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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 Aaliacao 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-QSAR

pharmacophore model for benzodiazepine receptor ligands. The LIV can be classified as a 3D local shape descriptor in

contraposition to the global shape descriptors. We have selected from the literature 49 non-benzodiazepine compounds as a

training data set and the model was obtained and evaluated by genetic algorithms (GA) and partial least-squares (PLS) methods

using 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 able

to predict affinity values for a series of nine compounds (test data set) that was not included into the training data set. © 2002

Editions 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 major

inhibitory neurotransmitters in the mammalian central

nervous 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, benzodiazepine

constitutes a well-known class of therapeutics displaying

hypnotic, anxiolytic and anticonvulsant effects. Conse-

quently, there has been an intensive search for GABA

modulatory agents via GABAA/BzR with a non-benzo-

diazepine structure and an improved therapeutic profile

[3].

Benzodiazepine enhances allosterically the actions of

GABA at GABAA receptors by increasing the fre-

quency of the opening of the chlorine channel, poten-tiating the inhibitory GABA action in the brain. The

consequent effect of this action is a continuum of

intrinsic efficacy, ranging from positive efficacy (ago-

nists causing anxiolytic, anticonvulsant, and sedative

effects), through null efficacy (antagonists), to negative

efficacy (inverse agonist causing anxiogenic, stimulant,

proconvulsant, and convulsant effects). Partial agonists

and partial inverse agonists exist among these three

categories [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: [email protected] (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 - 5 2 3 4 ( 0 2 ) 0 1 3 3 4 - X

mailto:[email protected]






H . Verli et al . / European Journal of Medicinal Chemistry 37 (2002) 219 – 229 220

comprehensive pharmacophore model (Fig. 1) for ago-

nists and inverse agonists at the GABAA/BzR with

non-benzodiazepine structures have been proposed by

Cook and co-workers [5 – 7]. This model consists of the

following sites: a hydrogen bond acceptor site (A2), a

hydrogen bond donor site (H1), a ‘bifuncional’ hydro-

gen bond donor/acceptor site (H2/A3), three lipophilic

pockets (L1, L2, and L3) and a region of steric repulsion

(S1).Quantitative structure – activity relationship (QSAR)

is a methodology mostly used to correlate properties (as

biological activities) with structures, but it also can be

applied to predict the activity value of non-synthesized

compounds structurally related to training sets. It is a

mathematical model of correlation statistically vali-

dated between the chemical structure and their activity

profile [8]. With the advent of molecular modeling,

three-dimensional (3D) descriptors have replaced the

traditional physicochemical and bidimensional descrip-

tors. The analysis of 3D shape can be roughly classified

into two categories, global shape-analysis, and localshape-analysis [9]. Global shape-analysis is a simpler

category, in which an entire structure is matched to

another entire structure. There is a variety of al-

gorithms for measuring degree of shape similarity, in-

cluding distance geometry [10] and the molecular shape

analysis (MSA) [11]. The descriptors on the MSA are

the overlapped and the non-overlapped steric van der

Waals volumes between a reference molecule and the

others. 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 fraction

of one structure is present in the other, local shape-

analysis involves comparing two structures. Various

statistical and syntactic hybrid methodologies have at-

tempted to solve the local shape-analysis problem [9].

There are at least two 3D-QSAR methods based on

the Goodford’s grid method [16]: the comparative

molecular field analysis (CoMFA) [17] and the 4D-

QSAR analysis [18]. The CoMFA method uses the van

der Waals steric (Lennard-Jones) and electrostatic

(Coulomb) interaction energy descriptors, calculated

with a probe charge over the 3D molecular surface. The

4D-QSAR method, in which the fourth dimension (4D)

corresponds to the conformational sample as a timefunction, uses descriptors of grid cell occupancy on the

3D space. Both methods, CoMFA and 4D-QSAR, use

statistical tools, e.g. genetic algorithm (GA) and partial

least-squares (PLS), that enable us to play with a huge

number of descriptors.

