Predictive QSAR modeling of CCR5 antagonist piperidine derivatives using chemometric tools

Figures & data

Table I.  Structure and CCR5 binding affinities of sulfonyl derivatives of piperidine containing compounds.

		Structural Features		Anti-HIV Activity ( − logIC50(mM))
Sl. No.	Number of oxygen atom (n)	R1	R2	obs	cal^a	cal^b	cal^c	cal^d
1	0	(S)-3,4 diCl-phenyl	Phenyl	3.000	3.829	3.659	3.834	3.752
2	1	(S)-3,4 diCl-phenyl	Phenyl	4.456	3.984	3.919	3.890	3.928
3	2	(S)-3,4 diCl-phenyl	Phenyl	4.000	4.072	4.063	3.580	3.920
4	1	(S)-3,4 diCl-phenyl	2-Thienyl	4.222	3.886	3.762	3.652	3.697
5	2	(S)-3,4 diCl-phenyl	2-Thienyl	3.921	3.867	4.007	3.368	3.683
6	1	(S)-3,4 diCl-phenyl	N-dimthyl	3.469	3.750	3.898	3.325	3.590
7^*	1	(S)-3,4 diCl-phenyl	Benzyl	3.229	4.319	4.263	4.021	4.119
8	1	(S)-3,4 diCl-phenyl	Methyl	3.071	3.375	3.581	2.948	3.314
9	1	(S)-3,4 diCl-phenyl	n-Octyl	2.854	4.462	4.548	4.240	4.795
10	1	(S)-3,4 diCl-phenyl	Cyclopentyl	4.000	3.876	3.857	3.482	3.815
11^*	1	(S)-3,4 diCl-phenyl	Cyclohexyl	4.000	4.044	3.717	3.793	4.014
12	1	(S)-3,4 diCl-phenyl	2-Cl-phenyl	4.097	4.044	3.693	3.814	4.025
13	1	(S)-3,4 diCl-phenyl	3-Cl-phenyl	4.155	4.099	4.099	3.804	4.047
14	1	(S)-3,4 diCl-phenyl	4-Cl-phenyl	4.398	4.131	4.122	3.876	4.052
15	2	(S)-3,4 diCl-phenyl	3-NO2-phenyl	3.824	4.554	4.809	3.989	4.169
16^*	2	(S)-3,4 diCl-phenyl	4-NO2-phenyl	4.222	4.595	4.969	3.968	4.254
17^*	1	(S)-3,4 diCl-phenyl	4-MeO-phenyl	4.398	4.294	4.212	4.093	4.259
18	1	(S)-3,4 diCl-phenyl	4-Phenyl-phenyl	4.398	4.579	4.572	4.638	4.591
19	1	(S)-3,4 diCl-phenyl	Naphth-1-yl	3.444	3.855	3.386	4.342	3.901
20	1	(S)-3,4 diCl-phenyl	Naphth-2-yl	4.222	4.098	4.264	4.222	4.073
21^*	1	(S)-3,4 diCl-phenyl	Indan-5-yl	4.155	4.302	3.998	4.015	4.225
22	1	(S)-3,4 diCl-phenyl	Pyridin-3-yl	4.000	3.879	3.805	3.882	3.826
23	1	(S)-3,4 diCl-phenyl	Quinolin-8-yl	4.046	3.965	3.585	4.473	4.096
24	1	(S)-3,4 diCl-phenyl	Quinolin-3-yl	3.921	4.152	4.140	4.336	4.035
25^*	1	(S)-3,4 diCl-phenyl	1-Me-Imidazol-4-yl	3.469	4.060	3.813	3.760	3.866
26	0	(R/S)-phenyl	Phenyl	3.347	3.572	3.599	3.759	3.594
27	1	(R/S)-phenyl	Phenyl	4.456	3.872	3.875	3.889	3.606
28	2	(R/S)-phenyl	Phenyl	4.523	3.883	3.690	3.853	3.693
29	1	(R/S)-2-Cl-phenyl	Phenyl	2.699	3.857	3.583	3.861	3.692
30	2	(R/S)-2-Cl-phenyl	Phenyl	2.886	3.886	3.521	3.634	3.690
31	0	(S)-3-Cl-phenyl	Phenyl	3.569	3.674	3.497	3.910	3.638
32	1	(S)-3-Cl-phenyl	Phenyl	5.000	4.029	4.106	3.949	3.808
33	2	(S)-3-Cl-phenyl	Phenyl	4.824	4.209	3.984	3.845	3.798
34^*	1	(S)-4-Cl-phenyl	Phenyl	3.569	4.043	3.972	3.928	3.714
35	1	(S)-4-F-phenyl	Phenyl	3.244	3.831	3.538	3.920	3.738
36^*	1	(R/S)-3,5 diCl-phenyl	Phenyl	4.046	4.253	4.238	3.817	3.910
37	2	(R/S)-3,5 diCl-phenyl	Phenyl	3.959	4.251	4.243	3.817	3.915

