studies there are also some results that could be explained better by oligomerization than by G-protein coupling, such as: (i) GTP-insensitive high-affinity agonist binding to dopamine D 3 and serotonin 5-HT 2A receptors, 28,29 (ii) detection of high-and low-affinity states of F I G U R E 2 GPCR activation (left circuit, open arrows) and GTP cycle (right circuit, solid arrows). As in Figure 1, the agonist is represented by a triangle, the G-protein by an ellipse and the receptor by a sinusoid line. The center of the figure shows the "ternary complex" consisting of agonist, receptor and G-protein. GPCR, G-protein-coupled receptor; GTP, guanosine triphosphate F I G U R E 3 Oligomerization-dependent high-affinity state. In this schematic representation, the receptors are drawn as homodimers. Most higher order G-protein-coupled receptor complexes are homodimers, heterodimers or tetramers consisting of two different homodimers. The high-affinity state of the receptor is pictured as a sinusoid, the low-affinity state as a compressed sinusoid, and the agonist as a triangle is pictured as a compressed sinusoid and the agonist as a triangle SHALGUNOV ET AL. | 1017 adenosine A 2A receptors by antagonist ligands, 30 and (iii) detection of several (more than two) binding sites with different affinities to agonists in the muscarinic M 2 receptor population. 31 If there is cooperativity between receptor-agonist and receptor-receptor interaction, agonist binding might influence the degree of receptor oligomerization. Some studies indeed report such phenomena 32,33 but, in general, experimental data on the relationship between ligand binding and oligomerization are contradictory both in terms of whether ligand binding really promotes formation or dissociation of oligomers and whether this action is correlated with intrinsic activity (see Cottet et al 34,35 for review).

| Influence of agonist binding on the high-affinity state
In both G-protein coupling and oligomerization-dependent models of high-affinity state, agonist binding to the receptor influences receptor interaction with other molecules and thus can alter the relative abundance of the high-affinity state.

| G-protein-dependent high-affinity state
Under conditions where no feedback loops are present, as is the case with in vitro binding studies with nonliving material like membrane homogenates and tissue slices, the relationship between agonist concentration and percentage of receptors in the high-affinity state at equilibrium is straightforward. In the absence of GTP, agonist binding can only increase G-protein recruitment. Therefore, increasing agonist concentration will make the percentage of receptors in the "G-protein-dependent" high-affinity state grow from some "floor" value (see Section 2.5) to the "ceiling" value determined by receptor-G-protein stoichiometry in the system (100% if the number of available G-proteins is greater than or equal to the number of receptors). On the other hand, in the presence of excess GTP and negligible GTP hydrolysis, all G-proteins activated by agonist-bound receptors will be dissociated and uncoupled from the receptors, so at any agonist concentration, there will be no discernible high-affinity state.
In living cells and tissues, however, the GTP cycle plays the role of a negative-feedback loop, which counteracts excess high-to-low or low-to-high conversion of affinity states caused by the agonist. Depending on the combination of concentrations and kinetic rates, either G-protein-recruiting or G-protein-dissociating effects of an agonist can become dominant. Indeed, mathematical simulations of GPCR signaling have demonstrated the possibility of both agonist-induced increase and decrease in the relative abundance of the G-protein-dependent high-affinity state. 22

| Oligomerization-dependent high-affinity state
Negative cooperativity in agonist binding to oligomerized receptors implies that increasing agonist concentration will bring more and more receptors into "low-affinity state." The percentage of receptors in the high-affinity state, equal to 100% in the absence of agonist, will decrease to 100%/N (N is the average number of receptors per oligomer) when the agonist occupies one receptor unit in each oligomer, converting all the other units to lowaffinity state. When agonist concentration raises so high that agonists start to occupy receptors in the low-affinity state, the relative abundance of the high-affinity state will fall even lower. There are no well described and widely accepted feedback loops for the oligomerization-dependent model of the high-affinity state.

| Agonist-induced receptor internalization
Activation of GPCRs by agonists promotes not only G-protein binding to them but also their phosphorylation by G-protein-coupled receptor kinase (GRK) and internalization mediated by β-arrestins. 36 This provides an extra pathway through which the agonist can influence the relative abundance of the high-affinity state. Internalized receptors are decoupled from G-proteins (coupled to β-arrestins instead) and removed from the cell surface to intracellular compartments, where the ionic environment and pH value can be different from extracellular conditions. This makes internalized receptors less accessible (especially for hydrophilic radioligands) and possibly also alters their affinity toward their ligands.
In vitro, β-arrestin recruitment can happen within minutes. 37,38 Internalization of dopamine D 2/3 receptors was observed within the same time frame in vivo and was shown to be dose-dependent. 39 Although it is not yet clear whether internalization mainly happens to receptors in the low-or high-affinity state, 40,41 internalized dopamine D 2/3 receptors on intact cells and µ-opioid receptors incubated in a buffer imitating endosomal medium were shown to have decreased affinities toward their ligands. 42,43 Therefore, high concentrations of an agonist can promote receptor internalization and change the number and relative abundances of receptor subpopulations with different affinities toward imaging radioligands. On the other hand, in internalization-deficient β-arrestin knockout mice, baseline binding of dopamine D 2/3 agonist and antagonist tracers was the same as in wild-type controls. 44 This may mean that at basal neurotransmitter levels there already is an equilibrium between neurotransmitter-induced receptor internalization and recycling.

