IAM Chromatographic Models of Skin Permeation

Abstract

Chromatographic retention factor log k_IAM obtained from IAM HPLC chromatography with buffered aqueous mobile phases and calculated molecular descriptors (surface area—S_a; molar volume—V_M; polar surface area—PSA; count of freely rotable bonds—FRB; H-bond acceptor count—HA; energy of the highest occupied molecular orbital—E_HOMO; energy of the lowest unoccupied orbital—E_LUMO; and polarizability—α) obtained for a group of 160 structurally unrelated compounds were tested in order to generate useful models of solutes’ skin permeability coefficient log K_p. It was established that log k_IAM obtained in the conditions described in this study is not sufficient as a sole predictor of the skin permeability coefficient. Simple put, potentially useful models based on log k_IAM and readily available calculated descriptors, accounting for 85 to 91% of the total variability, were generated using Multiple Linear Regression (MLR).The models proposed in the study were tested on a group of 20 compounds with known experimental log K_p values.

1. Introduction

Transepidermal absorption is an important route of chemicals’ entry into a human body. The skin permeability coefficient K_p is defined according to Equation (1):

$${\mathit{K}}_{\mathit{p}}=\frac{{\mathit{K}}_{\mathit{m}}\mathit{D}}{\mathit{h}}$$

(1)

where K_m is the partition coefficient between the stratum corneum and the vehicle; D is the effective compound’s diffusion coefficient through the stratum corneum; and h is the diffusional pathlength.

The experimental values of skin permeability coefficients obtained in vivo (on human volunteers), ex vivo (on excised human skin), or even on animal models [1] are scarce and often inconsistent due to variations in properties of different skin specimen; there are also some ethical considerations related to such models. For these reasons, several in vitro or in silico skin permeation models have been developed [2]. One of the most frequently cited in silico skin permeability models, based on just two descriptors known to have a very strong influence on compounds’ ability to cross biological barriers, namely lipophilicity (expressed as octanol-water partition coefficient K_ow) and molecular weight (M_w), has been proposed by Potts (Equation (2)) [3]:

log K_p = −2.80 + 0.66 log K_ow − 0.0056 M_w

(2)

The Potts model is widely acknowledged due to its simplicity [4], although it is criticized by some research studies because it gives erroneous results for compounds of extreme properties (very hydrophilic or lipophilic; non-hydrogen bonding or very strongly hydrogen-bonding) [5,6,7,8]. However, the predictions made using Pott’s model are sufficiently good for the majority of drug-like compounds [9,10], thus this model is a popular tool in drugs’ ADMET studies and calculations based on it are offered by some popular ADMET prediction software packages [11,12]. Other proposed theoretical K_p models are based on the descriptors, such as the melting point, McGowan’s characteristic volume, Abraham’s solvation parameters or H-bonding properties (total H-bond count, H-bond acceptor count, and H-bond donor count), and total nitrogen and oxygen atom count [13,14,15,16,17,18,19,20,21,22,23]. QSAR studies of skin permeation published to date prove that transdermal absorption is a complex property and there are several factors contributing to it [4,7,24,25,26,27,28,29].

Previous studies demonstrated the usefulness of chromatographic descriptors in skin permeability studies. Liquid chromatographic models of skin permeability are based on the notion that the solutes’ partition between a stationary phase and a mobile phase resembles the partition between the skin and the vehicle.The separation techniques capable of providing chromatographic skin permeability predictors are liquid chromatography (HPLC or TLC), biopartitioning micellar chromatography, micellar electrokinetic chromatography, liposome electrokinetic chromatography, and two-dimensional gas chromatography (GCxGC) [8,30,31,32,33,34,35,36,37,38,39,40]. Chromatographic techniques of skin permeability studies are growing in popularity because of their high throughput, low cost, and good repeatability/reproducibility (the majority of such studies are conducted on commercially available stationary phases).

In our earlier studies, we proposed models of K_p based on calculated molecular parameters and RP-18 TLC-derived descriptors (R_M or R_M/V_M) [23,41]:

log K_p = −1.66 (±0.24) − 0.011 (±0.005) PSA + 0.24 (±0.05) HD − 0.0036 (±0.0017) V_M + 2.01 (±0.24) R_M
(steroids, n = 16, R² = 0.99, R²_adj. = 0.98, F = 229.0, p < 0.01, s_e = 0.18)

(3)

log K_p = −1.65 (±0.90) − 0.37 (±0.03) (N+O) + 0.13 (±0.03) log D + 90.4 (±43.0) (R_M/V_M) − 0.0000058 (±0.0000019) E_T + 0.029 (±0.01) E_h
(structurally diverse compounds, n = 60, R² = 0.87, R²_adj. = 0.85, F = 70.9, p < 0.01, s_e = 0.40)

(4)

where R_M = log (1/R_f − 1) [42] and R_f values were collected on the RP-18 stationary phase with acetonitrile/pH 7.4 phosphate-buffered saline 70:30 (v/v) as a mobile phase; log D is the distribution coefficient; PSA is the polar surface area (Ų); HD is the H-bond donors count; V_M is the molar volume (ų); E_T is the total energy (kcal/mol); E_h is the hydration energy (kcal/mol); and (N + O) is the total oxygen and nitrogen atom count.

We have also studied the skin permeability of organic sunscreens using RP-18 TLC-derived descriptors obtained with mobile phases containing different organic modifiers [43].

Thanks to the ability of stationary phases based on phosphatidylcholine covalently linked to aminopropyl silica to mimic the natural membrane bilayer (or, to be precise, a half of it), Immobilized Artificial Membrane (IAM) chromatography performed on such sorbents has been used to predict physico-chemical and biological properties of solutes for many years [44]. The relationships between the IAM chromatographic retention factor (k_IAM) and the skin permeability coefficient have been studied for small groups of compounds (n = 10 to 32) and the resulting dependencies are mostly univariate (linear or quadratic) [30,31,34,36], the exceptions being the study in which McGowan’s characteristic volume V was incorporated in a model alongside with log k_IAM [31]:

log K_p = −3.58 + 2.56 log k_IAM − 1.12 V
(n = 32, R² = 0.74)

(5)

Additionally, the model proposed by Barbato, based on a combination of an IAM chromatographic descriptor and the octanol-water partition coefficient log K_ow, is as follows [30]:

log K_p= −2.136 Δlogk_w^IAM+ 0.037 log K_ow− 2.373
(n = 10, R² = 0.94)

(6)

where Δlogk_w^IAM is the difference between log k_w^IAM measured and predicted on the basis of log K_ow.

