Molecular Descriptors Family on Structure Activity Relationships 6. Octanol-Water Partition Coefficient of Polychlorinated Biphenyls

 

Lorentz Jäntschi and Sorana Bolboacă

 

Technical University of Cluj-Napoca, Romania, http://lori.academicdirect.org

“Iuliu Haţieganu” University of Medicine and Pharmacy, http://sorana.academicdirect.ro

 

 

Abstract

Octanol-water partition coefficient of two hundred and six polychlorinated biphenyls was model by the use of an original method based on complex information obtained from compounds structure. The regression analysis shows that best results are obtained in four-varied model (r2 = 0.9168). The prediction ability of the model was studied through leave-one-out analysis (r2cv(loo) = 0.9093) and in training and test sets analysis. Modeling the octanol-water partition coefficient of polychlorinated biphenyls by integration of complex structural information provide a stable and performing four-varied model, allowing us to make remarks about relationship between structure of polychlorinated biphenyls and associated octanol-water partition coefficients.

Keywords

PolyChlorinated Biphenyls (PCBs), Molecular Descriptors Family (MDF), Structure-Property Relationships (SAR), Octanol-water partition coefficient

 

 

Background

 

Polychlorinated biphenyls (PCBs), stable organic industrials chemicals widely used as insulating fluids, hydraulic and lubricating fluids, heat exchanger fluids and as additives in adhesive inks and paints [1] are persistent in the environment [2] as well as in the living tissue [3].

Quantitative structure-property relationships of PCBs were previous studied taking into consideration octanol-water partition coefficients and soil-water partition coefficients [4] and/or other physicochemical properties [5].

Based on the complex information offered by the structure of polychlorinated biphenyls congeners, octanol-water partition coefficients express as log Kow was modeled by applying of an original methodology. Thus, the aim of the paper is to present the performances of the original methodology in estimation and prediction of octanol-water partition coefficients of polychlorinated biphenyls.

 

 

Materials and Methods

 

A set of two-hundred and six polychlorinated biphenyls congeners with measured octanol-water partition coefficients were included into analysis. The values for the octanol-water partition coefficients were take from a previous reported study [6]. There were included ten PCBs congener group: mono-, di-, tri-, terta-, penta-, hexa-, hepta-, octa-, nona-, decachlorobiphenyl. Table 1 contains the PBCs number, the structure (chlorine-filled) and associated octanol-water partition coefficients (express as logKow).

            The original methodology is based on molecular descriptors family computed based on the structure of the PCBs. The steps used to model the activity of interest were presented in details on [7] and were:

·        Step 1: Sketch of the three-dimensional structure of polychlorinated biphenyls congeners;

·        Step 2: Create the file with the measured octanol-water partition coefficients of the polychlorinated biphenyls congeners;

·        Step 3: Generating, computing and filtering the members of molecular descriptors family for  polychlorinated biphenyls congeners;

·        Step 4: Finding and identifying the SAR models for polychlorinated biphenyls congeners;

·        Step 5: Validate the SAR model by a cross-validation analysis [8];

·        Step 6: Analyze the selected SAR model.

 

 

Results and Discussions

 

Modeling of the octanol-water partition coefficients of the polychlorinated biphenyls congeners was run on mono-, bi-, and tetra-varied SARs. The model which obtained best performance was the four-varied model and is presented here. The equation of the four varied model is:

ŶlogKow = 3.039 - 0.421·IIDDKGg + 0.044·IHDRKEg + 0.070·aHMmjQti - 37.502·aSMMjQg

The abbreviation associated with the studied PCBs congener (PBC no.), the measured octanol-water partition coefficients (express as logKow), the values of the descriptors used and estimated octanol-water partition coefficients by the model (ŶlogKow) and the absolute differences between estimated by the model and  measured octanol-water partition coefficients (|Ŷ-logKow|) are in table 1.

 

Table 1. Polychlorinated biphenyls abbreviation, logKow, values for descriptors used by model,

ŶlogKow, and |ŶlogKow - logKow|

PCB

no.

Structure
(chlorine-filled)

logKow

IIDDKGg

IHDRKEg

aHMmjQt

aSMMjQg

ŶlogKow

|Ŷ-logKow|

1

2

4.6010

5.7503

91.1540

0.0244

3.67·10-5

4.6477

0.0467

2

3

4.4210

6.8329

100.870

0.0286

5.60·10-4

4.6022

0.1812

3

4

4.4010

7.1099

105.020

0.0303

1.50·10-4

4.6845

0.2835

4

2,2'

5.0230

5.6688

98.0270

0.0454

2.17·10-4

4.9804

0.0426

5

2,3'

5.0210

6.0092

104.370

0.1765

4.61·10-5

5.1330

0.1120

6

2,4

5.1500

7.0663

113.130

0.0205

4.01·10-5

5.0646

0.0854

7

2,4'

5.3010

7.2970

115.000

0.0079

8.57·10-5

5.0476

0.2534

8

2,5

5.1800

5.8788

102.720

0.1013

4.82·10-5

5.1096

0.0704

9

2,6

5.3110

5.3684

95.9580

0.1265

4.87·10-5

5.0274

0.2836

10

3,3'

