# Exploring QSAR for Antimalarial Activities and Drug Distribution within Blood of a Series of 4-Aminoquinoline Drugs Using Genetic-MLR

Authors: Amir Najafi; Soheil Sobhanardakani; Mehdi Marjani
Journal: Journal of Chemistry
 (2013)

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## Abstract

Malaria has been one of the most significant public health problems for centuries. QSAR modeling of the antimalarial activity and blood-to-plasma concentration ratio of Chloroquine and a new series of 4-aminoquinoline derivatives were developed using genetic algorithms with multiple linear regression (GA-MLR) method. We obtained two different models against Chloroquine-sensitive (3D7) and Chloroquine-resistant (W2) strains ofPlasmodium falciparum with good adjustment levels. Drug distribution in blood, defined as drug blood-to-plasma concentration ratio (Rb), is related to molecular descriptors. Leave-many-out (LMO) and Y-randomization methods confirmed the models' robustness.


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## Body

## 1. Introduction

With approximately 243 million cases and 863,000 attributed deaths reported globally in 2009 [1], malaria is one of the most severe infectious diseases; primarily affecting the world’s most disadvantaged populations. Chloroquine (CQ), a low-cost drug, is widely used for antimalarial agents. However, the emergence of CQ-resistant malarial parasite strains has prompted the search for alternative strategies to combat the disease. The clones of P. falciparum were used most often for in vitro testing of the antimalarial activity on different strains, among which are Chloroquine-sensitive (NF54, NF54/64, 3D7, D6, F32, D10, HB3, FCC1-HN, Ghana), Chloroquine-resistant (FcB1, W2, FCM29, BHz26/86, Dd2, EN36, ENT30, FCR3, FCR-3/A2), and/or multidrug-resistant (K1, TM91C235) strains, to find effective compounds against resistant malaria. Some recent QSAR models and reviews are reported on antimalarial compounds [2–10].Blood-to-plasma concentration ratio (Rb defined as CB/Cp) is a measure of the drug distribution within the blood. Drugs, when reaching the blood stream, can bind to plasma proteins and/or to blood cells. If a drug binding in plasma exceeds its binding in blood cells, Rb values are below 1 (Cp>CB). When drug binding in blood cells exceeds its plasma binding (Cp>CB), then Rb values are above 1. Red blood cells (RBCs) are the host cells for malaria parasites, and any effect of the drug on red cell membranes might be relevant for its in vivo effects [11]. Rb may be an important parameter in drug potency and is therefore worthy of investigation. It is related to either the volume of distribution or clearance of the drug. Even though the determination of Rb is relatively simple, such data is absent in most pharmacokinetic studies [12, 13].The objective of this study was first to develop QSAR models and to explain the antimalarial activity of a new series of 4-aminoquinoline, structurally related to CQ, againstP. falciparum various clones (3D7, W2) in vitro using theoretical molecular descriptors. Second, the aim was to establish regression models to predict the blood-to-plasma concentration ratio (Rb) using mainly in silico molecular descriptors.


## 2. Materials and Methods

### 2.1. Software

A Pentium IV personal computer (CPU, 3.2 GHz) under Windows XP operating system was used. Molecular modeling and geometry optimization were employed by Hyperchem [14]. Dragon software [15] was employed for calculation of theoretical molecular descriptors. SPSS software [16] was used for MLR analysis. Other statistics calculations were also performed in the MATLAB [17] environment.


### 2.2. Ensemble Data and Molecular Descriptors

We used a series of 4-aminoquinoline antimalarial compounds with experimentally determined ADME properties, taken from the Ray et al. paper [18]. Based on the results of their research group, antimalarial compounds effective against drug-resistant strains of P. falciparum by varying the chemical substitutions around the heterocyclic ring and the basic amine side chain of the popular antimalarial drug chloroquine have developed [19, 20]. Recently, they have screened a panel of these novel antimalarial compounds for improved leads based on the evaluated ADMET properties [18]. Each compound in the studied database was characterized by growth inhibition of 3D7 and W2 strains of P. falciparum, blood-to-plasma concentration ratio. Figure 1 depicts all the structures used in this study. The panel includes a small number of CQ analogues with altered substitutions on the quinoline ring, although the majority of the compounds in the panel contain substitutions of the alkyl groups attached to the basic nitrogen position on the aminoalkyl side of the chain. Two data sets of log IC50 (each compound at 1 and 10 μM concentration) were used for the QSAR studies. The activity data has been given as IC50 (nM) values, referring to growth inhibition of chloroquine derivatives uptake into drug-resistant (W2) and drug-sensitive (3D7) strains of P. falciparum. The experimental values of these antimalarial activities are shown in Table 1. The red blood cells (RBCs) to plasma partition ratio (Rb defined as CB/Cp) were measured for each compound at 1 and 10 μM. The Rb values were normalized by transforming them to the logarithm of drug concentration in blood cells to plasma ratio (CB/Cp). The Rb values are summarized in Table 2. The molecular structures of all the Chloroquine derivatives were built with Hyperchem (Version 7, HyperCube, Inc.) software. AM1 semiempirical calculation was used to optimize the 3D geometry of the molecules. The Polak-Ribier algorithm with root mean squares gradient 0.1 kcal/mol was selected for optimization. By using DRAGON [15] we derived a total of 1481 1D, 2D, and 3D molecular descriptors from the 3D structure of each compound.Table 1
Experimental and calculated antimalarial activity (logIC50) for 3D7 and W2 strains.
Compounds
a
log (1/IC50) 3D7
log (1/IC50) W2
Exp.
Pred.b
Res.c
Exp.
Pred.b
Res.c
1
−1.23
−1.15
−0.08
−2.58
−2.38
−0.20
2
−2.06
−1.89
−0.17
−2.43
−2.67
0.24
3
−1.79
−1.89
0.10
−2.46
−2.70
0.24
4
−1.71
−1.70
−0.01
−2.46
−2.13
−0.33
5
−1.16
−1.18
0.02
−1.24
−1.34
0.10
6
−1.32
−1.38
0.06
−1.54
−1.28
−0.26
7
−1.70
−1.69
−0.01
−1.70
−1.69
−0.01
8
−1.65
−1.59
−0.06
−1.85
−1.88
0.03
9
−0.30
−0.40
0.10
−0.48
−0.63
0.15
10
−1.80
−2.02
0.22
−1.82
−1.88
0.06
11
−0.70
−0.71
0.01
−0.97
−1.03
0.06
12
−0.78
−0.64
−0.14
−0.90
−0.69
−0.21
13
−0.87
−1.04
0.17
−1.04
−1.06
0.02
14
0.00
−0.31
0.31
−0.59
−0.69
0.10
15
−1.85
−1.73
−0.12
−2.00
−2.00
0.00
16
−0.91
−0.94
0.03
−1.90
−1.78
−0.12
17
−1.11
−1.13
0.02
−1.53
−1.71
0.18
18
−0.70
−0.69
−0.01
−1.08
−1.05
−0.03
19
−0.40
−0.24
−0.16
−0.75
−0.89
0.14
20
−1.11
−0.77
−0.34
−2.26
−2.05
−0.21
21
−0.67
−0.72
0.05
−1.66
−1.70
0.04
aNumber of compounds given in Figure 1.
bValues calculated by equations in Table 10.
cObserved minus calculated values.Table 2
Experimental and calculated values for Blood-to-plasma concentration ratio (Rb).
Compounds
a
logRb, 1 μM
logRb, 10 μM
Exp.
Pred.
b
Res.
c
Exp.
Pred.
b
Res.
c
1
0.58
0.54
0.04
0.61
0.63
−0.02
2
0.61
0.66
−0.05
1.33
1.27
0.06
3
0.79
0.80
−0.01
0.83
0.79
0.04
4
0.69
0.65
0.04
0.74
0.80
−0.06
5
0.41
0.48
−0.07
0.56
0.47
0.09
6
0.52
0.46
0.06
0.71
0.75
−0.04
7
0.51
0.52
−0.01
0.57
0.65
−0.08
8
0.76
0.70
0.06
0.73
0.67
0.06
9
0.19
0.18
0.01
0.41
0.33
0.08
10
0.50
0.46
0.04
0.39
0.55
−0.16
11
0.45
0.45
0.00
0.40
0.48
−0.08
12
0.48
0.46
0.02
0.28
0.14
0.14
13
0.30
0.28
0.02
0.28
0.31
−0.03
14
0.50
0.61
−0.11
0.39
0.61
−0.22
15
0.51
0.52
−0.01
0.53
0.55
−0.02
16
0.39
0.35
0.04
0.37
0.27
0.10
17
0.44
0.46
−0.02
0.35
0.39
−0.04
18
0.37
0.39
−0.02
0.33
0.33
0.00
19
0.71
0.70
0.01
0.52
0.44
0.08
20
0.76
0.70
0.06
0.94
0.74
0.20
21
0.42
0.49
−0.07
−0.04
0.06
−0.10
aNumber of compounds given in Figure 1.
bValues calculated by equations in Table 12.
cObserved minus calculated values.Figure 1
Chemical structures of 4-aminoquinolines analogues used in this study.To decrease the redundancy existed in the descriptors data matrix, the correlation of descriptors with each other and with the properties of the drugs was examined, and collinear descriptors (i.e.,r>0.95) were detected. Among the collinear descriptors, one with the highest correlation with activity was retained, and the others were removed from the data matrix.The list and meaning of the molecular descriptors is provided by the DRAGON package, and the calculation procedure is explained in detail, with related literature references, in the Handbook of Molecular Descriptors [21].


