Sets of quinolizidinyl derivatives of bi and tricyclic (hetero) aromatic systems were studied as selective inhibitors. On the pattern, quantitative structureactivity relationship (QSAR) study has been done on quinolizidinyl derivatives as potent inhibitors of acetylcholinesterase in alzheimer’s disease (AD). Multiple linear regression (MLR), partial least squares (PLSs), principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO) were used to create QSAR models. Geometry optimization of compounds was carried out by B3LYP method employing 6–31 G basis set. HyperChem, Gaussian 98 W, and Dragon software programs were used for geometry optimization of the molecules and calculation of the quantum chemical descriptors. Finally, Unscrambler program was used for the analysis of data. In the present study, the root mean square error of the calibration and
Alzheimer’s disease (AD) is a debilitating illness with unmet medical needs [
The wellknown theory of the quantitative structureactivity relationships (QSARs) [
Today, QSARs are being applied in many disciplines with much emphasis on drug design. Over the years of development, many methods, algorithms, and techniques have been discovered and applied in QSAR studies [
Drug discovery often involves the use of QSAR to identify chemical structures that could have good inhibitory effects on specific targets [
PLS regression technique is especially useful in quite common case where the number of descriptors (independent variables) is comparable to or greater than the number of compounds (data points), and/or there exist other factors leading to correlations between variables. In this case, the solution of classical least squares problem does not exist or is unstable and unreliable. On the other hand, PLS approach leads to stable, correct, and highly predictive models even for correlated descriptors [
PCR is a combination of principal component analysis (PCA) and MLR. The first step in PCR is to decompose a spectral data matrix using PCA. Generally, there are two types of decomposition techniques. The first technique is by computing eigenvectors and eigenvalues. We used singular value decomposition (SVD) to decompose the spectral data matrix. This is because SVD is generally accepted as the most stable and numerically accurate technique [
LASSO translates each coefficient by a constant factor truncating at zero. This is called soft thresholding. Best subset selection drops all variables with coefficients smaller than the
The 3D structures of the molecules were drawn using the built optimum option of Hyperchem software (version 8.0). Then, the structures were fully optimized based on the ab initio method, using DFT level of theory. Hyperchem (version 3.0) and Dragon (version 3.0) programs were employed to calculate the molecular descriptors. All calculations were performed using Gaussian 98 W program series. Geometry optimization of compounds was carried out by B3LYP method employing 6–31 G basis set [
In this study, the independent variables were molecular descriptors, and the dependent variables were the actual half maximal inhibitory concentration (IC_{50}) values. More than 1498 theoretical descriptors were selected and calculated. These descriptors can be classified into several groups including: (i) constitutional, (ii) topological, (iii) molecular walk counts, (iv) BCUT, (v) Galvez topological charge indices, (vi) autocorrelations, (vii) charge, (viii) aromaticity indices, (ix) randic molecular profiles, (x) geometrical, (xi) RDF, (xii) MoRSE, (xiii) WHIM, (xiv) GETAWAY, (xv) functional groups, (xvi) atomcentred, (xvii) empirical, and (xviii) properties descriptors. Finally, Unscrambler (version 9.7) program was used for analysis of data and statistical calculation.
For each compound in the training sets, the correlation equation was derived with the same descriptors. Then, the obtained equation was used to predict log (1/IC_{50}) values for the compounds from the corresponding test sets. In the present work, the method of stepwise multiple linear regression (stepwise MLR) was used in order to select the most appropriate descriptor of all descriptors. Totally, 1498 descriptors were generated. In this study, two programs including SPSS (version 19) and Unscrambler were used for MLR, PLS, PCR, and LASSO.
The structures of the quinolizidinyl derivatives used in this study were shown in Table
G (
Structures of quinolizidinyl derivatives of bi and tricyclic systems used for QSAR model building [
General structure  X  Y  R  R 
Nr 


