European Journal of Medicinal Chemistry 37 (2002) 219–229

Original article

Local intersection volume: a new 3D descriptor applied to developa 3D-QSAR pharmacophore model for benzodiazepine receptor

ligands

Hugo Verli a,b, Magaly Girao Albuquerque b,*, Ricardo Bicca de Alencastro b,Eliezer J. Barreiro a

a Laboratorio de A�aliacao e Sıntese de Substancias Bioati�as (LASSBio), Departamento de Farmacos, Faculdade de Farmacia,Centro de Ciencias da Saude, Uni�ersidade Federal do Rio de Janeiro, CP 68006, Rio de Janeiro, RJ 21944-970, Brazil

b Laboratorio de Modelagem Molecular (LabMMol), Departamento de Quımica Organica, Instituto de Quımica,Centro de Ciencias Matematicas e da Natureza, Uni�ersidade Federal do Rio de Janeiro, CT, Bloco A, Lab. 609, Rio de Janeiro,

RJ CEP 21949-900, Brazil

Received 15 June 2001; received in revised form 3 January 2002; accepted 7 January 2002

Abstract

In this work, we have developed a new descriptor, named local intersection volume (LIV), in order to compose a 3D-QSARpharmacophore model for benzodiazepine receptor ligands. The LIV can be classified as a 3D local shape descriptor incontraposition to the global shape descriptors. We have selected from the literature 49 non-benzodiazepine compounds as atraining data set and the model was obtained and evaluated by genetic algorithms (GA) and partial least-squares (PLS) methodsusing LIVs as descriptors. The LIV 3D-QSAR model has a good predictive capacity according the cross-validation test by‘leave-one-out’ procedure (Q2=0.72). The developed model was compared to a comprehensive and extensive SAR pharma-cophore model, recently proposed by Cook and co-workers, for benzodiazepine receptor ligands [J. Med. Chem. 43 (2000) 71]. Itshowed a relevant correlation with the pharmacophore groups pointed out in that work. Our LIV 3D-QSAR model was also ableto predict affinity values for a series of nine compounds (test data set) that was not included into the training data set. © 2002Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Keywords: 3D-quantitative structure–activity relationship; Benzodiazepine receptor; Local intersection volume; Volume descriptor

www.elsevier.com/locate/ejmech

1. Introduction

The �-aminobutyric acid (GABA), one of the majorinhibitory neurotransmitters in the mammalian centralnervous system (CNS), binds to type GABA receptor A(GABAA) [1,2], a ligand-gated chloride ion channel [2].The GABAA/benzodiazepine receptor (GABAA/BzR)recognizes a large spectrum of compounds from diffe-rent chemical classes that are grouped together as ben-zodiazepine receptor ligands. Of these, benzodiazepineconstitutes a well-known class of therapeutics displayinghypnotic, anxiolytic and anticonvulsant effects. Conse-quently, there has been an intensive search for GABAmodulatory agents via GABAA/BzR with a non-benzo-

diazepine structure and an improved therapeutic profile[3].

Benzodiazepine enhances allosterically the actions ofGABA at GABAA receptors by increasing the fre-quency of the opening of the chlorine channel, poten-tiating the inhibitory GABA action in the brain. Theconsequent effect of this action is a continuum ofintrinsic efficacy, ranging from positive efficacy (ago-nists causing anxiolytic, anticonvulsant, and sedativeeffects), through null efficacy (antagonists), to negativeefficacy (inverse agonist causing anxiogenic, stimulant,proconvulsant, and convulsant effects). Partial agonistsand partial inverse agonists exist among these threecategories [1–3].

Different pharmacophore models have been pro-posed for the benzodiazepine receptor site [4]. Accor-ding to structure–activity relationship (SAR) studies, a

* Corresponding author. Tel./fax: +55-21-2562-7132/7256.E-mail address: girao@acd.ufrj.br (M.G. Albuquerque).

0223-5234/02/$ - see front matter © 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

PII: S 0 2 2 3 -5234 (02 )01334 -X

H. Verli et al. / European Journal of Medicinal Chemistry 37 (2002) 219–229220

comprehensive pharmacophore model (Fig. 1) for ago-nists and inverse agonists at the GABAA/BzR withnon-benzodiazepine structures have been proposed byCook and co-workers [5–7]. This model consists of thefollowing sites: a hydrogen bond acceptor site (A2), ahydrogen bond donor site (H1), a ‘bifuncional’ hydro-gen bond donor/acceptor site (H2/A3), three lipophilicpockets (L1, L2, and L3) and a region of steric repulsion(S1).

