Anno XL . N. 51L FARMACOEDIZIONE SCIENTIFICA Maggio 1985

THE USE OF COMPETlTlVE LIGAND BINDING

RESULTS IN QSAR STUDIES

I.S. GOMEZ-JERIA

UNIVERSIDAD DE CHILE - FACULTAD DE CIENCIAS BÁSICAS Y FARMACÉUTICAS

DEPARTAMENTQ DE QUíMICA' SANTIAGO (CHILE)

SUMMARY. - The use in QSAR studies of parameters measuring theability of an unlabeled rnolecule to compete for the binding site with a

. radioligand is examined.1t is shown that in order to employ them within a recently developed

formal model it is previously necessary to carry out a linear transformation.This necessarily demands the adoption by investigators of a standard measur­ing procedure.

RIASSUNTO. - Viene considerata la possibilita di applicare in relazioniquantitative struttura chimicaj attivita (OSAR) grandezze in grado di misurarela capacita di una molecola non marcata di competere con un legantemarcato per il sito recettoriale.

Viene dimostrato che per usare tali grandezze e necessaria una preli­minare trasformazione lineare. Cio richiede l'adozione di un procedimentostandard per la loro misura.

Recent1y (1), it has been shown that, if we consider a weakinteraction between a drug D, and a macromolecular receptor, thefoUowing formula accounts for the equilibrium constant, K:

log(K¡) = A + B 10g(MD) + C IOg(O'D)+ D 10g(ABC)Di + EAEi [1]

where A, B, C, D, E are constants, M, 0', and ABC are, respectively,the mass, the symmetry number and the product of the three momentsof inertia about the three principal axes of rotation, "i" refers to thei-th drug molecule and AE¡ is the difference between the ground-stateenergy of the complex and the ground-state energies of the drug and thereceptor. As the molecular structure of the receptor is normally notknown, AEjis calculated in an approximate way (1).

We must note that eq. [1] expresses a physically-based functionalrelation between 10g(K¡) and the drug's molecular-electronic properties,

300 GOMEZ·JERIA I.S., /1 Farmaeo - Ed. Se.• vol. 40 . fase. 5

that is originated from statistical-mechanical and quantum-mechanicallaws. Eq. [1] must not be confounded with a purely statistical correlationproblem. Here, statistical analysis is employed, not to see if there is agood equation, but to find the best one.

This method has given excellent results when applied to índolederivatives (2), phenylalkylamines (3, 4), carbamate insecticides (5) andMAO inhibitors (6).

Here we must keep in mind that the fitting of eq. [1] will give thesame results if we work with the true K¡'s or with values obtainedthrough linear transformations of them.

In recent years, investigations on the specificity of the receptorbinding have oíten measured the ability oí an unlabeled molecule tocompete for the binding site with a radioligand. The value generallyreported is the ICso, Le., the concentration of non-labeled ligand atwhich the binding of the radioJigand is decreased by 50%. Thistechnique has been employed extensively with narcotic analgesics (7),benzodiazepines (8) and adrenergic agents (9). As the ICso is not a trueequilibrium constant, it cannot be formal1y employed in eq. (1].

In this note, we analyze the conditions necessary to carry out OSARanalysis with the ICso instead of K in eq. [1]).

Let us consider a receptor saturation experiment using a radiolabeledligand for the case of a fixed concentration of labeled ligand and increasingconcentrations oí unlabeled· ligando In has been shown atht the IC50 maybe expressed as (10):

where K, f+, Rt and K+ are, respectively, the drug-receptor equilibriumconstant, the fractional saturation oí the receptors by the labeled ligandin the absence oí unlabeled competitor, the total concentration ofreceptors and the radioligand-receptor equilibrium constant.

If we consider a group oí ICso's obtained with a series of experimentsthat were carried out with the same total quantity oí receptors, withthe same labeled ligand and with the same final concentration oí labeledligand, it follows that Rt, f+ and K+ are constants for the whole group oímolecules under study. In these conditions, and using eq. [2], K; maybe written as:

ICso(l-f+)

1+(l-í+) (1---0.5 í+) Rt/K+

where a and b are constants.

0.5 Rt (l-f+)

1+0.5 (l-f+) Rt/K+== a ICso-b [3]

THE USE OF COMPETlTlVE LlGAND BINDING RESULTS IN OSAR STUDIES 301

The inspection of eq. [3] reveals that we cannot transform the ICsointo K because we do not know the constants a and b. This problemcan be avoided by the analysis of a and b. First, we must note that, asalways K¡>O.O, it folIows that:

a IC.so--b> 0.0 [4]

This condition will impose a restriction to the possible values ofa and b chosen for a given set of ICso's.