We have developed a new descriptor to 3D-QSAR

methodology: local intersection volume (LIV). The LIV

can be classified as a 3D local shape descriptor. The

LIV is the intersection volume between molecule atoms

and 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 fit

according Good and co-workers’ method [19,20] to a

template molecule. By the application of this methodol-

ogy, we have constructed successfully a predictive 3D-

QSAR pharmacophore model of statistical quality for

benzodiazepine receptor ligands. We selected from the

literature a series of 58 non-benzodiazepine compounds

(49 compounds as training data set and nine as test

data set) with rigid framework structure in order to

compose the model. This model was obtained and

evaluated by GA and PLS methods [21], and comparedto a previous comprehensive SAR pharmacophore

model proposed by Cook and co-workers [7]. The

developed method will be applied in the designing of

new 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 to

reduce the conformational search step and to avoid a

large set of conformations to be evaluated in the ali-

gnment step; (c) the same pharmacological protocol to

have a consistent biological data; and (d) a regular

distribution of the biological activity [8]. Following this

procedure, we selected from the literature a series of 58

non-benzodiazepine compounds in which their ability

to replace the [3H]-diazepam on the specific binding

assay for the GABAA

/BzR was used as a parameter for

the evaluation of the biological activity. The binding

Fig. 1. Schematic pharmacophore model of the GABAA/BzR as

proposed by Cook and co-workers and illustrated by the superposi-

tion of diazepam (gray) and compound 1 (dark gray). Hydrogen

bond 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].




af finities measured as IC50 (nM) were converted to IC50

(M) and then converted to pIC50, and those expressed

as K i (nM) were first converted to IC50 (M) according

to Cheng and Prussoff equation [22].

The structures and biological activities for the 58

compounds are shown in Table 1 and they represent

four different classes of non-benzodiazepine structures.

The first series comprise dihydroindolo--carboline

compounds 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 represents

the most rigid and bulky class of compounds. There-

fore, we may suppose that it will fill the cavity space in

the GABAA/BzR site better than the other compounds

would. The second and third series have almost the

same size of first series, but more conformational free-

dom. The fourth series, like the first series, represents a

rigid class, but as it is less bulky, we may suppose thatit will not fill the cavity space in the GABAA/BzR site

as well as the previous series does.

2 .1.1. The training data set

The 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 original

58 compounds. We were careful to include all classes of

compounds 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 hardware

Calculations using INSIGHT II [29], MOPAC 93 [30],

and WOLF 6.2 [31] computational programs were per-formed on an O

2 Silicon Graphics R5000 and R10000

workstation, under the UNIX based-operational system

IRIX 6.3. Calculations using MOPAC 6.0 [32] and

MOLDEN [33] computational programs were performed

on a Pentium II 266 MHz PC.

2 .2 .2 . Conformational search

Three-dimensional models of each of the 58 com-

pounds reported in Table 1 in their neutral forms, were

constructed using the Sketcher module from the IN-

SIGHT II software [29]. As a first step, the structures

were 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 was

done without any geometrical restriction, and the fol-

lowing keywords were used: AM1, PRECISE, EF,

HESS=1; in the conformational search the following

were used: AM1, STEP=30, POINT=13,

GNORM=1.0.As we have selected the most rigid structures, a

conformational search was performed only for com-

pounds 13 – 15, 24, 25, 27 – 29, 36 – 45, 47, 51 – 58 in

which the first torsion angle was rotated through 360°

with an increment of 30°, obtaining 12 geometries

starting with the AM1 geometry from the optimization

step. We have selected four geometries (0, 90, 180, and

270°) from the 12 conformers, obtained at the first

torsion angle, to rotate the second torsion angle

through 360° with the same angle increment. From the

12 geometries obtained, another four were selected to

rotate the third torsion angle, and so on.In order to discard duplicated conformations or very

similar conformations, the conformations obtained

were selected by means of root-mean-square (RMS)

distance. All geometries for each compound were super-

imposed using all atoms. The 20 geometries that show

the highest RMS values were selected because our goal

is to find neither every conformation nor the global

minimum conformation. Instead, we are trying to ge-

nerate the most distinct conformations. The global

minimum conformation was not used as there is no

guarantee that this geometry is the bioactive one; any-way, the energy barriers of these compounds are ca. 5

