[3H]QNB displays in vivo selectivity for the m2 subtype

Life Sciences, Vol. 55, No. 19, pp. 1493-1508, 1994 1994 Elsevier Science Ltd Printed in the USA. All fights reserved 0024-3205/94 $6.00 + .00

Pergamon 0024-3205(94)00308-4

[3H]QNB DISPLAYS IN VIVO SELECTIVITY FOR THE m2 SUBTYPE Miriam S. Gitler 1 , Rosanna De La Cruz 1 , Barry R. Zeeberg 1 , and Richard C. Reba 1,2 1Department of Radiology, Section of Radiopharmaceutical Chemistry, George Washington University Medical Center, 2300 Eye St., N.W., Washington D.C. and 2Department of Radiology, Nuclear Medicine Section, University of Chicago Hospital, 5841 S. Maryland Avenue, Chicago IL

(Received in final form September 2, 1994) Summary AIzheimer's disease (AD) involves selective loss of muscarinic m2, but not ml, subtype neuroreceptors in the posterior parietal cortex of the human brain. Emission tomographic study of the loss of m2 receptors in AD is limited by the fact that there is currently no available m2-selective radioligand which can penetrate the blood-brain barrier. [3H](R)-3-quinuclidinylbenzilate ([3H]QNB) is commonly used for performing in vitro studies of the muscarinic acetylcholine receptor (mAChR), either with membrane homogenates or with autoradiographic slices, in which [JH]QNB is nonsubtype-selective. We report here the results of in vivo studies, using both carrier-free and low specific activity [3H]QNB, which show that [3H]QNB exhibits a substantial in vivo m2-selectivity. Previously reported in vivo (R)-3-quinuclidinyl (R)-4-iodobenzilate ((R,R)-[1251]IQNB) binding appears to be nonsubtype-selective. Apparently the bulky iodine substitution in the 4 position reduces the subtype selectivity of QNB. It is possible that a less bulky fluorine substitution might permit retention of the selectivity exhibited by QNB itself. We conclude that a suitably radiolabeled derivative of QNB, possibly labeled with t8F, may be of potential use in positron emission tomographic (PET) study of the loss of m2 receptors in AD. Key Words: emission tomographic neuroreceptor, m2 muscarinic neuroreccptor subtype, [3H]QNB AIzheimer's disease (AD) appears to involve selective loss of m2 subtype neuroreceptors in the posterior parietal cortex of the human brain (1-5). Several studies (6-9) have recently attempted to determine whether single photon emission computed tomographic (SPECT) imaging of the distribution of (R)-3-quinuclidinyl (R)-4-iodobenzilate ((R,R)-[1251]IQNB) could be useful for detecting pathological changes in muscarinic neuroreceptor concentration in AD. These studies are subject to the limitation that the m2 subtype constitutes only about 19% of the total mAChR in the posterior parietal cortex (10). Even a complete loss of the small fraction of m2 receptors would correspond to a small relative change in the observed (R,R)-[1231]IQNB accumulation. Thus, it is essential to develop a radioligand which can penetrate the blood brain barrier (BBB) and which has high in vivo selectivity for the m2 subtype. The in vitro m2selective compounds AF-DX 116 (11-14) and DIBA (14) do not significantly penetrate the BBB (15), The in vitro m2-selective compounds AF-DX 384 (16) and AQ-RA 741 (15,17) are also Corresponding Author: B. Zeeberg, Radiopharmaceutical Chemistry, the George Washington University Medical Center, Room 662 Ross Hall, 2300 Eye St., N.W., Washington, D.C. 20037

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In Vivo Muscarinic m2 Selective Ligand

Voi. 55, No. 19, 1994

expected not to be able to penetrate the BBB. A recent report shows that the in vitro m2selective compound BIBN 99 is capable of antagonizing the centrally mediated pressor effects of arecoline in rats (18). The authors conclude that this observation demonstrates the ability of BIBN 99 to penetrate the BBB. However, in spite of the enormous potential of BIBN 99, as yet there is not direct biochemical evidence for significant penetration of the BBB by BIBN 99, for example by quantitating the brain distribution of radiolabeled BIBN 99. Furthermore, there has been no demonstration that BIBN 99 retains a functionally significant m2-selectivity in vivo. We have recently described the in vitro and in vivo characterization of a novel mAChR ligand DIBD (19), which appears to be able to penetrate the BBB and which has high in vivo selectivity for the m2 subtype. [3H](R)-3-quinuclidinylbenzilate ([3H]QNB) is commonly used for performing in vitro studies of the muscarinic acetylcholine receptor (mAChR),, either with membrane homogenates (20) or with autoradiographic slices (21), in which [,~H]QNB is nonsubtypeselective. We report here the results of in vivo studies, using both carrier-free and low specific activity [3H]QNB, which show that [3H]QNB exhibits a substantial in vivo m2selectivity. Theory Motivation The purpose of this section is to establish a relationship between certain macroscopic experimental observations and the corresponding molecular mechanisms, in the two cases discussed here, it may appear "intuitively obvious" that the macroscopic observation implies the molecular mechanism. However, these correspondences cannot legitimately be deduced without a mathematical derivation. The first derivation involves the observation of a substantial washout rate constant for [3H]QNB following postinjection of a large excess of a nonradioactive competitor. We would like to conclude that the macroscopically-observed substantial washout rate constant implies that the molecular rate constant for dissociation of specifically-bound [3H]QNB from its receptor is also substantial. This conclusion seems intuitively plausible, but should be demonstrated. The second derivation involves the observation that eventually both the unmetabolised plasma [3H]QNB and the brain tissue [3H]QNB are relatively time-invariant. We would like to conclude that this time-invariance implies that all subtypes of the mAChR are simultaneously in equilibrium with brain tissue [3H]QNB. Again, this conclusion seems intuitively plausible, but should be demonstrated. In order t o ~ u t the two derivations into perspective, the overall argument that will be developed is that [~H]QNB has a substantial receptor sensitivity. This argument will be based, in part, upon the theoretical conclusion that equilibrium implies substantial receptor sensitivity, and that the experimental observations involved in the two derivations imply that the subtypes of the mAChR are in equilibrium with brain tissue [3H]QNB. Model Equations A set of ordinary nonlinear differential equations based upon a m m dL(l)/dt = k 1 Cp(t) + ,~, ki, 4 MiL(I) - L(t) [k 2 + ~', ki,on Mi(t) ] i=1 i=1

