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Journal of Cerebral Blood Flow and Metabolism
21:982–994 2001 The International Society for Cerebral Blood Flow and Metabolism
Published by Lippincott Williams & Wilkins, Inc., Philadelphia
Quantification of Neuroreceptors in Living Human Brain. V.
Endogenous Neurotransmitter Inhibition of Haloperidol Binding Positron Emission Tomography Center, Aarhus University Hospitals, Aarhus, Denmark; and *Department of Radiology, Johns Hopkins Medical Institution, Baltimore, Maryland, U.S.A. Summary: The half-inhibition concentration (IC ) of a drug
nmol/L in patients with schizophrenia or bipolar disease with indicates its ability to inhibit the binding of other ligands of a receptor. The authors used positron emission tomography to with an 8-fold increased binding of dopamine and a 16-fold test the hypothesis that haloperidol’s IC elevated concentration of synaptic dopamine in psychosis. At tracer N-[11C]methylspiperone ([11C]NMSP) in brain must be the 80% haloperidol blockade of the receptors, the calculated increased in patients in whom more dopamine is bound to amount of neurotransmitter bound in the patients with psycho- receptors than in healthy volunteers. The IC sis declined to twice the value estimated in the nonpsychotic was significantly elevated from 1.5 nmol/L in healthy volun- subjects, that is, 5 pmol cm−3. Key Words: Dopamine—
teers and patients with bipolar disease without psychosis to 4.5 Neuroleptics—Neuroreceptors—Positron emission tomography.
Previous studies (Wong et al., 1986c, Dewey et al., haloperidol must decline in states of psychosis in which 1991, 1993; Laruelle et al., 1996) have claimed an effect the competition from dopamine is increased, the authors of endogenous dopamine on the binding of neuroleptics determined the apparent affinity for this neuroleptic in and analogous radioligands to D -like receptors in pri- previously examined healthy volunteers, volunteers with mate (human and monkey). Recently, Abi-Dargham et bipolar disease with or without psychosis, and volunteers al. (2000) reported findings suggestive of increased do- with schizophrenia (Wong et al., 1997b).
pamine concentration in brain of patients with schizo- The results are consistent with an elevation of the phrenia, compared with healthy volunteers. When in- concentration of dopamine in patients with psychosis, creased baseline dopamine concentration is associated whether from schizophrenia or bipolar illness, but de- with increased dopamine binding to receptors, it must cline of plasma protein binding or intrinsic receptor af- raise the half-inhibition concentration of exogenous an- finity for haloperidol also explain this finding.
tagonists of this binding. The authors tested this predic-tion by comparing measures of the half-inhibition con- MATERIALS AND METHODS
centration of haloperidol in healthy volunteers and in Operational equation
In the Appendix, the operational equation is derived, which To test the prediction, the authors derived a theoretical was used to determine the half-inhibition plasma concentration basis for the in vivo determination of the half-inhibition of an unlabeled neuroreceptor antagonist by means of a tracer constant of an exogenously supplied inhibitor. To spe- radioligand. The in vivo estimation of the half-inhibition con- cifically test the hypothesis that the apparent affinity to centration (IC ) of an inhibitor of specific neuroreceptors re- quires (at least) two measurements of the rate or degree ofbinding of the radioligand, for example, in the presence andabsence of the inhibitor (Gjedde et al., 1986; Gjedde and Wong, Received October 19, 1999; final revision received March 15, 2001; 1990a,b). The authors used the radioligand 3-N-[11C] methyl- spiperone ([11C]NMSP) to determine tho degree of dopamine Supported by NIH (USPHS) grants RO1 MH42821 and DA09482, D -like receptor occupancy of the neuroleptic haloperidol in and MRC (Denmark) grants 9305246, 9305427, and 9700555.
caudate nucleus, the dopamine D -like receptors being the only Address correspondence and reprint requests to Dr. Albert Gjedde, PET Center, Aarhus General Hospital, 44 Norrebrogade, DK-8000 Aarhus C, significant neuroreceptors shared by [11C]NMSP and haloper- idol (Wong et al., 1986b). The following six equations were ENDOGENOUS NEUROTRANSMITTER IN PSYCHOSIS derived in the Appendix and used to interpret the experimental endogenous competitor(s) in the absence of the exogenous results. They are listed here to show how estimates of the quantities of endogenous ligand and competitor can be madefrom the binding rate constant (k ) or time constant (␶ ס 1/ k ).
The assumptions underlying the equations include the claims that haloperidol and [11C]NMSP bind to the same binding sitewith single affinities, no change of the maximum binding ca- where ␴ (0) is the occupancy at the receptors achieved by occurs between the two administrations of the the putative endogenous competitor(s) in the absence of tracer, no average differences of haloperidol free fractions in exogenous inhibition. The calculation of ␴ (0) required that plasma and brain tissue exist between the groups of subjects, the true aqueous receptor affinity for haloperidol in vivo (K ) 3. The equation relating the concentration of the exogenous can be known (although it may not be known correctly) and inhibitor relative to its inhibitory constant to the binding is the same for all groups and both injections, haloperidol is time constants and the sum of the relative concentrations of in steady state, the plasma aqueous-free haloperidol concen- trations equal the synaptic aqueous-free haloperidol con-centrations, no differences of free fractions exist between the ␹ = I(pl)CI(pl) = ͩ␶͑I͒ − ␶ͪ͑1 + ␹ ͒ groups, and the binding of [11C]NMSP is unidirectional (that is, and at both injections. The effect(s) of departures from these where ␹ is the concentration of the exogenous inhibitor assumptions are examined in the Appendix.
relative to its inhibitory constant. The calculation of ␹ re- The operational equation relates the plasma IC quires that ␹ is known from Eq. 2.
idol to the binding time constant of the tracer, 4. The equation for the occupancy achieved by the exogenous antagonist in the presence of the endogenous competitor(s), where ␴ (x)is the occupancy achieved by the exogenous the steady-state plasma concentration of haloperidol, and ␶ inhibitor in the presence of the endogenous competitor(s).
symbolizes the time constant of unidirectional binding of the The calculation of ␴ (x) requires that ␹ is known from Eq.
