Anal. Chem. 1997, 69, 2575-2581
Determination of Lipophilicity by Gradient Elution High-Performance Liquid Chromatography Joachim D. Krass,† Bernd Jastorff,† and Hans-Gottfried Genieser*,‡
Zentrum fu¨ r Umweltschutz und Umwelttechnologie (UFT), Universita¨ t Bremen, Leobenerstrasse, D-28359 Bremen, FRG, and BIOLOG Life Science Institute, Flughafendamm 9a, P.O. Box 107125, D-28071 Bremen, FRG
A novel method for the determination of lipophilicity using a simple HPLC protocol based on gradient elution chromatography is presented and compared to the common isocratic log k′w procedure. Linear relationships with high correlation coefficients between both methods for biologically active nucleosides and cyclic nucleotides as well as for environmentally relevant aromatic hydrocarbons were found. A mathematical fit to support the empirically determined linear relationship is presented. It is shown that the observed relationship between log k′w and the apparent capacity factor (k′g) determined by gradient elution is derivable by theoretical considerations as well. Since the gradient method is much less time-consuming compared to other procedures, it represents a convenient alternative for determining lipophilicity data in the future. The lipophilicity of a certain chemical entity is an important parameter for its distribution in the environment and its action in biological systems. Consequently, there has been continued interest in methods and means to determine experimentally or to calculate corresponding physicochemical descriptors or data.1 Among the experimental procedures described so far, the determination of the octanol/water partition coefficient, log P,2,3 has gained general acceptance as a standard reference system, and corresponding data are available for a broad variety of chemical structures. However, the method is rather laborious and timeconsuming, which is a major drawback if several compounds have to be analyzed. Other critical aspects include the need for considerable amounts of pure, possibly rare analytes and the potential hazards in handling and disposal of toxic substances as well as of organic solvents. In addition, for some compounds, the log P is difficult to determine due to only poor solubility in one of the phases. The limited feasibility of the shake-flask methodology early has led to the development of alternative techniques, especially chromatographic approaches.4-7 Chromatography seems predestined for several reasons. Its principle already includes partition between phases of different lipophilicity, and, in addition, its dynamic character enables instrumental analysis and automation. Furthermore, chromatography allows simultaneous analysis of several compounds, gener†
Universita¨t Bremen. BIOLOG Life Science Institute. (1) Lambert, W. J. J. Chromatogr. 1993, A656, 469-484. (2) Leo, A.; Hansch, C.; Elkins, D. Chem. Rev. 1971, 71, 525-616. (3) Hansch, C.; Leo, A. Substituent Constants for Correlation Analysis in Chemistry and Biology; Wiley: New York, 1979. (4) Braumann, T. J. Chromatogr. 1986, 373, 191-225. (5) Kaliszan, R. Quantitative Structure-Activity Chromatographic Retention Relationships; Wiley: New York, 1987; p 232. (6) Kaliszan, R. Quant. Struct.-Act. Relat. 1990, 9, 83-87. (7) Kaliszan, R. Anal. Chem. 1992, 64, 619-631. ‡
S0003-2700(96)01246-2 CCC: $14.00
© 1997 American Chemical Society
ally accelerates time of analysis, copes with extremely polar or nonpolar solutes, and does not require pure analytes or large sample quantities. Moreover, this technique is used for quantitative analysis of the octanol and water phase during traditional log P determination, anyhow. Among the chromatographic methods, the determination of log k′ data from isocratic reversed-phase high-performance liquid chromatography (RP-HPLC) and their extrapolation to elution with 100% water (log k′w) has become a well-accepted method for the determination of lipophilicity.4,7-11 However, although the determination of log k′w has a clear advantage in comparison to the shake-flask method, the procedure is still laborious and time-consuming, especially when it comes to the preparation of several different elution media, which are necessary in order to determine isocratic retention data. In addition, due to large differences in solute hydrophobicity, this technique may lead to mistakes, since not all compounds can be run simultaneously at all isocratic conditions. Usually, large differences in retention behavior in RP-HPLC are managed in one chromatogram by taking advantage of gradient elution. Although it offers considerable improvements over isocratic methods, this technique has not been described for determining lipophilicity data so far. Therefore, this study investigates the potential benefits of an easy-to-use gradient elution technique as a convenient means for determination of lipophilicity. EXPERIMENTAL SECTION All chemicals used were regular products and of analytical grade. Methanol was of gradient quality (Merck, Darmstadt, FRG), and water was doubly distilled. Nucleosides and cyclic nucleotides were from BIOLOG Life Science Institute (Bremen, FRG) or synthesized according to published procedures. 2,4,6Trinitrotoluene was purchased from Promochem (Wesel, FRG), all other substituted aromatic hydrocarbons were from Aldrich (Steinheim, FRG). Chromatography was performed on a slurry technique-packed LiChrosorb RP-18 column (250 mm × 4 mm i.d.) at ambient temperature using a Lichrograph 655 A-12 pump, an L5000 LC gradient control system, an L4000 variable UV detector at 254 nm, and an 655A-40 autosampler (all Merck). Retention data of aromatic hydrocarbons and nucleosides were determined using an Intelligent Pump L-6200 A (Merck), an SM-4000 programmable UV detector at 254 nm (LDC Analytical), and an ISS-100 autosampler (Perkin Elmer). (8) Chen, B.-K.; Horvath, C. J. Chromatogr. 1979, 171, 15-28. (9) Krikorian, S. E.; Chorn, T. A.; King, J. W. Quant. Struct.-Act. Relat. 1987, 6, 65-69. (10) Lambert, W. J.; Wright, L. A.; Stevens, J. K. Pharm. Res. 1990, 7, 577586. (11) Yamagami, C.; Yokota, M.; Takao, N. J. Chromatogr. 1994, A662, 49-60.
