ORIGINAL RESEARCH

QSAR study of some CCR5 antagonists as anti-HIV agents usingradial basis function neural network and general regressionneural network on the basis of principal components

Mohsen Shahlaei • Armin Madadkar-Sobhani •

Afshin Fassihi • Lotfollah Saghaie • Elham Arkan

Received: 2 August 2011 / Accepted: 31 October 2011 / Published online: 16 November 2011

� Springer Science+Business Media, LLC 2011

Abstract Quantitative relationships between molecular

structures and bioactivities of a set of CCR5 inhibitor

derivatives were discovered. We have demonstrated the

detailed application of two efficient nonlinear methods,

general regression and radial basis function neural networks,

for evaluation of quantitative structure–activity relationships

of the studied compounds. Components produced by prin-

cipal component analysis were used as input of the devel-

oped nonlinear models. Comparison between predictability

of PC-GRNNs and PC-RBFNNs indicated that later method

has higher ability to predict the activity of the studied mol-

ecules. In order to design novel derivatives of inhibitors with

high activity and low side effects, and because experimental

and calculated activities of molecules employed in the model

development step, shown a good correlation, developed

PC-RBFNNs QSAR model was used to calculate inhibitory

activities of some suggested compounds.

Keywords QSAR � CCR5 antagonists �Principal components analysis �Radial basis function neural networks �General regression neural networks

Introduction

Acquired immunodeficiency syndrome (AIDS) is a fatal

disease for which no complete and successful chemotherapy

has been suggested so far. Human immunodeficiency virus

subtype 1 (HIV-1), a retrovirus of the lentivirus family, has

been found to be common in causing this disorder. HIV-1

generates a progressive immunosuppression disorder by

destruction of CD4?T lymphocytes, helper cells, which

attack directly against infections, and results in opportunistic

infections and death (Campiani et al., 2002). To decrease

HIV-1 replication, existing medications use a combination

of protease and reverse transcriptase inhibitors (Pomerantz,

1999). While suppression of viral replication through ther-

apy with protease and reverse transcriptase inhibitors delays

emergence of AIDS, the virus is not eliminated and the

immune system finally succumbs to infection (Chun and

Fauci, 1999; Finzi et al., 1999; Furtado et al., 1999).

In 1996, it was proved that infection of macrophages,

monocytes, and T cells by HIV-1 is mediated by interac-

tion with, as well as the cell surface molecule CD4, the

b-chemokine receptor CCR5 belonging to the G-protein

coupled receptors family (Dragic et al., 1996).

This finding opened a severe research attempts resulted

in development of CCR5 antagonists as potential anti-HIV

beneficial compounds.

M. Shahlaei (&)

Department of Medicinal Chemistry, Faculty of Pharmacy,

Kermanshah University of Medical Sciences, Kermanshah, Iran

e-mail: mohsenshahlaei@yahoo.com

M. Shahlaei � A. Fassihi � L. Saghaie

Department of Medicinal Chemistry, Faculty of Pharmacy,

Isfahan University of Medical Sciences, 81746-73461 Isfahan,

Iran

e-mail: Fassihi@pharm.mui.ac.ir

A. Madadkar-Sobhani

Department of Life Sciences, Barcelona Supercomputing Center,

C\ Jordi Girona 31, Edificio Nexus II, 08028 Barcelona, Spain

A. Madadkar-Sobhani

Department of Bioinformatics, Institute of Biochemistry and

Biophysics, University of Tehran, Tehran, Iran

E. Arkan

Department of Medical Nanotechnology, School of Advance

Medical Technologies, Tehran University of Medical Sciences,

Tehran, Iran

123

Med Chem Res (2012) 21:3246–3262

DOI 10.1007/s00044-011-9863-2

MEDICINALCHEMISTRYRESEARCH

In addition to its function in the development of HIV

infection, many studies show different roles for CCR5 and

its ligands in disorders, such as rheumatoid arthritis (Pipi-

tone and Pitzalis, 2000), multiple sclerosis (Sellebjerg

et al., 2000), transplant rejection (Fischereder et al., 2001),

and inflammatory bowel syndrome (Andres et al., 2000).

These studies propose that CCR5 receptor modulators

would have potential benefits in a wide variety of disorders.

In medical sciences field, many researchers are continu-

ously searching for new drug-like compounds having high

potency to treat AIDS. Using computer-aided drug-design

methods, such as quantitative structure–activity relationships

(QSARs), development of such ligands may be properly

performed and accelerated. Drug discovery process is often

faced with situations that a ligand should be discovered for a

target protein for which no experimentally verified structure is

yet available. The most well-known examples are possibly the

GPCRs, which play a key role in many physiological and

pathophysiological procedures. Today, 50% of all newly

launched drugs are targeted against GPCRs (Klabunde and

Hessler, 2002). Hence, designing an approach to suggest new

agonists and/or antagonists of GPCRs has a high degree of

importance. Due to the lack of knowledge about the 3D

structure of CCR5 and the way its antagonists interact with the

binding site, one of the best ways to recognize the initial lead

compounds is ligand-based method. Pharmacophore identi-

fication, structure–activity relationships (SARs), and QSARs

are some examples of ligand-based methods.

Over one hundred years after Fischer’s proposal of the

lock-and-key analogy (Fischer, 1894) and about half cen-

tury after the reports of Hansch, Fujita, Free, and Wilson

(Free and Wilson, 1964; Hansch and Fujita 1964) QSARs

have established as an extensively used approach, signifi-

cantly contributing to the drug-design procedure. QSAR

studies provide medicinal chemists valuable information

that is useful for drug design and prediction of drug activity

(Hansch et al., 1996, 2001; Schmidli, 1997). They are

frequently applied to develop a correlation between various

physicochemical properties of potential drug candidates

including quantum, geometrical, topological, and their

binding affinity towards a common biological target.

