Application of machine learning in predicting potentiometric selectivity (Mg 2+ /Ca 2+ ) of some amide ligands

Application of machine learning in predicting potentiometric selectivity (Mg 2+ /Ca 2+ ) of some amide ligands | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Application of machine learning in predicting potentiometric selectivity (Mg 2+ /Ca 2+ ) of some amide ligands Eslam Pourbasheer, Reza Mahmoudzadeh Laki, Suraj N. Mali, Abolghasem Beheshti This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8806544/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this study, in order to model the prediction of potentiometric selectivity (Mg 2+ /Ca 2+ ) of several amide ligands, the quantitative structure-property relationship (QSPR) approach was used along with two stepwise (SW) and genetic algorithm (GA) methods as variable selection techniques. Experimental data and molecular structures were entered into the models after calculating and screening the descriptors. The SW method identified five descriptors and GA five descriptors (with two common items) as key parameters. Using these variable selection methods and machine learning modeling methods of multiple linear regrassions (MLR) and support vector machine (SVM), various models including SW-MLR, GA-MLR, GA-SVM were created, and also, by identifying an outlier and removing it, GA-MLR and GA-SVM models were re-developed. The model obtained by GA-SVM (with one outlier removed) had R 2 train =0.893, R 2 test =0.757, RMSE train =0.322, and RMSE test =0.705, indicating the high predictive power and fit of the models. These values were a significant improvement compared to the reference paper (R 2 = 0.66 and RMSE = 0.53 even after removing 11 outliers). In addition, findings provide important mechanistic insights into the role of molecular features in potentiometric selectivity (Mg 2+ /Ca 2+ ) of amide ligands. Physical sciences/Chemistry Biological sciences/Computational biology and bioinformatics Amide ligands Potentiometric selectivity QSPR Machine learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Recently, there has been a great demand for selective and sensitive chemical sensors for clinical and environmental analysis, which has led to a lot of research in this field 1 – 3 . In view of these studies, sensors capable of accurately determining ionic activity in complex matrices have attracted attention 4 – 6 . Among these, sensors based on softened polymer membranes can be mentioned 7 – 10 . The ionophore is the main component of these sensors, which is embedded in the sensor membrane and is mainly composed of lipophilic organic ligands. The ionophore can be sensitive and selective towards specific analytes 11 – 13 . However, designing novel ionophores with high selectivity for the determination of similar chemical ions that are very difficult to distinguish from each other is a significant challenge. Chemical ions such as magnesium (Mg 2+ ) and calcium (Ca 2+ ), whose discrimination is of great importance in physiological and industrial problems, are an example of this type 14 . The experimental methods used to generate ionophores are both difficult and resource-intensive, such as the synthesis of potential ligands, the fabrication of sensing membranes, and comprehensive electrochemical analysis. However, there is less insight into the prediction of the final performance of the synthesized structures 15 , 16 . These limitations have led to the increasing use of computational techniques such as quantitative structure-property relationship (QSPR) modeling in the design of ionophores 17 , 18 . QSPR methods establish a relationship between molecular descriptors and experimental qualities, facilitating the prediction of ligand behavior based on structural features 19 – 25 . Although recent studies have been conducted on modeling complex physicochemical phenomena, including metal-ligand binding 26 – 28 , extraction efficiency, and sensor responses using the QSPR technique, there are not many studies focused on the selectivity of ISEs, and those that exist often have disappointing results 23 , 29 – 32 . As previously mentioned, the measurement of ions such as Mg 2+ and Ca 2+ together is of great importance due to their similar ionic radius and charge and their simultaneous presence in biological fluids. It can therefore be concluded that achieving high selectivity for Mg 2+ over Ca 2+ can be an accurate measure of ionophore performance. Advanced machine learning methods can uncover hidden patterns in property-structure relationships and handle multidimensional descriptor spaces. Therefore, this technique can be used to solve the existing challenge 33 . Among these methods, support vector machine (SVM) is a powerful tool as a modeling method that can prevent overfitting in high-dimensional data sets 3 , 34 – 36 . These features can make the SVM technique a choice for QSPR applications for fine-tuning the selectivity of ionophores. In this study, support vector machine (SVM) approach was used to predict the potentiometric selectivity of amide-based ionophores for Mg 2+ over Ca 2+ . This technique improves the creation of novel ionophores by studying the intricate and interactions between the molecular structure and its electrochemical response. The aim of this study is to apply more powerful computational tools for effective screening and rational design of novel ionophores with excellent Mg 2+ /Ca 2+ selectivity with reduced experimental workload. This technique can help speed the identification of interesting ligand candidates for next-generation potentiometric sensors. 2. Results and discussion In this study, various regression and machine learning models including SW-MLR, GA-MLR, and GA-SVM were used to predict the potentiometric selectivity (Mg 2+ /Ca 2+ ) of a number of amide ligands. The effect of outlier removal on the performance of the models was also investigated. To evaluate and validate the developed model, many statistical indices such as coefficient of determination (R 2 ), root mean square error (RMSE), and F-statistic were examined in both of the training and test sets. 2.1. SW-MLR model. In the SW-MLR method, effective descriptors were systematically and stepwise selected and the final model was built using them based on the training set. Finally, the resulting model was evaluated on the test set to determine its predictive power. Based on the stepwise selection process, five optimal descriptors including D22, D53, D61, D77 and D93 were identified as the most effective variables in the model. These descriptors have played a decisive role in describing the structure-property relationship of the studied system. To examine the collinearity between the selected descriptors, VIF (variance inflation factor) values were calculated for each variable 37 . The VIF values of all descriptors were less than 1.5, indicating that the model had adequate stability and there was no strong collinearity between the variables. These values are presented in Table 1 . Table 1 Correlation matrix between selected descriptors and their corresponding VIF values based on the SW-MLR model Correlate of selected descriptors D22 D53 D61 D77 D93 VIF D22 1 0 0 0 0 1.112 D53 -0.238 1 0 0 0 1.142 D61 -0.143 0.017 1 0 0 1.076 D77 0.156 -0.343 -0.025 1 0 1.410 D93 -0.124 0.237 0.101 -0.425 1 1.309 Equation 1 for the SW-MLR model was obtained based on the selected descriptors. After building the final model using the training set and evaluating it with the test set, statistical indicators including coefficient of determination (R 2 ), root mean square error (RMSE), F-statistic, etc. were obtained, which are reported in the Eq. 1. According to the results, the model has shown a acceptable results in both the training and test sets. A relatively high value of R 2 and a low value of RMSE indicate the quality and favorable predictability of the model. LogK = − 12.659(± 16.552) + 296.014(± 55.373) D22 + 137.354(± 60.006) D53 + 107.280(± 39.173) D61–127.098(± 31.301) D77 + 26.380(± 7.279) D93 (1) N train =54, R 2 train =0.654, RMSE train =0.580, R 2 adj =0.618, F train =18.159, Q 2 LOO =0.573, Q 2 LGO =0.544, N test =13, R 2 test =0.677, RMSE test =0.814, F test =1.056 Also, the plot of predicted values against experimental values is shown in Fig. 1 . As is clear, the distribution of data around the correlation line confirms the accuracy of the model. To assess the stability and non-randomness of the model, the Y-randomization test 38 was used. In this test, the values of the response variable (i.e., selectivity) are randomly rearranged and new models are then built based on the random data. If the original model is valid, the random models should have very low R 2 and Q 2 . The results of this test are presented in Table 2 and shows that none of the random models came close to the performance of the original model (R 2 and Q 2 < 0.3), indicating that the extracted structure-property relationships are realistic. Table 2 Results of the Y-randomization test for the SW-MLR model No Q 2 R 2 1 0.008 0.222 2 0.023 0.069 3 0.005 0.069 4 0.051 0.050 5 0.080 0.030 6 0.000 0.102 7 0.002 0.266 8 0.024 0.179 9 0.015 0.144 10 0.005 0.108 In addition, to assess the applicability of the model and identify possible outliers, a Williams plot was used. This plot, represents the standardized residuals against the leverage values for each compound. Compounds with a leverage value above the warning threshold (h*) is only structural outliers and may have a good prediction and can be retained in the model, but compounds with standardised residuals greater than 3 standard deviations (3δ) are considered as outliers. As can be seen in Fig. 2 , all the compounds were within the applicability domain of the model and none of them were outside the permissible limits. This indicates the reliability of the model and its generalizability to new data. 2.2. Genetic Algorithm-Based Multiple Linear Regression Model (GA-MLR). To achieve a more accurate and reliable model for predicting potentiometric selectivity (Mg 2+ /Ca 2+ ), a combination of genetic algorithm and multiple linear regression (GA-MLR) was used. Genetic algorithm, as a powerful optimization method, is able to automatically and purposefully select a set of effective descriptors from a large number of variables. In this model, five descriptors including D22, D32, D52, D66 and D93 were selected as effective variables that play an important role in describing the selectivity behavior of the system. To examine the collinearity between the selected descriptors, VIF values were calculated for each variable. The results showed that all selected descriptors have a VIF value of less than 1.4, which indicates the absence of strong internal correlation between them and the presence of statistical stability in the model. In other words, each variable adds independent information to the model and information overlap is prevented. The VIF values and correlation coefficients between descriptors are given in Table 3 . Table 3 Correlation matrix between selected descriptors in the GA-MLR model along with corresponding VIF values Correlate of selected descriptors D22 D32 D52 D66 D93 VIF D22 1 0 0 0 0 1.091 D32 0.069 1 0 0 0 1.348 D52 0.029 -0.465 1 0 0 1.392 D66 0.107 0.169 0.254 1 0 1.164 D93 -0.124 -0.244 0.137 0.053 1 1.104 Equation 2 presents the regression equation obtained from the GA-MLR model using the five selected descriptors, followed by the statistical parameters describing the model’s performance. LogK = − 47.321(± 14.473) + 239.906(± 53.397) D22–253.179(± 109.542) D32 + 289.854(± 39.173) D52–3368.525(± 1184.881) D66 + 37.598(± 6.744) D93 (2) N train =54, R 2 train =0.660, RMSE train =0.575, R 2 adj =0.625, F train =18.632, Q 2 LOO =0.572, Q 2 LGO =0.549, N test =13, R 2 test =0.786, RMSE