Anal. Chem. 2006, 78, 239-249
Simultaneous Determination of pKa and Lipophilicity by Gradient RP HPLC Paweł Wiczling, Piotr Kawczak, Antoni Nasal, and Roman Kaliszan*
Department of Biopharmaceutics and Pharmacodynamics, Medical University of Gdan˜sk, Gen. J. Hallera 107, 80-416 Gdan˜sk, Poland
High-performance methods of testing of drug candidates for properties of pharmacokinetics and pharmacodynamics importance, in particular lipophilicity and acidity, are necessary to overcome innovation stagnation in the pharmaceutical industry. Reversed-phase high-performance liquid chromatography (RP HPLC) might be a unique tool for the determination of both pKa and the apparent (pHdependent) partition coefficient, applicable in highthroughput analysis of multicomponent mixtures, e.g., samples originating from automated synthesis. In this work, the pH/organic modifier gradient RP HPLC is presented as a means of simultaneous determination of an analyte’s acidity and lipophilicity. The approach consists of retention measurements in a series of methanol gradient runs differing in pH range and duration of the gradient. Two different models of the influence of pH on retention in organic modifier gradient RP HPLC are compared regarding the quality of the simultaneously determined lipophilicity and dissociation constants. Advantages of the proposed approach over currently employed procedures are that it can be applied to compound mixtures, it requires only minute amounts of substances, and pKa values can be determined in the range 3-10 units and lipophilicity in the range 0-7 units. Verification of the reliability of the parameters determined by the new method was demonstrated on a series of 93 acidic and basic drug analytes. Knowledge of the aqueous ionization constant, pKa, lipophilicity, log P, and distribution coefficient, log D, of an analyte is of a primary concern in life and material sciences. In pharmaceutical research these structural parameters of drug candidates can be used for prediction of their pharmacokinetic properties, i.e., absorption, distribution, metabolism, elimination, and toxicity. Ionization constants, pKa, characterize the charge state of an analyte at particular pH of its environment. Partition coefficient, P, and apparent (pH-dependent) partition coefficient, D, refer to chemical equilibrium of partitioning of all the charge-state forms of the analyte between two immiscible liquids, like water and octanol.1 The critical explanation of instrumental methods available for determination of pKa, log P, and log D can be found in a report * To whom correspondence should be addressed.
[email protected]. (1) ) Avdeef, A. Curr. Top. Med. Chem. 2001, 1, 277-351. 10.1021/ac0512103 CCC: $33.50 Published on Web 11/25/2005
E-mail:
© 2006 American Chemical Society
by Avdeef.1 However, nowadays methods are not useful when an analyte is available in minute amounts only or as a complex mixture. Additionally, for many compounds sparingly soluble in water, the determination of pKa in aqueous solution can be problematic. To overcome the solubility problem, an organic solvent alone or a mixed-solvent approach is a necessity. The calculation of the experimental value is obtained by extrapolation of a previously established straight line, i.e., Yasuda-Shedlovsky extrapolation.2,3 The method that one can readily use for determination of pKa and lipophilicity is reversed-phase high-performance chromatography (RP HPLC). It has many advantages as it can deal with mixtures, the mass spectroscopy detection enables identification of analyzed components, and the appropriate equipment is now widely available. However, there has not yet been elaborated a strategy enabling a fast and accurate simultaneous determination of an analyte’s dissociation constant and lipophilicity. The isocratic determination of pKa is time-consuming and generally does not apply to complex mixtures. The pH-gradient method previously presented by us4,5 is faster, but each analyte in the mixture needs to be treated separately. As regards lipophilicity, the organic modifier gradient method , expressed as the hydrophobicity index, seems to be appropriate for a fast analysis of complex samples.6,7 The approach presented in this paper consists of examining the influence of pH on retention in organic modifier gradient RP HPLC for the purpose of simultaneous determination of dissociation constant and lipophilicity. The modeling of retention is based on the theory of combined pH/organic modifier gradient8,9 and on a simplified approach proposed by Canals et al.10 The comprehensive explanation of experimental details and factors influencing the determined parameters is presented. The validity (2) Avdeef, A.; Box, K. J.; Comer, J. E. A.; Gilges, M.; Hadley, M.; Hibbert, C.; Patterson, W.; Tam, K. Y. J. Pharm. Biomed. Anal. 1999, 20, 631-641. (3) Albert, A.; Serjeant, E. P. The Determination of Ionization Constants; Chapman and Hall: London, 1984. (4) Wiczling, P.; Markuszewski, M. J.; Kaliszan, R. Anal. Chem. 2004, 76, 30693077. (5) Kaliszan, R.; Wiczling, P.; Markuszewski, M. J. J Chromatogr., A 2004, 1060, 165-175. (6) Valko´, K.; Bevan, C.; Reynolds, D. Anal. Chem. 1997, 69, 2022-2029. (7) Du, Ch. M.; Valko´, K.; Bevan, C.; Reynolds, D.; Abraham, M. H. Anal. Chem. 1998, 70, 4228-4234. (8) Wiczling, P.; Markuszewski, M. J.; Kaliszan, M.; Kaliszan, R. Anal. Chem. 2005, 77, 449-458. (9) Kaliszan, R.; Markuszewski, M. J.; Wiczling, P. Pol. J. Chem. 2004, 78, 1047-1056. (10) Canals, I.; Valko´, K.; Bosch, E.; Hill, A. P.; Rose´s, M. Anal. Chem. 2001, 73, 4937-4945.