kcal mol−1, which are lower enough to be overcome in

biological conditions. The RMS fitting was realized in

the Search – Compare module from the INSIGHT II soft-

ware [29]. The final conformation for each compound

used to generate the model was selected from the

original generated conformations by means of the best

steric – 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 been

submitted to an electrostatic potential derived charges

(ESPq) calculation. The partial atomic charges derived

from the molecular electrostatic potential (MEP) [35]

were calculated using the MOPAC 93 program [30,32] to

which the following keywords were applied: AM1, ESP,

POTWRT. The default partial atomic charges (q) were

replaced by the derived ESPq in the resumed output file

from MOPAC 93 program so as to import them into the

INSIGHT II software [29].




Table 1

Experimental and calculated inhibition of [3H]-diazepam specific binding (pIC50) for 58 non-benzodiazepine GABAA/BzR ligands and their

residual 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 0.47

2 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 0.09

H Cl H H H HN NO24 H 6.90 7.08 −0.18

H H H H H H5 NH2N H 7.36 7.51 −0.15

H 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 0.13

Cl 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 1.13

N10 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 0.11

H H CH3 H H H12 HN H 6.65 7.46 −0.81

H 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 0.22

H 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 0.20

N17 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 −0.25

N19 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 0.42

H 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 0.05

H CH3 H H H H H H 8.1023 7.56N 0.54

H OCH3 H H H HN H24 H 8.10 7.41 0.69

H OH H H H H25 HN H 8.22 7.78 0.44

H 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 0.85

H 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 0.18

H H H H H CH330 HN H 5.94 6.21 −0.27

H H H H H HN H31 CH3 6.80 8.32 −1.52

H H H H H CH332 HN CH3 5.71 7.47 −1.76

H 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 0.27

H – 37 – – H – H H – 8.99 8.67 0.32

Cl – – H – H – H38 – 8.99 8.76 0.23

CH3 – – H – Cl39 H – – 8.96 9.09 −0.13

CH3 – – H – H – Cl40 – 9.06 8.96 0.10

– 41 CH3 – – H – F H – 9.05 8.85 0.20

CH3 – – H – H – F42 – 9.29 9.11 0.18

– 43 CH3 – – H – CH3 H – 8.87 9.19 −0.32

CH3 – 44 – – H – H CH3 – 9.27 9.36 0.09

CH3 – – CH3 – H – H45 – 6.52 6.46 0.06

N46 H H H – – – – – 5.79 5.62 0.17

H H C2H5 – – – – – 3.6047 3.59N 0.01

H H CH3 – – – N – 48 – 4.91 4.60 0.31Cl H49 HN – – – – – 7.35 6.59 0.76




Table 1 (Continued )

No. e R8/9X/R R1 R2 R3 R4/5 R6 R7 Residual f pIC50R10

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 spheres

In analogy to the grid method [16], we have con-

structed a grid matrix of 206 hard spheres, composed

by unitary cells, corresponding to a quadrangular base

pyramid (Fig. 2). The pyramid vertices correspond to

the Cartesian coordinates of the five carbon atoms and

their arrest lengths are 3.08 A (twice the carbon van der

Waals radii, 1.54 A ). The grid matrix was assembled

using the MOLDEN program [33]. The grid matrix of

carbon atoms was imported into the INSIGHT II pro-

gram [29] where we calculated the volume for each hard

sphere, using a radii length of 1.54 A in the Search – Compare module. Therefore, we have composed a grid

matrix of hard spheres where the volumes of each

sphere do not overlap each other. We have chosen the

quadrangular base pyramid figure because it means a

lower volume lost among the hard spheres, than a cubic

organization of the carbon atoms would mean. How-

ever, it is possible to use different geometric figures and

different 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 rules

The alignment step is critical for the development of

3D-QSAR and of pharmacophore models. The most

common alignment procedure is based on the RMS

fitting. Unfortunately, it does not take into account the

steric and electrostatic profiles of the compounds,

which leads a different orientation on the receptor site.For this reason, we have used a combined approach

applying a steric – electrostatic fitting [19,20] that needs

a 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 receptor

site; it is the most rigid compound, and a highly active

one. The overall alignment step was performed using

standard tools, available in the Search – Compare mo-

dule of the INSIGHT II program [29]. Compound 1 wasinserted in the grid matrix by the superimposition of

the Alternate – Space Axes of both compound 1 and the

grid matrix. Each conformation of the 58 compounds

was then superimposed to compound 1 (the reference

compound) in a two-step alignment procedure.

