In Silico Prediction and Screening of c-Secretase

In Silico Prediction and Screening of c-SecretaseInhibitors by Molecular Descriptors andMachine Learning MethodsXUE-GANG YANG,1WEI LV,1YU-ZONG CHEN,2,3YING XUE1,21Key Lab of Green Chemistry and Technology in Ministry of Education,College of Chemistry,Sichuan University,Chengdu610064,People’s Republic of China2State Key Laboratory of Biotherapy,Chengdu610041,People’s Republic of China3Bioinformatics and Drug Design Group,Department of Computational Science,NationalUniversity of Singapore,Blk SOC1,Level7,3Science Drive2,Singapore117543,SingaporeReceived19April2009;Revised26July2009;Accepted12August2009DOI10.1002/jcc.21411Published online in Wiley InterScience().Abstract:c-Secretase inhibitors have been explored for the prevention and treatment of Alzheimer’s disease(AD). Methods for prediction and screening of c-secretase inhibitors are highly desired for facilitating the design of novel therapeutic agents against AD,especially when incomplete knowledge about the mechanism and three-dimensional structure of c-secretase.We explored two machine learning methods,support vector machine(SVM)and random forest(RF),to develop models for predicting c-secretase inhibitors of diverse structures.Quantitative analysis of the receiver operating characteristic(ROC)curve was performed to further examine and optimize the models.Espe-cially,the Youden index(YI)was initially introduced into the ROC curve of RF so as to obtain an optimal threshold of probability for prediction.The developed models were validated by an external testing set with the prediction accuracies of SVM and RF96.48and98.83%for c-secretase inhibitors and98.18and99.27%for noninhibitors, respectively.The different feature selection methods were used to extract the physicochemical features most relevant to c-secretase inhibition.To the best of our knowledge,the RF model developed in this work is thefirst model with a broad applicability domain,based on which the virtual screening of c-secretase inhibitors against the ZINC data-base was performed,resulting in368potential hit candidates.q2009Wiley Periodicals,Inc.J Comput Chem00:000–000,2010Key words:c-secretase inhibitors;machine learning;support vector machine(SVM);random forest(RF);virtual screeningIntroductionAlzheimer’s disease(AD),the leading cause of dementia,is the most common progressive neurodegenerative disorder of the central nervous system in the elderly and poses a serious health-care problem worldwide.1,2AD is characterized pathologically by the accumulation of extracellular amyloid plaques predomi-nantly made up of amyloid-b(A b)peptides and intracellular neurofibrillary tangles composed of hyperphosphorylated Tau protein in the Alzheimer’s brains.3,4Because of the unique char-acteristic of the formation of amyloid plaques to AD,the production and deposition of A b in the brain are considered to play a causative role to the pathogenesis of AD.5,6A b is largely composed of40or42amino acids generated from sequential proteolytic cleavage of A b precursor protein(APP)by b-and c-secretases.7b-Secretase cleavage of APP produces the mem-brane-associated99-amino-acid C-terminal fragments(C99) which are subsequently cleaved by c-secretase to release A b.7–9 Therefore,inhibition of c-secretase to reduce A b levels has been widely regarded as a plausible strategy for the prevention and treatment of AD.7,9,10Additional Supporting Information may be found in the online version of this articleCorrespondence to:Y.Xue;e-mail:yxue@Contract/grant sponsor:National Natural Science Foundation of China; contract/grant numbers:20773089,20835003Contract/grant sponsor:Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry;contract/grant number:20071108-18-15Recently,intensive investigations have shown the minimal set of components required for the c-secretase complex assembly consisting of presenilin-1(Ps-1),nicastrin(Nct),anterior phar-ynx defective-1(Aph-1)and PS enhancer-2(Pen-2),9–12but the detailed mechanism of c-secretase complex assembly is not fully understood,10,11and it is difficult to quantitatively profile the elusive c-secretase mostly due to its unusual specificity.13On the other hand,a number of heterogeneous derivatives showing potent in vitro or in vivo c-secretase inhibitory activity have been widely reported in the numerous literatures,14–23and some of c-secretase inhibitors have entered preclinical or clinical trails.14,15,21–25It has been reported that different classes of c-secretase inhibitors may share different biological modes of action,19and many of the known c-secretase inhibitors show modest efficacy as opposed to halting the underlying pathophysiological onset and progression of the disease.22,23Moreover,some of the known c-secretase inhibitors cause defects in peripheral Notch function,leading to lower levels of