Anal. Chem. 1998, 70, 4228-4234
Rapid Gradient RP-HPLC Method for Lipophilicity Determination: A Solvation Equation Based Comparison with Isocratic Methods Chau My Du,*,† Klara Valko,‡ Chris Bevan,‡ Derek Reynolds,‡ and Michael H. Abraham†
Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom, and Physical Sciences, GlaxoWellcome Medicines Research Centre, Stevenage, Herts SG1 2NY, United Kingdom
The chromatographic hydrophobicity index (CHI) obtained from high-throughput gradient elution reversedphase HPLC with ODS column and acetonitrile mobile phase has been shown to be well correlated with log k values obtained by isocratic elution in the same system; between CHI and log k50, the correlation coefficient was 0.99 for a very diverse set of 55 compounds. CHI and log k50 are moderately correlated with log P (water/ octanol), and both can be used as alternative measures of lipophilicity. Analyses using the general solvation equation of Abraham shows that the solute factors that influence CHI and log k50 are not entirely the same as those that influence log P, so that neither CHI nor log k50 can be used as a direct measure of log P and vice versa. However, the factors that influence CHI are qualitatively and quantitatively the same as those that influence log k50, so that the rapidly determined CHI indexes encode exactly the same information as do isocratic log k values. Lipophilicity is an important property of molecules in relation to their biological activity.1,2 Its application has been shown in connection with blood/brain barrier distribution of drugs and intestinal absorption.3,4 It is modeled simply by partition of a solute between two immiscible liquid phases. The octanol/water (log P) showed good correlation with biological transport processes.1 A recent monograph5 provides an overview of the role of lipophilicity in drug action. The traditional “shake flask” method used in obtaining partition was unable to meet the high demand for gaining log P values with respect to the quantity, purity of the samples, and automation of the measurements. High-performance liquid chromatography in reversed-phase separation mode (RP-HPLC) has been used for lipophilicity determination for a long time, as mostly hydrophobic forces dominate the retention process. Several approaches have †
University College London. GlaxoWellcome Medicines Research Centre. (1) Hansch, C.; Fujita, T. J. Am. Chem. Soc. 1964, 86, 1616-1625. (2) Leo, A. J.; Hansch, C.; Elkins, D. Chem. Rev. 1971, 71, 525-616. (3) Seiler, P. Eur. J. Med. Chem. 1974, 9, 473-479. (4) Hansch, C.; Kutter, E. Absorption, distribution and metabolism of drug. In Quantitative Structure-Activity Relationships of Drugs; Topliss, J. G., Ed.; Academic Press: London, 1983; p 437. (5) Mannhold, R., Kubinyi, H., Timmerman, H., Eds. Lipophilicity in Drug Action and Toxicology; VCH: Weinheim, 1996. ‡
4228 Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
been published about the application of the RP-HPLC method to obtain lipophilicity data and correlate them with log P values.6-9 Lipophilicity Indexes log k and log kw. In RP-HPLC, the retention time is in correlation with the proportion of the molecules in the mobile and stationary phases as described by the following equation:
log
(tR - t0) ) log k ) log K + log(Vs/Vm) t0
(1)
where tR and t0 are the retention time and dead time, respectively; k is the retention factor, K is the equilibrium constant, equivalent to the partition coefficient of the compound between the mobile and the stationary phases; and log(Vs/Vm) is the phase ratio (volume of the two partitioning phases). With log k, only a limited range of lipophilicity measurements can be obtained for one mobile phase composition. To cover a range of solutes with different lipophilicity, several mobile phase compositions are required. By plotting the organic phase concentrations and the corresponding log k values for each compound, the extrapolated log kw values can be calculated and used as an estimate of the log k value of a compound at 0% organic phase. These values are quite often outside the measurable retention time range. To date, log kw is the most widely used chromatographic lipophilicity parameter.10 Recently, two other reversed-phase retention parameters have been introduced,11,12 φ0 and CHI (chromatographic hydrophobicity index). Lipophilicity Indexes φ0 and CHI. The φ0 index is the volume percent of organic phase concentration in the mobile phase by which the retention time is twice the dead time, which means log k ) 0. Compounds with higher hydrophobic character require a much higher organic phase concentration to allow log k ) 0 at a relatively short retention time. The higher the φ0, the more (6) Lambert, W. J. J. Chromatogr. A 1993, 656, 469-484. (7) Valko, K. J. Liq. Chromatogr. 1987, 7, 1405-1424. (8) Unger S. H.; Cook, J. R.; Hollenberg, J. S. J. Pharm. Sci. 1978, 67, 13641366. (9) Mirrlees, M. S.; Moulton, S. C.; Murphy, T.; Taylor, P. J. J. Med. Chem. 1976, 19, 615-619. (10) Harnisch, M.; Mockel, H. J.; Schulze, G. J. J. Chromatogr. 1983, 282, 315-328. (11) Valko, K.; Slegel, P. J. Chromatogr. 1993, 631, 49-61. (12) Valko, K.; Bevan, C.; Reynolds, D. Anal. Chem. 1997, 69, 2022-2029. S0003-2700(98)00435-1 CCC: $15.00
© 1998 American Chemical Society Published on Web 09/12/1998