Analytical Chemistry, Vol. 78, No. 1, January 1, 2006 239
of the presented method is experimentally verified on a set of basic and acidic analytes of different physicochemical properties. MATERIALS AND METHODS Experiments were done using a Merck-Hitachi LaChrome (Darmstadt, Germany, and San Jose, CA) apparatus of 2-mL dwell volume, Vd, equipped with a diode array detector, autosampler, and thermostat. Chromatographic data were collected using a D-7000 HPLC System Manager, version 3.1 (Merck-Hitachi). Numerical analysis and data processing were done with Matlab Software version 7.0 (The MathWorks, Inc., Natick, MA). An XTerra MS C-18 column, 150 × 4.6 mm i.d., particle size 5 µm (Waters Corp., Milford, MA), with a low silanol activity was used. A 1% urea solution was injected to determine the column dead volume, Vo, which was 1.60 ( 0.02 mL. Chromatographic measurements were done at 25 °C with an eluent flow rate of 1.0 mL/min. All the reagents and the analytes employed were of the highest commercially available quality. To determine pKa, a proper measurement of eluent pH is a precondition. The details of proper assessment of pH in mixed organic/water mobile phases are discussed by Rose´s.11 In this work, the pH of the mobile phase is measured after mixing the aqueous buffer and the organic modifier. The electrode system is calibrated with the usual aqueous standards. This leads to the absolute pH scale, swpH. This scale has been defined and recommended by IUPAC.12 Also the pKa obtained from data expressed in the swpH scale leads to the thermodynamically meaningful dissociation constant of the compound, also expressed in the same scale ( swpKa). To control pH changes during chromatographic runs, a universal buffer was used. The base buffer solution was formed using three compounds, each at a concentration of 0.008 M: citric acid, tris(hydroxymethyl)aminomethane, glycine. Buffer of wwpH ) 11.50 (buffer C) was made by adding 3 M KOH to the base solution to obtain the desired pH. Buffer of wwpH ) 2.50 (buffer D) was made by adding the necessary amounts of 1 M HCl. The mobile phases contained buffers D and C in different proportions and methanol as the organic modifier (solvent B). The pH of the buffers was measured at 25 °C. The measurements were done with an HI 9017 pH meter (Hanna Instruments, Bedfordshire, U.K.). Theory. The analyte retention can by predicted by an equation describing gradient liquid chromatography with programmed pH and organic modifier content changes for monoprotic acids and bases:8
∫t
t′ 1
0
0
1 + 10
s s wpH(t)-wpKa(φ(t))
) wwpKa + Rφ
(2)
Thus, combining eq 2 and eq 1 one obtains
∫
t′R
0
1 1 + 10wpH(t)-wpKa-Rφ(t) dt ) 1 -S φ(t) t0 k 10 1 + k 10-S2φ(t)10 swpH(t)-wwpKa-Rφ(t) w1 w2 (3) s
w
In Figure 1 are presented theoretical changes of retention times with pH in organic modifier gradient RP HPLC for three hypothetical analytes differing in R. The pH is assumed to be constant during whole chromatographic run. As can be seen, the three plots are sigmoidally shaped curves, which slightly differ in their slopes. These minimal differences in slope cause problems in obtaining a statistically significant R value by nonlinear curve fitting of eq 3. Even as many as 30 experiments do not produce satisfactory results. Thus, other and simpler models must be elaborated. Equation 3 can be simplified by neglecting changes of pKa with organic modifier content. Thus, eq 1 can be presented as
∫
t′R
0
1 t0
s
1 + 10wpH(t)-pKa chrom kw110
-S1φ(t)
+ kw210
-S2φ(t)
dt ) 1
s pH(t)-pK a chrom w
10
(4)
s
(1)
where t′R ) tR - t0 means the measured gradient retention time, tR, less the void time, t0, pH(t) and φ(t) are functions describing changes of mobile-phase pH and its composition at column inlet during a chromatographic run. The pH(t) and φ(t) functions are (11) Rose´s, M. J. Chromatogr., A 2004, 1037, 283-298. (12) IUPAC, Compendium of Analytical Nomenclature. Definitive Rules 1997, 3rd ed, Blackwell: Oxford, 1998. http://www.iupac.org/publications/analytical_compendium.
240
s wpKa
dt ) 1
kw110-S1φ(t) + kw210-S2φ(t)10wpH(t)-wpKa(φ(t)) s
defined by the pump program applied. kw1 and kw2 represent retention factors (usually hypothetical) for neat water as the mobile phase of individual ionized and un-ionized form of the analyte. For bases kw1 < kw2, thus kw1 refers to the ionized form and kw2 to the nonionized form of the analyte; in case of acids kw1 > kw2 and the reverse notation holds true. S is a parameter showing how rapidly retention factor is changing with changes in organic modifier content. pKa(φ) is a function describing changes of pKa value with changes of organic modifier content. The left-side indexes at the pH and pKa symbols indicate the scales in which these parameters were determined. Equation 1 is a general equation describing retention in any chromatographic mode, whether pH or organic solvent content changes or not, i.e., in isocratic, organic solvent gradient, pH gradient, and double pH/organic solvent gradient modes, and is valid for monoprotic acids and bases. The good retention prediction ability of eq 1 for a 12-compound mixture was confirmed in our previous work8 for linear changes of pKa with organic modifier content in the mobile phase:
Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
where pKa chrom cannot be considered as a thermodynamic pKa value, but it is still a parameter related to analyte dissociation. It can be treated as resultant of all swpKa values occurring during the chromatographic runs as a consequence of the changes in organic modifier contents. Among the advantages of this model are the following: the simpler form of equation and hence a better stability of fitting; the procedure can be applied when the analyte elutes after completing a gradient (at isocratic conditions). The lack of the extrapolation term (R) prohibits obtaining the thermodynamic pKa values, but instead, there is no risk of obtaining unreliable results due to inadequacy of the determined R values.
Figure 1. Theoretically predicted retention times for three hypothetical analytes characterized by the following: kw1 ) 100, kw2 ) 10, S1 ) S2 ) 3.5, pKa ) 7, and R ) 2 (analyte I); R ) 0 (analyte II); and R ) -2 (analyte III). The following parameters of the model RP HPLC system were used in the calculations: t0 ) 1 min, td ) 0 min, tG ) 20 min, and φ ranging from 0 to 0.8. Circle represents retention at pH equal to the analyte II pKa, and square represents the inflection point of the curve.
To determine constants of eq 4, one needs to collect either a set of isocratic RP HPLC data differing in swpH and organic modifier contents or a set of gradient data obtained at different pH and organic modifier content change rates. The most convenient seems to be using organic modifier gradients at constant s wpH or a double pH/organic modifier gradient with a wide organic modifier concentration range and a small variation of s wpH. From these data, one can calculate constants of eq 4 by nonlinear least-squares curve fitting. In this work, a double pH/ methanol gradient RP HPLC is used as simpler for carrying over. The changes of organic modifier gradient retention times with pH (Figure 1) can also be described by a sigmoid-shaped curve with slope parameters:10
tR )
tR1 + tR210s(pKa inf-pH) 1 + 10s(pKainf-pH)
(5)
examining analyte II retention profile presented in Figure 1, one realizes that there are differences between pKa inf and the analytes’ pKa. This seems to depend on many conditions, like analyte retention and parameters of the gradient, which are difficult to evaluate without numerical methods. To determine constants of eq 5 or 6, one needs to collect a set of gradient data at different swpH and organic modifier content changes. Using eq 5 or 6 requires less experiments to get significantly valid parameters than using eq 4, however. The correlation between the chromatographic lipophilicity parameters and the octanol/water partition data is generally poor when diverse sets of compounds are considered. To overcome this, a φ0 parameter was defined as a more appropriate chromatographic measure of lipophilicity.13 φ0 is the percentage of methanol required to achieve an equal distribution of the analyte between the mobile and the stationary phase.
