Brit. J. Pharmacol. (1956), 11, 379.

A MODIFICATION OF RECEPTOR THEORYBY

R. P. STEPHENSONFrom the Department of Pharmacology, University of Edinburgh

(RECEIVED MAY 12, 1956)

It is usually supposed that a drug combines withsome part of a tissue as a necessary step in pro-ducing its action on that tissue. This view wasexpressed by Langley in 1878 while discussingexperiments with pilocarpine and atropine. Helater referred to " receptive substance " (Langley,1905) and subsequently the term " receptor " hasbeen widely used to express the same concept.Clark (1937a) attempted to put the concept on aquantitative basis by applying the adsorption iso-therms of Langmuir which were derived from theapplication of the mass laws to the adsorption ofgases on metal surfaces. The derivation of theequations as they apply to drugs in solution, andreceptors or active patches in tissue, may be putas follows: Drug molecules combine with recep-\tors at a rate which is proportional to the concen-tration of molecules in solution and to the numberof free receptors. The resulting complex breaksdown at a rate proportional only to the numberof complexes. Thus the rate of combination isk1A(l- y) and the rate of dissociation is k2y, wherek1 and k2 are constants, A the concentration ofdrug, and y the proportion of receptors occupiedby the drug. When the two rates are equal wehave, putting K for k'

KA=Y ......1

When y=0.5, then

A=I

. la

Equation 1 therefore relates the concentration ofdrug and the proportion of receptors which are

occupied by drug molecules at equilibrium. Clark,however, went a step further than this and, bytaking y as the response, used equation 1 to relatethe response of the tissue to the concentration ofdrug. Thus there was in Clark's treatment theimplicit assumption that the percentage of recep-tors occupied is equal to the percentage responseof the tissue. When 50% of the receptors are

occupied there is 50% of the possible response;when the response is maximal all the receptors areoccupied.

Clark sought to show that the relation betweenconcentration of drug and the effect produced didin fact agree with equation 1, and his apparentsuccess was some justification for the assumption.The two situations he investigated were (a) thecontraction of the isolated frog rectus abdominisproduced by acetylcholine, and (b) the inhibitionproduced by acetylcholine of the contraction ofstrips of electrically stimulated frog ventricle.These tests have a common disadvantage in thatboth tissues contain enzymes which destroy acetyl-choline, so that the concentration of drug inequilibrium with the receptors is less than thatapplied externally, and, though the applied con-centration is known, that in the tissue is not. Thereceptors, indeed, may not all be in equilibriumwith the same concentration of acetylcholine; agradient is presumably established with a highconcentration near the surface and a lower concen-tration at the centre of the tissue-because thefurther the acetylcholine penetrates the greater isits chance of being destroyed. Such a gradientwould produce a log-concentration-effect curveflatter than the true curve. Furthermore, itcannot be assumed that the ratio of the appliedconcentration to the effective concentration (orconcentrations) is constant for different appliedconcentrations. A block of cholinesterase activitywould therefore be expected to alter the slope oflog-concentration-effect curves; Webb (1950) hasshown that this is so, and that the change of slopeis considerable. Calculation from his graphs showsthat, when the cholinesterase of isolated rabbitauricles is blocked with physostigmine, the slopeof the acetylcholine log-concentration-effect curveis about 10 times steeper than on normal auricles(see Table I). An attempt has been made to deter-mine the relation between log concentration andeffect for acetylcholine and the frog rectus afterblocking the cholinesterase with TEPP so that thesize of the effect could be assessed in one of the

R. P. STEPHENSON

systems used by Clark. This proved to be difficult, the relation between the proportion of receptorssince the response of the rectus, always slow, occupied and the response, and we can broadenbecame very much slower after TEPP, and the the application of the receptor theory by the fol-contractions continued to increase for an hour lowing hypotheses:after acetylcholine was applied. The action of< ' (1) A maximum effect can be produced by ancarbachol on normal recti was similarly slow. It agonist when occupying only a small propor-was therefore impossible to get an accurate esti- Ktin of the receptors.mate of slope, but it was evident that the increase (2) The response is not linearly proportionalof effect with increased concentration was greater to the number of receptors occupied.than required by equation 1. In any case it was W ( Dclear that reliable evidence in support of any par- (3) Dierent drugs may have varying capa-ticular equation would be difficult to obtain from cities to initiate a response and consequentlythis tissue. occupy different proportions of the receptors

Clark discussed several other drug-tissue systems, when producing equal responses. This propertybut he was mainly concerned to show that a H il be referred to as the efficacy of the drug.graded response was produced over a wide range The concept of efficacy, which may vary from zeroof concentration and, in most of the examples he to a large positive value, is at variance with Clark'squoted, the slopes of the log concentration curves (1937c) view ofWe action of a drug at a receptorare not in accord with equation 1. A simple way as all or none; an agonist (Reuse, 1948) causes anof reducing data about concentration-effect curves effect and an antagonist causes no effect so thatto a single figure which is independent of any the activity of a drug of either kind is simply a

theory of drug action, and which can therefore be measure of its affinity for the receptoig Accord-used to test any particular theory, is to use, as \mg to hypothesis 3, however, this remains trueClark did, the ratio of concentrations causing only for antagonists (which have zero efficacy):specified effects. Clark used the ratio for 84% the activity of agonists is the product of theirand 16% of the maximum contraction; but a nity and their efficacy. A drug with very lownarrower range is easier to cover, and there is no efficacy may produce a response which is less thanneed to restrict the ratio measured to any par- the maximum, even when it is occupying nearlyticular pair of responses. Evidence from which all the receptors-and because it is occupying thesuch ratios can be calculated is rare, because the Reeptors, it diminishes the action of a drug withmaximum response is seldom recorded, but a few h efficacy added simultaneously. Compoundsexamples are shown in Table I. Some of these with such a low efficacy that they possess proper-ratios represent new data for acetylcholine and ties intermediate between agonists and antagonistshistamine on guinea-pig ileum; details are given in will be called "partial agonists." (See p. 384.)the section on results. Furchgott and Bhadrakom -Ariens and Groot (1954) have also observed sub-commented on the theoretical implication of the stances with these intermediate properties, and theyslope, and considered that their results agreed with ascribe this to a low "intrinsic activity." Ariensequation 1; the ratio given in Table I expresses and Groot, however, continue to assume that allthis agreement. The other ratios in Table I have normal agonists have the same "intrinsic activity "been calculated from published graphs: they are and their concept is more limited in applicationnot in agreement with equation 1. than hypothesis 3.A variety of slopes can be accounted for by The above hypotheses account for the progres-

modifications of equation 1 obtained by postulating sive variation in properties in a series of alkyl-that a molecule of drug combines with either less trimethylammonium salts.or more than one receptor. The latter possibility The lower homologues have acetylcholine-likemay be true in some instances, but the postulate activity whereas the higher members have anis unlikely to be generally correct-particularly atropine-like blocking action (Ravent6s, 1937a andwhere fractions are involved. Equation 1 appears b; Clark and Ravent6s, 1937). It was expectedto be the most likely relation between concentra- that the members of such a simple homologoustion of drug and the percentage of receptors series would display some progressive change inoccupied, but Table I shows that there is no their affinity for the receptors, and consequently, ifexperimental justification for supposing that it Clark was correct, the reciprocals of the concen-

represents a general relation between concentra- trations of the agonists causing a 50% responsetions of drug and the response of the tissue. It (see equation la) would form part of the same pro-therefore becomes necessary to consider possi- gression as the affinity constants of the antagonists.bilities other than the one assumed by Clark for The demonstration of a sharp discontinuity be-

380

A MODIFICATION OF RECEPTOR THEORY

tween the two sets of constants, such that theagonists are effective in lower concentration thanthe antagonists, would, however, constitute goodevidence for hypothesis 1. Raventos showed thatthe acetylcholine-like activity of the lower homo-logues varied rather irregularly, but calculationfrom his data suggested that the expected discon-tinuity between agonist and antagonist activity didoccur. The nature of the evidence did not allowa firm conclusion. It was therefore decided tore-examine the compounds, with the intention ofobtaining accurate values for the affinity constantsof the first 4 or 5 antagonists, and to compare thesewith the reciprocals of the concentrations of theagonists which cause a 50% contraction.