| Relative abundance of high-affinity state in the absence of the agonist
The oligomerization-dependent model of the high-affinity state implies that this is the state in which all receptors are configured in the absence of the agonist.
For the G-protein-dependent high-affinity state, its baseline relative abundance, that is, the degree to which G-proteins interact with the receptors in the absence of agonist is a matter of debate. 45,46 One extreme view, called collision coupling ( Figure 4A), states that in living cells G-proteins are not normally bound to the receptors but instead interact with them transiently when receptors become activated. 47 Another extreme view ( Figure 4B) states that G-proteins are always bound (precoupled) to the receptors and do not decouple even after activation, which happens through structural rearrangement of the G-protein rather than through dissociation. [48][49][50] On the one hand, collision coupling provides a straightforward interpretation of differences in intrinsic activities of the agonists: agonist efficacy is related to the number of different G-proteins that an agonist-bound receptor can bind and activate per unit of time. Decoupling of G-proteins from the receptors upon activation explains the disappearance of the high-affinity state upon GTP addition in membrane homogenates. On the other hand, receptors and G-proteins are known to be coisolated by immunoprecipitation and bioluminescence resonance energy transfer/fluorescence resonance energy transfer (BRET/FRET) experiments with mutated proteins incorporating fluorescent or bioluminescent probe demonstrate close contact between receptors and G-proteins in the absence of agonists. 45 Moreover, in BRET studies with α 2 adrenergic and δ-opioid receptors, these receptors were found to interact with G-proteins both before and after activation by agonist. 49,50 F I G U R E 4 Two extreme modes of receptor-G-protein interaction. The agonist is represented by a triangle, the receptor by a sinusoid line and the G-protein by an ellipse. A, In the collision coupling model, G-proteins do not stably interact with receptors but agonist action on the receptor promotes G-protein recruitment to and activation by the receptors, which results in the dissociation of G-proteins. B, In the precoupling model, G-proteins are stably bound to the receptors and rearrange their structures upon activation instead of dissociating. GDP, guanosine diphosphate; GTP, guanosine triphosphate A middle ground between the extreme views is, of course, possible, where some G-proteins are bound to receptors at baseline but decoupled upon activation, or where G-proteins are uncoupled at baseline but become bound to receptors upon activation. Moreover, BRET and FRET experiments image the whole population of the receptors, so constant presence of a RET signal, while showing that a fraction of receptors are engaged with G-proteins, does not exclude the possibility of a rapid turnover of G-proteins with which these receptors interact.

| Summary
The existence of high-and low-affinity states of GPCRs is commonly thought to be due to receptor interaction with G-proteins. Being a part of the canonical GPCR signaling cascade, the receptor-G-protein coupling is directly related to the pharmacological activity of the agonists.
GPCR oligomerization (both homo and hetero), with negative cooperativity in agonist binding within the oligomer, can be an alternative mechanism leading to the formation of receptor subpopulations with different affinities for the agonist. It is plausible that at least for some GPCRs, oligomerization can contribute to the splitting of receptors into high-and low-affinity states instead of, or in addition to, G-protein coupling.
Both models of high-affinity state imply that agonists preferentially bind to receptors that are almost ready to launch the signaling cascade, although in the oligomerization model it is so just because agonist binding makes unoccupied receptors "less ready." Moreover, agonist binding can influence the relative abundance of the high-affinity state, potentially promoting its formation or disintegration and launching receptor internalization in intact cells and living tissues. Such influence is most directly demonstrated for the G-protein-dependent model of the high-affinity state.

| EXPECTED ADVANTAGES AND DISADVANTAGES OF AGONIST TRACERS RELATIVE TO ANTAGONIST TRACERS
From the notion that agonists preferentially bind to a high-affinity functional subset of receptors one can logically infer a number of applications in which agonist tracers should be superior, in theory, to antagonist tracers. Note that proposed advantages of agonist tracers mentioned below hold independently of whether the high-affinity state is G-protein-dependent or oligomerization-dependent.
3.1 | Applications where agonist tracers have comparative advantage over antagonist tracers

| Measurement of synaptic neurotransmission
An endogenous neurotransmitter is an agonist by definition, so it competes with the agonist tracer for the same subset of receptors-receptors configured in high-affinity state-while an antagonist tracer also binds to receptors in the low-affinity state that are "ignored" by the neurotransmitter except at very high concentrations. This means that a change in the concentration of neurotransmitter of a given magnitude will lead to greater change in agonist tracer binding compared with antagonist tracer binding ( Figure 5).
For some receptor families (eg, serotonin 5-HT 1A and 5-HT 2A receptors), all available antagonist tracers appear to be insensitive to alterations of endogenous neurotransmitter levels. 51 As agonist tracers are supposed to be more sensitive than antagonist tracers to endogenous neurotransmitter competition, developing agonist ligands is considered a promising way to obtain a tool for the measurement of synaptic neurotransmission via these receptors. 52

| Studies of (pathological) alterations in receptor availability
In Section 1, a few examples were given of how alterations of the percentage of receptors configured in the highaffinity state can accompany the disease. Since the high-affinity state is the active form of the receptor involved in signaling and may be primarily affected by the disease, the abundance of the high-affinity state could be a more meaningful biomarker than the total receptor density. Agonist tracers should then be a convenient tool for pinpointing alterations of the availability of receptors configured in the high-affinity state in disease.
The results of some in vitro experiments with agonist and antagonist radioligands have supported the hypothesis that agonist tracers are superior to antagonists in detecting pathological changes in neuroreceptor availability. In vitro binding of the 5-HT 1A agonists [ 18 F]F15599 and [ 18 F]F13640 but not of the antagonist [ 18 F] MPPF, in postmortem brain sections of Alzheimer's patients was decreased compared with control brains. 53,54 In unilateral 6-hydroxydopamine-induced lesions of the rat brain (exhibiting dopaminergic neurodegeneration similar to Parkinson's disease in humans, where upregulation of R high is hypothesized), the ex vivo binding of dopamine D 2/ 3 agonist [ 3 H]NPA was changed to a greater extent than the in vitro binding of D 2/3 antagonist [ 3 H]raclopride. 55

| Measurement of agonist drug occupancy
Many drugs owe their effect to their agonist activity at one or more kinds of receptors. For instance, many antiparkinsonian drugs are D 2/3 agonists 56 ; muscarinic receptor agonists like milameline were tried as treatment of Alzheimer's disease 57 ; the mechanism of action of antipsychotics may include not only D 2/3 antagonism but also 5-HT 1Aagonism 58,59 ; the active metabolite of clozapine (also an atypical antipsychotic) acts as an agonist at muscarinic M 1 receptors 60 ; opiate agonists are widely used as analgesics or antitussives and for treating diarrhea and opiate abuse. 61 Increased sensitivity of agonist tracers to displacement by agonist drugs may be an advantage in occupancy studies: the opioid receptor antagonist [ 11 C]diprenorphine failed to detect receptor occupancy by clinically relevant doses of opioid agonists. 62,63 However, no studies have so far been published, where the sensitivity of an agonist and an antagonist opioid receptor tracer with equal subtype-selectivity to displacement by an agonist drug was compared head-to-head.
Agonist tracers can also complement antagonist tracers in the investigations of the affinity-state preference of new drugs. The sensitivities of agonist and antagonist tracers to the displacement by the drug can be compared: drugs preferring the high-affinity state will displace the agonist tracer more readily, while drugs not distinguishing between affinity states will show no difference in displacement efficacy. Two studies attempting this approach have F I G U R E 5 Greater sensitivity of agonist tracers to displacement ("challenge") by neurotransmitter. Agonist tracers primarily bind to the receptors configured in the high-affinity state (ie, coupled to G-proteins), as do neurotransmitters. Therefore, the same change in receptor occupancy by the neurotransmitter displaces a greater fraction of bound agonist tracer (A) than of bound antagonist tracer (B). In this schematic diagram, the endogenous neurotransmitter is pictured as a circle, the agonist ligand as a triangle, the antagonist ligand as a diamond, the G-protein as an ellipse, and the receptor as a sinusoid line SHALGUNOV ET AL. | 1021 been published 64,65 but both reported equal displacement of agonist and antagonist tracers by the drug, which can be interpreted in two ways: either the tested drugs were ideal antagonists or the hypothesis of greater agonist tracer displacement by agonist drug does not hold.