Analytical Chemistry, Vol. 69, No. 13, July 1, 1997 2575
Table 1. Regression Analysis of the Relationship between the Volume Fraction of Methanol in Water (φ) and Log k′ According to Eq 7 from Isocratic Elution and Retention Data Obtained by the Gradient System for Selected Substituted Aromatic Hydrocarbonsa isocratic elution
gradient elution
no.
compound
log k′w
m
r
F ratio
n
φ range
Vg (mL)
k′g
log k′w calcd
log P
1 2 3 4 5 6 7 8 9 10 11 12 13
n-propylbenzene p-xylene ethylbenzene toluene anisole benzene 2,4,6-trinitrotoluene nitrobenzene p-dinitrobenzene benzaldehyde benzyl alcohol phenol aniline
3.76 (0.06) 3.24 (0.05) 3.18 (0.05) 2.75 (0.03) 2.31 (0.03) 2.17 (0.02) 2.27 (0.02) 2.12 (0.02) 1.91 (0.01) 1.88 (0.02) 1.44 (0.01) 1.39 (0.01) 1.23 (0.01)
3.88 (0.08) 3.36 (0.06) 3.35 (0.07) 2.99 (0.05) 2.69 (0.05) 2.48 (0.03) 2.88 (0.03) 2.60 (0.04) 2.50 (0.03) 2.59 (0.05) 2.20 (0.02) 2.10 (0.03) 1.94 (0.02)
0.999 0.999 0.998 0.999 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
2323 2810 2222 3492 2928 7344 8656 4588 8352 2778 10577 5390 7321
8 9 9 10 11 12 10 11 10 10 8 8 7
0.90-0.55 0.90-0.50 0.90-0.50 0.85-0.40 0.80-0.30 0.80-0.25 0.70-0.25 0.75-0.25 0.65-0.20 0.65-0.20 0.55-0.20 0.55-0.20 0.50-0.20
54.75 52.02 51.19 46.73 40.17 39.10 38.01 36.86 33.71 32.18 24.71 23.53 21.60
30.80 29.09 28.58 25.79 21.69 21.02 20.34 19.62 17.65 16.69 12.03 11.29 10.08
3.42 3.23 3.18 2.87 2.42 2.34 2.27 2.19 1.97 1.87 1.36 1.27 1.14
3.68 3.15 3.15 2.69 2.11 2.13 1.97 1.85 1.46 1.48 1.10 1.46 1.10
a Both the intercept (log k′ ) and slope (m) of linear regression analysis are shown; numbers in parentheses are the standard deviations. r w represents the correlation coefficient, and the F ratio stands for significance of the linear model. n is the number of data points used for regression analysis, and φ range indicates the concentration range of methanol wherein the retention data are measured. Vg is the retention volume, and k′g is the apparent capacity factor determined by eq 15 (Vd ) 3.87 mL; Vm ) 1.60 mL) in gradient elution. log k′w calcd is recalculated from eq 1. Log P values are from the literature.34
Isocratic log k′w determination for substituted aromatic hydrocarbons was performed using different aqueous eluents with varying methanol ratios (80/20 up to 10/90 v/v), as indicated in Table 1. For nucleosides, the different eluents consisted additionally of 10 mM triethylammonium phosphate buffer (TEAP) at pH 6.5, and the methanol concentration ranged from 92.5/7.5 up to 50/50 v/v. Under gradient conditions, eluent A consisted of 10 mM aqueous TEAP adjusted to pH 6.5 for nucleosides and cyclic nucleotides, and eluent B was 10 mM TEAP in methanol. For aromatic hydrocarbons, eluent A consisted of doubly distilled water of pH 7, and eluent B was methanol. A linear gradient starting with 100% eluent A and increasing the ratio of eluent B to 100% was applied within 1 h at a volume flow rate of 1 mL/ min. After solvent B was held for an additional 5 min, reequilibration to solvent A was performed for 15 min. All runs within a certain class of compounds were performed with the same lot of eluents. Samples were injected every 80 min without any break in order to maintain comparable conditions. In spite of the possibility to measure all compounds simultaneously, the analogues were run in groups of about six compounds in order to facilitate peak identification. All samples were dissolved and injected in eluent