test =0.630, F test =3.186 This model was able to provide a good fit in the training set with R 2 = 0.660 and F-statistic = 18.632. The evaluation of the model on the test set also showed that the model has good generalization ability; so that the value of R 2 test = 0.786 and F test = 3.186 were obtained. The Q 2 values obtained from leave one out (LOO) and leave group out (LGO) cross-validation also indicate the stability of the model, so that good values of Q 2 LOO = 0.572 and Q 2 LGO = 0.549 were obtained. The adjusted coefficient of determination (R 2 adj ) was also reported to be equal to 0.625, which confirms the accuracy and stability of the model. Figure 3 shows the predicted values versus experimental values for the GA-MLR model. The good fit between the data and the correlation line confirms the accuracy and validity of the model. In order to evaluate whether the model performance is due to real correlation between the data or to randomness, the Y-randomization test was performed. According to the results reported in Table 4 , the low R 2 and Q 2 values obtained from these random models (less than 0.3) indicated that the original model was formed based on the actual patterns of the data and not randomly. Therefore, the GA-MLR model has acceptable validity. Table 4 Results of the Y-randomization test for the GA-MLR model No Q 2 R 2 1 0.062 0.032 2 0.240 0.038 3 0.041 0.040 4 0.017 0.062 5 0.041 0.179 6 0.190 0.030 7 0.147 0.289 8 0.031 0.145 9 0.153 0.014 10 0.000 0.141 In addition, the Williams plot was used to examine the applicability of the model and identify outliers. Based on this plot, compound 55 was identified as an outlier as it had high standardized residual than the 3δ (Fig. 4 ). As a result, in the following sections, this molecule was removed from the dataset and the modeling process was repeated without it to examine its impact on model performance. 2.3. Genetic Algorithm - Support Vector Machine Model (GA-SVM). In addition to the MLR method, the support vector machine regression technique was also used to better investigate the relationships between the ligand structure and their selectivity towards Mg 2+ and Ca 2+ ions. Developing an effective SVM model requires fine-tuning of parameters such as the type of kernel function, the capacity parameter (C), the ε parameter (insensitive loss function), and the γ parameter related to the kernel function. The correct selection of these parameters has a direct impact on the accuracy and generalizability of the model. Therefore, to determine the optimal value of γ, a grid search was performed in the range of 2 to 15 with regular steps and at each step, the RMSE value was recorded using leave-one-out cross-validation. The result of this search showed that the value of γ = 5.6 provided the best performance. The graph resulting from this analysis is shown in Fig. 5 a. Next, the parameter ε, which has a direct impact on the model’s tolerance to noise, was also examined in the range of 0.001 to 0.005 with small steps. The value of ε = 0.0016 produced the lowest RMSE in the cross-validation and was selected as the optimal value (Fig. 5 b). Finally, a range of 10 to 200 was examined to adjust the capacity parameter C, which strikes a balance between overfitting and underfitting. After analyzing the results, the value of C = 100 was identified as optimal (Fig. 5 c). Accordingly, the final SVM model was developed with adjusted values of γ = 5.6, ε = 0.0016, and C = 100. After training the GA-SVM model with the optimal values, its performance in predicting the selectivity ratio (Mg 2+ /Ca 2+ ) was evaluated. The results are shown in Table 5 . Table 5 Statistical results obtained from the GA-SVM model Training N R 2 RMSE F R 2 adj Q 2 LOO Q 2 LGO 54 0.849 0.391 49.360 Test N R 2 RMSE F 0.833 0.369 0.369 13 0.740 0.718 2.242 Based on the above results, the GA-SVM model has shown a good performance. The value of R 2 = 0.849 in the training set indicates a strong fit of the model. Also, the value of R 2 = 0.740 in the test set is a testament to the generalizability of the model. The RMSE values for both the training and test sets (0.391 and 0.718, respectively) are at an acceptable level and confirm the numerical accuracy of the model. The adjusted coefficient of determination (R 2 adj = 0.833) is also another evidence of the accuracy of the model in the presence of several parameters. In addition to the numerical measures, the plot of predicted values against experimental values (Fig. 5 d) shows that the GA-SVM model is able to simulate the experimental behavior of the selectivity ratio with reasonable accuracy. 2.4. Re-modeling GA-MLR and GA-SVM after removing outliers. In order to increase the accuracy of the models and remove the effect of outliers, the molecule 55, which was identified as an outlier in the William’s plot, was removed from the data set and the two GA-MLR and GA-SVM models were re-developed. The GA-MLR model obtained after removing outliers showed better performance compared to the original model. The regression line equation and statistical indices of the model were obtained as follows (Eq. 3) : LogK = − 44.247(± 12.918) + 260.257(± 47.882) D22–225.815(± 97.852) D32 + 339.169(± 90.412) D52–3694.393(± 1059.083) D66 + 36.802(± 6.010) D93 (3) N train =53, R 2 train =0.723, RMSE train =0.512, R 2 adj =0.694, F train =24.565, Q 2 LOO =0.646, Q 2 LGO =0.634, N test =13, R 2 test =0.802, RMSE test =0.606, F test =3.768 The GA-SVM model was also redeveloped after removing the molecule 55 as an outlier and parameter optimization was performed using SVM. In this process, in order to achieve the best prediction accuracy and prevent overfitting, three key model parameters including γ, ε, and C were optimized simultaneously within the specified ranges. The search range for γ was defined as 0.1 to 10, for C as 5 to 200, and for ε as 0.0001 to 0.002. After running the SVM and evaluating the model using leave-one-out cross-validation, the optimal values were identified as γ = 5.6, ε = 0.0001, and C = 100 (Fig. 6 a-c, respectively). The statistical results of the redeveloped model showed that its fit and predictability indices are: R 2 train = 0.8930, F train = 72.2668, RMSE train = 0.3224, R 2 test = 0.7568, RMSE test = 0.7053, F test = 2.3884, R 2 adj = 0.8817, Q 2 LOO = 0.4396 and Q 2 LGO = 0.4396 These values indicate that the GA-SVM model, after removing the outlier (molecule 55), was able to maintain high accuracy in the training data and also provide good performance in the test data. The plot of predicted values against experimental values also shows a significant agreement between the data, which confirms the accuracy and stability of the model (Fig. 6 d). 2.5. Comparison of Model Performance. In order to comprehensively evaluate the performance of the developed models, the main statistical indices including coefficient of determination, root mean square error and Fisher’s exact statistic were calculated for the training and testing datasets before and after outlier removal and compared with the values reported in previous sources (Table 6 ) 29 . The results show that the GA-MLR and GA-SVM models outperformed the basic SW-MLR model in both cases. In particular, the GA-SVM model after outlier removal (molecule 55) presented the highest value of R² train = 0.893 and the lowest RMSE train = 0.322, indicating a very good fit to the training data. Also, this model was able to provide acceptable generalizability in the testing dataset with R² test = 0.757 and RMSE test = 0.705. The removal of outliers led to a significant improvement in the statistical indices of both GA-MLR and GA-SVM models; in that the R² values for training and testing data increased and the RMSE value decreased. This indicates that outliers can have a negative effect on the accuracy and stability of the models and that their removal improves the prediction performance. Comparison with the results reported in previous studies also indicates that the present approach performed better than the reference SW-MLR models even without the removal of outliers. Overall, the findings indicate that the use of genetic algorithms for variable selection and parameter optimization, whether in the linear or nonlinear regression framework, leads to a significant improvement in the accuracy and generalizability of the models. The experimental and predicted values of potentiometric selectivity obtained from the investigated models are also presented in Table 7 . Table 6 Comparison of statistical indices of different models before and after the removal of outliers with the previous reference models Study Model Number of outliers Training Test Ref R 2 RMSE F R 2 RMSE F This work SW-MLR 0 0.654 0.580 18.159 0.677 0.814 1.056 – This work GA-MLR 0 0.660 0.575 18.632 0.786 0.630 3.186 – This work GA-SVM 0 0.849 0.391 49.360 0.740 0.718 2.242 – This work GA-MLR (removed outlier) 1 0.723 0.512 24.565 0.802 0.606 3.768 – This work GA-SVM (removed outlier) 1 0.893 0.322 72.267 0.757 0.705 2.388 – Reference SW-MLR 0 0.400 0.880 – – – – 29 Reference SW-MLR (removed outlier) 11 0.660 0.530 – – – – 29 Table 7. Experimental and predicted values of potentiometric selectivity obtained from the investigated models Ligand No. LogK (Mg 2+ /Ca 2+ ) Exp. Predicted SW-MLR GA-MLR GA-SVM GA-MLR non-outlier GA-SVM non-outlier 1 -1.30 -0.79 -1.32 -1.30 -1.41 -1.30 2 -1.20 -0.48 -0.69 -1.20 -0.74 -1.20 3 0.90 0.19 0.17 0.61 0.20 0.62 4 -0.10 -0.14 -0.18 -0.10 -0.19 -0.10 5 -0.20 -0.03 0.00 -0.20 -0.01 -0.20 6 -0.10 -0.61 -0.52 -0.10 -0.57 -0.10 7 -1.00 0.12 -0.09 -0.57 -0.15 -0.59 8 t 0.60 -0.01 -0.15 -0.42 -0.19 -0.42 9 t -1.40 -0.04 -0.75 -0.45 -0.89 -0.51 10 -1.20 -0.25 -0.43 -0.86 -0.47 -0.87 11 -1.70 -0.74 -0.94 -1.20 -1.02 -1.20 12 0.00 0.07 -0.18 -0.01 -0.23 -0.02 13 0.90 1.24 1.53 0.90 1.41 0.90 14 -0.70 -0.08 -0.36 -0.70 -0.44 -0.70 15 -0.80 0.44 0.18 -0.16 0.11 -0.21 16 -0.90 -0.04 -0.24 -0.76 -0.30 -0.77 17 -0.90 -0.18 -0.29 -0.88 -0.34 -0.88 18 -0.80 -0.40 -0.43 -0.80 -0.48 -0.80 19 -0.40 -0.60 -0.39 -0.42 -0.43 -0.42 20 -0.60 -0.93 -0.71 -0.60 -0.76 -0.60 21 -1.00 -0.25 -0.25 -0.62 -0.29 -0.62 22 1.00 0.56 0.35 0.40 0.30 0.39 23 -0.50 -0.99 -1.53 -0.50 -1.61 -0.50 24 t -1.00 0.03 -0.24 -0.78 -0.29 -0.78 25 -0.50 -0.64 -0.32 -0.50 -0.44 -0.50 26 -1.00 -0.41 -0.43 -0.91 -0.44 -0.89 27 t -0.70 0.08 -0.07 0.00 -0.18 -0.09 28 0.30 0.50 0.50 0.30 0.51 0.30 29 -0.40 -0.14 -0.09 -0.40 -0.11 -0.40 30 0.10 -0.31 -0.16 0.10 -0.11 0.10 31 -0.20 -0.94 -0.46 -0.20 -0.43 -0.20 32 t -0.40 0.41 -0.07 -0.08 -0.11 -0.13 33 2.50 2.63 2.31 2.50 2.42 2.50 34 -0.50 -0.52 -0.41 -0.50 -0.52 -0.50 35 0.80 0.20 0.45 0.80 0.39 0.80 36 t 0.20 0.61 0.72 0.71 0.75 0.72 37 0.50 0.40 0.91 0.50 0.98 0.50 38 t 3.00 2.06 2.24 1.76 2.26 1.75 39 0.80 0.77 1.06 0.80 1.00 0.80 40 0.90 0.83 1.14 0.90 1.05 0.90 41 t 0.90 0.51 0.58 0.79 0.36 0.73 42 3.30 3.09 2.54 3.28 2.54 3.29 43 t 1.20 0.13 0.06 0.09 0.06 0.09 44 0.00 0.17 0.00 0.00 0.00 0.00 45 0.30 -0.26 -0.16 0.12 -0.17 0.12 46 -0.50 0.07 0.06 -0.50 0.05 -0.50 47 0.00 -0.04 0.17 0.00 0.12 0.00 48 0.00 0.06 0.35 0.00 0.28 0.00 49 1.40 1.28 0.93 1.40 0.76 1.40 50 0.10 -0.24 0.13 0.10 0.06 0.10 51 0.70 -0.15 -0.20 -0.30 -0.27 -0.31 52 t 0.00 0.10 -0.09 -0.53 -0.14 -0.53 53 0.60 0.22 -0.11 -0.37 -0.17 -0.38 54 1.30 0.09 -0.04 -0.04 -0.09 -0.06 55 1.60 -0.09 -0.34 -0.06 * * 56 -0.40 -0.31 -0.46 -0.40 -0.50 -0.40 57 0.00 -0.42 -0.62 -0.38 -0.64 -0.38 58 -0.20 0.17 0.09 -0.20 0.09 -0.20 59 -0.30 -0.09 -0.29 -0.30 -0.32 -0.30 60 0.20 -0.41 0.32 0.20 0.30 0.20 61 -0.70 -0.38 -0.23 -0.70 -0.36 -0.70 62 t 2.30 1.58 1.95 1.64 2.09 1.64 63 1.60 1.37 1.84 1.60 1.96 1.60 64 2.10 1.78 1.85 2.10 1.88 2.10 65 t 2.00 0.95 1.32 1.43 1.36 1.44 66 t 1.50 1.79 1.98 1.61 1.84 1.60 67 -0.20 -0.76 -0.41 -0.20 -0.39 -0.20 t Test set * Outlier 2.6. Overall