The inhibitory activity of aldose reductase of flavonoid compounds: Combining DFT and QSAR calculations

Peer review under responsibility of Taibah University

Figures & data

Fig. 1 Chemical structure of the studied compounds.

Table 1 Observed activity of studied flavonoids derivatives.

No.	Substituent	pIC50	No.	Substituent	pIC50
1	5,7,3′,4′-OH; 3,6-OCH3	7.590	23	7,3′,4′-OH; 3,5,8-OCH3	6.550
2	3′,4′-OH; 5,6,7,8-OCH3	7.490	24	5,6,3′,4′-OH; 7-OCH3	6.520
3	6,3′,4′-OH; 5,7,8-OCH3	7.440	25	6,3′,4′-OH; 3,5,7-OCH3	6.520
4	5,7,3′,4′-OH; 6-OCH3; 8-CH2Ph	7.470	26	5,3′,4′-OH; 3,6,7-OCH3	6.460
5	5,3′,4′-OH; 6,7,8-OCH3	7.410	27	5,7,4′-OH; 6,8-OCH3	6.390
6	3′,4′-OH; 5,7,8-OCH3	7.350	28	5,4′-OH; 6,7,8-OCH3	6.270
7	5,6,7,3′,4′-OH; 3-OCH3	7.240	29	5,6,3′,4′-OH; 3,7-OCH3	6.090
8	5,6,3′,4′-OH; 7,8-OCH3	7.190	30	3,5,7,3′,4′-OH	6.020
9^a	7,3′,4′-OH; 5,8-OCH3	7.130	31^a	5,6,7,4′-OH; 8-OCH3	5.920
10	5,3′,4′-OH; 7,8-OCH3	7.110	32	5,4′-OH; 6,7-OCH3	5.850
11	3′,4′-OH; 5,6,7-OCH3	7.040	33^a	5,7,4′-OH; 6,8,3′-OCH3	5.350
12	5,6,7,3′,4′-OH; 8-OCH3	6.920	34	6,4′-OH; 5,7,8,3′-OCH3	5.200
13	6,3′,4′-OH; 5,7-OCH3	6.850	35	5,4′-OH; 6,7,3′-OCH3	5.170
14	4′-OH; 5,6,7,8-OCH3	6.790	36^a	5,7-OH; 6,8,4′-OCH3	5.140
15^a	8,3′,4′-OH; 5,7-OCH3	6.790	37^a	5,6,7-OH; 8-OCH3	5.090
16	3′,4′-OH; 3,5,7,8-OCH3	6.770	38	5,6-OH; 7,8-OCH3	5.080
17^a	5,6,7,3′,4′-OH	6.690	39	3′,4′-OH; 5,6,7-OCH3; 3-COCH3	5.050
18	5,3′,4′-OH; 6,7-OCH3	6.920	40	4′-OH; 5,6,7,8,3′-OCH3	4.740
19	5,8,3′,4′-OH; 7-OCH3	6.640	41	5,7-OH; 6,8,3′,4′-OCH3	4.670
20	5,7,3′,4′-OH; 3,8-OCH3	6.620	42	5,4′-OH; 6,7,8,3′-OCH3	4.420
21^a	6,4′-OH; 5,7,8-OCH3	6.600	43	5,6,4′-OH; 7,8,3′-OCH3	3.960
22^a	5,7,3′,4′-OH; 8-OCH3	6.550	44	6-OH; 5,7,8-OCH3	4.440

a Test set.

Table 2 Values of the obtained parameters of the studied substituted flavonoids.

