Immobilized Keratin HPLC Stationary Phase—A Forgotten Model of Transdermal Absorption: To What Molecular and Biological Properties Is It Relevant?

Abstract

Chromatographic retention data collected on immobilized keratin (KER) or immobilized artificial membrane (IAM) stationary phases were used to predict skin permeability coefficient (log K_p) and bioconcentration factor (log BCF) of structurally unrelated compounds. Models of both properties contained, apart from chromatographic descriptors, calculated physico-chemical parameters. The log K_p model, containing keratin-based retention factor, has slightly better statistical parameters and is in a better agreement with experimental log K_p data than the model derived from IAM chromatography; both models are applicable primarily to non-ionized compounds.Based on the multiple linear regression (MLR) analyses conducted in this study, it was concluded that immobilized keratin chromatographic support is a moderately useful tool for skin permeability assessment.However, chromatography on immobilized keratin may also be of use for a different purpose—in studies of compounds’ bioconcentration in aquatic organisms.

1. Introduction

Many chemicals enter the human body through the skin. Transdermal absorption is an important route of drugs’ administration, and it is also very important in the context of environmental toxicology, since undesired xenobiotics are often absorbed transdermally. The skin permeability coefficient K_p is defined according to Equation (1):

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

(1)

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

The experimental values of skin permeability coefficients are measured in vivo (on human volunteers), ex vivo (on excised human skin), or on animal models [1], but such data are difficult to obtain due to ethical and financial problems, and the results of experiments in this area are often inconsistent due to variations in properties of different skin samples, even taken from the same human or animal.

Apart from skin absorption, an important property of compounds of environmental concern is their bioconcentration factor in aquatic organisms (BCF). The bioconcentration factor is the ratio of the chemical concentration in the organism (C_B) and water (C_w), accounting for the absorption via the respiratory route (e.g., gills) and skin. It is used to assess the bioaccumulation potential of compounds [2], especially in the absence of their bioaccumulation factor (BAF),which accounts for dietary, dermal, and respiratory exposures. According to different regulatory agencies, different criteria of bioaccumulation apply: bioaccumulative compounds have BCF > 5000 or BCF > 2000 [3]. In the absence of BAF or BCF data, lipophilicity measured as the octanol-water partition coefficient K_ow is used to assess the compounds’ ability to bioaccumulate; if this is the case, the log K_ow threshold for bioaccumulative compounds is 5 [3,4], 4.5 [5], or 3.3 [6]. Measured and estimated bioaccumulation data are also used to assign chemicals to three bioaccumulation categories: not significantly bioaccumulative (BCF or BAF < 1000), bioaccumulative (BCF or BAF between 1000 and 5000), and highly bioaccumulative (BCF or BAF > 5000) [7].

The ethical and financial problems related to BCF determination are similar to those encountered during K_p measurements. In in vivo experiments, the need to use human volunteers or lab animals, as well as the experiment timing, are the main limitations, and, for this reason, both K_p and BCF are frequently assessed in vitro (using cell/tissue assays or non-cell models based on chromatography or electrochromatography) or in silico (calculations that can provide valuable information even without the access to compounds’ samples) [8,9,10].

Biomimetic chromatography essentially involves the application of stationary phases, containing proteins or phospholipids, or mobile phases, including micelles or microemulsions [11,12,13,14]. The components of biomimetic chromatographic systems (stationary or mobile phases) are designed to mimic some elements or functions of biomembranes and the interactions between these components and studied molecules resemble transport and partition phenomena encountered in a living being.