analysis of descriptors. In this study, descriptor selection was performed using two approaches, SW and GA, each of which operated on a different feature selection algorithm and introduced a set of important parameters as key factors. The selected descriptors and their definitions are shown in Table 8. The SW method identified five descriptors D22, D53, D61, D77 and D93 as the most important parameters affecting selectivity. In contrast, the GA method selected a different set of five descriptors, two of which (D22 and D93) were shared with SW, but the other three descriptors represent different aspects of the molecule's properties: Table 8. The main descriptors selected by SW and GA methods and theire definitions No. Descriptor Definition SW GA 1 D22 Max partial charge for a N atom (Zefirov’s PC), which is an indicator of the local polarity and the tendency of the nitrogen atom to electrostatic interactions ✓ ✓ 2 D53 Min electroph. react. index for a O atom, which indicates the lowest electron-accepting ability of the oxygen atom. ✓ – 3 D61 Avg 1-electron react. index for a N atom, which describes the local chemical activity of nitrogen. ✓ – 4 D77 Ratio of fractional polar molecular surface area type 3 to total molecular surface area (FPSA-3 Fractional PPSA [Quantum-Chemical PC]), which is related to the charge distribution and surface polarity of the molecule. ✓ – 5 D93 Average bond valence (Avg valency) of oxygen atoms, which is related to the structure and bond geometry of the molecule. ✓ ✓ 6 D32 Ratio of fractional polar molecular surface area type 3 to total molecular surface area (FPSA-3 Fractional PPSA [Zefirov’s PC]). – ✓ 7 D52 Average electrophilic reactivity index for nitrogen atom, which indicates the tendency of nitrogen to accept an electron. – ✓ 8 D66 Average one-electron reactivity index for carbon atom, which indicates the degree of participation of carbons in electronic reactions. – ✓ Comparison of the two selected sets shows that although some features such as partial charge of nitrogen and oxygen binding capacity are of common importance in both methods, the difference in other descriptors indicates the influence of more diverse electronic and spatial parameters in the GA model 39 . Also, examination of the coefficients of these descriptors in the linear equations of MLR models showed that positive coefficients indicate a direct relationship with the model response; that is, increasing the value of that descriptor leads to an increase in the predicted activity or selectivity, and negative coefficients indicate an inverse relationship, and increasing the value of that descriptor causes a decrease in the model response. This situation could mean the inhibitory role of some structural or electronic features in the selectivity mechanism. For example, if a descriptor related to surface polarity has a negative coefficient, this could indicate that excessive increase in surface polarity reduces the favorable interaction of the ligand with the target ion, thereby weakening selectivity. Conversely, a positive coefficient for the parameter related to the partial charge of nitrogen could indicate strengthening of electrostatic interactions and an increased tendency of the ligand to form a stable complex. 3. Experimental 3.1. Dataset and procedure. In this study, the molecular structures of lipophilic amide-based magnesium ionophores, along with their logarithmic selectivity coefficients, were extracted as a dataset from the paper by Martinko et al 29 . They collected 67 ligands from various sources and made efforts to ensure the stability of the experimental conditions for these ligands. The coefficient associated with each structure indicates the selectivity of that ligand to Mg 2+ in the presence of Ca 2+ . All molecules were first drawn using HyperChem software and initially optimized by the MM+ force field in the molecular mechanics framework 40 . The chemical structures of these compounds are given in Table S1. After preparing the structures, all the required molecular descriptors were calculated based on these structures. The data set was divided into two parts: a training set of 54 compounds for model development and a test set of 13 compounds for evaluating its performance. 3.2. Molecular Descriptors. After drawing the molecules, molecular descriptors were calculated using CODESSA software 41 . Before calculating the descriptors, to obtain more accurate structures, re-optimization was performed using the semi-empirical AM1 method using AMPAC software 42 . The optimization process based on the Polak-Ribiere algorithm was continued until the root mean square (RMS) gradient value was less than 0.01 kcal/mol 43 . The outputs of AMPAC software were entered into CODESSA program to calculate a set of molecular descriptors. In order to reduce the number of descriptors, after removing descriptors with constant or almost constant values as well as descriptors with correlations above 0.9, the 161 uncorrelated descriptors were retained for the next steps. Next, in order to identify the most important and effective descriptors in modeling, stepwise (SW) 44 and genetic algorithm (GA) 45 variable selection methods were used for descriptor selection. 3.3. Variable selection by stepwise and genetic algorithm. In this study, two different variable selection methods were used to select the most effective and relevant molecular descriptors in the modeling process, including the stepwise method (SW) and the genetic algorithm (GA). In the stepwise method, descriptors are gradually added or removed from the model based on statistical criteria such as coefficient of determination (r) and significance test to obtain the best combination of variables with the highest predictive power 46 . In contrast, the genetic algorithm, as a meta-heuristic method inspired by natural evolution and developed by Holland et al., helps to find an optimal set of variables with the highest modeling power by generating successive generations of different combinations of descriptors and evaluating their performance 47 . This algorithm creates a population of random combinations of descriptors and applies crossover and mutation operators, while exploring the parameter space extensively, preventing it from getting stuck in local optima and enabling the finding of a global optimum. In this process, each combination is considered as an “individual” in the population and is evaluated based on the modeling performance (usually the cross-validation correlation coefficient or Q 2 LOO ). Using these two methods, allowed for comparison of results, increased model accuracy, and ensured the selection of the most effective descriptors. Further applications of these methods have been thoroughly reviewed in our previous studies 35,48,49 . 3.4. Support vector machine. Support vector machine (SVM) is one of the powerful machine learning methods that have found wide application in the field of chemometrics, especially in regression and classification problems 50 . SVM is designed with the aim of finding an optimal hyperplane that separates data with the largest margin. This unique feature reduces the risk of overfitting and increases the generalizability of the model. One of the most prominent features of SVM is the use of kernel functions to map data to a higher-dimensional feature space. This feature allows SVMs to linearly model complex nonlinear relationships between molecular structure and chemical properties in the new space 51 . There are various kernel functions, such as Radial Basis Kernel (RBF), Polynomial, and Linear, and their selection depends on the data type and modeling objective 52 . In the field of QSPR modeling, SVM has received much attention due to its high performance in conditions where the data has high dimensions and the number of samples is limited. In addition, the optimal adjustment of parameters such as the parameter (C) and the kernel parameter (such as gamma γ in the RBF kernel) plays an important role in improving the accuracy of the final model 53 . These adjustments are usually performed through methods such as cross-validation or grid search. Overall, SVM is a reliable tool for modeling complex chemical data and can be used as an effective approach in developing accurate and stable predictive models. 4. Conclusion In this study, QSAR modeling was performed to predict the selectivity of ligands towards Mg²⁺ and Ca²⁺ ions using different machine learning approaches including SW-MLR, GA-MLR, and GA-SVM. In the first step, feature selection was performed using the SW method and then the genetic algorithm was used to identify descriptors affecting selectivity. The results showed that the use of the genetic algorithm in variable selection, significantly improved R 2 and decreased RMSE in both training and testing datasets. The GA-SVM model, especially after removing outliers, provided the highest accuracy and stability; so that the training R² was 0.893 and the test R² was 0.757, which shows a significant improvement compared to other models. Also, removing outliers led to a decrease in RMSE and an increase in predictive power (R 2 and Q²), which shows the importance of identifying and managing outliers in the modeling process. Comparison with reference data also showed that even without removing outliers, the models developed in this study have higher performance. Moreover, analysis of the selected descriptors revealed that parameters related to the partial charge and electronic reactivity of nitrogen and oxygen atoms play a crucial role in determining ligand selectivity. Descriptors with positive coefficients, such as those associated with nitrogen partial charge, enhance electrostatic interactions and stabilize complex formation, while descriptors with negative coefficients, such as excessive surface polarity, may reduce favorable binding to the target ion. Overall, the results emphasize that combining genetic algorithm-based feature selection methods with MLR and SVM can lead to the development of accurate, stable, and highly generalizable QSAR models. Declarations Acknowledgement This research was carried out with the support of Mohaghegh Ardabili University (Research grant number: 1402.d.9.23917). Supporting Information: Includes a table of chemical structures of the ligands studied. Author Information Corresponding Authors Eslam Pourbasheer - Department of Chemistry, Faculty of Science, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran; Email: [email protected] Authors Reza Mahmoudzadeh Laki - Department of Chemistry, Faculty of Science, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran; Email: [email protected] Abolghasem Beheshti - Department of Chemistry, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran: Email: [email protected] Suraj N. Mali- School of Pharmacy, D.Y. Patil University, Navi Mumbai 400706, India. Email: [email protected] Author contributions The manuscript was prepared by all authors. The E.P., corresponding author, performed the calculations and supervised the research. R.M.L, S.N.M and A.B were the writers and compilers of the manuscript. All authors reviewed and approved the final version. Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Funding: No funding. Data availability All data generated or analyzed during this study are included in this published article and its supplementary information files. Additional datasets are available from the corresponding author on reasonable request. References Hu, J., Stein, A. & Bühlmann, P. Rational design of all-solid-state ion-selective electrodes and reference electrodes. TRAC Trends Anal. Chem. 76 , 102–114 (2016). Vladimirova, N. et al. Predicting the potentiometric sensitivity of membrane sensors based on modified diphenylphosphoryl acetamide ionophores with QSPR modeling. Membranes 12 , 953 (2022). Pourbasheer, E., Mahmoudzadeh Laki, R. & Sarafraz Khalifehlou, M. Heavy Metals Potentiometric Sensitivity Prediction by Firefly-Support Vector Machine Modeling Method. Anal. 