lipophilic is the compound. The advantage of using φ0 is that it is more applicable to interlaboratory and column-to-column comparison than log kw, and it shows a significant correlation to the traditional octanol/water partition coefficients for a large number of structurally unrelated compounds.11 The φ0 values can be calculated from the intercept (log kw) and the slope (S) of the straight line plots of log k values with organic phase concentrations in the mobile phase, eq 2. For most compounds, the value lies between 0 and 100%; compounds that fall outside this region are those which are highly hydrophobic (i.e., log k > 0 with 100% organic phase) or very hydrophilic (i.e., log k < 0 with water only as mobile phase). The chromatographic hydrophobicity index (CHI), introduced recently,12 puts the gradient retention time onto an organic phase concentration (φ0) scale using a calibration set of compounds. Both φ0 and CHI are parameters designed to measure lipophilicity of compounds, and they are derived from the solvent strength needed to elute the compound from a reversed-phase HPLC column. They differ in their method of measurement: φ0 is derived from a series of isocratic measurements,11 while CHI is derived from the retention time in a calibrated generic gradient HPLC experiment12 and was introduced as a high-throughput method for lipophilicity determination. The absolute magnitude of the parameter CHI is dependent on the values assigned to the set of standards used to calibrate the gradient, and in the defined protocol12 they have been carefully selected to align the φ0 and CHI scales as closely as possible. Theory shows that there is a defined dependence of φ0 and CHI on the retention of the solute extrapolated to elution with no organic modifier present (log kw), as well as the rate of change in log k with increasing fraction of organic modifier in the eluent, the slope, S.5 The relationships are
φ0 ) -log kw/S
(2)
CHI ) AtR + B
(3)
and
Here, A and B are the constants of a linear plot of CHI values assigned for a determined set of standards against their gradient retention times. The constants, A and B, are used to calibrate the gradient system. The gradient retention time also can be related to kw and S according to eq 4.13
tR ) (t0/S) log(2.3kwSt0 + 1/tg) + t0 + tD
(4)
Here, tR is the isocratic elution retention time, t0 is the column dead time, tD is the dwell time for gradient elution, and tg is the gradient time taken from 0 to 100% organic modifier concentration. It would be very convenient if the high-throughput fast gradient elution could be adopted in preference to isocratic elution as a lipophilicity index. The major aim of this work is to ascertain the similarities and differences between CHI and retention data (log k, log kw) obtained by the isocratic method. In particular, (13) Quarry, M. A.; Grob, R. L.; Snyder, L. R. Anal. Chem. 1986, 58, 907-917.
we wish to compare the information encoded in CHI values with information contained in isocratic retention data. To accomplish these aims, we need a procedure that will allow the various factors that influence retention data to be evaluated; the general solvation equation14 is such a procedure. Linear Free Energy Relationship Solvation Equation. Hydrophobicity or lipophilicity is a complex property of a molecule. It has already been shown that several molecular factors play an important role in the overall lipophilic character of compounds. One such model that has been used is the general solvation equation,14 which describes the contribution of different solute-solvent interactions in many partition processes:
SP ) c + rR2 + sπ2H + aΣR2H + bΣβ20 + vVx
(5)
where SP is a solute property (e.g., logarithm of partition coefficients, RP-HPLC retention parameters, such as log k, log kw, etc.), and the explanatory variables are solute descriptors as follows: R2 is an excess molar refraction that can be obtained from a compound’s measured refractive index, π2H is the solute dipolarity/polarizability, ∑R2H and ∑β20 are the solute overall or effective hydrogen bond acidity and basicity1 (note that an alternative ∑β20 parameter is used here, as required for some special solutes), and Vx is the McGowan characteristic volume (in cm3/100 mol) that can be calculated for any solute simply from molecular structure using a table of atomic constants.15 The regression coefficients are c, r, s, a, b, and v. The coefficient r is a measure of the propensity of the phase to interact with solute π- and n-electron pairs, the coefficient s is a measure of the system dipolarity/polarizability, the coefficient a measures hydrogen bond basicity (because an acidic solute will interact with the basic phase), the coefficient b measures hydrogen bond acidity, and v is a measure of the phase lipophilicity. The molecular descriptors of more than 4000 compounds can be found in the UCL database.16 To apply eq 5, a set of solutes with known descriptors sufficiently varied to describe all interactions in the equation and of a sufficient number to establish the statistical validity of the model is required. The regression coefficients of the equations show the sensitivity of the partition system toward each particular molecular property. The general solvation model has been applied to numerous processes that involve transport of solutes between phases, especially to water-solvent partitions and to reversed-phase HPLC.17 Solvation equations were successfully set up with log k values and log kw values on various reversed-phase chromatographic systems.18-20 The CHI values obtained with various reversed-phase types of columns also showed good correlation with the molecular descriptors as described by eq 5.21 (14) Abraham, M. H. Chem. Soc. Rev. 1993, 22, 73-83. (15) Abraham, M. H.; McGowan J. C. Chromatographia 1987, 23, 243-246. (16) Abraham, M. H. University College London Database, 1997. (17) Abraham, M. H.; Rose´s, M. J. Phys. Org. Chem. 1994, 7, 672-684. (18) Abraham, M. H.; Chadha, H. S.; Leo, A. J. J. Chromatogr. 1994, 685, 203211. (19) Abraham, M. H.; Chadha, H. S.; Leitao, R. A. E.; Mitchell, R. C.; Lambert, W. J.; Kaliszan, R.; Nasal, A.; Haber, P. J. Chromatogr. A 1997, 766, 3547. (20) Abraham, M. H.; Rose´s, M.; Poole C. F.; Poole, S. K. J. Phys Org. Chem. 1997, 10, 358-368.