(a) Pre-alignment step by RMS : we have selected two

or three atoms from each compound to be pre-aligned

to the corresponding atoms of the reference compound

1 by RMS procedure. We have used two criteria to

choose these atoms. First, they are in accordance with

the proposed pharmacophore groups in the Cook and

co-workers’ model (Fig. 1) [7]. Secondly, we have

Fig. 2. The grid matrix of hard spheres (A) composed by the

quadrangular base pyramid unitary cell (B), and the associatedcarbon atom volumes (C) used to calculate the LIVs.




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 compound

1 were, respectively, superimposed to: atom numbers 5 ,

7 , and 12 of compounds 2 – 33; atom numbers 5 , 3 , and

1 of compounds 34, 35, 36 – 45; atom numbers 9 and 2

of compounds 46 – 58. As it may be seen, there is no

correspondence 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 atoms

from the rigid heterocycle framework of all compounds,

we have discarded these options. Anyway, the RMS

pre-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 a

steric and electrostatic fit. The similarity index is in

accordance with the method proposed by Good and

co-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 the

steric and electrostatic factors (50%). We have used the

steric and electrostatic fit with the purpose of not only

obtaining the spatial orientation of each compound in

the 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 have

generated multiple conformations. As it will be seen

later, the LIV descriptors are volume descriptors, andso the steric – electrostatic fit is used to include in the

3D-QSAR-pharmacophore model a ‘sense’ of electronic

property.

2 .2 .6 . The local intersection olume ( LIV ) descriptors

After 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 the

van der Waals radii. Subsequently, we have calculated

the intersection volume (or the overlapped volume — the 3D-QSAR descriptors) between the molecular volu-

me of each compound (1 – 58) and the volume of each

hard sphere that composes the grid matrix. We have

named this intersection volume local intersection olume

(LIV) since it can be located in 3D space according to

its Cartesian coordinates. Consequently, for each com-

pound, we have a set of LIV descriptors (independent

variables) and their corresponding biological activities

(dependent variables). The molecular volume and the

intersection volume calculations were performed using

the tools available in the Search – Compare module of

the INSIGHT II program [29].

2 .2 .7 . Data reduction

Two levels of data reduction were considered. The

first, a preliminary data reduction, uses both of the

following filtering criteria; one filter to exclude LIV

descriptors the variance of which (self-variance) over

the whole set of compounds is zero; other to eliminate

LIV descriptors in which the compound occurrence is

less than six. The first criterion excludes useless vari-

ables and the second harmonizes the data, not taking

into account structural peculiarities of a few com-

pounds, both criteria functions as a noise data reduc-

tion. A second level of data reduction consists of

constructing 3D-QSAR models using a genetic al-

gorithm optimization; i.e. at the same time, a data

reduction (variable selection) and a model construction.

As a next step in this study we employed in 3D-QSAR

model building and optimization, the genetic function

approximation (GFA) [37], using the WOLF 6.2 soft-

ware [31], implemented with PLS regression [21].

2 .2 .8 . 3 D-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 the

crossover optimization was set to a rate of 200% at

each ten-crossover operation. The smoothing factor

was set at 0.01. It controls the number of independent

variables 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 default

values. The five best 3D-QSAR models as scored by the

lack-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 the

training data set. The test data set was used only for the

external validation process. The GA-PLS analysis was

performed using the WOLF 6.2 software [31].