No.	pIC50	ET	EHOMO	ELUMO	DM	ω	η	χ	MW	MR	MV	Pc	n	γ	D
1^Footnoteb,Footnotec	7.590	−34,254.400	−5.484	−1.350	5.885	2.825	2.067	−3.417	346.288	83.460	208.700	651.900	1.731	95.100	1.650
2	7.490	−36,394.548	−5.742	−1.494	4.169	3.082	2.124	−3.618	374.341	94.680	272.100	740.600	1.612	54.800	1.375
3^b	7.440	−35,324.509	−5.629	−1.500	4.494	3.077	2.065	−3.564	360.000	89.880	246.500	697.200	1.649	63.900	1.461
4	7.470	−38,498.254	−5.694	−1.362	3.173	2.873	2.166	−3.528	406.385	107.720	276.300	807.300	1.707	72.800	1.470
5	7.410	−35,324.908	−5.550	−1.695	6.296	3.405	1.927	−3.623	360.315	89.880	246.500	697.200	1.649	63.900	1.461
6	7.350	−33,276.487	−5.503	−1.264	2.697	2.701	2.119	−3.384	344.315	88.000	248.100	682.000	1.627	57.000	1.387
7	7.240	−33,184.078	−5.489	−1.364	5.096	2.846	2.063	−3.426	322.262	78.630	183.800	608.500	1.800	120.000	1.800
8	7.190	−34,254.815	−5.460	−1.715	5.974	3.437	1.872	−3.587	346.288	85.090	220.900	653.800	1.696	76.600	1.566
9^a	7.130	−32,206.181	−5.572	−1.293	2.342	2.754	2.139	−3.433	330.289	83.200	222.500	638.600	1.670	67.700	1.483
10	7.110	−32,206.882	−5.571	−1.664	6.662	3.350	1.953	−3.618	330.289	83.200	222.500	638.600	1.670	67.700	1.483
11	7.040	−33,276.448	−5.830	−1.535	3.691	3.158	2.147	−3.683	344.315	88.000	248.100	682.000	1.627	57.000	1.387
12^c	6.920	−33,184.761	−5.545	−1.708	5.445	3.427	1.919	−3.626	332.262	80.290	195.400	610.400	1.758	95.200	1.700
13^Footnoteb,Footnotec	6.850	−32,206.399	−5.701	−1.538	3.602	3.146	2.081	−3.619	330.289	83.200	222.500	638.600	1.670	67.700	1.483
14^b	6.790	−34,346.416	−5.845	−1.506	5.014	3.114	2.169	−3.676	358.342	92.800	273.700	725.400	1.593	49.300	1.309
15^a	6.790	−32,206.333	−5.247	−1.235	2.863	2.618	2.006	−3.241	330.289	83.200	222.500	638.600	1.670	67.700	1.483
16	6.770	−36,394.693	−5.327	−1.251	5.678	2.654	2.038	−3.289	374.341	93.130	258.500	738.700	1.639	66.600	1.440
17^a	6.690	−30,066.647	−5.657	−1.725	4.870	3.465	1.966	−3.691	302.236	73.610	171.400	551.800	1.804	107.400	1.763
18	6.920	−32,206.811	−5.718	−1.708	4.994	3.437	2.005	−3.713	330.289	83.200	222.500	638.600	1.670	67.700	1.483
19	6.640	−31,136.717	−5.240	−1.630	3.980	3.268	1.805	−3.435	316.262	78.410	196.900	595.200	1.727	83.300	1.605
20	6.620	−34,254.747	−5.543	−1.675	5.184	3.368	1.934	−3.609	346.288	83.460	208.700	651.900	1.731	95.100	1.650
21^Footnotea,Footnotec	6.600	−33,276.378	−5.673	−1.513	4.725	3.104	2.080	−3.593	344.315	88.000	248.100	682.000	1.627	57.000	1.387
22^a	6.550	−31,136.575	−5.664	−1.700	6.423	3.421	1.982	−3.682	316.262	78.410	196.900	595.200	1.727	83.300	1.605
23	6.550	−35,324.389	−5.375	−1.275	5.037	2.696	2.050	−3.325	360.315	88.300	233.600	695.300	1.680	78.400	1.540
24	6.520	−31,136.716	−5.553	−1.732	5.098	3.472	1.911	−3.643	316.262	78.410	196.900	595.200	1.727	83.300	1.605
25	6.520	−35,324.585	−5.572	−1.539	3.903	3.135	2.016	−3.555	360.315	88.300	233.600	695.300	1.680	78.400	1.540
26^b	6.460	−35,324.539	−5.485	−1.381	6.360	2.871	2.052	−3.433	360.315	88.300	233.600	695.300	1.680	78.400	1.540
27^c	6.390	−32,206.813	−5.628	−1.704	4.190	3.425	1.962	−3.666	330.289	83.200	222.500	638.600	1.670	67.700	1.483
28^c	6.270	−33,276.782	−5.532	−1.705	4.901	3.421	1.914	−3.619	344.315	88.000	248.100	682.000	1.627	57.000	1.387
29	6.090	−34,254.436	−5.383	−1.277	8.794	2.701	2.053	−3.330	346.288	83.460	208.700	651.900	1.731	95.100	1.650
30	6.020	−30,066.680	−5.476	−1.802	2.582	3.605	1.837	−3.639	302.236	73.310	167.900	549.900	1.823	114.800	1.799
31^a	5.920	−31,136.624	−5.565	−1.719	4.111	3.448	1.923	−3.642	316.262	78.410	196.900	595.200	1.727	83.300	1.605
32	5.850	−30,158.665	−5.723	−1.708	3.938	3.439	2.007	−3.716	314.289	81.320	224.100	623.400	1.645	59.800	1.402
33^a	5.350	−35,325.052	−5.616	−1.711	4.831	3.437	1.953	−3.663	360.315	89.880	246.500	697.200	1.649	63.900	1.461
34^b	5.200	−36,394.605	−5.650	−1.512	5.014	3.100	2.069	−3.581	374.341	94.680	272.100	740.600	1.612	54.800	1.375
35^b	5.170	−33,276.904	−5.701	−1.708	4.021	3.436	1.997	−3.704	344.315	88.000	248.100	682.000	1.627	57.000	1.387
36^a	5.140	−33,277.134	−5.597	−1.673	4.645	3.367	1.962	−3.635	344.315	88.000	248.100	682.000	1.627	57.000	1.387
37^a	5.090	−29,088.443	−5.620	−1.865	2.969	3.731	1.878	−3.743	300.263	76.530	198.500	580.000	1.697	72.800	1.512
38^Footnoteb,Footnotec	5.080	−30,158.533	−5.542	−1.913	3.522	3.828	1.814	−3.727	314.289	81.320	224.100	623.400	1.645	59.800	1.402
39	5.050	−37,432.725	−5.930	−1.616	3.534	3.301	2.157	−3.773	386.352	97.200	277.300	763.600	1.618	57.400	1.392
40	4.740	−37,464.656	−5.829	−1.512	5.022	3.120	2.159	−3.670	388.368	99.480	297.700	784.000	1.582	48.100	1.304
41^c	4.670	−36,395.369	−5.590	−1.679	5.249	3.378	1.955	−3.634	374.341	94.680	272.100	740.600	1.612	54.800	1.375
42^b	4.420	−36,395.021	−5.521	−1.708	5.609	3.427	1.906	−3.615	374.341	94.680	272.100	740.600	1.612	54.800	1.375
43	3.960	−35,324.943	−5.461	−1.763	4.739	3.528	1.849	−3.612	360.315	89.880	246.500	697.200	1.649	63.900	1.461
44^c	4.440	−31,228.250	−5.738	−1.694	2.854	3.414	2.022	−3.716	328.316	86.120	249.700	666.800	1.606	50.800	1.314