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Imbalance classification in a scaled-down wind turbine using radial basis function kernel and support vector machines. Energy 238 , 122064 (2022). Zhou, J. et al. Predicting tunnel squeezing using support vector machine optimized by whale optimization algorithm. Acta Geotech. 17 , 1343–1366 (2022). Additional Declarations No competing interests reported. Supplementary Files supportinginformation.pdf Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8806544","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":591231236,"identity":"3dc6b8b2-613b-42c0-bc4d-c8741e546c5c","order_by":0,"name":"Eslam Pourbasheer","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8ElEQVRIiWNgGAWjYPCCAwwMEiC6AiZgQLSWMyRrYWwjwkX8DLwHH/PuuSMvP7v54OPKeYej+RuYH35gKLiHU4tkA1+yMc+zZ4Yb7hxLNjy77XDujANsxhIMBsU4tRgc4DGT5jlwmHGDRI6ZZCNQS8MBBjOgeAJOLfZQLfbzZ+R//9k453Du/APs3/BqMWCAaElsuJHDxtjYcDh3A9AQvFokDvMlG8458Cx5w400Y8mGY+m5Gw/zFEsk4NHC39578MGbA3ds589IfvixocY6d97x9o0fPvzBrYWBmQdDBIjxaAACDC2jYBSMglEwCtAAAFxVVgy6H/6jAAAAAElFTkSuQmCC","orcid":"","institution":"University of Mohaghegh Ardabili","correspondingAuthor":true,"prefix":"","firstName":"Eslam","middleName":"","lastName":"Pourbasheer","suffix":""},{"id":591231243,"identity":"3b6dd87c-7ac6-4181-8ae9-288415cb8d65","order_by":1,"name":"Reza Mahmoudzadeh Laki","email":"","orcid":"","institution":"University of Mohaghegh Ardabili","correspondingAuthor":false,"prefix":"","firstName":"Reza","middleName":"Mahmoudzadeh","lastName":"Laki","suffix":""},{"id":591231247,"identity":"51dc9f84-4da4-4bab-ae69-4523c4db7d37","order_by":2,"name":"Suraj N. 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experimental values for the SW-MLR model\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8806544/v1/6363a18fba2192ceaa728ad1.png"},{"id":102846064,"identity":"69aad156-9194-43e6-aaa7-e22f3037ff86","added_by":"auto","created_at":"2026-02-17 13:15:14","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":97289,"visible":true,"origin":"","legend":"\u003cp\u003eWilliams plot for assessing the applicability domain of the SW-MLR model\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8806544/v1/3dbd5ac587159819f1c11f26.png"},{"id":102846060,"identity":"5733e921-f33f-441b-a678-81877977dbb6","added_by":"auto","created_at":"2026-02-17 13:15:14","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":124097,"visible":true,"origin":"","legend":"\u003cp\u003ePredicted values versus experimental values for the GA-MLR model in the training and test sets.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8806544/v1/5877fcb9363c7b560208ec58.png"},{"id":102963484,"identity":"f8102ba1-ad65-43b6-8b2a-336d32497a8d","added_by":"auto","created_at":"2026-02-19 04:18:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":95830,"visible":true,"origin":"","legend":"\u003cp\u003eWilliams plot to examine the applicability of the GA-MLR model and identify outliers\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8806544/v1/30f96dd09332925c682b1a2a.png"},{"id":102962841,"identity":"a1f95e09-da84-4d0b-a389-4325b0473097","added_by":"auto","created_at":"2026-02-19 04:11:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":220621,"visible":true,"origin":"","legend":"\u003cp\u003eOptimization of GA-SVM model parameters including: (a) investigating the effect of parameter γ on model accuracy, (b) evaluating different values of ε to determine the model's tolerance to noise, (c) optimizing the capacity parameter C to create a balance between overfitting and underfitting, and (d) comparing predicted values with experimental values for the selectivity ratio under optimal conditions.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8806544/v1/950ac1c816845ce839bc3c30.png"},{"id":102846066,"identity":"468b94aa-24c4-4c66-9ab6-b220cdfaa23e","added_by":"auto","created_at":"2026-02-17 13:15:14","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":222683,"visible":true,"origin":"","legend":"\u003cp\u003eOptimization of GA-SVM model parameters including: (a) γ parameter (b) different values of ε, (c) capacity parameter C, and (d) comparison of predicted values with experimental values for selectivity ratio under optimal conditions after removing outlier.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8806544/v1/ae68d56b40a1c86eedcb0695.png"},{"id":108803994,"identity":"6898f977-c9c1-4271-b3dc-1971c3b06e0a","added_by":"auto","created_at":"2026-05-08 15:14:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1458302,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8806544/v1/16e5ee42-44e0-4534-a87b-d9d6d5ff02da.pdf"},{"id":102846062,"identity":"75456262-63cd-474b-a795-8c34d3e75912","added_by":"auto","created_at":"2026-02-17 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Introduction","content":"\u003cp\u003eRecently, there has been a great demand for selective and sensitive chemical sensors for clinical and environmental analysis, which has led to a lot of research in this field \u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. In view of these studies, sensors capable of accurately determining ionic activity in complex matrices have attracted attention \u003csup\u003e\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Among these, sensors based on softened polymer membranes can be mentioned \u003csup\u003e\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. The ionophore is the main component of these sensors, which is embedded in the sensor membrane and is mainly composed of lipophilic organic ligands. The ionophore can be sensitive and selective towards specific analytes \u003csup\u003e\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. However, designing novel ionophores with high selectivity for the determination of similar chemical ions that are very difficult to distinguish from each other is a significant challenge. Chemical ions such as magnesium (Mg\u003csup\u003e2+\u003c/sup\u003e) and calcium (Ca\u003csup\u003e2+\u003c/sup\u003e), whose discrimination is of great importance in physiological and industrial problems, are an example of this type \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe experimental methods used to generate ionophores are both difficult and resource-intensive, such as the synthesis of potential ligands, the fabrication of sensing membranes, and comprehensive electrochemical analysis. However, there is less insight into the prediction of the final performance of the synthesized structures \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. These limitations have led to the increasing use of computational techniques such as quantitative structure-property relationship (QSPR) modeling in the design of ionophores \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. QSPR methods establish a relationship between molecular descriptors and experimental qualities, facilitating the prediction of ligand behavior based on structural features \u003csup\u003e\u003cspan additionalcitationids=\"CR20 CR21 CR22 CR23 CR24\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAlthough recent studies have been conducted on modeling complex physicochemical phenomena, including metal-ligand binding \u003csup\u003e\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, extraction efficiency, and sensor responses using the QSPR technique, there are not many studies focused on the selectivity of ISEs, and those that exist often have disappointing results \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e,\u003cspan additionalcitationids=\"CR30 CR31\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. As previously mentioned, the measurement of ions such as Mg\u003csup\u003e2+\u003c/sup\u003e and Ca\u003csup\u003e2+\u003c/sup\u003e together is of great importance due to their similar ionic radius and charge and their simultaneous presence in biological fluids. It can therefore be concluded that achieving high selectivity for Mg\u003csup\u003e2+\u003c/sup\u003e over Ca\u003csup\u003e2+\u003c/sup\u003e can be an accurate measure of ionophore performance.\u003c/p\u003e \u003cp\u003eAdvanced machine learning methods can uncover hidden patterns in property-structure relationships and handle multidimensional descriptor spaces. Therefore, this technique can be used to solve the existing challenge \u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Among these methods, support vector machine (SVM) is a powerful tool as a modeling method that can prevent overfitting in high-dimensional data sets \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan additionalcitationids=\"CR35\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. These features can make the SVM technique a choice for QSPR applications for fine-tuning the selectivity of ionophores.\u003c/p\u003e \u003cp\u003eIn this study, support vector machine (SVM) approach was used to predict the potentiometric selectivity of amide-based ionophores for Mg\u003csup\u003e2+\u003c/sup\u003e over Ca\u003csup\u003e2+\u003c/sup\u003e. This technique improves the creation of novel ionophores by studying the intricate and interactions between the molecular structure and its electrochemical response. The aim of this study is to apply more powerful computational tools for effective screening and rational design of novel ionophores with excellent Mg\u003csup\u003e2+\u003c/sup\u003e/Ca\u003csup\u003e2+\u003c/sup\u003e selectivity with reduced experimental workload. This technique can help speed the identification of interesting ligand candidates for next-generation potentiometric sensors.\u003c/p\u003e"},{"header":"2. Results and discussion","content":"\u003cp\u003eIn this study, various regression and machine learning models including SW-MLR, GA-MLR, and GA-SVM were used to predict the potentiometric selectivity (Mg\u003csup\u003e2+\u003c/sup\u003e/Ca\u003csup\u003e2+\u003c/sup\u003e) of a number of amide ligands. The effect of outlier removal on the performance of the models was also investigated. To evaluate and validate the developed model, many statistical indices such as coefficient of determination (R\u003csup\u003e2\u003c/sup\u003e), root mean square error (RMSE), and F-statistic were examined in both of the training and test sets.\u003c/p\u003e \u003cp\u003e \u003cb\u003e2.1. SW-MLR model.\u003c/b\u003e In the SW-MLR method, effective descriptors were systematically and stepwise selected and the final model was built using them based on the training set. Finally, the resulting model was evaluated on the test set to determine its predictive power. Based on the stepwise selection process, five optimal descriptors including D22, D53, D61, D77 and D93 were identified as the most effective variables in the model. These descriptors have played a decisive role in describing the structure-property relationship of the studied system. To examine the collinearity between the selected descriptors, VIF (variance inflation factor) values were calculated for each variable \u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. The VIF values of all descriptors were less than 1.5, indicating that the model had adequate stability and there was no strong collinearity between the variables. These values are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCorrelation matrix between selected descriptors and their corresponding VIF values based on the SW-MLR model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCorrelate of selected descriptors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eD22\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eD53\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eD61\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD77\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eD93\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eVIF\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.112\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.142\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.076\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.410\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.237\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.101\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.309\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eEquation 1 for the SW-MLR model was obtained based on the selected descriptors. After building the final model using the training set and evaluating it with the test set, statistical indicators including coefficient of determination (R\u003csup\u003e2\u003c/sup\u003e), root mean square error (RMSE), F-statistic, etc. were obtained, which are reported in the Eq.