| Intrinsic shortcomings of agonist tracers
Though the preference for the high-affinity state makes agonist tracers potentially superior to antagonists in certain imaging applications, it also results in a number of specific difficulties associated with the development and use of agonist tracers.

| Lower signal-to-noise ratios
The signal-to-noise ratio of a PET tracer is proportional to the density of receptors the tracer binds to in the brain (B avail ) and to the tracer's affinity toward these receptors (1/K d ). The density of receptors configured in the highaffinity state (and thus recognized by agonist tracers) is by definition lower than the total receptor density.
Moreover, estimates of agonist affinity toward the high-affinity state, acquired in membrane homogenates in vitro, may be systematically higher than the actual affinity in vivo. The reason why it may be so is the negativefeedback between agonist-receptor and receptor-G-protein binding in the GTP cycle (see Section 2.3), which is part of the G-protein-dependent model of the high-affinity state. Indeed, GTP depletion was shown to increase the affinity of agonist but not antagonist ligands to opioid receptors in cultured cells. 66 Therefore, affinity and nonspecific binding requirements for agonist tracers are stricter than for antagonists.

| Greater likelihood of unwanted pharmacological effects
As agonist tracers preferentially bind to the functional subpopulation of the receptors, they may induce significant physiological responses at a rather low dose, which can distort the experimental results and cause discomfort to the patients.
Indeed, staying below the pharmacological dose range is a concern in opioid receptor imaging with agonist tracers. [67][68][69] It was also reported as a potential concern in serotonin 5-HT 1A receptor imaging with the agonist [ 11 C] CUMI-101, 70 even though first tests of the same compound in humans showed no adverse effects. 71 Exceeding the pharmacological threshold is especially easy with tracers with low specific radioactivity and a related high injected mass of the radioligand. The risk of low specific radioactivity is increased when labeling chemistry is complex. For instance, the dopamine D 2/3 receptor agonist [ 11 C](+)PHNO was originally labeled via a four-step route, resulting in a relatively low specific radioactivity. 72 As a consequence, a high incidence of nausea (emesis is a typical effect of D 2 agonism) was reported in patients injected with [ 11 C](+)PHNO, 73 and it was later found that [ 11 C](+)PHNO human PET studies had frequently been performed under nontracer conditions. 74

| EXISTING PET AGONIST TRACERS FOR GPCR IMAGING IN THE CENTRAL NERVOUS SYSTEM
The greatest number of agonist PET tracers has been developed for the imaging of dopamine D 2/3 receptors (see 75 for a review). Tracer development efforts in the last two decades have yielded a number of agonist radioligands for other receptors as well. The most promising agonist tracers developed for PET imaging of neuroreceptors are presented in Table 1, Figure 6 and Figure 7.

| Definition and properties of an agonist tracer
An agonist tracer is usually defined as "a radiolabeled analog of a ligand with agonist activity." There are many ways to confirm and measure the degree of agonist activity: behavioral or ex vivo studies examining the physiological effect of the drug, functional in vitro assays measuring the levels of certain secondary messengers, or the recruiting of proteins involved in signaling cascades to the receptors.
Because the intrinsic activity of a ligand is known to be correlated with the ratio of its affinities to the highand low-affinity receptor states, 18,19 it seems evident that agonists will preferentially bind to the high-affinity state. However, agonism does not necessarily imply preferential binding to receptor-G-protein complexes, since noncanonical signaling pathways do exist. One example is cariprazine, a drug which was recently labeled with carbon-11 and evaluated as a dopamine D 2/3 receptor PET tracer. This compound showed partial D 2/3 agonist activity in secondary messenger assays but did not recruit G-proteins in vitro. [176][177][178] Observations of G-protein recruitment may also differ between in vitro setups. For instance, [ 11 C]CUMI-101, a tracer for serotonin 5-HT 1A receptors, was defined as an agonist based on the [ 35 S]GTPyS assay (indirect measurement of G-protein F I G U R E 6 Chemical structures of agonist radioligands for dopaminergic receptors (see also Table 1). The position of the radionuclide in each molecule is indicated by an asterisk recruiting to receptors) in membrane homogenates from cell cultures expressing recombinant human receptors but was later found to act as an antagonist when the same assay was done in primate and rat brain homogenates. 118,119 Therefore, the most certain proof of the agonist radioligand's in vitro preference to the high-affinity state is directly demonstrating that it recognizes high-and low-affinity states of its receptor in natural tissue or in transfected cell culture. It is worth noting that for some agonist tracers, preferential in vitro binding to R high was demonstrated only after the tracer had been evaluated in vivo (compare 105 and 28 ), while for some other radioligands the capability to discern affinity states in vitro was not assessed at all. 80,135 F I G U R E 7 Chemical structures of agonist radioligands for serotonin, opioid, and muscarinic receptors (see also Table 1). [ 11 C]PEO is not shown; its structure can be found in Van Waarde et al. 175 The position of the radionuclide in each molecule is indicated by an asterisk SHALGUNOV ET AL.