Quantitative structure–activity relationship (QSAR)is a methodology mostly used to correlate properties (asbiological activities) with structures, but it also can beapplied to predict the activity value of non-synthesizedcompounds structurally related to training sets. It is amathematical model of correlation statistically vali-dated between the chemical structure and their activityprofile [8]. With the advent of molecular modeling,three-dimensional (3D) descriptors have replaced thetraditional physicochemical and bidimensional descrip-tors. The analysis of 3D shape can be roughly classifiedinto two categories, global shape-analysis, and localshape-analysis [9]. Global shape-analysis is a simplercategory, in which an entire structure is matched toanother entire structure. There is a variety of al-gorithms for measuring degree of shape similarity, in-cluding distance geometry [10] and the molecular shapeanalysis (MSA) [11]. The descriptors on the MSA arethe overlapped and the non-overlapped steric van derWaals volumes between a reference molecule and theothers. The MSA methodology has normally been ap-plied [12–15] to construct QSAR models and to postu-late an active conformation. When only a small fractionof one structure is present in the other, local shape-analysis involves comparing two structures. Variousstatistical and syntactic hybrid methodologies have at-tempted to solve the local shape-analysis problem [9].

There are at least two 3D-QSAR methods based onthe Goodford’s grid method [16]: the comparativemolecular field analysis (CoMFA) [17] and the 4D-QSAR analysis [18]. The CoMFA method uses the vander Waals steric (Lennard-Jones) and electrostatic(Coulomb) interaction energy descriptors, calculatedwith a probe charge over the 3D molecular surface. The4D-QSAR method, in which the fourth dimension (4D)corresponds to the conformational sample as a timefunction, uses descriptors of grid cell occupancy on the3D space. Both methods, CoMFA and 4D-QSAR, usestatistical tools, e.g. genetic algorithm (GA) and partialleast-squares (PLS), that enable us to play with a hugenumber of descriptors.

We have developed a new descriptor to 3D-QSARmethodology: local intersection volume (LIV). The LIVcan be classified as a 3D local shape descriptor. TheLIV is the intersection volume between molecule atomsand a set of spheres of carbon atom size, which com-pose a tridimensional ‘box’, in analogy to grid method.The molecules are included in this ‘box’ with a previousalignment derived from the best steric–electrostatic fitaccording Good and co-workers’ method [19,20] to atemplate molecule. By the application of this methodol-ogy, we have constructed successfully a predictive 3D-QSAR pharmacophore model of statistical quality forbenzodiazepine receptor ligands. We selected from theliterature a series of 58 non-benzodiazepine compounds(49 compounds as training data set and nine as testdata set) with rigid framework structure in order tocompose the model. This model was obtained andevaluated by GA and PLS methods [21], and comparedto a previous comprehensive SAR pharmacophoremodel proposed by Cook and co-workers [7]. Thedeveloped method will be applied in the designing ofnew benzodiazepine receptor ligands with a non-benzo-diazepine structure.

2. Methods

2.1. Biological data

The biological data were chosen carefully to contem-plate the following requirements: (a) non-benzo-diazepine structures; (b) the most rigid structures toreduce the conformational search step and to avoid alarge set of conformations to be evaluated in the ali-gnment step; (c) the same pharmacological protocol tohave a consistent biological data; and (d) a regulardistribution of the biological activity [8]. Following thisprocedure, we selected from the literature a series of 58non-benzodiazepine compounds in which their abilityto replace the [3H]-diazepam on the specific bindingassay for the GABAA/BzR was used as a parameter forthe evaluation of the biological activity. The binding

Fig. 1. Schematic pharmacophore model of the GABAA/BzR asproposed by Cook and co-workers and illustrated by the superposi-tion of diazepam (gray) and compound 1 (dark gray). Hydrogenbond sub-sites are labeled as A2 (acceptor), H1 (donor), H2/A3

(donor/acceptor). Lipophilic sub-sites are labeled as L1–3, and steric-repulsive sub-site as S1. Adapted from references [5] and [6].

H. Verli et al. / European Journal of Medicinal Chemistry 37 (2002) 219–229 221

affinities measured as IC50 (nM) were converted to IC50

(M) and then converted to pIC50, and those expressedas Ki (nM) were first converted to IC50 (M) accordingto Cheng and Prussoff equation [22].

The structures and biological activities for the 58compounds are shown in Table 1 and they representfour different classes of non-benzodiazepine structures.The first series comprise dihydroindolo-�-carbolinecompounds 1–32 [23,24] and the related analogue 33[24,25]. The second and third series comprise dihydro-pyrazolo-quinolinone compounds 34 and 35 [24,26–28]and 36–45 [27,28], respectively. The fourth series com-prise �-carboline compounds 46–53 [24] and their re-lated analogues 54–58 [24]. The first series representsthe most rigid and bulky class of compounds. There-fore, we may suppose that it will fill the cavity space inthe GABAA/BzR site better than the other compoundswould. The second and third series have almost thesame size of first series, but more conformational free-dom. The fourth series, like the first series, represents arigid class, but as it is less bulky, we may suppose thatit will not fill the cavity space in the GABAA/BzR siteas well as the previous series does.

2.1.1. The training data setThe 3D-QSAR model was developed using a set of

49 compounds (1–8, 10, 12–15, 17–30, 33, 34, 36–43,45–49, and 52–58), randomly selected from the original58 compounds. We were careful to include all classes ofcompounds in this data set.