\u0026nbsp;1. According to the results, the model has shown a acceptable results in both the training and test sets. A relatively high value of R\u003csup\u003e2\u003c/sup\u003e and a low value of RMSE indicate the quality and favorable predictability of the model.\u003c/p\u003e \u003cp\u003eLogK = \u0026minus;\u0026thinsp;12.659(\u0026plusmn;\u0026thinsp;16.552)\u0026thinsp;+\u0026thinsp;296.014(\u0026plusmn;\u0026thinsp;55.373) D22\u0026thinsp;+\u0026thinsp;137.354(\u0026plusmn;\u0026thinsp;60.006) D53\u0026thinsp;+\u0026thinsp;107.280(\u0026plusmn;\u0026thinsp;39.173) D61\u0026ndash;127.098(\u0026plusmn;\u0026thinsp;31.301) D77\u0026thinsp;+\u0026thinsp;26.380(\u0026plusmn;\u0026thinsp;7.279) D93 (1)\u003c/p\u003e \u003cp\u003eN\u003csub\u003etrain\u003c/sub\u003e=54, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etrain\u003c/sub\u003e=0.654, RMSE\u003csub\u003etrain\u003c/sub\u003e=0.580, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadj\u003c/sub\u003e=0.618, F\u003csub\u003etrain\u003c/sub\u003e=18.159, Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLOO\u003c/sub\u003e=0.573, Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLGO\u003c/sub\u003e=0.544, N\u003csub\u003etest\u003c/sub\u003e=13, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etest\u003c/sub\u003e=0.677, RMSE\u003csub\u003etest\u003c/sub\u003e=0.814, F\u003csub\u003etest\u003c/sub\u003e=1.056\u003c/p\u003e \u003cp\u003eAlso, the plot of predicted values against experimental values is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. As is clear, the distribution of data around the correlation line confirms the accuracy of the model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo assess the stability and non-randomness of the model, the Y-randomization test \u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e was used. In this test, the values of the response variable (i.e., selectivity) are randomly rearranged and new models are then built based on the random data. If the original model is valid, the random models should have very low R\u003csup\u003e2\u003c/sup\u003e and Q\u003csup\u003e2\u003c/sup\u003e. The results of this test are presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and shows that none of the random models came close to the performance of the original model (R\u003csup\u003e2\u003c/sup\u003e and Q\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.3), indicating that the extracted structure-property relationships are realistic.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of the Y-randomization test for the SW-MLR model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eQ\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.222\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.069\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.069\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.050\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.080\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.030\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.102\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.266\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.179\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.144\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.108\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn addition, to assess the applicability of the model and identify possible outliers, a Williams plot was used. This plot, represents the standardized residuals against the leverage values for each compound. Compounds with a leverage value above the warning threshold (h*) is only structural outliers and may have a good prediction and can be retained in the model, but compounds with standardised residuals greater than 3 standard deviations (3δ) are considered as outliers. As can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, all the compounds were within the applicability domain of the model and none of them were outside the permissible limits. This indicates the reliability of the model and its generalizability to new data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e2.2. Genetic Algorithm-Based Multiple Linear Regression Model (GA-MLR).\u003c/b\u003e To achieve a more accurate and reliable model for predicting potentiometric selectivity (Mg\u003csup\u003e2+\u003c/sup\u003e/Ca\u003csup\u003e2+\u003c/sup\u003e), a combination of genetic algorithm and multiple linear regression (GA-MLR) was used. Genetic algorithm, as a powerful optimization method, is able to automatically and purposefully select a set of effective descriptors from a large number of variables. In this model, five descriptors including D22, D32, D52, D66 and D93 were selected as effective variables that play an important role in describing the selectivity behavior of the system.\u003c/p\u003e \u003cp\u003eTo examine the collinearity between the selected descriptors, VIF values were calculated for each variable. The results showed that all selected descriptors have a VIF value of less than 1.4, which indicates the absence of strong internal correlation between them and the presence of statistical stability in the model. In other words, each variable adds independent information to the model and information overlap is prevented. The VIF values and correlation coefficients between descriptors are given in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCorrelation matrix between selected descriptors in the GA-MLR model along with corresponding VIF values\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCorrelate of selected descriptors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eD22\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eD32\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eD52\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD66\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eD93\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eVIF\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.091\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.069\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.348\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.465\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.392\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.169\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.254\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.164\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.244\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.104\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eEquation 2 presents the regression equation obtained from the GA-MLR model using the five selected descriptors, followed by the statistical parameters describing the model\u0026rsquo;s performance.\u003c/p\u003e \u003cp\u003eLogK = \u0026minus;\u0026thinsp;47.321(\u0026plusmn;\u0026thinsp;14.473)\u0026thinsp;+\u0026thinsp;239.906(\u0026plusmn;\u0026thinsp;53.397) D22\u0026ndash;253.179(\u0026plusmn;\u0026thinsp;109.542) D32\u0026thinsp;+\u0026thinsp;289.854(\u0026plusmn;\u0026thinsp;39.173) D52\u0026ndash;3368.525(\u0026plusmn;\u0026thinsp;1184.881) D66\u0026thinsp;+\u0026thinsp;37.598(\u0026plusmn;\u0026thinsp;6.744) D93 (2)\u003c/p\u003e \u003cp\u003eN\u003csub\u003etrain\u003c/sub\u003e=54, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etrain\u003c/sub\u003e=0.660, RMSE\u003csub\u003etrain\u003c/sub\u003e=0.575, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadj\u003c/sub\u003e=0.625, F\u003csub\u003etrain\u003c/sub\u003e=18.632, Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLOO\u003c/sub\u003e=0.572, Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLGO\u003c/sub\u003e=0.549, N\u003csub\u003etest\u003c/sub\u003e=13, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etest\u003c/sub\u003e=0.786, RMSE\u003csub\u003etest\u003c/sub\u003e=0.630, F\u003csub\u003etest\u003c/sub\u003e=3.186\u003c/p\u003e \u003cp\u003eThis model was able to provide a good fit in the training set with R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.660 and F-statistic\u0026thinsp;=\u0026thinsp;18.632. The evaluation of the model on the test set also showed that the model has good generalization ability; so that the value of R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etest\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.786 and F\u003csub\u003etest\u003c/sub\u003e = 3.186 were obtained. The Q\u003csup\u003e2\u003c/sup\u003e values obtained from leave one out (LOO) and leave group out (LGO) cross-validation also indicate the stability of the model, so that good values of Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLOO\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.572 and Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLGO\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.549 were obtained. The adjusted coefficient of determination (R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadj\u003c/sub\u003e) was also reported to be equal to 0.625, which confirms the accuracy and stability of the model.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the predicted values versus experimental values for the GA-MLR model. The good fit between the data and the correlation line confirms the accuracy and validity of the model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn order to evaluate whether the model performance is due to real correlation between the data or to randomness, the Y-randomization test was performed. According to the results reported in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the low R\u003csup\u003e2\u003c/sup\u003e and Q\u003csup\u003e2\u003c/sup\u003e values obtained from these random models (less than 0.3) indicated that the original model was formed based on the actual patterns of the data and not randomly. Therefore, the GA-MLR model has acceptable validity.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of the Y-randomization test for the GA-MLR model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eQ\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.032\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.038\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.062\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.179\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.030\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.147\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.289\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.145\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.141\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn addition, the Williams plot was used to examine the applicability of the model and identify outliers. Based on this plot, compound 55 was identified as an outlier as it had high standardized residual than the 3δ (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). As a result, in the following sections, this molecule was removed from the dataset and the modeling process was repeated without it to examine its impact on model performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e2.3. Genetic Algorithm - Support Vector Machine Model (GA-SVM).