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Article

Predicting Aqueous Solubility of Chlorinated Hydrocarbons by the MCI Approach

College of Chemistry and Chemical Engineering, Ocean University of China, Qingdao 266003, People’s Republic of China.
*
Author to whom correspondence should be addressed.
Int. J. Mol. Sci. 2006, 7(2), 47-58; https://0-doi-org.brum.beds.ac.uk/10.3390/i7020047
Received: 24 November 2005 / Accepted: 17 February 2006 / Published: 28 February 2006

Abstract

Correlation for estimation of the aqueous solubility (logSw) of chlorinatedhydrocarbons molecules is proposed. The MCI based quantitative structure-propertyrelationship (QSPR) model proposed is predictive and requires only three connectivityindices in the calculation. The correlation equation obtained which is based on a training setof 50 chlorinated hydrocarbons has a correlation coefficient of 0.9670 and a standard errorof 0.44 log10 units. Application of the developed model to a testing set of 73 chlorinatedhydrocarbons demonstrates that the new model is reliable with good predictive accuracy andsimple formulation. Besides, the model does not require any experimental physicochemicalproperties in the calculation, so it is easy to apply, especially in cases where it isinconvenient or impossible to measure the physicochemical properties.
Keywords: molecular connectivity index; aqueous solubility; QSPR; chlorinated hydrocarbons; property model molecular connectivity index; aqueous solubility; QSPR; chlorinated hydrocarbons; property model

1. Introduction

Aqueous solubility is a particularly important physicochemical property of organic chemicals that plays a significant role in various physical and biological processes, especially in drug transport and environment impact. Comparing with the time-consuming experimental procedures to determine aqueous solubility directly, reliable computational methods to predict aqueous solubility are more popular in today’s research [1,2,3].
There are a large number of successful prediction methods, which can be divided into two main groups. The first approach [4,5,6,7,8] is to build model from more easily measured physicochemical properties, such as melting point, boiling point, molar volume, partition coefficient, chromatographic retention time, etc. The other method is based on the information from the molecular of the organic chemicals, which can be further divided into two classes, one is group contributions method [9,10,11,12] and the other is QSPR approach [1,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32].
The molecular connectivity indices which were proposed 30 years ago, have been successfully used in the correlation of various physiochemical properties of organic substances [33,34,35] especially in the recent applications to computational molecular design studies [36]. In the previous works, correlations of aqueous solubility using molecular connectivity indices and other descriptors have been studied and demonstrated the possibility of molecular connectivity indices in modeling aqueous solubility. In this study, we use different indices comparing with the already existing models to correlate the aqueous solubility and obtain the simpler model with the same or higher accuracy.

2. Data Set

The data set that has been studied by Eduardo J. Delgado [22] is adopted as the training set and listed in Table 2. To test the predictive ability of the proposed model, the aqueous solubility data for 73 chlorinated hydrocarbons were collected from the literature [6,10,27], as the testing set, and shown in Table 3. Both the training set and the testing set contain saturated, unsaturated, aliphatic and aromatic compounds, dioxins and PCBs.

3. Methods

Molecular connectivity indices have been widely used as molecular structural descriptors to correlate the physical properties of organic chemicals and used in computational molecular design studies. Recently, higher-order connectivity indices have been demonstrated the advantage of incorporating effects that are due to larger-scale structural features in a molecule on physical properties [36].
The simple and valence connectivity indices defined and developed by Randic [34,35,37,38,39], Kier [40,41,42] and Hall [43,44] are used in this work which can be expressed by the following equation.
Ijms 07 00047 i001
where m is the order of the connectivity index; k denotes a contiguous path type of fragment, which is divided into paths (P), clusters (C), etc; p denotes which type connectivity index is(simple, valence or other type); nm is the number of the relevant paths; δip is the connectivity index.
In this work, for each chemical the values of the connectivity indices up to third order are calculated using the vertex adjacency matrix. The simple connectivity index (δ) and the valence connectivity index (δv) used in this study are summarized in Table 1.
Table 1. Connectivity Index (δ and δv) values of groups used in this work
Table 1. Connectivity Index (δ and δv) values of groups used in this work
GroupδδvGroupδδv
-CH311=CH212
-CH2-22=CH-23
>CH-33=C<34
>C<44-Cl17/9
The detailed equations for the simple and valence molecular connectivity indices for zeroeth, first, second, and third orders are listed as follows:
Ijms 07 00047 i002
Ijms 07 00047 i003
Ijms 07 00047 i004
Ijms 07 00047 i005
Ijms 07 00047 i006
Ijms 07 00047 i007
Ijms 07 00047 i008
Ijms 07 00047 i009
Ijms 07 00047 i010
Ijms 07 00047 i011
After the calculation of ten molecular connectivity indices, stepwise regression using MATLAB Statistics Toolbox [45] is used for choosing the variables and fitting the experimental data of the data set.
The average absolute error (AAE) and the root-mean-square error (RMSE) were calculated as the following equations to compare with the existing model.
The AAE was calculated as
Ijms 07 00047 i012
The RMSE was calculated as
Ijms 07 00047 i013
where N=number of compounds.