φ0 ) Which, for additional changes in pH, can be rearranged to (Appendix)
∫
t′R
0
1 + 10
s(pKa inf-pH(t))
t′R1 + t′R210s(pKainf-pH(t))
)1
(6)
where for bases tR1 < tR2 and tR1 refers to the retention of ionized and tR2 to the retention of nonionized form of the analyte; in the case of acids, tR1 > tR2 and the notation is reversed. t′R denotes adjusted retention time, s is the slope parameter, and pKa inf denotes the curve inflection point. It could intuitively be the assumed that pKa inf corresponds to the pKa value.10 However, by
log kw × 100% S
(7)
The φ0 correlates better with lipophilicity determined in octanol/water partition systems than log kw.14 In this work, different lipophilicity parameters are related to each other. The retention time of the nonionized form of the analyte, obtained directly from methanol gradient RP HPLC, is shown to provide comparable results as φ0 when related to log P. RESULTS To obtain well-fitted constants of eq 4 and eq 6, 18 RP HPLC runs in total were carried out at different pH/organic solvent (13) Valko´, K. TrAC, Trends Anal. Chem. 1987, 6, 214-216. (14) Valko´, K.; Slegel, P. J. Chromatogr. 1993, 631, 49-61.
Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
241
Table 1. Changes of the Content of the Eluent during the pH/Methanol Double-Gradient RP HPLC Serving To Determine the Experimental Data Necessary for Eq 3a pump program eluent component %Bo - %Bf %Co - %Cf %Do - %Df a
1
2
3
4
5
6
7
8
9
5-80 83-17 12-3
5-80 74-15 21-5
5-80 65-13 30-7
5-80 56-11 39-9
5-80 46-8 49-12
5-80 37-6 58-14
5-80 28-4 67-16
5-80 19-2 76-18
5-80 10-0 85-20
Lower right index 0 denotes initial and f final content of the components B-D in the eluent.
Figure 2. Changes of pHsw with increasing methanol content during individual pH/methanol double gradient RP HPLC runs (1-9) characterized in Table 1.
gradient conditions. These included two series of experiments during which the mobile-phase component concentrations change as shown in Table 1. The two series differed in duration of gradient: tG ) 20 min (series I) and tG ) 60 min (series II). The changes of methanol (solvent B), buffer C, and buffer D contents (Table 1) produced changes in swpH as shown in Figure 2. The chromatographic results (retention times, tR) are presented in Figure 3 for an eight-component mixture. Retention data from the two analysis series (18 experiments) were used for fitting to eq 4. Only series II of nine experiments (tG ) 60 min) was used in the case of eq 6. The advantage of the procedure is that generally all the analytes are washed out of the column and there is not need to search for specific conditions providing measurable retention times as in the case at isocratic conditions. Additionally, small variations in pH of the eluent in each series of experiments ensure approximately sigmoidal changes of retention times in nine individual experiments. That gives an opportunity of recognizing peaks in the chromatograms. From Figure 4 it can be seen that an eight-component mixture can readily be separated and the peaks can be identified using standard UV-visible detection. Of course, identification can be facilitated when using mass spectrometry detection. All the studied test drug analytes were divided into subgroups of ∼5, and their mixtures were chromatographed. Identification 242 Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
of individual analytes was done by applying onto the column the single analyte in one of the 18 chromatographic runs. Its retention in the remaining RP HPLC runs was evaluated,keeping in mind the approximately sigmoidal changes of the given analyte retention parameter. The experimental data obtained for 93 monoprotic acids and bases in 18 RP HPLC runs were fitted to eq 4. The fitted parameters are presented in Table 2. Figure 5 presents the dependence between the literature pKa data and the here obtained experimental pKa chrom data using eq 4. The corresponding square of the correlation coefficient, R2 ) 0.890, and root-mean-square error, RMSE ) 0.650, indicate a good agreement between the pKa chrom and the reference pKa data ( wwpKa). The difference between the literature and the experimental values is due to the influence of organic modifier, which was neglected employing eq 4. Nevertheless, the differences are not that large when methanol is used as the organic modifier of the RP HPLC mobile phase. The chromatographically derived parameters of lipophilicity, φ0 and log kw, are related to the reference slow equilibrium lipophilicity parameter, log P, in Figure 6 and Figure 7, respectively. The agreement between the chromatographically obtained parameters and the literature octanol/water partition data is moderate. Evidently φ0 better correlates (R2 ) 0.782) with log P than log kw (R2 ) 0.637). The simpler approach utilizing eq 6 involves one series of retention data in organic modifier gradient at different pH. The
Figure 3. Retention times of eight-component analyte mixture (1, salicylamide; 2, phenobarbital; 3, p-anisidine; 4, warfarine; 5, prazosine; 7, haloperidol; 8, promethazine; 6, diclofenac) in two series (I and II) of nine experiments each.
Figure 4. Example chromatograms obtained for eight-component analyte mixture (1, salicylamide; 2, phenobarbital; 3, p-anisidine; 4, warfarine; 5, prazosine; 7, haloperidol; 8, promethazine; 6, diclofenac) in series I (tG ) 20 min) of nine experiments.