### 2.3. MLR Modeling Procedure

Multiple Linear Regression (MLR) which demonstrates great ease of implementation along with the interpretability of resulting equations were the statistical method of choice for building the QSAR model. The forward-stepping variant of MLR was utilized, starting with the selection of a single variable which contributes most to the model based on its highestF-statistics or lowest P value. At each step, MLR alters the model from the previous step by adding predictor variables and terminating the search when a statistically significant model has been obtained [22, 23]. QSAR Modeling [24] is free JAVA-based software developed by the courtesy of the Theoretical and Applied Chemometrics Laboratory’s research group. Genetic algorithm (GA) search was carried out exploring MLR models. The GA used was the same as that previously used [25, 26].


## 2.1. Software

A Pentium IV personal computer (CPU, 3.2 GHz) under Windows XP operating system was used. Molecular modeling and geometry optimization were employed by Hyperchem [14]. Dragon software [15] was employed for calculation of theoretical molecular descriptors. SPSS software [16] was used for MLR analysis. Other statistics calculations were also performed in the MATLAB [17] environment.


## 2.2. Ensemble Data and Molecular Descriptors

We used a series of 4-aminoquinoline antimalarial compounds with experimentally determined ADME properties, taken from the Ray et al. paper [18]. Based on the results of their research group, antimalarial compounds effective against drug-resistant strains of P. falciparum by varying the chemical substitutions around the heterocyclic ring and the basic amine side chain of the popular antimalarial drug chloroquine have developed [19, 20]. Recently, they have screened a panel of these novel antimalarial compounds for improved leads based on the evaluated ADMET properties [18]. Each compound in the studied database was characterized by growth inhibition of 3D7 and W2 strains of P. falciparum, blood-to-plasma concentration ratio. Figure 1 depicts all the structures used in this study. The panel includes a small number of CQ analogues with altered substitutions on the quinoline ring, although the majority of the compounds in the panel contain substitutions of the alkyl groups attached to the basic nitrogen position on the aminoalkyl side of the chain. Two data sets of log IC50 (each compound at 1 and 10 μM concentration) were used for the QSAR studies. The activity data has been given as IC50 (nM) values, referring to growth inhibition of chloroquine derivatives uptake into drug-resistant (W2) and drug-sensitive (3D7) strains of P. falciparum. The experimental values of these antimalarial activities are shown in Table 1. The red blood cells (RBCs) to plasma partition ratio (Rb defined as CB/Cp) were measured for each compound at 1 and 10 μM. The Rb values were normalized by transforming them to the logarithm of drug concentration in blood cells to plasma ratio (CB/Cp). The Rb values are summarized in Table 2. The molecular structures of all the Chloroquine derivatives were built with Hyperchem (Version 7, HyperCube, Inc.) software. AM1 semiempirical calculation was used to optimize the 3D geometry of the molecules. The Polak-Ribier algorithm with root mean squares gradient 0.1 kcal/mol was selected for optimization. By using DRAGON [15] we derived a total of 1481 1D, 2D, and 3D molecular descriptors from the 3D structure of each compound.Table 1
Experimental and calculated antimalarial activity (logIC50) for 3D7 and W2 strains.
Compounds
a
log (1/IC50) 3D7
log (1/IC50) W2
Exp.
Pred.b
Res.c
Exp.
Pred.b
Res.c
1
−1.23
−1.15
−0.08
−2.58
−2.38
−0.20
2
−2.06
−1.89
−0.17
−2.43
−2.67
0.24
3
−1.79
−1.89
0.10
−2.46
−2.70
0.24
4
−1.71
−1.70
−0.01
−2.46
−2.13
−0.33
5
−1.16
−1.18
0.02
−1.24
−1.34
0.10
6
−1.32
−1.38
0.06
−1.54
−1.28
−0.26
7
−1.70
−1.69
−0.01
−1.70
−1.69
−0.01
8
−1.65
−1.59
−0.06
−1.85
−1.88
0.03
9
−0.30
−0.40
0.10
−0.48
−0.63
0.15
10
−1.80
−2.02
0.22
−1.82
−1.88
0.06
11
−0.70
−0.71
0.01
−0.97
−1.03
0.06
12
−0.78
−0.64
−0.14
−0.90
−0.69
−0.21
13
−0.87
−1.04
0.17
−1.04
−1.06
0.02
14
0.00
−0.31
0.31
−0.59
−0.69
0.10
15
−1.85
−1.73
−0.12
−2.00
−2.00
0.00
16
−0.91
−0.94
0.03
−1.90
−1.78
−0.12
17
−1.11
−1.13
0.02
−1.53
−1.71
0.18
18
−0.70
−0.69
−0.01
−1.08
−1.05
−0.03
19
−0.40
−0.24
−0.16
−0.75
−0.89
0.14
20
−1.11
−0.77
−0.34
−2.26
−2.05
−0.21
21
−0.67
−0.72
0.05
−1.66
−1.70
0.04
aNumber of compounds given in Figure 1.
bValues calculated by equations in Table 10.
cObserved minus calculated values.Table 2
Experimental and calculated values for Blood-to-plasma concentration ratio (Rb).
Compounds
a
logRb, 1 μM
logRb, 10 μM
Exp.
Pred.
b
Res.
c
Exp.
Pred.
b
Res.
c
1
0.58
0.54
0.04
0.61
0.63
−0.02
2
0.61
0.66
−0.05
1.33
1.27
0.06
3
0.79
0.80
−0.01
0.83
0.79
0.04
4
0.69
0.65
0.04
0.74
0.80
−0.06
5
0.41
0.48
−0.07
0.56
0.47
0.09
6
0.52
0.46
0.06
0.71
0.75
−0.04
7
0.51
0.52
−0.01
0.57
0.65
−0.08
8
0.76
0.70
0.06
0.73
0.67
0.06
9
0.19
0.18
0.01
0.41
0.33
0.08
10
0.50
0.46
0.04
0.39
0.55
−0.16
11
0.45
0.45
0.00
0.40
0.48
−0.08
12
0.48
0.46
0.02
0.28
0.14
0.14
13
0.30
0.28
0.02
0.28
0.31
−0.03
14
0.50
0.61
−0.11
0.39
0.61
−0.22
15
0.51
0.52
−0.01
0.53
0.55
−0.02
16
0.39
0.35
0.04
0.37
0.27
0.10
17
0.44
0.46
−0.02
0.35
0.39
−0.04
18
0.37
0.39
−0.02
0.33
0.33
0.00
19
0.71
0.70
0.01
0.52
0.44
0.08
20
0.76
0.70
0.06
0.94
0.74
0.20
21
0.42
0.49
−0.07
−0.04
0.06
−0.10
aNumber of compounds given in Figure 1.
bValues calculated by equations in Table 12.
cObserved minus calculated values.Figure 1
Chemical structures of 4-aminoquinolines analogues used in this study.To decrease the redundancy existed in the descriptors data matrix, the correlation of descriptors with each other and with the properties of the drugs was examined, and collinear descriptors (i.e.,r>0.95) were detected. Among the collinear descriptors, one with the highest correlation with activity was retained, and the others were removed from the data matrix.The list and meaning of the molecular descriptors is provided by the DRAGON package, and the calculation procedure is explained in detail, with related literature references, in the Handbook of Molecular Descriptors [21].


## 2.3. MLR Modeling Procedure

Multiple Linear Regression (MLR) which demonstrates great ease of implementation along with the interpretability of resulting equations were the statistical method of choice for building the QSAR model. The forward-stepping variant of MLR was utilized, starting with the selection of a single variable which contributes most to the model based on its highestF-statistics or lowest P value. At each step, MLR alters the model from the previous step by adding predictor variables and terminating the search when a statistically significant model has been obtained [22, 23]. QSAR Modeling [24] is free JAVA-based software developed by the courtesy of the Theoretical and Applied Chemometrics Laboratory’s research group. Genetic algorithm (GA) search was carried out exploring MLR models. The GA used was the same as that previously used [25, 26].