Several data mining methodologies have been devel-

oped to evaluate quantitative relationships between struc-

ture and activity. These relationships might express a linear

regression model or may provide to the researcher non-

linear regression ones. Multiple linear regression (MLR),

partial least squares (PLS), and principal component

regression (PCR) are most common linear regression

methods (Arkan et al., 2010; Saghaie et al., 1111; Saghaie

et al., 2010; Shahlaei et al., 2010b). Artificial neural net-

works (ANNs) and support vector machine (SVM) are

examples of nonlinear regression approaches to build up

mathematical relationships between selected descriptors

and activity of the compounds (Arkan et al., 2010; Saghaie

et al., 2010; Shahlaei et al., 2010a, b).

Nonlinear regression methods are often employed to

model the SARs because of the complexity of such rela-

tionships in many bioactive molecules. The development of

these methods also opened up the field to the simultaneous

analysis of a wider diversity of structures with potentially

varying modes of action and noncongeneric compounds

(Pompe et al., 1997).

Artificial systems emulate function of the brain, where a

very high number of information-processing neurons are

interconnected. These systems are known for their capability

to model a broad set of functions, including linear and

nonlinear, without knowing the analytic forms in advance.

The mathematical flexibility of ANNs praises them as an

efficient method for pattern recognition and regression and

constructing predictive models. A particular benefit of

ANNs is their intrinsic ability to show nonlinear relation-

ships between the dependent and independent variables

without using an explicit mathematical equation(s).

Although there are a number of different neural networks

models, the most frequently used type of neural network in

QSAR is the feed-forward back-propagation network.

This algorithm has some disadvantages such as being

caught in local minima during learning phase, very poor

convergence rate, time-consuming procedures, and diffi-

culty in explicit optimum network configuration (Walczak

and Massart, 2000).

The radial basis function neural networks (RBFNNs) let

us construct regression model between independent and

dependent variables using a fast linear approach. RBFNNs

have advantages of short training time and reaching to the

optimal unique solution by attaining the global minimum

of error surface during training of network. The topology

and parameters of developed RBFNNs are straightforward

to optimize (Specht, 1991; Tetteh et al., 1998).

The generalized regression neural network (GRNN) is a

special kind of normalized radial basis function networks,

where the sigmoid activation functions often used in neural

networks are replaced by radial basis functions (Chtioui

et al., 1999).

Compared with the back-propagation neural networks,

the architecture of the GRNNs, namely the numbers of

layers and units, is defined by the numbers of objects and

predictor in the training dataset. In this algorithm, the only

one training parameter to be optimized is the width (spread)

of radial basis functions. Due to the straightforwardness of

the network structure and its implementation, it has been

extensively used in many fields (Celikoglu, 2006; Klocker

et al., 2002; Mosier and Jurs, 2002; Niwa, 2003).

Thanks to the modern softwares and hardwares, numerous

descriptors (variables in QSAR) can be easily obtained in a

short time. To extract the most relevant and significant

Med Chem Res (2012) 21:3246–3262 3247

123

information from such raw data, using of multivariate

regression methods and also data compression and/or vari-

able selection is necessary. Multivariate regression methods

are used to develop a quantitative relation, i.e., a model,

between the calculated descriptors, stored in a data matrix, X,

and the activities of compounds, stored in a data matrix,

called Y. One of the most common problems in multivariate

regression methods is multicollinearity between variables.

Multicollinearity occurs when ratio of descriptors to con-

sidered compounds is large. This situation makes the

developed model unstable. So reduction of dimensionality of

original descriptors is necessary. One of the most common

ways to reduce the number of variables without missing

useful information is principal component analysis (PCA).

PCA is an approach suitable for overcoming the insta-

bility in developed model related to multicollinear

descriptors. PCA is used to compress a pool of descriptors

into principal components (PCs) as new variables. PCA

approach assumes that despite the numerous number of

descriptors the QSAR model is governed by a compara-

tively small number of latent variables namely PCs.

In the present study two different algorithms of ANNs

are exploited to correlate the anti-HIV activity of 48 drug-

like molecules with the PCs extracted from calculated

structural descriptors. These algorithms are (i) RBFNNs

and (ii) GRNNs.

We are going to use the obtained information from

QSAR to design novel drug-like compounds in this study.

Here, key goal was to model potentially active anti-HIV

molecules by using the two nonlinear models namely

PC-RBFNNs and PC-GRNNs.

Methods

Descriptor generation and assigning calibration and test

sets

The in vitro biological activity data used in this study were

CCR5 inhibitory (in terms of log IC50), of a set of 48

compounds selected from literature (Dorn et al., 2001;

Finke et al., 2001). General chemical structures and the

structural details of these compounds as well as biological

activity data are given in Table 1.

In order to calculate the theoretical molecular descriptors,

molecular structures were built by Hyperchem version 7.0 and

were optimized using the AM1 algorithm. A gradient cutoff of

0.01 was used for all geometry optimizations. The resulted

geometries were transferred into Dragon program (developed

by Milano Chemometrics and QSAR Group) (Todeschini

et al., 2002). It was used for calculation of a large number of

descriptors including 16 different groups. In the computation

of descriptors with dragon, descriptors with constant value for

all compounds were eliminated. The name and number of

calculated descriptors are reported in the Table 2. In addition

to these groups of descriptor, a number of quantum-electronic

descriptors, such as frontier orbital energies (HOMO and

LUMO), most positive charge, lowest negative charge

and indices of electronegativity, electrophilicity, hardness,

and softness were calculated according to the method pro-

posed by Thanikaivelan et al. (2000). In addition, some different

descriptors, such as Log P, surface area, and polarizability

were calculated by Hyperchem for each molecule.