experimental data fitted to eq 6 produce results given in Table 2. One gets the tR versus swpH curve inflection point, pKa inf, which correlates to the literature pKa as shown in Figure 8. R2 is 0.760 and RMSE is 0.954. The results are worse than those provided by the previously discussed model (Figure 5). In Figure 8, a clear separation of acids and bases is observed. Acidic analytes pKa values are overestimated, and the pKa values of bases are generally lower than the literature pKa values. It might be because the inflection point is not a proper indicator of pKa value. The pKa values appear to be shifted by a constant value from the inflection
point: negatively in the case of acids and positively in the case of bases. Interestingly, retention times of nonionized form of analytes in organic modifier gradient RP HPLC correlate to log P equally as well as φ0 (Figure 9). Thus, using the proposed method, one can simultaneously determine analyte dissociation constant and lipophilicity after performing a series of nine methanol gradient RP HPLC runs at different pH. Comparison of the pKa values obtained by fitting chromatographic data to eq 4 and to eq 6, presented in Figure 10, leads to Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
243
Table 2. log kw1, S1, log kw2, S2, and pKa chrom Parameters Obtained by Nonlinear Fitting to Eq 4 and tR1, tR2, pKa and s Parameters Obtained by Nonlinear Fitting to Eq 6a eq 4 analytesb acetaminophen (A) acridine (B) allobarbital (A) 2-amino-5-methylpyridine (B) aminophenazone (B) amitriptyline (B) aniline (B) p-anisidine (B) barbital (A) benzoic acid (A) Benzyllamine (B) betaxolol (B) 2,2′-bipyridene (B) brucine (B) carteolol (B) celiprolol (B) chinoline (B) chlordiazepoxide (B) 2-chloro-4-nitrophenol (A) chloropropamide (A) chlorpromazine (B) chlorprotixene (B) cimetidine (B) clomipramine (B) Clonidine (B) clotrimazole (B) cocaine (B) codeine (B) cyclobarbital (A) desipramine (B) diclofenac (A) diltiazem (B) 2,6-dimethyl-4-nitrophenol (A) diphenhydramine (B) dizopyramide (B) doxepine (B) esmolol (B) fenbufen (A) glipizide (B) haloperidol (B) imipramine (B) indomethacine (A)
244
inf,
eq 6
log kw1
S1
log kw2
S2
pKa chrom
φ0
t′R1
t′R2
pKa inf
s
pKalit
log P
0.99 ((0.04) 1.97 ((0.76) 1.82 ((0.04) 0.74 ((0.54) 1.34 ((0.14) 3.67 ((0.54) 0.35 ((1.48) 0.60 ((0.55) 2.02 ((0.08) 1.74 ((0.19) 0.45 ((0.92) 2.76 ((0.22) 1.06 ((0.18) 2.37 ((0.22) 2.02 ((0.22) 2.73 ((0.18) 0.94 ((0.28) 2.36 ((0.29) 2.36 ((0.22) 2.71 ((0.18) 3.78 ((0.57) 3.88 ((0.55) 1.42 ((0.07) 3.84 ((0.62) 1.19 ((0.08) 3.60 ((1.54) 2.17 ((0.18) 1.30 ((0.19) 2.27 ((0.10) 3.44 ((0.41) 3.82 ((0.41) 3.65 ((0.39) 2.58 ((0.15) 2.77 ((0.29) 2.32 ((0.20) 3.04 ((0.51) 2.40 ((0.15) 3.53 ((0.19) 3.79 ((0.69) 3.27 ((0.53) 3.30 ((0.56) 3.98 ((0.32)
5.09 ((0.42) 6.53 ((4.16) 3.65 ((0.19) 8.50 ((9.90) 7.12 ((1.41) 5.77 ((1.15) 8.58 ((30.11) 6.09 ((10.12) 4.03 ((0.32) 2.95 ((0.79) 5.11 ((17.85) 4.99 ((0.63) 6.14 ((1.94) 7.49 ((1.03) 7.07 ((1.25) 6.42 ((0.63) 7.31 ((3.65) 4.84 ((1.01) 3.58 ((0.63) 4.42 ((0.47) 5.61 ((1.13) 5.73 ((1.07) 7.80 ((0.72) 5.63 ((1.21) 4.74 ((0.75) 5.67 ((3.31) 5.25 ((0.74) 6.19 ((1.78) 3.93 ((0.31) 5.45 ((0.89) 4.73 ((0.70) 6.49 ((0.91) 3.71 ((0.37) 4.92 ((0.81) 5.96 ((0.85) 5.27 ((1.31) 5.56 ((0.57) 4.96 ((0.37) 6.00 ((1.45) 5.73 ((1.31) 5.26 ((1.27) 4.96 ((0.53)
0.00 ((2.98) 3.17 ((0.19) 0.81 ((0.10) 1.43 ((0.06) 2.21 ((0.04) 4.38 ((0.45) 1.05 ((0.01) 1.18 ((0.05) 0.80 ((0.12) 0.34 ((0.36) 1.41 ((0.13) 4.14 ((0.59) 2.13 ((0.02) 2.96 ((0.17) 3.13 ((0.40) 3.49 ((0.35) 2.29 ((0.04) 3.23 ((0.10) 0.98 ((0.10) 2.03 ((0.11) 4.54 ((0.49) 4.45 ((0.39) 1.91 ((0.05) 4.44 ((0.50) 1.85 ((0.08) 3.88 ((0.37) 3.54 ((0.29) 2.88 ((0.23) 1.12 ((0.13) 4.68 ((0.92) 3.39 ((0.41) 4.13 ((0.32) 1.15 ((0.14) 4.32 ((0.59) 4.83 ((0.81) 4.11 ((0.66) 3.71 ((0.39) 3.14 ((0.23) 3.17 ((0.57) 4.22 ((0.75) 4.53 ((0.68) 3.71 ((0.29)