## 3. Results and Discussions

### 3.1. The Selected Descriptors

The majority of the selected descriptors in our GA-MLR modeling are composite descriptors, which can be divided into five groups: GETAWAY, 3D-MoRSE, RDF, WHIM, and 2D autocorrelations descriptors. The GETAWAY (Geometry, Topology, and Atom Weights AssemblY) try to match the 3D molecular geometry provided by the molecular influence matrix and atom relatedness by topology with chemical information by using various atomic weighting schemes. 3D-MoRSE descriptors, which are representations of the 3D structure of a molecule and encode features such as molecular weight, van der Waals volume, electronegativities, and polarizabilities. The radial distribution function (RDF) descriptors are based on the distance distribution of the compounds. WHIM descriptors are based on statistical indices calculated on the projections of atoms along principal axes. 2D autocorrelations descriptors, in general, explain how the considered property is distributed along the topological structure. Three spatial autocorrelation vectors including unweighted and weighted Moran and Geary and Broto-Moreau autocorrelation vectors were calculated. The physicochemical property was considered in atomic masses (m), atomic van der Waals volumes (v), atomic Sanderson electronegativities (e), and atomic polarizabilities (p) as weighting properties [21]. Table 3 depicts the names and meanings of the molecular descriptors used in this work.Table 3
Brief description of molecular descriptors used in the different modeling approaches.
GETAWAY descriptors
H4u
H autocorrelation of lag 4/unweighted
HATS5u
leverage-weighted autocorrelation of lag 5/unweighted
R2u+
R maximal autocorrelation of lag 2/unweighted
R8u+
R maximal autocorrelation of lag 8/unweighted
R3m
R autocorrelation of lag 3/weighted by atomic masses
R4m+
R maximal autocorrelation of lag 4/weighted by atomic masses
3D-MoRSE descriptors
Mor16u
3D-MoRSE—signal 16/unweighted
Mor06m
3D-MoRSE—signal 06/weighted by atomic masses
Mor24m
3D-MoRSE—signal 24/weighted by atomic masses
Mor32v
3D-MoRSE—signal 32/weighted by atomic van der Waals volumes
RDF descriptors
RDF020u
Radial Distribution Function—2.0/unweighted
RDF095u
Radial Distribution Function—9.5/unweighted
RDF040m
Radial Distribution Function—4.0/weighted by atomic masses
RDF090m
Radial Distribution Function—9.0/weighted by atomic masses
RDF095m
Radial Distribution Function—9.5/weighted by atomic masses
WHIM descriptors
G3p
3st component symmetry directional WHIM index/weighted by atomic polarizabilities
Gu
G total symmetry index/unweighted
2D autocorrelations
MATS4m
Moran autocorrelation—lag 4/weighted by atomic masses
MATS6m
Moran autocorrelation—lag 6/weighted by atomic massesTables4 and 5 show the data of the descriptors used in this study. The correlation matrixes of the descriptors used in this study are given in Tables 6, 7, 8, and 9. Inspection of these results shows that all the values deviate from unity are noticeable so there is no significant correlation between the independent variables.Table 4
Data of the selected descriptors used in this study for 3D7 and W2 strains.
Log (1/IC50) 3D7
RDF020u
Mor06m
R8u+
Gu
HATS5u
Log (1/IC50) W2
RDF040m
H4u
MATS6m
Mor16u
Mor32v
−1.23
8.482
2.855
0.143
0.155
0.426
−2.58
8.088
1.518
1.019
−0.265
−0.057
−2.06
8.817
2.123
0.091
0.145
0.296
−2.43
2.966
2.046
1.007
−0.423
−0.322
−1.79
8.592
1.032
0.121
0.154
0.406
−2.46
2.441
1.788
1.021
0.034
−0.152
−1.71
8.680
1.334
0.128
0.153
0.397
−2.46
2.882
1.914
1.023
−0.175
−0.136
−1.16
8.878
2.716
0.117
0.154
0.366
−1.24
8.036
1.752
1.027
−0.464
0.012
−1.32
7.909
2.389
0.115
0.149
0.284
−1.54
10.184
2.005
1.013
−0.429
−0.311
−1.70
8.912
2.561
0.092
0.151
0.356
−1.70
12.780
1.882
1.018
−0.075
−0.006
−1.65
9.702
2.375
0.091
0.151
0.359
−1.85
10.177
1.887
1.021
0.073
−0.020
−0.30
12.872
2.769
0.093
0.153
0.328
−0.48
14.434
2.048
1.022
−0.018
−0.163
−1.80
10.114
2.523
0.085
0.150
0.433
−1.82
9.494
1.785
1.016
−0.405
−0.100
−0.70
11.126
3.597
0.077
0.156
0.345
−0.97
9.788
2.408
1.016
−0.335
−0.134
−0.78
9.626
3.510
0.121
0.149
0.295
−0.90
11.126
2.455
1.020
0.237
−0.292
−0.87
9.082
3.078
0.094
0.158
0.357
−1.04
13.566
1.859
1.024
−0.133
0.006
0.00
11.243
3.620
0.118
0.149
0.302
−0.59
9.226
2.530
1.011
−0.680
−0.291
−1.85
8.718
2.504
0.070
0.150
0.286
−2.00
8.821
2.107
1.015
0.258
−0.246
−0.91
10.266
3.272
0.077
0.150
0.267
−1.90
9.700
1.892
1.012
−0.391
−0.234
−1.11
11.035
2.470
0.078
0.153
0.328
−1.53
8.216
2.259
1.012
−0.047
−0.302
−0.70
11.287
2.756
0.092
0.147
0.242
−1.08
10.521
2.068
1.021
−0.106
−0.191
−0.40
14.060
3.062
0.108
0.153
0.401
−0.75
14.526
1.566
1.026
0.000
−0.170
−1.11
10.814
3.041
0.100
0.158
0.394
−2.26
8.180
2.092
1.012
−0.235
−0.154
−0.67
10.923
2.321
0.099
0.164
0.419
−1.66
8.161
1.855
1.020
−0.183
−0.164Table 5
Data of the selected descriptors used in this study for blood-to-plasma concentration ratio.
logRbB/P, (1 μM)
RDF065u
GATS8m
RDF090m
R2u+
Mor24m
logRbB/P, (10 μM)
R3m
RDF095u
G3p
R4m+
MATS4m
0.58
23.742
0.015
5.156
0.154
0.186
0.61
0.489
7.467
0.152
0.105
0.989
0.61
23.858
0.012
4.671
0.138
0.364
1.33
0.449
14.299
0.145
0.047
0.984
0.79
24.983
0.011
3.94
0.158
0.355
0.83
0.465
11.956
0.149
0.123
0.997
0.69
26.309
0.013
4.879
0.167
0.187
0.74
0.541
10.008
0.15
0.074
0.991
0.41
23.585
0.015
4.594
0.137
0.081
0.56
0.563
12.042
0.151
0.112
0.992
0.52
37.224
0.014
4.197
0.161
0.109
0.71
0.56
13.736
0.146
0.103
1.005
0.51
27.16
0.019
3.306
0.143
0.511
0.57
0.604
13.682
0.151
0.106
1.003
0.76
27.772
0.014
3.272
0.15
0.476
0.73
0.588
13.495
0.151
0.106
1.001
0.19
40.32
0.013
7.91
0.137
0.19
0.41
0.618
10.831
0.147
0.093
0.994
0.50
27.305
0.014
6.23
0.154
0.155
0.39
0.569
12.303
0.15
0.11
0.997
0.45
29.435
0.015
7.557
0.173
0.295
0.40
0.677
17.95
0.155
0.089
0.988
0.48
35.825
0.012
8.155
0.186
0.21
0.28
0.739
17.215
0.146
0.107
1.005
0.30
26.939
0.019
5.981
0.126
0.415
0.28
0.709
12.81
0.151
0.103
1.006
0.50
33.143
0.014
7.632
0.213
0.351
0.39
0.642
12.969
0.159
0.09
0.991
0.51
28.33
0.014
8.646
0.195
0.278
0.53
0.674
18.473
0.156
0.12
1.003
0.39
30.342
0.014
11.978
0.2
0.326
0.37
0.624
13.339
0.147
0.09
0.987
0.44
43.146
0.014
2.297
0.153
0.116
0.35
0.578
8.218
0.147
0.095
0.995
0.37
41.129
0.014
8.602
0.206
0.207
0.33
0.613
10.168
0.147
0.088
0.992
0.71
20.145
0.013
4.075
0.145
0.26
0.52
0.677
6.122
0.169
0.108
0.995
0.76
26.134
0.014
7.038
0.22
0.163
0.94
0.593
8.183
0.162
0.091
0.992
0.42
24.48
0.014
6.615
0.16
0.113
−0.04
0.624
3.403
0.152
0.096
0.989Table 6
Correlation matrix of the 5 selected descriptors for 3D7 strain.
RDF020u
Mor06m
R8u+
Gu
HATS5u
RDF020u
1.000
Mor06m
0.434
1.000
R8u+
−0.261
−0.190
1.000
Gu
0.151
−0.013
0.098
1.000
HATS5u
0.012
−0.320
0.363
0.646
1.000Table 7
Correlation matrix of the 5 selected descriptors for W2 strain.
RDF040m
H4u
MATS6m
Mor16u
Mor32v
1.000
0.010
1.000
0.296
−0.486
1.000
0.201
−0.039
0.383
1.000
0.214
−0.574
0.650
0.053
1.000Table 8
Correlation matrix of the 5 selected descriptors forRb B/P, 1 μM.
RDF065u
GATS8m
RDF090m
R2u+
Mor24m
RDF065u
1.000
GATS8m
−0.092
1.000
RDF090m
0.210
−0.097
1.000
R2u+
0.259
−0.247
0.636
1.000
Mor24m
−0.239
0.335
−0.060
−0.109
1.000Table 9
Correlation matrix of the 5 selected descriptors forRb B/P, 10 μM.
R3m
RDF095u
G3p
R4m+
MATS4m
R3m
1.000
RDF095u
0.248
1.000
G3p
0.323
−0.268
1.000
R4m+
0.267
0.062
0.216
1.000
MATS4m
0.406
0.355
−0.069
0.628
1.000