(Eq. 1)

dMiL(t)/dt = ki,on Mi(t ) L(t) - ki, 4 MiL(t )

(Eq. 2)

modification and extension of Model 6 of Sawada et al. (22) describes the in vivo binding of [3H]QNB to multiple mAChR subtypes, t is the time; k 1 and k 2 are the first-order rate constants for transfer of radioligand between capillary plasma and brain; Cp(t)is the unmetabolized capillary plasma radioligand; L(t) is the unbound plus nonspecifically bound radioligand in brain; MiL(t)is the i th receptor-radioligand complex; ki, 4 is the first-order rate constant for dissociation of radioligand from MiL(t); Mi(t) is the unoccupied ith receptor concentration; Mi(0 ) = Mi(t ) + MiL(t), the total ith receptor concentration; ki,on is the

Vol. 55, No. 19, 1994

hz Vivo Muscarinic m2 Selective Ligand

1495

100"

f

t'

to

80"

"6

60

40" Eqs. 1 and 2

(n

Eqs. 1 - 4

.E ,Q

20"

~

\

Eqs. 5 - 18

"

\ \

O'

50

100 t i m e (rain)

150

200

Fig. 1 Illustration of generic brain tissue [3H]QNB time course and its relationship to the equations. The solid line indicates the time-dependent phase, the dotted line indicates the time-invariant phase, and the dashed line indicates the washout phase. The legend indicates which equations apply to each of the three phases. second-order rate constant for binding of L(t) to Mi(t); and m is the number of receptor subtypes.

Washout Kinetics In order to relate the macroscopically-observed washout rate constant kap p to the molecular rate constant k 4 for radioligand dissociation from the receptor, we will analyze the simplified case of a single receptor (m = 1). We assume that, prior to injection of nonradioactive ligand at t = t o (t o > t') the observed radioactivity is time-invariant for t > t ° (see illustration). Combining Eqs. 1 and 2 for t O > t _> t' results in d[L(t)

+ ML(t)]/dt

= dL(t)/dt

+ dML(t)/dt

= k 1 C p ( t ) - k 2 L(t) = 0

(t o > t _ > t ' )

(Eq. 3)

Thus it follows from Eq. 3 that k 1 Cp(t) -- k 2 L(t)

(t O > t_>t')

(Eq. 4)

Now assume that nonradioactive ligand is injected at t = t O (t O > t'). Since the concentrations are continuous at t = t 0, Eq. 4 still holds at t = t 0, so that k 1 Cp(t 0)-

k 2 L(t 0)

(t O > t')

(Eq. 4')

(see Appendix). However, there is a discontinuity in the slope at t = t O. For t > t O the timeinvariance no longer holds, since washout kinetics are induced by the injection of nonradioactive ligand at t o dL(t)/dt = k 1 Cp(t) + k 4 ML(t) - k 2 L(t) dML(t)/dt = - k 4 ML(t)

(t > to)

and the observed washout rate will be given by

(t > to)

(Eq. 5) (Eq. 6)

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hz Vivo Musearinie m2 Selective Ligand

d[L(t) + ML(t)]/dt = dL(t)/dt + dML(t)/dt

Vol. 55, No. 19, 1994

(t > to)

(Eq. 7)

under the assumptions that the nonradioactive ligand effectively occupies all of the available receptor sites [M(t) = 0 (t > to) ]. The differential equations (Eqs. 5 and 6) can be solved for the time-dependent values of ML(t) and L(t) under the assumption that, for t _> t', the unmetabolized [3H]QNB in plasma will be given as a monoexponential Cp(t) = Cp(t0) e-k(t-t0)

(t _> t')

(Eq. 8)

where k is the rate constant for loss of unmetabolized [3H]QNB in plasma, equal to 0.00022 min "1 [k83 given in legend to Fig. 2 in (23)]. The solution is ML(t) = ML(t0) e-k4(t-t0)

(t > to)

(Eq. 9)

and L(t) = Lk e-k(t-t0) + L2 e-k2(t-t0) + L4 e-k4(t-t0) (k 2 ¢ k 4,k)

(t>t0)

(Eq. 10)

where Lk = - k 1 Cp(t0) (k - k2)-1

(t > to)