7.90 ((63.77) 4.26 ((0.37) 3.23 ((1.20) 3.35 ((0.34) 4.52 ((0.15) 4.76 ((0.63) 2.62 ((0.10) 3.39 ((0.42) 2.90 ((1.45) 1.92 ((6.84) 2.73 ((0.69) 5.55 ((1.01) 3.97 ((0.09) 4.71 ((0.41) 5.42 ((0.94) 5.54 ((0.76) 3.81 ((0.14) 4.59 ((0.22) 2.26 ((0.93) 3.91 ((0.42) 4.99 ((0.68) 4.73 ((0.52) 5.12 ((0.25) 4.76 ((0.68) 3.53 ((0.35) 4.41 ((0.58) 4.89 ((0.55) 5.11 ((0.61) 3.27 ((1.09) 5.49 ((1.31) 4.94 ((0.85) 5.40 ((0.55) 3.31 ((1.18) 5.39 ((0.93) 6.58 ((0.89) 4.82 ((1.01) 5.63 ((0.76) 5.11 ((0.55) 5.82 ((1.49) 5.48 ((1.26) 5.09 ((0.96) 5.24 ((0.57)
10.30 ((0.24) 5.15 ((0.10) 8.53 ((0.06) 7.15 ((0.10) 5.03 ((0.03) 8.77 ((0.15) 4.58 ((0.09) 5.64 ((0.14) 8.31 ((0.09) 4.68 ((0.25) 9.46 ((0.22) 9.62 ((0.21) 4.36 ((0.03) 8.36 ((0.08) 10.06 ((0.20) 9.93 ((0.14) 5.02 ((0.03) 4.70 ((0.06) 5.60 ((0.17) 5.49 ((0.13) 8.46 ((0.16) 8.20 ((0.13) 7.56 ((0.04) 8.56 ((0.16) 8.76 ((0.07) 5.21 ((0.17) 8.66 ((0.12) 8.32 ((0.12) 8.55 ((0.09) 10.15 ((0.31) 5.53 ((0.19) 7.51 ((0.10) 7.45 ((0.11) 9.07 ((0.20) 10.98 ((0.53) 8.59 ((0.22) 9.95 ((0.17) 5.95 ((0.11) 6.74 ((0.32) 8.45 ((0.23) 8.85 ((0.23) 5.74 ((0.15)
19.46
4.17 ((0.04) 10.50 ((0.42) 13.70 ((0.04) 2.01 ((0.10) 5.07 ((0.06) 25.39 ((0.17) 0.80 ((0.10) 1.73 ((0.09) 15.00 ((0.11) 14.97 ((0.73) 1.47 ((0.09) 19.97 ((0.12) 4.29 ((0.28) 11.53 ((0.14) 9.62 ((0.11) 15.91 ((0.09) 3.05 ((0.17) 16.80 ((0.41) 21.19 ((0.47) 21.82 ((0.27) 26.96 ((0.12) 27.47 ((0.19) 5.37 ((0.05) 27.41 ((0.14) 5.76 ((0.12) 25.28 ((0.41) 13.59 ((0.09) 5.51 ((0.13) 18.39 ((0.03) 24.68 ((0.18) 32.10 ((0.28) 22.83 ((0.19) 23.24 ((0.08) 20.19 ((0.10) 13.53 ((0.11) 21.52 ((0.16) 15.07 ((0.09) 27.92 ((0.12) 26.21 ((0.40) 22.05 ((0.15) 23.95 ((0.10) 32.49 ((0.24)
-1.26 ((18.86) 27.65 ((0.11) 3.97 ((0.13) 9.55 ((0.11) 15.82 ((0.02) 38.27 ((0.32) 6.36 ((0.03) 6.90 ((0.05) 4.05 ((0.29) 1.68 ((0.28) 11.45 ((0.52) 31.39 ((0.48) 16.50 ((0.04) 23.24 ((0.22) 23.06 ((0.78) 25.58 ((0.53) 19.04 ((0.05) 26.57 ((0.07) 5.85 ((0.33) 15.49 ((0.23) 38.21 ((0.18) 39.10 ((0.24) 11.52 ((0.06) 38.99 ((0.23) 14.24 ((0.24) 35.10 ((0.09) 28.60 ((0.15) 20.99 ((0.18) 6.76 ((0.08) 37.87 ((1.88) 26.70 ((0.25) 31.50 ((0.20) 6.77 ((0.13) 33.66 ((0.22) 32.69 ((1.50) 35.16 ((0.26) 27.20 ((0.51) 23.45 ((0.17) 20.50 ((0.40) 32.27 ((0.25) 37.65 ((0.21) 28.36 ((0.18)
10.77 ((2.89) 4.29 ((0.04) 8.86 ((0.03) 6.92 ((0.05) 4.52 ((0.01) 8.04 ((0.06) 4.44 ((0.03) 5.48 ((0.04) 8.74 ((0.05) 5.00 ((0.11) 9.36 ((0.09) 8.99 ((0.08) 3.87 ((0.03) 7.79 ((0.05) 9.50 ((0.10) 9.49 ((0.09) 4.40 ((0.02) 4.07 ((0.05) 6.12 ((0.09) 5.65 ((0.11) 7.69 ((0.05) 7.43 ((0.07) 7.29 ((0.03) 7.86 ((0.06) 8.46 ((0.06) 4.46 ((0.06) 7.87 ((0.03) 7.51 ((0.03) 8.97 ((0.01) 9.67 ((0.26) 5.42 ((0.11) 6.87 ((0.08) 8.01 ((0.02) 8.26 ((0.04) 9.84 ((0.13) 7.81 ((0.06) 9.33 ((0.07) 5.87 ((0.07) 6.92 ((0.26) 7.78 ((0.07) 8.04 ((0.04) 5.55 ((0.13)
0.88 ((0.77) 1.12 ((0.07) 0.98 ((0.05) 1.16 ((0.10) 0.91 ((0.01) 0.70 ((0.07) 0.96 ((0.06) 0.75 ((0.05) 0.94 ((0.10) 0.83 ((0.15) 0.76 ((0.08) 0.70 ((0.07) 1.03 ((0.05) 0.93 ((0.10) 0.73 ((0.08) 0.78 ((0.08) 0.97 ((0.03) 1.15 ((0.12) 0.74 ((0.11) 0.83 ((0.17) 0.70 ((0.05) 0.80 ((0.08) 0.95 ((0.06) 0.68 ((0.06) 1.07 ((0.15) 1.12 ((0.14) 0.76 ((0.04) 0.78 ((0.04) 1.00 ((0.02) 0.60 ((0.11) 1.20 ((0.34) 0.89 ((0.13) 0.92 ((0.04) 0.68 ((0.04) 0.63 ((0.06) 0.66 ((0.05) 0.74 ((0.06) 1.01 ((0.17) 0.42 ((0.12) 0.64 ((0.06) 0.62 ((0.03) 1.12 ((0.36)
9.38
0.46
5.45
3.40
7.77
1.15
7.22
1.02
5.00
1.00
9.40
4.92
4.60
0.90
5.34
0.95
8.14
0.65
4.21
0.65
9.33
1.09
9.40
2.81
4.33
1.50
8.28
0.98
9.74
1.42
9.66
1.92
4.90
2.03
4.80
2.44
5.45
2.55
5.13
2.27
9.30
5.41
8.80
5.18
6.80
0.40
9.50
5.19
8.05
1.59
6.12
6.26
8.61
2.30
8.10
1.40
7.51
1.77
10.40
4.90
4.15
4.51
7.70
2.70
7.07
3.00
8.98
3.27
10.40
2.58
9.00
4.29
9.17
2.01
4.51
3.20
5.90
1.91
8.66
4.30
9.50
4.80
4.50
4.27
Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
74.48 49.92 42.74 48.80 91.92 40.08 34.68 49.97 58.99 51.87 74.56 53.55 62.96 57.71 63.12 59.97 70.34 65.91 61.43 91.08 94.14 37.21 93.29 52.26 88.03 72.40 56.48 57.78 85.15 80.77 76.51 69.45 80.05 73.49 85.36 65.86 71.21 63.26 76.98 88.85 80.39
Table 2 (Continued) eq 4
eq 6
analytesb
log kw1
S1
log kw2
S2
pKa chrom
φ0
t′R1
t′R2
pKa inf
s
pKalit
log P
indoramine (B)
