The ad hoc supermolecule approach to receptor ligand design

The ad hoc supermolecule approach to receptor ligand design

P.G. De Benedetti* , F. Fanelli, M.C. Menziani, M. Cocchi

Dipartimento di Chimica, Universita` di Modena e Reggio Emilia, Via Campi 183, 41100 Modena, Italy

Abstract

Among the ligand design methods based on the theoretical QSAR paradigm, the simple ad hoc supermolecule approach ispresented and applied to a highly non-congeneric set ofa1-adrenergic receptor antagonists. The performance of the approach issatisfactory and highlights its (semi)quantitative ligand design potentiality.q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Ligand design methods;a1-Adrenergic receptor antagonists; Theoretical QSAR models

1. Ligand design based on theoretical QSARs

Two very similar molecules are two differentphysical objects, hence, chemical similarity is a subtleand relative concept that acquires significance in awell-defined reference physical context. In otherwords, it is necessary to define in what respect andto what extent two different molecules are similar [1].Molecular series of specific ligands interacting, invitro and in equilibrium conditions, with a specificbio-receptor constitute a sophisticated example ofchemical similarity–diversity classification. Thisclassification is based on the measured binding affin-ity data values that quantify a particular molecularrecognition phenomenon, which is, essentially, anon-covalent process [2]. This implies, according tothe Fisher’s lock and key model, that structuralcomplementarity (static and, even more, dynamic)between the interacting partners is the most importantfeature of the process, raising the problem of itschemical–structural description at a (sub)molecularlevel [3,4].

Many modelling strategies are currently used inthe design of new drugs [5–9]. However, they canbe broadly classified into “direct” and “indirect”methods, according to the known (direct or receptorstructure-based) or hypothetical (indirect or ligand-based) three dimensional (3D) structure of the targetbinding site.

The structure activity relationship (SAR) baseddrug design procedures are the most used bymedicinal chemists. These lie on the two-dimensional(2D) chemical formalism. The neglect of one spatialdimension and a generic qualitative description of thecharge distribution frequently lead to totally wronginferences, especially when dealing with newhypothetical molecular structures. To avoid, at leastin part, this drawback, quantitative modelling and 3Dligand comparison is in order. The quantitativecomparison of the optimised 3D structure of a selectedset of ligands allows the development of their minimal3D structural requirements for a productive bio-targetrecognition and activation, i.e. the pharmacophorichypothesis, and gives a sound 3D rationale to theavailable SARs [3,5]. A more complete and mechan-istically relevant approach to the development of the3D-pharmacophore consists in its translation into anumerical molecular descriptor that quantify the

Journal of Molecular Structure (Theochem) 503 (2000) 1–16

0166-1280/00/$ - see front matterq 2000 Elsevier Science B.V. All rights reserved.PII: S0166-1280(99)00359-0

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* Corresponding author. Tel.:139-59-378463; fax:139-59-270406.

E-mail address:[email protected] (P.G. De Benedetti).

molecular–pharmacophore similarity–diversity fortheoretical quantitative SAR (TQSAR) modelling [10].

The methods of theoretical and computationalchemistry are being applied increasingly in thecomputer aided drug design procedures and TQSARstudies [3,11].

QSAR analysis, that is a fundamental prerequisiteto rational drug design methods, addresses theproblem of generating statistics based correlativemodels between experimentally determined biologi-cal–pharmacological data for a set of compounds andtheir experimental and/or theoretical physico-chemi-cal/structural parameters [8,10].

The aim is twofold: to explain the bio-data, at the(sub)molecular level, in terms of physico-chemical/structural properties of the ligands and to estimatesimilar bio-data for new analogues. This implies thatthe variation of the bio-activity of the set ofcompounds under study (molecular series� statisticalpopulation of ligands) is reduced and translated into achemical formalism (molecular descriptors), withgreat benefit to the physical interpretability of theQSAR model produced. This is particularly true iftheoretical descriptors are used in QSAR modelling.In fact, the interpretative and predictive aspects ofTQSAR models allow the design of new ligands andthe interpolation of their estimated bio-activity priorto synthesis. Hence, sound and validated TQSARmodels can help the synthesis of potentially activecompounds selected by a virtual screening procedure,i.e. ligand design based on theoretical moleculardescriptors, interpolation of the bio-activity byTQSAR models and selection of the most promisingmolecular structures for the synthesis and bio-testing.

Scheme 1 illustrates the important elements ofrational ligand–drug design procedure, assisted byTQSAR modelling and classified according to theknowledge level of the target 3D structure. In fact,when any structural information on the bio-target isunknown, the indirect ligand design approach and theassociated indirect QSAR modelling procedure arethe only applicable. Theoretical indirect methods ofQSAR analysis, including those called 3D-QSAR,constitute the natural evolution of classical 2D-QSAR or “Hansch approach” [8], with one or moreadded dimension and by using theoretical descriptorsinstead of empirical parameters. This allows to over-come some intrinsic limitations of classical 2D-QSAR

that heavily influence their use in the ligand designexercise. In fact, only a congeneric molecular series ofcompounds can be considered in the analysis tooptimise the bio-activity, by changing the positionof different substituents on an extended commonstructural framework (2D-pharmacophore). Thus, inthe Hammett’s “linear free energy relationships(LFERs)” framework [12], the variation of bio-activity in closely related compounds has been usuallydescribed and optimised in terms of electronic, stericand lipophilic variation induced by the differentsubstituents on the ligands and expressed in terms ofthe available and most representative substituentconstants (s, p, Es, MR, etc.).