(Eq. 11)

L2 = L(t0) + k 1 Cp(t0) (k - k2)-1 + k 4 ML(t0) (k 4 _ k2)-1

(t > to)

(Eq. 12)

and L4 = - k 4 M L ( t 0 ) (k 4 - k2)-1

(t > to)

(Eq. 13)

The constant terms Cp(t0) , L(t0) , and ML(t0) appear as initial boundary conditions for the solution of the differential equations during the washout phase (Eqs. 5, 6). Their values are determined as the result of the particular kinetic behavior occurring during the time course from t = 0 to t = t O prior to the washout phase (see illustration). According to Eq. 4' since t O > t', we can substitute the constant expression k2 L(t0) in place of the constant expression k 1 Cp(t0) in Eqs. 11 and 12. Thus t

Lk = - k 2 L(t0) (k - k2)-1

(t > to)

(Eq. 14)

and L2 = k L(t0) (k - k2)-1 + k 4 M L ( t 0 ) (k 4 _ k2)-1

(t > to)

(Eq. 15)

Combining Eqs. 9 and 10 demonstrates that the total observed radioactivity will be given as ME(t) + L(t) = MLk e-k(t-t0) + ML2 e-k2(t-t0) + ML4 e-k4(t-t0)

(t > to)

(Eq. 16)

where MLk = Lk

(t>t0)

(Eq. 17)

ML2 = L2

(t>t0)

(Eq. 18)

and ML4 = - k 2 k4-1 L4

(t > to)

(Eq. 19)

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h~ l~vo Muscarinic m2 Selective Ligand

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According to Eq. 16, the total observed radioactivity will be given as the sum of three exponentials. The first exponential k is so slow, corresponding to a half-time for dissociation of approximately 52 hours, that it makes no contribution to the observed apparent washout rate constant kap p whose half-time is on the order of one to two hours (24). Thus, kapl3 reflects k 2 and/or k4, sc) that k 2 = kap p and/or k 4 = kap p. Thus, if k 4 > k 2, it follows that'k 4 > If k 2 > k 4, then it follows that k2>_ kap p > k, and'Eqs. 18 and 19 reduce to - kapp" M L 2 = - [k L(t0) + k 4 ML(t0) ] k 2 -1

(t > to)

(Eq. 20)

and ML4 = ML(t 0)

( t > to)

(Eq. 21)

respectively. Since I ML4 ) > [ ML2 [, the relaxation corresponding to k 4 dominates the observed kap, p, and it again follows that k 4 = kap p. We have thus shown that k4 >- kapp whether k 4 > k 2 or K2 > k 4. The solution of Eqs. 5 and'6 for the case k 4 = k 2 (not shown) again leads to the conclusion that k 4 > kap p. This conclusion provides an important relationship between the molecular rate constant k4 and the macroscopically-observed measured washout rate constant kapp: a substantial value for kap p implies a substantial value for k 4. Time-lnvariance In order to demonstrate that, under certain conditions, macroscopically-observed time-invariance implies that all molecular components are at equilibrium, we note that if, after some time r, the radioactivity in the brain tissue is timeinvariant, then

m m d[L(t) + ~ MiL(t)]/dt = dL(t)/dt + ~'. dMiL(t)/dt = 0 i=1 i=1

(t--_ t')

(Eq. 22)

If, in addition, after some time t', Cp(t) is time-invariant, then, according to Eq. 4, L(t) is also time-invariant, so that dL(t)/dt = 0

(t _> t')

(Eq. 23)

It follows from Eqs. 22 and 23 that m ,~, dMiL(t)/dt = 0 i=1

(t >_ r)

(Eq. 24)

AS a result of the fact that L(t) is time-invariant for t > t' (Eq. 23), the time courses for the MiL are uncoupled from each other, and Eq. 2 can be solved analytically for MiL(t), even in the presence of significant receptor occupancy MiL(t ) = MiL(t' ) e[ki,onL(t) + ki,4](t-t') + ki,onL(t ) Mi(0 ) {1- e-[ki,onL(t)

+ ki,4](t-r)}[ki,onL(t ) + ki,4] -1

(t > t')

(Eq. 25)

Now assume that for some particular i = i0 we have MinL(t ) is time-dependent. Then, in order to satisfy Eq. 24 we would require that some linear combination of the other MiL(t)'s exactly cancel the time-dependence of MioL(t). However, since each MiL(t ) is an exponential function of its own k i on and k i 4, it is only ~n certain special cases that such a cancellation could occur. Although t h ' s ' s not Impossible, the probability is exceedingly low that the observed t~meindependence (Eq. 22) has resulted from such a cancellation. Thus, we reject the possibility that MioL(t ) is time-dependent. Since the same argument holds for whichever i was designated as i 0, we reject the possibility that any MiL(t ) is time-dependent, and conclude that the observed time-independence implies that all components of the closed system [that is, Cp(t), L(t), and MiL(t)] are time-independent and therefore at equilibrium. This conclusion provides an important relationship between the molecular equilibria and the macroscopically-observed

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hz Vivo Muscarinie m2 Selective Ligand