* stands for a member of the test set; cal^a obtained from the best result of ANN (Model 6); cal^b obtained from the best result of GFA-MLR (Equation 11); cal^c obtained from the best result of stepwise regression (Equation 7); cal^d obtained from the best result of PLS (Equation 8)

Table II.  Structure and CCR5 binding affinities of non-spiro piperidine derivatives.

	Structural Features			Anti-HIV Activity (-logIC50(mM))
Sl. No.	R1	R2	Y	obs	cal^a	cal^b	cal^c	cal^d
38	Phenyl	(R/S)-Phenyl	–CH–	3.921	3.552	3.732	3.931	3.737
39	Phenyl	(R/S)-2-Cl-phenyl	–CH–	2.523	3.518	3.322	3.895	3.839
40^*	Phenyl	(S)-3-Cl-phenyl	–CH–	4.523	3.659	3.709	3.887	3.864
41	Phenyl	(S)-4-F-phenyl	–CH–	3.000	3.522	3.505	3.828	3.767
42^*	Phenyl	(R/S)-3,5-diCl-phenyl	–CH–	3.523	3.632	3.798	3.740	3.973
43	Phenyl	(R/S)-3-F-phenyl	–CH–	4.000	3.505	3.344	3.895	3.762
44^*	Phenyl	(R/S)-3-Me-phenyl	–CH–	4.097	3.717	3.832	3.824	3.885
45^*	Phenyl	(R/S)-3-Et-phenyl	–CH–	3.959	3.815	3.895	4.141	4.098
46	Phenyl	(R/S)-3-CF3-phenyl	–CH–	3.301	3.828	3.736	3.949	3.935
47	Phenyl	(R/S)-4-Me-phenyl	–CH–	3.699	3.764	3.932	3.910	3.894
48^*	Phenyl	(R/S)-3,5-di-Me-phenyl	–CH–	3.796	3.802	3.954	3.939	4.021
49^*	Phenyl	(R/S)-3,4-di-F-phenyl	–CH–	3.244	3.161	3.207	4.026	3.724
50	Phenyl	(R/S)-3,4-di-Me-phenyl	–CH–	4.222	3.761	3.974	3.890	4.015
51	Phenyl	(R/S)-3-Me-4-F-phenyl	–CH–	3.745	3.806	3.571	4.010	3.902
52	Phenyl	(R/S)-3-F-4-Me-phenyl	–CH–	3.959	3.853	3.867	3.760	3.923
53	Phenyl	3-Cl-phenyl	–N–	3.155	3.720	3.724	4.054	3.836
54^*	2-Methyl-phenyl	3-Cl-phenyl	–N–	2.620	3.704	3.840	3.896	3.946
55	2-Methyl-phenyl	3-Cl-phenyl	–CH–	3.398	3.868	3.924	3.883	3.984
56	2-MeO-phenyl	3-Cl-phenyl	–CH–	4.155	4.166	3.819	4.335	4.211
57	3-CF3-phenyl	3-Cl-phenyl	–CH–	3.921	4.041	4.216	4.057	4.115
58^*	4-Cl-phenyl	3-Cl-phenyl	–CH–	3.699	3.846	4.026	3.850	3.996
59	4-F-phenyl	3-Cl-phenyl	–CH–	4.602	3.774	3.877	3.917	3.924
60	Benzyl	3-Cl-phenyl	–CH–	3.602	3.839	3.822	3.825	4.080
61	C6H5CH2CH2	3-Cl-phenyl	–CH–	4.187	3.937	4.237	3.993	4.318
62	C6H5CH2CH2CH2	3-Cl-phenyl	–CH–	5.301	4.209	4.553	4.338	4.573