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In this paper, we compare the solvation equations obtained for various reversed phase chromatographic retention parameters, log k (isocratic), log kw, φ0, and CHI, obtained on the same Inertsil ODS column for 62 compounds, to ascertain if the rapidly determined CHI parameter contains the same information as the more usual isocratic retention parameters. EXPERIMENTAL SECTION The compounds studied are listed in Table 1, together with their molecular descriptors16 and log Poct.22 They are all commercially available and were purchased from Sigma-Aldrich Co. Ltd. (UK). A Hewlett-Packard 1090 series high-performance liquid chromatograph was used. Data acquisition and processing were performed on HP Vectra IBM-compatible PC with HP Chemstation software running under Windows’95 (Hewlett-Packard Co., Amsterdam, The Netherlands). The reversed-phase HPLC measurements were carried out on an ODS2-IK5 Inertsil column with the dimensions of 150 × 4.6 mm (Capital HPLC Ltd., Broxburn, Scotland). The aqueous component of the mobile phase was 0.1% phosphoric acid. For the basic compounds (4-nitroaniline, propranolol, p-toluidine, pyridine, aniline, m-nitroaniline, procaine, nicotine), 50 mM ammonium acetate buffer was used, adjusted to pH 9.5 by concentrated ammonium hydroxide solutions (analytical grade, Fisher). The organic phase was HPLC grade acetonitrile (Rathburn, Walkerburn, Scotland). The mobile phase flow rate was 1.00 mL/min. Both the gradient and the isocratic mixing have been carried out by a low-pressure gradient mixer built into HP 1090 and controlled by the Chemstation program. The individual isocratic runs consisted of a 20-min isocratic flow with various volume percentages (30, 40, 50, 60, 70) of acetonitrile, followed by a fast gradient (0.2 min) to 100% acetonitrile, a 2-min wash with 100% acetonitrile, and then 10 min of reequilibrating with the original volume percentage of acetonitrile. For the fast gradient retention time measurements, the following gradient program was applied: 0-1.5 min, 0% acetonitrile; 1.5-10.5 min, 0-100% acetonitrile; 11.5-12.0 min, 0% acetonitrile; 12-15 min, 0% acetonitrile. The gradient system was calibrated with the same test mixture as described earlier.12 The CHI values listed in Table 2 were correlated with the actual retention times, and the constants of the straight lines were used to convert the sample retention time to CHI. The dead time (t0) was measured by injecting sodium nitrate solution together with the sample. Retention times were measured in duplicate, and the average value was used for the log k and CHI calculations. The slope and the intercept (log kw) of the log k versus volume percentage of acetonitrile were calculated by using the Microsoft Excel 5.0 software package. The multiple regression analysis was carried out by using the Drugidea software package (Chemicro Ltd., Budapest, Hungary) with built-in cross validation. RESULTS AND DISCUSSION Table 1 shows the names of the compounds selected as a training set for establishing the coefficients of the solvation (21) Valko, K.; Plass, M.; Bevan, C.; Reynolds, D.; Abraham, M. H. J. Chromatogr. A 1998, 803, 51-60. (22) Hansch, C.; Leo, A. c log P Program, Medicinal Chemistry Project; Pomona, CA, 1993.