2.1.2. The test data setThe 3D-QSAR model was externally validated with

the use of nine compounds (9, 11, 16, 31, 32, 35, 44, 50,and 58), randomly selected from the original 58 com-pounds. We were careful to include all classes of com-pounds in this data set to validate the model.

2.2. Molecular modeling

2.2.1. General software and hardwareCalculations using INSIGHT II [29], MOPAC 93 [30],

and WOLF 6.2 [31] computational programs were per-formed on an O2 Silicon Graphics R5000 and R10000workstation, under the UNIX based-operational systemIRIX 6.3. Calculations using MOPAC 6.0 [32] andMOLDEN [33] computational programs were performedon a Pentium II 266 MHz PC.

2.2.2. Conformational searchThree-dimensional models of each of the 58 com-

pounds reported in Table 1 in their neutral forms, wereconstructed using the Sketcher module from the IN-

SIGHT II software [29]. As a first step, the structureswere geometry-optimized using the CVFF molecular

mechanics force field [34] from the INSIGHT II software[29]. Each structure was then submitted to the MOPAC

6.0 semi-empirical software [32] for geometry-optimiza-tion and conformational search. The optimization wasdone without any geometrical restriction, and the fol-lowing keywords were used: AM1, PRECISE, EF,HESS=1; in the conformational search the followingwere used: AM1, STEP=30, POINT=13,GNORM=1.0.

As we have selected the most rigid structures, aconformational search was performed only for com-pounds 13–15, 24, 25, 27–29, 36–45, 47, 51–58 inwhich the first torsion angle was rotated through 360°with an increment of 30°, obtaining 12 geometriesstarting with the AM1 geometry from the optimizationstep. We have selected four geometries (0, 90, 180, and270°) from the 12 conformers, obtained at the firsttorsion angle, to rotate the second torsion anglethrough 360° with the same angle increment. From the12 geometries obtained, another four were selected torotate the third torsion angle, and so on.

In order to discard duplicated conformations or verysimilar conformations, the conformations obtainedwere selected by means of root-mean-square (RMS)distance. All geometries for each compound were super-imposed using all atoms. The 20 geometries that showthe highest RMS values were selected because our goalis to find neither every conformation nor the globalminimum conformation. Instead, we are trying to ge-nerate the most distinct conformations. The globalminimum conformation was not used as there is noguarantee that this geometry is the bioactive one; any-way, the energy barriers of these compounds are ca. 5kcal mol−1, which are lower enough to be overcome inbiological conditions. The RMS fitting was realized inthe Search–Compare module from the INSIGHT II soft-ware [29]. The final conformation for each compoundused to generate the model was selected from theoriginal generated conformations by means of the beststeric–electrostatic fit to a reference compound.

2.2.3. Electrostatic potential deri�ed charges (ESPq)To obtain the charges that will be used in the align-

ment step, the resultant geometries from the conforma-tional search for the 58 compounds have beensubmitted to an electrostatic potential derived charges(ESPq) calculation. The partial atomic charges derivedfrom the molecular electrostatic potential (MEP) [35]were calculated using the MOPAC 93 program [30,32] towhich the following keywords were applied: AM1, ESP,POTWRT. The default partial atomic charges (q) werereplaced by the derived ESPq in the resumed output filefrom MOPAC 93 program so as to import them into theINSIGHT II software [29].

H. Verli et al. / European Journal of Medicinal Chemistry 37 (2002) 219–229222

Table 1Experimental and calculated inhibition of [3H]-diazepam specific binding (pIC50) for 58 non-benzodiazepine GABAA/BzR ligands and theirresidual values (pIC50 exp–pIC50 calc.)

R1 R2 R3 R4/5No. e R6X/R R7 R8/9 R10 pIC50 Residual f

Exp. Calc.

H H H H H1 HN H H 8.40 7.93 0.472 N H H H H H H NO2 H 8.40 7.92 0.48

H H Cl H H H3 NO2N H 5.92 5.83 0.09H Cl H H H HN NO24 H 6.90 7.08 −0.18H H H H H H5 NH2N H 7.36 7.51 −0.15H Cl H H H HN NH26 H 7.01 7.13 −0.12

N7 H H H H H H Br H 8.22 8.09 0.13Cl H H H H HN Cl8 H 6.51 6.73 −0.22

N9� H H F H H H H H 8.22 7.09 1.13N10 H H Cl H H H H H 5.67 5.88 −0.21

H H Br H H HN H11 H 6.12 6.01 0.11H H CH3 H H H12 HN H 6.65 7.46 −0.81H H OCH3 H H HN H13 H 6.05 6.56 −0.51

N14 H H Obn g H H H H H 5.80 5.58 0.22H H OH H H HN H15 H 6.94 7.06 −0.12

N16 F H H H H H H H 7.92 7.72 0.20N17 Cl H H H H H H H 7.10 6.68 0.42

Br H H H H HN H18 H 7.55 7.80 −0.25N19 CH3 H H H H H H H 7.08 7.90 −0.82

H F H H H H20 HN H 8.15 7.73 0.42H Cl H H H HN H21 H 8.00 7.53 0.47

N22 H Br H H H H H H 7.72 7.67 0.05H CH3 H H H H H H 8.1023 7.56N 0.54H OCH3 H H H HN H24 H 8.10 7.41 0.69H OH H H H H25 HN H 8.22 7.78 0.44H H H Cl H HN H26 H 6.15 6.64 −0.49