A. Column void volume (Vm) was determined with sodium nitrate. The system delay volume (Vd) of the gradient systems, caused by mixing devices, was observed upon changing of detector absorbance after switching from water to 0.1 mM NaNO3 without column. An internal standard mixture was included in each run, providing low, medium, and high lipophilicity in order to check gradient reproducibility. For the determination of aryl hydrocarbons, a quartet consisting of n-propylbenzene (1), 2,4,6-trinitrotoluene (7), p-dinitrobenzene (9), and benzyl alcohol (11) was used. The standard mixture for the nucleosides consisted of 5,6dimethyl-1-β-D-ribofuranosylbenzimidazole (15), adenosine (22), and guanosine (27). For cyclic nucleotides, a triplet consisting of a rather lipophilic cAMP analogue with benzimidazole base (31), 8-piperidino-cAMP (34), and the polar adenosine-3′,5′monophosphate (cAMP, 41) was applied. 2576
Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
Compounds with identical nucleobases but with different phosphate modifications were pooled in the same group. RESULTS In order to compare both isocratic and gradient elution procedures, log k′w data were determined for aromatic hydrocarbons and nucleoside analogues according to the isocratic HPLC standard procedure4 (Tables 1 and 2). Corresponding data for cyclic nucleotides were taken from a published study12 (Table 3). The results of linear regression analysis of isocratic capacity factors (k′) with volume fractions of methanol (φ) for aromatic hydrocarbons and nucleosides are shown in Tables 1 and 2. The correlation coefficients are higher than 0.998 and 0.924, respectively. For all relationships, the F statistic demonstrates the validity of the applied linear model within the 5% significance level. In addition, all three classes of compounds were run in a linear gradient elution program. The gradient program started with water or buffer, respectively, and went up to 100% organic modifier (methanol). The apparent capacity factors k′g (viz. eq 15) obtained were compared to the corresponding log k′w factors yielded by the conventional method (Tables 1-3). It would have been of interest to perform gradient elution of cyclic nucleotides with exactly the same eluent as has been used in a previous isocratic study.12 However, eluents containing 100 mM phosphate buffer at high concentrations of the organic modifier precipitate phosphate, which seriously limits their use in gradient chromatography. The TEAP buffer used as a substitute here turned out to be miscible with methanol at all ratios. The reproducibility of the applied gradient was monitored by comparison of the retention factors of the internal standards included in each analysis and turned out to be satisfactory, since standard deviations of mean retention factors were less than 1.04% for all gradient runs. For all three classes of compounds, the correlation of both sets of retention data (log k′w and k′g) turned out to be strictly linear, with high correlation coefficients, as calculated by regression analysis (eqs 1-3 and Figure 1). The F (12) Braumann, T.; Jastorff, B. J. Chromatogr. 1985, 350, 105-118.
Table 2. Regression Analysis of the Relationship between the Volume Fraction of Methanol in Water (φ) and Log k′ According to Eq 7 from Isocratic Elution and Retention Data Obtained by the Gradient System for Some Biologically Active Nucleosidesa isocratic elution
gradient elution
no.