\u003c/b\u003e In addition to the MLR method, the support vector machine regression technique was also used to better investigate the relationships between the ligand structure and their selectivity towards Mg\u003csup\u003e2+\u003c/sup\u003e and Ca\u003csup\u003e2+\u003c/sup\u003e ions. Developing an effective SVM model requires fine-tuning of parameters such as the type of kernel function, the capacity parameter (C), the ε parameter (insensitive loss function), and the γ parameter related to the kernel function. The correct selection of these parameters has a direct impact on the accuracy and generalizability of the model.\u003c/p\u003e \u003cp\u003eTherefore, to determine the optimal value of γ, a grid search was performed in the range of 2 to 15 with regular steps and at each step, the RMSE value was recorded using leave-one-out cross-validation. The result of this search showed that the value of γ\u0026thinsp;=\u0026thinsp;5.6 provided the best performance. The graph resulting from this analysis is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea. Next, the parameter ε, which has a direct impact on the model\u0026rsquo;s tolerance to noise, was also examined in the range of 0.001 to 0.005 with small steps. The value of ε\u0026thinsp;=\u0026thinsp;0.0016 produced the lowest RMSE in the cross-validation and was selected as the optimal value (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb). Finally, a range of 10 to 200 was examined to adjust the capacity parameter C, which strikes a balance between overfitting and underfitting. After analyzing the results, the value of C\u0026thinsp;=\u0026thinsp;100 was identified as optimal (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec). Accordingly, the final SVM model was developed with adjusted values of γ\u0026thinsp;=\u0026thinsp;5.6, ε\u0026thinsp;=\u0026thinsp;0.0016, and C\u0026thinsp;=\u0026thinsp;100.\u003c/p\u003e \u003cp\u003eAfter training the GA-SVM model with the optimal values, its performance in predicting the selectivity ratio (Mg\u003csup\u003e2+\u003c/sup\u003e/Ca\u003csup\u003e2+\u003c/sup\u003e) was evaluated. The results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical results obtained from the GA-SVM model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTraining\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadj\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eQ\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLOO\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eQ\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLGO\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.849\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.391\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e49.360\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.833\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.369\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.369\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.740\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.718\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.242\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBased on the above results, the GA-SVM model has shown a good performance. The value of R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.849 in the training set indicates a strong fit of the model. Also, the value of R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.740 in the test set is a testament to the generalizability of the model. The RMSE values for both the training and test sets (0.391 and 0.718, respectively) are at an acceptable level and confirm the numerical accuracy of the model. The adjusted coefficient of determination (R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadj\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.833) is also another evidence of the accuracy of the model in the presence of several parameters. In addition to the numerical measures, the plot of predicted values against experimental values (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed) shows that the GA-SVM model is able to simulate the experimental behavior of the selectivity ratio with reasonable accuracy.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e2.4. Re-modeling GA-MLR and GA-SVM after removing outliers.\u003c/b\u003e In order to increase the accuracy of the models and remove the effect of outliers, the molecule 55, which was identified as an outlier in the William\u0026rsquo;s plot, was removed from the data set and the two GA-MLR and GA-SVM models were re-developed.\u003c/p\u003e \u003cp\u003eThe GA-MLR model obtained after removing outliers showed better performance compared to the original model. The regression line equation and statistical indices of the model were obtained as follows (Eq.\u0026nbsp;3) :\u003c/p\u003e \u003cp\u003eLogK = \u0026minus;\u0026thinsp;44.247(\u0026plusmn;\u0026thinsp;12.918)\u0026thinsp;+\u0026thinsp;260.257(\u0026plusmn;\u0026thinsp;47.882) D22\u0026ndash;225.815(\u0026plusmn;\u0026thinsp;97.852) D32\u0026thinsp;+\u0026thinsp;339.169(\u0026plusmn;\u0026thinsp;90.412) D52\u0026ndash;3694.393(\u0026plusmn;\u0026thinsp;1059.083) D66\u0026thinsp;+\u0026thinsp;36.802(\u0026plusmn;\u0026thinsp;6.010) D93 (3)\u003c/p\u003e \u003cp\u003eN\u003csub\u003etrain\u003c/sub\u003e=53, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etrain\u003c/sub\u003e=0.723, RMSE\u003csub\u003etrain\u003c/sub\u003e=0.512, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadj\u003c/sub\u003e=0.694, F\u003csub\u003etrain\u003c/sub\u003e=24.565, Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLOO\u003c/sub\u003e=0.646, Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLGO\u003c/sub\u003e=0.634, N\u003csub\u003etest\u003c/sub\u003e=13, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etest\u003c/sub\u003e=0.802, RMSE\u003csub\u003etest\u003c/sub\u003e=0.606, F\u003csub\u003etest\u003c/sub\u003e=3.768\u003c/p\u003e \u003cp\u003eThe GA-SVM model was also redeveloped after removing the molecule 55 as an outlier and parameter optimization was performed using SVM. In this process, in order to achieve the best prediction accuracy and prevent overfitting, three key model parameters including γ, ε, and C were optimized simultaneously within the specified ranges. The search range for γ was defined as 0.1 to 10, for C as 5 to 200, and for ε as 0.0001 to 0.002. After running the SVM and evaluating the model using leave-one-out cross-validation, the optimal values were identified as γ\u0026thinsp;=\u0026thinsp;5.6, ε\u0026thinsp;=\u0026thinsp;0.0001, and C\u0026thinsp;=\u0026thinsp;100 (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea-c, respectively).\u003c/p\u003e \u003cp\u003eThe statistical results of the redeveloped model showed that its fit and predictability indices are:\u003c/p\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etrain\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8930, F\u003csub\u003etrain\u003c/sub\u003e = 72.2668, RMSE\u003csub\u003etrain\u003c/sub\u003e = 0.3224, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etest\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.7568, RMSE\u003csub\u003etest\u003c/sub\u003e = 0.7053, F\u003csub\u003etest\u003c/sub\u003e = 2.3884, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eadj\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.8817, Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLOO\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4396 and Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLGO\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.4396\u003c/p\u003e \u003cp\u003eThese values indicate that the GA-SVM model, after removing the outlier (molecule 55), was able to maintain high accuracy in the training data and also provide good performance in the test data. The plot of predicted values against experimental values also shows a significant agreement between the data, which confirms the accuracy and stability of the model (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e2.5. Comparison of Model Performance.\u003c/b\u003e In order to comprehensively evaluate the performance of the developed models, the main statistical indices including coefficient of determination, root mean square error and Fisher\u0026rsquo;s exact statistic were calculated for the training and testing datasets before and after outlier removal and compared with the values reported in previous sources (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) \u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. The results show that the GA-MLR and GA-SVM models outperformed the basic SW-MLR model in both cases. In particular, the GA-SVM model after outlier removal (molecule 55) presented the highest value of R\u0026sup2;\u003csub\u003etrain\u003c/sub\u003e = 0.893 and the lowest RMSE\u003csub\u003etrain\u003c/sub\u003e = 0.322, indicating a very good fit to the training data. Also, this model was able to provide acceptable generalizability in the testing dataset with R\u0026sup2;\u003csub\u003etest\u003c/sub\u003e = 0.757 and RMSE\u003csub\u003etest\u003c/sub\u003e = 0.705. The removal of outliers led to a significant improvement in the statistical indices of both GA-MLR and GA-SVM models; in that the R\u0026sup2; values for training and testing data increased and the RMSE value decreased. This indicates that outliers can have a negative effect on the accuracy and stability of the models and that their removal improves the prediction performance. Comparison with the results reported in previous studies also indicates that the present approach performed better than the reference SW-MLR models even without the removal of outliers. Overall, the findings indicate that the use of genetic algorithms for variable selection and parameter optimization, whether in the linear or nonlinear regression framework, leads to a significant improvement in the accuracy and generalizability of the models.