5.3430

6.8183

115.510

0.0464

2.30·10-4

5.2688

0.0742

11

3,4

5.2950

7.2304

118.150

0.0067

4.30·10-5

5.2163

0.0787

12

3,5

5.4040

6.7261

115.520

0.0357

5.34·10-4

5.2959

0.1081

13

4,4'

5.3350

7.3646

124.560

0.0065

1.00·10-4

5.4409

0.1059

14

2,2',3

5.3110

6.5110

114.030

0.0668

2.44·10-4

5.3336

0.0226

15

2,2',4

5.7610

6.9032

119.960

0.0867

2.52·10-4

5.4317

0.3293

16

2,2',5

5.5510

6.8266

120.050

0.0579

2.66·10-4

5.4654

0.0856

17

2,2',6

5.4810

5.8973

106.490

0.0865

3.80·10-4

5.2550

0.2260

18

2,3,3'

5.5770

7.8504

128.320

0.7667

8.00·10-5

5.4564

0.1206

19

2,3,4

5.5170

7.4010

125.250

0.0235

5.28·10-5

5.4591

0.0579

20

2,3,4'

5.4210

8.1564

132.790

0.0508

7.75·10-5

5.4753

0.0543

21

2,3,5

5.5770

6.5446

122.510

0.7310

1.40·10-4

5.7444

0.1674

22

2,3,6

5.6710

6.2218

110.890

0.0325

1.01·10-4

5.3195

0.3515

23

2,3',4

5.6770

8.1210

134.330

0.0325

5.58·10-5

5.5578

0.1192

24

2,3',5

5.6670

7.3770

129.310

0.1674

8.11·10-5

5.6575

0.0095

25

2,3',6

5.4470

6.2046

113.400

0.0385

1.01·10-4

5.4381

0.0089

26

2,4,4'

5.6910

8.4470

139.210

0.0266

6.66·10-5

5.6355

0.0555

27

2,4,5

5.7430

7.1079

126.640

0.0245

5.28·10-5

5.6439

0.0991

28

2,4,6

5.5040

6.5149

114.430

0.0420

1.50·10-4

5.3515

0.1525

29

2,4',5

5.6770

7.5935

133.180

0.0270

7.78·10-5

5.7278

0.0508

30

2,4',6

5.7510

6.4853

116.740

0.0429

1.60·10-4

5.4657

0.2853

31

2',3,4

5.5720

7.7422

129.640

0.0889

7.82·10-5

5.5131

0.0589

32

2',3,5

5.6670

7.2479

126.270

0.0128

7.99·10-5

5.5668

0.1002

33

3,3',4

5.8270

8.6854

141.730

0.1163

3.69·10-4

5.6414

0.1856

34

3,3',5

4.1510

8.1095

137.500

0.3422

3.53·10-2

4.4021

0.2511

35

3,4,4'

4.9410

8.9668

146.520

0.3565

1.86·10-4

5.7583

0.8173

36

3,4,5

5.7670

7.0857

129.590

0.0297

1.89·10-3

5.7151

0.0519

37

3,4',5

5.8970

8.3823

142.120

0.0550

3.49·10-4

5.7827

0.1143

38

2,2',3,3'

5.5610

7.7406

134.940

0.1340

2.94·10-4

5.7430

0.1820

39

2,2',3,4

6.1110

7.8567

137.950

0.0258

2.88·10-4

5.8198

0.2912

40

2,2',3,4'

5.7670

8.0115

139.920

0.1247

2.83·10-4

5.8488

0.0818

41

2,2',3,5

5.7570

7.2531

133.770

0.0875

2.68·10-4

5.8942

0.1372

42

2,2',3,5'

5.8110

7.5381

135.540

0.0446

3.09·10-4

5.8479

0.0369

43

2,2',3,6

5.5370

6.5064

121.120

0.1066

3.47·10-4

5.6478

0.1108

44

2,2',3,6'

5.5370

6.6121

121.520

0.1112

4.71·10-4

5.6166

0.0796

45

2,2',4,4'

6.2910

8.1688

145.660

0.2853

3.00·10-4

6.0468

0.2442

46

2,2'4,5

5.7870

7.2785

136.050

0.0489

2.52·10-4

5.9821

0.1951

47

2,2',4,5'

6.2210

7.6295

141.160

0.1152

2.59·10-4

6.0646

0.1564

48

2,2',4,6

5.6370

6.6210

124.040

1.3559

4.02·10-4

5.8136

0.1766

49

2,2',4,6'

5.6370

6.7699

126.190

0.0853

3.62·10-4

5.7589

0.1219

50

2,2',5,5'

6.0910

6.6586

135.000

0.0994

2.62·10-4

6.1997

0.1087

51

2,2',5,6'

5.6270

6.1810

121.830

0.0035

9.77·10-6

5.8215

0.1945

52

2,2',6,6'

