Microsoft Word - CET--006.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 59, 2017 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Zhuo Yang, Junjie Ba, Jing Pan Copyright © 2017, AIDIC Servizi S.r.l. ISBN 978-88-95608- 49-5; ISSN 2283-9216 Research on Thermodynamic Properties of Resveratrol Analogues Based on QSPR Wei Bua, Zheng Yuanyuana , Lianxin Liub, Weiping Heb, Yu liub,* a iangsu Normal University, Xuzhou 221116, China b Xuzhou College of Industrial Technology , Xuzhou 221140, China Liuyu0138@163.com This paper selects 60 types of resveratrol analogues were selected and discusses the relationship between thermodynamic properties and the molecular descriptors, including the topological indexes of principal quantum number (0P2, 0P4, 0P3) and the sum total of them ( 0P). For the sake of simplicity, 0P is confirmed as the fundamental variable for the models through comparative analysis. Based on the characteristics of sine series, sin(k0P) (k=1, 2, 3, …) are incorporated into the models to eliminate the residuals, resulting in the maximization of adjusted coefficient of determination (Radj 2). The introduction of sin(50P) and sin(80P) successfully eliminates the residuals and enhances the predictive power. The global correlation coefficients are greater than 0.99, and even close to 1. The stability and predictive power of each model are tested with additional resveratrol analogues other than the test samples by the cross-validation method. The test reveals that the QSPR model has a satisfactory stability and good predictive power. 1. Introduction Resveratrol is a highly bioactive polyphenolic substance. Its chemical structure is shown in Figure 1. Figure 1: Chemical Structural Formula of Resveratrol Resveratrol exists in many plants, ranging from the genus of Vitis (Vitaceae) to Polygonum (Polygonaceae). Resveratrol and its analogues has many biological functions, namely anti-inflammation, anti-tumortumor (Yuan et al., 2015), anti-oxidation (Farris et al., 2013), anti-bacteria and nerve protection (Han et al., 2012; Chen et al., 2015; Chen et al., 2015; Xia et al., 2014; Zhang et al., 2014). However, rarely any scholar has probed into the relationship between the structure and activity of resveratrol and its analogues. In light of the previous studies of structure-function relationship based on topological index (Qin, 2004), this paper explores the thermodynamic constitutive relationship (Du, 2014; Chen and Du, 2008; Xiao et al., 2015; He et al., 2015; Du, 2007; Du, 2010), aiming to disclose the properties of resveratrol analogues. The research results lay the theoretical basis for predicting the thermodynamic properties of the compounds. DOI: 10.3303/CET1759177 Please cite this article as: Wei Bu, Zheng Yuanyuan, Lianxin Liu, Weiping He, Yu liu, 2017, Research on thermodynamic properties of resveratrol analogues based on qspr, Chemical Engineering Transactions, 59, 1057-1062 DOI:10.3303/CET1759177 1057 2. Section headings 2.1 Thermodynamic data This study constructs the molecules of 60 types of resveratrol analogues with Chem3D software, using density functional B3LYP and 6-311++G(d, p) basis set optimization (Dunning and Hay, 1977; Liu et al., 2002), determines the stable configuration of molecules, and identifies the thermodynamic properties. Due to the limitation of space, only 39 results are given in Table 1. Table 1: Thermodynamic Properties of Resveratrol Analogues a. C1: methyl; C2: ethyl; 2C1: dimethyl; 3C1: trimethyl. b. The values of HΘ, EΘ, CV Θ and SΘ are relative to that of resveratrol. 