The structures and inhibitory activities (IC50) of 25 andrographolide derivatives (Figure 1) were collected from the literature, and served as the database to build QSAR models [13,14,31]. PLogIC50 was used as the dependent variable of QSAR model. PCA, HQSAR, CoMFA, CoMSIA were performed by Sybyl7.03 (Tripos Co., LTD) program.

Principle Component Analysis (PCA), employed to select the training set, could be applied to explain the differences among the 25 andrographolide derivatives through diversities of the structures’ parameters and to exhibit their distribution on a 2D plot [32]. Furthermore, the most descriptive compounds (MDC) or the largest minimum distance (LMD) methods were applied to select the training set according to the distribution of these compounds.

Hologram QSAR (HQSAR) offers the ability to rapidly generate QSAR models of high statistical quality and predicted value by SYBYL line notation (SLN), cyclic redundancy check (CRC) and partial least squares (PLS) [33–35]. The premise of HQSAR is that since the structure of a molecule is encoded within its 2D fingerprint and that structure is the key determinant of all molecular properties (including biological activity), it should be possible to predict the activity of a molecule from its fingerprint.

The training set was used to establish 2D-QSAR model by HQSAR, and the best 2D-QSAR model was applied by the criterion of cross-validation R². The test set’s biological activity was predicted by the best 2D-QSAR model, whose predictability was validated by correlation coefficient between the predicted and experimental values. The most common structure (MCS) could be calculated by HQSAR. Based on the MCS of andrographolide derivatives, the contributions of molecules’ fragments to biological activity should be analyzed for describing the QSAR of andrographolide derivatives as α-glucosidase inhibitors.

The three-D QSAR model applies PLS to explore the relationships between the physicochemical variables and biological activity. Cross-validation is used to estimate the QSAR model’s predictability. In general, a LOO cross-validated coefficient Q² (higher than 0.5) can be considered as statistically high predictive ability [36]. CoMFA, which is widely utilized in 3D-QSAR research, claims that if a group of similar compounds are ligands of the same receptor, their bioactivities depend on the differences of the molecules’ fields surrounding them [37]. CoMFA can exhibit a contour map in a 3D graph, which makes it easier to distinguish differences between compounds with strong and weak activities. CoMSIA is another 3D-QSAR method that adopts a Gaussian function instead of traditional Coulomb and Lennard-Jones’ function used in CoMFA [38]. Therefore, CoMSIA efficiently avoids the shortcomings of CoMFA in which only the steric and electrostatic fields are used. The leave-one-out (LOO) method is employed to validate the predictability of the models and Y-Randomization test is used to validate the robustness of the models [39].

In this study, CoMFA and CoMSIA were both utilized to generate 3D-QSAR models, and then the relative higher predictive 3D-QSAR models were selected by comparison. Subsequently, the selected models were further optimized by the Focusing method [40]. This method describes the different contributions of different grids in CoMFA and CoMSIA to the bioactivities of the compounds by weighting, which was expected to selectively enhance or impair the contributions of different grids and improve the resolution. Moreover, the biological activities of test set were predicted by the optimized QSAR model. The best QSAR model was determined by comparing the parameters of the model and correlation between the predicted and experimental values of the test sets.

The selection of the training set is one of the most important steps in QSAR modeling, since the establishment and optimization of a QSAR model are based on this training set. Predictability and applicability of a QSAR model also depend on the training set selection [41,42]. Usually, the compounds serving as the training set should have three characteristics: (1) maximum structural diversity; (2) maximum activity diversity; (3) similarity of interactions [43]. Besides, both molecular structures and biological activities of the test set should be covered by the ranges of the training set. In this research, PCA was applied to select a training set from among 25 andrographolide derivatives. PCA is a statistical technique useful for summarizing all the information encoded in the structures of compounds. It is also very helpful for understanding the distribution of the compounds.

The distribution pattern of the 25 andrographolide derivatives is shown in Figure 2. There were different population densities in the Figure. Eighteen compounds (1, 3–8, 11, 13, 16–21 and 23–25) were selected as the raining set by the MDC method. The rest of them (compounds 2, 9, 10, 14, 15 and 22) were used as the test set whose biological activities were covered by the training set.

