Isomerization of the Muscarinic Receptor l Antagonist Complex*

The mechanism of binding of two antagonists, 3-q& nuclidinyl benzilate and IV-methyl-4-piperidinyl benzi- late, to the muscarinic receptor was studied. The pseudo-first order rate constant of association showed a hyperbolic dependence on the concentration of the antagonist(s) indicating that the interaction involves two equilibria. The first binding equilibrium is reached rapidly and is characterized by dissociation constants 2.7 + 0.4 11~ and 6.7 -C 2.5 u in phosphate buffer (0.05 M, pH = 7.4) for 3-quinuclidinyl be&late and N-methyl- I-piperidinyl benzilate, respectively. The first binding equilibrium is followed by a slower isomerization step of the receptor l antagonist complex. The equilibrium constants for the isomerization step of the complex for both ligands were about 0.15. The overall constant of binding obtained as the product of the above constants shows good agreement with the results of equilibrium binding studies.

The mechanism of binding of two antagonists, 3-q& nuclidinyl benzilate and IV-methyl-4-piperidinyl benzilate, to the muscarinic receptor was studied. The pseudo-first order rate constant of association showed a hyperbolic dependence on the concentration of the antagonist (s) indicating that the interaction involves two equilibria.
The first binding equilibrium is reached rapidly and is characterized by dissociation constants 2.7 + 0.4 11~ and 6.7 -C 2.5 u in phosphate buffer (0.05 M, pH = 7.4) for 3-quinuclidinyl be&late and N-methyl-I-piperidinyl benzilate, respectively. The first binding equilibrium is followed by a slower isomerization step of the receptor l antagonist complex. The equilibrium constants for the isomerization step of the complex for both ligands were about 0.15. The overall constant of binding obtained as the product of the above constants shows good agreement with the results of equilibrium binding studies.
Muscarinic acetylcholine receptors have been characterized in the central nervous system and in the periphery by binding of radiolabeled antagonists of very high affinity (cf for review Refs. 1 and 2). The most extensively used ligands include 3quinuclidinyl benzilate (3), N-methyl-4-piperidinyl benzilate (4), and propylbenzilylcholine mustard (5). The fust two benzilic esters interact reversibly with the receptor binding sites and the single binding isotherms obtained for this process may be ascribed to a simple bimolecular association reaction (1,3): where R stands for receptor, A for antagonist, k,, and kdb the association and dissociation rate constants, respectively. The few kinetic studies on the reversible binding of antagonist to muscarinic receptors, however, have indicated that the value of the dissociation constant of receptor.antagonist complex calculated from the equilibrium binding measurements for the reaction in Equation does not agree with the equilibrium constant calculated as the ratio of the rate constants k&k, (6). In addition to this, deviations from the first order kinetics of the dissociation of the receptor. antagonist complex were found in several studies (7)(8)(9). Other experiments showed that formation of the complex under the pseudo-first order conditions ([A] >> [RI) also deviated from first order kinetics (8-11). Among several possible reasons for these findings, it has been suggested that muscarinic receptor interaction with antagonist(s) involves more than one reaction step with different rates of equilibration (8-11). The simplest reaction scheme for this case proposes the existence of two different receptor. antagonist complexes, AR and AR*: Kloog and Sokolovsky (7), in addition to the above scheme, have also proposed isomerization of the free receptor according to Equation 4 R=R* and ligand binding to both isomers leading to a cyclic reaction scheme.
Although deviations from linearity of semilogarithmic plots implicated a mechanism involving isomerization of the receptor . antagonist complex, they did not prove its existence. The presence of such isomerization steps in protein-ligand interactions has been demonstrated in several systems by showing hyperbolic dependence of the pseudo-frst order rate constant of association on the ligand concentration (12). In view of this, we decided to carry out an extensive study of binding of benzilic esters to the muscarinic receptor, since these compounds are widely used for investigation of the interaction of the receptor with other antagonists and agonists and, therefore, the establishment of the formal kinetic mechanism for these ligands is crucially important for interpretation of later data.
The present study, using two different receptor preparations and two different antagonists, provides kinetic evidence for the existence of two consecutive equilibria in antagonist binding to the muscarinic receptor and provides data on the corresponding equilibrium constants.

