Computational neural network analysis of the affinity of N-n-alkylnicotinium salts for the α4β2* nicotinic acetylcholine receptor

Figures & data

Table I.  Structures, experimentally determined pK_i values (with K_i value in μM) from [³H]nicotine binding assays, and pK_i values (with K_i value in μM) calculated by the NN731 model and its leave-one-out validation results for 85 quaternary ammonium salts^†.

No.	Cmpd Name	R	pKi (Expt)	pKi (NN)	pKi (NNLOO)
Nicotine
1	NIC		2.7	2.59	2.44
N-Alkylnicotinium Salts
2^*	NMNI	CH3	− 0.55	− 0.36	− 0.26
3^*	NENI	n-C2H5	− 0.02	− 0.37	− 0.65
4^*	NPNI	n-C3H7	− 1.33	− 0.59	− 0.25
5^*	NnBNI	n-C4H9	− 1.04	− 0.60	− 0.51
6^*	NHxNI	n-C6H13	0.28	− 0.61	− 0.84
7^*	NHpNI	n-C7H15	− 0.32	− 0.59	− 0.67
8^*	NONI	n-C8H17	− 1.29	− 0.44	− 0.24
9^*	NNNI	n-C9H19	0.08	− 0.25	− 0.32
10^*	NDNI	n-C10H21	1.05	0.23	0.01
11^*	NDDNI	n-C12H25	0.85	0.70	0.56
12^*	GZ511A	n-C13H27	− 0.42	− 0.29	− 0.38
13^*	GZ511B	n-C14H29	− 0.85	− 0.35	0.01
14^*	GZ512A	n-C15H31	0.96	0.65	0.54
15^*	GZ512B	n-C16H33	1.07	0.81	0.74
16^*	GZ521A	n-C17H35	1.28	1.40	1.41
17^*	GZ521B	n-C18H37	1.85	1.46	1.25
18^*	GZ522B	n-C20H41	0.89	1.22	2.14
19	NONB-7M	(CH2)6CH(CH3)2	− 0.37	− 0.21	− 0.15
20	NCyNB-4	cyclobutyl-(CH2)6CH(CH2)3	− 0.66	− 0.49	− 0.47
21	NCyNB-5	cyclopentyl-(CH2)6CH(CH2)4	− 0.74	− 0.47	− 0.84
22	NCyNB-6	cyclohexyl-(CH2)6CH(CH2)5	− 0.86	− 0.41	0.13
23	NBzNB	CH2C6H5	− 0.43	− 0.33	− 0.22
24	NANI	CH2CH = CH2	− 0.32	− 0.34	− 0.33
25	NONB-3c	cis-(CH2)2CH = CH(CH2)3CH3	1.10	− 0.56	− 0.77
26	NONB-3t	trans-(CH2)2CH = CH(CH2)3CH3	− 0.65	− 0.50	− 0.47
27	NONB-7e	(CH2)6CH = CH2	0.34	0.18	0.24
28	NONB-3y	(CH2)2CC(CH2)3CH3	0.70	0.14	− 0.39
29	NONB-6e7m	(CH2)5CH = CH(CH3)2	0.35	− 0.39	− 0.49
30	NDNB-4c	cis-(CH2)3CH = CH(CH2)4CH3	− 0.87	0.05	0.29
31	NDNB-4t	trans-(CH2)3CH = CH(CH2)4CH3	0.49	0.69	0.49
32	NDNB-9e	(CH2)8CH = CH2	1.30	1.51	0.41
33	NDNB-3y	(CH2)2CC(CH2)5CH3	0.24	0.70	0.64
34	NUNB-10e	(CH2)9CH = CH2	0.80	0.77	1.17
bis-N,N′-Alkylnicotinium Salts
35	bNHxI	(CH2)6	− 1.30	− 1.09	− 0.87
36	bNOI	(CH2)8	− 0.19	− 0.11	− 0.07
37	bNNB	(CH2)9	− 0.70	− 0.63	− 0.24