### 3.2. Validation of the Models

A good fit was assessed based on the determination squared correlation coefficients (R2), adjusted determination coefficient (Radj2), standard deviation (s), root-mean-square error (RMSE), Fisher’s statistic (F) and number of variables. Most of the QSAR modeling methods implement the leave-one-out (LOO) or leave-many-out (LMO) cross-validation procedure, which are internal validation techniques [27]. LOO cross-validation procedure consists of removing one data point from the training set and constructing the model only on the basis of the remaining training data and then testing on the removed point. LMO cross-validation procedure calculate the models leaving multiple observations out at a time, reducing the number of times it has to recalculate a model. The outcome from the cross-validation procedure is cross-validated R2 (LOO-Q2 or LMO-Q2), which is used as a criterion of both robustness and predictive ability of the model. In this paper, we have performed the LOO cross-validation and leave-5-out cross-validation method as the internal validation tool. The robustness of the model was examined by the Y-randomization test [28]. For the Y-randomization test, performed ten times, R2 ≤ 0.3 and QLoo2 ≤ 0.05 for all results were considered acceptable. These limits were selected based on Eriksson and coworkers’ suggestions [28]. The Y-randomization test is capable of verifying if models with high values of R2 and QLoo2 present chance correlation [29, 30].In order to make more realistic validation of the predictive power of the models, external validation was also performed. For that purpose, six Chloroquine derivatives (3, 6, 8, 15, 18 and 19) were selected from 21 compounds at random to construct the external test set, and the remaining 15 Chloroquine derivatives comprised the training set that was employed to calibrate the QSAR models.


### 3.3. QSAR Models for 2D7 and W2 Strains

By using the best multilinear regression method equations for both antimalarial activities against Chloroquine-sensitive (3D7) and Chloroquine-resistant (W2) strains ofP. falciparum were constructed with up to five descriptors. The predicted log IC50 values and the residuals for the compounds are listed in Table 1. QSAR models generated for the two strains (3D7, W2) are shown in Table 10. These models have good capacity to explain the observed values of biological activity because it possesses excellent adjustment level: high correlation coefficient and low root-mean-square error (R2= 0.94, Radj2 = 0.92 and RMSE = 0.14 for 3D7 strain and R2= 0.94, Radj2 = 0.91, and RMSE = 0.16 for W2 strain). To validate the selected prediction function, a cross-validation, and an external test were carried out. The models also have good predictive capacity (Q2 = 0.86 for the both strains). In general, MLR models were able to explain data variance and were quite stable to the inclusion-exclusion of compounds as measured by LOO correlation coefficients (Q2 > 0.5). Also, the results of the LMO test are collected in Table 4. From a theoretically acceptable model the R2 cannot have smaller values than QLOO2 and QLMO2 or REXT2. Overall, the best model is achieved when QLOO2 ≤ R2 ≥ QLMO2 and QLOO2≈QLMO2. Y-randomization results are in agreement with the suggested limits [28]. This indicates that the explained variance by the model is not due to chance correlation. Y-randomization results are shown in Figures 2 and 3. Each of related training set equations and statistical parameters is summarized in Table 11. In turn, plots of LOO cross-validation and test set predictions versus experimental log IC50 values (for 3D7 and W2 strains) for the MLR models are shown in Figure 4.Table 10
Multivariate linear regression models and statistical parameters for 3D7 and W2 strains.
Log (1/IC50)
Equation
R
2
R
a
d
j
2
RMSE
F
Q
2
Q
L
5
o
2
3D7
−13.327 (1.632) + 0.236 (0.028) RDF020u + 0.280 (0.069) Mor06m + 13.883 (2.181) R8u+ + 63.224 (12.011) Gu − 5.649 (1.022) HATS5u
0.94
0.92
0.14
44.81
0.86
0.87
W2
−93.816 (12.475) + 0.131 (0.014) RDF040m + 1.285 (0.204) H4u + 86.388 (12.118) MATS6m − 1.021 (0.201) Mor16u − 2.177 (0.581) Mor32v
0.94
0.91
0.16
44.43
0.86
0.77Table 11
Evaluation of the prediction ability of the MLR models in the external validation set for 3D7 and W2 strains.
Training set
Test set
Log (1/IC50)
R
2
R
a
d
j
2
RMSE
F
R
p
r
e
d
2
RMSE
3D7
0.93
0.89
0.15
23.86
0.96
0.18
W2
0.96
0.93
0.14
38.38
0.90
0.28Figure 2
Plots ofY-randomization for log (1/IC50) 3D7.Figure 3
Plots ofY-randomization for log (1/IC50) W2.Plot of the predicted versus the observed of log (1/IC50) growth inhibition of 3D7 and W2 strains of P. falciparum. The LOO cross-validation compounds are represented as grey dots and six derivatives, used as test set, as black dots.
(a)
(b)