METHODSA guinea-pig (usually weighing 150-200 g.) was

killed by a blow on the head and bled. The terminal3-4 cm. (avoiding the patch of lymph tissue) of theileum was suspended in Tyrode solution maintainedat 37.0± 0.10 C. It was attached to an isotonic frontalwriting lever giving a magnification of 4 and a loadof 0.5 g. The bath was connected to coils of glasstubing so that the fluid in the bath could be changedby upward displacement and overflow, either byTyrode alone or by Tyrode containing drugs at pre-determined concentrations. The volume of the bathwas about 2.5 ml. and that of the coils 10 or 20 ml.,so that sufficient solution could be run through theorgan bath to effect a complete exchange (verified byusing strongly coloured solution) without exposing themuscle to air and without cooling (less than 0.1° C.).Events in the bath were controlled by an automaticapparatus similar to that described by Schild (1947).Contractions were produced either by agonist solu-tions replacing the Tyrode or by additions from atuberculin syringe at a signal from the apparatus. Inaddition to the uniselector controlling the cycle ofoperations a second uniselector could be used to per-form an assay; 4 different agonist solutions being usedin varying order to produce the contractions: up to48 contractions could be used in the assay (12 groupsof 4 arranged in 3 Latin squares). A similar arrange-ment has been used by Boura, Mongar, and Schild(1954).

RESULTSSlopes of Acetylcholine and Histamine Concen-

tration-Effect Curves.These experiments were performed primarily to

investigate the action of antagonists, but concen-tration-effect curves were obtained before theantagonist was applied and these are relevant here.As soon as the ileum was put in the bath a smallconcentration of agonist (usually 2.5 or 5.0 ng./ml. acetylcholine or 5 or 10 ng./ ml. histamine) wasapplied to the muscle for 10 or 15 sec. and then

washed away. This was repeated at intervals of1+ min. until the responses became steady: thisusually took about an hour. About 4 concentra-tions of agonist differing by a factor of 2 werethen tested: each concentration was used for 3 or4 successive contractions before being replaced byanother. At least two such groups of contractionswere obtained for each concentration and the orderin which the concentrations were tested was varied.The maximum contraction was obtained at the endof the experiment, after the antagonist being testedhad been washed from the bath but sometimes ata time when the muscle was still to some extentunder the influence of the antagonist. A large doseof agonist (about 100 times that giving a 50%response) was, however, used to obtain the maxi-mum contraction, and there appeared no reason tosuppose that the response was different from thatwhich would have been produced before the antag-onist was tested. The contractions were measuredto the nearest 0.5 mm., plotted against logconcentration, and a curve fitted by eye. The con-centrations producing 20, 50 and 80% contractionswere read from this curve. The results from 13experiments with acetylcholine have been analysed.In only 8 of these were responses less than 20%of the maximum obtained, so that in five experi-ments the dose ratio could only be calculated forthe 80% /50% response ratio. All the results havebeen included in Table I, since a biased samplecould result if only the experiments giving a widerange of responses were presented. (Only fourconcentrations, covering a 16-fold range, wereusually tested so that 20% and 80% responsescould not both be obtained in a preparation inwhich the dose ratio for these responses was morethan 16; and would often not be obtained if theratio was only slightly less than 16.) The experi-ments with histamine were done on ileum suspen-ded in Locke solution containing 10' atropine.The results of 38 experiments have been examined;only 13 included both 20% and 80% responses, 10did not include the 80% and 15 did not include the20% response. The slopes varied considerably,particularly those for histamine. The geometricmeans and the standard deviations were calculatedfrom the logarithms of the ratios. These meansand the values of the ratios corresponding to onestandard deviation above and below the mean(being the values between which two-thirds of theobservations would be expected to lie) are shownin Table I. None of the acetylcholine slopes andonly a small proportion of those for histaminewere as shallow as required by equation 1. Thevariations in slope are probably genuine and notdue to error, and this in itself would show that

381

R. P. STEPHENSON

TABLE I

SLOPES OF CONCENTRATION-EFFECT CURVESThe numerals in column A give values of the ratio-

concentration ofdrug producing 80% responseconcentration ofdrug producing 20% response'

and cols. B and C the ratios for the 80%/50%, and the 50%/20%responses, respectively. The values expected from equation I are

16, 4 and 4, in cols. A, B, and C respectively

Slopes Drugs, andAuthors System on

A B C which Tested

Gaddum, 1926 1-8 Adrenaline: contrac-tion of rabbit uterus

Ravent6s, 2 Acetylcholine: inhibi-1937 tion of amplitude of

beat of electricallystimulated frog aur-icle

Schild, 1947 2-5 Histamine: contractionof guinea-pig ileum

Webb, 1950 56 Acetylcholine: reduc-tion in amplitude ofspontaneously beat-ing rabbit auricles

5.4 Carbachol: ditto

5.3 Acetylcholine: dittowith physostigmine10-£

12 9 Acetylcholine: reduc-tion of rate of beat-ing of isolated rabbitauricles

3-7 Acetylcholine: dittoafter treatment withphysostigmine 10-6

Van Maanen, 30 Acetylcholine: contrac-1950 tion of frog rectus

Stephenson 4 Ditto after TEPP(see text)

Furchgott and 16 Adrenaline: contrac-Bhadrakom, tion of rabbit aorta1953 strips

Stephenson 7-7 (8) 2-7 (15) 30 (8) Acetylcholine:contrac-(see text) tion of guinea-pig

ileum. Mean and(no. of observations)

6-4, 9-2 2-2, 3-4 2-6, 3-4 Range (P=0-67)

11-1 (13) 3-2 (23) 34 (28) Histamine: contrac-tions of guinea-pigileum. Mean and(no. of observations)

6-3, 19-5 2-5. 4-0 2-5, 5-3 Range (P-=067)(see Fig. 1) 10 Butyl trimethylam-

imonium: contrac-tion of guinea-pigileum

equation 1 does not represent the dose-effect curve.If, however, the variation is interpreted as randomerror, five of the six mean estimates of slope aresignificantly different from the values .expectedfrom equation 1. For the 50% /20% ratio forhistamine P lies between 0.2 and 0.1: for the80% /50% ratio for histamine P<0.05, and for theother ratios P<0.001.