* stands for a member of the test set; cal^a obtained from the best result of ANN (Model 6); cal^b obtained from the best result of GFA-MLR (Equation 11); cal^c obtained from the best result of stepwise regression (Equation 7); cal^d obtained from the best result of PLS (Equation 8)

Table III.  Structure and CCR5 binding affinities of spiro piperidine derivatives.

	Structural Features		Anti-HIV Activity ( − logIC50(mM))
Sl. No.	X	Y-Z	obs	cal^a	cal^b	cal^c	cal^d
63	-^e	–CH2CH2–	3.745	3.834	3.611	3.956	3.686
64^*	-^e	–NHCH2–	4.301	3.852	3.813	3.877	3.776
65	-^e	–C(O)CH2–	5.301	3.809	3.745	4.085	3.671
66	-^e	–C(O)NH–	4.347	4.027	4.073	4.009	3.726
67	-^e	–C(O)N(Me)	4.000	4.016	3.943	3.854	3.796
68	-^e	–C(O)NHCH2–	4.456	4.060	4.204	4.113	3.862
69	-^e	–NHC(O)CH2–	4.456	4.145	4.401	3.890	3.886
70	-^e	–CH(OH)CH2–	4.000	4.029	4.280	3.952	3.899
71	–CH2–	–O–	3.585	3.632	3.586	3.427	3.703

* stands for a member of the test set; cal^a obtained from the best result of ANN (Model 6); cal^b obtained from the best result of GFA-MLR (Equation 11); cal^c obtained from the best result of stepwise regression (Equation 7); cal^d obtained from the best result of PLS (Equation 8); ^eThe X in these structures is a single bond

Table IV.  Structure and CCR5 binding affinities of piperidine derivatives.