5.9040

5.3274

109.030

0.1105

4.85·10-4

5.6047

0.2993

53

2,3,3',4

6.1170

8.3206

146.050

0.0345

4.93·10-5

5.9921

0.1249

54

2,3,3',4'

6.1170

8.3589

146.460

0.0962

5.52·10-5

5.9982

0.1188

55

2,3,3',5

6.1770

7.8097

142.860

0.8606

7.89·10-5

6.1226

0.0544

56

2,3,3',5'

6.1770

7.9437

142.850

0.0479

5.54·10-5

6.0100

0.1670

57

2,3,3',6

5.9570

6.9758

129.260

0.0476

9.87·10-5

5.8151

0.1419

58

2,3,4,4'

5.4520

8.2526

145.460

0.0345

4.82·10-5

5.9947

0.5427

59

2,3,4,5

5.9430

6.7297

133.750

0.0286

3.72·10-5

6.1181

0.1751

60

2,3,4,6

5.8970

6.2938

123.830

0.0630

1.40·10-4

5.8617

0.0353

61

2,3,4',5

6.1770

8.0492

147.320

0.0969

6.32·10-5

6.1662

0.0108

62

2,3,4',6

5.9570

7.2049

133.110

0.0597

1.63·10-4

5.8873

0.0697

63

2,3,5,6

5.8670

5.6388

122.010

0.1451

9.11·10-5

6.0644

0.1974

64

2,3',4,4'

5.4520

8.6051

153.380

0.0353

5.40·10-5

6.1961

0.7441

65

2,3',4,5

6.2070

8.1728

148.280

0.0359

5.11·10-5

6.1529

0.0541

66

2,3',4,5'

6.2670

8.1003

148.960

0.0334

5.87·10-5

6.2129

0.0541

67

2,3',4,6

6.0470

7.2353

133.270

0.0631

1.66·10-4

5.8817

0.1653

68

2,3',4',5

6.2310

7.5977

146.340

0.1246

5.56·10-5

6.3151

0.0841

69

2,3',4',6

5.9870

6.4091

128.760

0.0684

1.26·10-4

6.0319

0.0449

70

2,3',5,5'

6.2670

7.2087

143.450

0.0517

5.87·10-5

6.3459

0.0789

71

2,3',5',6

6.0470

6.0292

126.110

0.0503

1.18·10-4

6.0737

0.0267

72

2,4,4',5

6.6710

8.2735

152.290

0.0305

5.04·10-5

6.2873

0.3837

73

2,4,4',6

6.0570

7.4294

137.080

0.1203

4.40·10-4

5.9621

0.0949

74

2',3,4,5

6.1370

7.3073

139.090

0.0521

5.68·10-5

6.1119

0.0251

75

3,3',4,4'

6.5230

9.1490

161.430

0.2535

9.76·10-5

6.3366

0.1864

76

3,3',4,5

6.3570

8.1041

151.240

1.4919

1.77·10-4

6.4093

0.0523

77

3,3',4,5'

6.4270

8.5725

156.830

0.5807

1.28·10-4

6.3975

0.0295

78

3,3',5,5'

6.5830

7.9892

152.370

0.3196

2.56·10-4

6.4229

0.1601

79

3,4,4',5

6.3670

8.5262

157.620

0.1010

1.19·10-4

6.4188

0.0518

80

2,2',3,3',4

6.1420

8.2976

153.620

0.4084

3.31·10-4

6.3517

0.2097

81

2,2',3,3',5

6.2670

7.6890

148.730

0.7941

3.69·10-4

6.4172

0.1502

82

2,2',3,3',6

6.0410

6.9185

136.000

0.0442

3.88·10-4

6.1260

0.0850

83

2,2',3,4,4'

6.6110

8.4996

159.160

0.2075

3.32·10-4

6.4975

0.1135

84

2,2',3,4,5

6.2040

7.2394

145.350

0.1531

2.73·10-4

6.4160

0.2120

85

2,2',3,4,5'

6.3710

7.9248

154.060

0.0658

3.42·10-4

6.5038

0.1328

86

2,2',3,4,6

7.5160

6.7474

135.070

19.1930

3.56·10-4

7.4926

0.0234

87

2,2',3,4,6'

6.0770

6.8822

137.480

0.1178

8.98·10-4

6.1927

0.1157

88

2,2',3,4',5

6.3670

7.9310

154.600

0.1001

2.65·10-4

6.5303

0.1633

89

2,2',3,4',6

6.1370

7.1280

140.750

0.1762

3.36·10-4

6.2589

0.1219

90

2,2',3,5,5'

6.3570

7.3803

149.770

0.4452

3.11·10-4

6.5710

0.2140

91

2,2',3,5,6

6.0470

6.3200

132.670

0.5266

3.58·10-4

6.2654

0.2184

92

2,2',3,5,6'