| In vivo evaluation of a PET neuroreceptor tracer
Characteristics desirable for a PET tracer for brain imaging include the ability to pass the blood-brain-barrier, a low degree of metabolism, a high contrast between target (specific) and nontarget (nonspecific) binding, and pharmacokinetics that can be reliably quantified from a 60 to 90 minute-long PET scan (see [179][180][181] for review). An important aim in PET imaging is the measurement of synaptic neurotransmission. For this reason, neuroreceptor tracers are tested for the sensitivity of their binding to changes of endogenous neurotransmitter levels, and agonists are supposed to be more sensitive than antagonists.
Neuroreceptor tracers are usually evaluated in rodents or non-human primates before being moved to human studies. In non-human primates, one can investigate the binding of the tracers with high spatial detail using clinical PET cameras. Evaluation in rodents is cheaper and enables the use of more invasive methods but interspecies differences in rodent, primate, and human physiology can be a confounding factor. In addition, the small size of rodents forces the researchers to use dedicated nonclinical "micro-PET" cameras and does not permit to reliably image minor brain structures. To strike the right balance between controllability of the experimental conditions and image quality, tracers are sometimes evaluated in (relatively) large mammals, such as cats or pigs.

| Availability of agonist PET neuroreceptor tracers
Agonist PET tracers can be divided into three categories (see Table 1). specifically bind to D 3 receptors in monkey brain but specific binding was only measurable under dopamine depletion conditions. 115 The muscarinic M 1 receptor tracer [ 11 C]AF-150(S) showed both specific binding and sensitivity to endogenous acetylcholine levels in the rat brain but the low signal-to-noise ratios of this ligand cast doubt on its suitability for further research. 165,166 To demonstrate the preferential binding of agonist tracers to receptor high-affinity state, a head-to-head comparison with reference tracers binding to all receptors (ie, antagonist tracers) is required. For D 1/5 , D 2/3 , buprenorphine. 159 175,190 In theory, non-subtypeselective radioactive antagonists might be used in head-to-head comparisons with radioactive agonists if receptors to which the antagonist, but not the agonist, binds are fully blocked with a nonradioactive drug, but the feasibility of that approach is questionable because of the possible pharmacological effects of such blockade.

| 1029
Binding potentials (BPs) and target/nontarget ratios are "raw" measures representing receptor availability, which can later be recalculated to receptor densities or occupancies.

| Binding potentials
The typical outcome measure of in vivo imaging experiments is the BP. This parameter is defined as the product of the density of binding sites (B max ) and the affinity of the radioligand for these sites (inverse of the dissociation constant, 1/K d ). BP is equal to the ratio of the concentrations of specifically bound and free ligand in the tissue of interest at equilibrium, provided that the administered dose of radioligand is sufficiently low (see the Appendix for more explanation). BP is estimated by fitting a kinetic model to measured time-activity curves. Time-dependent radioactivity in the region of interest and a reference region in the brain can be measured by PET imaging, and plasma radioactivity can be determined by blood sampling. 191 Note that in vivo not all receptors may be available for binding, as they can be internalized, converted to low-affinity state (for an agonist) or occupied by neurotransmitter, so in the in vivo context the term B avail is more suitable than B max .
Given the difficulty of determining the true concentration of the free ligand in the living tissue, other concentrations proportional to free ligand concentration in tissue are substituted in its place. Specifically, bound concentration is related to free plasma concentration (BP F ), total plasma concentration (BP P ), or "nondisplaceable" concentration (BP ND ), that is, the total concentration of free and nonspecifically bound ligand in the tissue. 192 It is reasonable to assume that free ligand concentrations in the plasma and in the interstitial liquid of the brain tissue are equal at equilibrium, so BP F can be considered the "true" BP.

| Target/nontarget ratios
When regions of interest are small relative to PET camera resolution (ie, subsections of rodent brain) it is often hard to obtain a reliable time-activity curve with high temporal resolution. Also, in situations when a lot of experimental conditions have to be tested and compared, it is often infeasible to obtain time-activity curves by PET or to sacrifice large groups of animals at different time points. In these situations, one can take advantage of the "pseudoequilibrium" state when the concentration ratios between receptor-rich and receptor-free tissues remain constant even as absolute concentrations are changing. For a typical neuroreceptor ligand, one can reasonably expect the pseudoequilibrium state to be reached within half an hour after injection. Once the time range in which the pseudoequilibrium exists is validated, specific binding can be estimated from tissue concentrations at a single time point within this time range. Such concentrations can be obtained by ex vivo dissection and radioactivity counting or from a static PET scan. Target/nontarget concentration ratios can be used as is or be recalculated to specific binding ratios (SBRs): where T and NT are radioligand concentrations in receptor-rich ("target") and receptor-poor ("nontarget") regions of interest. In the absence of specific binding, SBR = 0, while T/NT = 1.
"Raw" specific binding, that is, the difference between radioligand concentrations in receptor-poor and receptor-rich regions can also be used as an outcome measure. However, when specific ligand binding is not normalized to the nonspecific binding at the same time point, its value is prone to intrasubject variations in pharmacokinetics. Therefore, the use of binding ratios is preferred.

| Available receptor density
Available receptor density (B avail ) can be estimated in a saturation experiment. Specific binding of a radioligand is determined by two parameters: the density of binding sites in the region of interest (B avail ) and the affinity of the radioligand toward these receptors (1/K d ). To independently estimate these two parameters, bound and free radioligand concentrations at equilibrium have to be estimated at least at two different injected doses (for radiotracers, injected dose is usually varied by changing molar radioactivity). Bound concentration can be estimated from a difference in equilibrium tracer concentrations between the target and nontarget regions, while free concentration can be back-calculated from the binding potential (see Appendix). B avail can then be quantified by regression analysis. In PET imaging, the regression is often performed on "linearized" binding data: binding potential is plotted against absolute specific binding (Scatchard plot). Scatchard plot requires a simple linear regression and is therefore straightforward but also bias-prone, as the X and

| Receptor occupancy
Displacement of a tracer from its receptors by a competing ligand decreases the binding potential of the tracer.
Receptor occupancy can be calculated as the change in binding potential or target-nontarget ratio after drug administration, relative to baseline. The same holds for the occupancy of the receptors by endogenous neurotransmitter, when drugs stimulating neurotransmitter release or depletion are administered.