Alkyltrimethylammonium Salts (Alkyl-TMA)The action of the first six members of the series,

tetramethylammonium (methyl-TMA), ethyl-TMA,propyl-TMA, butyl-TMA, amyl-TMA and hexyl-TMA, appeared to be fairly straightforward, and aseries of (2 and 2) dose assays were made to com-pare their potencies. Ileum was set up as alreadydescribed and assays started when the responsesbecame regular. To facilitate detection of anydifference of slope a dose ratio of 4 was at firstused. However, the contractions produced by thehigh concentrations were observed to depress thesubsequent response to a small concentration,thereby increasing both the variation and theapparent slope. Deviation from parallelism wasnot seen except with propyl-TMA, which some-times had a steeper slope than amyl-TMA, andmost of the assays were done with a dose ratio of2. The effect of the first 3 members was reducedby the addition of hexamethonium to the Tyrode;50 mg./l. and 100 mg./l. were tested and the latterconcentration adopted as a routine. This concen-tration of hexamethonium produced a small con-tinuous activity which was prevented by mepy-ramine and was presumably due to histamineliberation. Mepyramine 10 ptg./1. was thereforealso added to the Tyrode in all subsequent experi-ments. Amyl-TMA, the most active of the series,was used as the standard in each assay. Afterpreliminary tests, 33 assays on 12 pieces of ileum(each from a different guinea-pig) were performed.Each assay consisted of 10 or 12 groups of 4 con-tractions. The results are summarized in Table 11.The assays performed in the presence of 100 mg./l.hexamethonium gave very uniform results exceptfor those of propyl-TMA, where the standarddeviation of the population of assays (n=6) wasabout 15% of the mean. With butyl-TMA thestandard deviation was only about 1.7% of themean. An experimental error of at least this sizeis to be expected so that there can be little if anyvariation due to differences between guinea-pigs.The change in relative activity caused by hexa-

methonium indicates that a nicotine type of actioncontributes to the response obtained with methyl-,ethyl-, and propyl-TMA. The fourfold change inactivity with propyl-TMA suggests that in theabsence of hexamethonium the contraction of theileum is largely due to nicotinic rather than mus-carinic activity.The concentration of agonist required to pro-

duce a 50% response varies both from one pieceof ileum to another and with one piece at differenttimes. If the ileum is handled with great careduring preparation, is not picked up with forceps,

382

A MODIFICATION OF RECEPTOR THEORY

not subjected to a pressure of more than 1 or 2cm. of water when the lumen is washed out, andnot stimulated with high concentrations of agonistin the early insensitive period, the variation is notwide. Even with great care there remains a resi-dual variation, and values for concentrations pro-ducing 50% effect can only be statistical means.The responses to amyl-TMA for that assay duringwhich each ileum showed its greatest sensitivitywere calculated as a percentage of its maximum;the concentration for 50% effect was obtained byinterpolation or a short extrapolation. The maxi-mum contraction was only obtained for 7 of the9 pieces of ileum on which assays were done inthe presence of 100 mg./l. hexamethonium. Forthese 7 pieces of ileum the concentration of amyl-TMA required for a 50% contraction was 5.8 + 0.9X 10-7M (mean + SE, n =7). The correspondingconcentration for each of the other compoundswas calculated from the ratios in column 3 of TableII and the results are shown in column 4 of thattable.The transition from agonist to antagonist acti-

vity in the higher members of the series was notas simple as expected; some compounds showedintermediate effects. This should perhaps havebeen foreseen, since Ravent6s (1937) made passingreference to hexyl-TMA and octyl-TMA producingeffects, on the frog heart and rat ileum respec-tively, which could not be increased by increasingthe concentration. In the present experiments

TABLE 1 ICOMPARISON OF ACTIVITY OF ALKYL TRIMETHYL-

AMMONIUM IONS ON GUINEA-PIG ILEUMAssays of five compounds against amyl-TMA. Col. A gives resultsobtained in the absence of hexamethonium; cols. B and C thoseobtained in the presence of 50 mg./l. and 100 mg. 1. hexamethoniumrespectively, together with mepyramine maleate 10 pg./i., exceptin the one assay marked t in col. C. The numerals in cols. A, B,and C are for individual assays except in two cases, where the meanand standard deviation, based on the number of assays shown inparentheses, are given. The numerals in the last column are cal-culated from the means of the results in the preceding column andthe mean of the observed values for amyl-TMA. In all assays, exceptwhere otherwise indicated, the ratio of high doses to low doses was 2

Activity as Percentage of Amyl-TMA Concn.Producing50% of

Drug MaximumContrac-

A B C tion(M x 106)

Methyl-TMA *2-08 156, 1-54, 1 48, 1 30, 43-51-38 1-25

Ethyl-TMA *1 50 141, 125 1-17. 1-13, 52-01.07

Propyl-TMA *I-15, *1 12 (6) 0d299±0 08 195Butyl-TMA *49-0, *44.9, *45-0,445 (5) t43.8 ±034 1-33

*42.0Amyl-TMA 100 100 100 0 582±

0.092Hexyl-TMA - - 22-7, 24-3 2-48

* Assays done with dose ratio of 4.t Includes one assay done with dose ratio of 4.

on guinea-pig ileum, heptyl-, octyl-, nonyl-,and decyl-TMA all produced contractions, butincreasing the concentration failed to produce themaximum contraction. The largest contractionwhich could be obtained decreased as the lengthof the carbon chain increased, and decyl-TMAwas only able to produce a contraction about 15%of the maximum produced by acetylcholine andby the alkyl TMA ions up to hexyl-TMA. Thesize of the largest contraction produced by any ofthese four partially active compounds varied frompreparation to preparation and from time to time.This variation appeared to parallel the variationin sensitivity to normal agonists, the differencebeing, of course, that lowered sensitivity to a nor-mally active compound did not reduce the size ofthe maximum contraction but only required anincreased concentration to produce it.

In Fig. 1 the contractions have been expressedas a percentage of the maximum obtainable with atrue agonist. All the observations were made onthe same piece of ileum over a period of about 5hours. During this time there were small changesin sensitivity, but the relative positions of thecurves give a good idea of the differences between

11

c

0

u

0to

(U

cLV)U)

a-

10-7 1e0-6 It an0-4Molar concentration

FIG. 1.-Concentration-effect curves for some alkyl-TMA ions onguinea-pig ileum. The contractions were produced by additionsto the bath to give the final concentrations indicated; eachconcentration was left in contact with the ileum for about 15 sec.and then washed away. All the points for a given substancewere obtained in consecutive contractions, starting with a lowdose which was progressively doubled until the response rangewas covered. This was done twice with octyl-TMA and bothsets of points are plotted.