tolerance and higher instan-ces of unfavorable side effects.26–30Therefore,the discovery of novel c-secretase inhibitors with high efficiency and selectivity is highly needed.As part of the effort for facilitating the development of new c-secretase inhibitors in a cost-effective manner,we intended to explore machine learning methods for prediction and screening of structurally diverse c-secretase inhibitors,which do not require the knowledge about the mechanisms of action,the three-dimensional(3D)structures of biological targets,and the intrinsic relationships between activities and molecular proper-ties.31–33Many different machine learning methods have been successfully applied in quantitative structure activity relationship (QSAR)modeling.31–36In this work,two popularly used meth-ods were explored,which include support vector machine (SVM)37,38and random forest(RF),39,40to develop the predic-tion models,in which the internal5-fold cross-validation and out-of-bag(OOB)estimate were conducted to optimize the train-ing models so as to obtain good and reliable prediction perform-ance.Moreover,the important physicochemical features most relevant to c-secretase inhibition were also extracted from the models by different feature selection methods.These interesting results are very useful for predicting c-secretase inhibitors and conducting virtual screening of c-secretase inhibitors against large compound libraries in the drug discovery stages,before in vitro or in vivo pharmacological assays.Computational MethodsData Sets and Molecular DescriptorsA diverse range of675c-secretase inhibitors with known A b lowering IC50values were collected from a number of published articles(Supporting Information).These compounds are distrib-uted in diverse structural groups including natural product inter-mediates,2tetrahydroquinoline sulfonamides,5,18arylsulfona-mides,15,19aryl sulfones,20cyclohexyl sulfones,21N-arylsulfonyl piperidines,16succinoyl-caprolactam derivatives,22dibenzazepi-none derivatives,14thiazole-diamides,17hydroxytriamides23and so on.To sufficiently represent the vastness of c-secretase nonin-hibitors,758putative noninhibitors were extracted from the MDL Drug Data Report(MDDR)database by means of k-means clustering.41We divided more than150,000compounds from MDDR(removing those entries that have invalid structures or molecular descriptors)which have not been reported to have c-secretase inhibitory activity into758clusters based on189cal-culated molecular descriptors(vide infra).The scale of generated compound clusters in this work is consistent with that reported in other studies.42–44For each cluster,the compound closest to the centroid of the corresponding cluster was selected.All of these675c-secretase inhibitors and758noninhibitors were fur-ther divided into the training and external testing set according to their distribution in the chemical space.45The training set is used to develop the prediction models and select most appropri-ate sets of molecular descriptors,and the external testing set is used for evaluating the performance of the resulting models.The compounds in the training and external testing set are listed in Supporting Information Tables SI1and SI2,respectively.Molecular descriptors are routinely used for quantitative description of the structural and physicochemical properties of molecules in the development of various QSAR models.45–48A set of189molecular descriptors involved in this work was calculated relying on the3D structure of each compound by using our in-house developed molecular descriptor computing program.These descriptors,described in the early studies,31–33include18constitutional descriptors,124topologi-cal descriptors,22quantum chemical descriptors and25geomet-rical descriptors.Machine Learning MethodsWe employed two state-of-the-art machine learning methods, including SVM and RF.The prediction task performed here by SVM and RF was considered to be a binary classification prob-lem(c-secretase inhibitors or noninhibitors).The detailed intro-ductions of SVM and RF are easily available from a number of excellent books and literatures.Thus,only a brief summarization for the main ideas of SVM and RF is given here.SVM37,38is a well-known kernel-trick machine learning method which is based on the structural risk minimization (SRM)principle from statistical learning theory.It projects the input vectors into a high-dimensional feature space by using the kernel function such as the Gaussian radial basis function (RBF),49then an optimal separation hyperplane is constructed in the transformed space by selecting a small subset of so-called SVs from the input vectors to separate two different classes of vectors with a maximum margin.RF39,40is an ensemble of dissimilar classification trees grown from separate bootstrap samples of the training data set and ran-domly selected subsets of m try variables as candidates to deter-mine the best possible split at each node during the tree induc-tion.Each tree is grown to the maximum size without pruning and gives its own prediction for a new data point.Thefinal pre-diction is generally made by consensus voting among all the n tree trees generated in the forest,but other appropriate thresh-olds of prediction probability based on the number of votes can also been assigned by users.50The performance of RF is inter-nally evaluated by using an unbiased OOB estimate of the gen-2Yang et al.