tracer [11C]NMSP, equal to the reciprocal of the binding rate constant (1/k ) in the absence (␶) and presence (␶(I)) of the 5. The equation for the occupancy achieved by the putative exogenous inhibitor. The symbol in parentheses, I, refers to the endogenous competitor(s) in the presence of the exogenous presence of the exogenous inhibitor haloperidol, that is, at the second tomography session, 4 hours after the oral administra-tion of haloperidol. To calculate K the plasma concentration of the inhibitor and the binding time constants of the tracer. With this value, the authors estimated the concentrations and occupancies of hypothetical endogenous where ␴ (I)is the occupancy achieved by the putative en- dogenous competitor(s) after the blockade of the receptorsby the exogenous inhibitor. The calculation of ␴ (I) requires Equations of inference
that ␹ is known from Eq. 2 and that ␹ is known from To evaluate the influence of changes of the half-inhibition concentration of the inhibitor, five additional equations werederived, which allowed the authors to make inferences about These equations were derived in the Appendix for a radio- several factors that affect the interpretation of the results of the ligand that binds unidirectionally to the neuroreceptors during the time available for positron emission tomography. In addi-tion, in the Appendix, the criteria are established that must be 1. The equation relating the concentration of one or more pos- fulfilled for the authors to claim that binding of the radioligand tulated endogenous competitors to the binding of haloperi- was in fact unidirectional for the duration of the positron emis- dol, the concentration expressed relative to the competitors’ unknown Michaelis half-inhibition concentrations, Volunteers
All healthy subjects and patients volunteered and gave their informed consent to the study, in compliance with the Johns Hopkins Committee on Clinical Investigation. The details of where ␹ is the sum of the putative endogenous competitors, the volunteers participating in this study were presented previ- relative to their half-saturation constants, ⌺C /K , and where ously (Wong et al., 1986a,c, 1997b). The distribution of the is the plasma “free” fraction of haloperidol at steady subjects between the years 1986 and 1997 is listed in Table 1.
state. K is the aqueous half-inhibition concentration of halo- Briefly, 14 patients with bipolar affective disorder (7 men peridol in the absence of other inhibitors of the binding, that and 7 women, mean age ס 43 years), 22 drug-naive patients is, in the absence of the putative endogenous inhibitors.
with schizophrenia (17 men and 5 women, mean age ס 36 Calculation of ␹ requires that K years), 5 drug-free but previously medicated patients with 1 and that the free fraction of the inhibitor and the aqueous schizophrenia (mean age ס 27 years), and 22 healthy volun- half-inhibition concentration of the inhibitor is known from teers (17 men and 5 women, mean age ס 33 years) were the literature or measured separately in plasma.
recruited. Of the patients with bipolar disease, 11 were drug- 2. The equation for the occupancy achieved by the putative naive and 3 drug-free for at least 2 months. Of the patients with J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 TABLE 1. Number of subjects in 1986 and 1997 cohorts
Blood samples for radioactivity and haloperidol concentra- tion measurements were obtained from the dorsal vein of the hand contralateral to the injection hand, after “arterialization”by heating to 44°C, and, in some cases, from the radial artery.
The sampling schedule consisted of 4 to 6 samples the first minute after the tracer injection, 3 to 6 samples the second minute, 2 samples the third and every subsequent minute until the tenth minute, and samples at 25, 30, 45, 60, 75, and 90minutes. Blood samples were centrifuged and samples of theplasma were counted in a gamma-scintillation spectrometer. In bipolar disease, 3 were depressed and 11 were manic at the time previous comparisons, results obtained with arterialized venous sampling did not differ significantly from results obtained with On the basis of DSM-III, -IIIR, and -IV criteria as described arterial sampling (Wong et al., 1997a).
in Wong et al. (1986a,c, 1997b), the patients with bipolar dis- Quantitative analysis
ease were divided in two groups—patients without episodes ofpsychosis and patients with episodes of psychosis during the Quantitative analysis of the studies was performed by an tomography. Subjects were divided categorically into those investigator blinded to the clinical diagnosis, as described by who were psychotic by definition at all times for the drug naive Wong et al. (1986a,b,c). Calculations of IC schizophrenic patients or specifically at the time of scanning from values of the time constants of unidirectional binding of for the psychotic bipolar patients, in contrast with the nonpsy- tracer [11C]NMSP in the caudate nucleus in the absence and chotic bipolar patients. In patients with bipolar disease, the presence of haloperidol in all subject groups, according to Eqs.
episodic nature necessary required the identification of active 1 and 2. Analysis of variance detected the significant differ- hallucinations and delusions during the positron emission to- mography scan time. Patients with bipolar illness who exhib- Time constants (␶ ס 1/ k ) of unidirectional binding of tracer ited active hallucinations and delusions were considered psy- [11C]NMSP were directly estimated from the time-radioactivity chotic, whereas those that did not present with these symptoms curves in brain tissue, as described by Gjedde et al. (1986).
were considered nonpsychotic. Patients and healthy volunteers Plasma haloperidol concentrations were determined as de- did not differ significantly with respect to blood pressure, scribed by Wong et al. (1997b) and the grand average of the pulse, weight, and nutritional status at the time of study. Further measurements was used as listed in Table 2. The average free clinical details were given by Tune et al. (1993) and Pearlson , mean ± SD (n)] for [18F]haloperidol of the individual groups were 0.035 ± 0.002 (10) for schizophrenia,0.041 ± 0.008 (5) for bipolar illness, and 0.033 ± 0.005 (7) for Tomography
The tomography is described in details in previous articles Putative endogenous competitor concentration ratios were by Wong et al. (1986c, 1997a). Briefly, in each patient, the computed from Eq. 2, using the value of the haloperidol “free” binding time constant of N-[11C]methylspiperone, labeled ac- cording to Burns et al. (1984) to the high specific activity of 2 (1997a), and an aqueous haloperidol half-inhibition concentra- mCi pmol−1, was measured twice by positron emission tomog- tion of 0.043 nmol/L in the absence of endogenous or other raphy after 10- to 20-second injection of 20 mCi into an ante- exogenous inhibitors, as reported by Ishizu et al. (2000) for the cubital vein. The injected mass averaged 30 pmol (kg body weight)−1. The specific activities did not differ between the Equations 3 to 6 were used to predict the degrees of receptor occupancy established by the putative endogenous competition Each tomography session lasted 90 minutes. Emitted radio- and exogenous inhibition and the actual neurotransmitter bind- activity was recorded with the NeuroECAT tomograph (CTI; ing to the receptors in the groups of volunteers.