In order to test the final model performances, about 20%

of the molecules (10 out of 48) were selected as external

test set molecules (Table 1). The best situation of this stage

of model building is dividing dataset to guarantee that both

training and test sets individually cover the total space

occupied by original data set. Then ideal splitting of data

set as each of objects in test set is close to at least one of the

objects in the training set. Various methods were used for

splitting the original data set to the training and test sets.

According to Tropsha the best models would be built when

Kennard and Stone algorithm was used (Tropsha et al.,

2003). So this algorithm was applied in this study (Kennard

and Stone, 1969). This method has some advantages: the

training set molecules map the measured region of the

input variable space completely with respect to the induced

metric. The other advantage is that the test molecules all

fall inside the measured region.

All calculations were performed in the MATLAB

(version 7.1, MathWorks, Inc.) environment.

Model development

PCA was used to compress a pool of descriptors into PCs

as new variables. In the PCA, the first step is data pre-

processing on the calculated descriptors by mean centering

and autoscaling. Suppose Xi,j be the column mean-centered

and autoscaled matrix of descriptors for i samples and

j descriptors, and yi,1 the vector of the activities (pIC50).

After generation of PCs using matrix Xi,j, a new matrix,

containing scores of PCs, is created. Then, we use these

scores as new variables for regression. Scores as new

variables possess two interesting properties:

(i) These new variables are sorted as the information

content (variance) that they explain decreases from the

first PC to the last one. As a result, the last PCs can be

deleted, because they do not have useful information.

(ii) PCs are orthogonal, resulting to solving correlation

problem that exist in the pool of descriptors.

As a matter of fact, PCR is MLR using the scores matrix

as new variables for model building.

The using of calculated PCs as input variables for

GRNNs is referred as PC-GRNNs. For selecting optimum

3248 Med Chem Res (2012) 21:3246–3262

123

Table 1 General structures and details of the compounds used in this study

N

Cl

Cl

S

Me

OO

R2

N

S

On

Compound Structure

n R2

1 2 2-Thienyl

2 1 NMe2

3 1 Benzyl

4 1 Methyl

5 1 n-Octyl

6 1 Cyclopentyl

7 1 Cyclohexyl

8 1 2-Cl-Phenyl

9 1 3-Cl-Phenyl

10 1 4-Cl-Phenyl

11 1 4-MeO-Phenyl

12 1 4-Ph-Phenyl

13 1 Naphth-1-yl

14 1 Naphth-2-yl

15 1 Indan-5-yl

16 1 Pyridin-3-yl

17 1 Quinolin-8-yl

18 1 Quinolin-3-yl

19 1 1-Me-Imidazol-4-

yl

20 2 3-NO2-Phenyl

21 2 4-NO2-Phenyl

22 0 Phenyl

23 1 Phenyl

24a 2 Phenyl

25 1 2-Thienyl

Med Chem Res (2012) 21:3246–3262 3249

123

Table 1 continued

N

N

S

Me

O O

Z

Y

X

Cl

Compound X Y–Z

26a – –SCH2–

27 – –S(O)CH2–

28a – –S(O)2CH2–

29a – –CH2CH2–

30 – –NHCH2–

31 – –C(O)CH2–

32a – –C(O)NH–

33 – –C(O)N(Me)–

34a – –C(O)NHCH2–

35 – –NHC(O)CH2–

36 – –CH(OH)CH2–

37 –CH2– –O–

N

N

S

Me

O OY

Cl

R

Compound R Y

38a C6H5– –CH–

39 C6H5– –N–

40a 2-MeC6H4– –N–

41 2-MeC6H4– –CH–

42 2-MeOC6H4– –CH–

43 3-CF3C6H4– –CH–

44a 4-ClC6H4– –CH–

45 4-FC6H4– –CH–

46 C6H5CH2– –CH–

47 C6H5CH2CH2– –CH–

48 C6H5CH2CH2CH2– –CH–

a Molecules selected as test set

3250 Med Chem Res (2012) 21:3246–3262

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number of PCs to use as input of model, root mean square

error of cross validation (RMSECV) was used. The main

advantage of GRNNs is that it does not require iterative

learning (Esbensen et al., 1994). It is an interesting prop-

erty that makes the method very attractive for model

building and hence GRNNs is much faster than the well-

known back-propagation neural network (Specht, 1991).

A GRNN consists of four neuron layers: input, pattern

(radial basis), summation, and output layers that are shown

Fig. 1 schematically. Input layer receives the input X block

and distributes it to the neurons in the next layer for pro-

cessing that is radial basis layer or pattern layer. Thus, the

number of neurons in the first layer is equal to the number

of columns, n, in the input X block. Each neuron in the

pattern layer will then generate an intermediate output by

using of Gaussian radial basis function. The duty of neu-

rons in the subsequent summation layer is performing

summation of outputs of pattern layer. This layer consists

of two types of neurons, numerator and denominator neu-

rons. Number of numerator neurons is equal to number of

elements of output y vector. Duty of these types of neurons

is computation of weighted sum of the outputs from the

previous layer. Another neuron in this layer, the denomi-

nator neuron, has a different operation. Duty of this single

neuron is simple summation of outputs of pervious layer.

The neurons in the output layer will then carry out divi-

sions of the sums computed by neurons in the summation

layer.

GRNN is able to approximate any relationship between

X block and its y vector. The operation of approximation of

y vector by network was performed during training of

network. After figuring out the relationship between input

and output of networks, this relationship was used for

computation of the output of networks. In the GRNNs

model, approximation of an output vector with respect to

an X block can be regarded as finding the expected value of

y conditional upon the X block.