383

R. P. STEPHENSON

the substances. The highest two doses of decyl-TMA were sufficient to reduce the surface tensionof water so that there was some frothing; this maybe associated with the fact that these doses pro-duced less effect than the smaller dose.The fact that these four compounds were neither

true agonists nor true antagonists made impossiblethe comparison of potency of very closely relatedagonists and antagonists which had been envis-aged. It was evident, however, that the actionsof these compounds were consistent with, andtherefore supported, the hypotheses under con-sideration. If different agonists have differentefficacies then compounds with very small effi-cacies may be envisaged, and it is suggested thatthe observed actions of heptyl-, octyl-, nonyl-, anddecyl-TMA are due to their having efficacies whichare so low that, unlike the more familiar agonists,they must occupy a large proportion of thereceptors in order to produce a contraction.Evidence in support of this explanation wasobtained when one of the active members of theseries was tested simultaneously with one of thepartially active substances. Fig. 2 shows the effectof adding a dose of butyl-TMA which alone pro-duced a near maximum contraction with a dose ofoctyl-TMA which alone produced a much smallercontraction. The two together produced very littlemore effect than octyl-TMA alone, indicating thatoctyl-TMA was occupying the receptors to theexclusion of butyl-TMA. Even four times the con-centration of butyl-TMA added with the octyl-TMA did not produce an effect as large as the

single dose of butyl-TMA act-ing alone. The four substancesheptyl- to decyl-TMA thusseem to possess a type ofaction which is a mixture ofagonist and antagonist effects,and they will-as pointed outon p. 380-be referred to aspartial agonists.More elaborate experiments

of the type shown in Fig. 2made it possible to estimate

B 0- 4B

0 O --2B

0- B

FIG. 2.-Guinea-pig ileum. Tyrode withhexamethonium iodide 100 mg.jI. andmepyramine maleate 10 pg/i1., at370 C. Contractions produced byadding octyl-TMA and butyl-TMA togive the following concentrations inthe bath. At 0, 4 x 10'M-octyl-TMA; at B, 1.6x 109M-butyl-TMA;at O+B the same concentrations act-ing together; at 0+2B and 0+4Bthe same concentration of octyl-TMAtogether with 3.2x 105M- and 6.4x10M-butyl-TMA respectively. Re-cording drum stopped simultaneouslywith wash-out.

the proportion of the receptors which were occu-pied by given concentrations of partial agonistsand hence to calculate their affinity constant.To interpret these experiments the following

theoretical relations of the response, R, the efficacy,e, and the proportion of receptors occupied, y, areadvanced. SinceR is not proportioned to y (hypo-thesis 2) it is useful to introduce the quantity S.which may be regarded as the stimulus given tothe tissue, and which is defined as the product ofe and y. We can write R==f(S) signifying that forany value of S the value of R is determined, butthat we do not know how the two are related. Wehave by definition S=ey, therefore from the masslaw, equation 1, we have

KA2S=el+KA. .21~I+KA ..............

For an active agonist, where e is high and only asmall proportion of the receptors are occupied,KA is small compared with 1 and equation 2reduces to

S=eKA .. .... 2aThe efficacy e can have any positive value; there

will presumably be some practical limit, but notheoretical limit can be imposed. It is convenientto adopt the convention that S =1 for a 50%response. When this is done a drug which occu-pies all the receptors to produce an effect which isonly 50% of the true maximum has an efficacye= 1, since S= ey.

Let Al, A2, and A3 be concentrations of anactive agonist (with efficacy ea) and let P be theconcentration of a partial agonist (efficacy ep)such that A, produces the same contraction as Pand that A, produces the same contraction as Pand A3 acting simultaneously. We have, for thetwo sizes of contraction, RL=f(S1) and R=f(S2).If x is the proportion of receptors occupied by thepartial agonist (which will be the same whether A,is present or not since, according to hypothesis 1,an active agonist occupies a negligible proportionof the receptors to produce an effect) we haveSI=ea x and also, using equation 2a, Si=eaKaAIso that

epx= eaKaA5 ................ 3again S2= eaKaAs and, if values of S are assumedadditive, S2= epx+eaKaA3(l-x) since the partialagonist occupies a significant proportion of thereceptors. We therefore have

eaKaA2-epx + eaKaA3(1-x) ........ 4Combining equations 3 and 4

eaKaA2=eaKaAj + eaKaA1(l-x)A2-A . 5x--A ........

384

A MODIFICATION OF RECEPTOR THEORY

more than 80% were occupiedthe concentration A3 of butyl-TMA had to be large and thecontractions persisted afterwashing and upset the assay.Within these limits the calcu-lated values of x agreed wellwith the mass law relation(equation 1). This was clearestwith octyl-TMA and nonyl-TMA, and the results of allthe tests made with these sub-stances are shown in Table III.These results suggest thatequation 5 is valid.Most of the tests with

heptyl-TMA were done whilethe procedure was being estab-

- li~~~~~~~ehi-AnnA thi- rpeiilte uuir,--]FIG. 3.-Guinea-pig ileum, conditions as in Fig. 2. Contractions produced by filling the bath

for 15 sec. with solution containing: 1, 1.4x 10M-butyl-TMA; 2, 2.8 x 10M-butyl-TMA;3, 6.4 x l05M-octyl-TMA; 4, 6.4x l0'M-octyl-TMA+5 x l06M-butyl-TMA. The completeassay consisted of 48 contractions; the first 24 are shown.

Fig. 3 shows the first half of an experiment with higher concarranged to find values to insert in equation 5. were done withContractions of guinea-pig ileum were produced that the total vaby four different solutions; 1, which contained most pieces of i1.4 x 10-6M-butyl-TMA; 2, which contained 2.8 x became quite m10-6M-butyl-TMA; 3, which contained 6.4 x tractions were in10-5 M-octyl-TMA; and 4, which contained both seem feasible to6.4 x 10-5M-octyl-TMA and 5.0 x 10-6M-butyl- decyl-TMA. The_TMA. The concentrations of butyl-TMA were gave the reasonschosen so that the contractions produced by and 2.02X 10-5 fcsolution 1 were similar to those produced by 3, the four partial asand those produced by 4 were similar to those pro- V) increase steadduced by 2. Over small ranges the response tobutyl-TMA (as with other agonists) may beregarded as linearly related to the logarithm of the RESULTS 0concentration, and this relation was used to calcu-late from the measured responses that concentra- Octyl-TMAtions of 1.482 x 10-6M- and 2.462 x 10 6M-butyl- Receptors to OC*TMA would have produced contractions equal in Concn. Apparently Reheight to those produced by solutions 3 and 4 Occupiedrespectively. Inserting these values in equation 5 MX 10 M

indicates that for 6.4 x 10-5M-octyl-TMA the pro- 04 22-1portion of receptors occupied is 0.804 and equation 1-6 46-81 indicates that 1.56 x 10-5M would occupy 50% of 1-6 56 2the receptors or K0, = 6.4 x 104. 16 47.7Experiments similar to that described above 6-4 786

-were done with different concentrations of heptyl-, 6.4 8074octyl-, and nonyl-TMA. The range over which the 6-4 79 9concentration could reasonably be varied was notvery wide. If the partial agonist occupied less -than 20% of the receptors the experimental error Means±S. E. 1-60

Xbecame disproportionately great, while if much Corresp. values ofK 0-6,

WN1IVU UH LCalbl ktb:WI1 C

more variable. Tests withlow concentrations of heptyl-TMA gave slightly highervalues for KHe, than did tests

entrations. Most of the testsintermediate concentrations soariation was not large. Withileum the spontaneous activitylarked when only small con-iduced, and only twice did itdo assays of this type with

ese two experiments, however,ably consistent values of 1.74or K~,6c. The values for K forgonists (which are listed in Tablelily with the increase in chain

TABLE IIIOF ADDITION EXPERIMENTS

Nonyl-TMADoncn. Y. of Concn.ccupy 50%/. Receptors to Occupy 50%Dceptors Concn. Apparently Receptors