Knoxville) in its highest resolution mode. Radioactivity wassimultaneously detected in caudate nucleus and cerebellum in 5 frames of 2 minutes, 5 frames of 5 minutes, and single framesof 15 and 30 minutes each. Between the 2 tomography sessions, The authors confirmed the unidirectionality of 4 hours before the second session, all subjects ingested 300 to [11C]NMSP uptake into the caudate nucleus by modeling 400 nmol kg−1 haloperidol resulting in steady-state plasma con- the uptake with and without dissociation from the recep- centrations that averaged less than 10 nmol/L in subjects with-out psychotic episodes and more than 10 nmol/L in subjects tors at the rate reported by Logan et al. (1987) and listed in Table 2. The plasma free fraction of haloperidol listed TABLE 2. Constants used in analysis of NMSP and haloperidol binding
Logan et al. (1987); Ishizu et al. (2000) Asterisks indicate transfer coefficients reflecting under the influence of competititors. [11C]NMSP, J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 ENDOGENOUS NEUROTRANSMITTER IN PSYCHOSIS in Table 2 was measured in the second group of subjects added to the Wong et al. (1986c) group by Wong et al.
[age in years], P ס 0.01). No other group showed a (1997a). The K of haloperidol in aqueous solution (listed in Table 2) was calculated from studies of people insignificantly from the 1.5 nmol/L average for healthy by Logan et al. (1987) and pigs by Ishizu et al. (2000).
volunteers and patients with bipolar disease without epi- The [11C]NMSP dissociation rate constant k of 0.003 sodes of psychosis, and 4.5 nmol/L for patients with min−1 (0.18 h−1) was not sufficient to render the binding schizophrenia or psychosis of other origin.
less than approximately unidirectional during the 90-minute tomography, assuming unlimited specific activity DISCUSSION
of the tracer. In the 90 minutes, the accumulation was95% of the accumulation expected with complete unidi- In 1986, the authors reported that therapeutic doses of rectionality. In terms of the total amounts of radioligand, haloperidol block 70% to 90% of the dopamine receptors the authors estimated that the s/␴ ratio (Appendix, Eqs.
imaged by [11C]NMSP (Wong et al.,1986b), but they 12 and 14) never exceeded 0.05 during the 90 minutes and that the transfer therefore must be effectively unidi- patients suffering from psychosis than in subjects not so rectional, even if the inclusion of dissociation would afflicted (Wong et al.,1986c). Hence, the results of these yield different estimates of the magnitude of ␶. There- experiments do not reject the hypothesis that patients fore, the authors limited the regression for ␶ to three with psychosis have a higher endogenous neurotransmit- ter binding to dopamine receptors than subjects without In agreement with the previous analysis (Wong et al., psychosis (Abi-Dargham et al., 2000). Nonetheless, nu- 1997b), the average estimates of the magnitude of ␶ did merous assumptions underlie the equations used, and not differ among the groups, except for the nonpsychotic multiple factors influence the results. Increased endog- patients with bipolar disease. Plasma haloperidol concen- enous neurotransmitter level is only one among a multi- trations did not vary significantly among the subject tude of possible interpretations of the data. A theoretical groups, although the concentration averages were twice description of some of the many possible interpretations as high in the psychotic patients, as shown in Table 3.
This variation is well known from the literature (Midha Increased intrasynaptic dopamine has been hypoth- et al., 1989; Goff et al., 1991) but remains unexplained.
esized since the earliest formulation of the dopamine When the measurements were lumped according to the theory of schizophrenia. Early evidence originated from patients’ condition at the positron emission tomography an in vivo study of the binding of [11C]NMSP in ventral measurement (nonpsychotic or psychotic), the plasma striatum and nucleus accumbens in schizophrenia (Wong haloperidol concentrations were significantly elevated in et al., 1986c). Using the procedure described here, the the psychotic subjects. The average neuroleptic blockade authors noted an apparent increase of the haloperidol corresponded to group mean haloperidol occupancies of affinity constant in the patients, which was interpreted as a possible increase of endogenous dopamine (footnote 16, Wong et al., 1986c). In the current study, the authors calculated from Eq. 1 as normally distributed, because extend the calculation to include bipolar illness and pro- denominator values generally were large rather than vide a theoretical basis for the interpretation of the re- small. Averages differed significantly among the five sults in terms of dopamine binding, as shown in Table 4.
groups (F ס 2.81, P ס 0.05). The apparent affinity was For the purpose of inference about dopamine binding, significantly decreased in the drug-naive patients with the group averages were lumped into the three classes schizophrenia, compared with healthy volunteers (t ס listed in Table 4. The class averages formed the basis of 2.84, P ס 0.008). Multiple regression against age speculations on the quantities of free and bound neuro- showed a significant relation between the IC transmitter and antagonist, incorporating previously pub- the patients with bipolar disease who had had psychotic lished estimates of the maximum binding capacities TABLE 3. Average IC
Means are ±SEM for comparison among groups.
J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 TABLE 4. Predicted neurotransmitter binding in psychosis
schizophrenia andbipolar disease withpsychosis) is the concentration of the exogenous inhibitor in arterial plasma. K is the apparent half-inhibition concentration of the inhibitor in arterial plasma. ␹ is the sum of putative endogenous competitors, relative to their half-saturation concentrations. B capacity in ventral caudate nucleus at age 40 reported by Wong et al. (1997b). ␴ (0) is the occupancy of the endogenous competitor(s) in the absence is the predicted binding of neurotransmitter x at age 40. ␹ is the concentration of exogenous inhibitor, relative to its inhibitory constant. ␴ (x) is the occupancy of the exogenous inhibitor in the presence of the endogenous competitor(s). ␴ (I) is the occupancy of the putative endogenous competitor(s) in the presence of the exogenous inhibitor. B is the predicted binding of neurotransmitter x after neuroleptic blockade at age 40. Remaining symbols are defined in relation to the equations indicated in the table.
) of the three subject classes (Wong et al., 1997b).
receptor sites, as the bound endogenous competitors dif- Using the same value of the plasma “free” fraction f fered little between the two groups (␹ 2.53 vs. 2.45).
for all groups, and the aqueous half-inhibition concen- The theoretical treatment (Appendix) revealed that es- tration K of 0.043 nmol/L for haloperidol listed in Table timates of the apparent affinity of an administered recep- 2, the total relative concentration of putative endogenous tor antagonist can be used to infer changes of neurotrans- competitors averaged 0.15 in the nonpsychotic or healthy mitter concentration in brain only on certain conditions.
subjects, corresponding to an average receptor occu- This means that the significant elevation of the haloper- pancy of 13%. The quantity of bound endogenous com- petitors was estimated to be 2.5 pmol cm−3 at a total other possible explanations. In the Appendix, an expres- [11C]NMSP receptor density of 19 pmol cm−3 at age 40.