In many respects, the “Hansch approach” has beengeneralised by using theoretical descriptors in gener-ating different kinds of TQSAR models, and, hence,expanding the ligand design techniques. In fact,computer-aided TQSAR modelling allows us toconsider a training set of non-congeneric ligands, bymodulating the chemical diversity, for the compara-tive analysis of their 3D stereo-electronic similari-ties–differences in terms of their recognitioncapabilities with respect to a common bio-receptor(3D-pharmacophore hypothesis). An essential aspectconnected to the 3D-pharmacophore generation is thesearch for different and specific prototropic bio-activemolecular forms, and their corresponding conforma-tions, present in the bio-test solution [9]. Accordingly,the theoretical descriptors should be defined andcomputed, in principle, on all the conformationallyoptimised prototropic forms, energetically accessibleby the ligands. The selection of the most physicallyand statistically informative descriptors will thenproceed according to the different (but consistent)roles of these prototropic forms (and their associatedconformations) on the hypothetical mechanism ofinteraction with the receptor binding site, accordingto the ligand 3D-pharmacophore similarity/targetreceptor complementarity paradigm.

Many different chemometric techniques are avail-able for descriptor–predictor selections and TQSARmodelling [10]. However, a crucial point that shouldbe met to succeed in the ligand design task based onTQSAR models is to check the physico-chemicalmeaning of the theoretical descriptors pre-selectedon the basis of their predictive power. Moreover,their interpretability in terms of molecular structure

P.G. De Benedetti et al. / Journal of Molecular Structure (Theochem) 503 (2000) 1–162

P.G. De Benedetti et al. / Journal of Molecular Structure (Theochem) 503 (2000) 1–16 3

THEORETICAL QSAR MODELING ANDLIGAND DESIGN

3D STRUCTURE OF THEBIO-TARGET

Unknown Predictable Known

IndirectApproach

Heuristic-DirectApproach

Direct or Structure BasedApproach

Ligand-LigandComparison and

Modeling

Bio-Target 3D ModelBuildin g

Selection of TheoreticalDescriptors Receptor-Ligand

Modeling

Selection of IntermolecularInteraction Descriptors

Ligand/PharmacophoreBased QSAR Models

3D Data BaseSearch

Ligand-Receptor InteractionBased QSAR Models

Direct Ligand DesignTheoretical Molecules

Bio-Pharmacological DataInterpolation and Virtual

Screening

Synthesis and Bio-Testing

Model Validation

Indirect Ligand Design

Scheme 1.

has to be finalised to the design of new molecules. Inthis respect, numerical (scalar or vectorial)(sub)molecular descriptors directly related to the3D-pharmacophore should be more handleable, bear-ing the useful chemical information content for liganddesign purposes (Scheme 1).

There are many kinds of more or less sophisticatedtheoretical descriptors able to satisfy the ligand designrequirements. Those derived by ligand–ligand model-ling comparison and 3D-pharmacophore developmentcan be schematically classified as: (a) intramolecular;(b) surface–volume; and (c) intermolecular or inter-acting/field descriptors. This classification implies adefinition of a boundary molecular surface thatseparates the internal molecular space from the exter-nal one. Many kinds of molecular surfaces have beenproposed [1,3], but the most popular and simple one isthe van der Waals (vdw) molecular surface whichincludes the vdw molecular volume. Typical intra-molecular descriptors are most of those obtained byMO calculations at different levels of accuracy, suchas charge distribution, local or total molecular dipolemoment, quadrupole moment, reactivity indexes, etc.[13]. They contain information related to the electro-nic wavefunction and, more implicitly, to the geo-metry of the molecule. Hence, intramoleculardescriptors can be viewed as electronic descriptorsassociated to atoms, functional groups, or molecu-lar–pharmacophoric moieties of the ligands consid-ered. Surface and volume descriptors are peculiarchemical descriptors based on molecular geometryand its 3D molecular graph. They describe the sizeand shape properties of the ligands, encoding themolecular similarity–complementarity and stericeffects, that are considered the most importantfeatures of ligand bio-specificity. Many sophisticatedvariants of surface descriptors exist that include,together with ligand size and shape information,surface area charge distribution, hydrogen bondacceptor or donor properties, hydrophilic–hydropho-bic surface areas, etc. [1,3]. Finally, the intermolecu-lar field descriptors belong to the ever-growing familyof the high-dimensional chemical descriptors. Theadvent of accessible computing facilities, the easycomputer data generation, acquisition and theirelaboration by multivariate statistical techniqueshave stimulated the use of high-dimensional descrip-tors for TQSAR modelling and ligand design proce-

dures. Electrostatic potential maps corresponding tothe electrostatic potential of a molecule, calculated ona lattice of points surrounding the molecule, constitutethe first example of field descriptors [14]. TheComparative Molecular Field Analysis (COMFA)developed by Cramer et al. [15] is based on a concep-tually similar approach. This technique generatessteric and electrostatic maps after matching the ligandon a reference molecule, according to an appropriatealignment rule. These electrostatic maps quantify theinteraction between the ligand of interest and a chosenprobe atom or group. Many extensions and variants ofthis technique have been successively proposed inorder to introduce a lipophilic description of theligands [10].