4. Results and Discussion

Delgado22 used CODESSA to develop QSPR model and carried out a correlation analysis to find the best QSPR model using a heuristic method. He succeeded in obtaining the two descriptors that have definite physical meaning corresponding to different intermolecular interactions.
In our work, the coefficients of the best correlation model for aqueous solubility of the 50 chlorinated hydrocarbons used as training set in this study are shown in table 2 and equation (14). The 0χ that reflects the size of the molecule is the most significant descriptor, as can be seen by its highest t-test value. This conclusion is in agreement with the existing models22, 27. The other descriptors 3χc and 3χcv that reflect the contribution of clusters in a molecule to aqueous solubility are also important in describing the aqueous solubility of chlorinated hydrocarbons. This demonstrates again that higher-order connectivity indices contain a large amount of information about the molecule, especially the larger-scale structural features (such as branching)36.
Table 2. The best correlation model of logSw of 50 compounds
Table 2. The best correlation model of logSw of 50 compounds
nDescriptorCoefficientt-test
0Intercept0.3556
10χ-0.4373-7.7127
23χc-3.0857-4.7889
33χcv1.96574.2359
The model we obtained is as the following general correlation:
Ijms 07 00047 i014
R2=0.9670, F=450.0, RMSE=0.444, n=50
The results calculated with equation (14) are shown in Table 3, where the experimental values and the calculated results from the Delgado method are also listed, and the scatter plot is shown in Fig 1.
The AAE for our model is 0.31 which is smaller than the 0.32 for the Delgado model, indicating that the new model has comparable accuracy to the existing model.
Table 3. Calculated results of the molar aqueous solubility of the 50 compounds (logSw).
Table 3. Calculated results of the molar aqueous solubility of the 50 compounds (logSw).
NoCAS No.NameExperimentalDelgadoThis work
175-09-2Dichloromethane-0.74-0.77 -0.83
267-66-3Trichloromethane-1.19-1.32 -1.34
356-23-5Tetrachloromethane-2.26-1.20 -2.05
479-34-51,1,2,2-Tetrachloroethane-1.76-2.42 -2.27
5540-59-01,2-Dichloroethene-1.07-1.54 -1.14
679-01-6Trichloroethene-2.04-2.05 -2.05
7127-18-4Tetrachloroethene-2.57-2.51 -2.69
Benzene
8108-90-7Monochloro-2.42-2.46-2.40
9541-73-11,3-Dichloro-3.04-3.31 -3.30
1095-50-11,2-Dichloro-3.02-3.17 -3.07
11106-46-71,4-Dichloro-3.31-3.33 -3.30
12120-82-11,2,4-Trichloro-3.64-4.11 -3.97
1387-61-61,2,3-Trichloro-4.08-3.94 -3.77
14108-70-31,3,5-Trichloro-4.55-4.26 -4.20
15634-66-21,2,3,4-Tetrachloro-4.38-4.72 -4.46
1695-94-31,2,4,5-Tetrachloro-5.19-4.94 -4.64
17634-90-21,2,3,5-Tetrachloro-4.73-4.94 -4.67
18608-93-5Pentachloro-5.37-5.56 -5.16
Dibenzo-p-dioxin
1939227-53-71-Chloro-5.72-5.66-6.05
2039227-54-82-Chloro-5.86-5.92 -6.24
2129446-15-92,3-Dichloro-7.23-6.83 -6.91
2233857-26-02,7-Dichloro-7.83-7.02 -7.14
2339227-58-21,2,4-Trichloro-7.53-7.50 -8.11
