Dose-response curves and mechanisms of drug action

I XS - iltWrnher

ose-response curves and mechanisms of drug action Dennis Mackay

Much of phartnacology has been. and still is, concernedwith the interpretationof concentration-responsecurves %Nhich stuntmarize the relation between the concentration of an agonist and the change which it produces in some measured property of a living system. The responsesproduced by an agonistmay be modified by the presence of other dtugs. ln this review I shall exclude born consideration drugs which modify only the removal of an agonist; for example by metabolism or &rough uptake tnechanisms. I shall limit the discussiorrto drugs which modify the responsesby {a) interacting with the samereceptorsas the agonistor (b) producing a change ia the state of the living system by interacting with another kind of receptor or by some non-receptor mechanism (i.e. functional interaction)LZ. In particular, this review deals with the use of nufl equations, especially that recently derived for functional interaction. to obtain information about mechanisms of drug action from concentration-respons data. Although the quantitative methods discussed here are interudedprimarily for experiments on isolated tissues they may have wider application.

Comparisim of concentratiou-respon curves The interaction of an agonist A with its receptor R to produce a measurable resposse can be represented in general terms as shown in Fig. 1.Theprimary stimulus!L depends on the concent~tion of agonist-receptorcomplexes. AR. and their intrinsic effKacy, f~. The primary stimulus leadsto a secondarystimulus. SR. and so on until the observed responseis produced. If the measured‘response’is, for instance. the amount of fictively labelled drug bound to its receptors then the laws of chemical kitteticscan be applied directly to analyse the relation between the amount of drug bound and the concentration of free drug. A similar analysis can be made if a detailed model is available of the steps be

I V82

cu:+s the use of null equations derived recently for furiction~l intemction’,z. However, a clearer picture will be obtained of the gelleral use of null equationsto study mechanistnsof drug action if we look first at null equationsderived for dtugs acting on the same receptors. Null equatiuns for drugs acting uu the

same receptors

Examples of such equationsare summarized in Table I. In each example the fust curve is obtained for the agonist A acting alone on the tissue. The second curve is obtained under the conditions specified in the table. For each null equation a p~icul~ graphical method is suggestedfor estimattween Sn and the observedresponsebut this ing how well experimental data fit the equs becomes increasingly difficult as the (ion (see Table I), although other methods number of stepsbetween them iq increased. are sometimes available. It should be At the present time theseintermediate steps remembered that these null equations have are so poorly understoodthat a single con- been derived on the basis of the classical cen~tio~es~n~ curve me&y summar- occupation theory of drug action but that izes the experimental data and by itself very similar equationsresult from the useof gives little at no information about mechan- alternative ?heoriesXn~Y. Obviously, the equationslisted in Table 1 ism of drug action. This problem can be overcome to some extent if we compare two can be usedto test whether two agonistsact or more concentration-responsecurves for on the samereceptors(equations I and 2)or different drugs applied singly or in com- whether an antagonist acts competitiveb, bination to the same piece of Mated tissue. (equation 3) or no~com~titively {eqesua(ion 4). Examples of such curves are shown in Fig. Since the aflinity constant of a competi. 2a where one curve is for the agonist A acttive antagonist for a receptor should be ing alone and the rther is for the same agon is?acting in the presenceof a fixed concen- independent of which agonist is used. tration of another drug, B. The concentra- provided that the agonists act on the same tion of agonist required to producea chosen receptors, equation 3 can also be employed magnitude of the responsecan be interpo- to test indirectly whether different agonists Iated from the firs? curve and is given the do act on the same receptors. These equasymbol (A), while the concen?ratlOn tions have also been usedto obtain informa required to produce the same magnitude of lion about the properties of drug-receptor response in the presence of l3 can be read complexes and to characterize receptors. from the second curve and is given the symbol (A)‘. If this procedureis carried out A null equatiua for fimctional for several responselevels then each =:alue antagonism and synergism Tbc q~litative model for functions of (A) can be plotted against the corresinteraction is shown in Fig, 3. In this ease ponding vahte of (A)’ as shown in Fig. 2b. The tnathemaiieal equation relating those the interactingdrugs do no?act on the same concentrations of agonist, or agonists. receptors. In order to derive a null equation which produce equal responsesis called a for this model it was necessaryto assumea null equation. The precision with which particular form of relatian between the experimental data fit a Wretical null equa- primary stimulus S, and any subsequent tion. derived on :he basis of some chosen stimulus (such as Su) so that. for example, modei of drug action, can be testedby using either graphical methods or curvefitting techniques. The derivation of theoretical whett: u and b are called chain constants. null equations and the assumptions These are not truly constant since they may involved in their use have been discussed vaty from one tissue sample to another and elsewhere3r’J. will depend on the position of !&I in the The main purposr:of this article is to dis- chain of ~uential stimuli. It was also necessary to distinguish clearly between the ‘response’ of a tissue and its’state’. Theiatter may be assessedby some measurable propeny, such as muscle tension. On the other hand the term ‘res ponse’ is often used to mean a change in