Once obtained the ligand–pharmacophore modelfollowing the indirect approach (Scheme 1), the nextstep consists in the ligand design by making use of themost suitable theoretical descriptors and the derivedpharmacophore hypothesis, for both database searchand molecular structure design. The outcome will be acollection of theoretical molecules whose bio-potencywill be estimated by TQSAR model interpolation(virtual screening). Then, the most promising moleculeswill be synthesised and tested and the TQSAR modelschecked for their quality (model validation).

The same procedure is followed by the direct liganddesign approach by using ligand–receptor interactionbased QSAR models (Scheme 1) and the relative theo-retical (intermolecular) descriptors. Hence, the differ-ences between the indirect and direct theoreticalapproaches to ligand design of Scheme 1 depend onthe fact that the second one generates QSAR modelswhich explicitly consider the 3D structure of the bio-target binding site. The direct or structure-basedapproach is a well-established procedure and consti-tutes the ideal situation, starting from the experimen-tal structure of the bio-target [3,11]. Once the 3Dstructure of the bio-target has been energetically opti-mised and the ligand binding site identified, ligand–receptor docking simulations and energy minimisa-tion of the ligand–target complex obtained allow theexplicit optimisation of the ligand–target complemen-tarity in terms of intermolecular forces (electrostatic,vdw, hydrogen bonds, steric), computed at different levelof accuracy, according to the potential energy functionemployed. Hence, a detailed picture of the bio-targetamino acids involved in the interaction with the different


ligand moieties can be obtained and the correspondingtheoretical descriptors extracted. On these bases, TQSARequations can be modelled and used both for liganddesign purposes and bio-potency prediction.

A good and probably the first example thatcompares direct and indirect theoretical QSARmodelling approaches was done by Menziani et al.[16,17] on a large series of congeneric sulfonamidecarbonic anhydrase inhibitors. Interestingly, theresults obtained revealed that the information neces-sary for the bio-response that the inhibitor elicits fromthe interaction is largely encoded in the molecularstructure of the drugs and in their appropriate theore-tical descriptors. The theoretical direct QSAR model-ling approach developed on the carbonic anhydrase–sulfonamide inhibitor complexes was subsequentlygeneralised and extended to the bio-target withknow primary sequence but unknown 3D structure.This approach, named heuristic-direct and applicablewhen the atomic resolved structure of the bio-target isunknown but predictable by means of the availableexperimental information, is able to handle the hetero-geneous experimental information on the ligands andtheir bio-target and synthesise and translate them intoTQSAR models [18–25]. The first step of this proce-dure consists of the computer-aided 3D-model build-ing of the receptor. The second step involves dockingsimulations with selected ligand, maximising thecomplementarity between ligand and receptor. In thefinal step, a detailed and extensive correlation analysisbetween the computed intermolecular interactiondescriptors and the experimental binding affinities iscarried out in order to evaluate the consistency of theQSAR model proposed. This procedure, althoughcomputationally quite intensive, gives a detailed andexplicit picture of the interacting atoms or groups andtheir energetics in the ligand–bio-target complex, alsotaking advantage from its strong complementaritywith the indirect TQSAR approaches, and, aboveall, from correlative models based on size and shapetheoretical descriptors. In other words, recalling theFisher’s lock and key model, all the stereo-electronicinformation gained on the ligands (keys) that fit indir-ect TQSAR models should be used in a complemen-tary and synergistic manner in the 3D bio-targetbinding site (lock) modelling. Then, docking simula-tions are carried out to maximise the complementaritybetween ligand and bio-target, through the optimisa-

tion of the intermolecular forces. Hence, indirectTQSAR modelling approaches constitute an essentialpre-requisite to the heuristic-direct TQSAR modellingapproach. In this respect, the indirect QSARs based ontheoretical size and shape descriptors seem to be themost consistent with direct TQSAR models.