a Test set.

b Test set 2.

c Test set 3.

Table 3 Correlation matrix between different obtained descriptors.

	pIC50	ET	EHOMO	ELUMO	DM	ω	η	χ	MW	MR	MV	Pc	n	γ	D
pIC50	1
ET	0.034	1
EHOMO	0.162	0.126	1
ELUMO	0.471	−0.425	0.268	1
DM	0.095	−0.274	0.209	0.073	1
ω	−0.475	0.426	−0.292	−0.999	−0.093	1
η	0.303	−0.475	−0.500	0.700	−0.089	−0.682	1
χ	0.415	−0.221	0.750	0.838	0.168	−0.851	0.198	1
MW	−0.088	−0.982	−0.207	0.397	0.187	−0.394	0.510	0.155	1
MR	−0.152	−0.896	−0.331	0.328	0.030	−0.319	0.541	0.038	0.960	1
MV	−0.289	−0.760	−0.421	0.218	−0.039	−0.207	0.508	−0.088	0.853	0.937	1
Pc	−0.171	−0.915	−0.307	0.359	0.079	−0.351	0.551	0.073	0.970	0.990	0.947	1
n	0.363	0.438	0.408	−0.060	0.112	0.050	−0.357	0.190	−0.558	−0.685	−0.889	−0.717	1
γ	0.357	0.327	0.434	0.039	0.205	−0.051	−0.286	0.272	−0.467	−0.632	−0.839	−0.638	0.975	1
D	0.366	0.361	0.456	−0.015	0.213	0.001	−0.351	0.247	−0.505	−0.675	−0.872	−0.684	0.982	0.989	1