6.1370

6.4532

134.510

0.0738

1.69·10-4

6.2662

0.1292

93

2,2',3,5',6

6.1370

6.6477

136.300

0.4964

7.70·10-4

6.2704

0.1334

94

2,2',3,6,6

5.7170

5.9325

123.370

0.0920

3.78·10-4

5.9865

0.2695

95

2,2',3',4,5

6.6710

7.8560

152.750

0.1031

3.34·10-4

6.4778

0.1932

96

2,2',3',4,6

6.1370

7.0705

139.710

0.1352

7.49·10-4

6.2187

0.0817

97

2,2',4,4',5

7.2110

8.1412

159.410

0.0577

2.85·10-4

6.6507

0.5603

98

2,2',4,4',6

6.2370

7.3053

144.740

0.2006

5.63·10-4

6.3537

0.1167

99

2,2',4,5,5'

7.0710

7.6259

154.880

0.1225

3.04·10-4

6.6712

0.3998

100

2,2',4,5,6'

6.1670

6.7261

138.380

0.0262

2.22·10-5

6.3246

0.1576

101

2,2',4,5',6

6.2270

6.8046

140.120

0.0279

5.27·10-5

6.3674

0.1404

102

2,2',4,6,6

5.8170

6.0829

126.540

0.0922

3.76·10-4

6.0634

0.2464

103

2,3,3',4,4'

6.6570

9.1546

168.730

0.0365

4.78·10-5

6.6435

0.0135

104

2,3,3',4,5

6.6470

8.2227

158.650

0.0384

3.80·10-5

6.5907

0.0563

105

2,3,3',4',5

6.7170

8.5882

164.350

0.0579

5.64·10-5

6.6895

0.0275

106

2,3,3',4,5'

6.7170

8.6053

163.610

0.0364

5.31·10-5

6.6482

0.0688

107

2,3,3',4,6

6.4870

7.5286

145.840

0.0862

1.67·10-4

6.3153

0.1717

108

2,3,3',4',6

6.5320

7.5906

148.130

0.3660

1.60·10-4

6.4101

0.1219

109

2,3,3',5,5'

6.7670

8.0899

159.630

0.0377

5.85·10-5

6.6891

0.0779

110

2,3,3',5,6

6.4570

7.1659

142.920

0.1454

9.27·10-5

6.3458

0.1112

111

2,3,3',5',6

6.5470

7.2338

144.320

0.0712

1.41·10-4

6.3721

0.1749

112

2,3,4,4',5

6.6570

8.2871

163.400

0.0322

3.75·10-5

6.7731

0.1161

113

2,3,4,4',6

6.4970

7.7007

150.180

0.1935

6.47·10-4

6.4241

0.0729

114

2,3,4,5,6

6.3040

6.1425

134.100

0.0371

1.31·10-4

6.3777

0.0737

115

2,3,4',5,6

6.4670

7.3123

146.830

0.3320

1.63·10-4

6.4673

0.0003

116

2,3',4,4',5

7.1210

8.7170

168.800

0.0387

4.74·10-5

6.8309

0.2901

117

2,3',4,4',6

6.5870

7.7307

152.260

0.0954

5.32·10-4

6.5009

0.0861

118

2,3',4,5,5'

6.7970

8.1850

163.840

0.0386

5.17·10-5

6.8354

0.0384

119

2,3',4,5',6

6.6470

7.2928

148.060

0.1874

2.93·10-4

6.5149

0.1321

120

2',3,3',4,5

6.6470

8.3558

159.300

0.0339

5.32·10-5

6.5626

0.0844

121

2',3,4,4',5

6.7470

8.5776

165.470

0.0506

1.30·10-4

6.7401

0.0069

122

2',3,4,5,5'

6.7370

7.8399

159.710

0.0350

5.59·10-5

6.7977

0.0607

123

2',3,4,5,6'

6.5170

6.9321

142.900

0.2070

7.11·10-4

6.4244

0.0926

124

3,3',4,4'5

6.8970

9.2142

175.600

0.2341

9.05·10-5

6.9342

0.0372

125

3,3',4,5,5'

6.9570

8.6661

170.560

0.0774

1.16·10-4

6.9302

0.0268

126

2,2',3,3',4,4'

6.9610

9.3307

179.190

0.7685

7.25·10-4

7.0572

0.0962

127

2,2',3,3',4,5

7.3210

8.5439

169.150

0.0167

1.44·10-3

6.8653

0.4557

128

2,2',3,3',4,5'

7.3910

8.6910

172.480

0.0174

1.04·10-3

6.9659

0.4251

129

2,2',3,3',4,6

6.5870

7.6941

154.760

0.0299

8.40·10-4

6.6106

0.0236

130

2,2',3,3',4,6'

6.5870

7.8668

157.060

0.0471

6.20·10-4

6.6490

0.0620

131

2,2',3,3',5,5'

6.8670

7.8751

165.430

0.3205

3.97·10-4

7.0428

0.1758

132

2,2',3,3',5,6

7.3040

7.1724

150.190

0.2877

1.26·10-3

6.6304

0.6736

133

2,2',3,3',5,6'

7.1510

7.1833

151.550

0.0310

1.92·10-4

6.7081

0.4429

134

2,2',3,3',6,6'

6.5110

6.4063

138.560

0.0789

2.98·10-4

6.4604

0.0506

135

2,2',3,4,4',5'