The predicted value of the y vector yðxÞ is the most

probable value, E [y/x], which is determined by following

equation.

yðxÞ ¼ E½x=y� ¼Rþ1�1 y:f ðX; yÞdyRþ1�1 f ðX; yÞdy

where y is the output value estimated by GRNNs, X is the

input vector for the estimation of y, and f (X, y) is the joint

probability density function of X and y that can be

calculated by Parzen’s nonparametric estimator.

Substituting Parzen’s nonparametric estimator for joint

probability density function and calculating the

integrations leads to the following equation of GRNNs:

yðX; yÞ ¼Pn

i¼1 yi exp�D2

i

2r2

h i

Pni¼1 exp

�D2i

2r2

h i

where r is spread of network (smoothing parameter) and

D2i = (xi - x)T - (xi - x). Training the GRNNs involves

finding the optimal values for the r parameters in above

equation.

In another ANNs model building, The combination of

PCs of X matrix as input of radial basis function neural

networks is referred as PC-RBFNNs.

In PC-RBFNNs same with PC-GRNNs, the original data

matrix is reduced to an orthogonal PC and their scores are

used as inputs for RBFNNs. In PC-RBFNNs model, the use

Table 2 Calculated theoretical groups of descriptors used in this

study and the number of descriptors remained after removing constant

descriptors

No. Type of descriptors No. of descriptors

1 2D autocorrelations 98

2 3D-MoRSE descriptors 160

3 Aromaticity indices 4

4 Atom-centered fragments 38

5 BCUT 64

6 Charge descriptors 14

7 Constitutional 36

8 Functional groups 18

9 Galvez topological charge indices 21

10 Geometrical descriptors 36

11 GETAWAY 196

12 Molecular walk counts 19

13 Randic molecular profiles 31

14 RDF descriptors 138

15 Topological 214

16 WHIM descriptors 93

17 Quantum chemical 16

18 Chemical descriptors 6

19 All calculated descriptors 1156

Fig. 1 General GRNNs construct

Med Chem Res (2012) 21:3246–3262 3251

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of scores instead of original descriptors reduces input

nodes, so training time of the network is shortened. Also,

noisy information and random error in the original data will

be excluded. So using PCs generates a more accurate

RBFNNs model. Here number of independent variables is

very large, so data reduction is very necessary.

The main advantage of radial basis function neural

networks is that it does not require iterative learning. It is

an interesting property that makes the method very

attractive for model building and hence RBFNNs is very

faster than the well-known back-propagation neural net-

work. The complete explanation behind the theory of radial

basis function neural networks is adequately described

elsewhere (Shi et al., 2006; Yao et al., 2004). Here only a

brief description of this type of neural network is presented.

RBFNNs include three layers: input layer, hidden layer,

and output layer as presented in Fig. 2 schematically. Each

neuron in each layer is fully connected to the next layer but

there is not any connection between neuron in a given

layer. No processing occurs on the input information in the

input layer and the duty of this layer is only distribution of

input to the hidden layer. In the hidden layer of RBFNNs

there are a number of radial basis function units (nh) and

bias (bk). Each hidden layer unit represents a single radial

basis function, with associated center position and width.

In the hidden layer each neuron applies a radial basis

function as nonlinear transfer function to operate on the

input information coming from the previous layer. The

most often used RBF is Gaussian function that is charac-

terized by a center (cj) and width (rj). By measuring the

Euclidean distance between input vector (x) and the radial

basis function center (cj) the RBF function performs the

nonlinear transformation using following equation in the

hidden layer:

hjðxÞ ¼ expð� x� cj

��

��2=r2

j Þ

where hj is the notation for the output of the jth RBF unit.

For the jth RBF, cj and rj are the center and width,

respectively. The operation of the output layer is linear,

which is given in:

ykðxÞ ¼Xnh

j¼1

wkjhjðxÞ þ bk

where yk is the kth output unit for the input vector x, wkj is

the weight connection between the kth output unit and the

jth hidden layer unit, and bk is the bias.

In order to optimize RBFNNs, centers, number of hidden

layer units, width, and weights should be selected. Random

subset selection, K-means clustering, orthogonal least-

squares learning algorithm, and RBF-PLS are various ways

for choosing the centers. The same widths of the radial basis

function networks for all the units or different widths for

each unit could be selected for optimizing RBFNNs.

In this article, Gaussian functions with a constant width,

which was the same for all units were selected. Using

training set molecules the centers were optimized by for-

ward subset selection routine. After the selection of opti-

mum values of centers and width of radial basis functions

the connection weight between hidden layer and output

layer was adjusted using a least-squares solution.

The overall performance of RBFNNs is evaluated in

terms of root mean square error cross validation

(RMSECV) according to the following equation:

RMSECV ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPns

i¼1 ðyk � ykÞ2

ns

s

where yk is the experimental value of biological activity, yk

is the output predicted activity of network calculated by

cross validation. ns is the number of compounds in the

analyzed set.

Model validation, predictability, and robustness

of model

To demonstrate that the resulted models have good pre-

dictability and reliability, some different methods of eval-

uation of model performance have been used. Here, R2,

which presents the explained variance for a given set, was

used to determine the goodness of model’s fit performance.

In addition, the prediction performance of the generated

models must be estimated in order to build a successful

QSAR model. In this study, we evaluated the prediction

performance of developed models using the root mean

square error (RMSE).

Cross validation is a technique used to explore the

reliability of statistical models. Root mean square errorFig. 2 The architecture of PC-RBFNNs

3252 Med Chem Res (2012) 21:3246–3262

123

cross validation (RMSECV) as a standard index to measure

the accuracy of a modeling method which is based on the

cross validation technique and R2LOO as another criterion of

predictability of developed models were applied.