2. Ligand design based on size and shapetheoretical descriptors and indirect TQSARmodelling

A relevant aspect of chemical research is to predictthe behaviour of new molecules from their structure,prior to synthesis [13]. Most often, structurally similarmolecules have a comparable range of physico-chemical properties and biological activities. On thecontrary, structurally dissimilar molecules differ intheir properties both qualitatively and quantitatively.Correlation analysis and, hence, QSAR and QSPR(quantitative structure-property relationships) areimplicitly based on this simple fact. It is generallyassumed that non-covalent forces control drug–recep-tor interactions and that these forces can be describedin terms of steric and electrostatic effects, whichdepend on molecular size and shape. The quantitativedescription of molecular shape and its applications inthe context of molecular similarity comparisons,correlation analysis of chemical properties (QSPR)and QSAR modelling has been object of many studiesand a number of approaches have been presented[1,3,10,13]. However, in our opinion, all theseapproaches have been mainly developed (andcompared) for the optimisation of the predictiveaspect of TQSAR analysis. In fact, these approachesuse, in many cases, sophisticated descriptors of prop-erties related to molecular shape that, while improv-ing, in some cases, the statistics of the TQSAR models(i.e. they are good predictors for similar molecules ofthe test set) they, however, loose the structuralpropensity for suggesting new and differentmolecules, i.e. new leads. In other words, if we recallthe well-known dualistic aspect of QSAR models, i.e.the interpretative aspect and the predictive one, a sortof “uncertainty principle” governs their performance:if we improve the predictive aspect we obscure theinterpretative one and vice versa. Hence, simplifying,we can state that when molecular descriptors are good


predictors they are, concomitantly, poor “designers”,i.e. they have poor propensity to suggest directly newleads. There is an intrinsic circularity in the correla-tion analysis and QSAR modelling paradigm due tothe interdependencies of the concepts used in theprocedure. In fact, as shown in Scheme 2, the speci-fication of the series of existing compounds on whichthe study is based (training set) determines the level ofcongenericity (similarity–dissimilarity) of the mole-cular set which defines both the variance of the experi-mental property we are interested in and the choice ofdescriptors of those compounds the predictingformula is based on. Then, appropriate statistics willbe applied both for descriptor selection and QSAR–QSPR modelling. The models thus obtained, aftertheir validation, can be used for ligand designpurposes, according to Scheme 1. However, aspreviously stated, different QSAR–QSPR models,being calibrated on different molecular propertyspaces, show different predictive, interpretative andmolecular design capabilities. Usually, strict conge-neric molecular series generate sound predictive andinterpretative QSAR models. However, ligand designexercises are confined to a limited (local) variance ofthe molecular structural–chemical space consideredin the model, which can be adequate for lead optimi-sation procedure, but absolutely insufficient fordesigning new leads. In order to overcome this limita-tion, many de novo ligand design methods have beenproposed [1,3,10,11]. However, these methods, as arule, do not employ the QSAR paradigm. Recently,we have shown that the supermolecule approach andthe derived ad hoc size–shape descriptors defined onthe ligand bio-active prototropic molecular form havebeen successful in deriving TQSAR models for mole-cular series of very structurally heterogeneous ligandsof cationic neurotransmitter G protein coupled recep-tors (GPCRs) [26–34]. According to the ligand 3D-pharmacophore, the supermolecule approach assumesthat the volume obtained by superimposing the moststructurally different ligands (supermolecule) thatshow the highest affinities for the same receptormight reflect the overall shape and conformationalflexibility of the high-affinity receptor binding site.Therefore, size and shape descriptors can be definedad hoc (that is, on a specific molecular series and inconnection with a specific bio-activity) with respect tothe supermolecule, and this constitutes the main

advantage over molecular descriptors defined andperformed for a single structure and a single confor-mation. The use of the supermolecule approach toderive ad hoc molecular similarity descriptors hasbeen successful in TQSAR modelling procedures[26–34]. In fact, it represents a flexible tool whichcan be used to describe both congeneric and non-congeneric series of compounds in an extended(global) chemical space, and can be continuouslyupgraded with new coming experimental data.

Recently, TQSAR based on ad hoc defined super-molecule and the corresponding size–shape descrip-tors have been employed for deciphering themolecular features responsible for the affinity andselectivity in a wide ranging series of non-congenericantagonists of the cloned bovinea1a-, the hamstera1b- and the rata1d-adrenergic receptors (ARs) [2].The TQSAR models presented by Montorsi et al. [2]have been challenged in this article in their ability topredict the binding affinity of “new” ligands withsatisfactory results.

3. Application of the ad hoc supermoleculeapproach toa1-AR antagonists

When dealing with the rationalisation of biologicalresponses (binding affinity, selectivity and efficacy) ofligands for GPCRs, the crucial problem of the largemolecular diversity of the receptors and their subtypesmust be faced [35]. On the one hand, there exists ageneral mode of interaction of bio-amine ligands withtheir receptors, which has been strictly conservedthrough receptor evolution: that is, all ligands havebasic nitrogen function protonated at physiologicalpH; therefore a long-range electrostatic interactionshould constitute the first recognition step. On theother hand, a large variation in the details of molecu-lar interactions between the chemical signalling mole-cules (transmitters) and the receptors exists, and fewmolecular determinants are responsible for discrimi-nating compounds among receptor classes, subtypesor variants. Thus, the ability to obtain a goodquantitative rationalisation of the binding propertiesof highly active ligands showing a large structuralvariability depends primarily on the availability ofdescriptors able to capture the strict ligand–receptorcomplementarity criteria, which determine the


biological property of interest. Schemes 3 and 4 showthe wide variety of structural features of thea1-ARantagonists considered in this study.