Immobilized artificial membrane (IAM) chromatography, with stationary phases containing adsorbed or covalently bound phosphatidylcholine (or, more recently, sphyngomyelin) groups, is used in modern lipohilicity studies, as well as in investigations of compounds’ affinity for phospholipids, related to many biological properties of solutes [15,16,17]. Chromatography on immobilized protein stationary phases was originally developed to separate enantiomers [18]; apart from that, some protein-based stationary phases simulate the interaction between a molecule and main plasma proteins, such as human serum albumin (HSA) [19,20,21,22] or α₁ acid glycoprotein (AGP) [21,23,24,25]. Retention data obtained from chromatography in biomimetic systems are used to predict ADME (absorption, distribution, metabolism, and excretion) properties of compounds in early drug discovery phases [11,26], as well as their environmental impact—mobility in soil, bioconcentration/bioaccumulation, or aquatic toxicity [27,28,29,30,31]. Elements of natural biomembranes, incorporated in chromatographic systems used in pharmacokinetic studies, include also cholesterol or amide moieties [32,33].

Chromatographic descriptors have been used in skin permeability studies for many years, and separation (chromatographic or electrochromatographic) techniques used in these studies are liquid chromatography (HPLC or TLC), biopartitioning micellar chromatography, micellar electrokinetic chromatography, liposome electrokinetic chromatography, and two-dimensional gas chromatography (GC × GC) [34,35,36,37,38,39,40,41,42,43,44,45,46,47].

The relationships between the IAM chromatographic retention factor (k_IAM) and the skin permeability coefficient have been studied most frequently for small groups of compounds (n = 10 to 32), and the resulting dependencies are mostly univariate (linear or quadratic) [35,36,39,41], the exceptions being the studies in which additional variables, e.g., McGowan’s characteristic volume V or the octanol-water partition coefficient log K_ow [33,35,36] were incorporated. In our earlier study [48] conducted for a large group of structurally unrelated compounds (n = 160), we demonstrated that log k_IAM accounts for ca. 46% of total log K_p variability, and the parameters whose contribution to log K_p predictions is also significant are polar surface area (PSA) or polarizability (α).

Bioconcentration of compounds in aquatic organisms can be studied in vitro using descriptors derived from HPLC chromatography on C₁₈, C₈, C₂, and phenyl-bonded silica sorbents (aromatic hydrocarbons [49]), C₁₈ and cyanopropyl- and phenyl-bonded silica (aromatic hydrocarbons, alkylbenzenes, chlorinated benzenes, phthalates, nitroaromatics, phenols, and aniline [50]), and RP-18 TLC (organic sunscreens and cosmetic preservatives [51]).

More recently, the bioconcentration of compounds in aquatic organisms has been investigated using chromatography on IAM stationary phases, developed initially to mimic molecule–biomembrane interactions in ADME studies [31,52]. Earlier research pointed to the importance of additional parameters, incorporated alongside log k_IAM: (i) a biodegradation estimate, BioWin5, calculated using the EPISuite^TM software and (to a lesser extent) topological polar surface area (TPSA) [52]; (ii) TPSA—the fraction of sp³ carbon atoms (F_Csp3) and hydrogen bond donor count (#HD) [31].

Turowski and Kaliszan postulated that predicting skin permeability of compounds should be based on molecules’ lipophilicity and interactions with keratin, which is an important constituent of the outmost layer of the epidermis [34]. An immobilized keratin-based stationary phase, developed by Turowski and Kaliszan, was initially proposed to be an in vitro tool in investigations of solutes′ skin permeability (log K_p) [34]. However, it was discovered that the retention factor obtained on this sorbent (log k_KER) is not a sufficiently good predictor of skin permeability coefficient, and it cannot be used as a sole descriptor in log K_p models. Turowski and Kaliszan reported that this descriptor can be combined with the chromatographic retention factor obtained by immobilized artificial membrane chromatography (log k_IAM), and the results of log K_p predictions using multiple linear regression (MLR) models satisfy (Equation (2)):

log K_p = −6.56 + 1.92 log k_IAM − 1.04 log k_KER (n = 17, R² = 0.86)

(2)

Turowski and Kaliszan concluded that skin permeability increases with the lipophilicity of solutes (encoded primarily by log k_IAM) and decreases with their affinity for keratin (expressed as log k_KER). Unfortunately, the model they proposed (Equation (2)) requires two sets of chromatographic data, obtained on different stationary phases, this being the likely reason why the immobilized keratin stationary phase they proposed has never become widely popular and, to the best of our knowledge, it is not commercially available.