2430746-58-81,2,3,4-Tetrachloro-8.77-8.08 -8.63
Biphenyl
252051-60-72-Chloro-4.63-4.55-4.66
262051-61-83-Chloro-4.88-5.38 -4.84
272051-62-94-Chloro-5.25-5.35 -4.84
282050-68-24,4’-Dichloro-6.63-6.05 -5.74
2934883-39-12,5-Dichloro-5.27-5.52 -5.56
3033284-50-32,4-Dichloro-5.29-6.28 -5.56
3133146-45-12,6-Dichloro-5.07-4.86 -5.38
322050-68-22,4’-Dichloro-5.60-5.57 -5.56
3313029-08-82,2’-Dichloro-5.36-4.76 -5.37
3437680-65-22,2’,5-Trichloro-5.65-5.60 -6.27
3535693-92-62,4,6-Trichloro-6.07-5.93 -6.28
3615862-07-42,4,5-Trichloro-6.27-6.47 -6.23
3732598-13-33,3’,4,4’-Tetrachloro-8.68-7.90 -7.09
3835693-99-32,2’,5,5’-Tetrachloro-6.44-6.33 -7.17
3933284-53-62,3,4,5-Tetrachloro-7.26-7.04 -6.74
4018259-05-72,3,4,5,6-Pentachloro-7.78-8.40 -7.29
4137680-73-22,2’,4,5,5’-Pentachloro-7.44-7.53 -7.84
4255312-69-12,2’,3,4,5-Pentachloro-7.10-7.21 -7.46
4374472-44-92,3,3’,4’,5,6-Hexachloro-7.83-8.40 -8.35
4455215-18-42,2’,3,3’,4,5-Hexachloro-8.04-9.30 -8.15
4533979-03-22,2’,4,4’,6,6’-Hexachloro-8.48-8.26 -8.63
4635065-27-12,2’,4,4’,5,5’-Hexachloro-8.57-8.61 -8.51
4738411-22-22,2’,3,3’,6,6’-Hexachloro-7.86-7.27 -8.22
4838380-07-32,2’,3,3’,4,4’-Hexachloro-9.00-8.53 -8.15
492136-99-42,2’,3,3’,5,5’,6,6’-Octachloro-9.30-9.45 -9.61
5040186-72-92,2’,3,3’,4,4’,5,5’,6-Nonachloro-9.93-9.88-10.09
Figure 1. Calculated values versus experimental values of logSw for the two models (□: Delgado, ○: This work).
Figure 1. Calculated values versus experimental values of logSw for the two models (□: Delgado, ○: This work).
Ijms 07 00047 g001
To test the predictive ability of our model, the aqueous solubility data for 73 chlorinated hydrocarbons were collected from the literature [6,10,27] as the testing set. The predictive results calculated with equation (14) are shown in Table 4, where the experimental values and the residual values are also listed, and the scatter plot is shown in Fig 2.
The AAE for the testing set is 0.38 and demonstrates that the proposed model is reliable and has good predictive ability.
Table 4. Predicted Results of the Molar Aqueous Solubility for 73 compounds (logSw)
Table 4. Predicted Results of the Molar Aqueous Solubility for 73 compounds (logSw)
No.CAS No.NameExperi-mentalCalcula-tedResidual
158-89-9Lindane-4.59-4.77 0.18
216606-02-32,4',5-PCB-6.25-6.46 0.21
331508-00-62,3',4,4',5-Pentachlorobiphenyl-7.39-7.80 0.41
432598-11-12,3',4',5-Tetrachlorobiphenyl-7.25-7.13 -0.12
535065-28-22,2',3,4,4',5'-Hexachlorobiphenyl-8.32-8.33 0.01
635694-08-72,2',3,3',4,4',5,5'-octachlorobiphenyl-9.16-9.54 0.38
738380-02-82,2',3,4,5'-Pentachlorodiphenyl-7.91-7.66 -0.25
838380-08-42,3,3',4,4',5-Hexachlorobiphenyl-7.82-8.32 0.50
938444-85-82,3,4'-Trichlorobiphenyl-6.26-6.25 -0.01
1041464-39-52,2',3,5'-Tetrachlorobiphenyl-6.47-6.97 0.50
1152663-63-52,2',3,5,5',6-Hexachlorobiphenyl-7.42-8.39 0.97
1252663-69-12,2',3,4,4',5',6-Heptachlorobiphenyl-7.92-9.06 1.14
1352663-77-12,2',3,3',4,5,5',6,6'-Nonachlorobiphenyl-10.40-10.12 -0.28