S  N 

H  1 
S  N  –(H_{2}C)_{3}–N(Et)_{2}  CF_{3}  2  
S  N 

CN  3  
S  N 

H  4  
S  N 

CF_{3}  5  
O  N 

H  6  
CH_{2}  N 

H  7  
H_{2}C–CH_{2}  N 

H  8  
HC=CH  N 

H  9  
S  CH 

H  10  
S  CH 

H  11  
S  C–OH 

H  12  
S  C 

H  13  
H_{2}C–CH_{2}  C 

H  14  
HC=CH  C 

H  15  
 

N 

16  
CH 

17  
CH 

18  
 

N 

19  
CH 

20  
C 

21  
CH 

22  
 

S  CH 

H  23 
S  CH 

H  24  
S  CH 

H  25  
S  CH 

H  26  
S  CH 

OCH_{3}  27  
S  CH 

H  28  
S  CH 

H  29  
S  CH 

H  30  
S  CH 

H  31  
H_{2}C–CH_{2}  CH 

H  32  
HN–CO  N 

H  33  
HN–CO  N 

H  34  
 

NH 

35  
NH 

36  
NH 

37  
NH 

38  
S 

39  
 


40  

41  

42 
The mean values of selected descriptors are shown in Table
The mean of selected descriptors.
Descriptor 
Descriptor group  Meaning 

G ( 
Geometrical descriptors  Sum of geometrical distances between N 
ARR  Constitutional descriptors  Aromatic ratio 
Te  WHIM descriptors  T total size index/weighted by atomic Sanderson electronegativities 
MATS6e  2D autocorrelations  Moran autocorrelation—lag 6/weighted by atomic Sanderson electronegativities 
Mor31m  3DMoRSE descriptors  3DMoRSE— signal 31/weighted by atomic masses 
Mor18m  3DMoRSE descriptors  3DMoRSE—signal 18/weighted by atomic masses 
The selected descriptors through these methods were used to construct some linear models using PCR and PLS methods. Statistical parameters of different constructed QSAR models are shown in Table
The statistical parameters of different constructed QSAR models.
Method  RMSE 
 

Calibration  Prediction  Calibration  Prediction  
PLS  0.372616  0.466533  0.624241  0.426009 
PCR  0.372537  0.484057  0.624401  0.407646 
LASSO  —  —  0.766 
Considering the experimental error, the overall prediction of the log (1/IC_{50}) values was quite satisfactory. The results of MLR method were much better than the two other methods.
In the present study, linear variable selection methods were used to select the most significant descriptors (stepwise MLR) (Table
Descriptors values for stepwise MLR model.
Molecule  G ( 
ARR  Te  MATS6e  Mor31m  Mor18m 

