Alternative molecular interpretations of binding curves: compelling competition?

TIPS - N o v e m b e r 1987 [Vol. 8]

scientific significance. Dr U n w i n ' s matrix is particularly useful h e r e and I s h o u l d add that the Bloody O b v i o u s test w o u l d reveal a failure in case (2). In case (4) w h e r e the Bloody O b v i o u s test and statistics are at odds it is the Bloody O b v i o u s Test that should win. It has b e e n said that medics and scientists a d h e r e to a religion called statistics and engage in ritual k n o w n as ' h u n t i n g for p values '1. W h e t h e r y o u use statistio cal ~packages or 't'-test to obtain

421 those p values the q u e s t i o n should always be w e i g h t e d to w h e t h e r the results are scientifically significant rather than statistically significant. Sadly, several of the gods of statistics preside on editorial b o a r d s and w i t h o u t p values their w r a t h can be incurred. There is an old adage which I think w e should not lose sight o f - 'statistics should be used as a drunk uses a lamp-post; for support rather than illumination'. Finally, what of Dr U n w i n ' s headaches. Like his alternatives in

IAN KITCHEN

Department of Biochemistry, Division of Pharmacology and Toxicology, University of Surrey, Guildford, Surrey GU2 5XH, UK.

Reference 1 Salsburg, D. S. (1985) The American Statistician 39, 220-223

interaction of that drug with the receptor is not strictly competitive. H o w e v e r , w h e n the Bmax is u n altered (and the Kd is increased) the interaction is competitive. C o m p e t i t i v e interactions are most c o m m o n l y o b s e r v e d in simple situations in w h i c h the radioligand and drug each b i n d reversibly to a c o m m o n b i n d i n g site w i t h o u t altering receptors in other ways. We w i s h to point out here that similar data can be o b t a i n e d e v e n w h e n the situation is more complicated.

Alternative molecular interpretations of binding curves: compelling competition? Antonio DeBlasi and Harvey J. Motulsky A drug which increases the Kd of a radioligand without altering its Bmax has a competitive interaction with the receptors. Although such data occur most commonly in simple situations in which the drug and radioligand bind reversibly to a common binding site without altering the receptors in other ways, A n t o n i o DeBlasi and H a r v e y Motulsky point out that similar data can also be obtained in more complicated situations.

Radioligand b i n d i n g studies are a direct m e t h o d for i d e n t i f y i n g drugs that interact w i t h receptors. In o r d e r to d e t e r m i n e w h e t h e r the interaction of a drug w i t h a receptor is competitive or n o n competitive, saturation b i n d i n g experiments are c o m m o n l y performed. In these experiments, various concentrations of radioligand are i n c u b a t e d with tissue in the presence or absence of a fixed concentration of the drug b e i n g investigated, and specific radioligand b i n d i n g is determined. The data are often p r e s e n t e d as Scatchard plots as illustrated in Fig. 1. The X-intercept of a Scatchard plot

statistics, I could offer alternative drugs to p a r a c e t a m o l - aspirin or ponstan for example. But if the truth be told, like statistics, there is not m u c h to choose b e t w e e n them. If the headaches continue, I recomm e n d he increases the dose!

represents the maximal a m o u n t of b i n d i n g (Bmax) a n d the slope is inversely p r o p o r t i o n a l to the dissociation constant (Kd). A decrease in the Bmax indicates that the

• Example 1 Agonists cause ~adrenergic receptors to b e c o m e s e q u e s t e r e d or internalized w i t h i n cells. This can be q u a n t i t a t e d b y m e a s u r i n g the loss of b i n d i n g of [3H]CGP-12177 (4-[3-tertiarybutylamino-2-hydroxypropoxy]benzimidazolo-onHC1), a h y d r o philic antagonist which selectively b i n d s to surface receptors. The s e q u e s t e r e d receptors are located in an e n v i r o n m e n t inaccessible to this ligand. Figure 2 s h o w s

.~ Noncompettive,~etdwe g

g

I

Antonio DeBlasi is a Senior Researcher at the Istituto de Ricerche Farmacologiche "Mario Negri', Via Eritrea 62, Milano, Italy and Harvey J. Motulsky is Assistant Professor in Residence at the Department of Pharmacology, University of California, San Diego, La Jolla CA 92093, USA.