	Structural Features				Anti-HIV Activity ( − logIC50(mM))
Sl. No.	R1	R2	X	Y	obs	cal^a	cal^b	cal^c	cal^d
72	Me	H	O	H	3.000	3.612	3.720	4.017	3.823
73	t-Bu	H	O	H	3.000	3.902	4.063	3.332	4.225
74	t-Bu	Et	O	H	4.523	4.640	4.580	4.137	4.562
75^*	Me	Me	O	H	3.824	3.957	3.586	4.071	3.944
76	Me	Et	O	H	4.398	4.108	4.121	4.216	4.143
77	Me	n-Pr	O	H	4.699	4.199	4.257	4.492	4.405
78	Me	n-Bu	O	H	4.824	4.634	4.449	4.598	4.628
79	Me	n-C6H13	O	H	5.000	4.792	4.776	5.170	5.123
80	Me	c-C6H11–CH2	O	H	5.222	4.841	4.363	4.694	4.840
81^*	Me	Bn	O	H	4.000	4.869	4.476	4.862	4.731
82	Et	c-C6H11–CH2	O	H	4.456	4.705	4.634	4.728	5.109
83	Bn	c-C6H11–CH2	O	H	3.097	5.026	5.010	5.258	5.446
84^*	Et	Et	O	H	4.398	4.370	4.221	4.516	4.408
85	t-Bu	Et	O	H	4.602	4.609	4.760	3.877	4.564
86	c-C6H11–CH2	Et	O	H	4.824	5.060	4.791	4.796	4.957
87^*	Ph	Et	O	H	5.000	4.756	4.608	4.955	4.752
88	Bn	Et	O	H	5.699	5.017	4.879	5.070	4.834
89	Bn	Et	O	Cl	5.699	5.324	4.924	5.283	5.011
90	Bn	Me	O	H	5.301	4.917	4.834	4.856	4.653
91^*	Bn	n-Pr	O	H	5.699	5.134	5.101	5.179	5.190
92	Bn	n-Pr	O	Cl	5.398	5.501	5.269	5.445	5.219
93	Bn	n-Bu	O	H	5.301	5.329	5.116	5.237	5.341
94	Bn	Allyl	O	H	5.824	5.264	5.410	5.220	5.181
95^*	2-Me-C6H4–CH2	n-Pr	O	H	5.398	5.191	4.952	5.141	5.156
96	3-Me-C6H4–CH2	n-Pr	O	H	5.523	5.239	4.943	4.968	5.191
97	4-Me-C6H4–CH2	n-Pr	O	H	5.523	5.503	5.518	5.402	5.358
98	4-CF3–C6H4–CH2	n-Pr	O	H	5.222	5.049	4.887	4.914	5.202
99	4-NO2–C6H4–CH2	n-Pr	O	H	5.824	5.330	5.185	5.288	5.262
100	4-NO2–C6H4–CH2	Allyl	O	H	5.699	5.740	5.684	5.605	5.486
101^*	4-NO2–C6H4-CH2	Allyl	O	Cl	5.699	5.967	6.184	5.669	5.579
102	3-NH2COC6H4–CH2	n-Pr	O	H	6.097	5.951	6.041	5.667	5.653
103	4-NH2COC6H4–CH2	n-Pr	O	H	5.699	5.545	5.718	5.596	5.572
104	4-NH2COC6H4–CH2	n-Pr	O	Cl	5.523	5.670	5.835	5.627	5.680
105	Bn	n-Pr	O	H	5.699	5.165	5.080	5.300	5.142
106	Me	H	NH	H	3.000	3.768	3.894	3.938	3.856
107	Me	Et	NH	H	3.921	4.159	4.097	4.257	4.180
108^*	Bn	H	NH	H	4.000	4.351	4.798	4.672	4.535
109	Bn	n-Pr	NH	H	5.602	5.344	5.649	5.695	5.193
110	Ph	n-Pr	NH	H	5.398	4.969	5.150	5.027	5.001
111	Bn	n-Pr	N-Me	H	4.699	5.166	5.627	5.222	5.267
112^*	(S)-α-Me-Bn	n-Pr	NH	H	4.125	5.026	5.245	5.360	5.147
113^*	4-NO2-Bn	Allyl	NH	H	6.125	5.731	6.041	6.011	5.461
114^*	Me	Et	–	H	3.921	4.188	4.255	4.276	4.167
115	Ph	n-Pr	–	H	4.000	4.852	5.214	4.958	4.975
116	Bn	n-Pr	–	H	5.523	5.180	5.201	5.258	5.186
117	PhOCH2	n-Pr	–	H	5.398	5.397	5.349	5.410	5.486
118^*	PhCH2CH2	n-Pr	–	H	4.699	5.104	5.419	5.489	5.468
119	4-NO2-Bn	Allyl	–	H	5.699	5.471	5.672	5.803	5.240

* stands for a member of the test set; cal^a obtained from the best result of ANN (Model 6); cal^b obtained from the best result of GFA-MLR (Equation 11); cal^c obtained from the best result of stepwise regression (Equation 7); cal^d obtained from the best result of PLS (Equation 8)

Table V.  Categorical list of descriptors used in the development of models.