7.4410

8.6591

174.490

0.3322

6.17·10-4

7.1058

0.3352

136

2,2',3,4,4',6

6.6770

7.7162

158.610

0.0244

6.15·10-4

6.7795

0.1025

137

2,2',3,4,4',6'

6.6770

7.8664

159.440

17.463

4.04·10-2

6.4781

0.1989

138

2,2',3,4,5,5'

7.5920

7.8362

166.540

0.1417

4.20·10-4

7.0949

0.4971

139

2,2',3,4,5,6

6.5170

6.7464

146.160

0.0415

5.16·10-4

6.6424

0.1254

140

2,2',3,4,5,6'

6.6070

6.9031

149.310

0.5610

1.94·10-4

6.7639

0.1569

141

2,2',3,4,5',6

6.6770

7.1854

153.300

0.1587

1.13·10-2

6.3768

0.3002

142

2,2',3,4,6,6'

6.2570

6.4146

138.950

0.0774

2.91·10-4

6.4743

0.2173

143

2,2',3,4',5,5'

6.8970

8.0823

169.690

0.0963

6.14·10-4

7.1201

0.2231

144

2,2',3,4',5,6

6.6470

7.3016

154.700

0.0982

5.27·10-4

6.7896

0.1426

145

2,2',3,4',5,6'

6.7370

7.4207

155.500

0.1185

1.83·10-4

6.7892

0.0522

146

2,2',3,4',5',6

7.2810

7.1955

153.590

0.0208

1.48·10-3

6.7440

0.5370

147

2,2',3,4',6,6'

6.3270

6.5980

141.640

0.0790

3.00·10-4

6.5158

0.1888

148

2,2',3,5,5',6

6.6470

6.7917

149.800

0.0450

1.87·10-4

6.7967

0.1497

149

2,2',3,5,6,6'

6.2270

6.0509

135.760

0.0815

2.94·10-4

6.4866

0.2596

150

2,2',4,4',5,5'

7.7510

8.1709

174.310

0.1986

4.17·10-4

7.3015

0.4495

151

2,2',4,4',5,6'

6.7670

7.4824

159.260

0.0188

9.35·10-5

6.9258

0.1588

152

2,2',4,4',6,6'

7.1230

6.7120

145.340

0.0787

2.99·10-4

6.6313

0.4917

153

2,3,3',4,4',5

7.1870

8.9450

180.720

0.0383

2.82·10-5

7.2624

0.0754

154

2,3,3',4,4',5'

7.1870

8.9295

180.060

0.0500

3.70·10-5

7.2402

0.0532

155

2,3,3',4,4',6

7.0270

8.1071

166.380

0.3064

2.87·10-4

6.9903

0.0367

156

2,3,3',4,5,5'

7.2470

8.4424

175.580

0.0401

3.17·10-5

7.2467

0.0003

157

2,3,3',4,5,6

6.9370

7.3571

156.700

0.0739

1.34·10-4

6.8677

0.0693

158

2,3,3',4,5',6

7.0870

7.6904

161.910

1.6216

2.19·10-4

7.0623

0.0247

159

2,3,3',4',5,5'

7.2470

8.1738

174.530

0.0248

3.74·10-5

7.3121

0.0651

160

2,3,3',4',5,6

6.9970

7.5592

161.980

0.2656

9.21·10-5

7.0309

0.0339

161

2,3,3',4',5',6

7.0270

7.2468

158.640

0.1114

1.16·10-4

7.0031

0.0239

162

2,3,3',5,5',6

7.0570

7.2209

157.930

0.1685

9.63·10-5

6.9874

0.0696

163

2,3,4,4',5,6

6.9370

7.4614

161.140

0.5263

4.59·10-4

7.0393

0.1023

164

2,3',4,4',5,5'

7.2770

8.4739

180.990

0.0537

4.30·10-5

7.4731

0.1961

165

2,3',4,4',5',6

7.1170

7.4940

163.550

0.2913

5.09·10-4

7.1138

0.0032

166

3,3',4,4',5,5'

7.4270

9.1962

189.460

0.0633

8.19·10-5

7.5426

0.1156

167

2,2',3,3',4,4',5

7.2770

8.9382

188.200

0.1129

9.03·10-5

7.5986

0.3216

168

2,2',3,3',4,4',6

6.7040

8.1822

173.820

0.1327

1.78·10-3

7.2194

0.5154

169

2,2',3,3',4,5,5'

7.3370

8.4591

183.610

0.0758

9.65·10-4

7.5620

0.2250

170

2,2',3,3',4,5,6

7.0270

7.6027

165.040

0.0482

9.50·10-4

7.1005

0.0735

171

2,2',3,3',4,5,6'

7.1170

7.5973

167.060

0.0124

8.87·10-5

7.2218

0.1048

172

2,2',3,3',4,5',6

7.1770

7.7165

169.220

0.0266

8.26·10-5

7.2683

0.0913

173

2,2',3,3',4,6,6'