In the psychotic patients with bipolar disease or drug- eral factors that could have contributed to the measured naive schizophrenic patients, the total relative concentra- tion of putative endogenous competitors averaged 2.45, a 16-fold increase, corresponding to an 8-fold increase of receptor occupancy (71%, or 21 pmol cm−3 of a total [11C]NMSP receptor density of 29 pmol cm−3 at age 40).
including the free plasma fraction of the inhibitor (f After haloperidol blockade, the putative endogenous the intrinsic affinity constant of the inhibitor itself (K ), competitor occupancy declined to 2.2% in the combined the possible endogenous nonagonist competitors (␹ ), the groups I and II and to 16% in the combined groups III endogenous agonists (␹ ), the G-protein-induced affinity and IV (0.4 pmol cm−3 and 4.7 pmol cm−3, respectively), change of the agonists (⌫), and the inhibitor-induced as shown in Table 3. Thus, even at the higher plasma relative increase of the endogenous agonists (␯).
haloperidol concentration, patients in groups III and IV The claim that the level of endogenous competition of had a lower haloperidol occupancy and a 12-fold higher the haloperidol binding (exerted by ␹ , or ␹ , or both) is putative endogenous neurotransmitter binding than the elevated in the patients assumes that neither the inhibi- tor’s plasma “free” fraction nor the intrinsic affinity of its Notably, the predicted residual neurotransmitter bind- receptors has changed. The current calculation used the ing in the haloperidol-blocked patients in groups III and same plasma “free” fraction of haloperidol in all the IV was only twice as high as the predicted neurotrans- subject groups. As previously discussed by Wong et al.
mitter binding in the volunteers in groups I and II (those (1997b), it is unlikely that the change of the IC without psychosis). These results show that the haloper- because of different degrees of protein binding.
idol blockade tended to normalize the neurotransmitter The calculation assumes that haloperidol binds com- binding in the patients with psychosis.
petitively to the receptors, which also bind NMSP, and The analysis predicted that patients with schizophrenia that the inhibition in theory can reach 100%. Although who had received neuroleptics previously did not have a the group mean occupancies averaged 70% to 87%, the higher neurotransmitter binding than did the patients calculated occupancy reached 100% in some subjects.
who never received medication (4 vs. 4.7 pmol cm−3).
Lyon et al. (1986) and Frost et al. (1987) recorded near- Thus, the plasma haloperidol concentration was not el- 100% occupancies of NMSP receptors in rodents, and evated by greatly increased agonist competition at the Ishizu et al. (2000) showed that haloperidol bound J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 ENDOGENOUS NEUROTRANSMITTER IN PSYCHOSIS competitively over a range of multiple concentrations, Laruelle et al. (1996, 1997) reported a decline of the although no concentration reached as high as recorded in binding potential of a labeled benzamide tracer induced by administration of amphetamine to healthy volunteers The calculation also assumes a single value for the and patients with schizophrenia. The decline of the bind- intrinsic haloperidol half-inhibition concentration (K ), ing potential was inferred from calculations of the ratio but there is no direct evidence that the affinities of the of specific-to-nonspecific binding of the tracer that relevant neuroreceptors for haloperidol in fact remain would not reveal the baseline concentration of the en- unchanged. For this reason, it can not be ruled out that a dogenous neurotransmitter, as argued above, but would fundamental change of the receptors occurred in patients reveal the transient change induced by the administered with the psychotic potential that caused the inherent af- amphetamine. In schizophrenic patients, the decline was finity toward haloperidol to decline. In the final analysis, significantly more pronounced than in the healthy con- however, it is difficult to distinguish between an intrinsic trol subjects. On the basis of this finding, Laruelle et al.
decline of affinity and a decline imposed by the elevation (1997) claimed that the release of an endogenous com- of a competitor, because it is not known how the affinity petitor of the tracer binding was more pronounced in schizophrenia. Equation 7 shows that not only the release The interpretation that the level of endogenous com- of the agonist but also a G-protein-induced increase of petitors of the haloperidol binding is elevated in the pa- the agonist’s affinity could explain the finding.
tients is consistent with previous claims that extracellular Amphetamine is not the only agent capable of releas- dopamine levels may be high in patients with active psy- ing dopamine to the extracellular space; both haloperidol chosis, or that the administration of a neuroleptic leads and raclopride are neuroleptics known to have this effect to greater extracellular release of dopamine in patients (Westerink and de Vries, 1989). Equation 7 shows that it with psychotic tendencies than in patients without these is possible to miss increases of receptor density and half- inhibition concentration if pathologically elevated but Rather than making distinctions among the different transient increases of the endogenous competitor occur roles of nonagonists, agonists, and G-proteins, the cur- as a consequence of the administration of the exogenous rent analysis yielded a single estimate of the “lumped” inhibitor, as has been shown for schizophrenia. This is baseline endogenous competitor concentration relative to also possible when the exogenous inhibitor is itself a its affinity constant (␹ ). In Eq. 7, the apparent concen- tracer administered at low specific activity, as is the case tration of this “lumped” competitor, relative to a when raclopride is used as a tracer of dopamine D -like receptor density (Farde et al., 1990, 1995). In the currentexperimental design, the authors were not in a position to ascertain whether any such “hidden” agonist increase persisted long enough after the administration of the ex-ogenous antagonist to affect the estimates reported.
according to which the calculated increase is an estimate However, if the estimates were affected, it would lower of an extracellular dopamine elevation only when the rather than further increase the estimates of the Michaelis level of other competitors and G-protein action remain constants. Thus, a “hidden” agonist surge would render unchanged and when the inhibitor itself induces no change of dopamine or G-protein action. Thus, it was not Recently, Abi-Dargham et al. (2000) attempted to possible to give a direct estimate of the absolute agonist measure the baseline endogenous competitor level by concentration because the apparent affinities of partial increasing the binding of an exogenous competitor with and complete agonists probably do change as functions drugs that deplete the dopamine (for example, AMPT).
of the agonist concentration itself.