4230 Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
Table 1. Compounds Studied and Their Molecular Descriptors Obtained from the UCL Database16 name
R2
n-octanophenone n-heptanophenone n-hexanophenone n-valerophenone n-butyrophenone n-propiophenone acetophenone paracetamol acetanilide theophylline dibenzothiophene caffeine indazole benzonitrile cyclohexanone chlorobenzene naphthalene 1,4-dinitrobenzene hydrocortisone cortisone-21-acetate pyrene progesterone anisole benzamide butalbarbital 3,4-di-Cl-phenol phenol 4-nitrophenol 4-Cl-phenol 4-I-phenol resorcinol 4-CN-phenol 4-nitrobenzoic acid benzoic acid 3-CF3-phenol 4-OH-benzyl alcohol salicylic acid phenylacetic acid 4-nitroaniline propranolol p-toluidine pyridine aniline 3-nitroaniline procaine nicotine methyl 4-hydroxybenzoate n-ethyl 4-hydroxybenzoate n-propyl 4-hydroxybenzoate n-butyl 4-hydroxybenzoate benzene toluene n-ethylbenzene n-propylbenzene n-butylbenzene n-hexylbenzene nitromethane n-nitroethane n-nitropropane n-nitrobuthane n-nitropentane n-nitrohexane
0.72 0.72 0.72 0.8 0.8 0.8 0.82 1.06 0.87 1.5 1.959 1.5 1.18 0.742 0.403 0.718 1.34 1.13 2.03 1.82 2.808 1.45 0.71 0.99 1.03 1.02 0.805 1.07 0.915 1.38 0.98 0.94 0.99 0.73 0.425 0.998 0.89 0.73 1.22 1.843 0.923 0.631 0.955 1.2 1.14 0.865 0.9 0.86 0.86 0.86 0.61 0.601 0.613 0.604 0.6 0.59 0.313 0.27 0.242 0.227 0.212 0.203
π2H ∑R2H ∑β20 0.95 0.95 0.95 0.95 0.95 0.95 1.01 1.78 1.4 1.6 1.31 1.6 1.22 1.11 0.86 0.65 0.92 1.63 3.49 3.11 1.71 3.29 0.75 1.5 1.14 1.14 0.89 1.72 1.08 1.22 1 1.63 1.07 0.9 0.87 1.15 0.7 0.97 1.91 1.5 0.95 0.84 0.96 1.71 1.67 1.44 1.37 1.35 1.35 1.35 0.52 0.52 0.51 0.5 0.51 0.5 0.95 0.95 0.95 0.95 0.95 0.95
0 0 0 0 0 0 0 1.09 0.5 0.54 0 0 0.53 0 0 0 0 0 0.71 0.21 0 0 0 0.49 0.47 0.85 0.6 0.82 0.67 0.68 1.1 0.8 0.62 0.59 0.72 0.88 0.72 0.6 0.42 0.6 0.23 0 0.26 0.4 0.32 0 0.69 0.69 0.69 0.69 0 0 0 0 0 0 0.06 0.02 0 0 0 0
0.5 0.5 0.5 0.5 0.51 0.51 0.48 0.81 0.67 1.15 0.2 1.33 0.35 0.33 0.56 0.07 0.2 0.46 1.9 2.13 0.28 1.14 0.29 0.67 1.18 0.03 0.3 0.26 0.2 0.2 0.58 0.29 0.54 0.4 0.09 0.85 0.41 0.61 0.38 1.27 0.52 0.47 0.5 0.35 1.36 0.9 0.45 0.45 0.45 0.45 0.14 0.15 0.15 0.15 0.15 0.15 0.31 0.33 0.31 0.29 0.29 0.29
Vx
log P
1.859 1.718 1.578 1.437 3.28 1.296 2.66 1.155 2.19 1.014 1.58 1.172 0.51 1.1133 1.16 1.2223 -0.02 1.3791 4.38 1.3632 -0.07 0.9053 1.77 0.8711 1.56 0.8611 0.81 0.8388 2.89 1.0854 3.3 1.0648 1.47 2.7976 1.55 3.0521 2.1 1.5846 5.0 2.6215 3.7 0.916 2.11 0.9728 0.64 1.6557 1.89 1.0199 3.33 0.7751 1.5 0.9493 1.91 0.8975 2.15 1.0333 2.91 0.8338 0.8 0.9298 1.6 1.1059 1.89 0.9317 1.87 0.9691 2.95 0.9747 0.25 0.9904 2.26 1.0726 1.41 0.9904 1.39 2.148 3.37 0.9571 1.39 0.6753 0.65 0.8162 0.9 0.9904 1.37 1.9767 1.89 1.371 1.17 1.1313 1.96 1.2722 2.47 1.4131 3.04 1.554 3.57 0.716 2.13 0.857 2.73 0.998 3.15 1.139 3.72 1.28 4.26 1.562 5.52 0.424 -0.33 0.564 0.18 0.7055 0.87 0.8464 1.47 0.9873 2.01 1.1282 2.7
equations using various reversed-phase retention data as solute property. The molecular descriptors spanned a wide range and did not show unduly large intercorrelation. The correlation matrix in terms of F is given in Table 3. Table 4 shows the log k values obtained at 30, 40, 50, 60, and 70% acetonitrile in the aqueous mobile phases.