N27 H H H OCH3 H H H H 6.60 5.75 0.85H H H OH H HN H28 H 6.24 7.76 −1.52

N29 H H H H C2H5 H H H 6.60 6.42 0.18H H H H H CH330 HN H 5.94 6.21 −0.27H H H H H HN H31 CH3 6.80 8.32 −1.52H H H H H CH332 HN CH3 5.71 7.47 −1.76H H H H H HCH H33 H 5.72 7.30 −1.58

H34 – – – – – – – – 9.51 8.92 0.59– – – – – –Cl –35 – 8.94 9.50 −0.56

–36 CH3 – – H – H H – 9.35 9.08 0.27H –37 –– H – H H – 8.99 8.67 0.32Cl – – H – H– H38 – 8.99 8.76 0.23CH3 – – H – Cl39 H– – 8.96 9.09 −0.13CH3 – – H – H– Cl40 – 9.06 8.96 0.10

–41 CH3 – – H – F H – 9.05 8.85 0.20CH3 – – H – H– F42 – 9.29 9.11 0.18

–43 CH3 – – H – CH3 H – 8.87 9.19 −0.32CH3 –44 –– H – H CH3 – 9.27 9.36 0.09CH3 – – CH3 – H– H45 – 6.52 6.46 0.06

N46 H H H – – – – – 5.79 5.62 0.17H H C2H5 – – – – – 3.6047 3.59N 0.01H H CH3 – – –N –48 – 4.91 4.60 0.31Cl H49 HN – – – – – 7.35 6.59 0.76

H. Verli et al. / European Journal of Medicinal Chemistry 37 (2002) 219–229 223

Table 1 (Continued)

No. e R8/9X/R R1 R2 R3 R4/5 R6 R7 Residual fpIC50R10

Exp. Calc.

– 0.81– – 6.90 6.0950 N NO2 H H – –51 −1.016.415.40–––––HHOHN

5.866.91–––– 1.05–HHOCH3N52– – – – – 8.30 6.93 1.3753 N CO2CH3 H H

−1.18– – – 4.59 5.7754 C CO2C2H5 �O H – –– – – – – 5.30 4.67 0.6355 C CO2C2H5 �NOH H

−1.496.535.04––––56 –H–CO2C2H5O–– – 6.17––H–CO2C2H5CH257 6.51 −0.34

– −0.64S CO2C2H558 H – – 6.415.77–––

a Ref. [23–25].b Ref. [24,26–28].c Ref. [27,28].d Ref. [24].e The underlined compound numbers are from the test data set.f The residual values in bold are the outlier compounds (2×SD of the residual values for the training data set).g Obn=benzyloxy.

2.2.4. The grid matrix of hard spheresIn analogy to the grid method [16], we have con-

structed a grid matrix of 206 hard spheres, composedby unitary cells, corresponding to a quadrangular basepyramid (Fig. 2). The pyramid vertices correspond tothe Cartesian coordinates of the five carbon atoms andtheir arrest lengths are 3.08 A� (twice the carbon van derWaals radii, 1.54 A� ). The grid matrix was assembledusing the MOLDEN program [33]. The grid matrix ofcarbon atoms was imported into the INSIGHT II pro-gram [29] where we calculated the volume for each hardsphere, using a radii length of 1.54 A� in the Search–Compare module. Therefore, we have composed a gridmatrix of hard spheres where the volumes of eachsphere do not overlap each other. We have chosen thequadrangular base pyramid figure because it means alower volume lost among the hard spheres, than a cubicorganization of the carbon atoms would mean. How-

ever, it is possible to use different geometric figures anddifferent scale factors for the van der Waals radii,having in mind that we cannot lose so much informa-tion in terms of volumes between the spheres.

2.2.5. Alignment rulesThe alignment step is critical for the development of

3D-QSAR and of pharmacophore models. The mostcommon alignment procedure is based on the RMSfitting. Unfortunately, it does not take into account thesteric and electrostatic profiles of the compounds,which leads a different orientation on the receptor site.For this reason, we have used a combined approachapplying a steric–electrostatic fitting [19,20] that needsa previous alignment by RMS. The reference com-pound chosen for the alignment step was compound 1.It was chosen because its series is the most representa-tive one for the following reasons: we have more com-pounds from this class than from all the others;presents the highest occupation level of the receptorsite; it is the most rigid compound, and a highly activeone. The overall alignment step was performed usingstandard tools, available in the Search–Compare mo-dule of the INSIGHT II program [29]. Compound 1 wasinserted in the grid matrix by the superimposition ofthe Alternate–Space Axes of both compound 1 and thegrid matrix. Each conformation of the 58 compoundswas then superimposed to compound 1 (the referencecompound) in a two-step alignment procedure.