compound
log k′w
m
r
F ratio
n
φ range
Vg (mL)
k′g
log k′w calcd
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
5,6-dichloro-1-β-D-ribofuranosylbenzimidazole 5,6-dimethyl-1-β-D-ribofuranosylbenzimidazole 8-iodoadenosine 8-bromoadenosine 1-β-D-ribofuranosylbenzimidazole 2-chloroadenosine 8-bromoguanosine 2′-deoxyadenosine adenosine 2-aminopurine riboside purine riboside thymidine 2′-deoxyguanosine guanosine inosine uridine cytidine
2.90 (0.12) 2.48 (0.06) 1.96 (0.06) 1.93 (0.12) 1.59 (0.05) 1.46 (0.06) 1.52 (0.12) 1.43 (0.11) 1.26 (0.11) 0.95 (0.11) 1.06 (0.10) 0.92 (0.09) 0.89 (0.11) 0.63 (0.11) 0.28 (0.07) 0.32 (0.07) 0.16 (0.06)
3.98 (0.29) 3.99 (0.16) 3.98 (0.33) 4.02 (0.36) 2.99 (0.17) 3.11 (0.20) 3.68 (0.41) 3.70 (0.40) 3.36 (0.39) 2.65 (0.35) 2.90 (0.37) 2.69 (0.33) 2.82 (0.38) 2.16 (0.35) 1.31 (0.21) 1.56 (0.24) 1.26 (0.21)
0.997 0.998 0.989 0.984 0.991 0.992 0.971 0.967 0.961 0.958 0.956 0.957 0.950 0.940 0.963 0.933 0.924
192.5 629.7 141.4 126.6 294.2 246.6 80.7 86.8 73.2 56.0 62.6 64.9 55.0 37.6 38.0 40.7 34.8
3 4 5 6 7 6 7 8 8 7 8 8 8 7 5 8 8
0.50-0.30 0.50-0.25 0.50-0.20 0.50-0.15 0.50-0.10 0.50-0.10 0.50-0.10 0.50-0.075 0.50-0.075 0.50-0.10 0.50-0.075 0.50-0.075 0.50-0.075 0.50-0.10 0.50-0.20 0.50-0.075 0.50-0.075
40.09 33.70 26.64 25.61 23.61 23.15 21.13 19.53 18.41 16.98 16.87 15.45 15.43 14.26 13.62 10.14 8.34
21.09 17.19 12.88 12.26 11.04 10.76 9.52 8.55 7.87 6.99 6.93 6.06 6.05 5.34 4.95 2.82 1.73
3.20 2.62 1.98 1.89 1.70 1.66 1.48 1.33 1.23 1.10 1.09 0.96 0.96 0.86 0.80 0.48 0.32
a Both the intercept (log k′ ) and slope (m) of linear regression analysis are shown; numbers in parentheses are the standard deviations. r w represents the correlation coefficient, and the F ratio stands for significance of the linear model. n is the number of data points used for regression analysis, and φ range indicates the concentration range of methanol wherein the retention data are measured. Vg is the retention volume, and k′g is the apparent capacity factor determined by eq 15 (Vd ) 3.87 mL; Vm ) 1.64 mL) in gradient elution. Log k′w calcd is recalculated from eq 2.
Table 3. Retention Data Obtained by the Gradient System for Some Biologically Active Cyclic Nucleotidesa isocratic elution log k′w12
no.
compound
31
5,6-dichloro-1-β-D-ribofuranosylbenzimidazole-3′,5′monophosphorothioate, Sp isomer 8-(4-chlorophenylthio)adenosine-3′,5′-monophosphate N6,O2′-dibutyryladenosine-3′,5′-monophosphate 8-piperidinoadenosine-3′,5′-monophosphate 8-bromoadenosine-3′,5′-monophosphate 1,N6-ethenoadenosine-3′,5′-monophosphate adenosine-3′,5′-monophosphorothioate, Sp isomer 2-chloroadenosine-3′,5′-monophosphate adenosine-3′,5′-monophosphorothioate, Rp isomer 8-methylaminoadenosine-3′,5′-monophosphate adenosine-3′,5′-monophosphate purine riboside-3′,5′-monophosphate guanosine-3′,5′-monophosphorothioate, Sp isomer guanosine-3′,5′-monophosphate
32 33 34 35 36 37 38 39 40 41 42 43 44
Vg (mL)
gradient elution k′g log k′w calcd
nd
40.24
12.12
2.98
2.76 (0.04) 2.25 (0.05) nd 1.41 (0.06) 1.31 (0.08) 1.35 (0.05) 1.29 (0.04) 1.27 (0.02) 1.15 (0.02) 1.10 (0.04) 1.01 (0.01) 1.02 (0.01) 0.68 (0.01)
36.24 33.62 30.73 21.27 21.18 20.87 20.77 19.64 18.39 18.30 17.51 17.44 14.61
10.74 9.84 8.84 5.58 5.55 5.44 5.41 5.02 4.59 4.56 4.29 4.26 3.26
2.64 2.41 2.16 1.35 1.34 1.31 1.30 1.21 1.10 1.09 1.02 1.02 0.77
a V is the retention volume and k′ the apparent capacity factor determined by eq 15 (V ) 2.18 mL; V ) 2.90 mL) in gradient elution. Log g g d m k′w calcd is recalculated from eq 3. nd, not determined.
statistic for testing the linear model confirms the quality of the assumed relationship within a 5% confidence interval.