### 3.4. QSAR Model for Blood-to-Plasma Concentration Ratio

The best linear models consisted of the five descriptors in order to relate them to the logRb values tabulated in Table 12. The predicted Rb values and the residuals for the compounds are listed in Table 2. As can be seen, the MLR models have good statistical quality with low prediction error. The models obtained were validated by calculating the cross-validated Q2 values obtained using the LOO cross-validation method. This is the measure of the predictive power of regression equations. The Q2 values for the best regression models for log Rb were suggestive of robust models. The results of the LMO test are collected in Table 3. On average, the overall test steps R2≥QLMO2 and QLOO2≈QLMO2 which is another proof that the model is not underdetermined. The model was further validated by applying the Y-randomization. Several random shuffles of the Y vector were performed. Y-randomization results are in agreement with the suggested limits [28]. Y-randomization results are shown in Figures 5 and 6. The Rb prediction ability of the MLR models were also tested using the validation set of data (Table 13). The correlations between the predicted and experimental values of Rb (from LOO cross-validation and external test) are shown in Figure 7.Table 12
Multivariate linear regression models and statistical parameters for blood-to-plasma concentration ratio.
logRb
Equation
R
2
R
a
d
j
2
RMSE
F
Q
2
Q
L
5
o
2
B/P, (1μM)
0.948 (0.140) − 0.013 (0.002) RDF065u − 33.174 (6.778) GATS8m − 0.055 (0.007) RDF090m + 4.018 (0.582) R2u+ + 0.305 (0.104) Mor24m
0.92
0.89
0.04
32.69
0.84
0.85
B/P, (10μM)
−21.744 (6.135) − 3.861 (0.431) R3m + 0.033(0.008) RDF095m + 28.454 (5.396) G3p − 9.616 (2.220) R4m+ + 20.931 (6.131) MATS4m
0.87
0.83
0.10
20.55
0.74
0.80Table 13
Evaluation of the prediction ability of the MLR models in the external validation set forRb.
Training set
Test set
logRb
R
2
R
a
d
j
2
RMSE
F
R
p
r
e
d
2
RMSE
B/P (1μM)
0.89
0.83
0.05
14.57
0.93
0.06
B/P (10μM)
0.87
0.80
0.11
12.03
0.84
0.09Figure 5
Plots ofY-randomization for log Rb, B/P(1 μM).Figure 6
Plots ofY-randomization for log Rb, B/P(10 μM).Plot of the predicted versus the observed logRb that was measured for each of the compounds at 1 and 10 μM. The LOO cross-validation of compounds is represented as grey dots and test set as black dots.
(a)
(b)