1 rtOccupied ....Lyoc t K~onX 105 MX 105 MX 106

1-41 0-4 30-15 0-930 4 39-2 0-62

1.811-25 1-6 63-1 0-94142 1-6 63-2 0 931-75 1-6 63-4 0-92

1-6 67-8 0761-74 1-6 62-7 0-951-84 1-6 63-8 0-96156 1-6 70-6 0-671-6

6-4 86-4 1S0185-6 1-08

)±0-06825 x 105

0-89+0-043x 10-

1-125 x 10'

-385

R. P. STEPHENSON

IOL

c

0

40

c

0

I-

t2

1o-'L

10-a3V

10-'

7~

Me Et Pr Bu Am Hex Hept Oct Non DecChain length

Fla. 4.-Relation between chain length and activity in the alkyl trirammonium series. The points plotted X-X for the first 6 meof the series are the concentrations which produce 50% of the macontraction (data from Table II). The points for the next 4 mlare the estimates of the concentrations which occupy 50%receptors. Standard errors are shown in two instances. The oxon the left is concentration (log scale) and that on the rightreciprocal concentration. On the right the points plotted for theagonists becomo affi iity constants. If Clark's assumption is cthe points plotted for the agonists also represent affinity conThe extrapolations are discussed in the text.

length of the molecules. In Fig. 4 the mean valuesfor K are plotted on a log scale together with thefigures from Table II of the concentrations of theagonists which produce 50% of the maximum con-traction. The straight line drawn through theaffinity constants passes, when extrapolated, wellbelow the points for 50% response for theagonists other than propyl-TMA. It would seemlikely that the affinity constants for the trueagonists also lie on or near this line. It is evident,however, that a straight line does not give anaccurate estimate of the affinity constant of propyl-TMA, since the value indicated is little less thanthe reciprocal of the concentration which produceda 50% response; if the concentration at which 50%of the receptors are occupied is, in fact, onlyslightly greater than the concentration which pro-duces 50% response, then the occupation of all thereceptors would not produce a maximum response(see discussion). In fact this substance did pro-duce the maximum contraction. The position iscomplicated by the possibility that part of theresponse of the ileum to propyl-TMA was due toa nicotine effect despite the presence of 100 mg./1.hexamethonium. With 500 mg. /1. hexamethonium

K propyl-TMA still produced maximum con-- 10 tractions, but the slope of the log-concentra-

tion-effect curve was reduced: these were notgood experiments, since the ileum did notbehave well with this high concentration ofhexamethonium. With the usual 100 mg./1.

10 hexamethonium the nature of the contractiondue to propyl-TMA was different from thatof the other members of the series (andACh); it reached its peak in a few secondsand then declined quite quickly-perhapshalfway to the base line in 15 sec. It wasprobably for this reason that propyl-TMAdid not give additive effects with butyl-TMA.This lack of addition was at first misinter-

-o0 preted as showing that quite small concentra-tions of propyl-TMA occupied an appreciableproportion of the receptors. With higherconcentrations of propyl-TMA, however, the

102 percentage of receptors apparently occupieddid not increase in accordance with equation1, and it became clear that the value of K

nethyl- for propyl-TMA was certainly less than thatimbers indicated by the straight line of Fig. 4.miMUM If the affinity constants of the short chaintembers

of the compounds increase in the regular way shown,rdinate by the partial agonists, the surprisingly lowtis thepartial muscarinic activity of propyl-TMA (Table 11)correct must be due to a relatively low efficacy. Thisstants. was confirmed in pieces of ileum in which the

sensitivity became low in experiments pro-longed for 2 or 3 days. It was observed thatpropyl-TMA lost its ability to produce the nor-mal maximum contraction though this was stillreadily obtained with both ethyl- and butyl-TMA.Hexyl-TMA was also unable to produce maxi-mum contractions in these tests. It is possibleto estimate relative efficacies from the height ofmaximal contractions where these are less thanthe true maximum (see discussion), and itappeared that the efficacy of hexyl-TMA was 4-5

[ times that of propyl-TMA. The curved line inFig. 4 extending from the estimated affinity con-stants of the partial agonist has been drawn so that

I the affinity constant indicated for propyl-TMAcorresponds to an appropriate value for efficacy.It will be assumed that the affinity constants of allthe compounds lie on this line.The gap between this line and the points for

50% response supports the hypothesis that activecompounds of this series, and by inference othersimilar substances, including acetylcholine, producetheir effects when only a small fraction of thereceptors are occupied.An interesting effect was observed when the

partial agonists acted on the ileum in the presence

386

I

I,

I I I I I

A MODIFICATION OF RECEPTOR THEORY

5 59 ng. ml. ACh0 2 ng. ml. Atropine

Octyl 6 10-475 sec.

FIG. 5.-Guinea-pig ileum, conditionsas in Fig. 2. Regular con-tractions produced by acetylcholine acting for 15 sec. at 1 min.intervals. The first 6 contractions were produced by ACh5 ng./ml. After the 6th contraction the ACh was washed fromthe bath with Tyrode containing atropine 2 ng./ml. (in additionto hexamethonium and mepyramine) and this concentration wasthen maintained continuously: subsequent contractions wereproduced by ACh 50 ng./ml. At thejvertical arrow octyl-TMAwas added to give a concentration of 6 x 10'4m and left in thebath for 75 sec.: ACh was then applied 45 sec. later and atI min. intervals.

of atropine. The dose had, of course, to beincreased to produce a contraction, but whensufficient was applied the contraction was muchslower than usual and the partial agonist had tobe left in the bath for about 100 sec. to allow thecontraction to develop fully. This compares withthe 5 or 10 sec. which is usual for the partialagonists in the absence of atropine and for normalagonists whether atropine is present or not. Whensuch a slowly developing contraction was elicitedduring an interruption in a series of acetylcholinecontractions, a sensitizationof the ileum was observedwhen the acetylcholine con-tractions were resumed. Thesize of the contractions thendeclined again at a rate verysimilar to that of the declinewhen atropine was firstapplied. This similarity isevident in the experimentshown in Fig. 5, where theatropine produced a 10-foldreduction in sensitivity toacetylcholine. These effects Twere only seen with the 80partial agonists; when amyl- 75 sec.TMA was allowed to act for (a)a similar period no sensitiza- FIG. 6.-Guinea-pig ileum

out; regular contracttion occurred. However, to give the concentral

when amyl-TMA was used instead of acetyl-choline to produce the series of control contrac-tions, octyl-TMA caused the usual increase insensitivity, so that the effect is clearly not due toinhibition of cholinesterase activity.

These experiments provide strong support forhypotheses 1 and 3. When atropine occupiessome, or even most, of the receptors, plenty ofothers remain; if the concentration of agonist isincreased to counter the reduction in the numberof receptors available to the agonist, a contractionwill occur without the agonist displacing the antag-onist. The partial agonists, however, have such alow efficacy that a significant proportion of thereceptors must be occupied if a contraction is tobe produced; this can only occur when atropinevacates the receptors and the contraction is con-sequently slow. When the contraction is estab-lished most of the receptors will have been freedfrom atropine, so that when the partial agonist isremoved acetylcholine produces nearly its usualeffect until the atropine re-establishes itself.