Vol. 55, No. 19, 1994

measured time-invariance: the macroscopically-observed measured time-invariance implies the molecular equilibria. Methods Radiopharmaceuticals

and

chemicals

(R)-[3H]3-Quinuclidinyl benzilate ([3H]QNB; 36-45 Ci/mmol) was purchased from New England Nuclear. The racemic mixture of (R)- and (S)-QNB was synthesized as previously described (25). The concentration of (R)-QNB used in the experiments was calculated by dividing the concentration of the racemic mixture by a factor of two. It was assumed that the (S)-QNB was inactive relative to the (R) stereoisomer (24, 26). In vivo

studies

General Experimental Procedures Male Sprague-Dawley rats weighing 200-250 g were used in the experiments. Animals were anesthetized with ketamine:xylazine (100:10 mg/kg i.p.) and the right jugular vein was exposed for intravenous injection of all compounds (see Experimental Design section). Animals were maintained under anesthesia until time of sacrifice. At the end of each study, animals were sacrificed by decapitation and the brains were rapidly removed, blotted free of excess blood and placed on ice. Tissue samples (20-70 mg) of specific brain regions were dissected and placed in vials containing 0.5 ml of Hyamine hydroxide (ICN Biomedicals, Inc., Costa Mesa, CA), a tissue solubilizer, and incubated overnight at 50°C. Following the incubation, 10 ml of Liquid Scintillation Cocktail (Cytoscint, ICN Biomedicals, Inc.) were added, and the samples were dark-adapted and then counted for 3H on a liquid scintillation counter (Beckman LS 6800; counting efficiency of 40%). Lack of bioluminescence was determined by repeated counting of the samples. The brain regions of interest included the cerebral cortex, corpus striatum, thalamus, hippocampus, superior colliculus, inferior colliculus, and cerebellum. In order to determine if there were any differences in the in vivo accumulation of [3H]QNB between the right versus left cerebral hemispheres, the left and right cerebral cortex, corpus striatum, and thalamus were dissected and studied as separate entities.

Experimental Design Animals were injected with carrier-free [3H]QNB or low specific activity [3H]QNB (10 uCi [OH]QNB plus 0 to 1500 nmol (R)-QNB) in a final volume of 0.1 ml normal saline containing up to 65% ethanol into the exposed jugular vein. The doses injected were 0.22, 4.12, 8.20, 20.0, 50.0, 114.0, 228.0, 354.0, 472.0, 708.0, and 1500.0 nmol. Animals were sacrificed 5 h after the [3H]QNB injection. The brains were rapidly removed, and tissue samples were dissected and treated as described above. Data Analysis In all studies, a minimum of 6 animals was used per reported result. The results are expressed as the radioligand accumulation in units of pmol/g, or equivalently, nM, under the assumption that the density of brain tissue is 1.0 g/ml. The concentration was computed by dividing the measured radioactivity/g tissue by the known specific activity of the [3H]QNB. The specific activity of the [3H]QNB was computed by dividing the injected radioactivity by the sum of the mass of QNB contributed by the carrier free [3H]QNB plus added cold (R)-QNB. All values are presented as the mean + SEM. Iterative Curve-Fitting At equilibrium, the [3H]QNB concentration Rj, k (nM) defined as Rj,k = specific + nonspecific binding of [3H]QNB

(Eq. 26)

for binding to multiple subtypes within the jth brain region for dose Dk, was computed as m

Rj,k = Dk [NSNS + (z ~ Bi,j (Ki + Dk) -1 + BNss,j (KNss + Dk) -1] i=1

(Eq. 27)

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TABLE 1 Fixed Values for Bi,j's (nM) used in the Iteration Procedure 1

Bml Bm2 Bm3 Bm4

csl/csr 2

hipp

ccl/ccr

t h lit h r

72.79 30.12 16.32 112.95

76.14 27.54 16.20 30.78

70.38 39.33 20.7 49.68

13.76 36.12 5.16 17.20

cb 0.42 15.75 1.05 0.53

1Computed from the data reported in refs. 10, 28-30. 2Abbreviations are defined in Fig. 2. 0.6

0.5

O

•

A +

~

csl

• + []

csr

•

thr

•

cb

Zl

0.4 O

0 "0

o~

o

+

A

0.3

; I"1

QQ Z 0 "1"

hipp

ccl ccr thl

9 x

0.2 +

I¢

®

+

0.1

0,0

M

0"

1 0°

r~Q

A N

10'

1 02

nmoI [3 H]QNB

1 03

0'

inj

Fig. 2 Regional % dose/g of [3H]QNB as a function of the injected dose of [3H]QNB. Regions to which each % dose/g corresponds are: csl (left corpus striatum), csr (right corpus striatum), hipp (hippocampus), ccl (left cerebral cortex), ccr (right cerebral cortex), thl (left thalamus), thr (right thalamus), and cb (cerebellum). where NSNS (nM/nmol) is the nonspecific nonsaturable binding (as described by Seeman (legend to Fig. 3 and section IX. A in (27))) of [3H]QNB (including unbound radioactive ligand), m is the number of receptor subtypes, Bi,j (nM) is the concentration of the ith receptor subtype within the jth brain region, (z is a scale factor relating the in vitro values for Bi,j (Table 1) to the corresponding in vivo values, Ki (nmol) is the dose required for 50% occupancy of the ith receptor subtype, BNssj (nM) is the nonspecific saturable binding site (as described by Seeman (legend to Fig. 3 and'section IX. B in (27))) within the jth brain region, KNSS (nmol) is the dose required for 50% occupancy of the nonspecific saturable binding site, and Dk (nmol) is the kth dose of [3H]QNB injected. The sum of squares (SSQ) error was computed as