•Vol.00,No.00•Journal of Computational Chemistryeralization error.The OOB estimate is an excellent measure of the prediction capability of the model which can be regarded as equivalent to cross-validation.51Additionally,a built-in measure of the importance of a variable can also been derived from RF according to the degree of the decrease of the performance resulting from random permutation of the values of variables.Although RF performs relatively well ‘‘off the shelf’’without expending much effort on parameter tuning or variable selec-tion,39it is also of importance for some tentative investigations on the changes of m try or descriptor selection to optimize the performance of RF.Feature Selection and ModelingFeature selection methods have often been used for selecting descriptors most related to the discrimination of two data sets and for improving the performance of different machine learning methods.52–55In the process of SVM model development,a bet-ter-behaved feature selection method,recursive feature elimina-tion (RFE),55incorporated with SVM (SVM 1RFE)wasinitially used for selecting the most appropriate set of descriptors by means of 5-fold cross-validation within the training set.After the feature selection,the whole training set with the RFE selected descriptors was used to develop a SVM model.With respect to RF,each tree was grown by using a different boot-strap sample of the training data set with randomly selected descriptors.The performance of RF was internally evaluated by means of OOB estimate in parallel with the forest building.In addition,a collection of relatively important descriptors can also be aggregated in the course of RF training.Finally,the externalTable 1.The D (A )Value of the Investigated Data Sets and the NCIDiversity Set II.Date set (A)No.of compoundsD (A )value The NCI diversity set II13640.401The training set (in this work)9030.414The external testing set (in this work)5300.419The training and external testing set (in this work)14330.416Table 2.The Prediction Performance of SVM for c -Secretase Inhibitors and Noninhibitors Evaluated by Using5-Fold Cross-Validation Within the Training Set.aMethod Cross-validationc -Secretase inhibitorsc -Secretasenoninhibitors Q (%)MCC TP FN SE (%)TN FP SP (%)SVM187792.5579594.0593.260.8651284693.33105199.0696.430.9290382297.62970100.0098.900.9780461395.3193991.1892.770.8524583495.4093297.8996.700.9341Average 94.8496.4495.610.9117SD 1.99 3.71 2.560.0522SVM 1RFE190495.7482297.6296.630.9327288297.78103397.1797.450.94873840100.0094396.9198.340.96734640100.0095793.1495.780.91635870100.0090594.7497.250.9465Average 98.7095.9297.090.9423SD1.921.910.950.0191aThe results are given in TP (true positive),FN (false negative),SE (sensitivity)which is the prediction accuracy for c -secretase inhibitors,TN (true negative),FP (false positive),SP (specificity)which is the prediction accu-racy for c -secretase noninhibitors,Q (overall prediction accuracy),and MCC (Matthews correlation coefficient).Statistical significance is indicated by S.D.(standard deviation).Figure 1.The effect of the different values of m try (1 m try 189)on the OOB ERs of RF within the training set.3In Silico Prediction and Screening of c -Secretase Inhibitorstesting set was involved to validate the performance of the developed models and the virtual screening of c -secretase inhibi-tors against the ‘‘fragment-like’’subset of the ZINC database 56was also performed in this work.Performance MeasuresThe effectiveness of machine learning methods can be measured by using true positive (TP),true negative (TN),false positive (FP),false negative (FN),sensitivity (SE)[SE 5TP/(TP 1FN)]and specificity (SP)[SP 5TN/(TN 1FP)],57where TP is the number of c -secretase inhibitors predicted correctly,TN is the number of c -secretase noninhibitors predicted correctly,FN is the number of c -secretase inhibitors predicted as noninhibi-tors,FP is the number of c -secretase noninhibitors predicted as inhibitors,SE is the prediction accuracy of c -secretase inhibitors,and SP is the prediction accuracy of c -secretase noninhibitors.Besides,error rate (ER)[ER 5(FP 1FN)/(TP 1TN 1FP 1FN)],overall prediction accuracy (Q)[Q 5(TP 1TN)/(TP 1TN 1FP 1FN)]and Matthews correlation coefficient (MCC)58[MCC 5(TP 3TN 2FN 3FP)/[(TP 1FN)(TP 