QSAR Studies on the Inhibitory Activityof Levofloxacin-thiadiazole HDACi Conjugates to Histone Deacetylases①

WANG Chao FENG Chang-Jun

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QSAR Studies on the Inhibitory Activityof Levofloxacin-thiadiazole HDACi Conjugates to Histone Deacetylases①

WANG Chao FENG Chang-Jun②

(221018)

A molecular electronegativity distance vector (t)based on 13 atomic types has been used to describe the structures of 19 conjugates (LHCc)of levofloxacin-thiadiazole HDACinhibitor (HDACi) and related inhibitory activities (pi,= 1, 2, 6) of LHCc against histone deacetylases (HDACs, such as HDAC1, HDAC2 and HDAC6). The quantitative structure-activity relationships (QSAR) were established by using leaps-and-bounds regression analysis for the inhibitory activities (pi) of 19 above compounds to HDAC1, HDAC2 and HDAC6 along witht. The correlation coefficients (2) and the leave-one-out (LOO) cross validationcv2for the p1, p2and p6models were 0.976 and 0.949; 0.985 and 0.977; 0.976 and 0.932, respectively. The QSAR models had favorable correlations, as well as robustness and good prediction capability by2,,cv2,ICITandIFtests. Validated by using 3876 training sets, the models have good external prediction ability. The results indicate that the molecular structural units: –CH– (= 1, 2), –NH2, –OH, =O, –O– and –S–are the main factors which can affect the inhibitory activity of p1, p2as well as p6bioactivities of these compounds directly. Accordingly, the main interactions between HDACs inhibitor and HDACs are hydrophobic interaction, hydrogen bond, and coordination with Zn2+to form compounds, which is consistent with the results in reports.

levofloxacin-thiadiazole HDACi conjugates (LHCc), histone deacetylases (HDACs), inhibitory activity (pi,= 1, 2, 6), molecular electronegativity distance vector, quantitative structure-activity relationship (QSAR);

1 INTRODUCTION

A lot of labor and financial forces are required for experimentally determining the biological activities for all compounds, while the quantitative structure- activity relationship (QSAR) is effective. The mathematical relationship between the structures of set compounds and their biological activities was studied by QSARmodels[1-8]which can estimate and predict the relative properties (such as toxicity, mutagenicity, carcinogenicity,) of other com- pounds, or to explore the possible mechanisms of microbial structures on the biological activity at the molecular levels.

It is crucial for QSAR researchers to establish descriptors for molecular structures, like the establi- shment of two-dimensional (2) descriptors. Topolo- gical indexes are 2descriptors encoding the molecular structures in digital form, such as mole- cular size, shape, branching, hetero-atoms, and multiple bonds. They could be directly derived from molecular structures, independent of the experi- mental measurements. Therefore, topological indexes are popular for the development of reliable QSAR models. Molecular connectivity indexes put forward by Randic[9]and developed by Kier and Hall[10]are of the most widely used topological indexes. Recently, a novel molecular electronegativity dis- tance vector (t)[11-13]based on 2topologies and 13 atomic types has been reported, which further leads to the successful establishment of QSAR models between multiple (t) and organic compounds.

Histone deacetylases (HDACs) are the key enzyme families that regulate gene transcription and expression. Over expression of HDACs in cancer cells leads to excessive deacetylation of histones in transcription and expression, and enhances the binding of histones to DNA, leading to tumori- genesis[14]. Especially, these three subtypes of HDAC1, HDAC2 and HDAC6 are among the mostly studied gene transcription and expression subsets[15]. Histone deacetylase inhibitors (HDACi) can inhibit the activity of HDACs in tumor cells, increase the degree of acetylation of histamine N-terminal lysine residues in tumor cells and reactivate inhibited tumor suppressor genes, thus leading to the tumor cell growth retardation, differentiation and apoptosis.

Therefore, HDACs is a new target of anti-tumor research in recent years, and HDACi has become a hot research topic of anti-tumor drugs both at home and abroad. Eighteen types of new, efficient and low toxicic levofloxacin-thiadiazole HDACi conjugates (referred to as LHCc) were designed and synthesized from levofloxacin by Li Hui and others[16]. The results showed that these new conjugates displayed potent inhibitory activity against HDAC1, HDAC2 and HDAC6. Specifically, conjugate 10 exhibited the highest activities, which was more potent than SAHA (Vorinostat). Therefore, it is important to study the levofloxacin-HDACi conjugation by QSAR method.