1500

hz Vivo Muscarinic m2 Selective Ligand

SSQ = ~ (Rmeas,j,k- Rj,k) 2 j,k

Vol. 55, No. 19, 1994

(Eq. 28)

where Rmeas,j,k (nM) is the measured quantity analogous to Rj k as described by Eq. 27. The floating parameters always included NSNS, BNss,j, KNss, and the Ki°s. The relative proportions Bii of subtypes within each brain region was always fixed in the same ratio indicated in Table 1,''but the total receptor in all regions was scaled by the single floating parameter (z. 1 In some studies several subtypes were combined in a single pool, in order to reduce the standard error of the parameter estimates by reducing the number of floating parameters when initial studies had shown that these subtypes had indistinguishable Ki's. The resultant pooled subtype is named so as to reflect the identities of the individual subtypes which had been pooled. For example, if ml, m3, and m4 are to be pooled, the new pooled subtypes is referred to as "m134." The value of Bi,j used for the pool are the sum of the values of Bi,j for the several subtypes. For example, for the pooled subtype m134, the value of Bi,j would be equal to Bml,j + Bm3,j + Bin4 ' Since ml m3 and m4 would now share a common value for Ki in Table 2 column 2 we have listed K1, K3, and K4, as each having this common fitted value for Ki, along with the standard error computed for the pooled m134 subtype. The data obtained with carrier-free [3H]QNB have a special significance: The regional distribution of carrier-free [3H]QNB in brain tissue is nearly independent of the regional concentration of mAChR. This observation has been difficult to explain (31), and the main purpose of the work reported here is to provide an explanation in terms of in vivo m2selectivity for [3H]QNB. We therefore want to ensure that any set of estimated parameter values is weighted to fit the carrier-free data accurately. Otherwise, the estimated parameter values might "ignore" the very observation we wish to explain. Because of the special significance and the low absolute values for the residual errors of the data obtained with carrier-free [3H]QNB, these residual errors were scaled by multiplication by an empirically-determined constant equal to 1000. This particular value for the constant was determined by assessing a range of possible values and selecting that value equal to 1000 which resulted in the residual errors of the data obtained with carrier-free [3H]QNB being of similar magnitude to the remaining residual errors. SSQ was minimized by nonlinear iterative least squares (32). A standard technique for evaluating the suitability of a model is to apply Akaike's Information Criterion (AIC) (33), defined as AIC = n In(SSQ) + 2p

(Eq. 29)

where n is the number of data points fitted by the model, SSQ is the sum of squares error in the fit of the data points to the model, and p is the number of floating parameters used in fitting the data to the model. As described by Kawai et al (34), "AIC is essentially based on the maximum likelihood estimation and will present a minimum value when the most suitable model is applied in fitting the experimental data." Results A graph of the regional % dose/g of [3H]QNB as a function of the injected dose of [3H]QNB (Fig. 2) shows that all the brain regions (with the exception of the left corpus striatum, which was omitted at the dose of 1500 nmol because of inexplicably high variance) achieve a limiting value averaging 0.0427 + 0.0017 % dose/g. We thus consider that 0.0427 % dose/g represents an estimate of the average nonspecific binding (NSNS + NSS) which is approximately equal in all the brain regions studied. The accuracy of the model fit to the measured data (Figs. 3, 4) indicate that the model (Eq. 27) is consistent with the data. The estimated parameter values (Table 2, column 1) are ~1For superior and inferior colliculi, the total mAChR was allowed to float since Bij values were not published for these regions (10, 28 - 30). We assumed that the proportions of the individual subtypes within these regions were similar to those reported for pons and medulla.