Table 2. Compounds and Their CHI Values in the Test Mixture Used for Calibrating the Gradient System compound
CHI
compound
CHI
theophylline phenyltetrazole benzimidazole colchicine phenyltheophylline
18.4 23.6 34.3 42.0 51.2
acetophenone indole propiophenone butyrophenone valerophenone
65.1 71.5 77.9 87.5 96.2
Table 3. Correlation Coefficients (G) between the Molecular Descriptors R2 R2 π2H ∑R2H ∑β20 Vx
1.00 0.65 0.21 0.49 0.56
π2H 1.00 0.25 0.73 0.70
∑R2H
1.00 0.15 -0.02
∑β20
1.00 0.74
Vx
1.00
It can be seen that some of the compounds had very short and some had very long retention times, and, therefore, no log k data are given in the table. For compounds asterisked, the log k values (not shown in Table 4) were determined using lower than 30 and higher than 70% of acetonitrile at a minimum of three different concentrations. The slope (S) and the intercept (log kw) values were calculated by fitting the data points (vol % acetonitrile, log k) to a straight line (eq 6),
log k ) Sφ + log kw
(6)
where log k is the retention factor, log kw is the intercept of the straight line and represents a log k at 100% water as mobile phase, φ is the actual organic phase concentration (vol % term) when the log k is determined, and S is the slope of the straight line, which has a reciprocal concentration unit, to give a dimensionless number to Sφ. It was found that, in some cases, the data points fit better to a parabola by addition of the square term of volume percentage of acetonitrile. It was decided to use the linear portion of this function, keeping the log k values between 1.2 and -0.5. The fit was accepted as linear when the correlation coefficient was above 0.995. The φ0 values can be derived from eq 6 when log k ) 0 according to eq 7.11
0 ) Sφ0 + log kw
(7)
φ0 ) -log kw/S
(2)
By rearranging eq 7,
Table 4. Isocratic Log k Values Obtained at Various Acetonitrile Concentrations log k compound n-octanophenone n-heptanophenone n-hexanophenone n-valerophenone n-butyrophenone n-propiophenone acetophenone paracetamola acetanilide theophylline dibenzothiophene caffeinea indazole benzonitrile cyclohexanone chlorobenzene naphthalene 1,4-dinitrobenzene hydrocortisone cortisone-21-acetate pyrenea progesterone anisole benzamide butalbarbital 3,4-di-Cl-phenol phenol 4-nitrophenol 4-Cl-phenol 4-I-phenol resorcinol 4-CN-phenol 4-nitrobenzoic acid benzoic acid 3-CF3-phenol 4-OH-benzyl alcohola salicylic acid phenylacetic acid 4-nitroaniline propranolol p-toluidine pyridine aniline 3-nitroaniline procaine nicotine methyl 4-hydroxybenzoate n-ethyl 4-hydroxybenzoate n-propyl 4-hydroxybenzoate n-butyl 4-hydroxybenzoate benzene toluene n-ethylbenzene n-propylbenzenea n-butylbenzenea n-hexylbenzenea nitromethane n-nitroethane n-nitropropane n-nitrobutane n-nitropentane n-nitrohexane
30%
0.778 -0.215 0.306 -0.193 -0.209 0.474 0.829 0.372
0.586 0.951
40%
50%
0.981 1.074 0.763 0.816 0.556 0.524 0.319 -0.282 -0.394 0.119 -0.042 -0.436 -0.527 1.163 -0.282 -0.387 0.243 0.056 0.574 0.358 0.236 0.106 0.855 1.014 0.722 0.447 0.192 -0.051 0.490 0.200
60% 1.038 0.845 0.659 0.483 0.318 0.127 -0.478 -0.176 -0.566 1.007 -0.434 -0.098 0.149 -0.017 0.572 0.700 0.203 -0.206 0.010
70% 0.898 0.731 0.569 0.415 0.272 0.139 -0.015
0.722 -0.197 -0.007 -0.102 0.359 0.462 0.007 -0.288 -0.108 0.928 0.465 0.166 -0.387 -0.227 0.084 -0.180 -0.191 -0.078 0.038 -0.417 -0.259 -0.203 -0.228 0.007
1.019 0.696 1.124 0.843 0.586 0.346 -0.001 -0.125 -0.249 -0.343 0.562 0.271 0.061 -0.114 0.561 0.289 0.465 0.268 0.093 -0.068 0.656 0.381 0.154 -0.049 0.809 0.519 0.283 0.076 0.776 0.476 0.222 -0.013 -0.116 -0.239 -0.349 0.437 0.217 0.027 -0.142 0.663 0.365 0.130 -0.067 0.493 0.243 0.045 -0.118 0.798 0.480 0.207 -0.201 -0.259 -0.364 -0.439 0.658 0.380 0.167 -0.017 0.513 0.257 0.056 -0.114 0.581 0.352 0.152 -0.041 1.016 0.684 0.466 0.595 0.432 0.242 0.067 0.005 -0.099 -0.174 0.413 0.265 0.115 -0.035 0.620 0.445 0.234 0.693 0.461 0.248 0.545 0.446 0.310 0.525 0.274 0.073 -0.104 -0.224 0.813 0.484 0.234 0.022 -0.128 0.729 0.420 0.169 0.114 0.989 0.620 0.328 0.253 1.123 0.893 0.635 0.406 0.222 0.843 0.578 0.366 1.039 0.737 0.496 0.929 0.658 1.119 0.821 0.009 -0.008 -0.091 -0.190 0.268 0.187 0.062 -0.072 0.578 0.418 0.239 0.065 -0.074 0.915 0.672 0.432 0.215 0.041 0.936 0.634 0.373 0.166 0.848 0.544 0.303
a Log k values were determined using lower than 30 and higher than 70% of acetonitrile.