According to Tropsha High R2LOO does not routinely

mean a high predictability of the developed model

(Tropsha et al., 2003). Thus, the high value of R2LOO is the

necessary but not the sufficient condition for the developed

model to have a high predictability. In addition to a high

R2LOO, a reliable model should also be characterized by a

high R2 between the calculated and experimental values of

compounds from a test set (Afantitis et al., 2006).

Also, some criteria by Tropsha were suggested, if these

criteria were satisfied then it can be said that the model is

predictive (Tropsha et al., 2003). These criteria include:

R2LOO [ 0:5

R2 [ 0:6

R2 � R20

R2\0:1

R2 � R020

R2\0:1

0:85\k\1:15 or 0:85\k0\1:15

R2 is the correlation coefficient of regression between the

predicted and observed activities of compounds in training

and test set. R20 is the correlation coefficients for regres-

sions between predicted versus observed activities through

the origin, R020 is the correlation coefficients for regressions

between observed versus predicted activities through the

origin, and the slope of the regression lines through the

origin are assigned by k and k0, respectively. Details of

definitions of parameters, such as R20, R

020 , k, and k0 are

presented obviously in literature and are not written again

here for shortness (Tropsha et al., 2003).

Also, in addition, according to Roy and Roy (2008) the

difference between values of R20 and R

020 must be studied and

given importance. They suggested following modified R2 form

R2m ¼ R2 1�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 � R2

0

q����

����

� �

If R2m value for given model is [0.5, indicates good

external predictability of the developed model.

The actual predictability of each model developed on the

training set is confirmed on an external test set (Roy and

Roy, 2008) and is calculated from: R2p ¼ 1� PRESS=SD;

where PRESS is the sum of squared differences between the

measured activity and the predicted value for each com-

pound in the test set and SD is the sum of squared deviations

between the measured activity for each molecule in the test

set and the mean measured value of the training set.

Developed models are also tested for reliability and

robustness by Y-randomization testing: new models are

recalculated for randomly reordered response. We provided

evidence that the proposed models are well founded, and

not just the result of chance correlation, by obtaining new

models on randomized response with significantly lower R2

than the original models. If the results show high R2, it

implies that an acceptable QSAR model cannot be

obtained.

Results and discussion

At the first, a lot of descriptors (columns of X block) were

calculated for each molecule using optimized structures of

molecules.

Logarithms of the inverse of biological activity

(Log 1/IC50) data of 48 molecules were used to get the

relationship with independent variables.

Before the model development, and due to the quality of

data, a pretreatment of the original data was necessary.

Thus, autoscaling and deletion of columns with zero vari-

ance were performed.

After deleting zero variance columns of X block, PCs

analysis was performed on the pool of descriptors. PCA is a

valuable multivariate statistical approach in which new

orthogonal variables called PCs are derived as linear

combinations of the original variables. These new gener-

ated variables are sorted on the basis of information content

(i.e., explained variance of the original dataset). Priority of

PCs demonstrates their higher quota in the explained var-

iance, so most of the information is retained at the first few

PCs. A main characteristic in PCA is that the generated

PCs are uncorrelated. PCs can be used to obtain scores

which present most of the original variations in the original

data set in a smaller number of dimensions.

Among the generated PCs 16 eigenvalue ranked PCs

(eigenvalues [ 1) were selected for next model building

(Table 3). These PCs can explain more than 86.11% of the

variances in the original descriptors data matrix. Therefore,

we restricted the next model building to these 16 PCs.

To determine degree of homogeneities in the original

data set and recognize potential outliers and clusters in the

studied molecules, PCA was performed within the calcu-

lated descriptors space for all the molecules. Using three

more significant PCs (eigenvalues [ 1), which explains

53.63% of the variation in the data (30.25, 15.52, and

7.86%, respectively), distribution of molecules over the

three first PCs is shown in Fig. 3. As can be seen, none of

the molecules are outlier or no cluster is observed.

After evaluating outliers and dividing the molecules into

two parts, calibration and validation sets on the basis of

Kennard and Stones algorithm, model building using cal-

ibration set was performed. PCR as linear model show poor

results. Hence nonlinear models were applied as regression

methods that are PC-RBFNNs and PC-GRNNs. Developed

Med Chem Res (2012) 21:3246–3262 3253

123

models were used to predict the activity of molecules in

test set to evaluate performance of the developed models.

PC-RBFNNs

As it was discussed above, radial basis neural network was

chosen for constructing nonlinear model. To avoid the

problem of collinearity, calculated PCs of original

descriptors were used. One of the most important factors

determining quality of generated model is number of PCs

selected for model building. If the selected number of PC is

lower than optimum number, the derived model is called

underfitted model and may not calculate true activity of

molecules. On the other hand, if too many PCs are used the

network is overfitted. Thus for initial training of network,

we chose ten hidden nodes and the spread equal to 1.0 and

these values were used for finding optimum number of

PC-RBFNNs components. This optimization was performed

by jointly analyzing RMSEC and RMSECV. As it is shown

in Fig. 4a, two PCs were selected as optimum number of

PCs. The performance of PC-RBFNNs model is signifi-

cantly influenced by parameters of networks namely the

number of radial basis functions nh and spread of networks.

With two PCs, a response surface methodology was

used to optimize nh and spread of networks. As is shown in

Fig. 5 a contour surface plot of RMSECV as a function of

nh and spread was plotted. nh was changed from 1 to 50 and

spread from 0.1 to 3 in increments of 0.1. These ranges

were selected according to the previous studies. The results

show that a PC-RBFNNs with 13 nodes in hidden layer

and spread of 2.3 resulted in the optimum network

performance.