The outcome of this study was interpreted as showing a Independently of changes of membrane potential, do- greater baseline dopamine level in patients with schizo- pamine action at the D , D , and D receptors in the phrenia than in healthy volunteers. As such, that study striatum is mediated primarily by G proteins that form agrees with the conclusions drawn from the current ternary complexes with the agonist-activated receptor study, although the change calculated by Abi-Dargham (Wang et al., 1995; Beindl et al., 1996; Jiang et al., et al. (2000) is much smaller than determined in the 2001). The striatal D receptor is predominantly of the “long” isoform in which the long third cytoplasmic On the basis of the observations reported here, the loop mediates coupling to the G-proteins (Guivarc’h et authors speculate that the propensity for psychosis is al., 1995). As derived in the Appendix, this coupling associated with increased endogenous neurotransmitter leads to an increase of the apparent affinity of the recep- binding to dopamine D -like receptors in the most ven- tor to the agonist, which contributes to an increase of tral parts of the caudate nucleus. Variations of the base- line level of endogenous competition may invalidate J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 measures of binding rate or potential as index of receptor receptor density and affinity: a PET study with [11C]raclopride in density (Wolf et al., 1996), and transiently increased en- Frost JJ, Smith AC, Kuhar MJ, Daunals RF, Wagner HN (1987) In vivo dogenous competition, as a result of exogenous inhibitor binding of 3H-N-methylspiperone to dopamine and serotonin re- administration, may mask changes of receptor density, or Michaelis half-saturation concentration, or both (Farde et Gjedde A, Wong DF, Wagner HN Jr (1986) Transient analysis of irreversible and reversible tracer binding in human brain in vivo.
In: PET and NMR: new perspectives in neuroimaging and clinical Dopamine-induced inhibition of haloperidol binding neurochemistry (Battistin L, ed), Alan R Liss: New York, pp 223– speaks against the ‘denervation hypersensitivity’ theory Gjedde A, Wong DF (1990a) Modeling neuroreceptor binding of ra- of low extracellular dopamine as the explanation of epi- dioligands in vivo. In: Quantitative imaging of neuroreceptors sodes of psychosis in these disorders, unless it is also (Frost J, Wagner HN Jr, eds), New York: Raven Press, pp 51–79 argued that the extracellular dopamine is lowered outside Gjedde A, Wong DF (1990b) Modeling the dopamine system in vivo.
In: In vivo imaging of neurotransmitter functions in brain, heart the synapses and elevated in the synaptic cleft. Such a and tumors. Frontiers in nuclear medicine (Kuhl DE, ed), Wash- differential change would represent a shift of dopamine ington, D.C.: American College of Nuclear Physicians, U.S. De- from a more static pool outside vesicles and synapses to Goff DC, Midha KK, Brotman AW, Waites M, Baldessarini RJ (1991) the more dynamic pool in the vesicles and the synapses.
Elevation of plasma concentrations of haloperidol after the addi- The apparent (‘measurable‘) affinity of the D -like tion of fluoxetine. Am J Psychiatry 148:790–792 receptors to dopamine in the high-affinity state is 10-fold Guivarc’h D, Vernier P, Vincent JD (1995) Sex steroid hormones change the differential distribution of the isoforms of the D do- greater than the affinity of the D1-like receptors, ap- pamine receptor messenger RNA in the rat brain. Neuroscience proximately 1 nmol/L versus 10 nmol/L (Seeman and Van Tol, 1993, 1994). The intrinsic affinity is unknown.
Ishizu K, Smith DF, Bender D, Danielsen EH, Hansen SB, Wong DF, Cumming P, Gjedde A (2000) Positron emission tomography of Speculating on the basis of the G-protein effect discussed radioligand binding in porcine striatum in vivo: haloperidol inhi- above that the intrinsic affinity is no more than 1% of the bition linked to endogenous ligand release. Synapse 38:87–101 apparent agonist-induced affinity (that is, that K is no Jiang M, Spicher K, Boulay G, Wang Y, Birnbaumer L (2001) Most central nervous system D dopamine receptors are coupled to their less than 100 nmol/L), the intrasynaptic dopamine con- effectors by Go. Proc Natl Acad Sci U S A 98:3577–3582 centration is Ն15 nmol/L in the healthy volunteers stud- Laruelle M, Abi-Dargham A, van Dyck CH, Gil R, D’Souza CD, Erdos ied here, and 10-fold greater in the individuals with psy- J, McCance E, Rosenblatt W, Fingado C, Zoghbi SS, Baldwin RM,Seibyl JP, Krystal JH, Charney DS, Innis RB (1996) Single photon chosis. This speculation about the concentration of do- emission computerized tomography imaging of amphetamine- pamine on the basis of occupancy figures must take into induced dopamine release in drug-free schizophrenic subjects.
account agonist-induced affinity changes.
Proc Natl Acad Sci U S A 93:9235–9240 Laruelle M, D’Souza CD, Baldwin RM, Abi-Dargham A, Kanes SJ, Fingado CL, Seibyl JP, Zoghbi SS, Bowers MD, Jatlow P, Charney Acknowledgments: The authors thank Godfrey Pearlson
DS, Innis RB (1997) Imaging D receptor occupancy by endog- and Larry Tune for patient recruitment and support, and Bob enous dopamine in humans. Neuropsychopharmacology 17:162– Dannals, Alan Wilson, and Hayden Ravert for radiochemistry Logan J, Wolf AP, Shiue CY, Fowler JS (1987) Kinetic modeling of receptor-ligand binding applied to positron emission tomographicstudies with neuroleptic tracers. J Neurochem 48:73–83 REFERENCES
Lyon RA, Titeler M, Frost JJ, Whitehouse PJ, Wong DF, Wagner HN, Dannals RF, Links JM, Kuhar MJ (1986) 3H-3-N-Methylspiperone Abi-Dargham A, Rodenhiser J, Printz D, Zea-Ponce Y, Gil R, Kegeles labels D dopamine receptors in basal ganglia and S2 receptors in L, Weiss R, Cooper TB, Mann JJ, Van Heertum RL, Gorman J, cerebral cortex. J Neurosci 6:2941–2949 Laruelle M (2000) Increased baseline occupancy of D receptors Midha KK, Chakraborty BS, Ganes DA, Hawes EM Hubbard JW, by dopamine in schizophrenia. Proc Natl Acad Sci U S A 97:8104– Keegan DL, Korchinski ED, McKay G (1989) Intersubject varia- tion in the pharmacokinetics of haloperidol and reduced haloperi- Beindl W, Mitterauer T, Hohenegger M, Ijzerman AP, Nanoff C, Fre- dol. J Clin Psychopharmacol 9:98–104 issmuth M (1996) Inhibition of receptor/G protein coupling by Pearlson GD, Tune LE, Wong DF, Aylward EH, Barta PE, Powers RE, suramin analogues. Mol Pharmacol 50:415–423 Tien AY, Chase GA, Harris GJ, Rabins PV (1993) Quantitative D2 Burns HD, Dannals RF, Långström B, Ravert HT, Zemyan SE, Duelfer dopamine receptor PET and structural MRI changes in late-onset T, Wong DF, Frost JJ, Kuhar MJ, Wagner HNJr (1984) (3-N- schizophrenia. Schizophr Bull 19:783–795 [11C]methyl)spiperone, a ligand binding to dopamine receptors: Pearlson GD, Wong DF, Tune LE, Ross CA, Chase GA, Links JM, radiochemical synthesis and biodistribution studies in mice. J Nucl Dannals RF, Wilson AA, Ravert HT, Wagner HN Jr (1995) In vivo D dopamine receptor density in psychotic and nonpsychotic pa- Dewey SL, Logan J, Wolf AP, Brodie JD, Angrist B, Fowler JS, tients with bipolar disorder. Arch Gen Psychiatry 52:471–477 Volkow ND (1991) Amphetamine induced decreases in (18F)-N- Seeman P, Van Tol HH (1993) Dopamine receptor pharmacology. Curr methylspiroperidol binding in the baboon brain using positron emission tomography (PET). Synapse 7:324–327 Seeman P, Van Tol HH (1994) Dopamine receptor pharmacology.