3. Results and discussion

3 .1. Statistical parameters for the LIV 3 D-QSAR

model for GABAA/BzR ligands

The GA-PLS analysis gave us a series of good equa-

tions or good models. From them we chose the one

which had the highest activity prediction (Q2=0.722)

and the lowest number of variables (eight descriptors),

namely Eq. (1). The cross-correlation coef ficients of the

selected descriptors in Eq. (1) were calculated (data not

shown) in order to verify the non-redundancy of infor-

mation. The highest value was found for the pair of

descriptors LIV – 065 and LIV – 110 (R=−0.49), and

so we do not have high internal correlation among the

selected variables.




Fig. 3. Graphical representation of the LIV 3D-QSAR pharma-

cophore model for ligands of GABAA/BzR proposed in this work

using 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 their

maximum size.

data set, in accordance with the internal validation

process. The experimental af finity (pIC50 exp) and the

predicted af finity (pIC50 calc.) values can be seen in

Table 1 for the test data set.

3 .2 . Graphical representation for the LIV 3 D-QSAR

model for GABAA/BzR ligands

Fig. 3 shows a graphical 3D representation of thebest model (Eq. (1)) in which the LIVs are represented

as hard spheres in their maximal intersection volume

possible, using compound 1 as a template. Therefore,

this is not the representation of the LIV values for

compound 1. The LIVs that contribute positively for

the af finity are LIVs 110, 130, and 139, all of them

located on the core framework of compound 1. This

means that there is an almost constant contribution

from these variables to the af finity, since the com-

pounds are not so flexible. The LIVs that contribute

negatively for the af finity are LIVs 065, 074, 111, 140,and 168, all of them located around the core framework

of compound 1, more precisely at the northeast, the

south and the east sides of this compound. This means

that there is a steric limitation near these sides. On the

other 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), we

have observed a cooperative behavior between LIV – 110 of positive contribution and two LIVs of negative

contribution: LIV – 111 and LIV – 140. At a glance,LIV – 111 and LIV – 140 correspond to substituents on

R4 and R6 for compounds 1 – 33 and R1 and R3 forFig. 4. Examples of local intersection volumes (LIVs) for compounds

43 and 54 from the training data set, which are represented in the

same orientation as that of compound 1 in Fig. 3. LIVs of positive

contribution (gray): 110, 130, and 139. LIVs of negative contribution

(dark gray): 111 and 140.

Fig. 5. Superimposition of compound 1 (dark gray) (series I) to

compounds 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 af finity (pIC50 exp) and the calculated

af finity (pIC50 calc.) values for the training data set can

be seen in Table 1. The high Q2 value leaves us to

consider the model validated statistically (internal vali-

dation) since the model is generally considered inter-

nally predictive if Q20.5. The external validation

process corresponds to the af finity prediction of the test




Fig. 6. Experimental versus calculated (49 training compounds, )

and predicted (nine test compounds, ) af finity values (pIC50) for the

58 non-benzodiazepine compounds. The corresponding structures are

indicated in Table 1.

Fig. 4 shows a graphical representation of the LIVs

descriptors for compounds 43 and 54 (both from the

training data set) represented in their actual LIV size.

Compound 43 was selected for the reason that it is the

lowest active compound (pIC50exp=8.87) from series

III (the most active series) and compound 54 was

selected 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 (series

I) as an example.

3 .3 . The LIV 3 D-QSAR model ersus the Cook ’ s model

for GABAA/BzR ligands

LIV 3D-QSAR model was compared to Cook’s

Model (Fig. 1), the most comprehensive GABAA/BzR

model from the literature [7]. The following LIVs have

positive contribution to the af finity. LIV – 139 corres-

ponds to a hydrogen donor on the ligand molecule(Fig. 3, compound 1), and it is complementary to the

receptor sub-site A2 (hydrogen acceptor) on the Cook’s

receptor model. LIV – 110 corresponds to a hydrogen

acceptor on the ligand molecule, and it is complemen-

tary to sub-site H1 (hydrogen donator) on the receptor

model. LIV – 130 corresponds to a lipophilic region on

the ligand molecule and it corresponds to the sub-site

L3 on the receptor model.