In this study, a novel application of immobilized keratin stationary phases developed by Turowski and Kaliszan is proposed, and chromatography on immobilized keratin sorbent is used to model compounds’ bioconcentration in aquatic organisms.

2. Materials and Methods

2.1. IAM and Immobilized Keratin Chromatography

The chromatographic retention factors for the compounds analyzed in this study (

Table 1. Chromatographic retention factors and calculated physico-chemical properties of compounds 1 to 32.

No.	Compound	log kKER	log kIAM	Mw	#HvAt	#ArHvAt	FCsp3	#FRB	#HA	#HD	MR	TPSA	(N + O)	log Kow	log S
1	2-Cresole	−0.18	0.36	108.1	8	6	0.14	0	1	1	33.4	20.2	1	1.95	−2.29
2	2-Naphtol	0.88	1.25	144.2	11	10	0	0	1	1	46.0	20.2	1	2.70	−3.11
3	3-Cresole	−0.22	0.36	108.1	8	6	0.14	0	1	1	33.4	20.2	1	1.96	−2.30
4	3-Nitrophenol	0.24	0.60	139.1	10	6	0	1	3	1	37.3	66.1	4	2.00	−2.34
5	4-Bromophenol	0.34	1.00	173.0	8	6	0	0	1	1	36.2	20.2	1	2.59	−3.10
6	4-Chlorophenol	0.27	0.73	128.6	8	6	0	0	1	1	33.5	20.2	1	2.39	−2.70
7	4-Cresole	−0.08	0.42	108.1	8	6	0.14	0	1	1	33.4	20.2	1	1.94	−2.29
8	4-Ethylphenol	−0.25	0.76	122.2	9	6	0.25	1	1	1	38.2	20.2	1	2.58	−2.65
9	4-Nitrophenol	0.19	0.60	139.1	10	6	0	1	3	1	37.3	66.1	4	1.91	−2.28
10	Baclofen	−0.33	−0.73	213.7	14	6	0.3	4	3	2	55.3	63.3	3	−0.96	−0.61
11	Chlorocresole	0.68	1.18	142.6	9	6	0.14	0	1	1	38.4	20.2	1	2.70	−3.09
12	Methylparaben	0.04	0.52	152.2	11	6	0.12	2	3	1	39.7	46.5	3	1.96	−2.29
13	Phenol	−0.27	0.37	94.1	7	6	0	0	1	1	28.5	20.2	1	1.46	−1.98
14	Phenylalanine	−0.20	−0.65	165.2	12	6	0.22	3	3	2	45.5	63.3	3	−1.44	−0.08
15	Resorcinol	−0.38	−0.14	110.1	8	6	0	0	2	2	30.5	40.5	2	0.80	−1.58
16	Salcylic acid	−0.06	−0.58	138.1	10	6	0	1	3	2	35.4	57.5	3	2.26	−2.50
17	Thymol	0.52	1.34	150.2	11	6	0.4	1	1	1	48.0	20.2	1	3.30	−3.19
18	1,2,3-tris(1-methylethyl)benzene	0.75	2.43	204.4	15	6	0.6	3	0	0	70.2	0.0	0	6.36	−4.54
19	1,4-dinitrobenzene	0.45	0.16	168.1	12	6	0	2	4	0	44.1	91.6	6	1.46	−2.04
20	3-(trifluoromethyl)phenol	0.19	1.23	162.1	11	6	0.14	1	4	1	33.5	20.2	1	2.95	−3.04
21	4-cyanophenol	−0.05	0.77	119.1	9	6	0	0	2	1	33.2	44.0	2	1.60	−2.08
22	4-iodophenol	0.80	1.59	220.0	8	6	0	0	1	1	41.2	20.2	1	2.91	−3.59
23	4-nitrobenzoic acid	−0.23	−0.23	167.1	12	6	0	2	4	1	42.2	83.1	5	1.89	−2.30
24	Anizole	−0.09	0.31	108.1	8	6	0.14	1	1	0	32.9	9.2	1	2.11	−2.33
25	Benzamide	−0.04	−0.10	121.1	9	6	0	1	1	1	34.5	43.1	2	0.64	−1.42
26	benzene	−0.27	0.09	78.1	6	6	0	0	0	0	26.4	0.0	0	2.13	−2.41
27	benzoic acid	−0.21	−0.74	122.1	9	6	0	1	2	1	33.4	37.3	2	1.87	−2.20
28	Benzonitrile	0.02	0.15	103.1	8	6	0	0	1	0	31.2	23.8	1	1.56	−2.02
29	caffeine	0.08	−0.40	194.2	14	9	0.38	0	3	0	52.0	61.8	6	−0.07	−1.48
30	Chlorobenzene	0.13	0.66	112.6	7	6	0	0	0	0	31.5	0.0	0	2.84	−2.96
31	Indazole	0.23	0.71	118.1	9	9	0	0	1	1	36.1	28.7	2	1.77	−2.72
32	Toluene	−0.05	0.44	92.1	7	6	0.14	0	0	0	31.4	0.0	0	2.73	−2.77