R2CV, the ‘leave-one-out’ (LOO) cross-validated coeffi-

cient, is a practical and reliable method for testing the

predictive performance and stability of a regression model.

LOO approach involves developing a number of models

with one molecule deleted at a time. After developing each

model, the deleted data are predicted and the differences

between the experimental and predicted activity values are

Table 3 Eigenvalues of calculated PCs, % of explained variances

and cumulative variances

PC No. Eigenvalue % Variance

explained

Cumulative

variance

1 370.59 30.25 30.25

2 190.13 15.52 45.77

3 96.32 7.86 53.64

4 78.74 6.43 60.06

5 62.97 5.14 65.20

6 44.34 3.62 68.82

7 36.76 3.00 71.82

8 27.75 2.27 74.09

9 24.70 2.02 76.11

10 22.54 1.84 77.95

11 21.24 1.73 79.68

12 18.43 1.50 81.19

13 18.25 1.49 82.68

14 15.08 1.23 83.91

15 14.17 1.16 85.06

16 12.85 1.05 86.11

Fig. 3 Principal components analysis of the calculated descriptors of all molecules in data set

3254 Med Chem Res (2012) 21:3246–3262

123

calculated. R2CV values are then calculated according to the

following formula:

R2CV ¼ 1�

Pni¼1 ðyi � yiÞ2

Pni¼1 ðyi � �yÞ2

where yi is the actual experimental activity, �yi the average

actual experimental activity and yi is the predicted activity

of compound i computed by the new regression equation

obtained each time after leaving out one datum point

(No. i).

The developed model was trained using the data of

training set and it was evaluated by test compounds. For a

QSAR model, internal validation, although essential and

obligatory, does not adequately assure the predictability of

a model. In fact, we are strongly persuaded from pervious

experience that models with high apparent predictability,

emphasized only by internal validation approaches, can be

unpredictive when confirmed on new compounds not

applied in developing the model. Thus, for a stronger

assessment of model applicability for prediction on new

compounds, external validation of the generated models

should always be carried out.

In the present study, the generated models were vali-

dated externally by the additional test set.

The predicted values of inhibitory activity of the studied

compounds resulted from the optimized PC-RBFNNs

procedures are reported in Table 4, in association with

relative error of prediction (REP). The plots of predicted

activity versus experimental activity and the residuals

(predicted activity–experimental activity) versus experi-

mental activity value, obtained by the PC-RBFNNs

Fig. 4 Optimization number of PCs using root mean square error of

training set (RMSET) and root mean square error of cross validation

(RMSECV) in a PC-RBFNNs and b PC-GRNNs

Fig. 5 Optimization of number of nodes in hidden layer and spread in PC-RBFNNs using RMSECV

Med Chem Res (2012) 21:3246–3262 3255

123

Table 4 The experimental

pIC50 and the predicted values

of the data set and relative error

of prediction (REP)

Compound Activity Predicted activity

(PC-RBFNNs)

REP

(PC-RBFNNs)

Predicted activity

(PC-GRNNs)

REP

(PC-GRNNs)

1 5.921 5.889 -0.005 5.681 -0.041

2 5.569 5.792 0.040 5.382 -0.033

3 7.000 7.168 0.024 6.984 -0.002

4 6.824 7.157 0.049 6.982 0.023

5 5.745 5.888 0.025 5.981 0.041

6 6.301 6.199 -0.016 5.982 -0.051

7 7.301 7.181 -0.016 7.001 -0.041

8 6.347 6.482 0.021 6.683 0.053

9 6.000 5.843 -0.026 6.185 0.031

10 6.456 6.727 0.042 6.585 0.020

11 6.456 6.514 0.009 6.535 0.012

12 6.000 6.182 0.030 6.185 0.031

13 5.585 5.807 0.040 5.222 -0.065

14 5.469 5.262 -0.038 5.279 -0.035

15 5.229 5.455 0.043 5.082 -0.028

16 5.071 5.267 0.039 5.079 0.002

17 4.854 4.722 -0.027 4.981 0.026

18 6.000 5.821 -0.030 5.983 -0.003

19 6.000 6.106 0.018 6.079 0.013

20 6.097 6.299 0.033 5.979 -0.019

21 6.155 6.410 0.041 6.284 0.021

22 6.398 6.452 0.008 6.389 -0.001

23 6.398 6.180 -0.034 6.230 -0.026

24 6.398 6.221 -0.028 6.182 -0.034

25 5.444 5.184 -0.048 5.284 -0.029

26 6.222 6.404 0.029 5.986 -0.038

27 6.155 6.270 0.019 6.280 0.020

28 6.000 6.098 0.016 5.982 -0.003

29 6.046 6.271 0.037 6.074 0.005

30 5.921 5.800 -0.020 6.086 0.028

31 5.469 5.231 -0.043 5.166 -0.055

32 6.523 6.311 -0.032 6.775 0.039

33 5.824 5.833 0.002 5.982 0.027

34 6.222 6.334 0.018 6.385 0.026

35 5.155 4.864 -0.056 4.986 -0.033

36 4.620 4.867 0.054 4.985 0.079

37 5.398 5.635 0.044 5.287 -0.020

38 5.000 4.749 -0.050 5.089 0.018

39 6.155 6.297 0.023 6.088 -0.011

40 6.456 6.538 0.013 6.388 -0.010

41 5.921 5.702 -0.037 5.856 -0.011

42 6.000 5.987 -0.002 5.889 -0.019

43 5.699 5.401 -0.052 5.889 0.033

44 6.602 6.409 -0.029 6.485 -0.018

45 5.602 5.893 0.052 5.782 0.032

46 6.187 6.328 0.023 5.886 -0.049

47 6.222 6.323 0.016 6.386 0.026

48 7.301 7.195 -0.014 6.982 -0.044

3256 Med Chem Res (2012) 21:3246–3262

123

modeling, and the random distribution of residuals about

zero mean are shown in Figs. 6a and 7a, respectively.