The protonated structures of the ligands considered

(Schemes 3 and 4) were fully optimised by means ofsemi-empirical molecular orbital calculations (AM1)[36].

The ad hoc modelling consisted of comparing the


TRAINING SET OFMOLECULES:

CONGENERIC/NON-CONGENERIC

MOLECULARDESCRIPTORS

VARIANCE OF THEIRPHYSICAL-CHEMICAL-

BIOLOGICALPROPERTIES

APPROPRIATE STATISTICSFOR DESCRIPTOR

SELECTION AND QSAR/QSPRMODELLING

QSAR/QSPRMODELS

DIFFERENTPREDICTIVE/INTERPRETATIVE AND

LIGAND DESIGN CAPABILITIES

Scheme 2.


Scheme 3.


Scheme 4.

vdw volume of the minimised structure of each ligand(in its extended conformation) with the vdw volumeof a supermolecule chosen as a template. Threedifferent supermolecules were modelled for the threea1-AR subtypes. In the series of structurally hetero-geneous ligands considered in a previous study [2],subsets of analogues can be identified. For eachsubset, the ligand showing the highest affinity forthe specifica1-AR subtype was chosen as a compo-nent of the respective reference supermolecule. Thus,the ligands used for thea1a supermolecule are

compounds1–6, the ligands for thea1b supermole-cule are compounds7–10 and the ligands for thea1dsupermolecule are compounds7, 8, 10–12 (Scheme3). The supermolecule for thea1a-AR subtype (Fig.1) comprises a large number of structurally differentcompounds (1–6, Scheme 3). It is worth noting thatthe ad hoc generation of thea1a-AR supermoleculeinvolves four different types of protonated nitrogenatoms (quinazolinic, compound 1; alchil–aminic,compounds2–4; piperazinic, compound5 and piper-idinic, compound6). Fewer compounds constitute the


Fig. 1. Frontal (top) and side (bottom) views of the supermolecule obtained by superimposing the most active and structurally differentantagonists for the cloned bovinea1a-AR (compounds1–6, Scheme 3). The resultant van der Waals volume isVsup� 1016:00 �A3

:

supermolecule for thea1b- and thea1d-AR subtypes(compounds7–10 for the a1b and compounds7, 8,10–12 for a1d; Figs. 2 and 3). It is interesting to notethat the supermolecules for thea1b- anda1d-ARs(Figs. 2 and 3) have in common three ligands:compounds7, 8 and 10. However, a comparativevisual inspection of the supermolecules for the threea1-AR subtypes (Figs. 1–3) and of their vdw volumesshow significant size and shape diversity. This reflectsthe differences in the high-affinity binding site of theensemble of ligands that constitute each supermolecule.

The ligands chosen for the construction of eachsupermolecule were superimposed by a topologicrigid body fit procedure based on the following phar-macophoric criteria: (a) the hydrogen of the proto-nated nitrogen atom; and (b) the aromatic rings

closest to and farthest from the protonated nitrogen.All the other compounds were rigidly superimposedon the appropriate supermolecule with each ligandbeing superimposed on the analogue compound presentin the supermolecule or on its structurally closestcompound. The matching involved the moieties carringthe protonated nitrogen, i.e. the quinazolinic ring forcompounds13–18 (Scheme 4) and the piperazinicring for compounds20–28 (Scheme 4).

QUANTA molecular modelling package (release96; Molecular Simulation Inc., 200 Fifth Avenue,Waltham, MA 02154) was used for molecularcomparison and computation of the vdw volumes.We considered the following ad hoc defined sizeand shape descriptors:Vin andVout, which are, respec-tively, the intersection and the outer vdw volume of


Fig. 2. Frontal (top) and side (bottom) views of the supermolecule obtained by superimposing the most active and structurally differentantagonists for the cloned hamstera1b-AR (compounds7–10, Scheme 3). The resultant van der Waals volume isVsup� 680:75 �A3

:

the ligand considered with respect to the volume ofthe reference supermolecule; andVdif, which iscomputed according to the formulaVdif ��Vin 2 Vout�=Vsup; whereVsup is the molecular volumeof the reference supermolecule.

The size and shape heterogeneity of the compoundslisted in the schemes clearly emerges as do thetopologic and topographic differences of theprotonable nitrogen atoms that constitute crucialelement in the matching criteria together with othermolecular features. Some selected size and shapedescriptors of the compounds of Scheme 4 togetherwith the co-logarithmic form of their experimental

binding affinities [34,37,38] are listed in Tables 1–3.In particular, Tables 1–3 report the binding affinitydata values measured on the three cloneda1-ARsubtypes (pK1a, pK1b, and pK1d), the molecularvolume (Vmol) as well as the inner (Vin) and the outer(Vout) molecular volumes relative to the referencevolume of ad hoc defined supermolecules, one foreach subtype (Figs. 1–3).