Vol. 55, No. 19, 1994

bz Vivo Muscarinic m2 Selective Ligand

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consistent with the hypothesis that [3H]QNB exhibits an in vivo m2-selectivity. In particular, the parameter values are able to account for the fact that the regional carrier-free [3H]QNB binding is relatively invariant (Fig. 4) in spite of large regional variations in total mAChR (as described in the Discussion). There is an m2-selectivity, as indicated either as the ratio of the equilibrium constants or as the ratio of the binding potentials ~Table 2). The individual components of [3H]QNB binding which constitute the total observed ['~H]QNB binding (available as intermediate values during the iterative curve-fitting procedure) indicate that, in a representative brain region (left corpus striatum), at low mass doses of [3H]QNB m2 binding predominates, at higher mass doses m4 binding predominates, and at still higher mass doses NSS binding predominates (Fig. 5). Because of the similar magnitudes of K 1, K3, and K4 and the large standard errors of these fitted parameters, the ml, m3, and m4 subtypes were pooled into a single group, and the iterative curve-fitting was repeated (Table 2, column 2). The similar value of SSQ for the unpooled and pooled subtypes, the lower value of AIC for the pooled subtypes, and the improved standard errors justify pooling the subtypes. The correlation of the simulated and measured data for the pooled subtypes are nearly identical to that for the unpooled subtypes (not shown). As is the case for the unpooled values, there is again an m2-selectivity, as indicated either by the ratio of the dissociation constants or by the ratio of the binding potentials (Table 2). Several control studies were performed. To test whether a single subtype would be sufficient to fit the observed data, the ml, m2, m3, and m4 subtypes were pooled into a single group m1234, and the iterative curve-fitting was repeated (Table 2, column 3). The SSQ error and the AIC, and therefore the fit to the data, were somewhat poorer than in the mutiple-subtype cases (Table 2, columns 1 and 2). More importantly, however, the NSS site took on the characteristics of a relatively low-affinity specific receptor; that is, a second receptor subtype was created from what was intended to be the NSS site. In order to prevent this from occurring, KNSS was allowed to float but was constrained to be no lower than 500 nM during the iterative curve-fitting procedure. Also, the fitted values for the total receptor for ic and sc were unreasonably high relative to the values for the other receptors (23). In order to prevent this from occurring, these values were allowed to float but were constrained to be no higher than 50% greater than the values for the thalamus (that is, 1.5 x 86 nM = 129 nM) during the iterative curve-fitting procedure. The resulting SSQ error and AIC (Table 2, column 4) were high. In particular, the fit to the carrier-free data was inaccurate (Fig. 6). To test whether an alternative grouping of pooled subtypes would result in a fit to the data which is equivalent to that for the m134 grouping, the other possible groupings of m123, m124, and m234 were studied. In all three cases, as described above for the single subtype case m1234, the SSQ error, and therefore the fit to the data, was higher than in the mutiple-subtype cases; the NSS site took on the characteristics of a relatively low-affinity specific receptor; and the fitted values for the total receptor for ic and sc were unreasonably high relative to the values for the other receptors (data not shown). Therefore, the iterative curve-fitting procedure was performed again with the same constraints applied as described above for the m1234 case. Again, as exemplified by the m123 grouping, the resulting SSQ error and AIC (Table 2, column 5) were high. In particular, the fit to the carrier-free data was inaccurate (Fig. 7). Finally, the affinity of the m4 subtype is considerably lower than that of the pooled m123 subtypes, in direct contradiction to a hypothesis of selectivity of m4 relative to the pooled m123 subtype. Discussion It is well known that, in vitro, [3H]QNB binds about equally well to all subt,~pes of the mAChR (20). Therefore, the observation that the distribution of carrier-free [JH]QNB is relatively invariant from brain region to brain region (24, 31), in spite of the enormous variation of mAChR concentration (23), was interpreted as indicating that the [3H]QNB distribution has an exceedingly low in vivo sensitivity to variations in the mAChR concentration. However, this interpretation leads to a paradox.

1502

ht Vivo Muscarinic m2 Selective Ligand

Vol. 55, No. 19, 1994

800 w I o hlpp [3 cb

1000[ [] csl

8~ 0 0 t i~ csr 6

0

0

500

~

400 O

200 2OO

0

0

500 1000 Injected [3 H]QNB (nrnol)

1500

800

0 800

o sc

600 400600ZQI ~ Ic

I

500 1000 Injected [3 H]QNB (nmol)

1500

500 1000 Injected [3 H]QNB (nmol)

1500

o ccl o ccr v 0

4O0

200

(

2OO

l

~

500 1000 Injected [3 H]QNB (nmol) 800-

1500

[] thl o thr

,00

q

200 tQ

0

500 1000 Injected [3 H]ONB (nmol)

1500

Fig. 3 Simulated (corresponding to column 1 in Table 2) and measured values for the [3H]QNB binding in individual brain regions. Error bars represent SEM.

Vol. 55, No. 19, 1994

bz Vivo Muscarinic m2 Selective Ligand

NSS (simulated)

thl thr

1.0

II ~i

)1'

i

~i ~--~ 0.8

~//

o.,

|!I."

0.2

li

1503

-

"

,~

m4 m3(simulated) (simulated) m2(simulated) ml (simulated) NSNS (simulated)

//

'

~ m/

0.0

regions FIG. 4 Simulated individual components (left stacked bar graph of each pair) of regional [3H]QNB binding (corresponding to column 1 in Table 2) for carrier-free (0.22 nmol injected) [3H]QNB. The height of the stacked bar graph corresponds to the sum of the individual components of the simulated [3H]QNB binding and can be compared with the total measured [3H]QNB binding (right bar graph of each pair).

'°°t 400]

/

total

rn =, 300

.f-

o

200

100

0 0

500

1000

1500

injected [3 HIQNB(nmol) FIG. 5 Simulated individual components of left corpus striatum [3H]QNB binding (corresponding to column 1 in Table 2) for various doses of injected [3H]QNB.