6.7670

7.0135

155.320

0.0680

2.45·10-4

6.9467

0.1797

174

2,2',3,3',4',5,6

7.0870

7.6992

169.170

0.0578

2.24·10-4

7.2703

0.1833

175

2,2',3,3',5,5',6

7.1470

7.3049

165.140

0.1383

2.63·10-4

7.2622

0.1152

176

2,2',3,3',5,6,6'

6.7370

6.6644

151.780

0.0715

2.45·10-4

6.9374

0.2004

177

2,2',3,4,4',5,5'

7.3670

8.6195

188.140

0.0550

4.81·10-3

7.5491

0.1821

178

2,2',3,4,4',5,6

7.1170

7.7127

170.270

6.8760

6.77·10-3

7.5427

0.4257

179

2,2',3,4,4',5,6'

7.2070

7.8062

171.680

0.6290

2.78·10-4

7.3739

0.1669

180

2,2',3,4,4',5',6

7.2070

7.8790

173.190

0.1139

3.01·10-4

7.3733

0.1663

181

2,2',3,4,4',6,6'

6.8570

7.1523

158.990

0.0677

2.43·10-4

7.0505

0.1935

182

2,2',3,4,5,5',6

7.9330

6.8634

164.000

0.4577

1.39·10-5

7.4292

0.5038

183

2,2',3,4,5,6,6'

6.6970

6.2008

148.390

0.0693

2.38·10-4

6.9828

0.2858

184

2,2',3,4',5,5',6

7.1770

7.3776

168.560

0.0448

1.14·10-4

7.3819

0.2049

185

2,2',3,4',5,6,6'

6.8270

6.7527

155.210

0.0714

2.43·10-4

7.0519

0.2249

186

2,3,3',4,4',5,5'

7.7170

9.1221

195.930

0.0488

3.59·10-5

7.8604

0.1434

187

2,3,3',4,4',5,6

7.4670

8.2487

178.880

0.5202

6.32·10-4

7.4850

0.0180

188

2,3,3',4,4',5',6

7.5570

8.2502

179.590

0.6986

6.92·10-4

7.5259

0.0311

189

2,3,3',4,5,5',6

7.5270

7.7471

173.540

0.0626

2.84·10-4

7.4413

0.0857

190

2,3,3',4',5,5',6

7.5270

7.6407

174.490

0.4337

1.22·10-4

7.5600

0.0330

191

2,2',3,3',4,4',5,5'

8.6830

8.8559

201.230

0.0917

6.13·10-4

8.1879

0.4951

192

2,2',3,3',4,4',5,6

7.5670

8.1340

185.280

0.0365

5.66·10-5

7.8039

0.2369

193

2,2',3,3',4,4',5',6

7.6570

8.0500

185.640

0.0407

3.72·10-5

7.8562

0.1992

194

2,2',3,3',4,4',6,6'

7.3070

7.5022

173.290

0.0595

1.97·10-4

7.5363

0.2293

195

2,2',3,3',4,5,5',6

7.6270

7.7337

180.830

0.0627

1.47·10-4

7.7742

0.1472

196

2,2',3,3',4,5,6,6'

7.2070

6.9867

166.280

0.0619

1.96·10-4

7.4437

0.2367

197

2,2',3,3',4,5',6,6'

7.2770

7.1190

169.460

0.0626

1.98·10-4

7.5285

0.2515

198

2,2',3,3',4',5,5',6

7.6270

7.6994

180.700

0.0627

1.52·10-4

7.7827

0.1557

199

2,2',3,3',5,5',6,6'

8.4230

6.6004

165.330

0.0656

1.96·10-4

7.5645

0.8585

200

2,2',3,4,4',5,5',6

7.6570

7.7846

184.510

0.6727

3.23·10-4

7.9513

0.2943

201

2,2',3,4,4',5,6,6'

7.3070

7.0818

170.100

0.0617

1.93·10-4

7.5726

0.2656

202

2,3,3',4,4',5,5',6

8.0070

8.1803

191.360

1.1642

5.30·10-4

8.1139

0.1069

203

2,2',3,3',4,4',5,5',6

9.1430

7.9885

197.410

0.0270

6.07·10-5

8.4003

0.7427

204

2,2',3,3',4,4',5,6,6'

7.7470

7.4690

184.980

0.0550

1.57·10-4

8.0680

0.3210

205

2,2',3,3',4,5,5',6,6'

8.1640

7.1318

180.950

0.0577

1.60·10-4

8.0319

0.1321

206

2,2',3,3',4,4',5,5',6,6'

9.6030

7.4035

197.030

0.0512

1.33·10-4

8.6287

0.9743

 

Three molecular descriptors take into consideration the geometry of PCBs (IIDDKGg, IHDRKEg, and aSMMjQg) and one the topology of compounds (aHMmjQt). As atomic property, two descriptors consider the partial change (aHMmjQt, and aSMMjQg), one the group electronegativity (IIDDKGg) and one the atomic electronegativity (IHDRKEg). Looking at the interaction descriptor (the fifth letter in descriptors name) it can be observed that all descriptors consider the elastic force.