1  0.000  0.500  13.546  0.045  −0.099  0.381 
2  0.000  0.429  17.814  0.106  0.018  1.122 
3  20.250  0.448  18.480  0.007  −0.294  1.186 
4  0.000  0.414  15.923  0.007  −0.181  1.383 
5  0.000  0.364  17.411  0.090  0.014  1.615 
6  9.600  0.414  15.799  0.011  −0.113  0.104 
7  0.000  0.414  16.071  0.022  −0.084  0.469 
8  0.000  0.400  16.312  0.034  0.002  1.199 
9  0.000  0.400  16.108  0.019  −0.191  1.233 
10  0.000  0.480  14.345  0.088  0.225  1.547 
11  0.000  0.414  15.271  0.119  0.106  2.132 
12  4.490  0.400  15.838  −0.029  0.055  1.896 
13  0.000  0.414  16.287  0.090  0.085  2.410 
14  0.000  0.400  16.628  0.107  0.291  1.618 
15  0.000  0.400  16.514  0.098  0.091  1.494 
16  0.000  0.464  15.920  0.012  −0.039  0.330 
17  0.000  0.429  14.869  0.129  0.083  1.143 
18  0.000  0.429  14.841  0.129  0.083  0.946 
19  0.000  0.444  13.992  0.003  −0.167  1.393 
20  0.000  0.444  15.531  0.110  0.085  0.358 
21  0.000  0.444  15.794  0.086  0.151  0.396 
22  0.000  0.429  16.962  −0.002  0.004  0.488 
23  2.850  0.480  14.983  −0.219  −0.126  1.175 
24  3.590  0.387  14.711  −0.111  0.050  1.531 
25  4.490  0.387  15.677  −0.111  0.210  1.747 
26  6.090  0.364  19.718  −0.059  0.174  1.143 
27  19.660  0.343  22.226  0.086  0.082  1.374 
28  5.930  0.353  20.024  −0.050  −0.035  1.639 
29  6.420  0.353  25.383  −0.101  0.140  1.918 
30  7.620  0.343  28.305  −0.041  −0.007  1.792 
31  9.500  0.333  36.586  −0.050  0.071  2.232 
32  6.150  0.353  20.780  −0.113  −0.036  0.525 
33  25.410  0.364  14.812  −0.051  −0.164  0.240 
34  34.830  0.343  25.376  0.009  −0.292  0.729 
35  19.340  0.400  24.194  0.080  −0.158  0.643 
36  17.760  0.394  17.479  0.071  −0.267  1.192 
37  19.490  0.333  26.550  0.079  −0.329  1.476 
38  19.170  0.324  29.353  0.066  −0.033  1.304 
39  12.740  0.333  19.215  0.087  0.048  1.531 
40  43.630  0.200  17.259  −0.009  0.062  0.817 
41  29.170  0.200  23.440  0.002  0.058  0.737 
42  24.170  0.194  20.222  0.024  −0.122  0.665 
The performance of the QSAR model to predict log (IC_{50}) value was also estimated using the internal crossvalidation method. The resulted predictions of the log (1/IC_{50}) using PLS and PCR methods in gas phase were given in Table
Experimental and predicted values of log (1/IC_{50}) using PCR and PLS methods.
Observed log (1/IC50)  Predicted PCR  Predicted PLS 

1.531  1.534  1.426 
1.653  1.656  1.656 
0.854  1.340  1.327 
1.591  1.679  1.675 
1.771  1.713  1.893 
1.568  1.647  1.661 
1.699  1.657  1.660 
1.74  1.482  1.401 
0.919  1.429  1.351 
1.634  1.572  1.489 
0.845  1.684  1.677 
1.623  2.260  2.324 
1.763  1.630  1.625 
1.663  1.423  1.341 
0.919  1.282  1.203 
1.613  1.560  1.602 
1.653  1.574  1.614 
1.681  1.574  1.614 
0.949  1.047  1.080 
0.826  1.042  1.073 
1.544  1.068  1.100 
1.653  0.919  0.956 
1.653  1.767  1.701 
1.69  1.693  1.726 
1.477  1.689  1.722 
1.505  1.358  1.370 
1.672  1.212  1.275 
1.602  1.467  1.503 
1.672  1.160  1.153 
0.833  0.962  0.919 
0.756  0.733  0.630 
1.532  1.161  1.076 
1.623  1.579  1.584 
1.462  1.193  1.171 
1.69  1.491  1.387 
0.863  0.521  0.581 
−0.076  0.275  0.276 
−0.658  0.022  −0.026 
1.756  1.010  1.062 
0.82  0.417  0.497 
−0.456  0.431  0.495 
0.079  0.273  0.337 
In our study, the linear methods were used to select the most significant descriptors. The stepwise MLR, MLR, PLS, and PCR were used to construct a quantitative relation between the activities of quinolizidinyl derivatives and their calculated descriptors. MLR has been successfully used for finding a QSAR model for quinolizidinyl derivatives. It provides the best results in comparison with other studied methods. Our present attempt to correlate the log (1/IC_{50}) with theoretically calculated molecular descriptors has led to a relatively successful QSAR model that relates these derivatives. The results obtained from stepwise MLR method were suitable for drug design and classification.
The authors declare that they have no conflict of interests.
The authors thank the Research vice Presidency of Islamic Azad University, Rasht Branch, for their encouragement, permission, and financial support.