In reversed-phase liquid chromatography, the retention (that is, the compound distribution between the mobile and the stationary phases) is governed by hydrophobic forces; these parameters can be regarded as a measure of compound lipophilicity. The calculated slope, log kw, and φ0 values from isocratic
runs are shown in Table 5. When applying a linear change of the volume percentage of organic concentration during a gradient run, any retention time (tR) corresponds to a particular organic Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
4231
Table 5. Isocratic Slope, Log kw, φ0, and Gradient CHI Values for 62 Compounds compound
slope
log kw
φ0
CHI
n-octanophenone n-heptanophenone n-hexanophenone n-valerophenone n-butyrophenone n-propiophenone acetophenone paracetamol acetanilide theophylline dibenzothiophene caffeine indazole benzonitrile cyclohexanone chlorobenzene naphthalene 1,4-dinitrobenzene hydrocortisone cortisone-21-acetate pyrene progesterone anisole benzamide butalbarbital 3,4-di-Cl-phenol phenol 4-nitrophenol 4-Cl-phenol 4-I-phenol resorcinol 4-CN-phenol 4-nitrobenzoic acid benzoic acid 3-CF3-phenol 4-OH-benzyl alcohol salicylic acid phenylacetic acid 4-nitroaniline propranolol p-toluidine pyridine aniline 3-nitroaniline procaine nicotine methyl 4-hydroxybenzoate n-ethyl 4-hydroxybenzoate n-propyl 4-hydroxybenzoate n-butyl 4-hydroxybenzoate benzene toluene n-ethylbenzene n-propylbenzene n-butylbenzene n-hexylbenzene nitromethane n-nitroethane n-nitropropane n-nitrobutane n-nitropentane n-nitrohexane
-0.0282 -0.0284 -0.0255 -0.0282 -0.0246 -0.0209 -0.0219 -0.0216 -0.0163 -0.009 -0.0205 -0.0089 -0.0193 -0.0228 -0.0130 -0.0248 -0.0196 -0.0248 -0.0199 -0.024 -0.0251 -0.021 -0.0261 -0.0115 -0.0229 -0.0239 -0.0179 -0.0237 -0.0247 -0.0277 -0.0112 -0.0195 -0.0247 -0.0207 -0.0296 -0.008 -0.0228 -0.0211 -0.0209 -0.0275 -0.0177 -0.009 -0.015 -0.0193 -0.0222 -0.0117 -0.0189 -0.0231 -0.028 -0.033 -0.024 -0.020 -0.0227 -0.0256 -0.0283 -0.0324 -0.0091 -0.0130 -0.0177 -0.0234 -0.0281 -0.0273
2.864 2.734 2.368 2.337 1.979 1.589 1.429 0.437 0.788 0.048 2.180 0.063 1.046 1.509 0.758 2.083 1.834 1.690 0.973 1.433 2.673 1.949 1.901 0.341 1.238 1.742 0.998 1.361 1.542 1.876 0.323 1.016 1.393 1.104 1.973 0.037 1.333 1.14 1.206 2.097 1.129 0.358 0.865 1.205 1.357 0.904 1.026 1.402 1.839 2.298 1.84 1.777 2.098 2.463 2.812 3.436 0.359 0.707 1.123 1.612 2.055 2.2
101.6 96.38 92.9 83.0 80.6 76.2 65.3 20.6 48.3 5.3 106.4 7.1 54.2 66.2 58.4 84.0 93.5 68.1 48.9 59.7 106.5 92.8 72.8 29.65 54.06 72.90 55.75 57.43 62.43 67.74 28.80 52.10 56.40 53.33 66.75 4.63 58.46 54.03 57.70 76.25 63.97 40.02 57.67 62.44 61.00 76.91 54.29 60.68 65.69 69.54 76.67 88.64 92.20 96.03 99.36 106.20 39.41 54.56 63.64 68.87 73.01 80.73
119.6 112.8 105.1 96.5 87.1 76.9 63.3 18.8 42.4 17.9 113.4 24.5 49.9 65.1 44.1 92.2 99.4 70.9 50.8 56.8 124.1 100.4 78.4 29.2 52.6 77.4 48.4 56.3 62.6 73.4 25.2 48.0 56.3 50.2 73.2 18.9 56.9 50.8 53.5 87.1 58.1 28.9 45.3 58.3 61.3 58.8 52.0 61.5 71.1 80.0 80.8 92.0 100.6 109.5 116.9 130.6 41.0 51.8 61.4 70.9 79.8 88.3
phase concentration. Using the calibration set of compounds with known CHI values, the gradient retention times can be normalized and a calibration line constructed which gives the CHI12 values of any other compounds measured under the same conditions (eq 3). Table 5 contains the fast gradient CHI values for the selected 62 compounds. 4232 Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
Figure 1. Relative regression coefficients (r/v, s/v, a/v, and b/v) obtained in the solvation equations for log kaverage (1), CHI (2), φ0 (3), log kw (4), log Psubset (5), log P (6), and slope (7). Table 6. Correlation Coefficients between Various RP-HPLC Retention Data Based on the 62 Compounds
slope log kw log k50a φ0 CHI log P
slope
log kw
log k50a
φ0
CHI
log P
1.00 -0.88 -0.68 -0.71 -0.75 -0.80
1.00 0.92 0.91 0.96 0.94
1.00 0.95 0.99 0.86
1.00 0.96 0.87
1.00 0.92
1.00
a Only 55 out of the 62 compounds had a measurable retention at 50% acetonitrile; therefore, the correlation coefficients were calculated on the basis of the data from these 55 compounds.