1FP)(TN 1FN)(TN 1FP)]1/2]are also used for measuring the model per-formance.Results and DiscussionDiversity AnalysisThe diversity of the compounds used for modeling significantly affects the efficiency and robustness of the prediction models.The more diverse the compound set,the larger will be the applicability domain of the model.The diversity of a set of compounds can be measured by D (A )which is the average value of the dissimilarity between all the pairwise compounds in the data set A,59D A ðÞ¼P N A ðÞi ¼1PN A ðÞj ¼1;i ¼jdiss i ;j ðÞN A ðÞN A ðÞÀ1½(1)where diss (i,j )is a measure of the dissimilarity between com-pounds i and j ,and N (A )is the number of compounds intheFigure 2.The ROC curve for the prediction of the 903training samples from the OOB estimate of RF by using different thresholds of prediction probability.Table 3.The Prediction Performance of c -Secretase Inhibitors andNoninhibitors from SVM and RF Evaluated by Using the External Testing Set.Method Parameter c -Secretase inhibitorsc -Secretase noninhibitorsQ (%)MCC TP FN SE (%)TN FP SP (%)SVM r 50.05247996.48269598.1897.360.9472RFm try 512253398.83272299.2799.060.9811Figure 3.The performance measures of the OOB estimate of RFand 5-fold cross-validation ofSVM.Figure 4.The ROC curves of SVM and RF for the external testing set.4Yang et al.•Vol.00,No.00•Journal of Computational Chemistrydata set A.Dissimilarity is a complementary measure of similar-ity.In this work,the similarity between any two compounds was computed by using a commonly used similarity metric—Tani-moto coefficient,60,61sim i ;j ðÞ¼P ld ¼1X di X dj P ld ¼1X di ðÞ2þP ld ¼1X dj ÀÁ2ÀP ld ¼1X di X dj(2)where l is the number of descriptors computed for the com-pounds in the data set,X di and X dj are the values of d th descrip-tor for compounds i and j ,respectively.Then,the dissimilaritycan be simply denoted as (1-similarity).In this way,D (A )returns a value between 0and 1.The higher the value of D (A ),the more diverse is the data set A.In this work,the computed value of D (A )for the data set of 675c -secretase inhibitors and 758noninhibitors is 0.416,especially 0.414and 0.419for the training and external testing set,respectively.To assess to what extent the value of D (A )can reflect the diversity of the data set,we referred to the D (A )value of the NCI diversity set II.62The NCI diversity set II is a set of 1364compounds selected from the original NCI-3D database of the almost 140,000compounds based on their properties as unique three-point pharmaco-phores.63The computed value of D (A )for the NCI diversity set II is 0.401,which is comparable to those for the investigated data sets.The results are shown in Table 1,suggesting that the investigated data sets used in this work are of structural diversity.Feature Selection and Model DevelopmentThe performance of SVM and RF for predicting c -secretase inhibitors and noninhibitors was improved by means of the fea-ture selection methods.The SVM model was developed by using our own developed program,and RF was generated with the Fortran code proposed by Breiman and Cutler.64In the SVM model,the use of RFE method significantly improves the prediction performance based on the 5-fold cross-validation test against the training set.The detailed results are shown in Table 2.The average prediction accuracies of SVM without RFE for c -secretase inhibitors and noninhibitors are 94.84and 96.44%,as compared to 98.70%and 95.92%with SVM 1RFE,respectively.The average values of Q and MCC of SVM without RFE are 95.61%and 0.9117,and those with SVM 1RFE are 97.09%and 0.9423,respectively.Although the average prediction accuracy of SVM 1RFE for c -secretase noninhibitors slightly decreases compared to that of SVM without RFE,the average prediction accuracy of SVM 1RFE for c -secretase inhibitors,Q and MCC show significant improvement compared to those of SVM without RFE.Besides,the most appropriate set of descriptors was also obtained for the following SVM modeling with the whole training set.In the RF model,random feature selection was used at each node in the tree-building process to decrease the correlation between the trees in the forest,consequently improving the pre-diction performance of RF.The number of trees n tree was set to 500that has been used for generating stabilized OBB ERs.39The optimization parameter m try can range from one to the total number of descriptors.Here,1 m try 189.Although the value of m try is generally chosen to be the default (the square root of the total number of descriptors),we varied the value of m try from 1to 189to examine the values of OOB ERs so as to obtain an optimal value of m try .As shown in Figure 1,the varia-tion of OOB ERs roughly stays flat against the values of m try with the exception of a dramatic increment of OOB ER when m try 51(i.e.,the random split is essentially