2.2 Molecular descriptors Whereas the thermodynamic properties of the molecules are related to the specific topological index of principal quantum number, the valence of the bond atom is defined as ti: ( )= -1 + i i i i t m n h (1) No Moleculesa α (esu) HΘ(×103kJ.mol-1)b EΘ(kJ.mol-1) CVΘ(J.mol-1.K-1) SΘ(J.mol-1.K-1) 1 3’-C4 234.98 -412.677 310.959 86.119 125.926 2 2,4-2C1-3’-C2 236.018 -412.685 309.022 94.504 128.562 3 2-C3-3’-C2 251.163 -515.848 388.417 109.956 155.925 4 2,4-C2-3’-C3 273.285 -722.194 544.33 154.151 206.543 5 3’-C5 247.757 -515.843 389.028 106.466 154.54 6 2-C1-4-C2 225.336 -309.51 232.346 69.375 94.918 7 2,3’-2C3 263.545 -619.012 466.809 129.963 183.87 8 2-C2-4-C3 250.927 -515.846 389.363 108.525 149.733 9 4-C1 199.643 -103.17 76.96 24.623 37.715 10 2-C1-4-C2-3’-C3 261.288 -619.012 465.315 135.239 185.385 11 2-C3-4-C4 275.639 -722.194 544.259 151.047 221.852 12 2-C2-4-C4 262.997 -619.012 467.185 129.014 181.012 13 4-C2 212.551 -206.336 155.402 44.514 61.417 14 2-C1-4-C3 238.701 -412.679 310.352 89.78 125.424 15 2-C7 280.362 -722.194 545.635 145.478 214.284 16 2-C2-4-C5 275.707 -722.194 544.866 149.649 220.309 17 4-C3 224.395 -309.505 233.643 64.576 88.63 18 2-C1 202.617 -103.175 76.822 25.15 38.748 19 2,3’-2C1-4-C3 250.11 -515.859 386.748 115.181 161.13 20 2-C3 228.835 -309.51 233.593 64.283 89.328 21 4-C4 236.505 -412.674 311.34 85.232 123.968 22 2-C3-4-C2-3’-C1 264.222 -619.012 465.391 134.285 181.895 23 2-C1-4-C3-3’-C2 260.374 -619.012 465.621 134.691 187.468 24 2-C1-3’-C4 248.818 -515.851 387.953 111.244 159.657 25 4-C5 249.041 -515.84 389.38 105.5 156.067 26 2,4-2C3-3’-C2 286.45 -825.35 622.408 173.983 239.095 27 2-C1-4-C4 250.885 -515.848 388.539 109.771 154.561 28 2-C1-3’-C5 261.25 -619.012 465.654 131.783 205.418 29 3’-C1 200.14 -103.178 76.354 25.397 34.158 30 2,4,3’-3C3 298.266 -928.532 699.711 195.351 279.265 31 2-C1-4-C5 263.426 -619.012 466.529 130.143 187.744 32 2,4-2C1-3’-C3 248.377 -515.856 386.786 114.663 164.456 33 3’-C2 210.521 -206.339 155.005 45.083 64.011 34 2-C4 241.598 -412.679 311.511 84.759 121.248 35 2-C2 215.533 -206.341 155.498 44.212 62.643 36 2,4-2C1-3’-C4 259.824 -619.012 464.96 135.57 189.226 37 3’-C3 223.257 -309.508 232.819 66.095 95.462 38 2,3’-2C4 287.551 -825.35 622.629 170.841 246.04 39 2,3’-2C2 238.552 -412.679 310.93 88.939 119.144 1058 Where hi is the number of the hydrogen atoms directly connected with atom i; mi is the valence electrons of atom i; ni is the principal quantum number of atom i, i.e. the number of electrons. The order is denoted as n: ( )0.51 2P= n i i i t t t − − … (2) Where i-1 is the atoms directly connected with atom i, and the other atoms. The 0 order and 1 order exponents are expressed by the formulas below: 0 0.5P= i t (3) ( )0.51 1P= i it t − (4) Since resveratrol analogues share a common parent structure, this paper focuses on the calculation of 0P and 1P of the alkyl. In view of the linear relationship between 0P and 1P , the 0P values at the 2, 4 and 3' molecular positions are denoted as 0P2, 0P4 and 0P3', respectively. 3. Selection of model variables 3.1 Selection of basic independent variables The thermodynamic properties of {0P2, 0P4, 0P3’} and { 0P} are adopted to fit those of resveratrol analogues. For additional clarity, let 0P denote the 0P value at each of the 2, 4 and 3 ' molecular positions of the alkyl, R2, the determination coefficient, and Radj 2, the adjusted coefficient of determination. Radj 2 is expressed as: = / ( 1) 1 / ( 1)adj RSS n k R TSS n − − − − (5) The result shows that the R2 adj value (with the addition of α) of 0P2, 0P4 or 0P3’ is very close to that of 0P. Hence, 0P is adopted to express the thermodynamic properties. 