| Experimental paradigms used to demonstrate the existence of high-affinity state in vivo
To demonstrate that agonist tracers preferentially bind to a certain "high-affinity" subset of receptors in vivo three approaches have been used (summarized in Table 2). One approach is to directly measure the available binding site densities for agonist and antagonist tracers and demonstrate that the binding site density available to the agonist is lower. Another is to infer the ratio of high-affinity binding site density to total binding site density from the results of experiments where tracers compete for binding to the receptors with unlabeled ligands. A third approach is to demonstrate that agonist, but not antagonist, binding can be influenced by manipulations of receptor-G-protein coupling.
It is important to emphasize that to compare agonist and antagonist tracers with each other their pharmacological selectivity profiles (ie, relative binding affinities toward different receptor subtypes) should be identical within the region of interest used for comparison. Otherwise, any detected difference in binding behavior could be attributed to the relative preference of one of the tracers toward a certain receptor subtype.
In principle, all experiments described below can be performed not only with PET tracers labeled with short-lived positron-emitting isotopes but also with radioligands labeled with long-lived isotopes such as tritium (  As explained above, a minimum of two different radioligand doses needs to be tested to estimate binding site density (B avail ). More doses will add precision and can reveal potential cooperativity effects or the presence of multiple binding sites with different affinities (eg, receptor affinity states), provided that radioligand binding to all these sites is distinguishable from nonspecific binding. However, published PET studies comparing binding site densities of agonist and antagonist tracers were restricted to two doses. 90,193 Another study used single time point SBRs as outcome measure and built saturation curves based on 9 to 10 data points. 122 In two-dose PET studies aimed at quantifying B avail , the low dose corresponds to the minimum amount of radioligand that can be injected, that is, the "tracer dose," which should occupy less than or equal to 10% of the receptor population in the region of interest. The high-dose is chosen to occupy about two-thirds of that population. 90,193 Extracting density values from true binding potential measurements It should be noted that performing a saturation assay with agonist radioligands can lead to unwanted and dangerous pharmacological effects, especially in the case of opioid ligands. 68,69 In a head-to-head comparison of 5-HT 1A agonist and antagonist tracers, Kumar et al 70 attempted to circumvent this problem by comparing the "true" binding potentials (BP F ) for the two tracers at low injected dose instead of performing a second high-dose scan to independently measure B avail and K d . Given that BP F = B avail /K d , B avail can arguably be calculated from the BP F value using in vitro K d value for the corresponding tracer. However, there are two problems with this approach. First, to calculate BP F , one needs to obtain an arterial input curve and free fraction in plasma for the investigated radioligand, in addition to the time-activity curve for the region of interest.
Such a large amount of input data makes BP F prone to experimental error and bias. Second, the in vivo K d of the radioligand is not necessarily equal to the in vitro K d , especially if the latter is measured for receptors from a different animal species or in transfected cells.

Studying correlation between regional binding of agonist and antagonist
Binding potentials or target/nontarget ratios for an agonist tracer in various brain regions can be plotted against the corresponding measurements for an antagonist tracer, to examine their correlation. Such a plot may provide insight into the relationship between the densities of available binding sites for agonist and antagonist tracers while staying below the "tracer" threshold. If agonist binding in a certain brain region lies above the main trend on the correlation graph, it suggests that the relative abundance of receptors in the high-affinity state in this region is higher than average, and vice versa.
This approach, however, has many limitations. If the relative abundance of the high-affinity state is drastically different in each region, the correlation graph will be meaningless: there will be no main trend to pinpoint deviations from. If the relative abundance of the high-affinity state is the same in all regions, the correlation graph will be a straight line, revealing no differences in agonist and antagonist binding and thus no evidence in favor of the existence of the high-affinity state. Therefore, analysis of the correlation between agonist and antagonist binding cannot be the sole method of looking for the existence of high-affinity state but can be an extra piece of data analysis in experiments based on other paradigms.

Studying agonist binding in disorders presumably caused by high-affinity state dysregulation
In vitro experiments in membrane homogenates suggest that some neuropsychiatric disorders are accompanied by alterations in the relative abundance of the high-affinity state in a given receptor population, while changes in overall receptor density relative to the healthy condition are either absent or much less pronounced. One example is animal models of psychosis where the high-affinity state of dopamine D 2/3 receptors is upregulated. 14,201 Therefore, another way to demonstrate the existence of a high-affinity state in vivo is to show that its upregulation (or downregulation) can be noninvasively detected by agonist tracers. If the relative abundance of the high-affinity state is altered but the overall receptor density remains (relatively) constant, the binding of the agonist but not of the antagonist tracer will be different in the diseased state relative to the healthy state. Ratios of BP or SBR values for agonist and antagonist tracers can be used as outcome measures to normalize for possible concomitant alterations in total receptor density. 202 In this paradigm, the binding of each tracer only has to be assessed at a low and pharmacologically inactive dose. However, one has to demonstrate that the relative abundance of high-affinity state really differs between healthy and diseased states, using experimental approaches other than PET (typically, in vitro assays). Moreover, in the diseased state, alteration of the relative abundance of the high-affinity state may be accompanied by alterations in other parameters relevant for radioligand binding. For instance, changes in baseline neurotransmitter levels also differentially affect the binding of agonist and antagonist tracers (agonist binding is changed to a greater extent).
Concomitant changes in several parameters pressing agonist tracer binding in different directions can offset each other, leading to little or no change in overall receptor availability to the agonist tracer compared with the healthy state.

| Approach 2: studying tracer vulnerability to displacement by an unlabeled competitor
One important difference between tracer-drug competition experiments in vitro and in vivo is that in the latter case the concentration of both tracer and drug at the receptors is not constant. While for the radioligand a true equilibrium between its concentrations in blood and brain tissue can be achieved by using bolus-plus-infusion injection scheme, the same is virtually infeasible for the unlabeled drug (tissue concentrations of which are much harder to monitor). Nevertheless, one can usually safely assume that the pharmacokinetics of the competing drug are dose-linear within the investigated dose range, so the degree of displacement of the tracer by the drug is also dose-linear.

Building in vivo displacement curves
In vitro, the high-affinity state is detected by displacing an antagonist radioligand with ever increasing concentrations of unlabeled agonist drug. When the remaining specific binding of the radioligand is plotted against agonist concentrations, the displacement is shown to proceed in two phases: agonist first displaces the radioligand from high-affinity sites then from low-affinity sites. The same displacement curve can be built in vivo by plotting binding potentials or target/nontarget ratios for an antagonist tracer against an administered dose of unlabeled agonist drug.
The advantage of this paradigm is that it does not require an agonist radioligand. Antagonist radioligands are much more numerous than agonist radioligands, so the displacement curve paradigm is currently applicable to a wider range of receptors than other paradigms mentioned below.
The downside, however, is that the generation of a displacement curve is a laborious undertaking. The shape of the biphasic curve is determined by five parameters: maximum binding level (at no displacement), minimum binding level (full displacement), agonist affinities for high-and low-affinity states, and the percentage of receptors in the investigated population configured in the high-affinity state. This means that at least five different dose levels (including zero) have to be used to test whether the obtained curve is monophasic or biphasic.
Therefore, studies that used the displacement curve approach typically used SBRs obtained ex vivo at a single time point from large numbers of rodents, 86,196 though the use of PET scanning in primates has also been reported. 197,198 The actual number of dose levels tested was 6 to 9 in rodent and 9 in non-human primates. SHALGUNOV ET AL.