\u003c/p\u003e \u003cp\u003eThe experimental and predicted values of potentiometric selectivity obtained from the investigated models are also presented in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of statistical indices of different models before and after the removal of outliers with the previous reference models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eStudy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eNumber of outliers\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003eTraining\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eRef\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThis work\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSW-MLR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.654\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.580\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e18.159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.677\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.814\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.056\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThis work\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGA-MLR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.660\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.575\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e18.632\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.786\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.630\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.186\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThis work\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGA-SVM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.849\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.391\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e49.360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.740\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.718\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.242\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThis work\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGA-MLR\u003c/p\u003e \u003cp\u003e(removed outlier)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.723\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.512\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e24.565\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.802\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.606\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.768\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThis work\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGA-SVM\u003c/p\u003e \u003cp\u003e(removed outlier)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.893\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.322\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e72.267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.757\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.705\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.388\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSW-MLR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.880\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSW-MLR\u003c/p\u003e \u003cp\u003e(removed outlier)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.660\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.530\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eTable 7.\u003c/strong\u003e Experimental and predicted values of potentiometric selectivity obtained from the investigated models\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" style=\"width: 13px;\"\u003e\n \u003cp\u003eLigand No.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"6\" style=\"width: 86px;\"\u003e\n \u003cp\u003eLogK (Mg\u003csup\u003e2+\u003c/sup\u003e/Ca\u003csup\u003e2+\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 12px;\"\u003e\n \u003cp\u003eExp.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"5\" style=\"width: 74px;\"\u003e\n \u003cp\u003ePredicted\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003eSW-MLR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003eGA-MLR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003eGA-SVM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003eGA-MLR non-outlier\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003eGA-SVM non-outlier\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-1.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-1.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-1.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-1.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-1.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-1.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-1.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-1.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.19\u003c/p\u003e\n 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style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.59\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e8\u003csup\u003et\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n 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16px;\"\u003e\n \u003cp\u003e-0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.77\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n 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13px;\"\u003e\n \u003cp\u003e-0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-1.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e24\u003csup\u003et\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n 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13px;\"\u003e\n \u003cp\u003e-0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.89\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e27\u003csup\u003et\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n 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style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e2.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e2.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e2.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n 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13px;\"\u003e\n \u003cp\u003e0.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n 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style=\"width: 13px;\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.53\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e1.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e1.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e*\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e62\u003csup\u003et\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e2.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e2.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.64\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e1.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.60\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e2.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e2.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e2.10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e65\u003csup\u003et\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e2.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e0.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.44\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e66\u003csup\u003et\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e1.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e1.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e1.60\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12px;\"\u003e\n \u003cp\u003e-0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13px;\"\u003e\n \u003cp\u003e-0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 16px;\"\u003e\n \u003cp\u003e-0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003csup\u003et\u003c/sup\u003e Test set\u003c/p\u003e\n\u003cp\u003e* Outlier\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.6. Overall analysis of descriptors.\u003c/em\u003e\u003c/strong\u003e In this study, descriptor selection was performed using two approaches, SW and GA, each of which operated on a different feature selection algorithm and introduced a set of important parameters as key factors. The selected descriptors and their definitions are shown in Table 8. The SW method identified five descriptors D22, D53, D61, D77 and D93 as the most important parameters affecting selectivity. In contrast, the GA method selected a different set of five descriptors, two of which (D22 and D93) were shared with SW, but the other three descriptors represent different aspects of the molecule\u0026apos;s properties:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 8.\u003c/strong\u003e The main descriptors selected by SW and GA methods and theire definitions\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003eNo.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eDescriptor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eDefinition\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003eSW\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003eGA\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eD22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eMax partial charge for a N atom (Zefirov\u0026rsquo;s PC), which is an indicator of the local polarity and the tendency of the nitrogen atom to electrostatic interactions\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eD53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eMin electroph. react. index for a O atom, which indicates the lowest electron-accepting ability of the oxygen atom.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003e\u0026ndash;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eD61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eAvg 1-electron react. index for a N atom, which describes the local chemical activity of nitrogen.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003e\u0026ndash;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eD77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eRatio of fractional polar molecular surface area type 3 to total molecular surface area (FPSA-3 Fractional PPSA [Quantum-Chemical PC]), which is related to the charge distribution and surface polarity of the molecule.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003e\u0026ndash;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eD93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eAverage bond valence (Avg valency) of oxygen atoms, which is related to the structure and bond geometry of the molecule.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eD32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eRatio of fractional polar molecular surface area type 3 to total molecular surface area (FPSA-3 Fractional PPSA [Zefirov\u0026rsquo;s PC]).\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026ndash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eD52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eAverage electrophilic reactivity index for nitrogen atom, which indicates the tendency of nitrogen to accept an electron.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026ndash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eD66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 417px;\"\u003e\n \u003cp\u003eAverage one-electron reactivity index for carbon atom, which indicates the degree of participation of carbons in electronic reactions.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026ndash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 48px;\"\u003e\n \u003cp\u003e✓\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eComparison of the two selected sets shows that although some features such as partial charge of nitrogen and oxygen binding capacity are of common importance in both methods, the difference in other descriptors indicates the influence of more diverse electronic and spatial parameters in the GA model \u003csup\u003e39\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eAlso, examination of the coefficients of these descriptors in the linear equations of MLR models showed that positive coefficients indicate a direct relationship with the model response; that is, increasing the value of that descriptor leads to an increase in the predicted activity or selectivity, and negative coefficients indicate an inverse relationship, and increasing the value of that descriptor causes a decrease in the model response. This situation could mean the inhibitory role of some structural or electronic features in the selectivity mechanism. For example, if a descriptor related to surface polarity has a negative coefficient, this could indicate that excessive increase in surface polarity reduces the favorable interaction of the ligand with the target ion, thereby weakening selectivity. Conversely, a positive coefficient for the parameter related to the partial charge of nitrogen could indicate strengthening of electrostatic interactions and an increased tendency of the ligand to form a stable complex.\u003c/p\u003e"},{"header":"3. Experimental","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003e3.1. Dataset and procedure.