CHI ) AtR + B
(3)
As all of the data in Table 5 can be considered as various measures of lipophilicity, Table 6 shows the correlation coefficients (F) obtained between one set of isocratic log k values (log k50 has been chosen as a log k values obtained with an average concentration of acetonitrile), log kw, slope, φ0, the gradient CHI, and the octanol/water log P.22 It can be seen from Table 6 that the four chromatographic lipophilicity parameters (log k50, log kw, φ0, CHI) are reasonably well correlated with each other but are not identical. However, we can use eq 5 to explore the origin of these differences and
Table 7. Coefficients, Their Confidence Intervals, Multiple Correlation Coefficient (G), and Standard Error of the Estimate (sd) of Eq 2 Using the Various Reversed-Phase Retention Data from Tables 4 and 5
SP ) c + rR2 + sπ2H + aΣR2H + bΣβ20 + vVx SPa
c
r
s
a
b
v
F
sd
log k30, n ) 37 log k40, n ) 46 log k50, n ) 55 log k60, n ) 55 log k70, n ) 48 Slope, n ) 62 log kw, n ) 62 φ0, n ) 62 CHI, n ) 62 log P, n ) 61 log P, n ) 619
0.075 0.074 0.0003 0.134 0.274 0.0137 0.683 46.6 42.78 0.089 0.088
0.0968 ( 0.086 0.129 ( 0.059 0.092 ( 0.039 0.127 ( 0.038 0.130 ( 0.037 -0.0021 ( 0.0012 -0.029 ( 0.072 2.69 ( 2.65 5.39 ( 1.87 0.831 ( 0.034 0.562 ( 0.14
-0.324 ( 0.059 -0.309 ( 0.044 -0.280 ( 0.034 -0.284 ( 0.032 -0.252 ( 0.047 -0.0026 ( 0.0013 -0.450 ( 0.074 -6.80 ( 2.75 -14.12 ( 1.94 -1.010 ( 0.035 -1.054 ( 0.021
-0.407 ( 0.057 -0.471 ( 0.045 -0.470 ( 0.034 -0.443 ( 0.034 -0.368 ( 0.044 0.003 ( 0.0014 -0.290 ( 0.079 -23.53 ( 2.91 -25.40 ( 2.06 -0.071 ( 0.037 -0.034 ( 0.021
-1.720 ( 0.093 -1.450 ( 0.067 -1.223 ( 0.046 -1.044 ( 0.047 -0.888 ( 0.057 -0.0151 ( 0.0018 -1.955 ( 0.100 -60.18 ( 3.72 -70.19 ( 3.11 -3.543 ( 0.047 -3.460 ( 0.026
1.782 ( 0.092 1.438 ( 0.061 1.207 ( 0.047 1.043 ( 0.040 0.903 ( 0.053 0.0165 ( 0.0015 2.069 ( 0.086 52.43 ( 3.18 68.40 ( 2.75 3.858 ( 0.040 3.858 ( 0.015
0.968 0.973 0.981 0.983 0.972 0.843 0.969 0.956 0.985 0.998 0.997
0.100 0.090 0.081 0.079 0.095 0.0034 0.195 7.19 5.08 0.091 0.116
a
n is the number of compounds.
Table 8. Normalized Regression Coefficients of Equations Shown in Table 7 partition
r/v
s/v
a/v
b/v
log k30 log k40 log k50 log k60 log k70 slope log kw φ0 CHI log P (subset) log P averaged log k30-70
0.054 ( 0.048 0.030 ( 0.041 0.076 ( 0.032 0.122 ( 0.037 0.144 ( 0.042 -0.127 ( 0.074 -0.014 ( 0.035 0.051 ( 0.051 0.051 ( 0.034 0.138 ( 0.009 0.147 ( 0.004 0.082 ( 0.0472
-0.181 ( 0.034 -0.215 ( 0.032 -0.232 ( 0.030 -0.272 ( 0.032 -0.279 ( 0.055 -0.158 ( 0.080 -0.217 ( 0.037 -0.130 ( 0.053 -0.186 ( 0.036 -0.264 ( 0.010 -0.276 ( 0.006 -0.236 ( 0.041
-0.228 ( 0.034 -0.327 ( 0.034 -0.389 ( 0.032 -0.425 ( 0.036 -0.408 ( 0.054 +0.188 ( 0.086 -0.140 ( 0.039 -0.449 ( 0.248 -0.417 ( 0.041 -0.018 ( 0.010 0.009 ( 0.005 -0.356 ( 0.080
-0.965 ( 0.072 -1.008 ( 0.063 -1.013 ( 0.055 -1.001 ( 0.059 -0.983 ( 0.085 -0.915 ( 0.137 -0.945 ( 0.062 -1.148 ( 0.099 -1.053 ( 0.063 -0.918 ( 0.015 -0.907 ( 0.008 -0.994 ( 0.020
similarities. By applying multiple regression analysis using the isocratic and gradient retention parameters as dependent variables and the solute descriptors as independent variables, the obtained regression coefficients can reveal the impact of various molecular properties. Table 7 shows the coefficients of the solvation equation described by eq 5. Table 7 shows that all the chromatographic retention parameters (log k at various percentages of acetonitrile, log kw, φ0, and CHI values) are significantly correlated with the molecular descriptors. The highest correlation coefficient was obtained for the log P values. These solute properties (Table 7) are all measures of lipophilicity, and the factors that influence them are qualitatively the same; i.e., solute dipolarity/polarizability, hydrogen bond acidity, and hydrogen bond basicity result in a decrease of log k, log kw, φ0, CHI, and log P, while the solute volume increases lipophilicity values. The effect of the organic phase concentration on the solvation equation obtained for the various isocratic log k values was studied in detail by Abraham and Rose´s.17 They observed trends in the change of coefficients by changing the organic phase volume, and they suggested a general solvation equation for isocratic log k values. For an ODS type column with aqueous acetonitrile mobile phases, the equation is
log k ) c + v(0.08R2 - 0.24π2H 0.36ΣR2H - 0.99Σβ20 + 1.00Vx) (8) where c and v depend on the particular ODS column.