1452712-04-62,2',3,4,5,5'-Hexachlorobiphenyl-7.68-8.36 0.68
1552712-05-72,2',3,4,5,5',6-Heptachlorobiphenyl-8.94-8.90 -0.04
1655215-17-32,2',3,4,6-Pentachlorobiphenyl-7.43-7.49 0.06
1755702-45-92,3,6-Trichlorobiphenyl-6.29-6.08 -0.21
1856558-16-82,2',4,6,6'-Petachlorobiphenyl-7.32-7.73 0.41
1974472-42-72,3,3',4,4',6-Hexachlorobiphenyl-7.66-8.35 0.69
2075-09-2dichloromethane-0.63-0.83 0.20
2167-66-3trichloromethane-1.17-1.34 0.17
2256-23-5tetrachloromethane-2.31-2.05 -0.26
2375-34-31,1-dichloroethane-1.29-1.53 0.24
24107-06-21,2-dichloroethane-1.06-1.14 0.08
2571-55-61,1,1-trichlorcethane-2.00-2.56 0.56
2679-00-51,1,2-trichlorcethane-1.48-1.75 0.27
2779-34-51,1,2,2-tetrachlorcethane-1.74-2.27 0.53
28630-20-61,1,1,2-tetrachlorcethane-2.18-2.62 0.44
2976-01-7pentachlorcethane-2.60-3.06 0.46
302050-67-13,3'-PCB-5.80-5.74 -0.06
3138444-81-42,3',5-Trichlorobiphenyl-6.01-6.46 0.45
327012-37-52,4,4'-PCB-6.21-6.46 0.25
3338444-86-92',3,4-Trichlorodiphenyl-6.29-6.23 -0.06
342437-79-82,2',4,4'-Tetrachlorobiphenyl-6.51-7.17 0.66
3541464-41-92,2',5,6'-Tetrachlorobiphenyl-6.80-7.00 0.20
3652663-62-42,2',3,3',4-Pentachlorobiphenyl-7.05-7.46 0.41
3752663-71-52,2',3,3',4,4',6-Heptachlorobiphenyl-8.30-8.88 0.58
382051-24-32,2',3,3',4,4',5,5',6,6'-Decachloro-1,1'-biphenyl-11.62-11.27 -0.35
3967-72-1hexachloroethane-3.67-3.76 0.09
40540-54-51-chloropropane-1.47-1.14 -0.33
4175-29-62-chloropropane-1.41-1.70 0.29
42142-28-91,3-dichloropropane-1.62-1.45 -0.17
4378-87-51,2-dichloropropane-1.60-1.87 0.27
4496-18-41,2,3-trichloropropane-1.92-2.07 0.15
45109-69-31-chlorobutane-2.03-1.45 -0.58
4678-86-42-chlorobutane-1.96-1.87 -0.09
47513-36-01-chloro-2-methylpropane-2.00-1.98 -0.02
48541-33-31,1-dichlorobutane-2.40-2.06 -0.34
497581-97-72,3-dichlombulane-2.70-2.47 -0.23
50543-59-91-chloropentane-2.73-1.76 -0.97
51625-29-62-chloropenlane-2.63-2.18 -0.45
52616-20-63-chloropentane-2.63-2.07 -0.56
53594-36-52-chloro-2-methylbutane-2.51-3.35 0.84
54544-10-51-chlorohexane-3.12-2.07 -1.05
55319-86-8δ-hexachlorocyclohexane-4.51-4.77 0.26
5675-35-41,1-dichlorcethylene-1.64-2.10 0.46
57156-59-21,2-dichlorcethylene-1.30-1.14 -0.16
58107-05-13-chloropropylene-1.36-1.14 -0.22
5987-68-3hexachloro-1,3-butadiene-4.92-4.70 -0.22
6077-47-4hexachlorocyclo-pentadiene-5.18-5.59 0.41
6195-49-8 2-chlorotoluene-3.52-3.11 -0.41
62100-44-7alpha-chlorotoluene-2.39-2.59 0.20
63106-43-4p-chlorotoluene-3.08-3.34 0.26
6438444-93-82,2',3,3'-PCB-7.28-6.76 -0.52
6532598-10-02,3',4,4'-PCB-7.80-7.13 -0.67
6641464-40-82,2',4,5'-PCB-6.57-7.17 0.60
6715968-05-52,2',6,6'-PCB-8.03-6.83 -1.20
6852704-70-82,2',3,3',5,6-PCB-8.60-8.19 -0.41
6972-54-8DDD-7.20-7.44 0.24
7050-29-3DDT-7.15-8.22 1.07
7172-55-9DDE-6.90-7.74 0.84
7291-58-72-chloronaphthalme-4.14-4.22 0.08
7390-13-11-chloronaphthalene-3.93-4.04 0.11
Figure 2. Calculated values versus experimental values of logSw for the testing data set.
Figure 2. Calculated values versus experimental values of logSw for the testing data set.
Ijms 07 00047 g002