In this study it was our intention to investigate the potential of immobilized artificial membrane (IAM) chromatography in skin permeability studies of a large group of solutes from different chemical families.We hoped to provide simple and practical models based on the IAM chromatographic retention factors and calculated physico-chemical descriptors that could be used to predict the skin permeability coefficient of solutes by researchers both in drug discovery and environmental toxicology fields.

2. Results and Discussion

The experimentally determined values of K_p were available for only some drugs within the studied group.For this reason, the models of skin permeability involving IAM chromatographic and calculated descriptors were generated and validated using K_p values obtained in silico with the EpiSuite software (DERMWIN v. 2 module; log K_p^EPI), which is recommended by the US Environmental Protection Agency [12,45] and was tested on a sub-group of 20 solutes whose experimental log K_p values are known (log K_p^exp) [29]. The estimation methodology used by DERMWIN was based on the above-mentioned Equation (2) [3]. The values of log K_p^EPI obtained using DERMWIN are given in

Table 1. IAM HPLC retention factors: reference, experimental, and calculated values of log K_p.

No.	CAS No.		log kIAM	log KpEPI	log Kp(9)	log Kp(11)	log Kp(12)	log Kp(13)	log Kpexp
1	103-84-4	acetanilide	0.48	−2.79	−2.91	−2.83	−2.92	−2.69
2	98-86-2	acetophenone	0.76	−2.43	−2.42	−2.43	−2.55	−2.33
3	95-55-6	2-aminophenol	0.28	−3.01	−2.97	−3.01	−2.89	−3.11
4	100-66-3	anisole	1.06	−2.01	−2.08	−2.07	−2.19	−2.03
5	100-52-7	benzaldehyde	0.63	−2.42	−2.52	−2.47	−2.58	−2.39
6	55-21-0	benzamide	0.12	−3.06	−3.13	−3.14	−3.10	−3.13
7	71-43-2	benzene	0.96	−1.83	−1.98	−1.95	−2.10	−1.91
8	100-47-0	benzonitrile	0.77	−2.35	−2.43	−2.41	−2.41	−2.45
9	100-51-6	benzyl alcohol	0.35	−2.68	−2.58	−2.67	−2.77	−2.59
10	92-52-4	biphenyl	2.88	−1.01	−1.01	−0.93	−1.03	−0.94
11	90-11-9	1-bromonaphtalene	2.90	−1.27	−1.12	−0.92	−1.04	−0.93
12	591-20-8	3-bromophenol	1.71	−2.03	−1.81	−1.75	−1.68	−1.91
13	104-54-1	cinnamyl alcohol	1.02	−2.26	−2.43	−2.39	−2.52	−2.25
14	91-64-5	coumarin	0.99	−2.70	−2.55	−2.40	−2.44	−2.38
15	108-94-1	cyclohexanone	0.08	−2.82	−2.79	−2.80	−2.94	−2.67
16	84-66-2	diethyl phtalate	1.63	−2.44	−2.37	−2.50	−2.39	−2.54
17	576-26-1	2,6-dimethylphenol	1.25	−1.92	−2.11	−2.12	−2.15	−2.14
18	623-05-2	4-hydroxybenzyl alcohol	0.12	−3.34	−3.10	−3.10	−3.08	−3.08
19	95-48-7	2-methylphenol	1.02	−2.12	−2.21	−2.21	−2.23	−2.25	−1.80
20	106-44-5	4-methylphenol	1.02	−2.12	−2.21	−2.22	−2.23	−2.26	−1.76
21	91-20-3	naphtalene	2.47	−1.33	−1.25	−1.12	−1.22	−1.15
22	90-15-3	1-naphthol	2.08	−1.72	−1.76	−1.64	−1.62	−1.72
23	135-19-3	2-naphthol	1.93	−1.82	−1.88	−1.75	−1.76	−1.79	−1.55
24	88-74-4	2-nitroaniline	1.13	−2.35	−2.72	−2.70	−2.24	−3.16
25	100-01-6	4-nitroaniline	1.01	−2.66	−2.78	−2.78	−2.35	−3.22
26	98-95-3	nitrobenzene	1.04	−2.27	−2.49	−2.44	−2.20	−2.72
27	619-73-8	4-nitrobenzyl alcohol	0.72	−2.83	−3.03	−2.98	−2.67	−3.26
28	627-05-4	1-nitrobutane	0.42	−2.41	−2.70	−2.80	−2.59	−3.03
29	99-99-0	4-nitrotoluene	1.35	−2.00	−2.34	−2.29	−2.05	−2.56
30	108-95-2	phenol	0.68	−2.36	−2.38	−2.38	−2.40	−2.42	−2.09
31	60-12-8	2-phenylethanol	0.53	−2.59	−2.63	−2.65	−2.79	−2.50
32	92-69-3	4-phenylphenol	2.56	−1.63	−1.44	−1.39	−1.37	−1.47
33	108-88-3	toluene	1.40	−1.51	−1.71	−1.70	−1.83	−1.69
34	106-48-9	4-chlorophenol	1.48	−1.94	−1.89	−1.87	−1.81	−2.02	−1.44
35	271-89-6	2,3-benzofuran	1.50	−1.69	−1.83	−1.85	−1.89	−1.88
36	526-75-0	2,3-dimethylphenol	1.44	−1.84	−1.96	−1.98	−1.98	−2.04
37	105-67-9	2,4-dimethylphenol	1.46	−1.96	−1.96	−1.96	−1.96	−2.03
38	91-23-6	2-nitroanisole	1.09	−2.51	−2.66	−2.61	−2.34	−2.87
39	95-51-2	2-chloroaniline	1.21	−2.26	−2.16	−2.17	−2.12	−2.27
40	99-09-2	3-nitroaniline	0.93	−2.67	−2.85	−2.85	−2.42	−3.26
41	539-03-7	4-chloroacetanilide	1.27	−2.37	−2.45	−2.32	−2.35	−2.29
42	106-47-8	4-chloroaniline	1.16	−2.30	−2.21	−2.21	−2.17	−2.29
43	62-53-3	aniline	0.35	−2.73	−2.69	−2.73	−2.77	−2.70
44	60-80-0	antipyrine	0.22	−3.61	−3.48	−3.20	−3.55	−2.72
45	119-61-9	benzophenone	2.06	−1.71	−1.88	−1.79	−1.92	−1.67
46	120-51-4	benzyl benzoate	2.71	−1.36	−1.64	−1.50	−1.51	−1.51
47	108-86-1	bromobenzene	1.75	−1.70	−1.57	−1.49	−1.59	−1.51
48	68411-44-9	butylbenzene	2.78	−0.52	−0.84	−0.90	−0.96	−0.99
49	495-40-9	butyrophenone	1.56	−1.80	−1.95	−1.99	−2.08	−1.92
50	58-08-2	caffeine	−0.17	−3.94	−4.24	−3.71	−3.78	−3.47
51	108-90-7	chlorobenzene	1.58	−1.55	−1.60	−1.57	−1.67	−1.59
52	50-22-6	corticosterone	1.69	−3.46	−3.26	−3.25	−3.30	−2.92
53	53-06-5	cortisone	1.29	−3.85	−3.75	−3.72	−3.67	−3.44
54	50-28-2	estradiol	2.65	−1.67	−2.05	−1.96	−2.03	−1.80	−2.28
55	50-27-1	estriol	1.66	−2.80	−3.06	−2.93	−2.98	−2.68
56	100-41-4	ethylbenzene	1.81	−1.31	−1.46	−1.48	−1.59	−1.48
57	110-00-9	furan	0.32	−2.30	−2.38	−2.42	−2.46	−2.48
58	106-24-1	geraniol	1.80	−1.36	−1.74	−1.91	−1.98	−1.86
59	1671-75-6	heptanophenone	2.99	−1.13	−1.00	−1.16	−1.18	−1.20
60	50-23-7	hydrocortisone	1.30	−3.77	−3.79	−3.76	−3.70	−3.50	−3.92
61	108-39-4	3-methylphenol	1.05	−2.11	−2.19	−2.19	−2.20	−2.24
62	93-58-3	methyl benzoate	1.11	−2.16	−2.30	−2.29	−2.29	−2.32
63	150-68-5	monuron	1.24	−2.63	−2.78	−2.51	−2.60	−2.37
64	123-35-3	myrcene	3.01	−0.69	−0.56	−0.77	−0.82	−0.87
65	95-53-4	o-toluidine	0.65	−2.53	−2.51	−2.49	−2.63	−2.37
66	93-55-0	propiophenone	1.16	−2.10	−2.17	−2.21	−2.32	−2.12
67	103-65-1	propylbenzene	2.29	−1.03	−1.16	−1.20	−1.28	−1.24
68	106-42-3	p-xylene	1.83	−1.31	−1.46	−1.46	−1.57	−1.47
69	289-95-2	pyrimidine	−0.50	−3.52	−3.28	−3.22	−3.31	−3.13
70	120-80-9	pyrocatechol	0.49	−2.84	−2.75	−2.76	−2.63	−2.90