TABLE 2 SSQ Errors and Parameter Estimates Determined by the Iteration Procedure

nl S.~(3error p2 AIC - AIC (unpooled)3

column 2

column 3

unpooled

pooled m 134

pooled m 1234

106 176598 19 0

NSNS (nM/nmol)

O. 1O0

Bic (nM) Bsc (nM)

70.8 58.9

(nmol) (nmol) (nmo]) (nmol)

oc(dimensionless)

K1 K2 K3 K4

column 1

106 172312 17 -7 (0.146) 4

106 293681 16 48

column 4

column 5

pooled m1234

pooled m 123

106 1018990 16 180

106 701564 17 142

O.1O0

(0.123)

0.200

(0.024)

0.100

(0.153)

0.101

(0.116)

(4.1) (3.6)

70.3 58.4

(3.7)

(3.5)

1200.0 542.0

(1610.0) (630.0)

129.0 129.0

(28.3) (29.0)

129.0 129.0

(19.8) (19.8)

249.0 16.1 243.0 202.0

(410.0) (5.3) (1810.0) (94.5)

232.0 16.2 232.0 232.0

(74.8) (74.8)

44.8 44.8 44.8 44.8

(110.0) (110.0) (110.0) (110.0)

15.0 15.0 15.0 15.0

(17.1) (17.1) (17.1) (17.1)

18.1 18.1 18.1 241.0

(14.9) (14.9) (14.9) (657.0)

1.700

(0.587)

1.700

(0.505)

0.214

(1.160)

0.279

(0.322)

0.554

(O.5OO)

(580.0 (536.C (521 .C (469.0 (470.6 (497.0

(309.0) (309.0) (202.0) (256.0) (256.0) (112.0) (113.0) (1430.0) (652.0) (43.6)

745.0 745.0 676.0 641.0 643.0 645.0 667.0 549.0 670.0 605.0

(423.0) (424.0) (413.0) (394.0) (394.0) (420.0) (428.0) (378.0) (413.0) (423.0)

7O6.0 687.0 535.0 530.0 532.0 570.0 590.0 419.O 554.0 544.0

(357.0 (349.0 (316,0 (314.0 (314.0 (326.0 (332.0 (289.0 (319.0 (327.0

(14.3)

500.0

(427.0)

500.0

(374.0

(74.8)

(4.8)

B NSS,csl B NSS,csr B NSS.hipp B NSS.ccl B NSS,ccr B NSS.thl B NSS,thr B NSS,ic B NSS,sc B NSS,cb

(nM) (nM) (nM) (nM) (nM) (nM) (nM) (nM) (nM) (nM)

756.0 645.0 671.0 489.0 492.0 631.0 673.0 630.0 910.0 805.0

(669.0) (617.0) (625.0) (556.0) (557.0) (606.0) (625.0) (611.0) (733.0) (696.0)

736.0 629.0 640.0 468.0 471.0 607.0 646.0 607.0 876.0 774.0

(558.o

331.0 333.0 274.0 313.0 316.0 277.0 284.0 1.0 180.0 225.0

KNSS

(nmol)

1210.0

(1070.0)

1140.0

(837.0

78.7

(512.0 (497.0 (591.0

==

F~"

t"

IN VlVO M2 SELECTIVITYBASED UPON EQUILIBRIUM CONSTANTS K 1 /K 2 K3 ~ 2 K4 _

15.47 15.09 12.55

14.32 14.32 14.32

1.00 1.00 1.00

1.00 11"00.00

1.00 1.00 13,31

<

IN VlVO M2 SELECTIVITYBASED UPON REGIONALSUBTYPE CONCENTRATIONS/EQUILIBRIUMCONSTANTS ("BINDING POTENTIAL*) (B2 ~ 2 )/(B 1 /K1 ) IB 8 2 /K2 )/(B 3 /K 3 )

8.64 28.68

2 ~ 2 )/(e 4/K4 I

8.93

8.00 27.21 11.34

C~ 0.56 1.90 079

0.56 1.90 079

0.56 1.90 10.54

1 2 3 4 5 Number o| data points. Number ol floating parameters. Akaike Information Criterion. Standard error. The ratios of the subtypes correspond to those for ccl (Table 1).

Z .o

.<

C~ tJ1

Z P [ ] total(measured) 1.4[_

Lcsl 1.2 1.0

[ ] total (measured) ] • NSS (simulated) t I[~ m1234(simulated) i • NSNS(simulated) ic - e c l ¢cr)p

thl

thr,~

1.4 ] 1.2~-~sl r~ sr

[ ] NSS (simulated) • m123(simulated) [ ] m4 (simulated) ~_ (NSNS . simul.~._ated), ic ,..ccl c c r

1.0

0 0.4

0.4

0.2

~ 0.2

thl

r

,2

• [] [] •

1.0

m3 m2 ml NSNS

II

0.8

i

0.6

0.4

I

5. 0.2

~

F," N)

0.~

0 . ~ ~ regions

~ ~,

L. regions

0.0

A

B

C

D

E

F

Fig. 6

Fig. 7

Fig. 8

Simulated individual components of regional [3H]QNB binding (corresponding to column 4 in Table 2) for carrier-free (0.22 nmol injected) [3H]QNB. The height of the stacked bar graph corresponds to the sum of the individual components of the simulated [3H]QNB binding and can be compared with the total measured [3H]QNR binding (right bar graph of each pair).

Simulated individual components of regional [3H]QNB binding (corresponding to column 5 in Table 2) for carrier-free (0.22 nmol injected) [3H]QNB. The height of the stacked bar graph corresponds to the sum of the individual components of the simulated [3H]QNB binding and can be compared with the total measured [3H]QNB binding (right bar graph of each pair).

Effect of subtype selectivity on the potential to differentiate normal and disease states: simulated individual components of left cerebral cortex [3H]QNB binding for carrier-free (0.22 nmol injected) [3H]QNB. Affinities in A-C correspond to column 1 in Table 2; affinities in D-F differ from those in A-C in that K 1 = K2 = K3 = K4 = 60.0 nM. The effect of 50% (B and E) and 100% (C and F) loss of the m2 subtype in a "disease" state relative to a "normal" (A and D) is shown.