Based on the electronegativity distance vector (t) of Liu Shushen.[11-13], the robust QSAR models of LHCc biological activity[16]have been established by leaps-and-Bounds regressionto estimate and predict the inhibitory activity of LHCc and reveal the microstructure that affects its inhibitory activity at the molecular level. It provides theoretical reference for a reasonable design and screening of novel and highly effective lead compounds for LHCc.

2 MATERIALS AND METHODS

2.1 Studied compounds and their biological activity data

The compounds studied herein are a series of HDACs inhibitors with HDAC1, HDAC2 and HDAC6 inhibitory activity. The matrix structures[16]of these compounds are shown in Fig. 1. Their bioactivity data for HDACs were50, and drug concentrations resulted in 50% inhibition of HDACs inmmol·dm-3. The HDAC1, HDAC2 and HDAC6 inhibitory activities (50) were expressed as1,2and6, respectively. The biological activities (i,= 1, 2, 6) of 18 HDACs inhibitors and SAHA are listed in Table 1[16].

Fig. 1. Basic structure of levofloxacin-HDACi conjugates

Table 1. InhibitoryActivities (IC50) and Electronegativity Distance Vector (Mt) of Levofloxacin-HDACi Conjugates

2. 2 Molecular descriptors

The molecular structure information of the com- pounds is prerequisite for establishing a good struc- ture-activity relationship. At present, the two-dimen- sional descriptors used in structure characterization of QSAR are molecular holography, topological index and so on. They have been widely applied in environmental science, life sciences, drug design and so forth. In this paper, the molecular electro- negativity distance vector descriptor (t)[11-13]based on 13 atomic types is used to characterize the molecular structures of different classes of organic compounds. The calculation includes the following three steps.

First, the intrinsic attribute () of non-hydrogen atoms in the molecule is defined:

= (/4)0.5[(2/)2δ+ 1)]/(1)

whereis the number of valence electrons,is the principal quantum number for the valence shell of the non-hydrogen atom, andνandare the molecular connectivityvalues given as follows:

=?,v=+?(2)

whereandare respectively the number of electrons inandorbitals, andis the number of hydrogen atoms bound to the non-hydrogen atom. Considering the influence of other non-hydrogen atoms on themselves, the relative electronegativitywfor atom w is defined as below:

w=w+ ?w, ?w= ∑(w?u)/wu2(3)

The symbolwuis the shortest graph distance between theth andth atoms,the number of chemical bonds. In the same molecule, electrone- gativity distance vectorcan be calculated fromthe interaction between the relative electricityiof the non-hydrogen atoms.

t=jk= ∑(w×u)/wu2, 1≤,≤13 (4)

whereoris the atomic type of the atom w or u in the molecule, and w and u are the coding numbers or series numbers of two non-hydrogen atoms in the molecule, respectively.

In this paper, there are only 1, 2, 3, 5, 6, 7, 9, 10 and 13 species of atoms in the molecules. They interact with each other (including the interactions among themselves). Theoretically, 45 kinds of elec- trical distance vectors can be formed. Since not all atomic types exist, some interaction types do not occur. Only 41 electrical distance vectors are not all zero. Parts of the electrical distance vectors are listed in Table 1. The data of14,17,21,77and78descriptors in Table 1 do not show exactly the same values of the two molecules for the 19 compounds. That is, the molecular structure difference has a unique characterization, showing good structural selectivity.

2. 3 Statistical regression analysis

For QSAR derivation,50values act as the dependent variables, and electronegativity distance vectordescriptors as the independent variables. The regression analyses are carried out by using multiple linear regression (MLR), partial least-squares (PLS), and leaps-and-bounds regression (LBR) program. By using Fischer statistics (-tests) to eliminate insignificant descriptors when entering a new one, stepwise regression can identify the most important descriptors influencingthe inhibitory activities of the title compounds.

In model building, validation is an important step by which the reliability and accuracy of good models are established.The commonly used statistical verifi- cation indicators are as follows.

The correlation between variables in the model was estimated by the variance inflation factor (IF)[17]value.IFis defined below:

IF= 1/(1 –2) (5)

in whichis the correlation coefficient of multiple regressions between one variable and the others in the equation.IF= 1.0 suggests no self-correlation among each variable; ifIFranges from 1.0 to 5.0,there is no obvious autocorrelation between variables, and the model is stable; whenIFis larger than 5.0, the regression equation is unstable and rechecking the variables’ correlation coefficient is necessary.