In the experiment shown in Figs. 6 and 7 thepresence of atropine only reduced the sensitivity ofthe ileum to about a quarter, so that the atropinewas occupying about 75% of the receptors; thefree 25% allowed the partial agonists to produce arapid initial contraction which then increasedslowly as the atropine left the remaining receptors.When octyl-TMA was left in the bath only a littlelonger than was needed for the rapid phase of thecontraction to occur, there was little sensitization;but when the same, or even a smaller, concentrationwas left in longer the sensitization was moremarked (Fig. 6). The size of the rapid part of thecontraction due to the 25% free receptors

T I200 200

30 sec. 75 sec.(b) (C)

i, conditions as in Fig. 2. Atropine sulphate 1 ng./ml. present through-tions produced by ACh 20 ng./ml. Octyl-TMA was added at the arrowsLtions shown x 10M, and left in the bath for the time stated.

387

-214

---4

R. P. STEPHENSON

Octyl Amz Ht.Ee:Y. NCmY400 4 800 4l 32u

FIo. 7.-Same experiment as in Fig. 6. Atropine present throughout. Alkyl-TMA salts were added at the arrows to'give concentra-tions shown x 10`6m. These concentrations acted for 105 sec.

depended, as would be expected, on the efficacy ofthe partial agonist; it was smaller with octyl-TMAthan with heptyl-TMA; with nonyl-TMA it wassmaller still (Fig. 7).The partial agonists with a longer chain did not

show the de-atropinization effect so clearly: whenused in the concentrations necessary to displaceatropine they persisted in the tissue after washingand continued to occupy receptors. The sensitiza-tion then appeared as the partial agonist diffusedout, and disappeared as the atropine re-establisheditself. This effect is just apparent with the higherconcentration of nonyl-TMA in Fig. 7.

DISCUSSIONSo far as the main purpose of this paper is con-

cerned, the evidence about concentration-effectrelations is only of secondary interest, and will notbe discussed further, except to repeat that there islittle experimental justification for the idea that theequation KA= 1 expresses a general relationbetween drug concentration and tissue response;and that consequently it is unnecessary to assumethat the percentage of receptors occupied is equalto the percentage response. The view that such arelation does hold has never been explicitly pro-pounded, but was implied in Clark's discussion ofthe mode of action of drugs. When clearly stated,the improbability of this relation becomesapparent; but, since the action of drugs is usuallydiscussed within the framework of Clark's ideas,its widespread acceptance must be assumed. Aclear statement of this view occurs in the paper byRavent6s (1937b) in which, while discussing thefact that acetylcholine and methyl-TMA haveadditive inhibitory actions on the frog heart, hesays: "If the two drugs occupy a commonreceptor then the full additive effect must meanthat the gross difference in their activity is due

to a difference in the ease with which they combinewith the tissue. If the difference depended on theamount of drug required to be combined with thetissue in order to produce an effect, then thepresence of the weaker drug would tend toantagonize the action of the stronger drug, sincethe weaker drug would reduce the number of freereceptors available for the stronger drug withoutitself producing much action. . . . A number ofthe quaternary ammonium salts . . . were tested. . .and an additive effect was found in all suchcases between these salts and acetylcholine." Thedifficulty of allowing different efficacies at oncedisappears if it is assumed that the effects are pro-duced when only a very small proportion of thereceptors are occupied. Only with compounds ofvery low efficacy would an appreciable proportionof the receptors be occupied and the effect pos-tulated by Ravent6s appear. It would seem thatthis does in fact occur with four of the alkyl-TMAsalts when tested on. guinea-pig ileum.The surprising observation that the partial

agonists oppose the action of atropine, as well asthe action of true agonists, strongly supports theidea that the partial agonists, unlike normalagonists, occupy most of the receptors when pro-ducing a contraction. In the experiment shown inFig. 7 atropine reduced the sensitivity to acetyl-choline to about one quarter, and was thereforeoccupying about 75% of the receptors; the per-centage occupied by the alkyl-TMA salts has beencalculated from equation 1 using the affinity con-stants shown in Table V (see below). The results,shown in Table IV, are clearly of the right order toexplain the de-atropinization seen in Fig. 7 andillustrate the difference between amyl-TMA andthe partial agonists.

This displacement of atropine by the partialagonists would appear to be the effect that Clark(1937b) could not find with acetylcholine and

388

A MODIFICATION OF RECEPTOR THEORY

TABLE IVCALCULATED PERCENTAGE OF RECEPTORS OCCUPIEDBY THE COMPOUNDS TESTED IN THE EXPERIMENT

SHOWN IN FIG. 7

Alkyl-TMA Alkyl-TMAActing Alone Acting with Atropine

Drug Y. ofReceptors % of Receptorsand

Concentration Occupied Occupied byby Free Free

Alkyl- Alkyl- Atro-TMA TMA pine

AtropineHeptyl-TMA 8 x 10'Octyl-TMA 4 x 104m. .Nonyl-TMA 8 x 10-6MNonyl-TMA 3-2 x l -iMAmyl-TMA 4x 10M

96-696-090-097-33-3

3-44-010-02-7

96-7

88-186-669-390-00-8

758-9

10-123-07-574.4

25 W2-9 c

3-3 0

0.7-7 VA

25 0

248

atropine; he regarded the absence of this effect asevidence against the idea of competitive antag-onism. If there is a large excess of receptors thenacetylcholine can produce its effect-even thoughmost of the receptors are occupied by atropine-without actually displacing the antagonist from thereceptors. Since fewer receptors are available theconcentration of acetylcholine has to be increasedin order that the same number shall be occupied.Only with very high concentrations of atropinewould the production of an effect by acetylcholinerequire the displacement of atropine-and thenonly from a very small fraction of the total numberof receptors.The idea that the activity of acetylcholine-like

drugs is due to two separate properties-affinity forthe receptors, and efficacy-thus seems to explainmost of the observed facts; and,assuming its correctness, it be- 100comes interesting to attempt toseparate the contributions of thetwo factors to the total effect. 80No attempt has been made toobtain a theoretical relationbetween the stimulus S and theresponse R, but the empirical tU 60 -

relation can be obtained experi- -lmentally since S, like y, is pro- aportional to the concentration M

when y is small (equation 2a). @ 40 -

In Fig. 8 values of S have been /plotted against the responses tobutyl-TMA from the experiment 20shown in Fig. 1. From equa-tion 2, and Fig. 8, a set of log-concentration-effect curves fora series of hypothetical com-pounds with the same affinity, 07K= 103, but with efficacies vary-ing from 1,000 to 0.5 have been FIG. 9.-Set of log-calculated, and are plotted in same affinity co

0lS

FIG. 8.-Curve relating the response R to the stimulus S (= ey ) basedon the log-concentration-effect curve of butyl-TMA in Fig. 1.Here the effect is plotted against concentration, but the concen-tration scale is replaced by the arbitrary scale of S. That is, itis assumed that y-the percentage of receptors occupied bybutyl-TMA-is small so that y and consequently S are bothproportional to concentration.

10-4 10-4

Molar concentration

-concentration-effect curves for hypothetical substances. All have theinstant, K= 103, and the efficacy varies as shown from 1,000 to 0.5.