As the units are different for the various lipophilicity scales, for easy comparison between different equations, the regression coefficients were divided by the coefficient v of the volume term Vx. The normalized variables obtained in this way are summarized in Table 8. The ratios r/v are slightly increasing, and the s/v and a/v slightly decreasing with increasing acetonitrile concentration. The b/v values for log k at 30-70% acetonitrile are remarkably constant, when the errors23 are considered. Because the log k30-70 equations are so similar, they can thus be averaged20 and compared with the fast gradient CHI lipophilicity measure. Figure 1 shows the values of the normalized coefficients for the average isocratic log k (average), log kw, φ0, CHI, and log P. From Figure 1 and Table 7, it can be seen that the ratios r/v, s/v, and b/v are very similar for all the scales considered. Hence, they can all be regarded as somewhat similar lipophilicity scales. However, there are important differences, as revealed by eq 5 and by the ratios of coefficients, so that the scales are not identical. In particular, the a/v ratio for log P is close to zero, so that log P is totally insensitive to solute hydrogen bond acidity, whereas log k30-70, φ0, and CHI (and to some extent log kw) are all influenced by solute hydrogen bond acidity. As pointed out before, this is why log k cannot be used as a direct measure of log P.24 What is very important as regards the use of high-throughput gradient elution is that the coefficient ratios for CHI are very (23) Hinchen, J. D. J. Gas Chromatogr. 1967, 5, 641. (24) Leo, A. J. In Biological CorrelationssThe Hansch Approach; Gould, R. F., Ed.; ACS Advances in Chemistry Series 114; American Chemical Society: Washington, DC, 1972; p 51.
Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
4233
S
slope, d(log k)/dφ, for a given solute and organic solvent
CHI
gradient chromatographic hydrophobicity index obtained from gradient retention time by calibration as close to the φ0 scale as possible
A, B
constants of a linear plot of gradient retention times for a standard set against φ0
tg
retention time in gradient elution
tR
retention time in isocratic elution
t0
column dead time; the time for a unretained solute to pass through the column
tD
column dwell time in gradient elution; time for a solvent to travel to column inlet from the solvent mixer
Vs/Vm
phase ratio (volume of the two partitioning stationary and mobile phases)
log K
logarithm of equilibrium constant, equivalent to the partition coefficient of the compound between the mobile and the stationary phases
log P
logarithm of octanol/water partition coefficient of a neutral molecule
SP
solute property, such as log P, log k, log kw, CHI
R2
excess molar refraction
π2
solute dipolarity/polarizability
Figure 2. Plot of log k50 values against CHI values.
similar to those for the isocratic log k30-70 values. Indeed, the CHI and log k50 ratios are identical within the quoted errors in Table 8, and this is demonstrated clearly in Figure 2. We have thus demonstrated that the CHI value obtained by the rapid gradient elution method encodes the same information as the isocratic log k30-70 values. The high-throughput gradient elution procedure is, therefore, a very convenient and rapid alternative to isocratic elution for the determination of lipophilicity. ACKNOWLEDGMENT C.M.D. would like to thank GlaxoWellcome for a postdoctoral fellowship. DEFINITION OF SYMBOLS
H
∑R2H
overall or effective hydrogen bond acidity
∑β2
overall or effective hydrogen bond basicity
Vx
McGowan characteristic volume in cm3/100 mol
0
log k
solute retention factor
log kw
value of log k extrapolated to 0% organic modifier concentration
c, r, s, a, b, v
regression constants of the solvation equation obtained by multiple regression analysis
log k50
value of log k measured by 50% (v/v) organic phase in the mobile phase
F
correlation coefficient
φ
volume percent of organic modifier in the mobile phase
sd
standard error of the estimates
φ0
isocratic chromatographic hydrophobicity index, defined as the volume percent of organic solvent at which log k ) 0
4234 Analytical Chemistry, Vol. 70, No. 20, October 15, 1998
Received for review April 23, 1998. Accepted July 29, 1998. AC980435T
