{Quantitative structure-property relationship studies for prediction vapor pressure of volatile organic compounds} J. Serb. Chem. Soc. 84 (12) 1405–1414 (2019) UDC 547.1+532.11+621.5.02:544.112:539.12 JSCS–5273 Original scientific paper 1405 Quantitative structure–property relationship studies for the prediction of the vapor pressure of volatile organic compounds MOUNIA ZINE1, AMEL BOUAKKADIA1,2, LEILA LOURICI3 and DJELLOUL MESSADI1* 1Environmental and Food Safety Laboratory, Badji Mokhtar-Annaba University, BP. 12, 23000 Annaba, Algeria, 2Abbes Laghrour University, Faculty of sciences and technology, Khenchela, Algeria and 3Chadeli Ben Djedid University, BP. 73, 3600 El Taref, Algeria (Received 6 March, accepted 13 June 2019) Abstract: A theoretical model (QSPR) using multiple linear regression analysis for predicting the vapor pressure (pv) of volatile organic compounds (VOCs) has been developed. A series of 51 compounds were analyzed by multiple lin- ear regression analysis. First, the data set was separated arbitrarily into a train- ing set (39 chemicals) and a test set (12 chemicals) for statistical external valid- ation. A four-dimensional model was developed using as independent variables theoretical descriptors derived from Dragon software when applying the GA (genetic algorithm)–VSS (variable subset selection) procedure. The obtained model was used to predict the vapor pressure of the test set compounds, and an agreement between experimental and predicted values was verified. This model, with high statistical significance (R2 = 0.9090, Q2LOO = 0.8748, Q2ext = 0.8307, s = 0.24), could be used adequately for the prediction and description of the log pv value of other VOCs. The applicability domain of MLR model was investigated using a William‘s plot to detect outliers and outsides compounds. Keywords: molecular descriptors; VOCs; log pv; multiple linear regression. INTRODUCTION Volatile organic compounds (VOCs) are molecules which can contain H and C atoms but also other elements such as O, N, Cl, F, P, S,... and metals and/or metalloids, and which are almost entirely in the vapor state under normal condit- ions of temperature and pressure. They include 210 species and 23 large families. These compounds can be of natural origin (terpenes) but very often they are con- taminants mainly from human activity.1 The sectors of activities that are more strongly transmitters of VOCs are road transport, industry, agriculture, and the tertiary sector. Other air pollutants that could be cited are biological contaminants (bacteria, pollen, fungi), physical con- * Corresponding author. E-mail: d_messadi@yahoo.fr https://doi.org/10.2298/JSC190306059Z 1406 ZINE et al. taminants (metals, particles, dust, radioactivity), and chemical contaminants that are part of the VOCs represented by gases (CO, O3, NOx, SO2, fluorocarbons), dioxins and furans.1 Experience is a direct way to obtain activity data for organic compounds, which have many shortcomings, such as the need for large test organisms, high costs, long time duration, and value differences measured between different res- earchers. Consequently, it would be impossible to test experimentally the activity values for all organic compounds. As new compounds are emerging, other difficulties will also arise. There- fore, it is necessary to use theoretical methods to waiver the disadvantages of the experiment and to predict the data of compounds exactly. With the rapid development of computer science and theoretical quantum chemical studies, quantum chemical parameters of compounds can speedily and precisely obtained by computation. These structural parameters along with the introduction of the quantitative structure–activity relationship (QSAR) models can increase the interpretability and predict the activity of new organic com- pounds.2 Quantitative structure–property relationships (QSPR) have gained wide attention in the area of separation science recently. These models are based on the relationship between structures and property of compounds.3 The vapor pressure of different compounds can be predicted from their for- mula and even unknown compounds can be identified using this method. In gen- eral, QSPR models attempt to predict the vapor pressure of a molecule by char- acterizing it with a series of molecular descriptors. These models can effectively be used for the prediction of molecular structures and determination of vapor pressure. The aim of this