Another indicator used to evaluate the quality of model is the standard deviation (D). The model is good and the prediction accuracy is acceptable when the ratio of the standard deviation to the value range (the samples between the maximum and minimum values) is less than 10%[18].

The statistic significance of the model was vali- dated by-tests. If the absolute values offor all variables in the validated model are larger than the standard-value (α/2) at one confidence level, the model passes the-tests and has obvious statistic significance. We also applied Akaike’s information criterion (IC; Eq. 6; the model that produces the minimumICvalue is considered potentially to be the most useful) and Kubinyi function (IT; Eq. 7; the best model will present the highest value of this function)[19, 20]to determine if a variable should be included in the model. That is to say, if Akaike’s information criterion decreases when adding an additional variable and the Kubinyi function increases, the introduction of this new variable is justi?ed.

whereSSis the residual sum of squares,the number of compounds included in the model,the number of variables included in the model, and2the square of the correlation coefficient.

3 RESULTS AND DISCUSSION

According to the balance principle of physical chemistry, the free energy change and concentration is in logarithm relation with a logarithmic rela- tionship[21]. Therefore, the inhibitory activity (i)[16]of HDACs inhibitors to HDAC1, HDAC2 and HDAC6 is taken negative logarithm (pi= –logi)for modeling. The pi(= 1, 2, 6) is shown in Table 2.

Table 2. Inhibitory Activities (pHi) of HDACs Inhibitors to HDAC1, HDAC2 and HDAC6

3.1 QSAR equation of pHi

The electronegativity distance vector (t) and inhibitory activities (pi) of HDACs inhibitors were input into MINITAB14.0 statistical analysis software, and the leaps-and-bounds regression was used to select the best variable combinations and establish the best QSAR models. The results are shown in Tables 3 to 5, where2is the square of the correla- tion coefficient,adj2is the square of the adjusted correlation coefficient,cv2is the LOO cross-valida-tioncorrelation coefficient,Dis the standard devia- tion of the regression,CVis the standard deviation of the regression of LOO, andis the Fisher ratio.ICis the Akaike’s information criterion andITis the Kubinyi function.The QSAR models for p1andtare shown in Table 3.

With increasing the number of independent varia- bles in the model, in addition to2, all other statis- tical indicators show turning points in the three- variable equation, among whichadj2,cv2,IT,are the largest andIC,D,CVare the smallest, with the results summarized in Table 3. Therefore, the best QSAR model of the three variables is chosen:

p1= 12.061(±0.311) – 0.086(±0.006)14– 0.461(±0.021)77+ 2.900(±0.455)78(8)

= 19,2= 0.976adj2=0.971,= 201.833,

D=0.128 (Modeling);

cv2= 0.949,CV=0.187(LOO Cross-validation)

The QSAR models for p2andtare shown in Table 4. With the increase of the number of independent variables in the model, in addition to2andadj2, all other statistical indicators show turning points in the three-variable equation, among whichcv2,IT,are the largest andIC,D,CVare the smallest. The results are listed in Table 4. Thus, we choose the best QSAR model of three variables as below:

p2= 12.243(±0.347) – 0.346(±0.028)17– 0.149(±0.022)21– 0.584(±0.021)77(9)

= 19,2= 0.985adj2=0.982,= 319.745,

D=0.139 (Modeling);

cv2= 0.977,CV=0.171 (LOO Cross-validation)

The QSAR models for p6andtare shown in Table 5. Because the change rules of all statistical indicators shown in Table 5 are the same as those in Table 3, the best QSAR model of the three variables is chosen:

p6= 12.463(±0.323) – 0.092(±0.006)14– 0.485(±0.022)77+ 3.000(±0.306)78(10)

= 19,2= 0.976adj2=0.971,= 200.751,D=0.133 (Modeling);cv2= 0.932,CV=0.224

(LOO Cross-validation)

Table 3. Results of Electronegativity Distance Vector Descriptorsand Anti-tumor Activities pH1 with Leaps-and-bounds Regression

Table 4. Results of Mtand pH2 with Leaps-and-bounds Regression

Table 5. Results of Mtand pH6 with Leaps-and-bounds Regression

3.2 Validation of the QSAR models

QSAR model fitting ability is usually used to verify the correlationcoefficient (2) to be verified. When the confidence level is 95%, the thresholdvalue (0.05(3,15)) of Fisher ratio () for models (8), (9) and (10) is 3.29. Substituting0.05(3,15) = 3.29into the formula[22]between2and:

α2=α((–– 1)α)-1(11)

whereα2andαare the thresholdvalues of2and, respectively.α2obtainedis 0.397, and the critical value (0.05(3,15)2) of correlation coefficient for the above models is only 0.232[22]. They are significantly smaller than2of models (8), (9) and (10), which are 0.976, 0.985 and 0.976, respectively, indicating that the models have good robustness and prediction ability.