1506

hi Vivo Muscarinic m2 Selective Ligand

Vol. 55, No. 19, 1994

One way to see the paradox is to recognize that there are two separate lines of evidence each of which strongly implies that carrier-free [3H]QNB is at equilibrium shortly after injection. First, the time-independence of the [3H]QNB distribution (23, 24, 31) indicates that equilibrium has been achieved (see "Time-lnvariance" above). Second, the rapid in vivo dissociation kinetics (24) (see "Washout Kinetics" above) in conjunction with a previous derivation of sufficient conditions for equilibrium (35) also indicate that equilibrium has been achieved. In addition, the in vivo nonspecific binding of carrier-free [3H]QNB is low relative to the specific binding (24, 31). Taken together, the attainment of equilibrium and the low nonspecific binding imply that carrier-free [3H]QNB satisfies a set of conditions which are sufficient to ensure substantial sensitivity to variations in receptor concentration (36). Thus, the apparently low sensitivity is a paradox. Recent results of Wolfe and his colleagues, however, demonstrate that, unlike the total mAChR, the m2 subtype is distributed nearly uniformly throughout the grey matter structures (10, 28-30). This observation suggested that if [3H]QNB were binding in vivo preferentially to the m2 subtype, then the paradox would disappear. That is, the uniform distribution of [3H]QNB might simply reflect the uniform distribution of the m2 subtype. The results presented here suggest that this latter interpretation is likely to be correct, and are supported by recent results of in vivo studies of nonradioactive QNB competing with (R,R)-[]Zbl]3quinuclidin,.,yl-4-iodobenzilate ([1251]IQNB) (37). In spite of the nonselectivity demonstrated in vitro, [°H]QNB exhibits an effective in vivo m2 selectivity. As surprising as this observation may seem, there is precedent for an in vivo selectivity which differs from the in vitro selectivity: Frost et al (38) have shown that " . . . although diprenorphine appears to bind to the opiate receptor subtypes with approximately equal affinity in vitro, it may bind to only one subtype in v i v o . . . " The most important conseqence of the in vivo m2 selectivity is that radiolabeled QNB binding would be sensitive to changes in the regional m2 concentration which might result from a disease state (Fig. 8, A - C). Without the in vivo m2 selectivity, radiolabeled QNB binding would be insensitive to changes in the regional m2 concentration (Fig. 8, D - F). We conclude that a suitably radiolabeled derivative of QNB may be of potential use in emission tomographic study of the loss of m2 receptors in AD. Two h post injection, regional carrier-free (R,R)-4[1251]IQNB binding reflects the regional total mAChR (39). Thus, in vivo [1251]IQNB binding appears to be nonsubtype-selective. Apparently the bulky iodine substitution in the 4 position reduces the subtype selectivity of QNB. It is possible that a less bulky fluorine substitution might permit retention of the selectivity exhibited by QNB itself. APPendix We wish to test whether Eq. 4' is valid. Assume the contrary. Then our hypothesis is that L(t0) = k l / k 2 Cp(t0) + AL

(Eq. A1)

where &L (I AL J > 0) represents the discrepancy between the true value of L(t0) and that computed using Eq. 4'. Define At such that t O - t' > At > 0 (see illustration in Theory section). Then, from Eq. 4, it follows that k 1 Cp(t 0 - At) = k 2 L(t 0 - At)

(Eq. A2)

Based upon Eq. 8, Cp(t 0 - At) = Cp(t0) e-k(t0 - At) = ek At Cp(t0) e-kt0 = ek At Cp(t0)

(Eq. A3)

Substituting Eq. A3 into Eq. A2, kl e k At Cp(t0) = k2 L(t0 _ t~t) and substituting Eq. A4 into Eq. A1,

(Eq. A4)

Vol. 55, No. 19, 1994

hz Vivo Muscarinic m2 Selective Ligand

L(t0 ) = L(t0 . M)e-k At + AL

1507

(Eq. A5)

Let us select At to be sufficiently small that e-k At can be represented by the first terms of its Taylor's expansion (1 - k At) with arbitrarily good accuracy. Then Eq. A5 becomes L(t0) = L(t 0 - At)(1 - k At) + AL

(Eq. A6)

Rearranging Eq. A6 results in [L(t0) - L(t 0 - At)]/At = - k L(t 0 - At) + AL/At

(Eq. A7)

As At approaches 0, the left hand side of Eq. A7 approaches the derivative of L(t) evaluated at t O -At/2, and the right hand side approaches infinity. But the derivative of L(t) evaluated at t o -At/2 must have a finite value, so that the hypothesis leads to a contradiction and must therefore be false. Thus, Eq. 4' is valid. Acknowledaements The authors gratefully acknowledge Drs. Eckelman and Gibson for their comments. This work was supported by a grant from the National Institutes of Health (NS22215) and, in part, a grant from the Department of Energy (DE FG05 88ER60649). References 1. 2. 3. 4. 5. 6. 7. 8. 9. 1 0. 1 1. 1 2. 1 3. 1 4. 1 5. 1 6. 1 7.

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ht Vivo Muscarinic m2 Selective Ligand

Vol. 55, No. 19, 1994

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