71	109-97-7	pyrrole	0.18	−2.68	−2.64	−2.59	−2.65	−2.60
72	91-22-5	quinoline	2.07	−2.18	−1.68	−1.51	−1.53	−1.59
73	108-46-3	resorcinol	0.40	−2.89	−2.83	−2.82	−2.71	−2.95	−3.62
74	62-56-6	thiourea	−0.77	−3.95	−3.87	−3.96	−3.45	−4.43
75	89-83-8	thymol	2.19	−1.45	−1.52	−1.57	−1.55	−1.66	−1.28
76	1009-14-9	valerophenone	2.01	−1.62	−1.63	−1.73	−1.80	−1.70
77	109-66-0	pentane	2.28	−0.96	−0.89	−0.95	−0.87	−1.24
78	75-09-2	dichloromethane	0.22	−2.45	−2.30	−2.34	−2.49	−2.28
79	67-66-3	chloroform	0.62	−2.17	−2.12	−2.12	−2.26	−2.08
80	56-23-5	carbon tetrachloride	1.61	−1.79	−1.48	−1.46	−1.50	−1.58
81	1300-21-6	1,2-dichloroethane	0.34	−2.38	−2.28	−2.33	−2.51	−2.22
82	79-34-5	1,1,2,2-tetrachloroethane	1.28	−2.16	−1.77	−1.78	−1.93	−1.75
83	109-69-3	1-chlorobutane	1.05	−1.57	−1.76	−1.87	−1.99	−1.86
84	60-29-7	diethyl ether	−0.06	−2.63	−2.69	−2.74	−2.91	−2.60	−2.80
85	111-43-3	dipropyl ether	0.78	−2.03	−2.16	−2.26	−2.41	−2.17
86	79-20-9	methyl acetate	−0.66	−3.10	−3.23	−3.27	−3.33	−3.22
87	141-78-6	ethyl acetate	−0.25	−2.82	−2.98	−3.04	−3.08	−3.01
88	123-86-4	butyl acetate	0.62	−2.27	−2.24	−2.55	−2.55	−2.57
89	75-05-8	acetonitrile	−0.70	−3.26	−3.13	−3.17	−3.19	−3.19
90	107-12-0	propionitrile	−0.35	−3.01	−2.96	−2.98	−3.00	−3.01
91	64-17-5	ethanol	−0.62	−3.27	−3.09	−3.10	−3.16	−3.08	−3.10
92	71-23-8	1-propanol	−0.42	−2.97	−2.99	−3.03	−3.11	−2.98	−2.92
93	75-65-0	2-methyl-2-propanol	0.37	−2.99	−2.51	−2.52	−2.52	−2.58
94	71-41-0	1-pentanol	0.33	−2.30	−2.53	−2.62	−2.68	−2.60	−2.22
95	75-85-4	2-methyl-2-butanol	−0.08	−2.51	−2.88	−2.93	−3.05	−2.81
96	111-27-3	1-hexanol	0.83	−2.03	−2.21	−2.33	−2.36	−2.35	−1.89
97	64-18-6	formic acid	−0.65	−3.42	−3.18	−3.21	−3.06	−3.42
98	64-19-7	acetic acid	−0.68	−3.25	−3.29	−3.31	−3.21	−3.43	−3.21
99	79-09-4	propionic acid	−0.08	−3.00	−2.89	−2.94	−2.80	−3.13
100	107-92-6	butanoic acid	0.38	−2.77	−2.59	−2.67	−2.51	−2.89
101	109-99-9	tetrahydrofuran	−0.18	−2.90	−2.89	−2.79	−2.96	−2.66
102	93-89-0	ethyl benzoate	1.48	−1.89	−2.08	−2.09	−2.08	−2.13
103	88-73-3	1-chloro-2-nitrobenzene	1.44	−2.20	−2.20	−2.22	−1.98	−2.52
104	140-29-4	phenylacetonitrile	0.82	−2.43	−2.45	−2.44	−2.48	−2.42
105	91-59-8	2-naphthylamine	1.77	−2.09	−2.08	−1.96	−1.97	−1.98
106	108-43-0	3-chlorophenol	1.70	−1.87	−1.73	−1.71	−1.61	−1.91
107	99-04-7	3-methylbenzoic acid	1.43	−2.00	−2.17	−2.15	−1.99	−2.36
108	100-02-7	4-nitrophenol	1.28	−2.32	−2.52	−2.49	−2.04	−2.97	−2.25
109	17849-38-6	4-chlorobenzyl alcohol	1.06	−2.30	−2.29	−2.26	−2.32	−2.23
110	541-73-1	1,3-dichlorobenzene	2.48	−1.28	−1.04	−0.98	−0.99	−1.14
111	108-67-8	1,3,5-trimethylbenzene	2.61	−1.21	−0.98	−0.96	−1.00	−1.07
112	142-82-5	heptane	3.20	−0.27	−0.30	−0.41	−0.29	−0.78
113	110-54-3	hexane	1.97	−0.70	−1.17	−1.26	−1.28	−1.40
114	103-90-2	acetaminophen	0.38	−3.35	−3.24	−3.13	−3.07	−3.12
115	66085-59-4	nimodipine	3.06	−3.13	−2.88	−2.90	−2.45	−3.07
116	57-83-0	progesterone	2.98	−2.00	−1.88	−1.85	−2.05	−1.52
117	19387-91-8	tinidazole	0.26	−4.42	−4.15	−3.99	−3.63	−4.14
118	106-49-0	p-toluidine	1.15	−2.48	−2.18	−2.21	−2.17	−2.30
119	90-41-5	2-aminobiphenyl	2.13	−1.87	−1.82	−1.81	−1.83	−1.80
120	103-69-5	N-ethylaniline	1.06	−2.05	−2.29	−2.23	−2.40	−2.08
121	86-55-5	1-naphthoic acid	2.13	−1.71	−1.99	−1.85	−1.72	−2.01
122	103-82-2	phenylacetic acid	0.76	−2.63	−2.68	−2.64	−2.58	−2.70
123	1878-65-5	3-chlorophenylacetic acid	1.47	−2.37	−2.24	−2.20	−2.07	−2.34
124	1821-12-1	4-phenylbutanoic acid	1.52	−2.12	−2.20	−2.23	−2.15	−2.32
125	103-29-7	1,2-diphenylethane	3.77	−0.64	−0.53	−0.42	−0.49	−0.49
126	58-22-0	testosterone	2.23	−2.22	−2.38	−2.31	−2.51	−1.96
127	78-93-3	2-butanone	−0.38	−3.02	−2.91	−3.02	−3.16	−2.90	−2.95
128	110-86-1	pyridine	0.32	−2.82	−2.56	−2.52	−2.62	−2.47
129	123-07-9	4-ethylphenol	1.54	−1.78	−1.88	−1.90	−1.89	−1.99	−1.46
130	645-56-7	4-propylphenol	2.02	−1.44	−1.57	−1.62	−1.58	−1.75
131	1638-22-8	4-butylphenol	2.51	−1.22	−1.24	−1.33	−1.26	−1.50
132	371-41-5	4-fluorophenol	0.96	−2.26	−2.14	−2.18	−2.15	−2.29
133	106-41-2	4-bromophenol	1.81	−2.05	−1.74	−1.67	−1.59	−1.85	−1.44
134	540-38-5	4-iodophenol	2.10	−2.11	−1.65	−1.54	−1.47	−1.71
135	103-79-7	benzyl methyl ketone	0.38	−2.60	−2.76	−2.78	−3.01	−2.52
136	72509-76-3	felodipine	3.47	−2.40	−1.91	−1.86	−1.74	−1.84
137	63675-72-9	nisoldipine	3.26	−2.82	−2.53	−2.56	−2.09	−2.80
138	103890-78-4	lacidipine	4.00	−1.91	−2.04	−2.23	−2.11	−2.06
139	738-70-5	trimethoprim	0.95	−3.83	−4.05	−3.88	−3.59	−3.87
140	50-24-8	prednisolone	1.65	−3.75	−3.54	−3.50	−3.38	−3.32
141	50-78-2	acetylsalicylic acid	0.82	−3.03	−3.01	−2.98	−2.73	−3.16
142	65-85-0	benzoic acid	1.05	−2.25	−2.38	−2.36	−2.21	−2.56
143	140-65-8	pramocaine	2.56	−2.17	−2.04	−2.02	−2.25	−1.67
144	67-64-1	acetone	−0.75	−3.29	−3.13	−3.22	−3.37	−3.09	−3.21
145	123-30-8	4-aminophenol	−0.20	−3.39	−3.33	−3.36	−3.32	−3.35
146	93-60-7	methyl nicotinate	0.27	−3.02	−3.04	−3.00	−2.99	−2.98
147	68-12-2	N,N-dimethylformamide	−0.47	−3.89	−3.11	−3.11	−3.22	−3.01
148	26839-75-8	timolol	0.90	−3.36	−3.82	−3.97	−3.69	−3.94
149	2180-92-9	bupivacaine	1.88	−2.16	−2.56	−2.61	−2.98	−2.04
150	721-50-6	prilocaine	0.99	−2.64	−3.01	−3.01	−3.20	−2.66
151	29122-68-7	atenolol	0.65	−4.19	−3.71	−3.80	−3.70	−3.64
152	525-66-6	propranolol	2.20	−1.95	−1.90	−2.30	−2.43	−2.05
153	321-97-1	pseudoephedrine	0.36	−2.98	−3.07	−3.11	−3.30	−2.81
154	37517-30-9	acebutolol	1.57	−3.56	−3.42	−3.48	−3.43	−3.23
155	13655-52-2	alprenolol	2.08	−2.14	−2.16	−2.33	−2.43	−2.11
156	37350-58-6	metoprolol	1.21	−3.06	−3.00	−3.10	−3.27	−2.72
157	6452-71-7	oxprenolol	1.55	−2.90	−2.62	−2.84	−2.96	−2.55
158	18559-94-9	albuterol	0.48	−3.73	−3.61	−3.70	−3.68	−3.50
159	54910-89-3	fluoxetine	2.98	−2.00	−1.50	−1.54	−1.74	−1.28
160	52-53-9	verapamil	2.76	−2.84	−2.94	−2.98	−3.38	−2.19