5. Conclusion

Predictive QSPR model which is based on molecular connectivity indices is proposed in this work to correlate the aqueous solubility of 50 chlorinated hydrocarbons. Application of the developed model to a testing set of 73 chlorinated hydrocarbons demonstrates that the new model is reliable with good predictive accuracy and simple formulation. Besides, the new model does not require any experimental physicochemical properties in the calculation, so it is easy to apply, especially in cases where it is inconvenient or impossible to measure the physicochemical properties.

Acknowledgements

The authors thank the support of the Natural Science Foundation of China (Contract: 20376078) and thank the anonymous reviewers for their valuable critiques and suggestions.

References and Notes

  1. Butina, D.; Gola, J. M. R. Modeling Aqueous Solubility. J. Chem. Inf. Model. 2003, 43, 837–841. [Google Scholar] [CrossRef]
  2. Erös, D.; Kéria, G.; Kövesdi, I.; Szántai-Kis, C.; Mészáros, G.; Örfi, L. Comparison of Predictive Ability of Water Solubility QSPR Models Generated by MLR, PLS and ANN Methods. Mini-Rev. Med. Chem. 2004, 4, 167–177. [Google Scholar] [CrossRef]
  3. Delaney, J. S. Predicting aqueous solubility from structure. Drug. Discov. Today 2005, 10, 289–295. [Google Scholar] [CrossRef]
  4. Yalkowsky, S. H.; Pinal, R. Estimation of the aqueous solubility of complex organic molecules. Chemosphere. 1993, 26, 1239–1261. [Google Scholar] [CrossRef]
  5. Jain, N.; Yalkowsky, S. H. Estimation of the aqueous solubility I: Application to organic nonelectrolytes. J. Pharm. Sci. 2001, 90, 234–252. [Google Scholar] [CrossRef]
  6. Peterson, D. L.; Yalkowsky, S. H. Comparison of Two Methods for Predicting Aqueous Solubility. J. Chem. Inf. Model. 2001, 41, 1531–1534. [Google Scholar] [CrossRef]
  7. Tolls, J.; Dijk, J. V.; Verbruggen, E. J. M.; Hermens, J. L. M.; Loeprecht, B.; Schuurmann, G. Aqueous Solubility-Molecular Size Relationships: A Mechanistic Case Study Using C10- to C19-Alkanes. J. Phys. Chem. A 2002, 106, 2760–2765. [Google Scholar] [CrossRef]
  8. Yang, G.; Ran, Y.; Yalkowsky, S. H. Prediction of the aqueous solubility: Comparison of the general solubility equation and the method using an amended solvation energy relationship. J. Pharm. Sci. 2002, 91, 517–533. [Google Scholar] [CrossRef]
  9. Klopman, G.; Wang, S.; Balthasar, D. M. Estimation of Aqueous Solubility of Organic Molecules by the Group Contribution Approach. Application to the Study of Biodegradation. J. Chem. Inf. Model. 1992, 32, 474–482. [Google Scholar] [CrossRef]
  10. Kühne, R.; Ebert, R.-U.; Kleint, F.; Schmidt, G.; Schüürmann, G. Group Contribution Methods to Estimate Water Solubility of Organic Chemicals. Chemosphere. 1995, 30, 2061–2077. [Google Scholar] [CrossRef]
  11. Klopman, G.; Zhu, H. Estimation of the Aqueous Solubility of Organic Molecules by the Group Contribution Approach. J. Chem. Inf. Model. 2001, 41, 439–445. [Google Scholar] [CrossRef]
  12. Hou, T. J.; Xia, K.; Zhang, W.; Xu, X. J. ADME Evaluation in Drug Discovery. 4. Prediction of Aqueous Solubility Based on Atom Contribution Approach. J. Chem. Inf. Model. 2004, 44, 266–275. [Google Scholar] [CrossRef]