38	bNDI	(CH2)10	0.48	− 0.01	− 0.13
39	bNUB	(CH2)11	0.37	0.05	− 0.19
40	bNDDB	(CH2)12	− 0.29	0.00	0.63
N-Alkylpyridinium Salts
41^*	NMPI	CH3	− 1.30	− 1.27	− 1.25
42^*	NEPI	n-C2H5	− 1.46	− 1.21	− 1.17
43^*	NPrPI	n-C3H7	− 1.63	− 1.38	− 1.37
44^*	NBuPI	n-C4H9	− 0.98	− 1.13	− 1.14
45^*	NPePI	n-C5H11	− 0.94	− 1.30	− 1.36
46^*	NHxPI	n-C6H13	− 0.96	− 1.17	− 1.16
47^*	NHpPI	n-C7H15	− 1.18	− 1.33	− 1.34
48^*	NOPI	n-C8H17	− 1.30	− 1.20	− 1.15
49^*	NNPI	n-C9H19	− 1.28	− 1.39	− 1.38
50^*	NDPI	n-C10H21	− 1.22	− 1.47	− 1.48
51^*	NUPI	n-C11H23	− 1.23	− 1.51	− 1.53
52^*	NDDPI	n-C12H25	− 2.08	− 1.53	− 1.51
53^*	NPeDPI	n-C15H31	− 1.58	− 1.28	− 1.17
54	NAPB	CH2CH = CH2	− 1.75	− 1.76	− 1.26
55	JTO	cis-CH2CH = CH(CH2)4CH3	− 1.12	− 0.97	− 0.85
56	JCO	trans-CH2CH = CH(CH2)4CH3	− 1.28	− 1.25	− 1.24
57	LO	CH2CC(CH2)4CH3	− 1.24	− 1.44	− 1.45
58	MO	(CH2)6CH = CH2	− 1.05	− 1.33	− 1.35
59	LN	CH2CC(CH2)5CH3	− 1.46	− 1.32	− 1.28
60	JTN	cis-CH2CH = CH(CH2)5CH3	− 1.4	− 1.14	− 1.00
61	JCN	trans-CH2CH = CH(CH2)5CH3	− 1.38	− 1.36	− 1.37
62	LD	CH2CC(CH2)6CH3	− 0.98	− 1.08	− 1.00
63	MU	(CH2)9CH = CH2	− 1.09	− 0.93	− 0.80
64	NU	(CH2)9CCH	− 0.93	− 1.06	− 0.48
N-Alkyl-3-picolinium Salts
65^*	NNPiI	n-C9H19	− 1.79	− 1.53	− 1.50
66^*	NDPiI	n-C10H21	− 1.41	− 1.48	− 1.51
bis-N,N′-Alkylpyridinium Salts
67	bPHxI	(CH2)6	− 1.99	− 1.72	− 1.63
68	bPOI	(CH2)8	− 1.54	− 1.66	− 1.69
69	bPNB	(CH2)9	− 1.38	− 1.41	− 1.33
70	bPDI	(CH2)10	− 1.27	− 1.55	− 1.59
71	bPUB	(CH2)11	− 1.15	− 1.69	− 1.73
72	bPDDB	(CH2)12	− 0.96	− 1.65	− 1.70
bis-N,N′-Alkyl-3-picolinium Salts
73	bPiNB	(CH2)9	− 1.90	− 1.68	− 1.55
74	bPiUB	(CH2)11	− 1.84	− 1.44	− 0.71
75	bPiDDB	(CH2)12	− 1.69	− 1.65	− 1.69
bis-N,N′-Alkylquinolinium Salts
76	bQHxI	(CH2)6	− 1.59	− 1.35	− 1.08
77	bQNB	(CH2)9	− 1.35	− 1.73	− 1.87
78	bQUB	(CH2)11	− 1.58	− 1.70	− 1.75
bis-N,N′-Alkylisoquinolinium
79	bIQHxI	(CH2)6	− 1.25	− 1.27	− 1.24
80	bIQOI	(CH2)8	− 1.82	− 1.45	− 1.27
81	bIQNB	(CH2)9	− 0.90	− 0.93	− 1.03
82	bIQUB	(CH2)11	− 0.96	− 0.52	0.04
83	biQDDB	(CH2)12	− 0.79	− 1.24	− 1.47
bis-Quaternary Ammonium Salts
84	HEX	(CH2)6	− 1.34	− 1.40	− 1.45
85	DEC	(CH2)12	− 0.76	− 1.21	− 1.45