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Comparing vulnerability to displacement by unlabeled agonist An agonist tracer should be more vulnerable than an antagonist tracer to displacement (or "challenge") by other agonists because it competes with them for the same subpopulation of receptors. Displacement can be elicited by administering an appropriate agonist drug or by stimulating endogenous neurotransmitter release.
The advantage of using exogenous agonist drugs for displacement is that these drugs can be selected to be subtype-specific and to only occupy the receptor population that is being imaged (or even a defined subset of this population if the tracer binds to more than one receptor subtype).
On the other hand, manipulating neurotransmitter levels has the advantage of being "natural": one looks at the competition of the tracer with the endogenous ligand, the action of which on the receptors is thought to govern the functioning of the brain [see Laruelle 187 and Finnema 51 for reviews]. One can also reasonably expect that the competition will only happen at receptors that are really situated in the synapses. Moreover, neurotransmitter levels can be both increased and decreased relative to the baseline. In the latter case, the expected result is greater increase, rather than greater decrease, of binding for the agonist tracer. However, manipulating neurotransmitter release has its downsides, too. First, the effect vs time relationship between the administration of the drug that stimulates a rise or fall in endogenous neurotransmitter level and synaptic receptor occupancy is more complex than when receptors are occupied with exogenous agonist. Second, the released neurotransmitter can act on other receptor subtypes beyond the one being imaged. Third, some drugs used to manipulate neurotransmitter levels are known to manipulate levels of several neurotransmitters at once (eg, amphetamine stimulates both dopamine and norepinephrine release). The lack of selectivity regarding what neurotransmitter is manipulated and which receptors are occupied can confound the interpretation of cause-and-effect relationships.
If the "tracer condition" is satisfied (radioligands occupy a negligible fraction of all receptors), the ratio of agonist and antagonist radioligand vulnerabilities to displacement by a challenge is a constant value as long as less than 100% of the high-affinity state is occupied as a result of the challenge (Figure 8). Therefore, in theory, a single dose of agonist drug or neurotransmitter level manipulator should provide enough information to compare the vulnerability of agonist and antagonist tracers. In practice, because the actual percentage of receptors in the highaffinity state is unknown, several doses are often tried, resulting in occupancies of up to 100%, 86,90,107,196 except in the human studies where the maximum challenge magnitude is limited by ethical considerations. 93,102 F I G U R E 8 Relationship between agonist and antagonist tracer displacement (ΔB Ag and ΔB An ) and the fraction of receptors occupied by competing agonist drug or neurotransmitter. B max is the total receptor density available at baseline, X H is the fraction of receptors configured in the high-affinity state, B occ is the amount of receptors occupied as a result of the challenge. If B occ < X H B max , that is, not all high-affinity state receptors become occupied, the ratio of relative decreases of agonist and antagonist tracer binding is constant and equal to 1/X H An important limitation of the vulnerability comparison paradigm is that preference for the high-affinity state is not the only factor influencing the vulnerability of the radioligand to displacement by unlabeled drugs. For instance, many preclinical in vivo tracer binding experiments are performed in anesthetized animals, and isoflurane and ketamine anesthesia were found to increase the baseline binding of agonist D 2/3 tracers, exaggerating the vulnerability of agonist tracers relative to antagonists. 109,203 The mechanism of such selective influence is unclear, although there are reports that anesthetics interfere with receptor-G-protein (un)coupling 204,205 and alter endogenous neurotransmitter levels. 206,207 Furthermore, D 2/3 antagonist tracers are known to differ between themselves in the sensitivity to changes in dopamine levels. 187,208 The underlying reasons can be more or less favorable binding kinetics (see Finnema et al 51,209 for discussion) or differences in affinity toward the surface and internalized receptors. 210

| Studying vulnerability to G-protein uncoupling in vivo
Addition of GTP or its analogs decreases specific binding of agonist but not antagonist ligands in vitro, so uncoupling of G-proteins induced in vivo should lead to the same effects.
Seeman 15 demonstrated that GTP addition to tissues extracted from an animal after D 2/3 agonist radioligand injection accelerates radioligand dissociation from D 2/3 receptors in the tissue and proposed the use of pertussis toxin to promote G-protein decoupling from the receptors in vivo. Indeed, physiological effects of dopamine and opioid receptor agonists were inhibited by pertussis toxin injections. [212][213][214] This approach probes the nature of the high-affinity state, that is, it seeks an answer to the question "is Gprotein binding to the receptor significant for agonist binding to the receptor?" However, this question is not the same as "do agonists bind to a subset of all receptors?," which is addressed in other paradigms. As discussed in Section 2, all receptors may be precoupled to G-proteins. Moreover, G-protein decoupling agents (pertussis toxin or anything else) will have to be introduced locally into the region of interest rather than systemically through intravenous, intraperitoneal, or subcutaneous injections. For brain imaging, that means that intrathecal and intracerebral injections will have to be used. Such injections are technically challenging and hardly (if anyhow) translatable to the clinic. Therefore, this paradigm has not yet been used for head-to-head comparisons of agonist and antagonist radioligands. Binding site densities for D 2/3 agonist and antagonist tracers were found to be equal in one study, 90 while in another study the average relative abundance of D 2/3-high was found to be 79%, 193 which is close to the upper extreme of such percentages determined in vitro. 216 Saturation of [ 11 C](+)PHNO binding in monkey brain was found to be biphasic but the two binding sites most probably corresponded to D 2 and D 3 receptor subtypes rather than to high-and low-affinity states. 217 In rats with brain lesions induced by the dopaminergic neurotoxin 6-hydroxydopamine, binding levels of D 2/3 antagonist [ 11 C]raclopride and of D 2/3 agonist [ 3 H]PHNO were increased to the same extent. 194 No difference in SHALGUNOV ET AL.