) were taken from [34]. They were obtained on: (i) an IAM.PC.MG HPLC column purchased from Regis (150 × 4.6 mm, particle diameter 12 μm, pore diameter 300 Å) with a phosphate buffer (pH 6.0), including acetonitrile (95:5 v/v) mobile phase (flow rate—1 mL min⁻¹); (ii) physically immobilized keratin sorbent with pH 4.2 phosphate buffer as a mobile phase (column dimensions—125 × 4 mm; flow rate—1 mL min⁻¹). The mobile phase used in keratin chromatography (pH 4.2 buffer) was selected on the basis of QSRR studies as giving the “best” relationship between log k_KER and structural descriptors (molecular weight and dipole moment) [34].

2.2. Calculated Molecular Descriptors

Molecular weight (M_w), heavy atom count (#HvAt), aromatic heavy atom count (#ArHvAt), fraction of sp³ carbons (F_Csp3), rotatable bond count (#FRB), hydrogen donor count (#HD), hydrogen acceptor count (#HA), molecular refractivity (MR), aqueous solubility (log S), and topological polar surface area (TPSA) were calculated using Swiss ADME software available freely on-line [53]. The octanol–water partition coefficient (log K_ow) was predicted using EpiSuite [54]. Total counts of nitrogen and oxygen atoms (N + O) were calculated manually on the basis of compounds’ molecular formulas (Table 1).

2.3. Reference Values of Skin Permeability Coefficient (log K_p) and Bioconcentration Factor (log BCF)

The experimentally determined values of log K_p and log BCF are available for only some compounds within the studied group. For this reason, the models of skin permeability and bioconcentration factor, involving chromatographic and calculated descriptors, were generated and validated using log K_p and log BCF values obtained in silico with the EpiSuite v. 4.1 software (log K_p^EPI—DERMWIN v. 2.02 and log BCF_EPI—BCFBAF v. 3.02 modules, respectively), recommended by the US Environmental Protection Agency [54,55] and tested on sub-groups of solutes whose experimental log K_p or log BCF values are known (log K_p^exp, log BCF_exp) [56,57]. The estimation methodology used by DERMWIN is based on an algorithm developed by Potts [58], and the estimations provided by BCFBAF are based on methodology developed by Meylan [59] and Arnot and Gobas [3]. The values of log K_p^EPI and log BCF_EPI obtained using EpiSuite are given in

Table 2. Reference (EPI), predicted, and experimental values of log K_p.