Dewey SL, Smith GS, Logan J, Brodie JD, Fowler JS, Wolf AP (1993) Striatal binding of the PET ligand 11C-raclopride is altered by Tune LE, Wong DF, Pearlson G, Strauss M, Young T, Shaya EK, drugs that modify synaptic dopamine levels. Synapse 13:350–356 Dannals RF, Wilson AA, Ravert HT, Sapp J (1993) Dopamine D2 Farde L, Wiesel FA, Stone-Elander S, Halldin C, Nordström AL, Hall receptor density estimates in schizophrenia: a positron emission H, Sedvall G (1990) D dopamine receptors in neuroleptic-naive tomography study with 11C-N-methylspi-perone. Psychiatry Res schizophrenic patients. A positron emission tomography study with [11C]raclopride. Arch Gen Psychiatry 47:213–219 Wang HY, Undie AS, Friedman E (1995) Evidence for the coupling of Farde L, Hall H, Pauli S, Halldin C (1995) Variability in D -dopamine Gq protein to D1-like dopamine sites in rat striatum: possible role J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 ENDOGENOUS NEUROTRANSMITTER IN PSYCHOSIS in dopamine-mediated inositol phosphate formation. Mol Pharma- ␴, and ␶) represent time variables, upper case symbols represent constants in time. Equation 9 can be rear- Westerink BH, de Vries JB (1989) On the mechanism of neuroleptic induced increase in striatal dopamine release: brain dialysis pro- vides direct evidence for mediation by autoreceptors localized onnerve terminals. Neurosci Lett 99:197–202 Wolf SS, Jones DW, Knable MB, Gorey JG, Lee KS, Hyde TM, Coppola R, Weinberger DR (1996) Tourette syndrome: prediction of phenotypic variation in monozygotic twins by caudate nucleusD receptor binding. Science 273:1225–1227 where m is the mass of all nonspecifically bound or Wong DF, Gjedde A, Wagner HN Jr (1986a) Quantification of neuro- unbound ligand in the tissue, V represents the volume of receptors in the living human brain. I: Irreversible binding. J Cereb no-affinity and low-affinity (that is, transiently equili- Wong DF, Gjedde A, Wagner HN Jr, Dannals RF, Douglass KH, Links brating with immeasurable rapidity) distribution of the JM, Kuhar MJ (1986b) Quantification of neuroreceptors in the ligand in the tissue, equal to the ratio m /c, and K is the living human brain. II: Inhibition studies of receptor density. J Cereb Blood Flow Metab 6:147–153 Michaelis or half-saturation concentration constant of the Wong DF, Wagner HN Jr, Tune LE, Dannals RF, Pearlson GD, Links ligand, equal to the ratio between the magnitudes of kd JM, Tamminga CA, Broussole EP, Ravert HT, Wilson AA, Toung and k (in the absence of internalization or other transport JKT, Malat J, Williams JA, O’Tuama LA, Snyder SH, Kuhar MJ, of the bound ligand). When the magnitude of the variable Gjedde A (1986c) Positron emission tomography reveals elevatedD dopamine receptors in drug-naive schizophrenics. Science c is either negligible compared with the magnitude of the constant K or actually constant, b defines a single ki- Wong DF, Young D, Wilson PD, Meltzer CC, Gjedde A (1997a) Quantification of neuroreceptors in the living human brain. III.
D-2-like dopamine receptors - theory, validation, and changes dur- When the rate constant of uninhibited unidirectional ing normal aging. J Cereb Blood Flow Metab 17:316–330 binding, k , is defined as the term k B Wong DF, Pearlson GD, Tune LE, Young LT, Meltzer CC, Dannals RF, Ravert HT, Reith J, Kuhar MJ, Gjedde A (1997b) Quantifi-cation of neuroreceptors in the living human brain. IV. Effect ofaging and elevations of D-2-like receptors in schizophrenia and bipolar illness. J Cereb Blood Flow Metab 17:331–342 = k m 1 − ͩc + KD APPENDIX
Unidirectional binding
saturation (s) of the receptors by the radioligand, and the The criteria of unidirectional binding are inherent in ratio c/(c + K ) is the equilibrium fraction of occupancy the conventional binding equation of which the Micha- of the receptors (␴), that is, the occupancy theoretically elis–Menten equation is the equilibrium solution. The achievable at the radioligand concentration c. When claim of unidirectionality is essential to current use of the these symbols are introduced into Eq. 11, Woolf–Hanes Plot. This Appendix derives the theoretical criterion of unidirectionality that allowed the authors to make the claim on the basis of known rate constants of the brain uptake of the radioligand used in this study. Thebinding equation is the differential equation expressing it is evident that binding equilibrium exists when the s/␴ the simplest current understanding of the competitive ratio is unity. Because the magnitudes of s and ␴ by interaction between a radioligand and its neuroreceptors,1 definition are equal at equilibrium, the unidirectional rateof binding can not be measured although it may be more or less substantial, depending on the magnitude of k .