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baseline agonist binding relative to the healthy condition was found in dopamine β-hydroxylase knockout (Dβh-KO) mice, 103 in rats withdrawn from chronic ethanol and in amphetamine-sensitized rats. 194 In these three animal models, an upregulation of D 2/3-high was previously demonstrated in vitro by the group of Seeman et al. 201,[218][219][220] However, in vitro measurements of elevated striatal D 2/3-high in Dβh-KO mice could not be replicated by the group that performed the in vivo imaging study. 103  In clinical studies of diseases where alteration of D 2/3-high was suspected, binding potentials of agonist tracers in healthy and diseased subjects were similar, 202,221-224 although some recent reports buck this trend. 195,225 The dopamine D 2/3 antagonist radioligand raclopride ( 11 C-or 3 H-labeled) was displaced by D 2/3 agonist drugs in a monophasic manner. 86,196,197 In a more recent study, up to 70% of [ 11 C]raclopride binding was displaced by D 2/3 agonist quinpirole without any evidence of biphasicity. 39 The majority of studies comparing agonist and antagonist tracers' vulnerability to displacement by agonist drugs found no difference in vulnerabilities, 86,107,196 though some reports confirming greater vulnerability of agonist tracers do exist 199,200 and the relative timing of tracer and drug administration were claimed to be important. 200 Nevertheless, D 2/3 agonists did prove to be more sensitive than antagonists to endogenous dopamine levels in anesthetized rodents, 44 cats, 90 primates, 92,98,106 as well as in awake humans, 93,102 though not in awake rodents, 86,194,196,203 with a single exception. 199 However, lack of consistency in preclinical data on neurotransmitter and agonist drug challenge raises a question whether this advantage of the agonists stems from their preference for the high-affinity state or from other factors (see Section 5.2.2).
For dopamine D 1/5 receptors, an in vivo displacement curve was built in baboons using the D 1 -antagonist [ 11 C] NNC-112 and the D 1 -agonist drug DAR-0100A. 198 Occupancies above 40% were not investigated, but the best-fit curve was monophasic, not supporting the existence of a high-affinity receptor subpopulation.

| Serotonin receptors
A few head-to-head agonist-antagonist comparisons done with serotonin receptor radioligands yielded ambiguous results.
Two studies found that about 80-90% of the specific binding of antagonist 5-HT 1A ligand [ 11 C]WAY-100635 could be displaced by the 5-HT 1A agonist 8-OH-DPAT, 226 To sum up, the majority of data, both for dopamine and serotonin receptors, does not directly support the existence of a receptor subpopulation in vivo to which agonists preferentially bind. There are some undisputable differences in the behavior of agonist tracers and antagonist tracers, such as specific sensitivity of the former to anesthesia and greater sensitivity to synaptic neurotransmitter levels, but the reason for these differences is not clear.

| Experimental data in light of the nature of the high-affinity state
Some attempts to detect the high-affinity state in vivo may have failed because the used radioligands were not sufficiently subtype-selective or lacked sufficient intrinsic acitivity via the canonical GPCR pathway. 118,119,228 In other cases, however, the reasons for failure were completely unclear. Therefore, the nature and functioning of the high-affinity state in vivo has remained elusive.
Two explanations of the failure to detect high-and low-affinity states in vivo have been put forward. One explanation proposes that all, or almost all, receptors are configured in the high-affinity state in vivo 86 and permanently precoupled to G-proteins, so that these G-proteins, at least their Gα subunits, do not dissociate from the receptors after activation. 215 Another explanation states that, whatever the baseline degree of receptor-G-protein precoupling, receptors can and do recruit new G-proteins when occupied by agonists, so high agonist concentrations eventually make all receptors bind G-proteins and thus convert to the high-affinity state. 196,198 Indeed, receptors have been subjected to high agonist (drug or neurotransmitter) concentrations in virtually all experimental paradigms used for in vivo detection of the high-affinity state ( Table 2). In vivo imaging experiments last for tens of minutes, while time constants for receptor and G-protein activation and for receptor-ligand and receptor-G-protein binding vary from tens of milliseconds to a few seconds. 37 Gradual G-protein recruitment in response to agonist binding can thus confound experimental outcomes in currently used paradigms and can "inflate" the apparent relative abundance of the high-affinity state in vivo. Indeed, in studies comparing the vulnerability of dopamine D 2/3 agonist and antagonist tracers to drug challenge, the lowest doses of D 2/3 agonist drugs and the dopamine release stimulator amphetamine (resulting in the lowest receptor occupancies and therefore minimal G-protein recruitment) tended to produce the greatest relative difference between agonist and antagonist tracer displacement. In three such studies, the lowest dose of challenge drugs resulted in zero or (iii) Autoradiographic studies where densities (B max ) of D 2/3 receptors in tissue slices were estimated, tended to produce lower B max values for agonist than for antagonist radioligands, but the variance between studies was too high to consider the difference significant. 229 The majority of antagonist vs agonist drug displacement experiments demonstrated a single high-affinity population of D 2/3 receptors in tissue slices in vitro. 229 This is in agreement with the data from in vivo imaging (see Section 5.3.1).
To explain the low relative abundance of the high-affinity state in membrane homogenates within the precoupling model of receptor-G-protein interaction, one can assume that partial dissociation of receptor-G-protein complexes occurs during membrane preparation, but the exact mechanism is hard to define.
Alternatively, one can assume the existence of a large intracellular reserve of receptors in the high-affinity state.
In transfected cells, the affinity of agonist ligands used as PET tracers toward internalized D 2/3 receptors was shown to be about twofold lower than toward surface receptors, 42 a change that would hardly be noticeable in saturation or competition curves. However, the total densities of D 2/3 receptors measured in membrane homogenates by radioligand binding saturation and in vivo by PET are in good agreement, 229 which does not support the existence of extra D 2/3 receptors that are detectable in vivo but are not found in membrane homogenates.
The collision coupling model of receptor-G-protein interaction can be reconciled with measurements of the high-affinity state in membrane homogenates if one assumes that in these homogenates only a fraction of the total G-protein pool of the cell is available for recruitment to the receptors. Indeed, the number of G-proteins in living cells is likely equal to or much greater than the number of their cognate receptors. 45,232,233 However, given that G-proteins are anchored to the lipid bilayer, 234  were equilibrated with membrane homogenates for 2 hours before readout, which is much longer than the pre-incubation step. Therefore, even in the case of simultaneous addition of radioligands and (−)NPA, there should have been enough time during the equilibration step for (−)NPA to elicit recruitment of "spare" Gproteins to the receptors.
The absence of the high-affinity state of D 2/3 receptors in isolated intact cells 28,42,230 is even harder to reconcile with either of the two models mentioned above. Collision coupling at least provides a theoretical explanation of the disappearance of high-affinity state upon agonist addition due to a high level of GTP in living cells. Still it remains puzzling why agonists force D 2/3 receptors in dispersed cells from a natural tissue (bovine pituitary) to uncouple from G-proteins (convert into the low-affinity state), but promote G-protein recruitment (conversion to the high-affinity state) when they are acting on the same receptors in intact tissue.
Switching from the G-protein-dependent high-affinity state model to the oligomerization-dependent model leaves the same questions open: it is not clear how the degrees of receptor oligomerization can be different in membranes, dispersed cells and living tissues. Moreover, observation of almost all receptors configured in highaffinity state in vivo is hard to reconcile with the oligomerization-dependent model. At full oligomerization and full agonist occupancy, cooperativity-induced high-affinity state can have a relative abundance of no more than 50% (in the case of dimers), and higher values imply that few, if any, receptors are oligomerized.