According to the definition of ad hoc size and shapedescriptors, higher affinities are realised by maximis-ing Vin and minimisingVout. For its formulationVdif ��Vdif � �Vin 2 Vout�=Vsup� is a normalised size andshape descriptor, which takes into account the


Fig. 3. Frontal (top) and side (bottom) views of the supermolecule obtained by superimposing the most active and structurally differentantagonists for the cloned rata1d-AR (compounds7, 8, 10–12 Scheme 3). The resultant van der Waals volume isVsup� 754:13 �A3

:

information content codified by bothVin and Vout.Finally, Vin/Vmol is simplyVin normalised with respectto the vdw molecular volume (Vmol) of the ligand. Bydefinition, the ligands constituting the supermoleculesshow the following singularities:Vmol � Vin; Vout � 0andVin=Vmol � 1 [2].

To validate further the linear regression modelspreviously obtained (Tables 1–3, [2]), the moleculesof Scheme 4 have been considered. The predictedbinding affinities for the threea1-AR subtypes,according toVdif and Vin/Vmol are reported in Tables4 and 5, respectively, together with their experimentalbinding affinity data values [34,37,38] and the differ-ences (D) between the predicted and the experimentalbinding affinities.

The agreement between predicted and measuredvalues is satisfactory. A variation of up to a factorof 0.7 in a logarithmic scale has been reported onthe basis of several measurements published for thesame ligand-protein complex [39]. In particular, bymaking use of TQSAR models based onVdif descriptor(Table 4) few wrong predictions�D . 1� have beenobserved (pK1a: compound18; pK1b: compounds23,25, 26and27; pK1d: compounds18, 19, 21, 22and25).

The TQSAR models based on theVin/Vmol


Table 1Cloned bovinea1a-AR binding affinities (pK1a), van der Waalsmolecular volume (Vmol) and ad hoc defined size and shape descrip-tors (Vin, Vout, Vin/Vmol, andVdif) of the set of molecules reported inScheme 4

No. pK1aa Vmol (A3) Vin (A 3) Vout (A3) Vin/mol Vdif

13 7.96 357.50 300.38 57.62 0.8400 0.250114 8.25 370.25 297.75 76.50 0.8040 0.227915 8.83 423.13 337.63 85.62 0.7980 0.259616 7.72 367.75 295.75 75.25 0.8040 0.227217 7.44 394.13 293.63 100.37 0.7450 0.199118 6.81 428.50 307.63 120.37 0.7180 0.192919 7.85 401.50 330.38 70.37 0.8230 0.267920 8.85 429.88 403.38 22.12 0.9500 0.397921 8.27 443.63 345.88 98.62 0.7800 0.254722 8.96 448.88 355.88 94.00 0.7930 0.269823 8.83 375.88 322.38 53.37 0.8580 0.277124 8.73 391.00 337.00 53.00 0.8620 0.292625 8.81 404.63 338.50 63.38 0.8370 0.283426 8.20 379.38 321.88 58.25 0.8480 0.271627 8.20 394.25 336.50 58.00 0.8540 0.286928 7.73 396.25 328.13 66.62 0.8280 0.2694

a See Refs. [34,37,38].

Table 2Cloned hamstera1b-AR binding affinities (pK1b), van der Waalsmolecular volume (Vmol) and ad hoc defined size and shape descrip-tors (Vin, Vout, Vin/Vmol, andVdif) of the set of molecules reported inScheme 4

No. pK1ba Vmol (A 3) Vin (A 3) Vout (A3) Vin/mol Vdif

13 8.26 357.50 341.25 16.75 0.9550 0.498914 8.36 370.25 335.50 37.50 0.9060 0.458215 8.80 423.13 353.88 68.00 0.8360 0.439616 8.07 367.75 328.88 41.50 0.8940 0.441917 9.05 394.13 339.50 54.00 0.8610 0.439018 7.83 428.50 353.00 73.50 0.8240 0.429719 7.66 401.50 274.00 127.50 0.6820 0.225320 8.20 429.88 285.13 146.25 0.6630 0.213521 8.16 443.63 275.38 168.62 0.6210 0.164222 7.90 448.88 266.63 187.00 0.5940 0.122423 7.51 375.88 338.00 38.25 0.8990 0.460924 8.11 394.00 346.88 44.75 0.8870 0.464525 8.59 404.63 258.50 146.38 0.6390 0.172426 7.66 379.38 329.13 52.62 0.8680 0.425227 7.75 394.25 336.00 59.88 0.8520 0.424628 6.85 396.25 257.00 139.38 0.6490 0.1808

a See Refs. [34,37,38].