3.2 Residual analysis of a single independent variable Without loss of generality, the model with the lowest adjusted coefficient of determination (Radj 2) is identified as: SΘ=3.35+12.10P. Figure 2 shows its residual distribution. Figure 2: The residual distribution of SΘ As shown in Figure, the residual is roughly evenly distributed in the ∆SΘ and has nothing to do with the linear. 3.3 Introduction to sine series If a variable is introduced to improve the accuracy of the model without significantly changing the variable coefficient of the original model, the new variable should have the same degree of independence with the original variable. Therefore, the present study introduces the {sin(k0P)} (k=1, 2, 3…) to decompose the residual. 1059 The sine series is characterized by: (1) {sin(k0P)} randomly appears on both sides of the ∆Y=0 (Y=α, HΘ, EΘ, CVΘ and SΘ), and bears residual distribution characteristics; (2) If {k0P} changes continuously, then adopt {sin(k0P)} for the orthogonal series to minimize the number of multiple linearly independent variable. 3.4 Determination of independent variable Because {k0P} is a discrete variable, it is necessary to investigate the multiple linearly independent variables. In this study, the variance inflation factor (VIF) is introduced to investigate the linear independence of the independent variables: VIF=1/(1-R2) (6) Where R is the correlation coefficient between a variable and the other variables. Due to the limitation of space, only the k≤9 case is taken into consideration. The result indicates that none of {0P, sin(k0P), sin(20P), sin(90P)} is linearly independent. In pursuit of the minimum number of variables, this study determines the variables according to the following steps: (1) Introduce one of the variables to the calculation model of the Radj 2. (2) After introducing the variable, compare the Radj 2 value of each model, find the maximum, and determine the corresponding variable as the independent variable. (3) On the premise that all VIFs are smaller than 10, repeat the above steps until the Radj 2 value of the model reaches the maximum. 3.5 Determination of combined independent variables Following the steps in Section 3.4, introduce sin(50P) in the case of k ≤9 (continue to introduce sin(80P) to the structural model), add (α), and express the other thermodynamic properties by{0P, sin(50P)}. The expression is more accurate than the expression of the results on {0P2, 0P4, 0P3’}. 4. Model analysis Formulas (7)~(11) present the five quantitative structure–property relationships models (QSPR) and the final results. 0 0=189.541+4.869 -2.709 sin(5 )P Pα   , (SD=1.742, R2=99.51%, Radj2= 99.50%) (7) 0 0=0.143 - 41.054 +10.520 sin(5 )H P PΘ   , (SD= 1.362, R2= 100.00%, Radj2= 100.00%) (8) 0 0=-0.419+30.966 -9.305 sin(5 )E P PΘ   , (SD= 1.444, R2= 99.99%, Radj2= 99.99%) (9) 0 0=0.447+8.578 +3.653 sin(5 )VC P P Θ   , (SD=0.942, R 2=99.95%, Radj 2=99.95%) (10) 0 0 0=6.017+11.919 -3.013sin(5 ) 1.757 sin(8 )S P P PΘ   +  , (SD=5.022, R2=99.32%, Radj2=99.28%) (11) For the five QSPR models, the adjusted coefficients are all above 0.98, signifying high correlation. The estimated results are in good agreement with the theoretical results. 