Where: log k_IAM—IAM HPLC retention factors [46]; log K_p^exp—experimental values [29]; log K_p^EPI—values calculated using DERMWIN software [12]; and log K_p⁽⁹⁾ and log K_p⁽¹¹⁾ to log K_p⁽¹³⁾—values calculated according to Equations (9) and (11)–(13).

.

The compounds 1 to 160 were chromatographed on the IAM stationary phase using buffered aqueous mobile phases as described in Section 3. The retention factors (log k_IAM) were compiled from the published literature by Sprunger et al. [46] whose main objective was to propose an IAM chromatographic retention model based on Abraham’s solvation parameters. In our investigations, we focused mainly on drugs (that are or potentially could be administered transdermally) and environmentally relevant compounds (organic pollutants whose skin absorption can be a possible route of exposure). Log k_IAM values taken from Reference [46] were correlated with the log K_p^EPI values presented in Table 1. Unfortunately, the resulting linear correlation (7) is poor, with R² = 0.46.

log K_p^EPI = −2.98 (±0.07) + 0.52 (±0.04) log k_IAM
(n = 160, R² = 0.46, R²_adj. = 0.45, MSE = 0.32, F = 132.7, p < 0.01, s_e = 0.57)

(7)

Previous studies of the relationships between log K_p and log k_IAM (e.g., Equation (8)) for small groups of compounds [31,34,36] failed to provide general chromatographic models applicable to molecules from different chemical classes:

log K_p= −5.154 + 1.443 log k^IAM
(n = 32, R² = 0.26)

(8)

From this (and Equation (5) [31]), it was concluded that log k_IAM obtained as described in Section 3 is not sufficient as a sole predictor of log K_p. At this point, it was decided to seek a multivariate linear relationship that would meet the following requirements: (i) give the best possible fit with the log K_p^EPI reference values; (ii) fit the experimental log K_p^exp values for a subgroup of compounds whose experimental skin permeability data are available (preferably from a single source to avoid possible discrepancies between experimental data collected by different protocols); and (iii) be as simple as possible and contain the minimum number of independent variables needed to generate models of reasonable predictive power without the risk of overfitting.These goals were achieved in our study by taking the following steps:

• Generating a well-fitting model based on a relatively large number of independent variables selected by forward stepwise multiple regression;
• Validation of the model using two randomly selected subsets of compounds, namely a training set (n = 120) and a test set (n = 40);
• Validation of the initial model using experimental log K_p^exp data for a subset of compounds (n = 20);
• Analysis of every step of multiple stepwise regression in order to eliminate redundant independent variables; and
• Building a new model based on a reduced set of independent variables and its validation as described above.

In the first step of the multiple regression analysis, the calculated physicochemical parameters presented in

Table 2. Calculated descriptors for compounds 1 to 160.