f

some measured property and would then correspondto a change in state. If responses are measured From a stable and constant baseline then equal responsesalso corres. pond toequivalent states.If, however, pretreatment of a tissue with a drug B alters the baseline and the effect of an agonist A is then studied in the presence of B, it is reasonable to ask whether the ‘response’ should be measured fmm the baseline obtained after B was added or from the baseline before addition of B. This problem does not exist if we plot the state of the tis sue, as assessedby the measured property, against the agonist coneen~atjon. To avoid confusion, null equationsare therefore best defined as relating those drug conccntrations which produce equivalent states. To emphasize this point, the term co~tcerr~r~tion-response CUIIThas been replaced by

concentration-5iate curve. TL general null equation derived for functional interaction, based on the model shown in Fig. 3 and the assumptionsoutlined above, is (A)‘/(A)

= (1 t P (A)’ + ‘r/(A).

(6)

where (A)’ and (A) prcduce equivalent states of the tissue and (11,@ and y are adjustable constant!;. This equation is the most general form af null equation so far derived since it can, under appropriate conditions. reduce hJ the same algebraic form as other null equationslisted in Table 1. For example, if fi is zero, or if y is zero, or both @ and y are zero then equation 6 takes a

form which can be shown to br essentiaity similar to equations 2.4 and 5. and 3 res&vely. From this it will IX clear that iia pair of concentration-statecurves fits one of rtie null equations listed in Table I then the larrespondinp mechanism of interaction Snay & correct. However. more than one tnodel may fit a set ofex~~mental data and :n these eases other information. such as :vhether the drugs indeed act on the satne receptors. may be required to decide between altematibe mechanisms. Two major differences between the null equations in Table I and the general null t+&ion for functional interaction are worth emphasizing. The first is that if ft. iis

J

and y are all sipnifica=~ri~different from zero then [he precision wrth u hich data fit equation 6 cannot be testeddtr~l? u\top d tH@dimenGonal graphical pIi>: InrteaJ an equation of the form Y I( - /FL - ; XI can be fitted IO the datd. uhsre 1

&A) ;(At. XI

t.41 anlf s2

I,I Al

Programs for tittinp such lnultiple Ime~r regressionsarc available for mttct de&.-top programmable calculators. Tin\ u+nikln to the pmblemoirrtima~ing the twst-tit valusr ofrl. f.+and y ISnot ~dca!and ktter msthods are bemg developed. The bind imp%mt difierencr betwttn the null equattonsItstedin T&e I and the general null cqu.~nt>nfor tunctl~~rt;tl

4YS interaction i $ that the adjustable constants for the fatter iru, ~3and ~1 should depend on the particuhr piece of tissue and on the site of action c~f the functional interactant. These tissue-depen&nt and mechanismdependent cmanfitiescannot be eliminated by algebraic ~~f~kfiun of the tfdjusfabk ~onsfanr~ -1hrs is a major disadvantage *f we wiint !O WU: suchdafa roo&t~in iaformcption about me properties of dmg-receptor complexes. In fact, analysis of equation f~ leads to the con~lusiffn that rffnify COtiStanfs of agonist-receptor cofnplexcs cannot be estimated dependably using functional interactants. contrary to carlkr ideas. On fhr: other hz;odTuch studies may provide in~o~af~f~ about possibfe fnechanismsof action of furtctinnat interactants. as discus sed in the next section.