The following LIVs have negative contribution to the

af finity. LIV – 065, LIV – 074, and LIV – 111 correspond

to regions around the northeast and the east side of theligand molecule; they are correlated to the sub-site S1 of

steric limitation on the Cook’s receptor model. LIV – 140 corresponds to a region around the southeast side

of the ligand molecule. It is correlated to the sub-site

H1 that represents a hydrogen donator on the receptor

model, so the occupation of this region is detrimental to

the af finity because it prevents hydrogen bonding be-

tween the ligand and the receptor. Finally, LIV – 168

corresponds to a region around the south side of the

ligand molecule, and is correlated to sub-site A2, which

represents 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 set

that own a substituent (R10=CH3) in a region that

corresponds to sub-site H2/A3 from Cook’s model; un-

fortunately this region was not described by our LIV

3D-QSAR model, probably because these compounds

were not included in the training data set. This implies

that the model itself has no quantitative parameters to

describe this interaction with this significant site. On the

other hand, the substituent in R7 (1 – 33 series), R5 (to

36 – 45 series) and R2 (to 46 – 58 series) confer on the

Table 2

Standard deviation (SD) of the residual values (experimental pIC50 –

calculated pIC50) calculated for training data set (49 compounds), test

data set (nine compounds), and entire data set (58 compounds)

SDNumber of compounds 2×SD

0.64 1.2749

0.979 1.94

58 1.390.69

compounds 46 – 58, but these substituents, depending

on the alignment of the molecule in the space, can be

overlaid also on LIV – 110.

We also have observed a cooperative behavior

between LIV – 139 of positive contribution and two

LIVs of negative contribution: LIV – 140 and LIV – 168.

All of them correspond to substituents on R6 and R7

for compounds 1 – 33, R5 for compounds 36 – 45, and

R2 and R3 for compounds 46 – 58, but, depending onthe alignment, these substituents can be overlaid on

LIV – 139. Both cooperative behaviors are due in part

to the distant substituents because they can modify the

electronic distribution and, consequently, the molecular

electrostatic potential provokes a change in the

similarity function and so, in the final alignment.

Qualitatively LIV – 065 and LIV – 074 (negative

contribution) could be joined in a unique region

corresponding to the following substituents: R2 and R3

for compounds 1 – 33, R and R1 for compounds 34 – 45,

and R1 (in this case, on the furthermost distant point of

R1) for compounds 46 – 58.




model a calibration that is more accurate in reprodu-

cing the unfavorable effect of a methyl group at the

hydrogen bonding site (sub-site A2) than other group.

3 .4 . Outliers from the LIV 3 D-QSAR model for

GABAA/BzR ligands

Fig. 6 shows the experimental af finity values versus

the calculated (training data set) and predicted (testdata set) af finity values for the 58 compounds. As we

can see in Fig. 5 and Table 1 we have the compounds

28, 33, 53, and 56 as outliers from the training set and

compounds 31 and 32 as outliers from the test set.

These compounds have residual values (experimental

pIC50 – calculated pIC50) higher than twice the standard

deviation (SD) (Table 2) of the residuals calculated on

the training data set [38]. Except for compound 53, all

the outlier compounds have negative residuals, which

means that the calculated (or predicted) activities were

higher than the experimental ones.

Comparing compound 28 (R4=OH) to compound

27 (R4=OCH3), both with similar experimental pIC50,

respectively, 6.24 and 6.60, we can observe that the

calculated pIC50 are, respectively, 7.76 and 5.75 (Table

2). We cannot explain this discrepancy in terms of only

steric factor of these substituents around the N7 (a

hydrogen 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 for

compound 28. Therefore, although compound 28 does

not make intramolecular hydrogen bonding between

the 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 conformation

not observed by the model, and so, the oxygen atom

from the hydroxyl group (R4) can enter in a competi-

tion with the N7 for the hydrogen donor site (H1) from

the 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 compounds

from 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’s

model, Fig. 1), and both compounds are from the test

set, it is obvious that our model was not ‘trained’ to

recognize this situation. In fact, our model does not

contemplate any LIV descriptor near the H2/A3 recep-

tor sub-site region.