substituted benzenes log k′w ) (0.110 ( 0.005)k′g + (0.032 ( 0.124) r ) 0.985
F ) 362.8
(1)
n ) 13
nucleosides log k′w ) (0.149 ( 0.008)k′g - (0.060 ( 0.079) r ) 0.980
F ) 368.8
(2)
n ) 17
cyclic nucleotides log k′w ) (0.251 ( 0.011)k′g - (0.051 ( 0.064) r ) 0.991
F ) 566.5
(3)
n ) 12
Comparison of log k′w data recalculated from k′g by using eqs 1-3 with isocratically determined data (Tables 1-3) showed that
the differences were within an acceptable range. It remains to be investigated whether the close correlation is generally valid or if there are any restrictions. However, two other gradient profiles with a more shallow (120 min) or a steeper (30 min) increase of methanol concentration gave comparable results (data not shown). The correlation for cyclic nucleotides was further tested using some additional log k′w data from other references.13-15 Good relationships are obtained as well; however, some of the different data sets were parallely shifted (data not shown) and fitted only within those groups of compounds which had been determined (13) Nass, N.; Colling, C.; Cramer, M.; Genieser, H.-G.; Butt, E.; Winkler, E.; Jaenicke, L.; Jastorff, B. Biochem. J. 1992, 285, 129-136. (14) Genieser, H.-G.; Winkler, E.; Butt, E.; Zorn, M.; Schulz, S.; Iwitzki, F.; Sto¨rmann, R.; Jastorff, B.; Døskeland, S. O.; Øgreid, D.; Ruchaud, S.; Lanotte, M. Carbohydr. Res. 1992, 234, 217-235. (15) Schaap, P.; van Ments-Cohen, M.; Soede, R. D. M.; Brandt, R.; Firtel, R. A.; Dostmann, W.; Genieser, H.-G.; Jastorff, B.; van Haastert, P. J. M. J. Biol. Chem. 1993, 268, 6323-6331.
Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
2577
(5)
dV ) k′ dVm
By integrating between V ) 0 and V ) V ′g, eq 5 can be written as follows:
∫
V ′g
0
Figure 1. Correlation of log k ′w vs k ′g for aromatic hydrocarbons (9; Table 1), nucleosides (b; Table 2) and cyclic nucleotides (2; Table 3).
together in the respective isocratic runs. Since the isocratic study of Braumann and Jastorff12 appeared to be the most precise and comprehensive source available for log k′w data of cyclic nucleotides, it was used to calibrate the corresponding data set. The linear relationships observed led us to the hypothesis of a theoretically derivable dependence of log k′w from k′g. Using a gradient type of elution, the capacity factor (k′) for a given solute cannot be calculated as easily as in isocratic RP-HPLC, where k′ remains constant for given chromatographic conditions and is defined as shown in eq 4. tr and Vr are respectively the retention
k′ )
tr - tm Vr - Vm ) tm Vm
(4)
time and the retention volume of the solute, while tm and Vm are respectively the retention time and retention volume of an unretained solute. Since, during gradient elution, the composition of the mobile phase is changing constantly, k′ changes correspondingly. The capacity factors differ most at the beginning of elution, and for more retained solutes, the decrease is much steeper than for slightly retained compounds.16 As the capacity factors decrease during gradient elution, the migration of solutes increases. According to Jandera and Chura´cˇek,16 a differential increase in the column eluate volume, dV (the volume of the mobile phase that has passed through the column), causes a migration of the solute band maximum by a distance corresponding to a differential fraction of the column void volume, dVm. During this differential migration, the capacity factor of the given solute remains constant. From this, eq 5 can be derived: (16) Jandera, P.; Chura´cˇek, J. Gradient Elution in Column Liquid Chromatography; Journal of Chromatography Library 31; Elsevier Publ.: Amsterdam, 1985; Chapter 3. (17) Freiling, E. C. J. Am. Chem. Soc. 1955, 77, 2067-2071. (18) Freiling, E. C. J. Phys. Chem. 1957, 61, 543-548. (19) Snyder, L. R. Chromatogr. Rev. 1965, 7, 1-51. (20) Snyder, L. R. In High-Performance Liquid Chromatography, Advances and Perspectives; Horva´th, Cs., Ed.; Academic Press: New York, 1980; Vol. 1, pp 208-316. (21) Schoenmakers, P. J.; Billiet, H. A. H.; Tijssen, R.; de Galan, L. J. Chromatogr. 1978, 149, 519-537. (22) Jandera, P.; Chura´cˇek, J.; Svoboda, L. J. Chromatogr. 1979, 174, 35-50. (23) Snyder, L. R.; Dolan, J. W.; Gant, J. R. J. Chromatogr. 1979, 165, 3-30.