		PSA	FRB	HA	VM	α	EHOMO	ELUMO	Sa
1	Acetanilide	29.1	1	2	122.5	16.07	−8.82	−0.03	312.2
2	Acetophenone	17.1	1	1	121.0	14.38	−10.00	−0.44	293.2
3	2-aminophenol	46.3	2	2	90.1	12.83	−8.10	0.52	264.6
4	Anisole	9.2	1	1	113.4	13.05	−9.11	0.35	283.9
5	Benzaldehyde	17.1	1	1	101.1	13.08	−10.05	−0.48	266.7
6	Benzamide	43.1	1	2	108.1	13.95	−9.72	−0.36	286.2
7	Benzene	0.0	0	0	89.4	10.41	−9.75	0.40	241.1
8	Benzonitrile	23.8	0	1	100.0	12.42	−10.10	−0.58	271.7
9	Benzyl alcohol	20.2	2	1	109.3	12.09	−9.58	0.33	281.5
10	Biphenyl	0.0	0	0	154.7	20.16	−8.92	−0.36	345.0
11	1-bromonaphtalene	0.0	0	0	139.7	20.53	−8.99	−0.65	328.6
12	3-bromophenol	20.2	1	1	104.1	14.20	−9.41	−0.13	282.5
13	Cinnamyl alcohol	20.2	3	1	127.9	17.32	−8.95	−0.15	329.7
14	Coumarin	26.3	0	2	117.1	15.76	−9.45	−0.99	305.5
15	Cyclohexanone	17.1	0	1	103.0	11.02	−10.48	0.85	256.1
16	Diethyl phtalate	52.6	6	4	198.2	23.42	−10.24	−0.93	407.7
17	2,6-dimethylphenol	20.2	1	1	120.4	14.98	−8.96	0.29	296.7
18	4-hydroxybenzyl alcohol	40.5	3	2	101.7	13.71	−9.06	0.31	291.5
19	2-methylphenol	20.2	1	1	104.1	13.07	−9.06	0.28	275.6
20	4-methylphenol	20.2	1	1	104.1	13.07	−8.95	0.33	274.0
21	Naphtalene	0.0	0	0	123.6	17.48	−8.84	−0.41	299.8
22	1-naphthol	20.2	1	1	122.0	18.23	−8.54	−0.36	308.8
23	2-naphthol	20.2	1	1	122.0	18.23	−8.72	−0.45	311.6
24	2-nitroaniline	71.8	2	4	103.6	14.68	−8.75	−0.82	306.6
25	4-nitroaniline	71.8	2	4	103.6	14.68	−9.00	−0.78	291.6
26	Nitrobenzene	45.8	1	3	101.3	13.00	−10.60	−1.14	273.3
27	4-nitrobenzyl alcohol	66.1	3	4	115.1	15.56	−10.52	−1.13	315.5
28	1-nitrobutane	45.8	3	3	107.3	10.55	−12.01	0.06	275.0
29	4-nitrotoluene	45.8	1	3	117.6	14.91	−10.47	−1.11	299.3
30	Phenol	20.2	1	1	87.9	11.15	−9.18	0.29	248.4
31	2-phenylethanol	20.2	3	1	119.8	14.80	−9.55	0.29	312.0
32	4-phenylphenol	20.2	2	1	153.2	20.90	−8.64	−0.34	355.8
33	Toluene	0.0	0	0	105.7	12.32	−9.44	0.45	265.6
34	4-chlorophenol	20.2	1	1	99.8	13.09	−9.01	0.05	272.4
35	2,3-benzofuran	13.1	0	1	106.3	14.43	−9.07	−0.15	216.7
36	2,3-dimethylphenol	20.2	1	1	120.4	14.98	−9.00	0.29	293.8
37	2,4-dimethylphenol	20.2	1	1	120.4	14.98	−8.86	0.31	301.2
38	2-nitroanisole	55.1	2	4	125.3	15.65	−10.29	−0.89	316.0
39	2-chloroaniline	26.0	1	1	103.7	14.03	−8.17	0.31	277.6
40	3-nitroaniline	71.8	2	4	103.6	14.68	−9.28	−1.06	291.8
41	4-chloroacetanilide	29.1	1	2	134.5	18.01	−8.67	−0.06	341.5
42	4-chloroaniline	26.0	1	1	103.7	14.03	−8.11	0.38	282.0
43	Aniline	26.0	1	1	91.7	12.09	−8.07	0.62	257.9
44	Antipyrine	23.6	1	3	162.8	21.63	−9.04	−0.33	383.0
45	Benzophenone	17.1	2	1	167.6	22.22	−9.94	−0.67	374.7
46	Benzyl benzoate	26.3	4	2	188.0	24.78	−9.61	−0.34	438.6
47	Bromobenzene	0.0	0	0	105.6	13.46	−9.81	−0.05	273.0
48	Butylbenzene	0.0	3	0	155.3	17.87	−9.51	0.36	357.3
49	Butyrophenone	17.1	3	1	154.0	18.06	−9.99	−0.09	363.0
50	Caffeine	53.5	0	6	133.4	19.97	−8.89	−0.49	364.0
51	Chlorobenzene	0.0	0	0	101.4	12.36	−9.39	0.06	264.1
52	Corticosterone	74.6	4	4	284.3	37.27	−10.21	−0.15	531.3
53	Cortisone	91.7	4	5	280.3	37.33	−10.09	−0.07	533.8
54	Estradiol	40.5	2	2	232.6	31.52	−8.86	−0.35	468.3
55	Estriol	60.7	3	3	229.6	32.15	−8.88	0.34	481.2
56	Ethylbenzene	0.0	1	0	122.3	14.19	−9.51	0.38	294.0
57	Furan	13.1	0	1	72.2	7.35	−9.38	0.61	208.2
58	Geraniol	20.2	5	1	177.9	19.71	−9.33	0.99	397.4
59	Heptanophenone	17.1	6	1	203.5	23.57	−10.00	−0.42	438.5
60	Hydrocortisone	94.8	5	5	281.4	37.89	−10.25	−0.18	542.9
61	3-methylphenol	20.2	1	1	104.1	13.07	−9.09	0.29	275.6
62	Methyl benzoate	26.3	2	2	127.3	15.07	−10.11	−0.46	314.4
63	Monuron	32.2	1	3	158.2	21.32	−9.13	−0.20	387.9
64	Myrcene	0.0	4	0	177.0	18.86	−9.28	0.29	374.8
65	o-toluidine	16.0	1	1	108.0	14.00	−7.99	0.59	276.9
66	Propiophenone	17.1	2	1	137.5	16.22	−9.99	−0.42	322.0
67	Propylbenzene	0.0	2	0	138.8	16.03	−9.51	0.37	326.6
68	p-xylene	0.0	0	0	122.0	14.23	−9.18	0.36	289.8
69	Pyrimidine	25.8	0	2	75.9	8.89	−10.29	−0.41	226.2
70	Pyrocatechol	40.5	2	2	86.3	11.90	−9.07	0.26	257.3
71	Pyrrole	15.8	0	1	67.8	8.20	−8.93	1.11	216.7
72	Quinoline	12.9	0	1	116.8	16.72	−9.24	−0.65	297.7
73	Resorcinol	40.5	2	2	86.3	11.90	−9.06	0.27	259.6
74	Thiourea	88.7	0	2	29.9	7.26	−8.62	−0.27	212.2
75	Thymol	20.2	2	1	154.2	18.69	−9.00	0.28	346.2
76	Valerophenone	17.1	4	1	170.5	19.89	−9.99	−0.42	379.6
77	Pentane	0.0	2	0	111.1	10.00	−11.30	3.45	266.9
78	Dichloromethane	0.0	0	0	67.8	6.49	−10.48	0.52	199.3
79	Chloroform	0.0	0	0	79.6	8.40	−10.88	−0.12	224.5
80	Carbon tetrachloride	0.0	0	0	90.6	10.32	−10.99	−0.63	244.2
81	1,2-dichloroethane	0.0	1	0	84.3	8.33	−10.69	0.54	231.1