(a) Pre-alignment step by RMS: we have selected twoor three atoms from each compound to be pre-alignedto the corresponding atoms of the reference compound1 by RMS procedure. We have used two criteria tochoose these atoms. First, they are in accordance withthe proposed pharmacophore groups in the Cook andco-workers’ model (Fig. 1) [7]. Secondly, we have

Fig. 2. The grid matrix of hard spheres (A) composed by thequadrangular base pyramid unitary cell (B), and the associatedcarbon atom volumes (C) used to calculate the LIVs.

H. Verli et al. / European Journal of Medicinal Chemistry 37 (2002) 219–229224

selected only atoms from the rigid heterocycle frame-work of all compounds to avoid conformational uncer-tainty when choosing atoms from the flexible chains.Atom numbers (Table 1) 5, 7, and 12 from compound1 were, respectively, superimposed to: atom numbers 5,7, and 12 of compounds 2–33; atom numbers 5, 3, and1 of compounds 34, 35, 36–45; atom numbers 9 and 2of compounds 46–58. As it may be seen, there is nocorrespondence for atom number 12 of compound 1 inthe last series, although maybe we could find corre-sponding atoms if we looked at the substituent R1(Table 1). However, since we are choosing only atomsfrom the rigid heterocycle framework of all compounds,we have discarded these options. Anyway, the RMSpre-alignment step is only an initial step for the subse-quent alignment by steric–electrostatic fit [36].

(b) Alignment by steric and electrostatic fit: subse-quent to the pre-alignment step, we have realized asteric and electrostatic fit. The similarity index is inaccordance with the method proposed by Good andco-workers [19,20] to evaluate the steric and electro-static potential similarity between a pair of molecules.We have used the default option for the weights of thesteric and electrostatic factors (50%). We have used thesteric and electrostatic fit with the purpose of not onlyobtaining the spatial orientation of each compound inthe receptor site, but also as a parameter to select the‘best’ conformation for interaction with the receptor.This means that those conformations represent the‘bioactive’ conformations in the cases in which we havegenerated multiple conformations. As it will be seenlater, the LIV descriptors are volume descriptors, andso the steric–electrostatic fit is used to include in the3D-QSAR-pharmacophore model a ‘sense’ of electronicproperty.

2.2.6. The local intersection �olume (LIV) descriptorsAfter the superimposition of the 58 compounds to

reference compound 1, according to the described align-ment procedure, we have performed the molecular volu-me calculation for each of the 58 compounds, using thevan der Waals radii. Subsequently, we have calculatedthe intersection volume (or the overlapped volume—the 3D-QSAR descriptors) between the molecular volu-me of each compound (1–58) and the volume of eachhard sphere that composes the grid matrix. We havenamed this intersection volume local intersection �olume(LIV) since it can be located in 3D space according toits Cartesian coordinates. Consequently, for each com-pound, we have a set of LIV descriptors (independentvariables) and their corresponding biological activities(dependent variables). The molecular volume and theintersection volume calculations were performed usingthe tools available in the Search–Compare module ofthe INSIGHT II program [29].

2.2.7. Data reductionTwo levels of data reduction were considered. The

first, a preliminary data reduction, uses both of thefollowing filtering criteria; one filter to exclude LIVdescriptors the variance of which (self-variance) overthe whole set of compounds is zero; other to eliminateLIV descriptors in which the compound occurrence isless than six. The first criterion excludes useless vari-ables and the second harmonizes the data, not takinginto account structural peculiarities of a few com-pounds, both criteria functions as a noise data reduc-tion. A second level of data reduction consists ofconstructing 3D-QSAR models using a genetic al-gorithm optimization; i.e. at the same time, a datareduction (variable selection) and a model construction.As a next step in this study we employed in 3D-QSARmodel building and optimization, the genetic functionapproximation (GFA) [37], using the WOLF 6.2 soft-ware [31], implemented with PLS regression [21].

2.2.8. 3D-QSAR model calculation: GA-PLS approachThe GA-PLS optimizations were initiated using 200

randomly generated models (functions or equations),each model depending on four independent variables(base functions). Mutation probability over thecrossover optimization was set to a rate of 200% ateach ten-crossover operation. The smoothing factorwas set at 0.01. It controls the number of independentvariables in the models. We have used three compo-nents for the PLS regression and 20 000-crossover oper-ations. All other options were left in their defaultvalues. The five best 3D-QSAR models as scored by thelack-of-fit (LOF) measure [37] from the GA-PLS analy-sis were evaluated by an internal validation process.The internal validation process was carried out by the‘leave-one-out’ cross-validation procedure, using thetraining data set. The test data set was used only for theexternal validation process. The GA-PLS analysis wasperformed using the WOLF 6.2 software [31].