2.71 ((0.31) 4.20 ((0.80) 3.48 ((0.28) 1.43 ((0.12) 0.96 ((0.12) 2.02 ((0.12) 2.10 ((0.15) 0.83 ((0.26) 4.39 ((1.05) 2.12 ((0.15) 1.35 ((0.58) 2.77 ((0.52) 3.19 ((0.28) 0.82 ((0.28) 1.10 ((0.42) 0.47 ((0.25) 3.25 ((0.37) 1.62 ((0.03) 0.74 ((0.44) 3.56 ((0.48) 2.31 ((0.19) 3.13 ((0.44) 4.04 ((0.51) 2.06 ((0.10) 4.21 ((0.77) 1.88 ((0.18) 1.65 ((0.13) 2.69 ((0.07) 3.33 ((0.20) 1.08 ((0.26) 1.49 ((0.19) 3.23 ((0.53) 3.21 ((0.61) 3.53 ((0.52) 2.70 ((0.24) 3.08 ((0.16) 4.02 ((0.88) 1.37 ((0.02) 1.77 ((0.20) 2.83 ((0.30) 1.38 ((0.04) 2.89 ((0.12) 3.98 ((1.01)
5.71 ((1.00) 6.89 ((1.66) 5.00 ((0.56) 4.36 ((0.85) 5.22 ((1.47) 5.87 ((0.59) 5.29 ((0.68) 6.72 ((4.56) 5.96 ((1.82) 5.00 ((0.64) 6.66 ((5.45) 4.00 ((1.22) 4.35 ((0.58) 5.66 ((4.15) 7.88 ((5.29) 5.81 ((4.82) 4.92 ((0.81) 2.85 ((0.15) 9.27 ((7.63) 5.39 ((1.01) 4.91 ((0.70) 7.73 ((1.46) 5.65 ((0.94) 4.19 ((0.39) 5.75 ((1.35) 6.64 ((1.09) 5.59 ((0.88) 4.43 ((0.19) 7.25 ((0.59) 7.43 ((3.37) 8.54 ((1.89) 5.18 ((1.24) 5.30 ((1.46) 5.73 ((1.15) 4.83 ((0.68) 4.68 ((0.37) 6.41 ((1.82) 3.27 ((0.12) 2.43 ((0.63) 5.34 ((0.85) 5.30 ((0.31) 4.28 ((0.28) 5.69 ((1.91)
4.01 ((0.50) 4.37 ((0.33) 2.83 ((0.19) 3.42 ((0.19) 1.52 ((0.04) 3.21 ((0.22) 3.28 ((0.35) 1.03 ((0.01) 4.72 ((0.34) 3.54 ((0.28) 2.97 ((0.23) 1.94 ((0.24) 2.51 ((0.23) 2.50 ((0.15) 2.09 ((0.06) 2.11 ((0.04) 2.68 ((0.41) 0.45 ((0.14) 1.67 ((0.02) 4.95 ((1.02) 3.50 ((0.53) 3.42 ((0.19) 4.29 ((0.29) 0.75 ((0.12) 2.92 ((0.37) 2.94 ((0.22) 3.62 ((0.41) 2.88 ((0.15) 3.29 ((0.13) 2.37 ((0.29) 2.94 ((0.17) 4.20 ((0.64) 4.12 ((0.56) 4.52 ((1.00) 4.17 ((0.66) 2.63 ((1.45) 4.17 ((0.44) 0.13 ((0.47) 0.93 ((0.15) 3.89 ((0.41) 0.69 ((0.30) 1.82 ((0.14) 4.52 ((0.78)
5.67 ((0.91) 5.43 ((0.53) 4.87 ((0.52) 4.67 ((0.37) 3.13 ((0.24) 5.01 ((0.48) 5.06 ((0.76) 4.91 ((0.18) 5.15 ((0.46) 4.95 ((0.54) 3.29 ((0.42) 3.93 ((0.98) 4.41 ((0.68) 3.53 ((0.38) 3.07 ((0.18) 3.92 ((0.15) 4.89 ((1.20) 2.58 ((2.43) 2.72 ((0.09) 5.63 ((1.36) 5.06 ((1.02) 5.29 ((0.41) 4.95 ((0.44) 2.40 ((1.40) 4.63 ((0.89) 5.05 ((0.55) 6.35 ((0.84) 6.02 ((0.47) 5.53 ((0.31) 5.33 ((1.03) 4.86 ((0.40) 4.78 ((0.95) 4.66 ((0.83) 5.86 ((1.62) 5.57 ((1.12) 7.68 ((5.78) 4.91 ((0.69) 4.22 ((9.72) 3.53 ((1.65) 5.10 ((0.73) 6.94 ((5.21) 3.56 ((0.60) 4.70 ((1.03)
8.43 ((0.17) 5.94 ((0.10) 5.43 ((0.13) 8.13 ((0.11) 6.87 ((0.06) 9.60 ((0.11) 9.63 ((0.17) 2.94 ((0.32) 5.75 ((0.13) 8.61 ((0.12) 6.56 ((0.14) 5.00 ((0.30) 5.66 ((0.15) 8.74 ((0.10) 5.18 ((0.05) 8.17 ((0.04) 7.84 ((0.23) 7.21 ((0.06) 4.81 ((0.03) 10.08 ((0.34) 9.90 ((0.23) 6.19 ((0.07) 7.39 ((0.12) 8.30 ((0.11) 5.39 ((0.28) 8.42 ((0.11) 10.27 ((0.23) 5.92 ((0.07) 6.97 ((0.06) 9.42 ((0.18) 9.22 ((0.09) 8.73 ((0.22) 8.09 ((0.21) 9.29 ((0.28) 9.61 ((0.24) 9.43 ((0.09) 6.79 ((0.14) 8.79 ((0.06) 3.39 ((0.22) 8.17 ((0.14) 9.28 ((0.09) 8.82 ((0.09) 8.68 ((0.23)
70.79
17.34 ((0.13) 25.58 ((0.21) 27.16 ((0.28) 8.14 ((0.09) 3.92 ((0.11) 11.19 ((0.11) 12.90 ((0.08) 3.62 ((0.81) 30.61 ((0.51) 13.70 ((0.13) 5.83 ((0.26) 24.20 ((1.01) 27.46 ((0.28) 2.94 ((0.21) 3.86 ((0.11) 1.48 ((0.07) 25.52 ((0.14) 13.21 ((0.10) 1.97 ((0.15) 25.91 ((0.09) 15.71 ((0.14) 16.23 ((0.19) 29.22 ((0.18) 15.11 ((0.10) 30.47 ((0.39) 9.13 ((0.10) 8.61 ((0.16) 21.32 ((0.13) 18.41 ((0.09) 3.63 ((0.17) 5.36 ((0.14) 23.59 ((0.13) 22.98 ((0.17) 24.31 ((0.09) 19.88 ((0.07) 24.60 ((0.04) 26.03 ((0.07) 8.99 ((0.05) 16.00 ((2.06) 19.45 ((0.15) 6.78 ((0.04) 24.31 ((0.03) 28.30 ((0.23)
29.27 ((0.20) 33.47 ((0.09) 21.26 ((0.20) 28.41 ((0.11) 11.17 ((0.12) 24.73 ((0.38) 25.62 ((0.34) 4.50 ((0.02) 38.74 ((0.15) 28.15 ((0.21) 31.43 ((0.18) 14.44 ((0.46) 19.50 ((0.25) 23.31 ((0.39) 19.33 ((0.05) 16.55 ((0.07) 18.93 ((0.33) 2.11 ((0.13) 14.20 ((0.05) 40.47 ((1.02) 28.40 ((0.93) 25.26 ((0.12) 35.63 ((0.13) 3.98 ((0.30) 23.08 ((0.29) 21.77 ((0.16) 23.80 ((1.00) 18.07 ((0.20) 23.22 ((0.08) 15.74 ((0.60) 22.37 ((0.31) 36.46 ((0.25) 36.31 ((0.22) 33.65 ((0.39) 31.97 ((0.32) 13.05 ((0.47) 34.80 ((0.05) 0.79 ((0.18) 4.60 ((0.19) 30.95 ((0.20) 2.02 ((0.25) 14.05 ((0.12) 40.90 ((0.47)