82	1,1,2,2,-tetrachloroethane	0.0	1	0	107.8	12.14	−10.74	0.02	267.0
83	1-chlorobutane	0.0	2	0	106.0	10.08	−10.31	1.23	264.9
84	Diethyl ether	9.2	2	1	100.9	8.85	−10.48	2.86	260.9
85	Dipropyl ether	9.2	4	1	133.9	12.52	−10.49	2.76	317.2
86	Methyl acetate	26.3	1	2	81.5	7.03	−11.26	1.02	228.3
87	Ethyl acetate	26.3	2	2	98.0	8.83	−11.24	1.06	263.0
88	Butyl acetate	26.3	4	2	131.0	12.54	−11.25	1.05	232.4
89	Acetonitrile	23.8	0	1	54.9	4.45	−12.33	1.40	176.4
90	Propionitrile	23.8	0	1	71.4	6.29	−12.01	1.42	211.9
91	Ethanol	20.2	1	1	59.1	5.09	−10.90	3.33	191.0
92	1-propanol	20.2	2	1	75.6	6.93	−10.88	3.23	220.6
93	2-methyl-2-propanol	20.2	1	1	92.1	8.75	−11.28	3.26	244.4
94	1-pentanol	20.2	4	1	108.6	10.60	−10.89	3.11	281.4
95	2-methyl-2-butanol	20.2	2	1	108.6	10.59	−11.13	3.17	264.1
96	1-hexanol	20.2	5	1	125.1	12.44	−10.89	3.09	313.0
97	Formic acid	37.3	0	2	39.9	3.33	−11.57	0.97	158.3
98	Acetic acid	37.3	0	2	56.2	5.11	−11.43	0.93	192.8
99	Propionic acid	37.3	1	2	72.7	6.94	−11.31	0.96	222.4
100	Butanoic acid	37.3	2	2	89.2	8.78	−11.34	0.97	249.1
101	Tetrahydrofuran	9.2	0	1	79.8	7.95	−10.28	3.29	225.0
102	Ethyl benzoate	26.3	3	2	143.8	16.91	−10.08	−0.43	348.2
103	2-chloro-1-nitrobenzene	45.8	3	3	113.2	14.94	−9.94	−1.27	290.8
104	Phenylacetonitrile	23.8	1	1	115.7	14.16	−9.99	−0.09	300.7
105	2-naphthylamine	26.0	1	1	125.8	19.16	−7.92	−0.21	319.6
106	3-chlorophenol	20.2	1	1	99.8	13.09	−9.24	−0.01	272.6
107	3-methylbenzoic acid	37.3	1	2	118.2	15.07	−9.82	−0.49	304.5
108	4-nitrophenol	66.1	2	4	99.7	13.75	−10.17	−1.08	283.4
109	4-chlorobenzyl alcohol	20.2	2	1	115.2	14.91	−9.28	0.02	306.2
110	1,3-dichlorobenzene	0.0	0	0	113.3	14.29	−9.42	−0.19	288.6
111	1,3,5-trimethylbenzene	0.0	0	0	138.3	16.15	−9.28	0.44	320.3
112	Heptane	0.0	4	0	144.1	13.67	−11.27	3.30	327.7
113	Hexane	0.0	3	0	127.6	11.83	−11.28	3.36	297.7
114	Acetaminophen	49.3	1	3	121.0	16.81	−8.56	−0.02	323.6
115	Nimodipine	119.7	10	9	345.0	42.87	−9.21	−0.66	682.0
116	Progesterone	34.1	1	2	289.0	36.06	−10.14	−0.10	514.8
117	Tinidazole	101.2	5	7	172.4	23.36	−10.47	−1.21	432.8
118	p-toluidine	26.0	1	1	108.0	14.00	−7.95	0.64	285.0
119	2-aminobiphenyl	26.0	2	1	157.0	21.84	−7.98	−0.21	356.8
120	N-ethylaniline	12.0	2	1	125.4	16.05	−8.50	0.45	322.8
121	1-naphthoic acid	37.3	1	2	136.1	20.23	−9.13	−0.97	334.0
122	Phenylacetic acid	37.3	2	2	116.9	14.81	−9.81	0.22	313.7
123	3-chlorophenylacetic acid	37.3	2	2	128.8	16.75	−9.52	−0.20	337.0
124	4-phenylbutanoic acid	37.3	4	2	149.9	18.49	−9.67	0.21	372.0
125	1,2-diphenylethane	0.0	2	0	183.0	23.90	−9.48	0.32	402.0
126	Testosterone	37.3	1	2	257.0	32.95	−10.12	−0.09	477.5
127	2-butanone	17.1	1	1	91.7	8.17	−10.65	0.83	239.1
128	Pyridine	12.9	0	1	82.7	9.65	−10.10	0.01	231.9
129	4-ethylphenol	20.2	2	1	120.7	14.94	−9.00	0.32	305.7
130	4-propylphenol	20.2	3	1	137.2	16.78	−9.00	0.32	335.7
131	4-butylphenol	20.2	4	1	153.7	18.61	−8.99	0.32	360.8
132	4-fluorophenol	20.2	1	1	92.1	11.15	−9.27	−0.06	254.4
133	4-bromophenol	20.2	1	1	104.1	14.20	−9.31	−0.03	283.6
134	4-iodophenol	20.2	1	1	109.9	16.27	−8.84	−0.41	289.8
135	Benzyl methyl ketone	17.1	2	1	135.9	16.04	−9.71	0.07	320.4
136	Felodipine	64.6	6	5	300.8	37.97	−8.87	−0.18	588.5
137	Nisoldipine	110.5	8	8	322.2	40.34	−9.15	−0.73	628.4
138	Lacidipine	90.9	11	7	404.0	50.26	−8.91	−1.29	706.6
139	Trimethoprin	105.5	5	7	231.9	31.82	−8.73	−0.07	519.0
140	Prednisolone	94.8	5	5	274.7	37.85	−10.07	−0.42	527.4
141	Acetylsalicylic acid	63.6	3	4	139.6	17.65	−10.19	−0.54	355.9
142	Benzoic acid	37.3	1	2	102.0	13.15	−10.13	−0.53	278.6
143	Pramocaine	30.9	9	4	284.6	33.45	−8.78	0.24	595.7
144	Acetone	17.1	0	1	75.2	6.33	−10.76	0.80	206.7
145	4-aminophenol	46.3	2	2	90.1	12.83	−7.84	0.46	267.6
146	Methyl nicotinate	39.2	2	3	120.6	14.32	−10.44	−0.80	310.4
147	N,N-dimethylformamide	20.3	0	2	82.6	7.87	−9.26	1.36	228.9
148	Timolol	108.0	8	7	258.5	32.57	−9.24	−1.05	520.8
149	Bupivacaine	32.3	5	3	279.2	35.13	−7.46	−0.40	514.1
150	Prilocaine	41.1	5	3	214.0	26.73	−9.23	0.18	449.6
151	Atenolol	84.6	9	5	236.7	29.44	−9.30	−0.03	541.0
152	Propranolol	41.5	7	3	237.2	31.31	−8.62	−0.43	307.7
153	Pseudoefedrine	32.3	4	2	162.7	19.88	−9.44	0.29	371.4
154	Acebutolol	87.7	11	6	300.7	37.55	−9.15	−0.43	642.5
155	Alprenolol	41.5	9	3	247.5	29.75	−9.12	0.26	506.5
156	Metoprolol	50.7	10	4	258.7	30.55	−9.00	−0.27	569.8
157	Oxprenolol	50.7	10	4	255.2	30.45	−9.21	0.12	496.3
158	Albuterol	72.7	8	4	207.6	26.86	−8.97	0.16	474.7
159	Fluoxetine	21.3	6	2	266.7	31.67	−9.44	−0.39	541.6
160	Verapamil	64.0	13	6	429.4	52.28	−8.78	−0.95	817.4