  13. Nirmalakhandan, N. N.; Speece, R. E. Prediction of aqueous solubility of organic chemicals based on molecular structure. Environ. Sci. Technol. 1988, 22, 328–338. [Google Scholar] [CrossRef]
  14. Nelson, T. M.; Jurs, P. C. Prediction of Aqueous Solubility of Organic Compounds. J. Chem. Inf. Model. 1994, 34, 601–609. [Google Scholar] [CrossRef]
  15. Huibers, P. D. T.; Katritzky, A. R. Correlation of the Aqueous Solubility of Hydrocarbons and Halogenated Hydrocarbons with Molecular Structure. J. Chem. Inf. Model. 1998, 38, 283–292. [Google Scholar] [CrossRef]
  16. Huuskonen, J.; Salo, M.; Taskinen, J. Aqueous solubility prediction of drugs based on molecular topology and neural network modeling. J. Chem. Inf. Model. 1998, 38, 450–456. [Google Scholar] [CrossRef]
  17. Mitchell, B. E.; Jurs, P. C. Prediction of Aqueous Solubility of Organic Compounds from Molecular Structure. J. Chem. Inf. Model. 1998, 38, 489–496. [Google Scholar] [CrossRef]
  18. Makino, M. Prediction of aqueous solubility coefficients of polychlorinated biphenyls by use of computer-calculated molecular properties. Environ. Int. 1998, 24, 653–663. [Google Scholar] [CrossRef]
  19. Huuskonen, J. Estimation of Aqueous Solubility for a Diverse Set of Organic Compounds Based on Molecular Topology. J. Chem. Inf. Model. 2000, 40, 773–777. [Google Scholar] [CrossRef]
  20. Yaffe, D.; Cohen, Y.; Espinosa, G.; Arenas, A.; Giralt, F. A Fuzzy ARTMAP Based on Quantitative Structure-Property Relationships (QSPRs) for Predicting Aqueous Solubility of Organic Compounds. J. Chem. Inf. Model. 2001, 41, 1177–1207. [Google Scholar] [CrossRef]
  21. Liu, R.; So, S. S. Development of Quantitative Structure-Property Relationship Models for Early ADME Evaluation in Drug Discovery. 1. Aqueous Solubility. J. Chem. Inf. Model. 2001, 41, 1633–1639. [Google Scholar] [CrossRef]
  22. Delgado, E. J. Predicting aqueous solubility of chlorinated hydrocarbons from molecular structure. Fluid. Phase. Equilibr. 2002, 199, 101–107. [Google Scholar] [CrossRef]
  23. Hua, G.; Veerabahu, S.; Pil, L. Estimation of Aqueous Solubility of Organic Compounds with QSPR Approach. Pharm. Res. 2002, 19, 497–503. [Google Scholar] [CrossRef]
  24. Engkvist, O.; Wrede, P. High-Throughput, In Silico Prediction of Aqueous Solubility Based on One- and Two-Dimensional Descriptors. J. Chem. Inf. Model. 2002, 42, 1247–1249. [Google Scholar] [CrossRef]
  25. Chen, X.-Q.; Cho, S. J.; Li, Y.; Venkatesh, S. Prediction of aqueous solubility of organic compounds using a quantitative structure-property relationship. J. Pharm. Sci. 2002, 91, 1838–1852. [Google Scholar] [CrossRef]
  26. Yan, A.; Gasteiger, J. Prediction of Aqueous Solubility of Organic Compounds by Topological Descriptors. Qsar. Comb. Sci 2003, 22, 821–829. [Google Scholar] [CrossRef]
  27. Zhong, C.; Hu, Q. Estimation of the aqueous solubility of organic compounds using molecular connectivity indices. J. Pharm. Sci. 2003, 92, 2284–2294. [Google Scholar] [CrossRef]