	log KpEPI	Equation (6)	Equation (7)	Equation (8)	Equation (9)	log Kpexp
2-Cresole	−5.58	−5.71	−5.67	−5.89	−5.57	−5.36
2-Naphtol	−5.26	−4.99	−5.00	−5.05	−5.26	−4.76
3-Cresole	−5.57	−5.71	−5.75	−5.89	−5.65	−5.37
3-Nitrophenol	−5.73	−6.22	−6.06	−6.01	−5.98	−5.81
4-Bromophenol	−5.52	−5.20	−5.74	−5.30	−5.74	−5.00
4-Chlorophenol	−5.39	−5.42	−5.18	−5.55	−5.09	−5.00
4-Cresole	−5.58	−5.67	−5.50	−5.84	−5.39	−5.31
4-Ethylphenol	−5.21	−5.39	−5.88	−5.52	−5.80	−5.01
4-Nitrophenol	−5.79	−6.22	−6.15	−6.01	−6.08	−5.81
Baclofen	−8.28	−7.25	−7.66	−7.23	−7.69
Chlorocresole	−5.05	−5.05	−4.53	−5.12	−4.43	−4.82
Methylparaben	−5.84	−5.98	−6.09	−5.94	−6.02	−5.63
Phenol	−5.84	−5.71	−5.76	−5.89	−5.65	−5.61
Resorcinol	−6.40	−6.43	−6.48	−6.52	−6.40	−6.63
Thymol	−4.87	−4.92	−4.66	−4.97	−4.56	−4.77
1,2,3-tris(1-methylethyl)benzene	−3.78	−3.73	−4.13	−3.80	−4.06
1,4-dinitrobenzene	−6.29	−6.96	−6.38	−6.61	−6.32
3-(trifluoromethyl)phenol	−5.19	−5.01	−5.44	−5.07	−5.38
4-cyanophenol	−5.89	−5.74	−5.96	−5.68	−5.86	−5.73
4-iodophenol	−5.58	−4.71	−5.64	−4.74	−5.70
Anizole	−5.46	−5.59	−5.29	−5.86	−5.18
Benzamide	−6.58	−6.43	−5.96	−6.50	−5.86
Benzene	−5.26	−5.63	−5.22	−6.00	−5.09	−4.51
Benzonitrile	−5.82	−5.94	−5.31	−6.12	−5.19
Caffeine	−7.53	−6.96	−7.38	−6.91	−7.66	−7.56
Chlorobenzene	−4.97	−5.17	−4.92	−5.47	−4.81
Indazole	−5.44	−5.56	−5.94	−5.63	−6.11
Toluene	−4.92	−5.35	−4.92	−5.68	−4.78	−3.64

and

Table 3. Reference, predicted, and experimental values of log BCF.

	log BCFEPI	Equation (10)	Equation (11)	Equation (12)	Equation (13)	log BCFexp
2-Cresole	0.95	1.13	0.97	1.01	0.98	1.03
2-Naphtol	1.45	1.47	1.48	1.43	1.45
3-Cresole	0.96	1.13	0.94	1.01	0.94	1.23
3-Nitrophenol	0.99	0.85	0.64	0.98	0.67
4-Bromophenol	1.38	1.31	1.44	1.23	1.52	1.17
4-Chlorophenol	1.24	1.14	1.29	1.03	1.37	1.42
4-Cresole	0.95	1.17	1.04	1.06	1.06
4-Ethylphenol	1.37	1.55	1.11	1.52	1.10
4-Nitrophenol	0.93	0.85	0.60	0.98	0.63	0.71
Baclofen	0.50	0.51	0.99	0.53	0.90
Chlorocresole	1.45	1.64	1.77	1.63	1.90
Methylparaben	0.96	1.08	0.93	1.12	0.94
Phenol	0.63	0.92	0.71	0.76	0.71
Phenylalanine	0.50	0.44	0.70	0.44	0.65
Resorcinol	0.50	0.51	0.37	0.40	0.34
Salcylic acid	0.50	0.17	0.50	0.09	0.50
Thymol	1.84	2.13	2.03	2.23	2.12	1.48
1,2,3-tris(1-methylethyl)benzene	3.86	3.20	3.41	3.40	3.49
1,4-dinitrobenzene	0.63	0.46	0.62	0.67	0.65
3-(trifluoromethyl)phenol	1.61	1.67	1.23	1.67	1.30
4-cyanophenol	0.72	1.06	0.65	1.09	0.66	0.91
4-iodophenol	1.59	1.67	1.96	1.68	2.10
4-nitrobenzoic acid	0.50	0.27	0.21	0.37	0.15
Anizole	1.06	1.15	1.20	0.96	1.23
Benzamide	0.50	0.53	0.72	0.43	0.73
Benzene	1.07	0.84	0.98	0.53	1.00
Benzoic acid	0.50	0.16	0.66	−0.06	0.65	0.93
Benzonitrile	0.70	0.77	0.96	0.60	1.00
Caffeine	0.50	0.84	0.63	0.93	0.48
Chlorobenzene	1.54	1.19	1.45	0.95	1.52	1.34
Indazole	0.83	1.09	0.67	1.03	0.61
Toluene	1.47	1.27	1.33	1.05	1.37	1.02