Residuals both for training and test sets are distributed

normally around zero (the mean value), therefore the

nonlinear correlation between activity and selected PCs is

reliable. The plot of calculated versus experimental activity

tells the same theme, adding the information that visually

the calculated values appear to capture the experimental

values very well.

The statistical parameters and figures of merit as well as

Tropsha and Roy parameters for determining the predict-

ability of the developed model are presented for the best-

fitted model in Table 5. As presented in Table 5 the model

gave an RMSE of 0.180 for the training set and 0.216 for

the test set, and the corresponding correlation coefficient R2

of 0.901 and 0.916, respectively. Furthermore, on the basis

of criteria recommended by Tropsha and also R2m by Roy,

the obtained model is predictive.

The PC-RBFNNs was further validated by applying the

Y-randomization test. In particular, 10,000 random shuf-

fles of the Y-vector gave low R2 values. This shows that

the developed PC-RBFNN model was not obtained by

chance.

PC-GRNNs

In another model, a GRNN was employed. Same with

PC-RBFNNs, input of networks is PCs. Leave-one-out

cross validation procedure was used to choose the optimum

number of PCs for model formation. The number of PCs

that produced the least RMSECV was selected as optimum

value. A plot of RMSECV and RMSET for PC-GRNNs

model as a function of the number of factors is shown in

Fig. 4b. Based on this figure, four PCs was selected as the

optimum number. GRNN was trained to obtain the rela-

tionship between the PCs and activity of molecules. As

explained above, for the GRNNs, there is only one

parameter: ‘‘spread’’, which is the width that must be

optimized. RMSECV of the training set was applied to

choose the optimized value of spread. Figure 8 is the plot

of RMSECV versus spread and the minimum value was

chosen as the optimal value of spread, which was 1.5.

After determining the optimum value of spread, the

network was trained using training data and model was

evaluated by prediction of molecules in the test set. The

predicted activities by using this developed model are lis-

ted in Table 4 and are plotted in Fig. 6b. Same as

PC-RBFNNs, the calculated values are in good agreement

Fig. 6 Plots of predicted activity vs. actual concentration activity for

a PC-RBFNNs and b PC-GRNNsFig. 7 Scatter plots of the residuals vs. experimental activity for

a PC-RBFNNs and b PC-GRNNs

Med Chem Res (2012) 21:3246–3262 3257

123

with the experimental values. Also for investigating the

existence of any systematic error in the developed PC-

GRNNs model, the residual of calculated activity was

plotted versus experimental activity and is shown in the

Fig. 7b. As can be seen, propagation of residuals on both

sides of zero shows that there is not any systematic error in

the developed model. The figures of merit and criteria for

determining predictability of model for the GRNNs model

are reported in Table 5. In this table R2 that is a criterion of

goodness of fit was obtained for two sets and the high value

of this parameter indicates a good fit between input of

network and predicted activities values of compounds.

As a result, with respect to the developed GRNNs

model, it was found that correctly opted and trained neural

Table 5 Models and their validation and predictive ability parameters

Model R2 R2LOOCV RMSET RMSECV R2

p RMSEP PRESSR2�R2

0

R2

R2�R020

R2 k k0 R2m

PC-RBFNNs 0.901 0.881 0.180 0.213 0.916 0.215 1.244 -0.106 -0.107 0.995 1.003 0.621

PC-GRNNs 0.883 0.867 0.188 0.223 0.916 0.216 1.350 -0.132 -0.131 1.007 0.998 0.581

R,LOOCV2 = square regression coefficient for leave-one-out cross validation

RMSET = root mean square error of training set

RMSECV = root mean square error of cross validation

Rp2 = square regression coefficient for prediction set

RMSEP = root mean square error of prediction set

PRESS = predicted error sum of square for training set

k ¼P

yi yiPy2

i

k0 ¼P

yiyiPy2

i

Fig. 8 Optimization of spread using RMSECV in PC-GRNNs

Fig. 9 The overlaid 3D

structures of the some

derivatives used in this study

Fig. 10 General structure and highlighted subunits

3258 Med Chem Res (2012) 21:3246–3262

123

network could practically represent dependence of the

activity of CCR5 inhibitors on the extracted PCs from

calculated descriptors of molecules.

To evaluate the PC-GRNNs, a leave one out cross val-

idation technique, similar to that used for the PC-RBFNNs

model, was performed. The results are summarized in

Table 5.

Inspection of the results reveals the stability of the gener-

ated model. With the purpose of exhibiting that PC-GRNNs

does not consequence from happenstance, an extensively used

method to determine the model robustness is the so-called

Y-randomization. It consists of shuffling the experimental

activity in such a way that activities do not correspond to the

respective molecules. After analyzing 1,000 cases of Y-ran-

domization, R2 values obtained using this procedure were very

small when compared to the one found considering the true

calibration (R2 = 0.88). In this way, the robustness of the

developed PC-GRNNs model could be evaluated, indicating

that the regression was not a sequence of chance correlation

and therefore results in a true SAR.

As it can be seen in Table 5, the statistical parameters of

the results obtained from two studies for the same set of

compounds. The RMS errors of the PC-RBFNNs model for

the training, the test, and in the cross validation procedure

were lower than that of the model proposed in the

PC-GRNNs method. The correlation coefficient (R2) given

by the PC-RBFNNs model was higher than that of the

models in the PC-GRNNs method. From the Table 5, it can

be seen that the PC-RBFNNs model gives the highest R2

and low error values, so this model gives the most satis-

factory results, compared with the results obtained from the

PC-GRNNs method.