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Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
dVm ) Vm )
∫
V ′g 1
0
k′
dV
(6)
where V ′g is the net retention volume in gradient elution chromatography. V ′g can be obtained by correction of the measured retention volume for the column void volume (Vm) and the volume of the mixing devices of the gradient forming system (Vd). This procedure is allowed for solutes with capacity factors k′ > 10 for 100% water, since their migration along the column during delay time is negligible.16 Equation 6 was derived earlier17,18 and has been used in various modifications. An equivalent equation can be written by using the time instead of volume.19 Here, the retention volume is used, as it is shown in eq 6, since it is not dependent on the volume flow rate of the mobile phase for a given column. Equation 6 can be solved by introducing a function for the change in solvent composition (φ). For this reason, the concept of a linear solvent strength gradient was introduced.20 It is assumed that the mobile phase composition gradients are designed for each chromatographic system in such a way that the logarithms of the capacity factors of all compounds chromatographed decrease linearly with increasing volume of the eluent. A linear gradient of the concentration of the organic modifier in reversed-phase chromatography differs more or less from an ideal linear solvent strength gradient, especially at the end of the gradient run, where relatively high concentrations of organic solvent are reached.16 On chemically bonded nonpolar stationary phases, where the dependence of capacity factors on the concentration of the organic solvent in the mobile phase may be conveniently described by eq 7, linear solvent strength gradients are virtually identical with the gradients where the content of the organic modifier (φ) is changed in a linear manner. In eq 7, m is the slope and log k′w
log k′ ) log k′w - mφ
(7)
the intercept of the φ vs log k′ plot in isocratic elution chromatography. Equation 7 has been verified for many solutes in reversed-phase systems using chemically bonded hydrocarbon phases and various aqueous organic solvents as mobile phases.4,21-23 It is now necessary to introduce a function for the change of composition of the mobile phase during the gradient elution:
φ ) A + BV
(8)
Here, B is the steepness of the gradient, while A represents the content of the organic modifier at the start. The combination of eqs 7 and 8 gives
log k′ ) log k′0 - mA - mBV
(9)
where k′0 represents now the capacity factor of a solute under gradient starting conditions. In order to write eq 6 in a suitable form for integration, it is necessary to introduce a term for the change of k′. This can be taken from eq 9:
k′ ) k′0 × 10-m(A+BV)
(10)
Combination of eqs 6 and 10 yields
Vm )
∫
V ′g
0
1 × 10m(A+BV) dV k′0
(11)
is a useful tool to determine solute lipophilicity. Although the relationship of log P with log k′w data has already been investigated by several researchers,4,28-32 this correlation was determined here for the aromatic hydrocarbons again:
log P ) (1.085 ( 0.071)log k′w - (0.351 ( 0.170) r ) 0.977
By integration of eq 11, it is possible to derive the following relationship for the retention volume in reversed-phase chromatography where linear concentration gradients are applied:16
V ′g )
1 log(2.31mBk′0Vm × 10-mA + 1) mB
(12)
Equation 12 was introduced and validated by many researchers for reversed-phase chromatography where linear gradients of the concentration of the organic modifier are employed.22-26 By using a gradient with a starting mobile phase of 100% water, A in the equation above becomes 0 and k′0 becomes k′w. It is now possible to write
1 log(2.31mBk′wVm + 1) V ′g ) mB
(13)
Equation 13 can be rewritten to obtain a relationship for log k′w:
log k′w ) -log(2.31mBVm) + log(10mBV ′g - 1) (14) In the first term of this relationship, B and Vm are constants for a given chromatographic system. The value of m is dependent on the chemical structure and size of both solute and stationary phase used in the chromatographic system.27 The second term looks quite complex, but for larger values of V ′g the subtraction of 1 can be neglected, and the relationship becomes linear. For example, when plotting the function of eq 14, it can be shown that, for values of V ′g > 5, a correlation coefficient higher than 0.985 results from linear regression for the calculated values of log k′w vs V ′g. This shows that the linear relationship for log k′w measured by the conventional isocratic method and V ′g determined by gradient elution chromatography which was found in the experimental linear regression could also be derived theoretically. Since there is no extrapolation to water, actually log k′w is, of course, no longer an appropriate term for description of lipophilicity obtained by a gradient technique. In order to avoid any dependence on the chromatographic equipment, an apparent capacity factor (k′g) for gradient elution chromatography is defined if the net retention volume is divided by the column void volume:
Vg - Vd - Vm V ′g k′g ) ) Vm Vm
(15)
Since the solute capacity factor k′ changes constantly during gradient elution, k′g actually has no real physical meaning, but it (24) Jandera, P.; Chura´cˇek, J. J. Chromatogr. 1974, 91, 223-235. (25) Dolan, J. W.; Gant, J. R.; Snyder, L. R. J. Chromatogr. 1979, 165, 31-58. (26) Jandera, P.; Chura´cˇek, J.; Svoboda, L. J. Chromatogr. 1980, 192, 37-51. (27) Tan, L. C.; Carr, P. W. J. Chromatogr. 1993, A656, 521-535.