Bound

I

),

I

I

Bound I

I~'~"/

I'IM

Fig. 1. Competitive v. noncompetitive interactions of a drug with radioligand binding. The data are shown as Scatchard plots. ( ~ ) , control; (. . . . presence of inhibitor. The lower graph demonstrates competitive inhibition where the B,,~ is unchanged and the t~ is increased. The upper graph demonstrates noncompetitive inhibition where the Br,ax is decreased. H 1987, Elsevier Publications, Cambridge

0165 - 6147/87/$02.00

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Scatchard plots of [3H]CGP binding at 37°C to intact h u m a n lymphocytes in the presence and absence of isoprenaline 1. The interactions are complicated, as isoprenaline not only competes for [3H]CGP binding to surface receptors, but also causes many receptors to sequester to an environment inaccessible to that radioligand. Despite these complexities, the Scatchard plot is linear in the presence of isoprenaline. The apparent Kd for [3H]CGP binding to the cells is increased, and the Bma x i s unchanged. • Example 2 The ~-adrenoceptor antagonist tertatolol is unusual in that it has two effects2. First it binds as a typical antagonist. It then causes a loss in detectable receptor number (perhaps by binding tightly to the receptor; perhaps by other mechanisms). Figure 3 shows a Scatchard plot for p25I]-labelled pindolol binding to $49 lymphoma cells in the absence and presence of tertatolol. The binding is actually quite complicated, as tertatolol competes for [12sI]-labelled pindolol binding at some receptors and alters other receptors so that they cannot bind [12sI]-labelled pindolol. Nonetheless, the Scatchard plot is linear and the Bmax is unchanged.

Mathematical proof We consider model:

the

following

R + LK~_IRL

The receptor (R) binds to radioligand (L) with a single affinity (K1, expressed as an equilibrium dissociation constant in units of M). The drug or inhibitor (I) binds first with a dissociation constant K2, and the receptor then is reversibly converted to another form R' with a equilibrium constant K3 (a ratio without units). R' may or may not have inhibitor attached; in either case it cannot bind radioligand. R' thus can represent internalized receptors (Example 1), receptors with tightly bound competitor (? Example 2), or receptors modified so that they cannot bind any ligand (? Example 2). What does this model predict for saturation radioligand binding ex-

[RL] = Rc[L]/[L] + Ka

3

<9 I i "00 c~ 0 0

1000 2000 3000 bound (sites/cell)

Fig. 2. [aH]CGP binding to intact human mononuclear leukocytes in the absence and presence of 0.2 IzM isoprenaline. The incubations were conducted at 37°C for 1 hour using previously described methods 1. This concentration of isoprenaline is sufficient to cause substantial redistribution of the fl-adrenergic receptors. 0 , control; II, + 0.2 I~M isoprenaline.

periments in competitor?

the

presence

of

[RL] = [L]-[R]/K1

(1)

[RI] = [I].[R]/K2

(2)

[R'] = [RI].K3 = [I]'[R]'K3/K2 (3) Rt = [R] + [RI] + JR'] + [RL]

(=Bma~)

(4)

Substituting equations 1-3 into equations 4 and rearranging yields: [R] = Rt/(1 + [L]/K1 + [I]/K2 + [I]-K3/K2) (5) [RL] = Rt'[L]/[L] + (K1 + [I]/KI'K2 + [I].Ks/K1.K2) This last equation is in the same form as the equation describing a saturation binding isotherm:

4 ~

3

•

0

100 200 300 400 bound (sites/cell)

Fig. 3. [1251]-labelled pindolol binding to intact S49 cells in the absence and presence of O. 1 nM tertatoloF. @, control; II, + O. 1 nM tertatolol. The incubations were conducted at 37°C for 4 hours. In a one hour incubation, the Scetchard plot was also apparently competitive. Other experiments have demonstrated that preincubation with this concentration of tertatolol is sufficient to reduce detectable receptor number by haft (unpublished data).

(6)

Therefore the Scatchard plot will be linear, and the Bmaxwill not be altered by the inhibitor. The apparent Kd for radioligand binding to receptor will be equal to (K1 + [I]/Ka'K2 + [I]'K3/KI"K2), a combination of three different binding constants as well as the concentration of the inhibitor. In this model, inhibitor reduces the binding of radioligand in two ways: (1) it competes for the radioligand binding sites; and (2) it alters some of the receptors so that they cannot bind radioligand. Both these effects are dose-dependent. The extent of receptor alterations is determined in part by the concentration of radioligand; at high concentations of radioligand, little inhibitor binds and few receptors are altered. When equilibrium is reached, the Scatchard plots are linear, and there is nothing to indicate that the inhibitor did more than just compete for radioligand binding. The inhibitor only appears atypical in other types of experiments, for example experiments in which the cells are first treated with the inhibitor to modify the receptors before adding radioligand. Other manipulations are also helpful. For example we have extended Example 1 by first incubating cells with agonist at 37°C to sequester receptors, then washing the cells and performing binding experiments at 4°C to prevent externalization. Our model assumes that the receptor modification by the inhibitor is reversible, as is known for the two examples we present. Irreversible modifications of the receptors, in contrast, would lead to a decrease in B. . . . Our findings are intrinsic to the nature of competitive interactions, and are not affected by the method used to display the data. We displayed the data as Scatchard plots, but the same conclusions would have been reached had we shown saturation binding isotherms or Klotz plots 3. We derived the conclusions for experiments in which the inhibitor concentration is fixed and the radioligand concentration varies. However, the same conclusion would be reached in experiments in which radioligand concentration is fixed and the concentration of inhibitor varies.