^* Compounds were used in the 32 molecule dataset for mutilinear regression analysis

^† All compounds and experimental data in this table were generated in the laboratories of Dr. Peter A. Crooks and Dr. Linda P. Dwoskin. Most of these data have been published in References 7–13 and 20. Compounds 12–18 and their K_i values have not been published previously.

Table II.  Quality of linear regression and ANN models.

Model	Training cycles	r^2	rmsd	rcv^2	loormsd
LSF(17 mols)		0.46	0.69	0.33	0.77
MLR1(17 mols)		0.51	0.66	0.38	0.75
MLR2(32 mols)		0.79	0.48	0.71	0.57
MLR3(85 mols)		0.72	0.52	0.67	0.57
NN711(85 mols)	1000000	0.76	0.48	0.66	0.57
NN721(85 mols)	100000	0.82	0.42	0.68	0.56
NN731(85 mols)	80000	0.84	0.39	0.68	0.56
NN741(85 mols)	40000	0.82	0.42	0.66	0.57

Figure 1 pK_i values versus the number of carbon atoms in the N-n-alkyl chain of the N-n-alkylnicotinium salts from: a. [³H]nicotine binding assays; b. the MLR1 model with 17 molecules; c. the MLR2 model with 32 molecules; d. the MLR3 model with 85 molecules; e. the NN711 model; f. the NN721 model; g. the NN731 model; and h. the NN741 model with 85 molecules.

Table III.  Brief description of the descriptors used the linear regression relationship (MLR2) with a 32-molecule dataset.

Descriptor	Definition
E2u	2nd component accessibility directional WHIM index / unweighted.
Hy	Hydrophilic factor.
LUMO	LUMO molecular orbital energy.
Me	Mean atomic Sanderson electronegativity (scaled on Carbon atom).
Du	D total accessibility index / unweighted.
RDSUM	Reciprocal distance Wiener-type index.

Table IIIb.  Pearson correlation coefficient R between the descriptors used in MLR2 model.

	Eu	Hy	LUMO	Me	Du	RDSUM
Eu	1.00	0.21	− 0.24	0.28	0.22	− 0.18
Hy		1.00	− 0.15	0.85	− 0.49	− 0.62
LUMO			1.00	− 0.11	− 0.20	0.78
Me				1.00	− 0.36	− 0.47
Du					1.00	− 0.02
RDSUM						1.00

Table IV.  Correlation between the observed pK_i values from the [³H]nicotine binding assay and the calculated pK_i values for the series of 17 N-n-alkylnicotinium salts from various models.

Model	LSF	MLR1	MLR2	MLR3
R (Fitting)	0.68	0.71	0.73	0.70
Rmsd(Fitting)	0.69	0.66	0.65	0.73
R (LOO)	0.58	0.62	0.62	0.60
Rmsd(LOO)	0.77	0.75	0.75	0.77
Model	NN711	NN721	NN731	NN741
R (Fitting)	0.71	0.83	0.86	0.85
Rmsd(Fitting)	0.67	0.53	0.48	0.50
R (LOO)	0.59	0.61	0.68	0.65
Rmsd(LOO)	0.77	0.77	0.71	0.73

Table Va.  Brief description of the descriptors used in the ANN models.

Descriptor	Definition
PV	Polar volume.
PSA	Polar surface area.
LUMO	LUMO molecular orbital energy.
DISNN	Distances between nitrogen atoms.
L2u	2nd component size directional Whim index.
RDSUM	Reciprocal distance Wiener-type index.
MAXDN	Maximal electrotopological positive variation.

Table Vb.  Pearson correlation coefficient R between the descriptors used in the ANN models.

	PV	PSA	LUMO	DISNN	L2u	RDSUM	MAXDP
PV	1.00	0.11	− 0.27	0.40	− 0.19	0.60	0.16
PSA		1.00	0.18	0.11	− 0.02	− 0.04	0.37
LUMO			1.00	0.53	0.25	− 0.38	0.43
DISNN				1.00	0.34	0.37	0.49
W					1.00	0.33	0.11
RDSUM						1.00	0.11
MAXDP							1.00

Figure 2 The calculated versus the experimentally determined pK_i values from the [³H]nicotine binding assay for the trained (shown in black squares), leave-one-out cross-validation (shown in red diamonds) for the best NN731 QSAR model. The solid line represents a perfect correlation. The dotted lines represent one order difference from the perfect fitting. Most points around the dotted lines correspond to the N-n-alkylnicotinum compounds in Table VI.

Table VI.  Compounds with large errors between the experimentally determined pK_i values from [³H]nicotine binding assays and calculated pK_i/LOO pK_i values by model NN731.

	pKi (expt.)	pKi (NN731)	Diff.	pKi (NN731LOO)	Diff.
NONB-3C	1.10	− 0.56	1.66	− 0.77	1.86
NDNB-4C	− 0.87	0.05	− 0.92	0.29	− 1.16
NONB-6e7m	0.35	− 0.39	0.74	− 0.49	0.83
NHxNI	0.28	− 0.61	0.89	− 0.84	1.12
GZ-511B	− 0.85	− 0.35	− 0.50	0.01	− 0.85
NPNI	− 1.33	− 0.59	− 0.74	− 0.25	− 1.09
NDNI	1.05	0.23	0.82	0.01	1.04
NONI	− 1.29	− 0.44	− 0.86	− 0.24	− 1.05
NONB-3Y	0.70	0.14	0.55	− 0.39	1.08
NCYNB-6	− 0.86	− 0.41	− 0.45	0.13	− 0.99