The ratio between s and ␴ indicates the degree to which the binding is unidirectional within a given period of where b represents the bound mass of radioligand as a function of time, k represents the bimolecular associa- When the magnitude of c is negligible compared with tion constant, c represents the aqueous concentration of K (that is, when the specific activity of the radioligand the radioligand in extravascular fluid as a function of is infinitely high, as assumed in the current experiments), represents the maximal binding capacity of the halftime of approach to equilibrium, and hence the the receptors of the ligand in units of actual mass, and k unidirectionality of the binding, depend on the magni- represents the rate constant of dissociation of the ligand tude of the dissociation constant k . The reciprocal of k from the receptors. Lower case symbols (except for k, ␹, is the time constant of dissociation. For times sufficientlyshort relative to the magnitude of the time constant ofdissociation, s << ␴ and s/␴ is practically nil. Thus, the measured rate of binding is approximately unidirectional This formalism ignores the role of G-proteins, the effect of which J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 which is the same as stating that the binding is unidirec-tional when, where, again, the symbols C and K represent the steady- state and half-inhibition concentrations of the individual m = m + b mЈ + k ͐ mЈ dt inhibitors, respectively. As realized by Woolf (Haldane and Stern, 1932; Haldane, 1957) and later by Wong and where m is the total amount of tracer in the tissue, and Hanes (1962), this equation can be linearized to include mЈ is the quantity of unbound tracer remaining in the any number of competitors at any concentration, absence of dissociation of bound tracer from the recep-tors. In practical terms, according to Eq. 14, this require- ␶͑n͒ = ␶͑0͒ + ␶͑0͒␹ + ␶͑0͒␹ + … + ␶͑0͒␹ ment is upheld when the entire radioactivity actually in = ␶͑1͒ + ␶͑0͒␹ + … + ␶͑0͒␹ the tissue is not much less than the quantity predicted in the absence of significant loss from the brain of previ- ously bound tracer. Thus, what matters is not whethertracer dissociates from the binding compartment, but where ␶(0) ס 1/k is the time constant of undirectional whether any previously bound tracer is lost from the binding of the tracer radioligand in the absence of com- tissue as a whole and not registered by the scanning.
petitors of any kind. The symbols ␹ through ␹ represent the individual ratios between n inhibitors and their in- Woolf-Wong-Hanes plot of inhibition
hibitory constants. The equation is the multilinear (n + 1) It was necessary to establish the influence of one or dimensional Woolf-Wong-Hanes plot (Haldane and more competitors on the time constant of unidirectional Stern, 1932; Haldane, 1957; Wong and Hanes, 1962) of binding. The authors based the kinetics on the del Cas- the time constant of unidirectional binding of a ligand (at tillo-Katz-Lefkowitz-Costa formalism for calculating the negligible concentration) as a function of the steady-state effect of ternary G-protein complex model below. The concentrations of n inhibitors. The equation has the ad- model provides the link between the agonist-receptor-G- vantage that the slope of any of the relations between the protein ternary complex model (upper panel) and the time constant of unidirectional binding and the corre- antagonist binding model (lower panel).
sponding concentration of the inhibitor is ␶(0), and When the binding of the radioligand is inhibited by hence, independent of the absence or presence of other competition from a single other ligand, itself at steady state, Eq. 13 is recognized as a special case of a more The Woolf-Wong-Hanes plot has been recognized as a general equation derived by Gaddum (1937) for recep- particularly robust and stable linearization of the Micha- elis–Menten equation, which is less sensitive to outliersthan other linearizations such as the Eadie-Hofstee- Scatchard and Lineweaver-Burke plots (Keightley and Cressie, 1980; Keightley et al., 1983). Also, unlike thelinearization of the Michaelis-Menten equation used in enzyme kinetics, no lumping of dependent and indepen-dent variables occurs when Eq. 19 is applied to receptor binding (Gjedde et al., 1986). For these reasons, Wong et al. (1986a) chose Eq. 19 to determine the relation be-tween the time constant of unidirectional binding of where ␶ (I) is the time constant of the inhibited binding.
tracer [11C]NMSP and the concentration of a single ex- The symbols C and K represent the steady-state and half-inhibition concentrations of the inhibitor, respec-tively. When the binding of the radioligand is inhibited Single inhibitor
by competition from n other ligands at steady state, Eq.
The following treatment validates Eqs. 1 and 2 for the case of a single exogenous competitor: If the exogenousinhibitor is in fact the only competitor of the binding, Eq.
␶͑I͒ = ␶͑0͒ + ͩ␶͑0͒ͪ C J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 ENDOGENOUS NEUROTRANSMITTER IN PSYCHOSIS where ␶(0) ס 1/k . The magnitude of the slope of the tional binding of the radioligand to increase according to dependent variable ␶(I) as a function of the independent variable C equals V /(k K B concentration of the exogenous inhibitor is measured in n + I͒ = ␶͑n͒ + ͩfI͑pl͒ ␶͑0͒ C blood plasma, the slope also depends on the steady-state ratio between the concentration in blood plasma and the aqueous concentration in the fluid compartments of the ordinate intercept is ␶(n) and the absolute value of the negative abscissa intercept is the plasma IC ministered exogenous inhibitor with the steady-state I͒ = ␶͑0͒ + ͩfI͑pl͒ ␶͑0͒ C is the plasma concentration of the inhibitor is the steady-state ratio of inhibitor concentra- ␶͑n + I͒ − ␶͑n͒ tions in plasma water and blood plasma, equal to the “free” fraction. For inhibitor concentrations measured in In the absence of the exogenous (n + I)st inhibitor, the blood plasma, the slope of Eq. 20 is a lumped constant sum of the concentrations of the endogenous n competi- V /(k K ) . The ordinate intercept is V tors, relative to their inhibitory constants (␹ ס ∑n ), and the abscissa intercept is −K /f Michaelis constant or plasma half-inhibition concentra- , symbolized by K (pl). When only two mea- surements are available, the magnitude of K determined directly from the increase of the time con- ␶͑n + I͒ − ␶͑n͒ stant of unidirectional binding, relative to its baseline value in the absence of the exogenous inhibitor, In the presence of the (n − 1) other endogenous com- petitors, the equilibrium binding of any competing ago- The quantity of exogenous inhibitor bound to the re- nist with a concentration C obeys the equation, ceptors at steady state is the equilibrium solution to the The steady-state saturation together accomplished by the n endogenous competitors (␴ ס ⌺n Because the degree of occupancy of the inhibitor is such that, in the absence of the exogenous from which Eq. 3 follows. The occupancy of the exog-enous (n + 1)st inhibitor (␴ ) is B / B Multiple competitors