Table 3Cloned rata1d-AR binding affinities (pK1d), van der Waals mole-cular volume (Vmol) and ad hoc defined size and shape descriptors(Vin, Vout, Vin/Vmol, and Vdif) of the set of molecules reported inScheme 4

No. pK1da Vmol (A3) Vin (A3) Vout (A 3) Vin/mol Vdif

13 8.09 357.50 306.88 50.50 0.8580 0.356414 7.71 37.25 302.75 69.75 0.8180 0.323915 8.80 423.13 323.50 98.25 0.7650 0.313116 7.72 367.75 310.13 60.00 0.8430 0.347717 7.63 394.13 316.75 75.50 0.8040 0.335418 6.95 428.50 331.25 96.00 0.7730 0.327019 8.68 401.50 295.63 106.00 0.7360 0.263920 7.76 429.88 277.38 153.62 0.6450 0.172021 8.35 443.63 279.50 165.25 0.6300 0.158822 7.76 448.88 276.63 173.12 0.6160 0.143923 8.82 357.88 323.13 52.37 0.8600 0.376424 8.42 391.00 331.00 58.13 0.8470 0.379325 8.88 404.63 281.25 124.75 0.6950 0.217526 9.03 379.38 321.38 58.12 0.8470 0.366027 9.12 394.25 329.88 64.87 0.8370 0.368428 6.86 396.25 276.88 118.37 0.6990 0.2203

a See Refs. [34,37,38].

descriptor give, in general, better predictions (Table5). In fact, for pK1a, all the predicted binding affinitydata values are inside the standard deviation of theregression, whereas for pK1b and pK1d three andfive wrong predictions�D . 1; Table 5) can berespectively observed. However, the observedDvalues are, in general, smaller than those relative toVdif based TQSAR models. Moreover, by consideringthe two TQSAR models, the wrong predictions are insome cases different. This can help the predictionexercise by averaging the results obtained by differentTQSAR models for the same ligand.

4. Conclusions

Once the biological–pharmacological data ofinterest and an informative set of ligands (exploringan extended chemical space) have been selected, aspecific similarity–complementarity scale for theparticular molecular recognition problem understudy can be simply defined on the bases of the super-

molecule approach. Thus, ad hoc theoretical size andshape descriptors defined, with respect to a specificreference supermolecule, for a very heterogeneousseries of protonateda1-AR antagonists constitute asimple and useful example of indirect TQSARapproach that satisfies the electronic–electrostaticand vdw/size–shape complementarity paradigm.Although this approach is empirical, it is based onsound physico-chemical concepts, and, above all, iscomplementary to the direct structure-based and heur-istic-direct QSAR approaches and to the associatedligand design procedures. In this work, the referencesupermolecules for the threea1-AR subtypes and therelative TQSAR models have been challenged in theircapability to predict thea1-AR binding affinities of aset of highly non-congeneric antagonists, with satis-factory results. In fact: (a) by considering the verydifferent molecular moieties and molecular bridgesused in assembling the “new” ligands (Scheme 4),satisfactory binding affinity estimations have beenobtained, as preliminary filter, for ligand designpurposes; (b) better predictions have been obtained


Table 4Calculated byVdif based QSAR models (pK1a calc., pK1b calc., pK1d calc.) and experimental (pK1a exp., pK1b exp., pK1d exp.)a1-ARbinding affinities

No. pK1a calc.a pK1a exp. D pK1b calc.b pK1b exp. D pK1d calc.c pK1d exp. D

13 8.48 7.96 0.52 9.19 8.26 0.93 8.64 8.09 0.5514 8.37 8.25 0.12 8.95 8.36 0.59 8.32 7.71 0.6115 8.53 8.83 –0.30 8.84 8.80 0.04 8.22 8.80 20.5816 8.37 7.72 0.65 8.85 8.07 0.78 8.56 7.72 0.8417 8.22 7.44 0.78 8.84 9.05 –0.21 8.44 7.63 0.8118 8.19 6.81 1.38 8.78 7.83 0.95 8.35 6.95 1.4019 8.58 7.85 0.73 7.58 7.66 –0.08 7.74 8.68 20.9420 9.25 8.85 0.40 7.51 8.20 20.69 6.84 7.76 20.9221 8.51 8.27 0.24 7.22 8.16 20.94 6.72 8.35 21.6322 8.59 8.96 20.37 6.98 7.90 20.92 6.57 7.76 21.1923 8.62 8.83 20.21 8.96 7.51 1.45 8.84 8.82 0.0224 8.70 8.73 20.03 8.99 8.11 0.88 8.86 8.42 0.4425 8.66 8.81 20.15 7.27 8.59 21.32 7.29 8.88 21.5926 8.60 8.20 0.40 8.75 7.66 1.09 8.73 9.03 20.3027 8.68 8.20 0.48 8.75 7.75 1.00 8.76 9.12 20.3628 8.58 7.73 0.85 7.32 6.85 0.47 7.31 6.86 0.45

a pKa values have been calculated according to the following regression equation: pK1a� 5:18 ( 0.83)Vdif 1 7.19 ( 0.27),n� 34; r �0:74; s� 0:53 andF � 39:01; wheren is the number of compounds,r is the correlation coefficient, s is the standard deviation andF is the Fisherratio.