Using QSAR equations (8), (9) and (10), the pre- dicted values of inhibitory activity p1, p2, and p6(see p1(cal.), p2(cal.) and p6(cal.) in Table 2) are given respectively, which are very close to the corresponding experimental values (see p1(exp.), p2(exp.), and p6(exp.) in Table 2).

Where the values in models (8) to (10) with symbol ‘‘±’’ refer to the standard deviation, corres- ponding to the regression coefficient. All standarddeviationsare less than1/2 of the regression coefficients, indicating that the model is stable. The standard regression coefficients (R) andvalue of three independent variables in model (8) are listed in Table 6. When the confidence level is 95%, the standardvalue (α/2) of the models is 2.131. From Table 6, we can see that the absolute value ofof each independent variable in model (8) is bigger than the standardt/2value, which proves the credibility of the models. In the meantime, the absolute values ofof77,78and14decrease in turn, which is consistent with the law ofR, indicating that77has the strongest effect on p1. For models (9) and (10), a similar rule is obtained from Table 6:77is the strongest factor affecting the inhibitory activity. As shown in Table 6, theIFvalues of the variables in models (8)～(10) are less than 5.0, indicating that all the models are statistically significant with good stability.

Table 6. SRand t Values of in Dependent Variables in Models (8) to (10)

The inhibitory activity (p1) range of the samples between the maximum and minimum values is 2.30 (7.51～5.21 = 2.30). The ratio of the standard deviation (D= 0.128) to 2.30 is 5.57%. The standard deviation ratios for p2and p6are 4.51% and 5.36%, respectively. They are less than 10%, indica- ting that the model has acceptable predictive accuracy.

In order to further validate the external prediction capabilities of the QSAR model, the samples are usually divided into the training and test sets, and the number of compounds in the two sets is generally 4:1. The biological activity of the test set was predicted by the QSAR model of the training set. In this paper, 19 LHCcs were divided into 15 compounds in the training set and 4 compounds in the test set. 3876 training and test sets were formed according to the arrangement rules. The traditionalcorrelation coefficient (2) and cross validation correlation coefficient (cv-42) of the leave-four-out (LFO) of these training sets are calculated using the MATLAB program. The correlation coefficient average of the ternary equation for the 3876 p1training sets is 0.977 and the correspondingcv-42= 0.946. The correlation coefficient average of ternary equations for the 3876 p2training sets is 0.985, corresponding tocv-42= 0.976; The correlation coefficient average of ternary equations for the 3876 p6training sets is 0.977 and the correspondingcv-42= 0.933. Their correlation coefficients andcv-42are close to those of models (8)～(10).

After eliminating compounds 4, 8, 13 and 18 from the test set, the remaining is the training set for the establishment of the following models:

p1= 12.271(±0.357) – 0.091(±0.008)14– 0.479(±0.024)77+ 2.939(±0.325)78(12)

= 15,2= 0.980,adj2=0.975,=180.675,

D=0.130

p2= 12.489(±0.414) – 0.336(±0.031)17– 0.163(±0.026)21– 0.595(±0.023)77(13)

= 15,2= 0.987,adj2=0.983,= 268.301,

D=0.144

p6= 12.764(±0.350) – 0.099(±0.007)14– 0.507(±0.024)77+ 3.097(±0.318)78(14)

= 15,2= 0.982adj2=0.977,= 203.334,

D=0.128

The calculated and predicted values given by models (12)～(14) are in good agreement with the corresponding experimental values (Figs. 2 to 4). For the 4, 8, 13 and 18 compounds, the predicted relative error rates given by model (12) are 2.7%, 2.4%, –1.5% and 1.5%, respectively; 3.4%, –1.6%, –2.4%, –1.8% for model (13); and 3.2%, –3.2%, –0.8%, 2.1% for model (14); all are within the biometric deter- mination error ranges. It is shown that models (8)～(10) are highly robust with significant correlation.The models are not only for estimating and predic- ting the inhibitory activity of the title compounds, but also for explaining the inhibitory mechanism of the above compounds.