.

2.4. Statistical Tools

Multiple linear regression (MLR) models were generated using Statistica v. 13 by StatSoft Polska, Kraków, Poland, and this refers to the stepwise forward regression mode.

The models considered in this study were evaluated using the following procedures:

• Cross-validation was performed, with n compounds from the initial training set split into 2 subsets, one of which was used to train a new model and the remaining one to test it. After cross-validation, the RMSEP (root mean squared error of prediction) for the particular N-compound test subset was calculated as follows (Equation (3)):

$$RMSEP=\sqrt{\frac{\sum _{i=1}^N{\left(y_i^{pred}-y_i^{ref}\right)}^2}{N}}$$

(3)

• Comparison of the predicted log K_p^pred and log BCF_pred values (calculated for the compounds, whose experimental log K_p^exp and log BCF_exp data are available) was performed, and these data were analyzed using the squared coefficient of determination (R²_exp).

3. Results

3.1. Keratin vs. IAM HPLC Skin Permeability Models

In this study, we compared the log K_p models obtained using log k_IAM and TPSA (Equation (4)) with the models including log k_KER as a chromatographic parameter (Equation (5)).

log K_p = −5.61 (±0.24) + 0.68 (±0.17) log k_IAM − 0.014 (±0.005) TPSA
(n = 32, R² = 0.63, R²_adj. = 0.63, R²_exp = 0.72, F = 25.1, p< 0.01)

(4)

log K_p = −2.56 (±0.83) +1.74 (±0.38) log k_KER − 0.011 (±0.008) M_w
− 0.22 (±0.11) #ArHvAt − 0.014 (±0.005) TPSA
(n = 32, R² = 0.68, R²_adj. = 0.63, R²_exp= 0.73, F = 14.3, p< 0.01)

(5)

It was observed that neither Equation (4), nor (5), gives satisfying results of log K_p predictions for relatively strongly ionized solutes (compounds 14, 16, 23, and 27); when these compounds were excluded from the analysis, Equations (6) and (7) were obtained for a group of 28 neutral, basic, or weakly acidic compounds (Figure 1 and Figure 2, Table 2).

log K_p = −5.70 + 0.81 (±0.17) log k_IAM− 0.015 (±0.004) TPSA
(n = 28, R² = 0.80, R²_adj. = 0.78, R²_exp = 0.73, F = 49.7, p< 0.01)

(6)

log K_p = −2.73 (±0.54) +1.80 (±0.26) log k_KER − 0.015 (±0.003) M_w + 0.13 (±0.05) #HvAt − 0.27 (±0.07) #ArHvAt − 0.020 (±0.004) TPSA
(n = 28, R² = 0.85, R²_adj. = 0.81, R²_exp = 0.79, F = 24.8, p< 0.01)

(7)

The likely reason for such discrepancies between the predicted (Equations (4) and (5)) and reference values of log K_p for relatively strongly ionizable compounds is that the reference model has also its limitations: it overestimates the results for very hydrophilic molecules, underestimates the values for non-hydrogen bonding solutes, and fails for extremely lipophilic compounds or solutes having a very high tendency to hydrogen bonding [60,61,62].