The results of multiple linear regressions associated to the four-varied model (see table 2, and table 3) sustain the estimation and prediction abilities of the best performing SAR model.

In the table 3 are the 95% probability of confidence intervals - lower (95%CIL) and upper (95%CIU) boundaries, coefficients, standard error (StdErr) of the coefficient, Student test parameter (t) and Student probability (pt).

 

Table 2. Statistics associated with the tetra-varied model

Characteristic

Notation

Values

Correlation coefficient

r

0.9575

Squared correlation coefficient

r2

0.9168

Adjusted squared correlation coefficient

r2adj

0.9151

Standard error of estimated

sest

0.2420

Fisher parameter

Fest

554

Probability of wrong model

pest(%)

< 1·10-15

Cross-validation leave-one-out (loo) score

r2cv(loo)

0.9093

Fisher parameter for loo analysis

Fpred

504

Probability of wrong model for loo analysis

ppred(%)

< 1·10-15

Standard error for loo analysis

sloo

0.2526

The difference between r2 and r2cv(loo)

r2 - r2cv(loo)

0.0075

Squared correlation coefficients between each descriptor and measured octanol-water partition coefficients or between pairs of descriptors

r2(IIDDKGg, IHDRKEg)

0.48245

r2(IIDDKGg, aHMmjQt)

0.00005

r2(IIDDKGg, aSMMjQg)

0.00385

r2(IHDRKEg, aHMmjQt)

0.00039

r2(IHDRKEg, aSMMjQg)

0.00073

r2(aHMmjQt, aSMMjQg)

0.24805

r2(IIDDKGg, log Kow)

0.15111

r2(IHDRKEg, log Kow)

0.78907

r2(aSMMjQg, log Kow)

0.00932

r2(aHMmjQt, log Kow)

0.00786

 

Table 3. Statistics associated with the four-varied model

 

95%CIL

Coefficients

95%CIU

StdError

t

pt (%)

Intercept

2.735

3.039

3.343

0.154

19.716

7.27·10-47

IIDDKGg

-0.477

-0.421

-0.365

0.028

-14.804

5.09·10-32

IHDRKEg

0.042

0.044

0.046

0.001

41.725

5.97·10-99

aHMmjQt

0.049

0.070

0.090

0.010

6.639

2.89·10-8

aSMMjQg

-47.601

-37.499

-27.397

5.123

-7.319

5.86·10-10

 

The model which consider in estimation four molecular descriptors is significant statistically, having a probability of a wrong model less than 1·10-15 (%). The estimation ability of the SAR model is sustained by the value of the correlation coefficient (r = 0.9575), the confidence boundaries associated with the coefficients (see table 3), and probabilities associated with Student tests (for all coefficients less than 0.001 - see table 3). Almost ninety-two percent (r2 = 0.9168) from variation of octanol-water partition coefficient can be explained by its linear relationship with the variation of the four molecular descriptors used in the model. The probability of wrong model for leave-one-out analysis (ppred(%) < 1·10-15) and its associated Fisher parameter (Fpred = 504) sustains the estimation ability of the model. The four-varied SAR model is a stable one, stability sustained by the values of difference between correlation coefficient and cross validation leave-one-out correlation score (r2 - r2cv(loo) = 0.0075). The power of the four-varied model in octanol-water partition coefficient prediction of PCBs is sustained by the absence of multicolinearity of descriptors used by the model (see the squared correlation coefficients between pairs of descriptors, which always is less than 0.48 - table 2).

The plot of dependency between measured (logKow) and estimated based on the structure of polychlorinated biphenyls compounds obtained with the tetra-varied model is in figure 1.

 

Figure 1. Measured vs. estimated logKow by the tetra-varied model

 

The estimation values of octanol-water partition coefficients by the use of the four-varied model of are less or greater than measured values (see figure 2). Note that, the mean and 95% confidence intervals of the mean and standard error for measured (mMeasured = 6.4802, 95%CIMeasured = [6.3709, 6.5895], StdErrMeasured = 0.0554) and estimated (mEstimated = 6.4806, 95%CIEstimated = [6.3664, 6.5947], StdErrEstimated = 0.0579) octanol-water partition coefficients are almost equal.

 

Figure 2. Variation of measured (blue line) and estimated (red line) by the four-varied model of octanol-water partition coefficient for PCBs

 

            In order to seen the estimation abilities of four-varied model, measured and estimated values were sort by the absolute differences between estimated and measured octanol-water partition coefficient of PCBs and split into two subsets (first containing one-hundred PCBs and second containing the other one-hundred and six PBCs). The graphical representations are in figure 3a (one-hundred compounds) and 3b (one-hundred and six compounds), where the PCB number was associated with corresponding estimated and measured values.

 

 

Figure 3a. Measured (blue line) and estimated by the tetra-varied model (red-line)

of octanol-water partition coefficients for one-hundred PCBs

 

Figure 3b. Measured (blue line) and estimated by the tetra-varied model (red line)

of octanol-water partition coefficients for one-hundred and six PCB

Analyzing the residuals of the four-varied model allowed us to assess the suitability of the model. Looking at the differences between measured and estimated octanol-water partition coefficient for PCBs (figure 4) it can be observed that the values vary around zero and most of them between -0.5 and 0.5.