study was to find a statistical model for the prediction of vapor pressures of some volatiles organic compounds. The model was validated by dividing the data set arbitrarily into training (39 compounds) and test (12 compounds) sets. Different statistical techniques were used to develop the model to highlight the structural requirements for the ideal vapor pressure. The three objectives of the present paper were first, to explore the structure–activity relationships of vapor pressure of diverse volatiles organic compounds, second, to select the best predictive model from among all comparable chemometric models for the pro- perty and third, verification of the performance and stability of the obtained model by two approaches (MLR). The model obtained shows which descriptors play a significant role in the variation of log pv value of these compounds. QSPR STADIES OF VAPOR PRESSURE 1407 EXPERIMENTAL Data set The pv experimental values of 51 selected, structurally heterogeneous VOCs were col- lected from previous works,4 and converted to log pv values. Molecular descriptors generation The structures of the molecules were drawn using Hyperchem 6.03 software.5 The final geometries were obtained with the semi empirical PM3method. All calculations were realized at the RHF (restricted Hartree–Fock) level with non configuration interaction. The molecular structures were optimized using the Polak–Ribiere algorithm and a gradient norm limit of 0.01 kcal Ǻ-1 mol-1. The resulting geometry was transferred into the software Dragon version 5.5 to calculate 1600 descriptors of the type geometrical and GETAWAY (Geometry, Topology and Atoms Weighted AssemblY).6 Descriptors with constant or near constant values inside each group were discarded. For each pair of correlated descriptors (with correlation coefficient r ≥ 0.95), the one showing the highest pair correlation with the other descriptors was excluded. The genetic algorithm (GA)7 was considered superior to other methods of the variable selection techniques. Thus, variable selection was performed on the training set using GA in the MobyDigs version of Todeschini8 by maximizing the cross-validated explained variance Q2LOO. Model development and validation Models with four variables were performed by the software MOBYDYGS.8 The good- ness of fit of the calculated models were assessed by means of the multiple determination coefficients, R2, and the standard deviation error in calculation (SDEC): ( )2i i 1 1 ˆ = = − n i SDEC y y n (1) Cross validation techniques allow the assessment of the internal predictivity (Q2LMO cross validation; bootstrap) in addition to the robustness of the model (Q2LOO cross valid- ation). Cross validation methods consist in leaving out a given number of compounds from the training set and rebuilding the model, which is then used to predict the compounds left out. This procedure is repeated for all compounds of the training set, obtaining a prediction for everyone. If each compound is taken away one at a time, the cross validation procedure is called the leave-one-out technique (LOO), otherwise the leave-more-out technique (LMO). The LOO or LMO correlation coefficient, generally indicated with Q2, was computed by evaluating the accuracy of the prediction of these “test” compounds: 2 / 12 2 1 ˆ( ) 1 1 ( ) = = − = − = − −   n i i i i n i i y y PRESS Q TSS y y (2) The “hat” of the variable y, as is the usual statistical notation, indicates that it is a pre- dicted value of the studied property, and the sub index “i/i” indicates that the predicted values come from models built without the predicted compound. TSS is the total sum of squares. The predictive residual sum of squares (PRESS) measures the dispersion of the predicted values. It is used to define Q2 and the standard deviation error in prediction (SDEP). 