The residual value for compound 33 (Table 1) shows

the model’s incapacity to distinguish electronic aspects

of the aromatic carbon 7, which makes it less active

than the nitrogen atom of compound 1 in the same

position. In other words, the occupation of LIV –

110 is

similar between compounds 1 and 33, even under the

effect of steric – electrostatic alignment. The greatest

difference is that the LIV – 130 of positive contribution

has a higher value for compound 1 than for compound

33, and for LIV – 140 of negative contribution, it is the

reverse. The result is that, when superimposing com-

pound 33 on compound 1, the compound 33 is lightly

dislocated to the right side after the steric – electrostatic

fit.

The outlier compounds 53 and 56 are both from theseries IV and as a group (compounds 46 – 58), excluding

compound 53 (pIC50exp=8.30), it has the lowest

af finity. The low af finity of series IV is probably due

the incapacity of the compounds to occupy all receptor

sub-sites at the same time, since this series has the

smaller size among the four series and it does not have

all the pharmacophore groups. Compound 53 is the

unique outlier among the compounds with experimental

pIC507.0, it is the only compound from series IV that

has the minimal pharmacophore requirements, which

are 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 the

sub-site H2/A3. Since this R1 substituent is not in the

core framework of the molecule, like N12 and R10=H

on series I and N1 on series II and III, but instead, it is

a flexible substituent, it can lose af finity by entropy

reason. 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 atom

at this position (X9). However, in spite of their residual

value of −1.49, it is calculated as active as compound

57, 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 outlier

in its own group.

4. Conclusions

In this work, we have developed a new descriptor to

3D-QSAR methodology: local intersection olume

(LIV). The LIV can be classified as a 3D local shape

descriptor in contraposition to the global shape descrip-

tors. The LIV is the intersection volume betweenmolecule atoms and a set of spheres of defined atom

size, which compose a tridimensional ‘box’, in analogy

to grid method. The molecules are included in this ‘box’

with a previously defined alignment to a template

molecule.

In order to compose a 3D-QSAR model for benzo-

diazepine receptor ligands, we have selected from the

literature 49 non-benzodiazepine compounds with rigid

framework structure as training data set. Using the

LIVs as descriptors, we have obtained and evaluated by

GA-PLS methods [21] a LIV 3D-QSAR model. The

LIV 3D-QSAR model has a good predictive capacity




according the cross-validation test by ‘leave-one-out’

procedure (Q2=0.72). The LIV 3D-QSAR model is in

agreement with some previous studies developed by

Cook and co-workers in which they proposed a com-

prehensive pharmacophore model for benzodiazepine

receptor ligands [7]. It showed a relevant correlation

with the pharmacophore groups pointed out in that

work. In addition, the af finity values were correctly

predicted for seven compounds from the test data setconsisting of nine compounds that were not included in

the training data set.

It should be noted that a similarity function [19,20]

was used to align the compounds in space. This

methodology shows that some substituents, even if not

interacting directly with the receptor, can cause a de-

crease in the receptor af finity of some compounds.

These substituents modify the compound’s steric and

electronic properties in such way that its alignment at

the receptor cavity becomes different from that

achieved 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 receptor

and, therefore, reduce the receptor af finity for that

compound. This effect causes the convergence of posi-

tions R6 and R7, to series I, and of positions R2 and

R3, to series IV, to the same space, affecting the

interaction with the receptor, as discussed before.

Work is underway to apply this methodology to

other classes of compounds. We are also modifying the

grid box atom size, in order to have a more refined

resolution. Another change is to include a percentage of

conformations from the conformational analysis, par-ticularly important for compounds with more confor-

mational freedom, and to associate an electronic

component in each LIV descriptor, like charges derived

from the molecular electrostatic potential.

Acknowledgements

We thank the Conselho Nacional de Desenvolvi-

mento Cientıfico e Tecnologico (CNPq) of the Brazil

government, the Coordenacao de Aperfeicoamento de

Pessoal de Nıvel Superior (CAPES) of the Brasil go-vernment, the Fundacao de Amparo a Pesquisa do

Estado do Rio de Janeiro (FAPERJ), the Fundacao

Universitaria Jose Bonifacio (FUJB), and the Conselho

de Ensino para Graduados e Pesquisa (CEPG) da

Universidade Federal do Rio de Janeiro (UFRJ) for

their support.

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