b pK1b values have been calculated according to the following regression equation: pK1b� 5:87 ( 0.72)Vdif 1 6.26 ( 0.22),n� 30; r �0:83; s� 0:51 andF � 66:08:

c pK1d values have been calculated according to the following regression equation: pK1d� 9:74 ( 1.14)Vdif 1 5.17 ( 0.33),n� 31; r �0:84; s� 0:57 andF � 72:86:

for the a1a- binding affinity than fora1b- anda1d-AR, suggesting a better calibration of thea1a-ARsupermolecule; (c) the design of new leads withnovel molecular frameworks by the combinatorialassembling of very different molecular scaffolds isfacilitated by the estimation of thea1-AR subtypebinding affinity data values; (d) the matching criterionused for assembling the high-affinity ligands thatgenerate the three supermolecules considered is asimple three point pharmacophore model that can bealso used in structural database search, to find newpotential leads for thea1-ARs whose binding affi-nities can be estimated by the TQSAR modelsobtained; (e) these quantitative models allow the esti-mation of theoreticala1-AR subtype affinities ofexisting antagonists (theoretical screening); (f) thesupermolecule and the derived size and shapedescriptors can be continuously upgraded when newpotent and specifica1-AR subtype ligands are discov-ered; and (g) on an interpretative ground, thepreviously postulated mechanism of interactionbetween the threea1-ARs and their antagonists is

supported. In fact, while the protonated nitrogenatom is an essential pharmacophoric element for thelong range electrostatic recognition and productiveinteraction with the aspartate of thea1-AR bindingsite, its contribution to the binding energy is almostconstant [20,25]. The modulation of the binding affi-nity by the wide non-congeneric series of ligandsconsidered is described and explained by the variationof the size–shape features of the ligands with respectto the reference supermolecule. This implies thatshort-range forces (repulsive, dispersive, inductive,etc.), being correlated to molecular size and shape,modulate both ligand affinity and selectivity.

It is important to stress that the ad hoc super-molecule approach, when applied on a highlynon-congeneric set of ligands, is mainly focused onthe design of new bio-active compounds and, accord-ing to the highly heterogeneity of the chemical spaceconsidered, its predictive capability is reduced.However, the predictive capability of the QSARmodels can be integrated by using other complemen-tary QSAR approaches, based on more congeneric


Table 5Calculated byVin/Vmol based QSAR models (pK1a calc., pK1b calc., pK1d calc.) and experimental (pK1a exp., pK1b exp., pK1d exp.)a1-ARbinding affinities

No. pK1a calc.a pK1a exp. D pK1b calc.b pK1b exp. D pK1d calc.c pK1d exp. D

13 8.40 7.96 0.44 9.04 8.26 0.78 8.30 8.09 0.2114 8.18 8.25 20.07 8.76 8.36 0.40 8.02 7.71 0.3115 8.14 8.83 20.69 8.35 8.80 20.45 7.64 8.80 21.1616 8.18 7.72 0.46 8.69 8.07 0.62 8.20 7.72 0.4817 7.81 7.44 0.37 8.49 9.05 20.56 7.92 7.63 0.2918 7.64 6.81 0.83 8.28 7.83 0.45 7.70 6.95 0.7519 8.29 7.85 0.44 7.44 7.66 20.22 7.43 8.68 21.2520 9.09 8.85 0.24 7.33 8.20 20.90 6.78 7.76 20.9821 8.03 8.27 20.24 7.08 8.16 21.08 6.68 8.35 21.6722 8.11 8.96 20.85 6.93 7.90 20.97 6.58 7.76 21.1823 8.51 8.83 20.32 8.72 7.51 1.21 8.32 8.82 20.5024 8.54 8.73 20.19 8.65 8.11 0.54 8.23 8.42 20.1925 8.38 8.81 20.43 7.19 8.59 21.40 7.14 8.88 21.7426 8.45 8.20 0.25 8.53 7.66 0.87 8.23 9.03 20.8027 8.49 8.20 0.29 8.44 7.75 0.69 8.16 9.12 20.9628 8.33 7.73 0.60 7.25 6.85 0.40 7.17 6.86 0.31

a pKa values have been calculated according to the following regression equation: pK1a� 6:24 ( 0.84) Vin/mol 1 3.16 ( 0.76),n� 34;r � 0:79; s� 0:48 andF � 55:19; wheren is the number of compounds,r is the correlation coefficient,s is the standard deviation andF is theFisher ratio.

b pK1b values have been calculated according to the following regression equation: pK1b� 5:87 ( 0.69)Vin/mol 1 3.44 ( 0.53),n� 30;r � 0:84; s� 0:49 andF � 71:50:

c pK1d values have been calculated according to the following regression equation: pK1d� 7:14 ( 0.84)Vin/mol 1 2.18 ( 0.67),n� 31;r � 0:84; s� 0:58 andF � 71:99:

ligand sub-set and mainly focused on the improve-ment of the predictive aspect of the TQSAR model-ling. In other words, this implies that the differentQSAR based ligand design procedures acquire highlevel of complementarity when correctly combined,according to the congeneric level of the ligand set/sub-set considered and the knowledge available onthe bio-target.

Finally, the supermolecule based TQSAR model-ling and the associated ligand design procedure can besimply considered the (semi)quantitative versions ofthe most commonly used qualitative SAR basedligand design methods.

Acknowledgements

Financial support from CNR and technical supportfrom CICAIA (University of Modena) are acknowl-edged.

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The ad hoc supermolecule approach to receptor ligand design

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