1408 ZINE et al. =SDEP PRESS n (3) A value Q2 > 0.5 is generally regarded as a good result and Q2 > 0.9 as excellent.9,10 However, studies11,12 have indicated that while Q2 is a necessary condition for high predictive power a model, is not sufficient. To avoid overestimating the predictive power of the model the LMO procedure (repeated 5000 times, with 4 objects left out at each step) was also per- formed (Q2L(4)O). In the bootstrap validation technique K n-dimensional groups are generated by a ran- domly repeated selection of n-objects from the original data set. The model obtained on the first selected objects is used to predict the values for the excluded sample, and then Q2 is cal- culated for each model. The bootstrapping was repeated 8000 times for each validated model. By using the selected model, the values of the response for the test objects are calculated and the quality of these predictions is defined in terms of Q2ext, which is defined as: ext tr / ext ext12 ext tr2 tr tr 1 ˆ( )² / / 1 1 / ( ) / = = − = − = − −   n i i i i n i i y y n PRESS n Q TSS n y y n (4) Here next and ntr are the number of objects in the external set (or left out by bootstrap) and the number of training set objects, respectively. The data set was divided arbitrary into a training set (39 objects) used to develop the QSAR models and a validation set (12 objects), used only for statistical external validation. Other useful parameters are R2, calculated for the validation chemicals by applying the model developed from the training set, and external standard deviation error of the prediction (SDEPext), which is defined as: ( ) ext 2 ext ext 1 1 = = − n i i SDEP y y n (5) where the sum runs over the test set objects (next). According to Golbraikh and Tropsha,12 a QSPR model is successful if it satisfies several criteria as follows: 2CVext 0.5>R (6) R2 > 0.6 (7) ( ) ( )0 0² ² / ² 0.1 or ² ²’ / ² 0.1− < − h* will reinforce the model if the chemical is in the training set. But such a chemical in the valid- ation set and its predicted data may be unreliable. However, this chemical may not appear to be an outlier because its residual may be low. Thus the leverage and the jacknified residual should be combined for the characterization of the AD. In this stage, linear QSPR model was developed and evaluated to predict the log pv of the compounds. The study we conducted consists of the multiple linear regressions (MLR) avail- able in the MobyDygs software. RESULTS AND DISCUSSION In order to predict log pv, application of the GA–VSS lead to several good models for the prediction based on different sets of molecular descriptors. The best model obtained using 39 compounds is a four-dimensional model (X0sol, SpPosA_H2, GATS2e and Hy) with a high predictive power. The multiple linear regression model (MLR) is given by: log pv = 11.0490 – 0.4602X0sol – 12.3322SpPosA_H2 + + 1.1372GATS2e – 1.2333Hy (16) Statistical parameters for the model with: ntr = 39 next = 12 are: R² = 0.9009Q²LOO = 0.8748Q²Boot = 0.8555F = 77. 25Q2ext = 0.8307 SDEP = 0.256SDEC = 0. 227SDEPext =0.297s = 0.24Kxx = 38.51 Kxy = 45.57 1410 ZINE et al. The reported fitting and validation parameters have, as expected, high values indicating that the model has a very good predictive performance and the des- criptors involved in it well describe the vapor pressure. The high absolute t-values shown in Table I express that the regression coef- ficients of the descriptors involved in the MLR model are significantly larger than the standard deviation. The t-probability of a descriptor can describe the sta- tistical significance when combined together within an overall collective QSPR model (descriptors interactions). TABLE I. Characteristics of the selected descriptors in the best GA/MLR model Descriptor Coefficient regressed Standard error coefficient t t-Probability VIF Constant 11.0490 0.6288 17.57 0.000 – X0sol –0.4602 0.0460 –9.81 0.000 1.720 SpPosA_H2 –12.3320 1.2100 –10.19 0.000 1.528 GATS2e 1.1372 0.1423 7.99 0.000 1.074 Hy –1.2333 0.1275 –9.68 0.000 1.944 Descriptors with t-probability values below 0.05 (95 % confidence) are usu- ally considered statistically significant in a particular model, which means that their influence on the response variable is not merely by chance.13 A smaller t-probability suggests a more significant descriptor. The t-probability values of the four descriptors are very small, indicating that all of them are highly signific- ant descriptors. The VIF is uniform and equal to 1.00 if there is no linear correlation between a given variable and rest of the variables in the regression equations. Higher values of VIF in Table I indicate a more serious multi-co linearity problem. Models would not be accepted if they contain descriptors with VIFs above a value of five.14 2 1 1 = − j VIF R (17) where Rj2 is the squared correlation coefficient between the jth coefficient regressed against all the other descriptors in the model.15 Applicability domain On analyzing the domain of the applicability of the model from a Williams plot, all residuals were located within the range of