RESULTS
Kinetics of 3-QNB and 4-NMPB binding to muscarinic receptors were studied under the pseudo-fist order conditions involving a 7-to lOOO-fold excess of the antagonist over the receptor concentration.
It was found that the nonspecific binding reached saturation before the fist samples were filtered (50 to 60 s) and therefore the total change in radioligand  receptor from rat cerebral cortex in phosphate buffer (0.05 M, pH = 7.4, 1 mM EDTA, 0.1 mM phenylmethylsulfonyl fluoride).
The plot of kobs versus antagonist concentration yielded hyperbolic dependences (Fig. 2) with both antagonists. The simplest mechanism that describes these results is given by where &, Bnonsp, and B,, have the same meaning as in Equation 5. The results of the curve-fitting are shown in the form of semilogarithmic plots in Fig. 3. It is also shown that release of 4-NMPB from the cerebral cortical receptor. 4-NMPB complex occurred at the same rate as found for the release of the ligand bound to receptors from smooth muscle. The data did not indicate any breaks in the semilogarithmic plots.
As shown in Table II, the rate constants kdb for both benzilates are close to the values of k-2 calculated from Equation 6. The equality of kdis = k-2 suggests that the overall receptor-antagonist dissociation reaction is limited by the complex isomerization step. According to the reaction scheme (Equation 3), the constant Kd obtained from the binding experiments under equilibrium conditions is the product of two equilibrium constants: where KA = (k-l/k,) and Kk,,, = (k-Z/kz). The results of kinetic experiments in Table II Table I. This provides additional evidence for the two-step mechanism for benzilate binding to muscarinic receptor.  The kinetic study of muscarinic receptor interaction with 3-QNB and 4-NMPB over a wide range of antagonist concentrations allowed discrimination between the reaction mechanisms given by Equations 1 and 3. The existence of a mechanism involving two consecutive equilibria (Equation 3) has previously been suggested on the basis of deviations from linearity of semilogarithmic plots of association and dissociation rates of the receptor.antagonist complexes with both 3-QNB (10, 11) and 4-NMPB (7-9). These deviations could have several reasons and, in fact, could not be detected under our experimental conditions (using different receptor preparations and phosphate buffer instead of Krebs-Ringer buffer (7-11)).
Differences between results obtained in these buffers were also noted by Kloog 2). This type of evidence for isomerization of proteineligand complex has been discussed previously (12).
Our data concerning binding of both 3-QNB and 4-NMPB to the receptor can be explained by assuming a fast binding step followed by a slower isomerization of the receptoreantagonist complex. The isomerization step is slow enough to be characterized by the filtration method.
In contrast, the formation and dissociation of the preceding complex (AR) was too fast to be analyzed by the filtration assay under the conditions used in the present study. In such a case, the system can be described by a single exponential (12,13). A more detailed description of the first equilibrium cabs for the special methods of fast reaction kinetics, like those successfully applied in studies on the nicotinic acetylcholine receptor (13). It is interesting to note that the rapid protein.ligand complex formation was followed by a slower isomerization step also in the case of this acetylcholine receptor. Thus, the relatively slow isonerization seems to be general for acetylcholine receptors and may be connected with some of their biological functions in the cell membrane. The isomerization of the receptor.ligand complex involves probably a confor- It should be noted that the isomerization step increases the apparent affinity of benzilate binding to muscarinic receptor as the values of Kisom are about 0.15 for both 3-QNB and 4-NMPB.
The equilibration of the isomerization reaction is reached faster in the case of 4-NMPB, a property that may make this ligand a more convenient and valuable tool in binding studies than is 3-QNB.
The isomerization equilibrium involves monomolecular steps and, therefore, can not be shifted completely by addition of an excess of antagonist. As a result, a portion of receptor present in the fast dissociating complex escapes detection in filtration assay independently of the antagonist concentration used. This is important to consider when measuring the number of receptor binding sites by these ligands. In the case of both 3-QNB and 4-NMPB, the ratio of [AR]/[AR*] appears to be about 1:7, which explains the close agreement between results obtained measuring the number of receptors with these ligands. In general, however, the ratio of [AR]/[AR*] may be dependent on the ligand structure as well as on the reaction conditions.