Fig. 2. Relationship between experimental and calculated inhibitoryactivities of the title compounds toHDAC1

Fig. 3. Relationship between experimental and Calculated inhibitory activities of the title compounds to HDAC2

Fig. 4. Relationship between experimental and calculated inhibitory activities of the title compounds to HDAC6

3.3 Analysis of the QSAR equation

Li Hui.[16]chose the molecular docking of the strongest inhibitory activity between conjugate10 with HDAC1 and HDAC6, and the main interactions between HDACs inhibitor and HDACs are hydrophobic interaction, hydrogen bond, and coordination with Zn2+to form compounds.

According to the theory of molecular electrone- gativity distance vector, the electrical distance vector14in the models reflects the interaction of the second carbon atom (-CH-,= 1, 2) with the second carbon atom, and17reflects the interaction of the second type of carbon atom with the five groups of nitrogen atom (-NH2).21reflects the interaction between the ninth kind of oxygen atom (=O, -OH) and the second carbon atom,77reflects the interaction between the ninth kind of oxygen atoms themselves, and78reflects the interaction between the ninth kind of oxygen atom and the tenth kind of oxygen atom (-O-) in ether (-O-)) or sulfur atom (-S-) in thioether. The five electronegativity-distance vectors imply the structure information of six non- hydrogen atoms, respectively.

Wherein-CH- is a non-polar group with hydro- phobicity, while the remaining five classes are high charge polar groups capable of forming hydrogen bonds, and the lone electronic pairs can form coordination compounds with Zn2+.

In addition, the determination coefficient2is also called the reduction error ratio.2= 0.976 for model (8) indicatesthat14,77,78and constant items show 97.6% of the factors affecting the anti-tumor activities (p1) of HDACs inhibitors to HDAC1, and only 2.4% is random factors;2= 0.985 of model (9) means that17,21,77and constant items implies 98.5% of the factors affecting the inhibitory activities (p2) of HDACs inhibitors to HDAC2, and only 1.5% is random factors;2= 0.976 in model (10) suggest that14,77,78and constant items show 97.6% of the factors affecting the inhibitory activities (p6) of HDACs inhibitors to HDAC6, and only 2.4% is the random factors; which further prove the correctness of the models.

4 CONCLUSION

The optimal QSAR models of three variablesbetween the inhibitory activity (p1, p2and p6) and molecular electronegativity distance vector (t) of HDACi to HDACs was constructed by using the leaps-and-bounds regression method. The QSAR models show good correlation, as well as robustness and prediction ability by statistical indicators:2,cv2,R,IF,ITandICtests. To successfully establish QSAR models of three inhibitory activities is rarely seen in QSAR studies by using one class of topological indices. According to the electrical distance vector entering the three models, the main molecular structural units that affect their inhibitory activity p1, p2and p6may be-CH- (= 1, 2), -NH2, -OH, =O, -O- and -S-. The interactions between HDACsinhibitor molecules and HDACs are mainly the hydrophobic interaction, hydrogen bond, and coordination with Zn2+to form compounds,which is consistent with the molecular docking results of reference 16.77is the most important factor affecting the inhibitory activity. =O and -OH become the most important structural groups that affect the inhibitory activity. Hydrogen bond and Zn2+coordination compounds formed between LHCc and HDACs play a major role, greater than the hydrophobic interaction. According to above conclu- sions, it can be deduced that HDAC1, HDAC2 and HDAC6 have similar structures and belong to the histone deacetylase family.

In summary, this study provides theoretical gui- dance for further design of novel and efficient HDACs inhibitors.

(1) Feng, C. J.; Yang, W. H. Linear QSAR regression models for the prediction of bioconcentration factors of chloroanilines in fish by density functional theory.. 2014, 33, 830–834.

(2) Feng, C. J. Theoretical studies on quantitative structure-activity relationship and structural modification for 3-substituted sulfur-5-

(2-hydroxyphenyl)-4H-1,2,4-triazole compounds.2012, 70, 512–518.

(3) Wang, C.; Feng, C. J. Atomic partition parameter, partition connectivity index and their applications.2002, 18, 792–796.