 

Figure 4. The differences between measured and estimated by the tetra-varied model of octanol-water partition coefficients for PCBs

 

The prediction abilities of the four-varied SAR model were studied through training and test sets analysis, and the results are in table 4. There were analyzed twelve situations, starting with a training sample size equal with 116 and increasing the number of PCBs included into training sets through randomization with seven until one hundred ninety-three. In table 4, there were included the number of PCBs in training sets (Notr), the coefficients of the model, the squared correlation coefficient for training set (rtr2), Fisher parameter associated with training set regression (Ftr), the number of the PCBs in test sets (Nots), the squared correlation coefficient for test set (rts2), Fisher parameter associated with training set regression (Fts), the mean (Mean) and standard deviation (StDev) for squared correlation coefficients and the 95% probability CI [95%CIL and 95%CIU] for coefficients.

 

Table 4. Results of training vs. test sets analysis

Notr

intercept

IIDDKGg

IHDRKEg

aHMmjQt

aSMMjQg

 

rtr2

Ftr

Nots

rts2

Fts

116

3.070

-0.408

0.043

0.064

-34.937

 

0.9141

295*

90

0.9219

235*

123

3.058

-0.390

0.043

0.064

-43.454

 

0.9229

353*

83

0.9043

176*

130

2.957

-0.413

0.044

0.067

-33.462

 

0.9232

376*

76

0.9068

169*

137

3.011

-0.438

0.045

0.064

-32.008

 

0.9004

298*

69

0.9432

256*

144

3.090

-0.450

0.045

0.062

-45.236

 

0.9143

371*

62

0.9186

148*

151

3.102

-0.432

0.044

0.062

-42.983

 

0.9173

405*

55

0.9075

122*

158

3.137

-0.460

0.046

0.073

-37.319

 

0.9200

440*

48

0.9041

82*

165

3.091

-0.428

0.044

0.070

-37.661

 

0.9143

427*

41

0.9247

110*

172

3.063

-0.426

0.044

0.069

-36.945

 

0.9161

456*

34

0.9202

83*

179

3.085

-0.429

0.044

0.069

-37.219

 

0.9098

439*

27

0.9582

106*

186

2.990

-0.420

0.045

0.070

-37.650

 

0.9090

452*

20

0.9876

178*

193

3.067

-0.430

0.044

0.074

-37.466

 

0.9160

513*

13

0.9249

24*

 

 

 

 

 

 

 

 

 

 

* p < 0.001

95%CIL

3.028

-0.439

0.044

0.065

-40.566

 

0.9148

Mean

0.9268

 

95%CIU

3.092

-0.415

0.045

0.070

-35.490

 

0.0063

StDev

0.0250

 

           

All squared correlation coefficients in training as well as in test sets are greater than 0.9, sustaining the prediction ability of the four-varied model. More, the mean of squared correlation coefficients in test sets is a little bit higher compared with the mean of squared correlation coefficient in training sets, and the dispersions of squared correlation coefficients are very small for both sets. All the regressions in training and test sets are highly significant (p < 0.001).

Analyzing the regressions coefficients it can be observed that with no exception the values of coefficients respect the 95% confidence intervals associated to the four-varied model (see table 3 and table 4). More, as it is expected, the 95% CI values (table 4) obtained in training and test sets analyses are contained by the 95% CI values of four-varied model (table 3).

The plot of measured vs. estimated octanol-water partition coefficients in training set (blue line and dots) of sample size equal one-hundred thirty-seven (corresponding with 2/3 from total sample of PCBs) and corresponding test set (red line and dots) of sample size equal with sixty-nine (1/3 from total sample of PCBs) is in figure 5.

 

Figure 5. Training (137 PCBs) vs test (69 PCBs) analysis with four-varied model

 

            Starting with the above describe model, and by the use of the original software [9], the octanol-water partition coefficient of new polychlorinated biphenyls can be obtains in a short time, without any experiments, following the next steps: drawing by the use of HyperChem software the three dimensional structure of the new PCB, choosing the model of prediction from the list (in our case PCB_lkow), browsing the *.hin file, and computing the octanol-water partition coefficient based on the four-varied SAR equation.

 

 

Conclusions

 

Modeling the octanol-water partition coefficient of polychlorinated biphenyls by integration of complex structural information provide a stable and performing four-varied model, allowing us to make remarks about relationship between structure of PCBs and associated octanol-water partition coefficients. Thus, the octanol-water partition coefficient of studied PCBs is like to be of geometry and topology nature, depending by the partial change, group and atomic electronegativity as atomic properties, and being in relation with the elastic force.

 

 

Acknowledgement

 

Research was in part supported through project ET36/2005 by UEFISCSU Romania.

 

 

References

 


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[[8]] ***, Leave-one-out Analysis, © 2005, Virtual Library of Free Software, available at: http://vl.academicdirect.org/molecular_topology/mdf_findings/loo.

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