performed at each node for each tree in the forest).Despite this,the optimal pa-rameter m try was eventually selected to be 12with the smallest OOB ER.In addition,further examination and optimization of the model can also been performed by quantitatively analyzing the receiver operating characteristic (ROC)curve.65–68Figure 2gives the ROC curve for the predictions of the 903training sam-ples from the OOB estimate of RF by using different thresholds of prediction probability.69Although the final prediction is gen-erally made based on the consensus voting,an optimal threshold of prediction probability can also been derived from the ROC curve by maximizing the Youden index (YI)70,71[YI 5SE 2(12SP)].The optimal threshold of prediction probability was found to be 0.472from the obtained ROC curve of RF in this work.Furthermore,to objectively examine whether the OOB esti-mate is equivalent to cross-validation,we compared the perform-ance measures of the OOB estimate of RF with those of 5-fold cross-validation of SVM.As shown in Figure 3,the performance of the OOB estimate is substantially comparable to the classicalcross-validation.Figure 5.The visualized distributions of the 530external testing compounds in the developed models.(A)in the SVM model,and (B)in the RF model.5In Silico Prediction and Screening of c -Secretase InhibitorsModel ValidationThe efficiency and robustness of the derived models were further evaluated by using the external testing set.Table 3gives the performance of SVM and RF for predicting c -secretase inhibi-tors and noninhibitors in the external testing set.The predictionaccuracies of SVM are 96.48%for c -secretase inhibitors and 98.18%for noninhibitors,and those of RF are 98.83%for c -sec-retase inhibitors and 99.27%for noninhibitors.The values of Q and MCC are 97.36%and 0.9472for SVM whereas 99.06%and 0.9811for RF,respectively.These results indicate thattheFigure 6.The structures of the misclassified c -secretase inhibitors in the external testing set of the developed models.(A)in the SVM model,and (B)in the RF model.[Color figure can be viewed in the online issue,which is available at .]6Yang et al.•Vol.00,No.00•Journal of Computational Chemistrydeveloped SVM and RF models show good and robust predic-tion performance.The area under the ROC curve (AUC)66–68is also considered as an important criterion for measuring the performance of the model.An AUC value of 1indicates a theoretically perfect per-formance,while a value of 0.5denotes no prediction ability.Clearly,the closer the AUC value is to 1,the better is the model performance.Figure 4gives the ROC curves of SVM and RF for the external testing set.The computed AUC values of SVM and RF are 0.9979and 0.9997,respectively,which also suggests that the developed SVM and RF models have great prediction ability and reliability.Moreover,it is clearly noted that the prediction capability of RF slightly outperforms that of SVM.Figure 5gives the visual-ized distributions of the 530external testing compounds in both two developed models.As shown in Figure 5,c -secretase inhibi-tors and noninhibitors can be well discriminated by their respec-tive boundaries of the developed models.Only a very small fraction of compounds are distributed around the boundaries,suggesting that it is difficult to make acute prediction for these compounds using SVM or RF probably due to their limited learning capability.There are nine c -secretase inhibitors and five noninhibitors misclassified in the external testing set of SVM,whereas three c -secretase inhibitors and two noninhibitors mis-classified in the RF model.Surprisingly,all of these misclassi-fied compounds are substantially located around their respective boundaries.The structures of the misclassified c -secretase inhibi-tors and noninhibitors are shown in Figures 6and 7,respec-tively.With respect to these misclassified compounds,there are only one c -secretase inhibitor and one noninhibitor coincident for both two models,suggesting that different machine learning methods may have different learning processes despite the com-mon structural features probably extracted by different machine learning methods.Interpretation of the Developed ModelsBy using feature selection,the most appropriate sets of molecu-lar descriptors for predicting c -secretase inhibitors and noninhi-bitors were extracted from the SVM and RF prediction models,some of which likely provide some new insights into the physi-cochemical characteristics of c -secretase inhibition by specific classes of compounds.Although the relationship between the descriptors and prediction is hidden inside the SVM and RF models,more information can be also obtained from the scrutiny of the selected descriptors.Table 4gives the descriptors selected by SVM 1RFE ranked from high to low based on the descriptor weight in the SVM model.Figure 8shows the 25highest ranked descriptors with relative importance identified by RF and the corresponding descriptions are given in Table5.Figure 7.The structures of the misclassified c -secretase noninhibitors in the external testing set of the developed models.