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In summary, we have presented two examples and mathematical analysis to demonstrate that inhibitors can interact with receptors in a strictly competitive manner at equilibrium, even when the in-

hibitor is able to reversibly alter the receptors so that they cannot bind radioligand. References

1 DeBlasi,A., Lipartiti,M., Motulsky,H. J.,

, It, ..... ..l. .. II tlih II -l L -

-

I

T S I i-i i i--[ T - T Ll I .I.I..I I I I Ii i

Agonists, partial agonists, antagonists, inverse agonists and agonist/antagonists? Terry Kenakin The label placed on a drug influences its ultimate use. But interpretation of invivo data has complicated the simple receptor theory of agonists and antagonists for certain classes of drugs. Terry Kenakin argues that clarification of such data - described in an extremely complex system - at a molecular level, will either obviate the need for terms such as inverse agonist or agonist/antagonist, or result in the rewriting of the classical receptor theory.

Drugs are usually classified by their most prominent property and used accordingly as tools to investigate physiological systems and molecular mechanisms of receptor activation. Because of this fact, the label placed on a new drug can be important in terms of the manner in which it will be used and what conclusions will be drawn from experiments. Thus, drug labels should be unambiguous and relate as closely as possible to molecular mechanisms in order to avoid discordant classification of drugs and receptors as pharmacologic technology progresses. A complicated and sometimes contradictory nomenclature has arisen to describe the effects of some classes of drugs, notably opiates and benzodiazepines. In these classes drugs may produce complex patterns of response which have led to the terms inverse agonist and agonist/ antagonist. Specifically, an inverse agonist is defined as a drug which produces effects opposite to those of agonists 1"2 while an agonist/ Terry Kenakin is Section Head of Analytical Pharmacology, Glaxo Inc., 5 Moore Drive, Research Triangle Park, NC 27709, USA.

antagonist ('mixed agonist/antagonist') may alternately demonstrate properties of agonism or antagonism in various systems 2--4. At least in the instances where this nomenclature has resulted from classifications made in vivo, it is not clear whether they are helpful in defining molecular mechanisms or in fact they are obstructive to the understanding of the effects of these drugs. The basic problem with both these classifications is that often they are defined in multivariate in-vivo test systems; therefore the observed profiles may be the result of the complexity of the preparation and not a unique type of drug-receptor interaction at the molecular level. Assuming that the basic values of drug classifications are as descriptions of receptor events which are unique to drug-receptor pairs and therefore are predictive of drug effects across species and organ function, classifications made from data describing multivariate responses can be confusing. There are three basic levels of classification currently used to label these drugs. The first is by effects observed in vivo, clearly an unsatisfactory method considering the multitude of factors such as pharmacokinetics, reflex mechanisms and actions at

Insel, P. A. and Fratelli,M. (1985)J. Clin.

Endocrinol. Metab. 61, 1081-1088 2 DeBlasi, A., Lipartiti, M., Pirone, F., Rochat, C., Prost, J. F. and Garattini, S.

(1986) Clin. Pharmacol. Ther. 39, 245--254

3 Klotz,I. M. (1982)Science 217, 1247

multiple receptors which can affect observed responses. For example, dobutamine is a partial agonist for o¢-adrenoceptorss'6 yet in most invivo preparations, the ~-adrenoceptor agonist properties override this action and the ec-adrenoceptor effects are not observed. Thus, dobutamine would not be classified as an oc-agonist in vivo. Also, the factors which modify drug response in vivo can vary with animal species and even within species with differences in animal maturity thereby concomitantly changing the profile of activity of these drugs and subsequently their classification. A second level of classification has been associated with drug activity at subtypes of a general class of receptors, notably opiate receptors. Thus, 'mixed agonist/ antagonists' have been defined as agonists at one opiate receptor subtype and antagonists at another/. As stated by Martin 7 these current classifications should be considered ad hoc because they arbitrarily make the distinction between types and sub.types of receptors. For example, if adrenergic receptors were considered a general class of receptors much like opiate receptors, then methoxamine would be a mixed agonist/ antagonist of adrenergic receptors being an agonist at ot-adrenoceptors and an antagonist at ~-adrenoceptors s. Of more concern is the protean nature of receptor subclassifications which often are simply working hypotheses based on limited data with new molecules; reclassification would necessarily confuse drug nomenclatures based upon activities on multiple receptor subtypes. Most pharmacologic evidence to date indicates that the most usef u l - a n d enduring classifications emanate from descriptions of drug actions at the molecular level with single receptors. The desirability of such a result is obvious but often prevailing technology makes such data unattainable. The question then arises: is pharmacology aided or hindered by interim ad 1987, Elsevier Publications, Cambridge 0165- 6147/87/$02.00