The following treatment validates Eqs. 1 and 2 for the case of multiple competitors. In principle, inhibition by a single competitor is a special case of simultaneous inhi- bition by multiple competitors. The kinetic treatment ofthe case of multiple competitors can be used to make Multiple competitors and elevated binding capacity
inferences about endogenous competitors that cannot The following treatment validates Eqs. 1 or 2 for the otherwise be measured directly. In the presence of n cases in which the maximum receptor binding capacity endogenous competitors at steady state, an exogenous may change. Validation is necessary because Eq. 23 as- (n + 1)st inhibitor causes the time constant of unidirec- J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 logically linked to, or coincidentally associated with, the G-Protein action
release of one or more endogenous competitors, the The response to G-protein-mediated neurotransmis- value of the time constant of unidirectional binding must sion is generally believed to be proportional to the quan- tity of ternary agonist-receptor-G-protein complexes (Burstein et al., 1997), as defined by DeLean et al. (1980) n + I͒ = ␶͑0͒ ͩ1 + ͚ and Samama et al. (1993). The affinity of G-protein- coupled receptors for the activating agonist is low whenthe receptor is dissociated from its G-protein and high on is the binding capacity that coexists with the interaction with the GTP-free form of the protein (GTP- shift) (Jiang et al., 2001). This property of G-protein- coupled agonist binding sites affects the interpretation of ␶Ј͑n + I͒ = ␶Ј͑n͒ + ͩf studies of dopamine release and can be modeled by means of an extension of Eq. 28. The extension was where ␶Ј(0) equals V /(k B+ suggested by the original ternary complex model of del the slope of the linear relation expressed in Eq. 32, cor- Castillo and Katz (1957), according to which the quantity rectly reflects the binding capacity, regardless of the presence of endogenous competitors.2 The abscissa in-tercept of Eq. 32 correctly reflects the IC ministered inhibitor under the influence of the endog- enous competitors, whether or not they exist or are where the subscript “a” refers to the specific agonist, the term B refers to the amount of the receptor-agonist com- plex that is not coupled to G-protein, K refers to the ␶Ј͑n + I͒ − ␶Ј͑n͒ basal affinity to the agonist, and KЈ refers to the appar- ent receptor affinity as modified by G-protein binding, Therefore, the estimations of the elevated B+ the endogenous competitors, relative to their individual where C is the G-protein concentration and K the re- inhibitory constants, must be corrected for the change of ceptor affinity to the G-proteins. These equations show that Eq. 18 is also valid for the case of G-protein modu- lation of receptor affinity to the agonist. From the equa-tions follow the equation for the steady-state receptor- ␶Ј͑n + I͒ − ␶Ј͑n͒ is the ternary G-protein complex, and C is the According to Eq. 24, the total receptor occupancy of concentration of the G-protein that is not part of a ternary the endogenous competitors is unaffected by the eleva- number of receptors occupied by the agonist is therefore, But only when no steady-state changes of the binding capacity or endogenous competitors occur, and persist, after the administration In the absence of other putative endogenous competi- of the exogenous inhibitor. The effect of such a change is discussedbelow.
tors, this equation expresses the simple interaction of the J Cereb Blood Flow Metab, Vol. 21, No. 8, 2001 ENDOGENOUS NEUROTRANSMITTER IN PSYCHOSIS agonist and G-protein concentrations in determining the quantity of the agonist-receptor-G-protein complexes, ␶Љ͑n + I͒ = ␶Љ͑n͒ + ͫfI͑pl͒␶Ј͑0͒ 1+ͫ⌬Ca max K ͓C + K ͔ + C C where ␶Љ (n) ס V (1 + ⌺n−1 C /K + C /KЈ)/(k B+ ) and where, as above, ␶Ј(0) ס V /(k B+ also indicates the number of receptors respon- a constant fraction of the administered inhibitor concen- sible for the effect of the receptor occupancy. This quan- tration, the apparent maximum binding estimated from tity—that is, the ternary receptor-agonist-G-protein com- Eq. 31 or any other solution of the Michaelis–Menten plexes—depends on the concentration of the agonist, the equation will equal B+ /(1 + [(⌬C /K )/(C total quantities of receptor and G-protein, B and the affinity of the receptors to the G-protein. As Cg is artificially low by a fraction propor- must decline when G-protein associates with the receptor tional to the increase of endogenous competitor released protein, the total quantity of the ternary complexes (B ) after the administration of the exogenous inhibitor. The can be calculated by replacing the term C with the terms for the variables of which it is a function (V C ס G intercept of Eq. 32 or from any other solution of the − B ). Equation 39 shows that the apparent half- Michaelis–Menten equation. Also, the affinity estimate saturation concentration of the agonist in the elicitation of an effect may be much greater than indicated by the intrinsic affinity constant of the receptors toward the IC50͑pl͒ = KЈI͑pl͒ր͑1 + ⌫ ␯͒ agonist (K ).3 This difference between the simple affinity I(pl)րKI(pl)) and ⌫ ס Ka of the receptors to the agonist and the concentration that elicits a half-maximum effect may explain the character- istic GTP-shift or increase of agonist affinity in vivo that n + I͒ = ␶Љ͑n͒ + makes it difficult to predict the absolute concentration of the agonist associated with an observed effect.
Agonist release
where ␶Љ(0) ס ␶(0)(1 + ␯) B In the section above, Eq. 31 was derived under the tion underlying Eq. 1 such that ␶ ס ␶Љ(n) and ␶(I) ס ␶Љ(n assumption that the concentrations of endogenous com- + I). The measured or calculated half-inhibition plasma petitors do not change when the exogenous inhibitor is administered. However, if the administration of the ex- ogenous inhibitor is associated with release of the en- dogenous competitors, the value of the binding time con- stant changes from ␶Ј to ␶Љ in Eq. 26, where ␹ is the nonagonist inhibitor sum ⌺n−1 C / K , n + I͒ = ␶͑0͒ ͩ1 +͚ͫ + + + is the ratio K /KЈ (see Eq. 37), equal to the relative increase of the average agonist affinity because of G- protein binding to the occupied receptors, and ␹ is the where ⌬C represents the additional release of agonist, agonist ratio C /K . The formula shows that the ability of an antagonist or agonist to inhibit the binding of a ra-dioligand depends on several factors that are difficult orimpossible to monitor, including the local hematocrit of 3The maximum quantity of the ternary G-protein complexes and the the cerebral vascular bed, which may change as a func- apparent half-maximum agonist concentration can be predicted fromthis equation. The maximum quantity of the ternary complexes is tion of blood flow, and the local G-protein environmentof the receptors, which may change as a function of interventional effects not directly related to a change of ͌͑K V + G + B ͒2 − 4G B REFERENCES
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