At this point, the group of 28 studied compounds was divided into two subsets: a training set (1 to 20) and a test set (21 to 28). Equations (8) and (9) generated for the training set, and containing the same sets of independent variables as Equations (6) and (7), are as follows (Table 2):

log K_p = −6.09 (±0.27) + 0.94 (±0.17) log k_IAM − 0.0073 (±0.005) TPSA
(n = 20, R² = 0.80, R²_adj. = 0.78, RMSEP = 0.51, F = 34.2, p< 0.01)

(8)

log K_p = −1.93 (±0.54) +1.85 (±0.28) log k_KER − 0.017 (±0.003) M_w + 0.15 (±0.05) #HvAt − 0.37 (±0.11) #ArHvAt − 0.021 (±0.004) TPSA
(n = 20, R² = 0.87, R²_adj. = 0.83, RMSEP = 0.44, F = 19.0, p< 0.01)

(9)

3.2. Keratin HPLC Models of Bioconcentration Factor

According to our earlier research, the bioconcentration factor log BCF can be predicted using log k_IAM and two additional parameters: F_Csp3 and TPSA [31]. The predictive potential of Equation (10) (Figure 3) is compared to that of a model based on chromatographic retention factors obtained using immobilized keratine as a stationary phase (Equation (11), Figure 4).

log BCF = 0.79 (±0.11) + 0.62 (±0.07) log k_IAM + 1.53 (±0.31) F_Csp3
− 0.0046 (±0.0021) TPSA
(n = 32, R² = 0.87, R²_adj. = 0.86, R²_exp = 0.41, F = 63.9, p < 0.01)

(10)

log BCF = 1.23 (±0.34) + 0.70 (±0.15) log k_KER − 0.18 (±0.05)
#ArHvAt + 0.039 (±0.006) MR − 0.017 (±0.002) TPSA
(n = 32, R² = 0.88, R²_adj. = 0.86, R²_exp = 0.69, F = 50.3, p < 0.01)

(11)

At this point, the group of 32 studied compounds was divided into two subsets: a training set (1 to 20) and a test set (21 to 32). Equations (12) and (13) generated for the training set, and containing the same sets of independent variables as Equations (10) and (11) are as follows:

log BCF = 0.46 (±0.15) + 0.75 (±0.09) log k_IAM + 1.84 (±0.34) F_Csp3
+ 0.0010 (±0.0028) TPSA
(n = 20, R² = 0.93, R²_adj. = 0.92, RMSEP = 0.36, F = 72.2, p < 0.01)

(12)

log BCF = 1.59 (±0.57) + 0.85 (±0.20) log k_KER − 0.22 (±0.08)
#ArHvAt + 0.037 (±0.007) MR − 0.018 (±0.003) TPSA
(n = 20, R² = 0.90, R²_adj. = 0.88, RMSEP = 0.23, F = 35.1, p < 0.01)

(13)

4. Discussion

In our study, we investigated the possibility of using log k_KER in skin permeability models, alongside additional descriptors that were either not considered or not available when the keratin stationary phase was originally developed. We studied correlations between log k_KER and the key physico-chemical properties associated with compounds’ ability to cross biological barriers (

Table 4. Correlations ^® between chromatographic and calculated parameters (n= 32).