5. Model verification 5.1 Robustness test This section tests the robustness of the model. From Formulas (7)~(11), it is observed that SΘ has the lowest adjusted coefficient of determination. For example, out of the 60 molecues in Table 1, remove molecues 1, 5, 9...57 and take the remaining ones as a training set; similarly, remove molecues 2, 5, 10...58 and take the remaining ones as another training set. In this way, a total of four training sets are constructed. The independent variable is determined by the steps in Section 3.4. See Table 2 for the modeling results, where Q stands for the cross-validation correlation coefficient. Table 2 shows that the best variable obtained by the model based on each training set is consistent with the original sample (the 4th set is the control group). The main variables of 0P, sin(50P) and sin(80P) are expressed by SΘ. The cross-validation correlation coefficient (Q) of each set is greater than 0.97, an evidence to the good stability of the QSPR model. 1060 5.2 Predictive power To verify the predictive power of the proposed model, 7 samples are randomly selected in addition to those in Table 1, and are processed by the formulas (7)~(11). According to the results, the predicted thermodynamic parameters values are fairly close to the theoretical values. The maximum error for SΘ appears in 2-C3-4-C1-3 'C3 resveratrol (-2.50%). Overall, the relative error between the predicted results and the theoretical values is less than 5%. Thus, the proposed model is proved to have excellent predictive power. Table 2: Regression Results of Molecular Descriptors and SΘ No. Model R2/% Radj 2/% VIFmax Q 1 00.616 12.223S PΘ = +  99.00 98.98 1.000 0.9877 0 04.598 12.025 -3.432 sin(5 )S P PΘ = +   99.11 99.07 1.236 0.9823 0 0 04.069 12.033 -4.181sin(5 ) 3.272 sin(8 )S P P PΘ = +   +  99.26 99.21 1.280 0.9780 2 03.172 12.071S PΘ = +  98.81 98.78 1.000 0.9973 0 04.230 12.035 -1.524 sin(5 )S P PΘ = +   98.83 98.78 1.041 0.9980 0 0 05.558 11.912 -2.121sin(5 ) 1.961sin(8 )S P P PΘ = +   +  98.89 98.81 1.215 0.9981 3 04.304 12.026S PΘ = +  99.33 99.31 1.000 0.9888 0 05.750 11.954 -1.788 sin(5 )S P PΘ = +   99.35 99.32 1.159 0.9899 0 0 06.557 11.926 -2.679 sin(5 ) 2.029 sin(8 )S P P PΘ = +   +  99.39 99.35 1.305 0.9918 4 03.927 12.013S PΘ = +  99.53 99.52 1.000 0.9693 0 06.102 11.886 -2.431sin(5 )S P PΘ = +   99.57 99.55 1.270 0.9707 0 0 06.228 11.880 -2.574 sin(5 ) 0.332 sin(8 )S P P PΘ = +   +  a 99.57 99.55 1.421 0.9717 a. In the 4 th training set, the model with 0P, sin(50P) and sin(80P) has a greater VIFmax than the model with  0 P and sin(50P), indicating that the former has no better regression results than the latter. 6. Conclusions Taking the topological indexes of principal quantum number {0P2, 0P4, 0P3’} and the sum total of such indexes {0P} as molecular descriptors and the basic model variables, this paper introduces sine series to construct the thermodynamic structure-activity relationship model for resveratrol analogues, and proposes an adjustment judgment coefficient to obtain the satisfactory results. It is proved that the model has good stability and predictive power. Acknowledgments This project is financially supproted by grants from the Natural Science Foundation of China (NSFC) (Grant No. 61603160), Research project of Jiangsu Normal University (Grant No. 15XLR033). Reference Chen H.Y., Ji Y.J., Wu D., Wu Y., Jiang W., 2015, Protective effects of resveratrol on sepsis and its involved mechinism , Chinese Pharmacological Bulletin, 31, 1216-1221. Chen L., Wang M.F., Guan Y., Wang J.J., Chen Y., 2015, Effbct of borneol on the pharmacokinetic of trans- resveratrol in rat , Journal of Hubei University, 37, 316-321. Chen Y., Du