were incorporated by forward stepwise multiple regression (Equation (9), Figure 1):

log K_p^EPI = −1.66 (±0.30) + 0.75 (±0.03) log k_IAM − 0.0034 (±0.002) PSA + 0.033 (±0.016) FRB − 0.089 (±0.035) HA + 0.0090 (±0.003) V_M − 0.092 (±0.021) α + 0.035 (±0.028) E_HOMO− 0.031 (±0.024) E_LUMO − 0.0022 (±0.0008) S_a
(n = 160, R² = 0.96, R²_adj. = 0.92, MSE = 0.043, F = 216.6, p < 0.01, s_e = 0.21)

(9)

The model (9) was validated using the holdout method in which data points are assigned to two sets usually called the training set and the test set. The size of each set is arbitrary (the test set is usually smaller than the training set). The group of 160 studied compounds was divided into two subsets: a training set (1 to 120) and a test set (121 to 160).The Equation (10) generated for the training set and containing the same independent variables as Equation (9) is as follows:

log K_p^EPI = −1.71 (±0.35) + 0.76 (±0.03) log k_IAM − 0.0042 (±0.002) PSA + 0.038 (±0.02) FRB − 0.074 (±0.035) HA + 0.0087 (±0.003) V_M − 0.11 (±0.02) α + 0.050 (±0.029) E_HOMO − 0.028 (±0.023) E_LUMO − 0.00053 (±0.00138) S_a
(n = 120, R² = 0.95, R²_adj. = 0.94, MSE = 0.032, F = 210.5, p < 0.01, s_e = 0.18)

(10)

The values of log K_p⁽¹⁰⁾ were calculated for the test set according to Equation (10) and plotted against the reference log K_p^EPI values to furnish a linear relationship (R² = 0.87). The model (9) was also tested on the subgroup of 20 compounds whose log K_p^exp values were available (16 compounds belonging to the training set and four compounds belonging to the test set).The resulting relationship between log K_p⁽⁹⁾ and log K_p^exp is linear, with R² = 0.90.