  28. Delaney, J. S. ESOL: Estimating Aqueous Solubility Directly from Molecular Structure. J. Chem. Inf. Model. 2004, 44, 1000–1005. [Google Scholar] [CrossRef]
  29. Bergstrom, C. A. S.; Wassvik, C. M.; Norinder, U.; Luthman, K.; Artursson, P. Global and Local Computational Models for Aqueous Solubility Prediction of Drug-Like Molecules. J. Chem. Inf. Model. 2004, 44, 1477–1488. [Google Scholar] [CrossRef]
  30. Votano, J. R.; Parham, M.; Hall, L. H.; Kier, L. B.; Hall, L. M. Prediction of Aqueous Solubility Based on Large Datasets Using Several QSPR Models Utilizing Topological Structure Representation. Chem. Biodivers. 2004, 1, 1829–1841. [Google Scholar] [CrossRef]
  31. Yan, A.; Gasteiger, J.; Krug, M.; Anzali, S. Linear and nonlinear functions on modeling of aqueous solubility of organic compounds by two structure representation methods. J. Comput. Aid. Mol. Des. 2004, 15, 75–87. [Google Scholar]
  32. Catana, C.; Gao, H.; Orrenius, C.; Stouten, P. F. W. Linear and Nonlinear Methods in Modeling the Aqueous Solubility of Organic Compounds. J. Chem. Inf. Model. 2005, 45, 170–176. [Google Scholar] [CrossRef]
  33. Bicerano, J. Prediction of Polymer Properties; Marcel Dekker: New York, 1996. [Google Scholar]
  34. Randic, M. The connectivity index 25 years after. J. Mol. Graph. Model. 2001, 20, 19–35. [Google Scholar] [CrossRef]
  35. Randic, M.; Pompe, M.; Mills, D.; Basak, S. C. Variable connectivity index as a tool for modeling structure-property relationships. Molecules. 2004, 9, 1177–1193. [Google Scholar] [CrossRef]
  36. Camarda, K. V.; Sunderesan, P. An Optimization Approach to the Design of Value-Added Soybean Oil Products. Ind. Eng. Chem. Res. 2005, 44, 4361–4367. [Google Scholar] [CrossRef]
  37. Randic, M. On Characterization of Molecular Branching. J. Am. Chem. Soc. 1975, 97, 6609–6615. [Google Scholar] [CrossRef]
  38. Randic, M.; Hansen, P. J.; Jurs, P. C. Search for usefule graph theoretical invariants of molecular structure. J. Chem. Inf. Model. 1988, 28, 60–68. [Google Scholar] [CrossRef]
  39. Randic, M.; Plavsic, D.; Lers, N. Variable Connectivity Index for Cycle-Containing Structures. J. Chem. Inf. Model. 2001, 41, 657–662. [Google Scholar] [CrossRef]
  40. Kier, L. B.; Hall, L. H.; Murray, W. J.; Randic, M. Molecular connectivity. I: Relationship to nonspecific local anesthesia. J Pharm Sci 1975, 64, 1971–1974. [Google Scholar] [CrossRef]
  41. Kier, L. B.; Hall, L. H. Molecular connectivity in chemistry and drug research; Academic Press: New York, 1976. [Google Scholar]
  42. Kier, L. B.; Hall, L. H. Molecular connectivity in structure-activity analysis; Wiley: New York, 1986. [Google Scholar]
  43. Hall, L. H.; Kier, L. B. Structure-activity studies using valence molecular connectivity. J. Pharm. Sci. 1977, 66, 642–644. [Google Scholar] [CrossRef]
  44. Hall, L. H.; Kier, L. B. Molecular connectivity and substructure analysis. J. Pharm. Sci. 1978, 67, 1743–1747. [Google Scholar] [CrossRef]
  45. Martinez, W. L.; Martinez, A. R. Computational Statistics Handbook with MATLAB; Chapman & Hall/CRC: Boca Raton London New York Washington, D.C., 2002. [Google Scholar]
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