## 3.1. The Selected Descriptors

The majority of the selected descriptors in our GA-MLR modeling are composite descriptors, which can be divided into five groups: GETAWAY, 3D-MoRSE, RDF, WHIM, and 2D autocorrelations descriptors. The GETAWAY (Geometry, Topology, and Atom Weights AssemblY) try to match the 3D molecular geometry provided by the molecular influence matrix and atom relatedness by topology with chemical information by using various atomic weighting schemes. 3D-MoRSE descriptors, which are representations of the 3D structure of a molecule and encode features such as molecular weight, van der Waals volume, electronegativities, and polarizabilities. The radial distribution function (RDF) descriptors are based on the distance distribution of the compounds. WHIM descriptors are based on statistical indices calculated on the projections of atoms along principal axes. 2D autocorrelations descriptors, in general, explain how the considered property is distributed along the topological structure. Three spatial autocorrelation vectors including unweighted and weighted Moran and Geary and Broto-Moreau autocorrelation vectors were calculated. The physicochemical property was considered in atomic masses (m), atomic van der Waals volumes (v), atomic Sanderson electronegativities (e), and atomic polarizabilities (p) as weighting properties [21]. Table 3 depicts the names and meanings of the molecular descriptors used in this work.Table 3
Brief description of molecular descriptors used in the different modeling approaches.
GETAWAY descriptors
H4u
H autocorrelation of lag 4/unweighted
HATS5u
leverage-weighted autocorrelation of lag 5/unweighted
R2u+
R maximal autocorrelation of lag 2/unweighted
R8u+
R maximal autocorrelation of lag 8/unweighted
R3m
R autocorrelation of lag 3/weighted by atomic masses
R4m+
R maximal autocorrelation of lag 4/weighted by atomic masses
3D-MoRSE descriptors
Mor16u
3D-MoRSE—signal 16/unweighted
Mor06m
3D-MoRSE—signal 06/weighted by atomic masses
Mor24m
3D-MoRSE—signal 24/weighted by atomic masses
Mor32v
3D-MoRSE—signal 32/weighted by atomic van der Waals volumes
RDF descriptors
RDF020u
Radial Distribution Function—2.0/unweighted
RDF095u
Radial Distribution Function—9.5/unweighted
RDF040m
Radial Distribution Function—4.0/weighted by atomic masses
RDF090m
Radial Distribution Function—9.0/weighted by atomic masses
RDF095m
Radial Distribution Function—9.5/weighted by atomic masses
WHIM descriptors
G3p
3st component symmetry directional WHIM index/weighted by atomic polarizabilities
Gu
G total symmetry index/unweighted
2D autocorrelations
MATS4m
Moran autocorrelation—lag 4/weighted by atomic masses
MATS6m
Moran autocorrelation—lag 6/weighted by atomic massesTables4 and 5 show the data of the descriptors used in this study. The correlation matrixes of the descriptors used in this study are given in Tables 6, 7, 8, and 9. Inspection of these results shows that all the values deviate from unity are noticeable so there is no significant correlation between the independent variables.Table 4
Data of the selected descriptors used in this study for 3D7 and W2 strains.
Log (1/IC50) 3D7
RDF020u
Mor06m
R8u+
Gu
HATS5u
Log (1/IC50) W2
RDF040m
H4u
MATS6m
Mor16u
Mor32v
−1.23
8.482
2.855
0.143
0.155
0.426
−2.58
8.088
1.518
1.019
−0.265
−0.057
−2.06
8.817
2.123
0.091
0.145
0.296
−2.43
2.966
2.046
1.007
−0.423
−0.322
−1.79
8.592
1.032
0.121
0.154
0.406
−2.46
2.441
1.788
1.021
0.034
−0.152
−1.71
8.680
1.334
0.128
0.153
0.397
−2.46
2.882
1.914
1.023
−0.175
−0.136
−1.16
8.878
2.716
0.117
0.154
0.366
−1.24
8.036
1.752
1.027
−0.464
0.012
−1.32
7.909
2.389
0.115
0.149
0.284
−1.54
10.184
2.005
1.013
−0.429
−0.311
−1.70
8.912
2.561
0.092
0.151
0.356
−1.70
12.780
1.882
1.018
−0.075
−0.006
−1.65
9.702
2.375
0.091
0.151
0.359
−1.85
10.177
1.887
1.021
0.073
−0.020
−0.30
12.872
2.769
0.093
0.153
0.328
−0.48
14.434
2.048
1.022
−0.018
−0.163
−1.80
10.114
2.523
0.085
0.150
0.433
−1.82
9.494
1.785
1.016
−0.405
−0.100
−0.70
11.126
3.597
0.077
0.156
0.345
−0.97
9.788
2.408
1.016
−0.335
−0.134
−0.78
9.626
3.510
0.121
0.149
0.295
−0.90
11.126
2.455
1.020
0.237
−0.292
−0.87
9.082
3.078
0.094
0.158
0.357
−1.04
13.566
1.859
1.024
−0.133
0.006
0.00
11.243
3.620
0.118
0.149
0.302
−0.59
9.226
2.530
1.011
−0.680
−0.291
−1.85
8.718
2.504
0.070
0.150
0.286
−2.00
8.821
2.107
1.015
0.258
−0.246
−0.91
10.266
3.272
0.077
0.150
0.267
−1.90
9.700
1.892
1.012
−0.391
−0.234
−1.11
11.035
2.470
0.078
0.153
0.328
−1.53
8.216
2.259
1.012
−0.047
−0.302
−0.70
11.287
2.756
0.092
0.147
0.242
−1.08
10.521
2.068
1.021
−0.106
−0.191
−0.40
14.060
3.062
0.108
0.153
0.401
−0.75
14.526
1.566
1.026