389

R. P. STEPHENSON

Fig. 9, which shows how the maximal 100effects produced by partial agonistsvary with their efficacy. The ratio ofthe efficacies of two partial agonists isthe same as the ratio of the two con- 80

centrations of a true agonist which givecontractions equal to the two partialagonist maxima. In systems where thelog-concentration-effect curves for trueagonists have low slopes, compounds 6with a wider range of efficacies will 1come into the class of partial agonists. usIn these respects " efficacy " differs from c"intrinsic activity" which, as defined "v 40 -

by Ariens and Groot, is directly pro- afportional to the size of the maximalresponse. It is evident that the shapeof the curves in Fig. 9 varies little when 20 -

e is greater than 10, and the curve

shown for e= 100 is practically identicalin slope and position with the curve

which would result for K=2 x 102 and _e=5 x 102, or for any other pair of 10values such that Ke= 105. Only inspecial circumstances, therefore, can the FIG. 10.-L

separate contributions of K and e be the conin Fig.determined. the:exp

The extrapolation in Fig. 4 is such a

special circumstance, and it provides the basis forestimates of K and e which, though possibly notvery accurate, are of considerable interest. Thevalues for the efficacies of the agonists have beencalculated from equation 2 using the values of Kread from the curved line in Fig. 4 and the concen-trations for a 50% response from Table II (so thatS= 1). The efficacies of the partial agonists were

obtained by applying equation 3 to the com-

parisons with butyl-TMA given by the additionexperiments. Each experiment gave a value forthe appropriate e. The affinity constants and theefficacies of the compounds in the series are listedin Table V.Once it is accepted that the affinity of the alkyl-

TMA ions for acetylcholine receptors varies in a

regular way with chain length, it follows that thesharp peak of activity at amyl-TMA is due to high

TABLE VTHE EFFICACY AND AFFINITY OF ALKYL-TMA IONS

The affinity constants of heptyl-, octyl-, nonyl-, and decyl-TMA arethe mean experimental values; the others are read from the curvedline in Fig. 4. The values ofefficacy are related to the mean sensitivityof the pieces of ileum used to compare the activity of the first 6

members of the series

0-5Molar concentration

iog-concentration-effect curves for the alkylTMA ions reconstructed fromstants in Table V, using equation 4 and the curve relating R and S shown8. The curve in Fig. 8 is the only link between these curves anderiment on which Fig. 1 is based. Compare Fig. 10 with Fig. 1.

efficacy; this is apparent in Table V. The estimateof the efficacy of methyl-TMA is very dependenton the accuracy of the extrapolation in Fig. 4 andis consequently liable to error: the value obtainedis comparable with that for amyl-TMA, and thissuggests that most of the difference in the activityof these ions is due to the difference in affinity. Thelong-chain members of the series have a highaffinity and a low efficacy.These estimates of the affinity constants and of

the efficacies of the alkyl TMA salts enable theconcentration-effect curves to be reconstructed forcomparison with the experimental curves shown inFig. 1. Since the positions of the curves, and thesize of the response to the partial agonists, dependon the sensitivity of the individual piece of ileum,it is necessary to adjust the values of efficacy tothe individual case. The ileum on which Fig. 1 isbased required 2 x 10-6M-butyl-TMA for a 50%response, compared with the mean value of1.33 x 10-6M in Table II; the values of efficacyappropriate to Fig. 1 are consequently one-thirdless than those in Table V. From these adjustedefficacies, and the affinity constants in Table V, thecurves shown in Fig. 10 have been calculated,using equation 2 to give S, and Fig. 8 to give R.Fig. 10 is a fairly good reproduction of Fig. 1,indicating that the various assumptions which

Alkyl Group Me Et Pr Bu Am Hex Hep Oct Non Doc

Efflcacy . 94 31 4-3 200 200 21 2-2 1-4 1-0 0-6Affinity x 0- 024 0-63 1-6 3-8 8-5 19-0 41 63 110 190

390

A MODIFICATION OF RECEPTOR THEOR Y

have been made are not grossly at variance withthe experimental evidence.

Action of AntagonistsIt is interesting that some antagonists are effec-

tive in appreciably lower concentrations than thecorresponding agonists (e.g., atropine and acetyl-choline; mepyramine and histamine). It followsthat such antagonists have higher affinities than theagonists. This difference becomes more markedif we now accept that the agonists cause appre-ciable responses when * cry few receptors areinvolved ; and it may be that the incompatibilityof high affinity and high efficacy is general, and isnot particular to the alkyl-TMA ions.

If the new ideas expressed in this paper-par-ticularly hypothesis I-are accepted some modi-fication of ideas about drug antagonism will beinvolved. It is usual to postulate two types ofantagonism-competitive and non-competitive-the former being more usual. In competitiveantagonism, agonist and antagonist, simul-taneously present in solution, are each consideredto compete for receptors to the exclusion of theother; and the response is determined by the con-centrations of the two drugs and their relativeaffinity constants. Gaddum's equation (1937)relating these factors is derived from a considera-tion of the mass laws; its relevance is notaffected by hypothesis 1, provided it is realized thatthe equation gives information about receptors andnot about responses. Perhaps the most importantpoint about the type of antagonism usually caHedcompetitive is that it is possible to obtain maxi-mum responses with sufficient agonist, and thatthe slope of the log-concentration-effect curve isnot changed in the presence of the antagonist. If,however, considerably more receptors exist thanare needed to produce a maximum response,similar results will be possible with antagonistswhich block receptors irreversibly, or block atsome site beyond the receptor but before thenumber of receptor paths has been appreciablyreduced. Such antagonism would obey Gaddum'sequation until sufficient paths were blocked toreduce the number of functioning receptors almost-to the minimum required for the agonist to pro-duce a maximum response.There is evidence that the haloalkylamine type

of compound blocks several kinds of receptorsirreversibly-that is, the response is not restoredwhen the antagonist is removed from the environ-ment (Nickerson, 1949a; Furchgott, 1954), but theblocking action has nevertheless been supposed tobe competitive at first, and to become non-competitive only after more prolonged action. This

2D

has been discussed by Nickerson (1949b). Theimplication of a change in mode of action isavoided by the concept of spare receptors. As longas sufficient receptors remain free the antagonismis " surmountable ": it is only necessary toincrease the concentration of agonist in the inverseproportion to which the available receptors havebeen reduced. When, however, the number ofreceptors is irreversibly reduced below the mini-mum required, maximum responses become impos-sible; eventually all the receptors are blocked andno contraction can be obtained: the antagonism is" unsurmountable." The two phases of the actionare thus seen as stages in a single continuous pro-cess in which an increasing proportion of receptorsare irreversibly blocked.