3. Results and discussion

3.1. Statistical parameters for the LIV 3D-QSARmodel for GABAA/BzR ligands

The GA-PLS analysis gave us a series of good equa-tions or good models. From them we chose the onewhich had the highest activity prediction (Q2=0.722)and the lowest number of variables (eight descriptors),namely Eq. (1). The cross-correlation coefficients of theselected descriptors in Eq. (1) were calculated (data notshown) in order to verify the non-redundancy of infor-mation. The highest value was found for the pair ofdescriptors LIV–065 and LIV–110 (R= −0.49), andso we do not have high internal correlation among theselected variables.

H. Verli et al. / European Journal of Medicinal Chemistry 37 (2002) 219–229 225

Fig. 3. Graphical representation of the LIV 3D-QSAR pharma-cophore model for ligands of GABAA/BzR proposed in this workusing compound 1 as reference. LIVs of positive contribution (gray):110, 130, and 139. LIVs of negative contribution (dark gray): 065,074, 111, 140, and 168. The LIVs descriptors are represented in theirmaximum size.

data set, in accordance with the internal validationprocess. The experimental affinity (pIC50 exp) and thepredicted affinity (pIC50 calc.) values can be seen inTable 1 for the test data set.

3.2. Graphical representation for the LIV 3D-QSARmodel for GABAA/BzR ligands

Fig. 3 shows a graphical 3D representation of thebest model (Eq. (1)) in which the LIVs are representedas hard spheres in their maximal intersection volumepossible, using compound 1 as a template. Therefore,this is not the representation of the LIV values forcompound 1. The LIVs that contribute positively forthe affinity are LIVs 110, 130, and 139, all of themlocated on the core framework of compound 1. Thismeans that there is an almost constant contributionfrom these variables to the affinity, since the com-pounds are not so flexible. The LIVs that contributenegatively for the affinity are LIVs 065, 074, 111, 140,and 168, all of them located around the core frameworkof compound 1, more precisely at the northeast, thesouth and the east sides of this compound. This meansthat there is a steric limitation near these sides. On theother hand, we could not observe a LIV on the north,northwest, or west side of the molecule.

Although there is no significant internal cross-corre-lation between the descriptors (data not shown), wehave observed a cooperative behavior between LIV–110 of positive contribution and two LIVs of negativecontribution: LIV–111 and LIV–140. At a glance,LIV–111 and LIV–140 correspond to substituents onR4 and R6 for compounds 1–33 and R1 and R3 for

Fig. 4. Examples of local intersection volumes (LIVs) for compounds43 and 54 from the training data set, which are represented in thesame orientation as that of compound 1 in Fig. 3. LIVs of positivecontribution (gray): 110, 130, and 139. LIVs of negative contribution(dark gray): 111 and 140.

Fig. 5. Superimposition of compound 1 (dark gray) (series I) tocompounds 35 (series II) (A), 43 (series III) (B), and 54 (series IV)(C).

pIC50= −3.676−0.558(LIV–065)−0.780(LIV–074)

+0.602(LIV–110)−0.369(LIV–111)

+0.446(LIV–130)+0.481(LIV–139)

−0.393(LIV–140)−1.194(LIV–168)

N=49 R2=0.802 Q2=0.722 SE=0.744 (1)

The standard error of this equation after the cross-validation process equals 0.744 and R2 equals 0.802.The experimental affinity (pIC50 exp) and the calculatedaffinity (pIC50 calc.) values for the training data set canbe seen in Table 1. The high Q2 value leaves us toconsider the model validated statistically (internal vali-dation) since the model is generally considered inter-nally predictive if Q2�0.5. The external validationprocess corresponds to the affinity prediction of the test

H. Verli et al. / European Journal of Medicinal Chemistry 37 (2002) 219–229226

Fig. 6. Experimental versus calculated (49 training compounds, �)and predicted (nine test compounds, �) affinity values (pIC50) for the58 non-benzodiazepine compounds. The corresponding structures areindicated in Table 1.

Fig. 4 shows a graphical representation of the LIVsdescriptors for compounds 43 and 54 (both from thetraining data set) represented in their actual LIV size.Compound 43 was selected for the reason that it is thelowest active compound (pIC50exp=8.87) from seriesIII (the most active series) and compound 54 wasselected since it is the lowest active compound(pIC50exp=4.59) from series IV (the less active series)containing a ester group at R1. Fig. 5 shows theobtained alignment of compounds 35 (series II), 43(series III), and 54 (series IV) over compound 1 (seriesI) as an example.

3.3. The LIV 3D-QSAR model �ersus the Cook’s modelfor GABAA/BzR ligands

LIV 3D-QSAR model was compared to Cook’sModel (Fig. 1), the most comprehensive GABAA/BzRmodel from the literature [7]. The following LIVs havepositive contribution to the affinity. LIV–139 corres-ponds to a hydrogen donor on the ligand molecule(Fig. 3, compound 1), and it is complementary to thereceptor sub-site A2 (hydrogen acceptor) on the Cook’sreceptor model. LIV–110 corresponds to a hydrogenacceptor on the ligand molecule, and it is complemen-tary to sub-site H1 (hydrogen donator) on the receptormodel. LIV–130 corresponds to a lipophilic region onthe ligand molecule and it corresponds to the sub-siteL3 on the receptor model.