0.000
−0.170
−1.11
10.814
3.041
0.100
0.158
0.394
−2.26
8.180
2.092
1.012
−0.235
−0.154
−0.67
10.923
2.321
0.099
0.164
0.419
−1.66
8.161
1.855
1.020
−0.183
−0.164Table 5
Data of the selected descriptors used in this study for blood-to-plasma concentration ratio.
logRbB/P, (1 μM)
RDF065u
GATS8m
RDF090m
R2u+
Mor24m
logRbB/P, (10 μM)
R3m
RDF095u
G3p
R4m+
MATS4m
0.58
23.742
0.015
5.156
0.154
0.186
0.61
0.489
7.467
0.152
0.105
0.989
0.61
23.858
0.012
4.671
0.138
0.364
1.33
0.449
14.299
0.145
0.047
0.984
0.79
24.983
0.011
3.94
0.158
0.355
0.83
0.465
11.956
0.149
0.123
0.997
0.69
26.309
0.013
4.879
0.167
0.187
0.74
0.541
10.008
0.15
0.074
0.991
0.41
23.585
0.015
4.594
0.137
0.081
0.56
0.563
12.042
0.151
0.112
0.992
0.52
37.224
0.014
4.197
0.161
0.109
0.71
0.56
13.736
0.146
0.103
1.005
0.51
27.16
0.019
3.306
0.143
0.511
0.57
0.604
13.682
0.151
0.106
1.003
0.76
27.772
0.014
3.272
0.15
0.476
0.73
0.588
13.495
0.151
0.106
1.001
0.19
40.32
0.013
7.91
0.137
0.19
0.41
0.618
10.831
0.147
0.093
0.994
0.50
27.305
0.014
6.23
0.154
0.155
0.39
0.569
12.303
0.15
0.11
0.997
0.45
29.435
0.015
7.557
0.173
0.295
0.40
0.677
17.95
0.155
0.089
0.988
0.48
35.825
0.012
8.155
0.186
0.21
0.28
0.739
17.215
0.146
0.107
1.005
0.30
26.939
0.019
5.981
0.126
0.415
0.28
0.709
12.81
0.151
0.103
1.006
0.50
33.143
0.014
7.632
0.213
0.351
0.39
0.642
12.969
0.159
0.09
0.991
0.51
28.33
0.014
8.646
0.195
0.278
0.53
0.674
18.473
0.156
0.12
1.003
0.39
30.342
0.014
11.978
0.2
0.326
0.37
0.624
13.339
0.147
0.09
0.987
0.44
43.146
0.014
2.297
0.153
0.116
0.35
0.578
8.218
0.147
0.095
0.995
0.37
41.129
0.014
8.602
0.206
0.207
0.33
0.613
10.168
0.147
0.088
0.992
0.71
20.145
0.013
4.075
0.145
0.26
0.52
0.677
6.122
0.169
0.108
0.995
0.76
26.134
0.014
7.038
0.22
0.163
0.94
0.593
8.183
0.162
0.091
0.992
0.42
24.48
0.014
6.615
0.16
0.113
−0.04
0.624
3.403
0.152
0.096
0.989Table 6
Correlation matrix of the 5 selected descriptors for 3D7 strain.
RDF020u
Mor06m
R8u+
Gu
HATS5u
RDF020u
1.000
Mor06m
0.434
1.000
R8u+
−0.261
−0.190
1.000
Gu
0.151
−0.013
0.098
1.000
HATS5u
0.012
−0.320
0.363
0.646
1.000Table 7
Correlation matrix of the 5 selected descriptors for W2 strain.
RDF040m
H4u
MATS6m
Mor16u
Mor32v
1.000
0.010
1.000
0.296
−0.486
1.000
0.201
−0.039
0.383
1.000
0.214
−0.574
0.650
0.053
1.000Table 8
Correlation matrix of the 5 selected descriptors forRb B/P, 1 μM.
RDF065u
GATS8m
RDF090m
R2u+
Mor24m
RDF065u
1.000
GATS8m
−0.092
1.000
RDF090m
0.210
−0.097
1.000
R2u+
0.259
−0.247
0.636
1.000
Mor24m
−0.239
0.335
−0.060
−0.109
1.000Table 9
Correlation matrix of the 5 selected descriptors forRb B/P, 10 μM.
R3m
RDF095u
G3p
R4m+
MATS4m
R3m
1.000
RDF095u
0.248
1.000
G3p
0.323
−0.268
1.000
R4m+
0.267
0.062
0.216
1.000
MATS4m
0.406
0.355
−0.069
0.628
1.000


## 3.2. Validation of the Models

A good fit was assessed based on the determination squared correlation coefficients (R2), adjusted determination coefficient (Radj2), standard deviation (s), root-mean-square error (RMSE), Fisher’s statistic (F) and number of variables. Most of the QSAR modeling methods implement the leave-one-out (LOO) or leave-many-out (LMO) cross-validation procedure, which are internal validation techniques [27]. LOO cross-validation procedure consists of removing one data point from the training set and constructing the model only on the basis of the remaining training data and then testing on the removed point. LMO cross-validation procedure calculate the models leaving multiple observations out at a time, reducing the number of times it has to recalculate a model. The outcome from the cross-validation procedure is cross-validated R2 (LOO-Q2 or LMO-Q2), which is used as a criterion of both robustness and predictive ability of the model. In this paper, we have performed the LOO cross-validation and leave-5-out cross-validation method as the internal validation tool. The robustness of the model was examined by the Y-randomization test [28]. For the Y-randomization test, performed ten times, R2 ≤ 0.3 and QLoo2 ≤ 0.05 for all results were considered acceptable. These limits were selected based on Eriksson and coworkers’ suggestions [28]. The Y-randomization test is capable of verifying if models with high values of R2 and QLoo2 present chance correlation [29, 30].In order to make more realistic validation of the predictive power of the models, external validation was also performed. For that purpose, six Chloroquine derivatives (3, 6, 8, 15, 18 and 19) were selected from 21 compounds at random to construct the external test set, and the remaining 15 Chloroquine derivatives comprised the training set that was employed to calibrate the QSAR models.