X.h., 2008, QSPR research on thermodynamic properties of polychlorinated diphenyl ethers, of Journal of Chemical Industy and Engineering, 59, 2427-2435. Du X.H., 2007, QSPR research of thermodynamic properties of polychlorinated biphenyl, Journal of Chemical Industy and Engineering, 58, 2432-2436. Du X.H., 2010, QSPR study on thermodynamic properties of polybrominated dibenzofurans and polybrominated dibenzothiophenes, Journal of Chemical Industy and Engineering, 61, 3059-3066. Du X.H., 2014, Physicochemical property of polybrominated diphenyl ethers by new path location index and neural network, Journal of Chemical Industy and Engineering, 65, 1169-1178. Dunning T.H., Hay P.J., 1977, Gaussian Basis Sets for Molecular Calculations, The Journal of Chemical Physics, 90, 1007-1023. 1061 Farris P., Krutmann J., Li Y.H., 2013, Resveratrol: a unique antioxidant offering a multi-mechanistic approach for treating aging skin, Journal of Drugs in Dermatology, 12, 1389-1394. Han X.L., 2014, Pharmacological Research Progress of Reserveratrol and Its Analogues and Derivatives, Chemistry & Bioengineering, 31, 15-19. Han X.L., Gao J.f., Wang X.M., Zhu H.Z., 2012, Interaction between resveratrol analogue and human serum albumin, Chemical Research and Application, 24, 3-6. He W.P., Huang J., Wang D.t., 2015, QSPR study on thermodynamic properties of n-alkyl phenol, Journal of Chemical Industy and Engineering, 66, 67-68. He Y.Q., Hu Q.S., Hu W., Liu L.X., 2015, A theoretical study on the structures of cis/trans - resveratrol and the first triplet state, Journal of Atomic and Molecular Physics,32, 572-578. Li L., Liu X.Y., Wang Q.W., Cheng S.K., Zhang S.Y., Zhang M., 2013, Phannacokinetics, tissue distribution and excretion study of Iesveratrol and itsprodrug 3,5,4-tri-O-acetylresvemtml in rats, Phytomedicine, 20, 558-563. Liu P.J., Pan X., M., Zhao M., Sun H., Su Z.M., Wang R.S., 2002, Density Functional Theory Study on the Qin Z.l., 2004, Study on quantitative structure-property relationship of alkyl benzenes by the principal quantum number topological index, Chinese Journal of Organic Chemistry, 24, 338-342. Wang Q.F., Xu Q., Zhang R.L., Liu D.F., Ying D.S., Wang M., Li L.P., 2015, Resveratrol and its metabolites accumulation responding to abiotic stresses and hormones in peanut seedlings, Chinese Journal of Oil Crop Sciences, 37, 301-309. Xia H.J., WANG Y.P., Zhu W., 2014, Resveratrol inhibits doxrubicine-induced toxicity of H9c2 cells partly by upregulating expression of sirt1, Chinese Pharmacological Bulletin, 30, 220-224. Xiao J., He W.P., Huang J., 2015, QSPR Study on Thermodynamic Properties of the Nitro and Azido Derivatives of Benzene, Journal of Atomic and Molecular Physics, 32, 754-762. Xue L., 2014, Progress in anti-tumor research on resveratrol and its derivatives and analogues, Chemical Industy and Engineering Progress, 33, 1526-1532. Yu S., Guo Q.S., Wang H.L., Gao J.P., Xu X., 2015, Simultaneous Determination of Resveratrol and Polydatin in Polygonum Cuspidatum by Quantitative Nuclear Magnetic Resonance Spectroscopy, Chinese Journal of Analytical Chemistry, 43, 69-74. Yuan S.X., Wang X.D., Wu Q.X., 2015, Study on the relationship between anti-proliferation effect of reserveratrol on HCT116 colon cancer cells and Wnt/β-catenin, Chinese Pharmacological Bulletin, 31, 537-541. Zhang H.X., Duan G.L., Wang C.N., 2014, Protective effect of resveratrol against endotoxemia-induced lung injury involves the reduction of oxidative/nitrative stress, Pulmonary Pharmacology Therapeutics, 27, 150- 155. 1062