\u003c/em\u003e\u003c/strong\u003e In this study, the molecular structures of lipophilic amide-based magnesium ionophores, along with their logarithmic selectivity coefficients, were extracted as a dataset from the paper by Martinko et al \u003csup\u003e29\u003c/sup\u003e. They collected 67 ligands from various sources and made efforts to ensure the stability of the experimental conditions for these ligands.\u0026nbsp;The coefficient associated with each structure indicates the selectivity of that ligand to\u0026nbsp;Mg\u003csup\u003e2+\u003c/sup\u003e in the presence of\u0026nbsp;Ca\u003csup\u003e2+\u003c/sup\u003e. All molecules were first drawn using HyperChem software and initially optimized by the MM+ force field in the molecular mechanics framework\u0026nbsp;\u003csup\u003e40\u003c/sup\u003e. The chemical structures of these compounds are given in Table S1. After preparing the structures, all the required molecular descriptors were calculated based on these structures. The data set was divided into two parts: a training set of 54 compounds for model development and a test set of 13 compounds for evaluating its performance.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e3.2. Molecular Descriptors.\u003c/em\u003e\u003c/strong\u003e After drawing the molecules, molecular descriptors were calculated using CODESSA software \u003csup\u003e41\u003c/sup\u003e. Before calculating the descriptors, to obtain more accurate structures, re-optimization was performed using the semi-empirical AM1 method using AMPAC software \u003csup\u003e42\u003c/sup\u003e. The optimization process based on the Polak-Ribiere algorithm was continued until the root mean square (RMS) gradient value was less than 0.01 kcal/mol \u003csup\u003e43\u003c/sup\u003e. The outputs of AMPAC software were entered into CODESSA program to calculate a set of molecular descriptors. In order to reduce the number of descriptors, after removing descriptors with constant or almost constant values as well as descriptors with correlations above 0.9, the \u0026nbsp;161 uncorrelated descriptors were retained for the next steps. Next, in order to identify the most important and effective descriptors in modeling, stepwise (SW) \u003csup\u003e44\u003c/sup\u003e and genetic algorithm (GA) \u003csup\u003e45\u003c/sup\u003e variable selection methods were used for descriptor selection.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e3.3. Variable selection by stepwise and genetic algorithm.\u0026nbsp;\u003c/em\u003e\u003c/strong\u003eIn this study, two different variable selection methods were used to select the most effective and relevant molecular descriptors in the modeling process, including the stepwise method (SW) and the genetic algorithm (GA). In the stepwise method, descriptors are gradually added or removed from the model based on statistical criteria such as coefficient of determination (r) and significance test to obtain the best combination of variables with the highest predictive power \u003csup\u003e46\u003c/sup\u003e. In contrast, the genetic algorithm, as a meta-heuristic method inspired by natural evolution and developed by Holland et al., helps to find an optimal set of variables with the highest modeling power by generating successive generations of different combinations of descriptors and evaluating their performance \u003csup\u003e47\u003c/sup\u003e. This algorithm creates a population of random combinations of descriptors and applies crossover and mutation operators, while exploring the parameter space extensively, preventing it from getting stuck in local optima and enabling the finding of a global optimum. In this process, each combination is considered as an “individual” in the population and is evaluated based on the modeling performance (usually the cross-validation correlation coefficient or Q\u003csup\u003e2\u003c/sup\u003e\u003csub\u003eLOO\u003c/sub\u003e). Using these two methods, allowed for comparison of results, increased model accuracy, and ensured the selection of the most effective descriptors. Further applications of these methods have been thoroughly reviewed in our previous studies \u003csup\u003e35,48,49\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e3.4. Support vector machine.\u0026nbsp;\u003c/em\u003e\u003c/strong\u003eSupport vector machine (SVM) is one of the powerful machine learning methods that have found wide application in the field of chemometrics, especially in regression and classification problems \u003csup\u003e50\u003c/sup\u003e. SVM is designed with the aim of finding an optimal hyperplane that separates data with the largest margin. This unique feature reduces the risk of overfitting and increases the generalizability of the model. One of the most prominent features of SVM is the use of kernel functions to map data to a higher-dimensional feature space. This feature allows SVMs to linearly model complex nonlinear relationships between molecular structure and chemical properties in the new space \u003csup\u003e51\u003c/sup\u003e. There are various kernel functions, such as Radial Basis Kernel (RBF), Polynomial, and Linear, and their selection depends on the data type and modeling objective \u003csup\u003e52\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eIn the field of QSPR modeling, SVM has received much attention due to its high performance in conditions where the data has high dimensions and the number of samples is limited. In addition, the optimal adjustment of parameters such as the parameter (C) and the kernel parameter (such as gamma γ in the RBF kernel) plays an important role in improving the accuracy of the final model \u003csup\u003e53\u003c/sup\u003e. These adjustments are usually performed through methods such as cross-validation or grid search. Overall, SVM is a reliable tool for modeling complex chemical data and can be used as an effective approach in developing accurate and stable predictive models.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eIn this study, QSAR modeling was performed to predict the selectivity of ligands towards Mg\u0026sup2;⁺ and Ca\u0026sup2;⁺ ions using different machine learning approaches including SW-MLR, GA-MLR, and GA-SVM. In the first step, feature selection was performed using the SW method and then the genetic algorithm was used to identify descriptors affecting selectivity. The results showed that the use of the genetic algorithm in variable selection, significantly improved R\u003csup\u003e2\u003c/sup\u003e and decreased RMSE in both training and testing datasets. The GA-SVM model, especially after removing outliers, provided the highest accuracy and stability; so that the training R\u0026sup2; was 0.893 and the test R\u0026sup2; was 0.757, which shows a significant improvement compared to other models. Also, removing outliers led to a decrease in RMSE and an increase in predictive power (R\u003csup\u003e2\u003c/sup\u003e and Q\u0026sup2;), which shows the importance of identifying and managing outliers in the modeling process. Comparison with reference data also showed that even without removing outliers, the models developed in this study have higher performance. Moreover, analysis of the selected descriptors revealed that parameters related to the partial charge and electronic reactivity of nitrogen and oxygen atoms play a crucial role in determining ligand selectivity. Descriptors with positive coefficients, such as those associated with nitrogen partial charge, enhance electrostatic interactions and stabilize complex formation, while descriptors with negative coefficients, such as excessive surface polarity, may reduce favorable binding to the target ion. Overall, the results emphasize that combining genetic algorithm-based feature selection methods with MLR and SVM can lead to the development of accurate, stable, and highly generalizable QSAR models.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was carried out with the support of Mohaghegh Ardabili University (Research grant number:\u0026nbsp;1402.d.9.23917).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupporting Information:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIncludes a table of chemical structures of the ligands studied.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorresponding Authors\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEslam Pourbasheer - Department of Chemistry, Faculty of Science, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran; Email: [email protected]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eReza Mahmoudzadeh Laki - Department of Chemistry, Faculty of Science, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran; Email: [email protected]\u003c/p\u003e\n\u003cp\u003eAbolghasem Beheshti - Department of Chemistry, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran: Email:\u0026nbsp;\u003cu\[email protected]\u003c/u\u003e\u003c/p\u003e\n\u003cp\u003eSuraj N. Mali- School of Pharmacy, D.Y. Patil University, Navi Mumbai 400706, India. Email: \u003cu\[email protected]\u003c/u\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe manuscript was prepared by all authors. The E.P., corresponding author, performed the calculations and supervised the research. R.M.L, S.N.M and A.B were the writers and compilers of the manuscript. All authors reviewed and approved the final version.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e No funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data generated or analyzed during this study are included in this published article and its supplementary information files. Additional datasets are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHu, J., Stein, A. \u0026amp; B\u0026uuml;hlmann, P. 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Experimental data and molecular structures were entered into the models after calculating and screening the descriptors. The SW method identified five descriptors and GA five descriptors (with two common items) as key parameters. Using these variable selection methods and machine learning modeling methods of multiple linear regrassions (MLR) and support vector machine (SVM), various models including SW-MLR, GA-MLR, GA-SVM were created, and also, by identifying an outlier and removing it, GA-MLR and GA-SVM models were re-developed. The model obtained by GA-SVM (with one outlier removed) had R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etrain\u003c/sub\u003e=0.893, R\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etest\u003c/sub\u003e=0.757, RMSE \u003csub\u003etrain\u003c/sub\u003e =0.322, and RMSE\u003csub\u003etest\u003c/sub\u003e =0.705, indicating the high predictive power and fit of the models. These values were a significant improvement compared to the reference paper (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.66 and RMSE\u0026thinsp;=\u0026thinsp;0.53 even after removing 11 outliers). In addition, findings provide important mechanistic insights into the role of molecular features in potentiometric selectivity (Mg\u003csup\u003e2+\u003c/sup\u003e/Ca\u003csup\u003e2+\u003c/sup\u003e) of amide ligands.\u003c/p\u003e","manuscriptTitle":"Application of machine learning in predicting potentiometric selectivity (Mg 2+ /Ca 2+ ) of some amide ligands","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-17 13:15:09","doi":"10.21203/rs.3.rs-8806544/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"22223c64-3829-411d-b0a7-2aae38ca1cf7","owner":[],"postedDate":"February 17th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":62919344,"name":"Physical sciences/Chemistry"},{"id":62919345,"name":"Biological sciences/Computational biology and bioinformatics"}],"tags":[],"updatedAt":"2026-05-05T13:26:16+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-17 13:15:09","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8806544","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8806544","identity":"rs-8806544","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}