Suggestions of new CCR5 inhibitors

As a final point, one could dispute that how researchers can

interpret the developed models using PCs or how devel-

oped models can be applied to propose novel compounds

with improved activity. Said another way, what does the

developed models mean to medicinal chemists? As dis-

cussed above, the calculated PCs do not mean physico-

chemically, but they may be employed for building

statistical models which help the medicinal chemist limit

the number of compounds to be synthesized. For instance,

medicinal chemist can propose a training set comprised of

molecules which have the characters of two or more

chemical classes with the smallest amount of similarity.

Then he/she can use the developed models to predict the

activity of his/her proposed molecules. This practice may

lead to the introduction of biologically active molecules.

Table 6 Structures and details of the proposed molecules as novel CCR5 inhibitors

N

N

S

Me

O O

R2

Cl

R1

N

N

S

Me

O O

R2

Cl

R1

S

O

(A) (B)

Compound R1 R2 Type Activity

S1 Cl Benzyl A 7.182

S2 Cl Methyl A 7.167

S3 Cl Cyclohexyl A 7.172

S4 H Methyl A 7.174

S5 H Cyclohexyl A 7.186

S6 H Benzyl B 7.187

S7 H Methyl B 7.183

S8 H Cyclohexyl B 7.183

Med Chem Res (2012) 21:3246–3262 3259

123

In order to investigate the electronic requirements of

active CCR5 antagonist compounds, the molecular struc-

tures of all the studied derivatives were built with Hyper-

chem. Gas-phase full geometry optimization for the studied

drug-like molecules was performed. The structures were

optimized with ab initio method at the hybrid functional

B3LYP (Becke’s three-parameter (Becke, 1993)) and the

large-size basis set 6-311G**. Full optimization of all bond

lengths and angles was performed. Because the calculated

values of the electronic descriptors of the drug-like com-

pounds will be influenced by the geometry used, in the

current investigation we try to employ the most established

conformations of the studied molecules. To avoid the

caught in the local minima of geometry optimization pro-

cess, procedure was run many times with different starting

points for each compound, and in each molecule confor-

mation with the lowest energy was selected to use in next

steps of evaluation. The overlaid 3D structures of some of

the studied molecules (from the benzyl subunit) are shown

in Fig. 9. As it is seen the orientation of the sulphonyl

subunit of the molecules remains quite unchanged when

the structural pattern of the –R group or the number of

chlorine atom changes in the phenyl ring of the benzyl

subunit. To include the effects of the electronic descriptors

of the molecules on their CCR5 inhibitory activity, some

quantum chemical parameters such as local charges, most

positive charge, most negative charge, dipole moments and

HOMO and LUMO energies were calculated and applied in

the calculation of PCs. Also for evaluating SAR of com-

pounds and using of extracted information to in silico

suggestion of new CCR5 antagonists, general structure of

studied compound and highlighted subunits was shown in

Fig. 10. It is clear from Table 4 that the compounds 48, 7,

3, and 4 have highest bioactivities. With considering these

compounds, it is clear that in all of them R group in sul-

phonyl subunit is lipophile, such as phenyl (in the com-

pound 48) and cyclohexyl (in the compound 7) and also all

of these compounds have at least one withdrawing electron

atom on the phenyl ring in benzyl subunit. Also in all of

them except to 48, it is clear the beneficial binding affini-

ties of the sulfoxide moiety in pyperidine subunit, which it

confirms a hydrogen bond acceptor interaction or a simple

polar effect.

In order to design novel derivatives with high inhibition

effect of CCR5, and because experimental and computed

activities of compounds used in the model development

step, shown a good correlation, developed PC-RBFNNs

QSAR model was used to calculate inhibitory activities of

suggested compounds. Structures of novel antagonists of

CCR5 may then be suggested and bioactivities of them

could evaluate by using the generated model. Based on the

following strategy novel compounds were suggested.

Compounds owning the general structure of investigated

compounds in addition of the various substituents may

produce the novel compounds. Structures of these novel

ligands also were generated and then PCs of them were

generated. Hence, using calculated PCs and the developed

PC-RBFNs model, bioactivities of proposed ligands are

calculated.

The general structures of eight suggested compounds

and details and also their calculated activities are reported

in Table 6. The suggested compounds are combination of

the most potent compounds of Table 1 especially com-

pounds 48, 7, 3, and 4. The relative high predicted activi-

ties of suggested compounds confirm further study, such as

synthesis should be performed on such chemical structures.

Conclusion

The aim of the present study was to rationalize bioactivities

of some practically studied CCR5 antagonist compounds

through the use of developed QSAR models, in order to

finally aid design and suggestion of novel CCR5 antago-

nists and evaluation of bioactivity of these new compounds

computationally.

Two nonlinear methods, the radial basis function neural

networks and GRNNs were employed to obtain predictive

QSAR models for CCR5 inhibitory activity of a set of 48

compounds using different calculated descriptors. In both

methods, a comparison was made between obtained results

for the same set of compounds. The RMSE of the

PC-RBFNNs model for the training and the test sets, and in

the cross validation procedure were lower than RMSE of

the model developed by the PC-GRNNs method. The

correlation coefficient produced by the PC-RBFNNs model

was higher than that in the PC-GRNNs method. In order to

design novel derivatives with high inhibition effect of

CCR5, and because experimental and computed activities

of molecules used in the model development step, shown a

good correlation, developed QSAR model by PC-RBFNNs

was employed to calculate inhibitory activities of some

suggested compounds.

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