Category of Descriptors	Name of the Descriptors
Topological	Jx, ^1κ, ^2κ, ^3κ, ^1κam, ^2κam, ^3κam, Φ, SC-0, SC-1, SC-2, SC-3_P, SC-3_C, ^0χ, ^1χ, ^2χ, ^3χp, ^3χc, ^0χ^v, ^1χ^v, ^2χ^v, ^3χ^vp, ^3χ^vc, Wiener, Zagreb, S_sCH3, S_dCH2, S_ssCH2, S_dsCH, S_aaCH, S_sssCH, S_dssC, S_aasC, S_aaaC, S_ssssC, S_sNH2, S_ssNH, S_aaN, S_sssN, S_ddsN, S_aasN, S_sOH, S_dO, S_ssO, S_ssS, S_aaS, S_dssS, S_ddssS, S_sF, S_sCl.
Structural	MW, Rotlbonds, Hbond acceptor, Hbond donor, Chiral centers.
Physicochemical	AlogP, AlogP98, LogP, MR, MolRef.
Spatial	RadOfGyration, Jurs_SASA, Jurs_PPSA_1, Jurs_PNSA_1, Jurs_DPSA_1, Jurs_PPSA_2, Jurs_PNSA_2, Jurs_DPSA_2, Jurs_PPSA_3, Jurs_PNSA_3, Jurs_DPSA_3, Jurs_FPSA_1, Jurs_FNSA_1, Jurs_FPSA_2, Jurs_FNSA_2, Jurs_FPSA_3, Jurs_FNSA_3, Jurs_WPSA_1, Jurs_WNSA_1, Jurs_WPSA_2, Jurs_WNSA_2, Jurs_WPSA_3, Jurs_WNSA_3, Jurs_RPCG, Jurs_RNCG, Jurs_RPCS, Jurs_RNCS, Jurs_TPSA, Jurs_TASA, Jurs_RPSA, Jurs_RASA, Shadow_XY, Shadow_XZ, Shadow_YZ, Shadow_XYfrac, Shadow_XZfrac, Shadow_YZfrac, Shadow_nu, Shadow_Xlength, Shadow_Ylength, Shadow_Zlength, Area, Vm, Density, PMI_mag
Electronic	Charge, Fcharge, Apol, Dipole-mag, HOMO, LUMO, Sr.
Molecular Shape	DIFFV, COSV, Fo, NCOSV, ShapeRMS.

Table VI.  Serial numbers of compounds under different clusters.

Cluster No.	Serial Numbers of Compounds
1	1; 26; 31; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71.
2	79; 80; 81; 82; 83; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 105; 108; 109; 110; 111; 112; 115; 116; 117; 118.
3	98; 99; 100; 101; 102; 103; 104; 113; 119.
4	2; 4; 6; 7; 8; 9; 10; 11; 12; 13; 14; 17; 18; 19; 20; 21; 22; 23; 24; 25; 27; 29; 32; 34; 35.
5	3; 5; 15; 16; 28; 30; 33; 36; 37.
6	72; 73; 74; 75; 76; 77; 78; 84; 85; 106; 107; 114.

Table VII.  Comparative study of statistical parameters of classical QSAR models using different descriptors.

Type of Descriptors	Statistical Method	R^2 (Training Set)	Ra^2 (Training Set)	Q^2 (Training Set)	F	S	(Test Set)
Topological + structural	Stepwise	0.566	0.551	0.510	37.370	0.600	0.504
	PLS	0.511	0.506	0.488	92.060	0.349	0.565
	FA-MLR	0.561	0.546	0.514	36.630	0.604	0.470
Structural + physicochemical + spatial + electronic	Stepwise	0.628	0.602	0.562	23.390	0.565	0.438
	PLS	0.508	0.503	0.480	91.010	0.351	0.571
	FA-MLR	0.498	0.486	0.466	43.080	0.642	0.434
Topological + structural + physicochemical + spatial + electronic	Stepwise	0.567	0.552	0.530	37.600	0.599	0.549
	PLS	0.515	0.509	0.490	93.520	0.346	0.580
	FA-MLR	0.512	0.506	0.490	92.340	0.629	0.526

Figure 1.  Aligned view of the training set molecules.

Table VIII.  Comparative study of statistical parameters of GFA-MLR models using different descriptors.

Type of Descriptors	Eq. No.	R^2 (Training Set)	Ra^2 (Training Set)	Q^2 (Training Set)	LOF	F	s	(Test Set)
MSA + Structural + physicochemical + spatial + electronic	10	0.614	0.591	0.550	0.387	26.760	0.573	0.505
	11	0.593	0.574	0.537	0.389	30.990	0.585	0.520

Table IX.  Comparative study of best two network using different hidden layers.