The following LIVs have negative contribution to theaffinity. LIV–065, LIV–074, and LIV–111 correspondto regions around the northeast and the east side of theligand molecule; they are correlated to the sub-site S1 ofsteric limitation on the Cook’s receptor model. LIV–140 corresponds to a region around the southeast sideof the ligand molecule. It is correlated to the sub-siteH1 that represents a hydrogen donator on the receptormodel, so the occupation of this region is detrimental tothe affinity because it prevents hydrogen bonding be-tween the ligand and the receptor. Finally, LIV–168corresponds to a region around the south side of theligand molecule, and is correlated to sub-site A2, whichrepresents a hydrogen acceptor on the receptor model,and similarly, its occupation prevents a hydrogen bon-ding between the ligand and the receptor.

Compounds 31 and 32 (both compounds are outliers,see next section) are the only ones in all the data setthat own a substituent (R10=CH3) in a region thatcorresponds to sub-site H2/A3 from Cook’s model; un-fortunately this region was not described by our LIV3D-QSAR model, probably because these compoundswere not included in the training data set. This impliesthat the model itself has no quantitative parameters todescribe this interaction with this significant site. On theother hand, the substituent in R7 (1–33 series), R5 (to36–45 series) and R2 (to 46–58 series) confer on the

Table 2Standard deviation (SD) of the residual values (experimental pIC50–calculated pIC50) calculated for training data set (49 compounds), testdata set (nine compounds), and entire data set (58 compounds)

SDNumber of compounds 2×SD

0.64 1.27490.979 1.94

58 1.390.69

compounds 46–58, but these substituents, dependingon the alignment of the molecule in the space, can beoverlaid also on LIV–110.

We also have observed a cooperative behaviorbetween LIV–139 of positive contribution and twoLIVs of negative contribution: LIV–140 and LIV–168.All of them correspond to substituents on R6 and R7for compounds 1–33, R5 for compounds 36–45, andR2 and R3 for compounds 46–58, but, depending onthe alignment, these substituents can be overlaid onLIV–139. Both cooperative behaviors are due in partto the distant substituents because they can modify theelectronic distribution and, consequently, the molecularelectrostatic potential provokes a change in thesimilarity function and so, in the final alignment.

Qualitatively LIV–065 and LIV–074 (negativecontribution) could be joined in a unique regioncorresponding to the following substituents: R2 and R3for compounds 1–33, R and R1 for compounds 34–45,and R1 (in this case, on the furthermost distant point ofR1) for compounds 46–58.

H. Verli et al. / European Journal of Medicinal Chemistry 37 (2002) 219–229 227

model a calibration that is more accurate in reprodu-cing the unfavorable effect of a methyl group at thehydrogen bonding site (sub-site A2) than other group.

3.4. Outliers from the LIV 3D-QSAR model forGABAA/BzR ligands

Fig. 6 shows the experimental affinity values versusthe calculated (training data set) and predicted (testdata set) affinity values for the 58 compounds. As wecan see in Fig. 5 and Table 1 we have the compounds28, 33, 53, and 56 as outliers from the training set andcompounds 31 and 32 as outliers from the test set.These compounds have residual values (experimentalpIC50–calculated pIC50) higher than twice the standarddeviation (SD) (Table 2) of the residuals calculated onthe training data set [38]. Except for compound 53, allthe outlier compounds have negative residuals, whichmeans that the calculated (or predicted) activities werehigher than the experimental ones.

Comparing compound 28 (R4=OH) to compound27 (R4=OCH3), both with similar experimental pIC50,respectively, 6.24 and 6.60, we can observe that thecalculated pIC50 are, respectively, 7.76 and 5.75 (Table2). We cannot explain this discrepancy in terms of onlysteric factor of these substituents around the N7 (ahydrogen bonding acceptor site), since the LIV–111(the LIV that corresponds to region of substituent R4)for compound 27 is almost four times greater than forcompound 28. Therefore, although compound 28 doesnot make intramolecular hydrogen bonding betweenthe hydroxyl group (R4) and the pyridine nitrogen(data not shown), it can display some preferential in-tramolecular electrostatic interaction (of deleterious ef-fects) which implicates in some specific conformationnot observed by the model, and so, the oxygen atomfrom the hydroxyl group (R4) can enter in a competi-tion with the N7 for the hydrogen donor site (H1) fromthe receptor, according the Cook’s model (Fig. 1).

Compounds 31 and 32 have both a methyl group(R10) as a substituent on N12, all other compoundsfrom this series have a hydrogen atom in this position.As this region is implicated in a hydrogen bond interac-tion with the receptor (H2/A3 sub-site according Cook’smodel, Fig. 1), and both compounds are from the testset, it is obvious that our model was not ‘trained’ torecognize this situation. In fact, our model does notcontemplate any LIV descriptor near the H2/A3 recep-tor sub-site region.