This issue is confused because most experimentshave involved injecting doses into animals; in suchcircumstances it is not always clear how long thedrug remains in circulation and reversible com-petition remains possible. This difficulty is avoidedin experiments with isolated tissue. Experiments(which will be reported in a subsequent paper)with SY-28 and histamine on guinea-pig ileumshow that considerable irreversible block can beassociated with a normal slope for the log-concen-tration-effect curve and a normal maximum con-traction. Similar results have been obtained byNickerson (unpublished). These experiments agreewith the above interpretation. It is probable thatthe haloalkylamine antagonists act directly on thespecific receptors (Furchgott, 1954) ; but it is aconsiderable modification of the established con-cept to describe such block, which persists afterthe disappearance of the antagonist, as competitiveantagonism. If hypothesis 1 is correct it is alsopossible to envisage block occurring away from thereceptors producing similar antagonistic effects.Such block whether reversible or not might appearto follow Gaddum's equation over a limited range,but would clearly not be competitive. The equa-tion is strictly applicable only in equilibrium con-ditions. Equilibrium between receptors and anirreversible drug is only achieved when all thereceptors are blocked: it is only the rate at whichthis condition is approached that is determined bythe concentration of drug. Gaddum's equation,and some other expressions of the mass law, havenevertheless been applied in such situations byallowing an arbitrary time of action; sometimesdoses injected into animals have been used inplace of concentrations in the equation. Used insuch ways the equation can carry little theoreticalimplication and, even when applied to an appro-priate experiment, cannot prove that a pharmaco-logical antagonism is competitive. It is conse-

391

R. P. STEPHENSON

quently preferable to use the purely descriptiveterms "surmountable" and "'unsurmountable"(Gaddum, Hameed, Hathaway, and Stephens,1955) to distinguish between the two commonlyobserved situations. Whether an effect is competi-tive or not will probably have to be decided onquite different evidence.Antagonism which is surmountable but irrever-

sible is difficult to explain without acceptinghypothesis 1.

Structure-Action RelationsIn considering the structural features of a mole-

cule which determine its potency for some specificaction, authors, working within the framework ofClark's ideas, have usually considered that thesefeatures exert their effects only by modifying theaffinity of the molecule for the appropriatePreceptors. Only occasionally has some sugges-tion carried an implication of the concept of whathas here been termed efficacy. The clear recog-nition of two separate entities "affinity" and" efficacy," both of which might be altered by anyone structural change, should clarify the con-sideration of many structure-action problems.One example may be mentioned. Holton and Ing(1949) showed a progressive and sharp decline ofspecific activity as the methyl groups on the nitro-gen atom of acetylcholine were successivelyreplaced by ethyl groups. The authors discuss thisdecline solely in terms of the structural require-ments for fitting the acetylcholine receptor. In theclosely analogous compounds prepared by FordMoore and Ing (1945) which block the actions ofacetylcholine (the efficacy is reduced to zero by abenzilyl group at the other end of the molecule),the effect of progressively replacing the methylgroups on the nitrogen atom by ethyl groups is notnearly so drastic. The first ethyl group indeedincreases the blocking activity and the second andthird reduce activity only slightly. Since the acti-vity of blocking compounds must be consideredsolely in terms of affinity for the receptors, it wouldseem safe to assume that the trimethylammoniumgroup confers high efficacy rather than highaffinity on acetylcholine.Throughout this paper, receptors have been dis-

cussed very nearly as if they existed in isolation.This has been deliberate. What a drug combineswith to produce its effect is a subject for specula-tion. It is attractive to think of a part of someenzyme system at which a stimulant drug becomesa prosthetic group. This must have occurred tomost people with interests in this field and hasbeen expressed at least once (Welsh, 1948).

The approach to study of the action of drugsused in this paper is not universally popular amongpharmacologists; some, indeed, despise discussionin terms of receptors, so that it is perhaps worthwhile to try to state my position clearly. The onlybasic assumption involved when discussing drugaction in terms of receptors is that the drugs com-bine in some way with the tissue they affect. Inorder to develop a system of thought about drugaction it is necessary, in the absence of intimateknowledge, to make additional assumptions. It isimportant, however, that such assumptions shouldbe made explicitly so that they may be testedwhere possible; this, unfortunately, is not oftendone, with the result that mutually conflictingassumptions abound. In this paper one such addi-tional assumption, which is widely-but appar-

. ently unconsciously-held, has been challenged,and several other assumptions have been made.Implicit and erroneous assumptions may be con-cealed in the ideas which have been expressed inthis paper. If so, confusion may result and theconclusions drawn may be wrong. But, if the basicassumption is correct, it will be profitable to con-tinue the argument.

SUMMARY1. The inadequacy of the experimental evidence

in favour of the theory that the mass law relationbetween drug concentration and tissue receptorsaccounts for the slope of concentration-effectcurves is pointed out.

2. A new theory is proposed which avoids theassumption that the percentage effect is equal tohe percentage of receptors occupied by a drug.This theory allows a new factor, called efficacy,to be postulated which, together with affinity forthe receptors, determines the potency of an agonistdrug. This concept removes the absolute distinc-tion between agonist and antagonist drugs, and theexstence of an intermediate class of partialagonists is recognized.

3. Experimental evidence for this theory wasobtained from an examination of the actions andinteractions of the homologous series of alkyltrimethylammonium ions and atropine. Fourmembers of the series acted as partial agonists.

4. The assumption that the percentage responseis equal to the percentage of receptors occupied ishidden in much current discussion of drug action.If this assumption is wrong, as is now suggested,the conclusions to be drawn from a wide range ofexperimental observations will be modified. Theconcept of competitive antagonism, and ideas

392

A MODIFICATION OF RECEPTOR THEORY 393

about the relation of chemical structure to pharma-cological activity, are discussed.

The experimental work was possible only becauseDr. R. B. Barlow undertook the synthesis of the alkyltrimethylammonium salts. I am very grateful.

Some of the material in this paper was discussed atmeetings of the British Pharmacological Society inJuly, 1952, and January, 1954, and at the XIX Inter-national Physiological Congress (Stephenson, 1953).

REFERENCES

Aridns, E. J., and Groot, W. M. de (1954). Arch. int.Pharmacodyn., 99, 193.

Boura, A., Mongar, J. L., and Schild, H. 0. (1954).Brit. J. Pharmacol., 9, 24.

Clark, A. J. (1926). J. Physiol., 61, 530.(1927). Ibid., 64, 123.

- (1937a). In Heffter, Handbuch der experimentellenPharmakologie, Ergfinzungswerk, Bd. 4. Berlin:Springer.(1937b). Ibid., p. 73.

- (1937c). ]bid., p. 193.

Clark, A. J., and Ravent6s, J. (1937). Quart. J. exp.Physiol., 26, 375.

Ford Moore, A. H., and Ing, H. R. (1945). J. chem.Soc., 55.

Furchgott, R. F. (1954). J. Pharmacol., 111, 265.- and Bhadrakom, S. (1953). Ibid., 108, 129.Gaddum, J. H. (1926). J. Physiol., 61, 7P.

(1937). Ibid., 89, 144.Hameed, K. A., Hathway, D. E., and Stephens,F. F. (1955). Quart. J. exp. Physiol., 40, 49.

Holton, P., and Ing, H. R. (1949). Brit. J. Pharmacol.,4, 190.

Langley, J. N. (1878). J. Physiol., 1, 339.(1905). Ibid., 33, 374.

Nickerson, M. (1949a). Pharmacol. Rev., 1, 27.- (1949b). Ibid., 1, pp. 39 and 40.

Ravent6s, J. (1937a). Quart. J. exp. Physiol., 26, 361.- (1937b). Ibid., 27, 99.

Reuse, J. J. (1948). Brit. J. Pharmacol., 3, 174.Schild, H. 0. (1947). Ibid., 2, 189.Stephenson, R. P. (1953). Abstracts of Communications,

XIX International Physiological Congress, p. 801.Van Maanen, E. F. (1950). J. Pharmacol., 99, 255.Webb, J. L. (1950). Brit. J. Pharmacol., 5, 335.Welsh, J. H. (1948). Bull. Johns Hopk. Hosp., 83, 568.