7.64 ((0.05) 5.18 ((0.05) 5.47 ((0.11) 7.11 ((0.02) 6.71 ((0.06) 8.94 ((0.05) 9.06 ((0.05) 3.45 ((0.74) 4.92 ((0.11) 7.81 ((0.04) 5.65 ((0.02) 5.23 ((0.22) 5.77 ((0.09) 8.04 ((0.05) 4.71 ((0.01) 7.58 ((0.01) 8.12 ((0.13) 7.52 ((0.03) 4.50 ((0.02) 9.66 ((0.14) 9.42 ((0.13) 5.57 ((0.05) 6.79 ((0.08) 8.78 ((0.05) 5.57 ((0.12) 7.78 ((0.03) 9.39 ((0.11) 5.80 ((0.12) 6.61 ((0.06) 8.85 ((0.10) 8.41 ((0.04) 8.03 ((0.05) 7.33 ((0.06) 8.85 ((0.09) 8.99 ((0.05) 9.84 ((0.05) 6.06 ((0.02) 9.05 ((0.04) 3.72 ((0.19) 7.45 ((0.06) 9.53 ((0.07) 9.22 ((0.02) 8.03 ((0.10)
0.73 ((0.06) 0.99 ((0.11) 0.99 ((0.23) 0.79 ((0.02) 0.95 ((0.11) 0.81 ((0.07) 0.73 ((0.05) 1.66 ((2.49) 0.92 ((0.19) 0.79 ((0.05) 1.03 ((0.07) 0.99 ((0.42) 1.00 ((0.19) 0.86 ((0.07) 1.13 ((0.04) 0.93 ((0.03) 0.52 ((0.07) 0.99 ((0.07) 1.07 ((0.05) 0.54 ((0.05) 0.68 ((0.09) 1.14 ((0.15) 0.84 ((0.12) 0.92 ((0.09) 0.93 ((0.24) 0.80 ((0.05) 0.71 ((0.09) 1.04 ((0.28) 0.85 ((0.09) 0.78 ((0.11) 0.85 ((0.06) 0.63 ((0.04) 0.70 ((0.05) 0.54 ((0.05) 0.64 ((0.04) 0.91 ((0.06) 1.00 ((0.05) 0.94 ((0.06) 1.07 ((0.28) 0.78 ((0.07) 0.94 ((0.11) 0.92 ((0.03) 0.57 ((0.07)
7.70
3.60
6.51
4.35
4.29
3.12
8.01
2.44
6.19
1.43
9.27
2.62
9.68
1.88
2.62
-0.02
6.90
6.25
8.21
0.89
6.57
3.31
4.23
2.24
4.15
3.18
8.91
1.98
5.12
2.16
7.84
1.17
6.50
2.60
7.15
1.91
4.85
1.66
9.70
4.74
9.50
2.10
6.40
2.95
7.94
4.20
7.30
1.47
4.50
3.16
8.20
1.58
9.70
1.75
6.30
3.06
6.50
1.28
9.32
0.88
8.05
2.14
9.36
4.55
9.10
4.81
9.30
3.37
9.53
3.48
8.47
3.04
6.60
3.32
8.37
1.28
2.97
2.26
8.20
3.51
8.81
-0.02
7.55
2.85
9.50
5.90
ketoconazole (B) ketoprofen (A) lidocaine (B) 2-methylbenzimidazole (B) metoclopramid (B) metoprolol (B) metronidazole (B) miconazole (B) morphine (B) N,N-diethylaniline (B) 1-naphthylacetic acid (A) naproxen (A) N,N-dimethylbenzylamine (B) N-ethylaniline (B) nicotine (B) nimesulide (A) p-nitrophenol (A) N-methylaniline (B) nortriptyline (B) oxprenolol (B) papaverine (B) perphenazine (B) phenobarbital (A) phenylbutazone (A) physostigmine (B) pindolol (B) piroxicam (A) prazosine (B) procainamide (B) procaine (B) promazine (B) promethazine (B) propaphenone (B) propranolol (B) propylparaben (A) reserpine (B) salicylamide (A) salicylic acid (A) tetracaine (B) theophylline (A) thiopenthal (A) thiorhidazine (B)
80.39 69.55 73.32 48.54 64.04 64.81 20.91 91.70 71.76 90.07 69.16 73.43 70.81 67.96 53.99 66.16 56.99 61.21 88.01 69.24 64.67 86.57 49.20 73.24 58.17 56.93 60.63 59.56 44.50 60.38 87.78 88.58 77.20 75.00 65.86 84.93 41.70 72.97 76.31 26.00 67.52 96.15
Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
245
Table 2 (Continued) eq 4
eq 6
analytesb
log kw1
S1
log kw2
S2
pKa chrom
φ0
t′R1
t′R2
pKa inf
s
pKalit
log P
2,4,6-trimethylpypyridine (B) yohimbine (B)
0.90 ((0.53) 2.35 ((0.20) 2.05 ((0.14) 3.04 ((0.18) 1.91 ((((0.14) 4.06 ((0.68) 3.46 ((0.64) 3.87 ((0.90)
7.97 ((8.13) 5.70 ((0.80) 5.12 ((0.63) 4.80 ((0.42) 4.88 ((((0.70) 5.47 ((1.20) 5.99 ((1.51) 5.72 ((1.73)
2.38 ((0.15) 3.48 ((0.26) 3.51 ((0.35) 2.38 ((0.16) 3.28 ((0.29) 4.30 ((0.39) 4.61 ((0.82) 2.05 ((0.36)
3.54 ((0.41) 5.08 ((0.52) 5.16 ((0.68) 4.32 ((0.50) 4.45 ((0.56) 4.67 ((0.54) 5.94 ((1.32) 4.30 ((1.46)
7.22 ((0.10) 7.98 ((0.11) 9.81 ((0.17) 6.44 ((0.13) 9.44 ((0.14) 7.36 ((0.16) 8.05 ((0.24) 5.87 ((0.35)
67.25
2.77 ((0.14) 14.24 ((0.12) 12.79 ((0.10) 23.65 ((0.19) 11.93 ((0.15) 30.42 ((0.16) 22.75 ((0.16) 27.98 ((0.87)
21.45 ((0.14) 26.90 ((0.15) 27.37 ((0.44) 18.26 ((0.29) 28.24 ((0.42) 37.91 ((0.15) 33.12 ((0.20) 14.26 ((0.67)
6.58 ((0.02) 7.25 ((0.04) 9.10 ((0.06) 6.58 ((0.12) 8.71 ((0.05) 6.76 ((0.07) 7.27 ((0.07) 6.51 ((0.21)
0.97 ((0.06) 0.83 ((0.05) 0.74 ((0.05) 0.88 ((0.22) 0.80 ((0.07) 0.87 ((0.12) 0.67 ((0.06) 0.55 ((0.14)
7.43
1.88
7.13
2.73
9.20
1.83
5.16
2.34
9.41
1.35
8.10
5.03
8.92
3.79
5.08
2.60
timolol (B) tolbutamide (A) tramadol (B) trifluoperazine (B) verapamil (B) warfarine (A)
68.50 68.05 63.31 73.72 92.06 77.52 67.64
a Values in parentheses are errors at a confidence level of 95%. Literature dissociation constants, pK a lit, and lipophilicity parameters, log P, were taken from refs 17-20. φ0 was determined by use of eq 7. b A, acid; B, base.