The residual value for compound 33 (Table 1) showsthe model’s incapacity to distinguish electronic aspectsof the aromatic carbon 7, which makes it less activethan the nitrogen atom of compound 1 in the sameposition. In other words, the occupation of LIV–110 issimilar between compounds 1 and 33, even under the

effect of steric–electrostatic alignment. The greatestdifference is that the LIV–130 of positive contributionhas a higher value for compound 1 than for compound33, and for LIV–140 of negative contribution, it is thereverse. The result is that, when superimposing com-pound 33 on compound 1, the compound 33 is lightlydislocated to the right side after the steric–electrostaticfit.

The outlier compounds 53 and 56 are both from theseries IV and as a group (compounds 46–58), excludingcompound 53 (pIC50exp=8.30), it has the lowestaffinity. The low affinity of series IV is probably duethe incapacity of the compounds to occupy all receptorsub-sites at the same time, since this series has thesmaller size among the four series and it does not haveall the pharmacophore groups. Compound 53 is theunique outlier among the compounds with experimentalpIC50�7.0, it is the only compound from series IV thathas the minimal pharmacophore requirements, whichare N9 and R2=H related to the receptor sub-site A2

according Cook’s model (Fig. 1), N2 related to thereceptor sub-site H1, and R1=CO2CH3 related to thesub-site H2/A3. Since this R1 substituent is not in thecore framework of the molecule, like N12 and R10=Hon series I and N1 on series II and III, but instead, it isa flexible substituent, it can lose affinity by entropyreason. Compound 56 in contrast with compound 53,does not have a N�H group to interact with the recep-tor sub-site A2, instead of that, it has an oxygen atomat this position (X9). However, in spite of their residualvalue of −1.49, it is calculated as active as compound57, an analogue compound in which the oxygen atom isreplaced by a CH2 group on the same position. There-fore, in a qualitative sense, it was not a critical outlierin its own group.

4. Conclusions

In this work, we have developed a new descriptor to3D-QSAR methodology: local intersection �olume(LIV). The LIV can be classified as a 3D local shapedescriptor in contraposition to the global shape descrip-tors. The LIV is the intersection volume betweenmolecule atoms and a set of spheres of defined atomsize, which compose a tridimensional ‘box’, in analogyto grid method. The molecules are included in this ‘box’with a previously defined alignment to a templatemolecule.

In order to compose a 3D-QSAR model for benzo-diazepine receptor ligands, we have selected from theliterature 49 non-benzodiazepine compounds with rigidframework structure as training data set. Using theLIVs as descriptors, we have obtained and evaluated byGA-PLS methods [21] a LIV 3D-QSAR model. TheLIV 3D-QSAR model has a good predictive capacity

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according the cross-validation test by ‘leave-one-out’procedure (Q2=0.72). The LIV 3D-QSAR model is inagreement with some previous studies developed byCook and co-workers in which they proposed a com-prehensive pharmacophore model for benzodiazepinereceptor ligands [7]. It showed a relevant correlationwith the pharmacophore groups pointed out in thatwork. In addition, the affinity values were correctlypredicted for seven compounds from the test data setconsisting of nine compounds that were not included inthe training data set.

It should be noted that a similarity function [19,20]was used to align the compounds in space. Thismethodology shows that some substituents, even if notinteracting directly with the receptor, can cause a de-crease in the receptor affinity of some compounds.These substituents modify the compound’s steric andelectronic properties in such way that its alignment atthe receptor cavity becomes different from thatachieved when no substituents are in the same position.This new alignment can, for example, modify the opti-mal distance of the hydrogen bond with the receptorand, therefore, reduce the receptor affinity for thatcompound. This effect causes the convergence of posi-tions R6 and R7, to series I, and of positions R2 andR3, to series IV, to the same space, affecting theinteraction with the receptor, as discussed before.

Work is underway to apply this methodology toother classes of compounds. We are also modifying thegrid box atom size, in order to have a more refinedresolution. Another change is to include a percentage ofconformations from the conformational analysis, par-ticularly important for compounds with more confor-mational freedom, and to associate an electroniccomponent in each LIV descriptor, like charges derivedfrom the molecular electrostatic potential.

Acknowledgements

We thank the Conselho Nacional de Desenvolvi-mento Cientıfico e Tecnologico (CNPq) of the Brazilgovernment, the Coordenacao de Aperfeicoamento dePessoal de Nıvel Superior (CAPES) of the Brasil go-vernment, the Fundacao de Amparo a Pesquisa doEstado do Rio de Janeiro (FAPERJ), the FundacaoUniversitaria Jose Bonifacio (FUJB), and the Conselhode Ensino para Graduados e Pesquisa (CEPG) daUniversidade Federal do Rio de Janeiro (UFRJ) fortheir support.

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