The interactionbcfween an agnnist A and an intera~tant B can be clas_sedas type I if the value obtained for y differs signifiianfly from zem, 4-rtype II if this is not so. Tjpe I interaction occurs if the interactant produces a rfimulus which can add to or subtract from one of the sequential stimuli generatedby the ago&f A (Fig. 3). T)w iI infemC:ion cxxxtrs if the drug B mere& alters the magnitude of the chain consianfs between the formation of Al? complexes and the observedresponse. The general null equation for ~~a~~oaal interaction has been shown to fit experimental data extremely well. if can be used not only to differenriafe between type 1 and iype fl interactions but atso in summarize the position of one ~o~entrat~~sfat~ curve reiative to another. It can be said that, as a rough approximation EL, /$ and y depend 0;; the displacement of the two curves along the ing ~oncen~ation axis and the re&ve positions of the curves at high and tow con~n~af~ons of agonisf respecfivcly. Funsfional interaction may provide some inf~~ation about mechanisn~s of drug action but ra1y ifthe interaction iscftype 1. According to the model or depend< on AS, a, h; f~ and Rr, where 15 iri the ,timutus producedby the infcractanf. D and n are the approbate chain comiants, FI is the intrfnsicefficacy of the AU complex and R t is fhe Iota1 concenfrafion of receptors cap abk of Ltterscfin~ ;t Ifh fiLs sj,,,nist A (set Fig. 31. IYE value\ of ,?4and y furfher depend on the affinity consfant id A for ifs receptors as wcil as on the other factors listed above:.It must be emphasized th.atthe values cr. I>’affd 7 are not in any way true d~~recepf~~r~on~an~. fn particular, even for one piece of ttssue rh2y wol&l be expccfedto laf’y with AS and therefore with

dove different cstimnes of K’*

fhe concentration of R. However. if we equate (IY- I )/2y wffh Kt*l and ?@/(t~-I ) with h’tu then the model predictsthat these should be independentc:fLS. and therefore of fhe concentrationofdrugB. tin any ofte piece &tissue. K+*t andK’z shonldfhewfore be rno~ mcdningi‘ut than individ& setsofvaluesofc~. @and y. The model also predicts tha: h’b~~and K’ $2should each be equal to the funCfitxia1 r%nify Ccmsfanf k‘* * u here KiA - ~~(~r~‘~l/~

+ I).

If tw dmpr R and f each infemct functionally uifh the agonist A on the same piece of tissueand are type I inferactantsbut with different sites of &on (see Fig. 3) then the respective valuesofu and h wINtfd be expect~4 to be different. Thefefon?. different values of Kts would be obtained in the presence of edch of the intcracfanfs. Provided that the diffennces in K’ A are staristicali~ significant this would indicate different mechanismsof action for B and C. If will now tie clear why this argument can only be apphed to type I tuitional interactions. The method dependson the detection of differences in a and h v>adifferences in &b*. Since the mechanism of a type If interactant is to change the Yalues ofa and h there is no way of using fhse changes to defect the sites of acfion <+fsuch inferacrants. For an agonist A oflow if ~frinsic cffieacy fhe values of K’M and A 1.t: have been shotin to be nearly equal a,ld close to KA. For an agonist of high infrif+c effieaey the values ot’&? +.i and K&AZ have been shown to be markedly greafer thitn KA. PS predieted by the model. but K* Q and K(..t: did not 9zern to & equal”. The reason for fhis discrepancy is not clear. It may be an &fact since if is often diffitiulf to measure 41 fhree constanrstr. p and l ’ accurately for such an agonist on one piece of tissue. .Anofher possibiiifv is that the reiation bef**een S, and SII ts ffof qulae as simpk as assumed in the model. If fhts is so then the r&fian assumedtoex!st bet veen S,, and ,%I might still be expected to f+e valid over a jirnit~ range of S... The values nfa andh at IW values of SWmight then diKer from thoseat high W&eS .rl S.*. which could pro.