three standard deviations, and there was no influential compound both for the training or the prediction set, Fig. 1, which means that the model has a good external predictivity. A diagram of the statistical coefficients Q2 and R2 is presented Fig. 2 to compare the results obtained for the randomized models (circle) with the starting model (square). It is clear that the statistics obtained for the modified vectors of QSPR STADIES OF VAPOR PRESSURE 1411 the log pv are smaller than those of the real models; the Q2 values are lower (<10 %), as for the major part are the R2 values (<30 %). This ensures that the estab- lished model has a real base, and is not due arbitrarity. Fig. 1. Williams plot: jackknifed resi- duals and leverages. Fig. 2. Randomization test associated to the previous QSPR model. This technique, plot of cross-validation log pv versus experimental log pv values, shown in Fig. 3, ensures the robustness of a QSPR model (see also Tables S-I and S-II of the Supplementary material to this paper).16 Descriptor contributions analysis Based on a previously described procedure,17,18 the relative contributions of the four descriptors to the model were determined. It should be noted that the difference in contribution between two descriptors used in the model indicates that all the descriptors are essential to generate the predictive model (Fig. 4). Descriptors decrease according to the following order: SpPosA_H2 (27.7811 %) > X0sol (26.6809 %) > Hy (25.7967 %) > GATS2e (19.7413 %). 1412 ZINE et al. Fig. 3. Cross-validation versus exp- erimental log pv for the entire data set. Fig. 4. Relative contributions of the selected descriptors to the MLR model. CONCLUSIONS Multiple linear regressions were used to construct a quantitative structure property relation model of 51 VOCs for their vapor pressures binding propriety. The model was developed by a genetic algorithm selection of theoretical mole- cular descriptors from among a wide set obtained with several softwares. The data set were separated randomly into two subsets of 39 elements for training and 12 for external validation. The MLR model has good stability, robustness and predictivity. The chemical applicability domain of the studied MLR model and the reliability of the predictions were verified by the leverage approach. The equation obtained could be used successfully to estimate the vapor pressures for new compounds or for other compounds the experimental values of which are unknown. SUPPLEMENTARY MATERIAL Additional data are available electronically from http://www.shd.org.rs/JSCS/, or from the corresponding author on request. QSPR STADIES OF VAPOR PRESSURE 1413 И З В О Д ПРОУЧАВАЊА КВАНТИТАТИВНИХ РЕЛАЦИЈА СТРУКТУРЕ И РЕАКТИВНОСТИ ЗА ПРЕДВИЂАЊЕ НАПОНА ПАРЕ ИСПАРЉИВИХ ОРГАНСКИХ ЈЕДИЊЕЊА MOUNIA ZINE1, AMEL BOUAKKADIA1,2, LEILA LOURICI3 и DJELLOUL MESSADI1 1Environmental and Food Safety Laboratory, Badji Mokhtar-Annaba University, BP. 12, 23000 Annaba, Algeria, 2Abbes Laghrour University, Faculty of sciences and technology, Khenchela, Algeria и 3Chadeli Ben djedid University, BP.73, 3600 El taref, Algeria Развијен је теоријски модел (QSPR) коришћењем вишеструке линеарне регресионе ана- лизе за предвиђање напона паре (pv/Pa) испарљивих органских једињења (VOC), за серију од 51 једињења. На почетку је скуп података произвољно подељен у скуп за проучавање (39 једињења) и скуп за проверу (12 једињења) за екстерну статистичку валидацију. Развијен је четвородимензионални модел користећи као независне варијабле теоријске описнике изве- дене из софтвера Dragon применом GA (генетски алгоритам)–VSS (variable subset selection) процедуре. Добијени модел је употребљен за предвиђање напона паре једињења скупа за проверу, и потврђена је сагласност између експерименталних и претсказаних вредности. Овај модел, са високом статистичком значајношћу (R2 = 0,9090, Q2Loo = 0,8748, Q 2 Ext = 0,8307, s = 0,24), може бити адекватно употребљен за предвиђање и описивање log (pv/Pa) вредности других VOC. Област применљивости MLR модела испитивана је коришћењем Виљемсовог графа (William‘s plot) да се детектују једињења која се не уклапају у модел. (Примљено 6. марта, прихваћено 13. јуна 2019) REFERENCES 1. V. Cirimele, M. Etter, M. Villian, P. Kintez, Ann. Toxicol. Anal. 20 (2008) 67 (https://doi.org/10.1051/ata/2009002) 2. S. Chtita, R. Hmamouchi, M. Larif, M. Ghamali, M. Bouachrine, T. Lakhlifi, J. Taibah Univ. 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