The examination of receptor saturation experiments (7-9) shows thatin general Rt<ICso, 0.1 nM~ICso~1000 nM. With these data, we wayuse for example K+= 1.0, Rt=O.l nM and f+=0.7. This gives a=0.294and b = 0.0 147, that we propose to employ as transformation constantsin future OSAR studies. Note that it is possible to propose other valuesfor a and b from the analysis of a given experimento l t must remainclear that the couple of constants proposed are arbitrary and that theyonly serve as transformation constants. If, in a given experiment, thevalues of Rt, f" or K+ are determined, their values can be used to obtain

, values for a and b that also will be useful.Anyway, this or any other similar choice will permit us to use

eq. [3] to obtain a set of parametrized K¡ values and to apply theformal quantum-mechanical roodel developped in ref. (1).

On the other hand, if we arbitrarily make RI~O in eq. [2], we get:

ICso

K¡=ICso(1-f+) = ---- = O ICsol+W/K')

[5]

where f+ is the free concentration of tbe labeled ligand and O is constantfor the whole group of molecules considered. Eq. [5] is not rigorous,but is normally employed to calculate K (see refs. 11 and 12 for themathematical formalism). Note that if we employ eq. [5] we can replacedirectly log(K¡) by 10g(ICso),probably obtaining misleading results.

As an example of the lack of a standard method to measurethe ICso, we may cite the case of narcotic agonists and antagonists.In different receptor saturation experiments with rat brain, using the sameexperimental technique (13), it was employed 1.5 nM of [3H]-naloxone(13, 14),2.6 nM of eH]-naloxone (15), 1.0 nM of [3H]-naloxone (16)and 1.0 nM of [3H]-diprenorphine (17) as final concentration oflabeled ligando From the above analysis, it is clear that it is notpossible to use together the 1Csovalues reported in refs. 13 to 17 fora OSAR analysis. These facts indicate that it is absolutely necessarythat the workers in this field define a group of standard experimentsfor use in alI the laboratories.

302 GOMEZ-fERIAf.S., 11 Farmaeo - Ed. Se. - vol. 40 - fase. 5

The analysis presented here should open new areas for the applicationof the formal model exposed in ref. (1) to research on narcotícs,benzodiazepines, dopamíne and adrenergic molecules etc.

This work has received financial support Irom the Departamento delDesarrollo de la Investigación (University 01 Chile), Project 02001-84. Wethank the SESI (University 01 Chile), lor providing Iree computing time andMr. R. Gómez-Jeria lor helplul comments.

REFERENCES

1) GÓMEZ-fERIAJ.S., lnt. /. Quant. Chem., 23, 1969; 1983.2) GÓMEZ-fERIAf.S., MORALES-LAGOSD., J. Pharmaceutical Sci .. (in press).3) GÓMEZ-JERIAJ.S., MORALES-LAGOSD., CH..\VEZ H., Proc. of the IX Latinoame·

rican Congress on Pharrnacology and Therapeutícs, Santiago, 1982, p. 100.4) GÓMEZ·JERIAJ.S., MORALES-LAGOSD., The rnode of binding of phenylalkylarni­

nes to the serotonergic receptor in "OSAR in the design of bioactíve com­pounds", J.R. Prous, ed., Barcelona, 1984, pp. 145-173.

5) GÓMEZ-)ERIAJ.S., VENEGAS-GARRlDOR., Bol. Soe. Chil. Quim., 29, 52; 1984.6) G6MEZ-JERIA J .S., "Quantum-mechanical determination of the receptor affinity:

the ~-carbolines-MAO system", 9-th International Congress of Pharmacology.Londoll, 1984.

7) BARNETTG., TRSIC M., WILLETTE R.E., ed. "Ouantitative structure-aetivilYrelationships of analgesics, narcotic antagonísts and hallucinogens". NIDAResearch Monograph 22. Washington, 1978, pp. 129-145. 146-158 and 186-196.

8) COSTAE., DI CHIARAG., GESSA G.L., eds., "Advances in Biochemical Psycho­pharmacology". Vol. 26. Raven Press, Uew York, 1981, pp. 27-29. 139-146,147-155 and 157-167.

9) WILLlAMS L.T., LEFKOWITZ R.J., Receptor binding studies in adrenergiepharmacology, Raven Press, New York, 1978, pp. 53-82 and 93-109.

10) BOEYNAEMSJ.M., DUMONT J.E., Outlines of receptor theory, Elsevier North-Hol­land, Arnsterdam. 1980, p. 197.

tI) BnoNo J.B., in: "Receptor binding techinques", Society for Neuroscíence.Cincinnatí. 1980, p. 70.

12) JACORSS., CHANGK.J,. CUATRECASASP., Biochem. Biophys. Res. Commul1 .. 66.687; 1975.

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G.H., BERKOWITZD.S., f. Med. Chern., 21, 415; 1978.16) PERT C.B., SNYDERS.H., PORTOGHESEP.S., J. Med. Chem., 19, 1248; 1976.17) KOllYLECKIR., LANEA.O., SMITH C.F., WAKELlNL.P., CRUSE W.B.T .. EGERTE..

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Pervenuto in Redazione iI 28 Giugno 1984.