The bold values mean the interrelationship between descriptors, i.e. (great value, in absolute value, means a highest correlation between two descriptors) and (small value, in absolute value, means a lowest correlation between two descriptors).

Fig. 2 Graphical representation of calculated and observed activity and the residues values calculated by MLR.

Fig. 3 Graphical representation of calculated and observed activity and the residues values calculated by MNLR.

Fig. 4 Graphical representation of calculated and observed activity and the residues values calculated by ANN.

Table 4 Performance comparison between models obtained by MLR, RNLM and ANN.

Model	Training set			Test set
	R	$R_{cv}^2$	MSE	R	$R_{\text{ext}}^2$	MSE
MLR	0.758	0.616	0.552	0.575	0.775	0.552
MNLR	0.787	0.632	0.628	0.620	0.847	0.628
ANN	0.900	0.749	0.458	0.756	0.858	1.614

Table 5 Observed values and calculated values of pIC50 according to different methods.

No.	pIC50 (obs.)	pIC50 (calc.)
		MLR	NMLR	ANN
1	7.590	7.286	7.263	7.054
2	7.490	6.239	6.182	6.692
3	7.440	7.034	7.104	7.360
4	7.470	7.374	7.449	7.197
5	7.410	5.952	6.070	5.441
6	7.350	7.200	7.365	6.809
7	7.240	6.810	7.108	6.748
8	7.190	6.483	6.598	5.833
9^a	7.130	8.271	8.166	7.010
10	7.110	6.584	6.705	7.080
11	7.040	6.778	6.927	6.917
12	6.920	7.103	7.232	6.968
13	6.850	7.479	7.501	6.693
14	6.790	5.719	6.056	4.305
15^a	6.790	7.733	7.548	7.013
16	6.770	6.295	5.969	6.415
17^a	6.690	7.194	6.861	5.791
18	6.920	6.751	6.730	5.900
19	6.640	6.618	6.495	6.553
20	6.620	5.957	6.049	6.405
21^a	6.600	6.491	6.815	6.825
22^a	6.550	7.347	7.114	7.144
23	6.550	7.059	6.857	5.183
24	6.520	6.930	6.755	6.538
25	6.520	6.345	6.350	5.814
26	6.460	6.851	6.783	5.704
27	6.390	6.544	6.607	5.981
28	6.270	5.272	5.679	6.053
29	6.090	7.367	7.250	5.407
30	6.020	6.077	5.930	5.358
31^a	5.920	7.017	6.845	4.547
32	5.850	6.232	5.860	4.379
33^a	5.350	6.044	6.112	4.563
34	5.200	5.928	5.971	4.054
35	5.170	5.677	5.959	5.395
36^a	5.140	5.578	5.963	6.824
37^a	5.090	6.212	5.227	7.163
38	5.050	5.997	4.397	6.584
39	5.080	4.857	5.411	6.711
40	4.740	5.114	4.846	6.702
41	4.670	5.023	5.109	6.579
42	4.420	4.719	4.827	5.958
43	3.960	5.425	5.528	5.729
44	4.440	5.161	5.318	5.719

a Test set.

Table 6 Results of test sets generated.

	Test set 2			Test set 3
	R	$R_{\text{ext}}^2$	MSE	R	$R_{\text{ext}}^2$	MSE
MLR	0.502	0.616	0.606	0.445	0.711	0.600
MNLR	0.776	0.660	1.133	0.757	0.541	1.271
ANN	0.917	0.865	0.414	0.812	0.753	0.331