(4) Shi, J. C.; Tu, W. T.; Luo, M.; Huang, C. S. Structural insight into the design on oleanolic acid derivatives as potent protein tyrosine phosphatase 1B inhibitors.2017, 36, 1063–1076.

(5) Xiong, D.; Ma, Y. Z.; Zhao, Z. X.; Liu, Y. X.; Xiang, Y. Docking and 3D-QSAR analysis on a series of pyridone-based EZH2 inhibitors.2017, 36, 575–588.

(6) Wang, C.; Feng, C. J. QSAR study of the action strength ofOMof phenyl-isopropyl-amine dopes using MLR and BP-ANN.2017, 36, 1720–1728.

(7) Xiang, S. G.; Wang, J. Y.; Sun, X. Y. Quantum chemistry based computational study on the conformational population of a neodymium neodecanoate complex.2016, 35, 833–838.

(8) Liao, L. M.; Li, J. F.; Lei, G. D. Structural characterization andKovats retention indices (RI) prediction for alkylbenzene compounds.2016, 57, 1627–1634.

(9) Randic, M. On charmacterization of molecular branching.1975, 97, 6609–6615.

(10) Kier, L. B.; Hall, L. H.. Research Studies Press, England 1986, p82.

(11) Liu, S. S.; Yin, C. S.; Li, Z. L.; Cai, S. X. QSAR study of steroid benchmark and dipeptides based on MEDV-13.2001, 41,321–329.

(12) Liu, S. S.; Yin, C. S.; Wang, L. S. Combined MEDV-GA-MLR method for QSAR of three panels of steroids, dipeptides, and COX-2 inhibitors.2002, 42, 749–756.

(13) Zhang, Y. H.; Xia, Z. N.; Qin, L. T.; Liu, S. S. Prediction of blood-brain partitioning: a model based on molecular electronegativity distance vector descriptors.2010, 29, 214–220.

(14) Lai, M. J.; Huang, H. L.; Pan, S. L.; Liu, Y. M.; Peng, C. Y.; Lee, H. Y.; Yeh, T. K.; Huang, P. H.; Teng, C. M.; Chen, C. S.; Chuang, H. Y.; Liou, J. P. Synthesis and biological evaluation of 1-arylsulfonyl-5- (N-hydroxyacrylamide) indoles as potent histone deacetylase inhibitors with antitumor activity in vivo.2012, 55, 3777?3791.

(15) Tang, C.; Li, C. H.; Zhang, S. L.; Hu, Z. Y.; Jun, W.; Dong, C. N.; Huang, J.; Zhou, H. B. Novel bioactive hybrid compound dual targeting estrogen receptor and histone deacetylase for the treatment of breast cancer.2015, 58, 4550?4572.

(16) Li, H.; Han, X.; Li, D. W. Synthesis and anti-tumor activity of levofloxacin-thiadiazole histone deacetylase inhibitor conjugates.2017, 52, 582–591.

(17) Wei, D. B.; Zhang, A. Q.; Wu, C. D.; Han, S. K.; Wang, L. S. Progressive study and robustness test of QSAR model based on quantum chemical parameters for predicting BCF of selected polychlorinated organic compounds.2001, 44, 1421–1428.

(18) Sung-Sau, S.; Kaprlus, M. A comparative study of ligand-receptor complex binding affinity prediction methods based on glycogen phosphorylase inhibitors.1999, 13, 243–258.

(19) Urra, L. S.; Gonza′lez, M. P.; Teijeira, M. 2-autocorrelation descriptors for predicting cytotoxicity of naphthoquinone ester derivatives against oral human epidermoid carcinoma.2007, 15, 3565–3571.

(20) Urra, L. S.; Gonza′lez, M. P.; Teijeira, M. QSAR studies about cytotoxicity of benzophenazines with dual inhibition toward both topoisomerases I and II: 3-MoRSE descriptors and statistical considerations about variable selection.2006, 14, 7347–7358.

(21) Guo, Z. R.. Science Press, Beijing 2005, p20.

(22) Liu, H. L.. Shanghai University of Finance and Economics Press, Shanghai 1995, p238, 431.

① This project was supported by theNational Natural Science Foundation of China (21473081, 21075138) and special fund of State Key Laboratory of Structure Chemistry (20160028)

. Feng Chang-Jun, male, born in 1954, professor, majoring in quantitative structure-activity relationship. E-mail: fengcj@xzit.edu.cn

12 April 2018;

17 September 2018

10.14102/j.cnki.0254-5861.2011-1827