Model No.	No. of Hidden Layer	No. of units in 3 different layers			No. of cross validated resampling	No. of epoch in backpropagation followed by conjugate gradient descent	Absolute Error Mean	Correlation Coefficient (r^2) between Obs. and Pred. values of the test set
1	3	40	38	36	10	500, 200	0.482	0.634
2	3	43	39	36	20	700, 300	0.403	0.683
3	2	43		39	10	500, 200	0.369	0.659
4	2	43		39	15	800, 300	0.373	0.638
5	1		43		20	700, 400	0.387	0.641
6	1		43		25	700, 400	0.377	0.635

Table X.  Comparison of external predictability characteristics of different models obtained from the training set using classical QSAR.

Type of Descriptors	Statistical Method	r^2		(r^2 − )/r^2
Topological + structural	Stepwise	0.553	0.544	0.016	0.502
	PLS	0.578	0.577	0.001	0.562
	FA-MLR	0.535	0.526	0.018	0.483
Structural + physicochemical + spatial + electronic	Stepwise	0.578	0.563	0.027	0.506
	PLS	0.591	0.589	0.003	0.564
	FA-MLR	0.517	0.516	0.002	0.500
Topological + structural + physicochemical + spatial + electronic	Stepwise	0.592	0.591	0.003	0.568
	PLS	0.609	0.604	0.008	0.566
	FA-MLR	0.5473	0.5472	6.94E-06	0.546

Table XI.  Comparison of external predictability characteristics of different GFA-MLR models.

Type of Descriptors	Model No.	r^2		(r^2 − )/r^2
MSA + Structural + physicochemical + spatial + electronic	1	0.581	0.551	0.052	0.480
	2	0.572	0.555	0.029	0.480

Table XII.  Comparison of external predictability characteristics of different ANN models.

Model No.	r^2		(r^2 − )/r^2
1	0.634	0.560	0.117	0.461
2	0.683	0.548	0.198	0.432
3	0.659	0.637	0.034	0.560
4	0.638	0.632	0.011	0.586
5	0.641	0.634	0.011	0.586
6	0.6352	0.6350	0.0003	0.627

Table XIII.  Calculated values of k and k^/ for different models as defined by Golbraikh and Tropsha [49].

	k^/	k
Stepwise Regression (Equation 1)	1.0268	0.9593
PLS (Equation 2)	1.0144	0.9721
FA-MLR (Equation 3)	1.0323	0.9536
Stepwise Regression (Equation 4)	1.0529	0.9361
PLS (Equation 5)	1.0176	0.9695
FA-MLR (Equation 6)	1.0404	0.9459
Stepwise Regression (Equation 7)	1.0286	0.9592
PLS (Equation 8)	1.0213	0.9664
FA-MLR (Equation 9)	1.0188	0.967
GFA-MLR (Equation 10)	1.0295	0.9571
GFA-MLR (Equation 11)	1.025	0.9614
ANN (Model 1)	1.0425	0.9454
ANN (Model 2)	0.9746	1.0109
ANN (Model 3)	1.0097	0.9786
ANN (Model 4)	1.0156	0.9727
ANN (Model 5)	1.0164	0.9721
ANN (Model 6)	1.0209	0.9678

Table XIV.  Comparison of best between observed and predicted values of the test set compounds using different techniques.

Statistical Methods	value
Stepwise Regression (Equation 7)	0.568
PLS (Equation 8)	0.566
FA-MLR (Equation 9)	0.546
GFA-MLR (Equation 11)	0.480
ANN (Model 6)	0.627

Figure 2.  Scatter plots of observed versus predicted values of the test set compounds obtained from the best models (based on r_m² value for the test set compounds) using (i) stepwise regression (Equation 7), (ii) PLS (Equation 8), (iii) FA-MLR (Equation 9), (iv) GFA-MLR (Equation 11) and (v) ANN (6^th model).

http://www.port.ac.uk/research/cmd/research/selectionbiasinmultipleregression

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