	log kKER	log kIAM	Mw	#HvAt	#ArHvAt	FCsp3	#FRB	#HA	#HD	MR	TPSA	log Kow	log S
log kKER	1.00	0.75	0.48	0.26	0.33	0.15	−0.07	−0.15	−0.25	0.45	−0.16	0.57	−0.67
log kIAM	0.75	1.00	0.20	0.00	0.06	0.26	−0.19	−0.42	−0.31	0.26	−0.54	0.81	−0.85
Mw	0.48	0.20	1.00	0.77	0.12	0.43	0.57	0.43	0.18	0.80	0.39	0.01	−0.09
#HvAt	0.26	0.00	0.77	1.00	0.25	0.62	0.75	0.56	0.13	0.89	0.54	−0.08	0.11
#ArHvAt	0.33	0.06	0.12	0.25	1.00	0.03	−0.24	−0.02	−0.09	0.24	0.02	−0.09	−0.05
FCsp3	0.15	0.26	0.43	0.62	0.03	1.00	0.46	−0.09	−0.12	0.75	−0.16	0.21	−0.13
#FRB	−0.07	−0.19	0.57	0.75	−0.24	0.46	1.00	0.49	0.25	0.66	0.48	−0.18	0.30
#HA	−0.15	−0.42	0.43	0.56	−0.02	−0.09	0.49	1.00	0.38	0.18	0.87	−0.45	0.45
#HD	−0.25	−0.31	0.18	0.13	−0.09	−0.12	0.25	0.38	1.00	0.00	0.37	−0.42	0.40
MR	0.45	0.26	0.80	0.89	0.24	0.75	0.66	0.18	0.00	1.00	0.23	0.16	−0.14
TPSA	−0.16	−0.54	0.39	0.54	0.02	−0.16	0.48	0.87	0.37	0.23	1.00	−0.57	0.57
log Kow	0.57	0.81	0.01	−0.08	−0.09	0.21	−0.18	−0.45	−0.42	0.16	−0.57	1.00	−0.96
log S	−0.67	−0.85	−0.09	0.11	−0.05	−0.13	0.30	0.45	0.40	−0.14	0.57	−0.96	1.00

) and discovered that log k_KER encodes primarily lipophilicity (log K_ow) and aqueous solubility (log S), which are important factors governing the ability of compounds to cross the skin barrier, but the correlations are moderate.

Predictive models of log K_p, involving retention parameters obtained on immobilized keratin (Equations (7) and (9)), have similar (or, in fact, slightly better) statistical parameters compared to those reported for models based on IAM chromatography (Equations (6) and (8)). Log K_p values predicted using Equation (7) are in a slightly closer agreement with experimental log K_p^exp data available for a subset of 18 compounds than those calculated using Equation (6). It must be noted, however, that, in the process of descriptors’ selection by forward stepwise regression, chromatographic parameters log k_KER and log k_IAM behave differently. Log k_IAM (Equation (6)) is selected first, and it accounts for ca. 66% of total log K_p variability; log k_KER (Equation (7)) is selected second (after TPSA), and it accounts for just 16% of total log K_p variability.

The significance of log k_KER as an independent variable is much higher in models of bioconcentration factor log BCF. In Equation (11), log k_KER is the most important independent variable, accounting for 39% of total log K_p variability; further variables (selected as follows: TPSA, MR, and #ArHvAt) account for 24, 18, and 7% of total log K_p variability, respectively. In the IAM chromatography-based model of log BCF (Equation (10)), log k_IAM accounts for 73%, and other independent variables (F_Csp3 and TPSA) account for 12 and 2% of total log K_p variability, respectively. The keratin chromatographic retention-based model (11) has statistical parameters similar to those of Equation (10), derived from IAM chromatography; however, Equation (11) seems to fit the experimental data (log BCF_exp) reported for a subset of 10 compounds better than Equation (10).

5. Conclusions

Immobilized keratine-based chromatographic stationary phase was developed in the late 1990s to help in in vitro investigations of compounds’ transdermal absorption. A new model of a skin permeability coefficient was developed in the current study, which involves the chromatographic retention factor measured on the immobilized keratine sorbent (log k_KER) and four additional independent variables (Equation (7)). This model has slightly better statistical parameters and is in a better agreement with experimental log K_p data than the model derived from IAM chromatography (Equation (6)); both models are applicable primarily to non-ionized compounds (with carboxylic acids removed from Equations (4) and (5)). Based on the MLR analyses conducted in this study, it was concluded that immobilized keratin chromatographic support is a moderately useful tool for skin permeability assessment. However, similarly to IAM chromatography in the past, chromatography on immobilized keratin may serve a different purpose; designed for applications in pharmacokinetic studies, it may also be of use in the realm of environmental science, in studies of compounds’ bioconcentrations in aquatic organisms.