The best cross-validation r² (0.731) and standard error (0.225) illustrated that the 2D-QSAR model could be applied to predict the biological activity of andrographolide derivatives as α-glucosidase inhibitors. The predicted and experimental biological activities of andrographolide derivatives are shown in Table 1. The results of the correlation coefficient R², standard error of the training set (0.840, 0.174) and test set (0.949, 0.104) suggested that the 2D-QSAR model could be used to explain the QSAR of andrographolide derivatives as α-glucosidase inhibitors.

Furthermore, three key fragments (Figure 3) were selected according to PLS coefficient. The predicted activity = C 0 + ∑ i ( C i × b i ) where C₀ = the offset, C_i = the PLS coefficient associated with bin I in the hologram, b_i= the number of fragments hashed into bin i.

The PLS coefficient was the standardization for judging which fragment was the key fragment. The larger the PLS coefficient, the more important the fragment was for andrographolide derivatives’ biological activity. According to the criterion, C (=C©C)C=C or C[1]:C:C:C(:C:C:@1)C=C attached to C₃ of andrographolide (Figure 4) and C[1]:N:C:C(:C:C:@1)C(=C)O attached to C₁₇ of andrographolide were suggested as the key fragments.

The 18 compounds were energy minimized, added charges and aligned (Figure 5). CoMFA and CoMSIA were used to develop a number of QSAR models based on the properties of compounds belonging to different fields (steric, electrostatic, hydrophobic, H-donor and acceptor, Table 2). Since the QSAR model was employed to predict unknown compounds’ activity, the model’s predictability was the criterion to judge which QSAR model was the best. Predictability of a QSAR model was not only expressed by cross-validation (q²) but also by validation of the test set. The results illustrated that four models (4, 8, 10 and 11) had the top four predictabilities, so the Focus method was then applied to optimize these models, and further improved predictability for model 4, 10 and 11, but not for model 8. Among these models (model 8, 13, 15 and 16), model 16 exhibited the best predictability as indicated by the highest Q2 value. Predictability of these models (8, 13, 15 and 16) was further evaluated using a test set. Model 16 also provided the best prediction with a correlation coefficient R² (0.941) (Table 3). Overall, this model represented the best QSAR model (q² = 0.794, R²_cv = 0.915, SE_cv = 0.127, R²_{test set} = 0.941, SE_{test set} = 0.104). Y-Randomization test (q² = 0.199) suggested that the model also had a good robustness. Table 4 showed Comparison between predicted PLogIC50 of database and experimental values by using Model 16.

Model 16 used steric field, hydrophobic field and H-acceptor field together to describe the relationship between activities and structures of andrographolide derivatives. H-bond receptive atoms and groups in the region marked by blue lines (Figure 6) were favorable for the activities of the compounds, while the atoms and groups in the region marked by yellow lines impaired the activities. Hydrophobic groups were desirable in the region marked with blue lines but not the region marked by dark lines (Figure 7). In addition, the activities of the andrographolide derivatives were enhanced by the presence of steric groups in the region marked by purple lines instead of the region marked by green lines (Figure 8). The compounds with structures fitting well into the 3D contour maps derived from the model 16 usually exhibited potent inhibitory activity (e.g., compounds 20, 21, 22 and 23). In contrast, weak inhibitors such as compounds 3, 4, 13 and 16 did not have a good fit to the 3D contour maps.

Compound 21 (potent α-glucosidase inhibitor PLogIC₅₀ = 5.222) was layed in the 3D contour maps of model 16 to illustrate the key groups (marked by red dashed lines in Figures 5, 6, and 7) correlating with biological activity. C[1]:N:C:C(:C:C:@1)C(=C)O was a key group in all the 3D contour maps (steric, H-accept, hydrophobic) and C[1]:C:C:C(:C:C:@1)C=C was a key group in both steric and hydrophobic 3D contour maps. Both the groups were also calculated as key groups in HQSAR. Combining the results of HQSAR and CoMSIA, the two groups were considered as the key groups associated with biological activity and the result can also be used to screen potent α-glucosidase inhibitors from various databases by virtual screening.