(A)in the SVM model,and (B)in the RF model.[Color figure can be viewed in the online issue,which is available at .]7In Silico Prediction and Screening of c -Secretase InhibitorsIn the RF model,S(40)[atom-type electrotopological state (E-state)sum for ¼¼O]and S(55)(atom-type E-state sum for ¼¼S)are the top two relatively important descriptors,which arealso consistently selected by the SVM model.Together with the selected descriptors N sulph and N oxy ,it can be speculated that the functional group of ÀÀSO 2ÀÀis likely to be a significant indica-tion for c -secretase inhibition.In the SVM model,Q H,max (most positive charge on H atoms)is thought of as the most important descriptor which might be responsible for hydrogen bonding.Other selected descriptors are also suggested to associate with hydrogen bonding,including N oxy (number of O atoms),Q H,min (most negative charge on H atoms),Q O,max (most positive charge on O atoms),Q O,ss (sum of squares of charges on O atoms),S(12)[atom-type H E-state sum for C H n (saturated)],S(13)[atom-type H E-state sum for C H n (unsaturated)],S(40)and S(41)(atom-type E-state sum for ÀÀO ÀÀ).Moreover,the descriptors probably related to electrostatic property including Psa (polar molecular surface area),l (molecular dipole moment),Mpc (mean of positive charges),Rpc (relative positive charge),Mnc (mean of negative charges),Svpcw (sum of charge weighted van der Waals surface areas of positively charged atoms)and Sapcw (sum of charge weighted solvent accessible surface areas of positively charged atoms)are also selected,sug-gesting that the electrostatic property may be a crucial factor forTable 4.Twenty-Two Descriptors Selected by RFE Incorporated withSVM (SVM 1RFE)Ranked from High to Low Based on the Descriptor Weight in the SVM Model for the Prediction of c -Secretase Inhibitors and Noninhibitors.Descriptor DescriptionClass Q H,max Most positive charge on H atoms Quantum chemical Mpc Mean of positive charges Quantum chemical S(16)Atom-type E-state sum for ÀÀCH 3Topological N sulph Number of S atoms ConstitutionalRpc Relative positive charge Quantum chemical Hiwpb Hydrophobic intery moment Geometricall Molecular dipole momentQuantum chemical S(55)Atom-type E-state sum for ¼S Topological S(41)Atom-type E-state sum for ÀÀO ÀÀTopological S(18)Atom-type E-state sum for [CH 2Topological S(40)Atom-type E-state sum for ¼O Topological Hiwpl Hydrophilic intery moment Geometrical Capty Capacity factorGeometrical S(26)Atom-type E-state sum for:C ÀÀTopologicalQ N,min Most negative charge on N atoms Quantum chemical S(22)Atom-type E-state sum for [CH ÀÀTopologicalQ H,min Most negative charge on H atoms Quantum chemical 4v v pc Valence molecular connectivity Chi indices for path/cluster Topological Shpb Hydrophobic regionGeometricalMnc Mean of negative chargesQuantum chemical 6v v CH Valence molecular connectivity Chi indices for cycles of 6atoms Topological S (13)Atom-type H E-state sum for C H n (unsaturated)TopologicalTable 5.The Relatively Important Descriptors Identified by RF for thePrediction of c -Secretase Inhibitors and Noninhibitors.Descriptor DescriptionClass S(40)Atom-type E-state sum for ¼O Topological S(55)Atom-type E-state sum for ¼S Topological S(22)Atom-type E-state sum for [CH ÀÀTopologicalQ O,ss Sum of squares of charges on O atoms Quantum chemical Q O,max Most positive charge on O atoms Quantum chemical Q H,max Most positive charge on H atoms Quantum chemical S(25)Atom-type E-state sum for ¼C \TopologicalQ H,min Most negative charge on H atoms Quantum chemical SapcwSum of charge weighted solvent accessible surface areas of positively charged atoms GeometricalS(12)Atom-type H E-state sum for C H n (saturated)Topological SvpcwSum of charge weightedvan der Waals surface areas of positively charged atoms GeometricalShpl Hydrophilic regionGeometrical S het Sum of E-state indices of hetero atoms TopologicalQ N,ss Sum of squares of charges on N atoms Quantum chemical N sulph Number of S atomsConstitutionalQ N,min Most negative charge on N atoms Quantum chemical Psa Polar molecular surface area Geometrical 3v v pValence molecular connectivity Chi indices for path order 3Topological 2vvValence molecular connectivity Chi indices for path order 2Topological S(41)Atom-type E-state sum for ÀÀO ÀÀTopological Rugty Molecular rugosityGeometrical S hal Sum of E-state indices of halogen atoms Topological Hlb Hydrophilic-hydrophobic balance Geometrical N oxy Number of O atomsConstitutional S (13)Atom-type H E-state sum for C H n (unsaturated)Topological8Yang et al.•Vol.00,No.00•Journal of Computational Chemistry。