F ) 235.0
(16)
n ) 13
The resulting equation fits considerably well with corresponding data from Tayar et al.28 DISCUSSION As shown above, the empirically observed linear relationship between the two coefficients k′g and log k′w is predictable by theoretical considerations. Since log k′w, on the other hand, correlates strongly with log P data, the apparent gradient capacity factor k′g should correlate with log P as well. Indeed, comparable linearity is obtained, compared to eq 16, when k′g factors are compared directly with log P data from the literature:33,34
log P ) (0.120 ( 0.010)k′g - (0.321 ( 0.211) r ) 0.965
F ) 148.4
(17)
n ) 13
Interestingly, the differences observed between the corresponding correlation factors for the relationships of k′g and log k′w vs log P (eq 16) can be completely eliminated by introduction of a correction term for H-binding potentials:3,11,33,35
log P ) (0.592 ( 0.175)k′g - (0.040 ( 0.063)ha + (0.147 ( 0.013)hb - (0.964 ( 0.334) (18) r ) 0.989
F ) 130.7
n ) 13
log P ) (0.149 ( 0.158) log k′w - (0.112 ( 0.064)ha + (1.079 ( 0.103)hb - (0.277 ( 0.302) (19) r ) 0.987
F ) 109.0
n ) 13
Obviously, both log k′w and k′g are reliable descriptors of solute lipophilicity; however, the gradient technique appears to be considerably more facile and safer with respect to experimental errors. Since it is possible to include an internal standard for calibration in each run, the accuracy and reproducibility of the applied gradient are measured simultaneously, and potential deviations in retention behavior as well as apparative problems can easily be recognized. (28) El Tayar, N.; van de Waterbeemd, H.; Testa, B. Quant. Struct.-Act. Relat. 1985, 4, 69-77. (29) Braumann, T.; Genieser, H.-G.; Lu ¨ llmann, C.; Jastorff, B. Chromatographia 1987, 24, 777-782. (30) Minick, D. J.; Frenz, J. H.; Patrick, M. A.; Brent, D. A. J. Med. Chem. 1988, 31, 1923-1933. (31) Yamagami, C.; Takami, H.; Yamamoto, K.; Miyoshi, K.; Takano, N. Chem. Pharm. Bull. 1984, 32, 4994-5002. (32) Hong, H.; Wang, L.; Han, S.; Zou, G. Chemosphere 1996, 32, 343-351. (33) Hansch, C.; Leo, A. Pomona College Medical Chemistry Project Log P and Parameter Database, Issue 23, Comtex Scientific, New York, 1983. (34) Valko´, K.; Slegel, P. J. Chromatogr. 1993, A631, 49-61. (35) Tsantili-Kakoulidou, A.; Filippatos, E.; Todoulou, O.; Papadaki-Valiraki, A. J. Chromatogr. 1993, A654, 43-52.