Wm the

their concuntrationsare adjustedto produce the S:WK value of AS, on any one piece of tissue. these conr,entrations of I3 and C should prodffce~d~nf~~a~ shitis of the agonist curve and fherer’orcidentical valuesofrr. /3 and y using each interactant. In prs
WnSifivity.

if may

lktrforc

hc nt?Ces

sit? to accept ~~~n~cntr~lti~~ns of B and C shtch produce similar. ntber than identi~9, curve displar‘ementsas judged by the ~g~ifudes oftu. The ~o~s~ndi~g vahfes ofh”.r~ and X1-4: can then be esttmntedfor each of”the interactants. AS already pointed onf, valuesofK&AI and Kf-care morr meanin&l than ~nd~vid~i sets of v&es of<%.$ and y, so if the values of K%I and Kb.4: ~~bfainedin the presence of each of the IWO interactants are not significantly diffi,rent then fhere is no evidence that they act it’ different pcrintsin the chain [Fig. 3). It is piible that one of the interactants mi_et~f be able to pr&uce a bigger maximal value of LS than the other even if the twodrugs have the tir:le mechanism of action. The kind of comparison described above should therefore be made using only concentrationsof the two interactants which can {JrdffCe similar curve displacements as judged by the mag~if~e ofcr. The technique de.seribedabove is presenfly being used to compare the actions of smooth muscle relaxants, such as isoprenaline and atninophylline, on trachea using ~a~achol as the agonist. It has been shown that the K% values for carbachol in this system cannot be accurately m,:asuree but good estin~afesof &I can usually be obtain& For each tissue sampie fk: results can IX summarized as the r&c? ot’ fhe Kt-t value for carbachol using isoprenaline as the intcwtant to that obtained using amintrphylline. In tbc experiments carried ouf so far this ratio has varied befwsen I .If and 2.5, with v&es of<~ ranging front 3 fo 15. Although in general the v&e of K”s using isoprenalinc has tended to be greater than that obtained using aminophylfine the re&s have not as vet pmvi~d signi~~nt evidmce of a different site of action for thesecompounds.

Acknowledgemcttt I am grdtefui to I& Ryan Large for checktnp the clarity of the manu~rip:.

Angel dust? PCP (Phencvclidine): Historical and Current Perspeclves

There are few drugs which have been intro duced as exciting, new therapeutic agen:s only IO plummet IO the depths of major drugs of abuse within the spaceof 20 years. Such is the case with phencyclidine (PCP); first introduced as an intravenous anaes thetic agent it is now ‘one of the most prevalent illicit drugs used by the poly-drug abuse population’. This book provides a timely synthesisof ottrcurrent knowledgeofthec~nt~ actions of this powerful psychotomimetic agent. The editor has sought to produce a volume which covers the diverse areas of PCP related resarch. As such it will be of interest to both scientistsand clinicians working in this area. Commencing with several illuminating historical accounts of the development of PCP and its cogeners. the subject matter is then expanded to deal with the chemistry. neurochemistry, psychopbamracology and C!lmilLDl pharmacology of theseagents. Undou~~iy the most exciting, recent development in PCP related research is the discovery of saturable, moderately high affinity binding of PCP to membrane frag. ments prepared from brain tissue as described by two connotes to tms book. Such a finding has relevance not only to elucidating the nrechanismofnctionofPCP but also IO the possibility of the existence of an endogenous ligand for these binding sites and their role in menul health. It s unfortunate that the protag:onistsof PCP binding have not been afforded the oppor. tunity to reply to the criticisms of their etiology contained in a subplot chapter. Similarly, controversy has been avoided with respect to the relevance of

Chest therapy Drug Treatment of Respiratory Drseasc

This book is tbe tit& in the series‘Mono graphs in Clinical Phanna~ology’. In it Dr Cole describes. for the whole of chest tnedicine. how drugs work theu pharmacology and their use in zlintcal practtee. The wide scope of the hh>k retleets the dem.tnds made on the chest physician but leads to some unevenness in coverage. There are four chapters on treatment at inf~tious diseases, two on drugs for asthmaand oneeach for wugh and sputum, respiratory failure and pulmonar> cmhd-