| CONCLUSION
The concept of the high-affinity state postulates that a certain subset of receptors in the living brain is primarily responsible for signaling. Assessing the abundance of this subset is thus potentially very relevant for studies concerning the responses of neurotransmission to pharmacological or physical stimuli and the dysregulation of neurotransmission in neurological disorders.
A number of experimental paradigms have been developed for the estimation of the relative abundance of receptors configured in the high-affinity state. The high-affinity state is preferentially recognized by agonists in vitro, so the development of agonist PET tracers as tools for the noninvasive imaging of the high-affinity state has become popular in recent decades.
The greatest number of agonist tracers has been developed for dopamine D 2/3 receptors, but agonist tracers for dopamine D 1 , µ-opioid, and muscarinic M 2 receptors are also known, and in recent years, radiolabeled agonists for serotonin 5-HT 1A and 5-HT 2A , κ-opioid and muscarinic M 1 receptors have appeared. It should be noted, however, that for many of the nondopaminergic tracers the actual preference for the high-affinity state has not been directly tested, because functional agonism is often assumed to imply preferential binding to the high-affinity state.
For dopamine, serotonin and κ-opioid receptors, head-to-head comparisons of agonist and antagonist tracers are now possible, while matching antagonist tracers for muscarinic M 2 and µ-opioid receptors have yet to be developed. Given that, beyond head-to-head agonist-antagonist comparisons, antagonist tracers are also suitable for experiments like displacement curve generation (see Section 5.2.2), development of new antagonist tracers for muscarinic M 2 and µ-opioid receptors with a pharmacological selectivity matching that of existing agonist tracers will arguably be more useful for the assessment of the affinity states of these receptors than development of new agonist tracers.
Agonist tracers appear to be more sensitive to endogenous neurotransmitter challenge, as was originally expected. However, other expectations regarding agonist tracers have not been fulfilled. Agonist imaging did not reveal alterations in the relative abundance of the high-affinity state in neurological disorders. The benefits of agonist tracers for the imaging of receptor occupancies by drugs have also not been proven.
Moreover, though the separation of GPCRs into subsets with high-and low-affinity state is consistently observed in membrane homogenates in vitro, data from preclinical and clinical experiments do not support the existence of the high-and low-affinity states in vivo. The majority of these data concerns dopamine D 2/3 receptors but recent results on serotonin receptors paint the same picture.
The relative abundance of the high-affinity state in vivo may simply be close to (or equal to) 100%, making the detection of low-affinity state unfeasible. It is also possible that agonist drugs or tracers used for in vivo experiments may inflate the relative abundance of the high-affinity state.
Critical revision of experimental approaches and collection of experimental evidence for nondopaminergic receptors will help clarify whether the high-affinity state of GPCRs exists in vivo and whether agonist tracers really have advantages over antagonist tracers because of their preferential binding to the high-affinity state. SHALGUNOV ET AL.

APPENDIX CALCULATION OF BINDING POTENTIALS
The ratio of the concentrations of specifically bound tracer (B) and free tracer (F) in the tissue at equilibrium is equal to the ratio of available receptor density and ligand-receptor affinity (B max /K d ) when the tracer only occupies a negligible fraction of all receptors ( Figure A1).
In practice, specifically bound tracer concentration B is often calculated as a difference between tracer concentrations in a receptor-rich region of interest and a receptor-poor reference region. Free tracer concentration, on the other hand, is replaced with directly measurable concentrations that are linearly dependent on "true" F at equilibrium. 192 These concentrations can be: -Free tracer concentration in plasma (equal to F if the tracer is transferred from tissue to plasma by passive diffusion); -Total, that is, free and protein-bound, tracer concentration in plasma; -Nondisplaceable, that is, free and nonspecifically bound, tracer concentration in tissue.
To determine tracer concentration in plasma (whether free or total) one needs to obtain arterial plasma samples, which is an invasive procedure. Therefore, the last option is the most popular: tracer concentration in receptor-rich tissue is related to tracer concentration in receptor-poor tissue.
Binding potentials are defined at equilibrium. Plasma and tissue concentrations of a tracer can be directly equilibrated with each other by administering the tracer in an infusion but such paradigms are hard to implement. Therefore, in most positron emission tomography (PET) and single-photon emission computed tomography (SPECT) studies tracer is administered via a simple bolus injection. In that case, to calculate binding potentials, time-activity curves for regions of interest are used as input data for so-called kinetic modeling. A compartmental model is built up based on relevant theories. Tracer distribution is described in terms of its transfer between virtual compartments (like "free tracer," "nonspecifically bound tracer," and "specifically bound tracer"). The model is fitted to the time-activity curves acquired by the PET camera. If the model can adequately describe the experimental curves, the values of individual kinetic parameters or their combinations are determined from the model fit. Fewer fitting parameters often mean a more robust fit, so many simplifying assumptions are often made. Graphical analyses, simplifying the fitting process to linear regression, are also widely used. 235,236 Fitted parameters are then used to obtain binding potentials, essentially by extrapolating the kinetics observed in the imaging experiments to the situation of equilibrium.
F I G U R E A 1 Relationship between the fraction of ligand-occupied receptors and B/F ratio. At equilibrium, B/B max = F/(F + K d ), therefore B/F = B max /(F + K d ). If F ≪ K d , then B ≪ B max and B/F~B max /K d . Note that at low concentrations (F/K d ≪ 1), the ligand occupies only a small part of total receptor population, and the B/F ratio (binding potential) is stable (left part of the graph)