## 3.3. QSAR Models for 2D7 and W2 Strains

By using the best multilinear regression method equations for both antimalarial activities against Chloroquine-sensitive (3D7) and Chloroquine-resistant (W2) strains ofP. falciparum were constructed with up to five descriptors. The predicted log IC50 values and the residuals for the compounds are listed in Table 1. QSAR models generated for the two strains (3D7, W2) are shown in Table 10. These models have good capacity to explain the observed values of biological activity because it possesses excellent adjustment level: high correlation coefficient and low root-mean-square error (R2= 0.94, Radj2 = 0.92 and RMSE = 0.14 for 3D7 strain and R2= 0.94, Radj2 = 0.91, and RMSE = 0.16 for W2 strain). To validate the selected prediction function, a cross-validation, and an external test were carried out. The models also have good predictive capacity (Q2 = 0.86 for the both strains). In general, MLR models were able to explain data variance and were quite stable to the inclusion-exclusion of compounds as measured by LOO correlation coefficients (Q2 > 0.5). Also, the results of the LMO test are collected in Table 4. From a theoretically acceptable model the R2 cannot have smaller values than QLOO2 and QLMO2 or REXT2. Overall, the best model is achieved when QLOO2 ≤ R2 ≥ QLMO2 and QLOO2≈QLMO2. Y-randomization results are in agreement with the suggested limits [28]. This indicates that the explained variance by the model is not due to chance correlation. Y-randomization results are shown in Figures 2 and 3. Each of related training set equations and statistical parameters is summarized in Table 11. In turn, plots of LOO cross-validation and test set predictions versus experimental log IC50 values (for 3D7 and W2 strains) for the MLR models are shown in Figure 4.Table 10
Multivariate linear regression models and statistical parameters for 3D7 and W2 strains.
Log (1/IC50)
Equation
R
2
R
a
d
j
2
RMSE
F
Q
2
Q
L
5
o
2
3D7
−13.327 (1.632) + 0.236 (0.028) RDF020u + 0.280 (0.069) Mor06m + 13.883 (2.181) R8u+ + 63.224 (12.011) Gu − 5.649 (1.022) HATS5u
0.94
0.92
0.14
44.81
0.86
0.87
W2
−93.816 (12.475) + 0.131 (0.014) RDF040m + 1.285 (0.204) H4u + 86.388 (12.118) MATS6m − 1.021 (0.201) Mor16u − 2.177 (0.581) Mor32v
0.94
0.91
0.16
44.43
0.86
0.77Table 11
Evaluation of the prediction ability of the MLR models in the external validation set for 3D7 and W2 strains.
Training set
Test set
Log (1/IC50)
R
2
R
a
d
j
2
RMSE
F
R
p
r
e
d
2
RMSE
3D7
0.93
0.89
0.15
23.86
0.96
0.18
W2
0.96
0.93
0.14
38.38
0.90
0.28Figure 2
Plots ofY-randomization for log (1/IC50) 3D7.Figure 3
Plots ofY-randomization for log (1/IC50) W2.Plot of the predicted versus the observed of log (1/IC50) growth inhibition of 3D7 and W2 strains of P. falciparum. The LOO cross-validation compounds are represented as grey dots and six derivatives, used as test set, as black dots.
(a)
(b)


## 3.4. QSAR Model for Blood-to-Plasma Concentration Ratio

The best linear models consisted of the five descriptors in order to relate them to the logRb values tabulated in Table 12. The predicted Rb values and the residuals for the compounds are listed in Table 2. As can be seen, the MLR models have good statistical quality with low prediction error. The models obtained were validated by calculating the cross-validated Q2 values obtained using the LOO cross-validation method. This is the measure of the predictive power of regression equations. The Q2 values for the best regression models for log Rb were suggestive of robust models. The results of the LMO test are collected in Table 3. On average, the overall test steps R2≥QLMO2 and QLOO2≈QLMO2 which is another proof that the model is not underdetermined. The model was further validated by applying the Y-randomization. Several random shuffles of the Y vector were performed. Y-randomization results are in agreement with the suggested limits [28]. Y-randomization results are shown in Figures 5 and 6. The Rb prediction ability of the MLR models were also tested using the validation set of data (Table 13). The correlations between the predicted and experimental values of Rb (from LOO cross-validation and external test) are shown in Figure 7.Table 12
Multivariate linear regression models and statistical parameters for blood-to-plasma concentration ratio.
logRb
Equation
R
2
R
a
d
j
2
RMSE
F
Q
2
Q
L
5
o
2
B/P, (1μM)
0.948 (0.140) − 0.013 (0.002) RDF065u − 33.174 (6.778) GATS8m − 0.055 (0.007) RDF090m + 4.018 (0.582) R2u+ + 0.305 (0.104) Mor24m
0.92
0.89
0.04
32.69
0.84
0.85
B/P, (10μM)
−21.744 (6.135) − 3.861 (0.431) R3m + 0.033(0.008) RDF095m + 28.454 (5.396) G3p − 9.616 (2.220) R4m+ + 20.931 (6.131) MATS4m
0.87
0.83
0.10
20.55
0.74
0.80Table 13
Evaluation of the prediction ability of the MLR models in the external validation set forRb.
Training set
Test set
logRb
R
2
R
a
d
j
2
RMSE
F
R
p
r
e
d
2
RMSE
B/P (1μM)
0.89
0.83
0.05
14.57
0.93
0.06
B/P (10μM)
0.87
0.80
0.11
12.03
0.84
0.09Figure 5
Plots ofY-randomization for log Rb, B/P(1 μM).Figure 6
Plots ofY-randomization for log Rb, B/P(10 μM).Plot of the predicted versus the observed logRb that was measured for each of the compounds at 1 and 10 μM. The LOO cross-validation of compounds is represented as grey dots and test set as black dots.
(a)
(b)


## 4. Conclusions

A quantitative structure-activity relationship (QSAR) study was applied to the series of 4-aminoquinoline antimalarial compounds potentially active against the 3D7 and W2 strains ofP. falciparum. For each strain, statistically significant models were obtained using the GA-based MLR method. These models may be considered as mathematical equations for the prediction of antimalarial activities of the compounds structurally similar to those used in this study. Models based on GA-MLR were developed to predict the blood-to-plasma concentration ratio of the analogues based on selected molecular descriptors. The predictive ability of the test and its validation set were confirmed by the Rb models. The LOO and LMO cross-validation methods, the Y-randomization technique, and the external validation indicated that the model is significant, robust, and has good internal and external predictability. The use of these models may be an important tool in early drug discovery by providing a relevant pharmacokinetic parameter.



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*Source: 560415-2012-10-03.xml*