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Moreover, in contrast to the isocratic capacity factors, there is no need for transformation of the corresponding gradient retention factors by linear regression. Also, extrapolation to elution with water is not necessary, since k′g already represents an array of retention data from different elution conditions. The gradient method offers so many advantages that it could become an adequate alternative to the traditional log P shakeflask procedure, at least concerning uncharged molecules. For charged substances, however, the influence of pH, ion strength, and choice of buffer cannot be neglected. Particularly, the ability of building ion pairs has a very strong control over retention behavior. Compared to nucleosides, this ion-pairing capability of the lipophilic triethylammonium cation used in this study leads to excessive retention for the negatively charged cyclic nucleotides. Thus, the comparison of the lipophilicity data (k′g) for charged and uncharged compounds determined by chromatography should be done carefully since it depends strongly on the type of the buffer. The different retention behavior of the three types of compounds investigated is demonstrated by the deviating slopes of the corresponding k′g-log k′w plots (Figure 1). For positively charged solutes, the method must be modified by choosing a buffer system consisting of a lipophilic anion such as sodium dodecyl sulfate. The dependency on the buffer systems therefore gives reason for the division of solutes into different groups, discriminating at least between positively and negatively charged and neutral solutes, e.g., in QSRR investigations. Despite these limitations, k′g data can actually be obtained for chemically different structures within a single run. This opens up the interesting possibility to determine a lipophilic ranking even among structurally unknown components, e.g., in environmentally important samples. The presence of charged solutes, however, could then easily be detected by additional runs using ion pair reagents, which should considerably influence only their retention behavior. Using the presented experimental design, substances with a retention volume up to 75 mL can be analyzed. This is equivalent to a log k′w of approximately 5 for substituted aromatic hydrocarbons (log P ≈ 5) and 6 for nucleosides and cyclic nucleotides. For investigations concerning substances with higher lipophilicity, a modification of the RP-HPLC system using different stationary phases or organic modifiers is necessary. It remains to be investigated whether stationary phases with considerably shorter alkyl ligands such as RP-2 or RP-8 are suitable as well. Actually, the type of the reversed-phase column should not be critical, since it has been shown that columns based on octadecyl polyvinyl copolymer36 and even an octyl-modified stationary phase (RP-8)29 gave comparable results in log k′w determinations. In order to get closer to a linear solvent strength gradient, it would be interesting to apply nonlinear solvent composition gradients as well. In this case, eq 8 must be modified correspondingly. Since some of the nucleobases present in the nucleosides and the cyclic nucleotides, respectively, were identical, we also investigated a potential correlation between both classes of compounds: (36) Bechalany, A.; Tsantili-Kakoulidou, A.; El Tayar, N.; Testa, B. J. Chromatogr. 1991, 541, 221-229.
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k′g(nucleotides) ) (0.320 ( 0.049)k′g(nucleosides) + (1.856 ( 0.437) (20) r ) 0.967
F ) 43.5
n)5
Although the data set is limited, it is obvious that the lipophilicity of nucleotides can be predicted from corresponding nucleoside data and vice versa. CONCLUSIONS It could be shown that linear gradient reversed-phase HPLC is a facile tool for lipophilicity determinations and that the results are equivalent to those obtained by isocratic methods. However, the gradient technique has obvious advantages over the isocratic procedure in convenience and applicability. Our results open up the possibility to determine the lipophilicity of a given solute simply by measuring its retention on an RP-18 column during linear gradient elution accompanied by internal standards of known lipophilicity. These standards, of course, should have different hydrophobicity but should offer similar molecular interactions as compared to the sample. It is of particular convenience that analysis can be performed in only one run, which might be important if only a limited amount of a given compound is available. The chance for making mistakes is rather small and is mainly limited to technical parameters such as a constant flow rate and the linearity of the gradient applied. Deviations in gradient linearity, however, can easily be realized by the retention behavior of the internal standards. Based on these findings, it should be possible to adapt the reversed-phase gradient HPLC technique to any lipophilicity measurements, regardless of whether log P, log k′w, or other descriptors are preferred, provided that the system is linear also at high concentrations of the organic modifier methanol. As long as the solute lipophilicity does not exceed a certain limit (log P ≈ 5), the method is suitable as described. For more hydrophobic solutes, either the stationary phase or the length of the column has to be changed, or an organic modifier with a higher eluotropic property is required. The scope of the technique presented is obviously not limited to the three classes of compounds described but could serve as a method for lipophilicity determinations of various structures within multiple environmental and pharmacological purposes. A detailed analysis of lipophilicity data with respect to molecular and structural properties will be presented in subsequent papers. ACKNOWLEDGMENT The skillful technical assistance of Ursula Havemann is gratefully acknowledged. This work was supported by the Fonds der Chemischen Industrie. LIST OF SYMBOLS AND DEFINITIONS A
coefficient for the starting composition of the eluent in gradient HPLC
B
factor representing the steepness of the applied gradient
ha, hb
indicators for H-binding acceptor and donor potentials
k′
capacity factor of isocratic HPLC method
k′0
capacity factor for starting conditions in gradient HPLC
Vg
retention volume in gradient elution HPLC
k′g
apparent capacitiy factor of gradient HPLC method
V ′g
net retention volume in gradient elution HPLC
k′w
extrapolated capacity factor for 100% water in isocratic HPLC
Vm
retention volume of an unretained solute
Vr
retention volume in isocratic elution HPLC
m
slope of the φ vs log k′ plot
td
delay time of gradient system
tg
retention time in gradient elution HPLC
tm
retention time of an unretained solute
Received for review December 6, 1996. Accepted March 21, 1997.X
tr
retention time in isocratic elution HPLC
AC961246I
φ
volume fraction of methanol in isocratic elution HPLC
Vd
delay volume of the gradient forming system
X
Abstract published in Advance ACS Abstracts, May 1, 1997.
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