Figure 5. Correlation between pKa chrom determined experimentally and the literature data pKa lit. Results obtained using eq 4. Individual linear regression equations are as follows: for acids y ) 0.94x + 1.15, R2 ) 0.926, RMSE ) 0.914; for bases y ) 0.95x + 1.39, R2 ) 0.919, RMSE ) 0.504.
the conclusion that the two approaches give highly correlated results, but only when acidic and basic analytes are treated separately. This can be due to the earlier mentioned inconsistency of pKa and inflection point of the curve described by eq 6. The agreement between the retention times of nonionized forms of analytes and φ0 parameter is satisfactory. The differences can be explained by not taking into account in the calculations the changes of retention factors accompanying the changes of methanol content in the eluent. CONCLUSIONS Two different, simple in performance RP HPLC methods of determination of analyte dissociation constant and lipophilicity 246 Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
parameters are presented. They differ in the number of experiments required and the accuracy of the results obtained. One approach, based on eq 4, consists of 18 RP HPLC experiments and the second method, based on eq 6, requires only 9 experiments. Both methods are theoretically founded and give insight into the mechanism of partition of an analyte between the stationary and the mobile phases used and its changes with changing pH of the eluent. Thus, both methods can be used for preliminary determination of lipophilic and acidic properties of analytes, especially when one deals with complex analyte mixtures. The methods can easily be adjusted to polyprotic compounds. Possible application in high-throughput screening of drug candidates appears so far to be limited due to a rather long analysis
Figure 6. Correlation between φ0 values determined experimentally and literature log P data for nondissociated forms of analytes.
Figure 7. Correlation between log kw values determined experimentally and the literature log P data for nondissociated forms of analytes. Results obtained using eq 4.
time. Total time of evaluation of analyte lipophilicity and acidity parameters by the first method (eq 4) is ∼1 day, while the second method takes ∼0.5 day to be performed. However, analysis of set of compounds in a mixture and the possibility of speeding up both methods by using mass spectroscopy detection, high-speed liquid chromatography, or both are among the potential advantages of the approach developed here. Further studies must precede its routine usage, however, aimed at both speeding up the procedure and increasing the accuracy of the results.
APPENDIX For liquid chromatography with gradient elution the fundamental equation describing analyte retention is15,16
∫
t′R
0
1 dt )1 t0 ki
(8)
with t′R ) tR - t0 denoting the reduced retention time and ki as Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
247
Figure 8. Correlation between the inflection point, pKa inf, determined by fitting to eq 6 and the literature data pKa lit. Results obtained from series II of nine experiments. Individual linear regression equations are as follows: for acids y ) 1.00x + 1.06, R2 ) 0.932, RMSE ) 1.140; for bases y ) 0.92x + 0.05, R2 ) 0.878, RMSE ) 0.867.
Figure 9. Correlation between the experimentally determined retention times of nondissociated form obtained in a 60-min methanol gradient RP HPLC run and literature log P data. Results obtained using eq 6.
the analyte retention factor, corresponding to the composition of the mobile phase at column’s inlet. (15) Freiling, E. C. J. Am. Chem. Soc. 1955, 77, 2067-2071. (16) ) Snyder, L. C. Chromatogr. Rev. 1964, 7, 1-51. (17) Howard, P., Meylan, W., Eds. Physical/Chemical Property Database (PHYSPROP); Syracuse Research Corp.; Environmental Science Center; North Syracuse, NY, 1999. http://www.syrres.com/esc/physdemo.htm.
248
Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
Equation 5 can be rewritten in terms of retention factors to the following form:
k)
k1 + k210s(pKainf-pH) 1 + 10s(pKainf-pH)
(9)
Figure 10. Comparison of the results of simultaneous determination of acidity constant and lipophilicity parameter based on eq 4 (upper plots) and on eq 6 (lower plots).
Equation 9 describes retention in RP HPLC with organic modifier content changing at the given pH of the mobile phase. If additionally the changes in eluent pH are considered, along with the organic modifier changes, eq 9 becomes
where pH(t) is a function descibing pH changes at column’s inlet. Now, combining eqs 8 and 10, one obtains eq 6.
ACKNOWLEDGMENT
ki )
k1 + k210s(pKainf-pH(t)) 1 + 10s(pKa inf-pH(t))
(10)
(18) Smith, R. M.; Martel, A. E.; Motekaities, R. J. NIST Critically Selected Stability Constants of Metal Complexes Databases, Ver. 8; NIST Standard Reference Database 46, U.S. Department of Commerce, Gaithersburg, MD, 2004. (19) Slater, B.; McCormack, A.; Avdeef, A.; Comer, J. E. A. J. Pharm. Sci. 1994, 83, 1280-1283. (20) Moffat, A. C.m Ed. Clarke’s Isolation and Identification of Drugs, 2nd ed.; Pharmaceutical Press: London, U.K., 1986.
The project was financially supported by a grant from the Komitet Badan ˜ Naukowych, Warsaw, Poland (Grant KBN 2PO5F05529).
Received for review July 8, 2005. Accepted August 27, 2005. AC0512103
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