Equation (9), despite encouraging results of validation, was found unsatisfying because it seems over-parameterized; it contains nine independent variables whose contributions, apart from log k_IAM, α and PSA, are negligible (log k_IAM, α and PSA account for over 91% of the total variability and the remaining six variables for less than 4%).With so many independent variables, it is also difficult to avoid colinearity.A decision was made to simplify Equation (9) as much as possible; apart from log k_IAM, only two variables—PSA and α—seem to have a sufficient influence on log K_p to justify incorporating them in Equations (11)–(13) (Figure 2, Figure 3 and Figure 4).

log K_p^EPI = −2.22 (±0.04) + 0.75 (±0.03) log k_IAM − 0.042 (±0.004) α − 0.0096 (±0.0011) PSA
(n = 160, R² = 0.91, R²_adj. = 0.91, MSE = 0.052, F = 538.9, p < 0.01, s_e = 0.23)

(11)

logK_p^EPI = −2.24 (±0.05) + 0.91 (±0.03) logk_IAM − 0.070 (±0.003) α
(n = 160, R² = 0.87, R²_adj. = 0.87, MSE = 0.078, F = 524.7, p < 0.01, s_e = 0.28)

(12)

log K_p^EPI = −2.39 (±0.05) + 0.51 (±0.02) log k_IAM − 0.019 (±0.001) PSA
(n = 160, R² = 0.85, R²_adj. = 0.85, MSE = 0.088, F = 452.8, p < 0.01, s_e = 0.30)

(13)

The group of 160 studied compounds was divided into two subsets: a training set (1 to 120) and a test set (121 to 160). The Equations (14)–(16), generated for the training set and containing the same independent variables as Equations (11)–(13), are as follows:

log K_p^EPI = −2.17 (±0.05) + 0.79 (±0.03) log k_IAM − 0.0086 (±0.0012) PSA − 0.051 (±0.005) α
(n = 120, R² = 0.93, R²_adj. = 0.93, MSE = 0.042, F = 490.7, p < 0.01, s_e = 0.21)

(14)

log K_p^EPI = −2.17 (±0.05) + 0.95 (±0.03) log k_IAM − 0.077 (±0.004) α
(n = 120, R² = 0.90, R²_adj. = 0.89, MSE = 0.060, F = 500.1, p < 0.01, s_e = 0.25)

(15)

log K_p^EPI = −2.41 (±0.05) + 0.53 (±0.03) log k_IAM − 0.017 (±0.001) PSA
(n = 120, R² = 0.87, R²_adj. = 0.86, MSE = 0.077, F = 375.2, p < 0.01, s_e = 0.28)

(16)

The values of log K_p⁽¹⁴⁾, log K_p⁽¹⁵⁾, and log K_p⁽¹⁶⁾ were calculated for the test set according to Equations (14)–(16) and plotted against the reference log K_p^EPI values to furnish linear relationships (R² = 0.86, 0.79, and 0.83, respectively).The models (11), (12), and (13) were also tested on the subgroup of 20 compounds whose log K_p^exp values were available.The resulting relationships between log K_p⁽¹¹⁾, log K_p⁽¹²⁾, and log K_p⁽¹³⁾—as well as log K_p^exp—are linear, with R² = 0.88, 0.84, and 0.80, respectively.

Equation (13) involves log k_IAM, which encodes some important properties responsible for drugs’ absorption (lipophilicity and molecular size), but accounts for only 46% of the total log K_p variability and PSA, which is known to influence other absorption phenomena (e.g., transport through the blood–brain barrier and uptake from a gastrointestinal tract) [47,48,49]. A coefficient for PSA in Equation (13) is negative, which suggests (as already reported, e.g., for the blood–brain barrier passage or oral absorption) that compounds with large polar surface areas are not easily absorbed through skin.However, from the statistical point of view, Equation (11) is superior to Equations (12) and (13), and gives results comparable to those obtained using Equation (9) without the risk of overfitting.

3. Materials and Methods

3.1. IAM Chromatography

The chromatographic retention factors (log k_IAM) for the compounds analyzed in this study were compiled by Sprunger et al. [46]. They were obtained on a IAM.PC.DD2 HPLC column using an aqueous mobile phase buffered at pH ≤ 3 for carboxylic acids and in the pH range of 6.5 to 7.5 for other compounds.

3.2. Calculated Molecular Descriptors

The molecular descriptors for the compounds investigated during this study were calculated with HyperChem 8.0 utilizing the PM3 semi-empirical method with Polak–Ribiere’s algorithm: total dipole moment—DM (D), surface area (grid)—S_a (Ų), molecular weight—M_w (g mol⁻¹), energy of the highest occupied molecular orbital—E_HOMO (eV), and energy of the lowest unoccupied molecular orbital—E_LUMO (eV). Other physicochemical parameters (octanol-water partition coefficient—log P, polar surface area—PSA (Ų), H-bond donor count—HD, H-bond acceptor count—HA, polarizability—α (cm³), molar volume—V_M (cm³), and freely rotable bond count—FRB) were calculated using ACD/Labs 8.0 software. (N+O), which is the total nitrogen and oxygen atom count, was calculated from the molecular structures. The relevant calculated molecular descriptors are given in Table 2. Statistical analysis was done using Statistica v.13 or StatistiXL v.2.

4. Conclusions

Multiple regression models for predicting the skin permeability coefficient of structurally diverse compounds were developed.

Due to the limited availability of experimental permeability data for the solutes investigated in this study, the reference skin permeability coefficients were calculated according to a widely accepted theoretical model proposed by Potts. The values of log K_p obtained using this model are in good agreement with the experimental data for drug-like compounds.

The newly developed log K_p models are based on a set of IAM chromatographic and computational descriptors.The main descriptors, responsible for the variability of log K_p in MLR equations, are log k_IAM, polarizability (α), and polar surface area (PSA), and the MLR model gains very little in predictive power when other descriptors are incorporated. Linear relationships based on the IAM chromatographic retention factor and readily available calculated physico-chemical parameters give very good results and have the benefit of simplicity. The proposed models may be applied during the early steps of the drug discovery process when different drugs’ physico-chemical and biological properties are often studied in vitro using IAM chromatography and rapid predictions are required. IAM chromatographic and computational studies of the skin permeability of compounds may therefore be of interest to pharmaceutical and medicinal chemists, and to researchers in the area of environmental sciences since many compounds of environmental concern are absorbed through skin.