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Microscale Titrimetric and Spectrophotometric Methods for Determination of Ionization Constants and Partition Coefficients of New Drug Candidates
Microscale Titrimetric and Spectrophotometric Methods for Determination of Ionization Constants and Partition Coefficients of New Drug Candidates MICHAEL E. MORGAN, KUI LIU†,
AND
BRADLEY D. ANDERSON*
Contribution from the Department of Pharmaceutics and Pharmaceutical Chemistry, College of Pharmacy, University of Utah, Salt Lake City, Utah 84124 Received February 6, 1997.
Accepted for publication November 19, 1997.
Abstract 0 This study describes the adaptation of conventional titrimetric and spectrophotometric techniques to a microscale for the determination of drug ionization constants (pKa) and partition coefficients (log P). The apparatus for determining pKa and compound purity (or equivalent weight) consists of a three-port conical glass microvial maintained at 25 °C, a pH microelectrode, and a microinjection pump equipped with a 10 µL gastight syringe for titrant delivery. Sample mixing and protection from atmospheric CO2, which is particularly important at the microscale, is accomplished using a fine stream of water-saturated N2 bubbles. Simple titrimetric procedures combined with ionic equilibria models which allow the accurate determination of pKa and purity (or equivalent weight) using sample sizes in the microgram range and solution volumes of 10−100 µL were developed and validated using acetic acid and tromethamine. Simultaneous determinations of pKa, purity or equivalent weight, and octanol/water partition coefficient were shown to be possible from a single sample of a test solute by adapting the pH-metric technique to a microscale. Using benzoic acid as a model compound, a pKa of 4.24 and octanol/water partition coefficient of 64 were obtained, in close agreement with the literature values. The principles employed in titrimetric analysis were also applied to demonstrate the spectrophotometric determination of benzoic acid’s pKa and partition coefficient using only 6 µg of compound. The microscale titration method was then used to determine the two pKa values of an “unknown” diprotic acid containing a carboxyl and an aromatic SH group. The phenyl thiol pKa was confirmed using the microscale spectrophotometric procedure.
Introduction The development of quantitative microscale methods for determining various physicochemical properties of new drug candidates is becoming increasingly important as preformulation and formulation scientists become involved at earlier stages in the overall drug discovery/development process, as only limited quantities of drug are usually available in the early phases of development. Among the properties routinely determined early in the drug evaluation and candidate selection process are apparent purity as assessed by equivalent weight and other means, acid dissociation constants (pKa values), and lipophilicity, which is typically estimated by the compound’s octanol-water partition coefficient (Ko/w). Potentiometric titration is the most common technique employed in the determination of compound pKa values and * Corresponding author. Telephone: (801) 581-7216. Fax: (801) 5853614. E-mail: [email protected]. † Present address: Aradigm Corp., 26219 Eden Landing Road, Hayward, CA 94545.
238 / Journal of Pharmaceutical Sciences Vol. 87, No. 2, February 1998
in estimating apparent purity or equivalent weight of ionizable drugs.1 More recently, pH-metric procedures for simultaneously determining both pKa and Ko/w have gained in popularity.2-7 However, conventional titration methods typically utilize volumes of >5 mL and require several milligrams of compound per determination. In many cases, several milligrams of drug may represent a significant fraction of the total compound available for investigation at the early stages of evaluation. Ideally, therefore, methods for determining these physicochemical properties are needed which involve negligible compound consumption (e.g., microgram quantities). A recent survey of the literature by the authors revealed that, though several laboratories have developed compound sparing titrimetric methods,8-14 most studies have focused on reliable end-point detection without regard for pKa, and for the most part, the amount of compound consumed per determination in these reports has exceeded 1 mg. Sweileh and Dasgupta15 described an automated microbatch analyzer in which the sample is loaded into a loop injector and blown into a 1.5 mL reaction chamber by compressed gas. Various reagents are delivered to the chamber from pressurized reservoirs using high-speed valves under microcomputer control for precise delivery of microliter aliquots. Steele and Hieftje16 introduced a computer-controlled, automatic titrator in which titrant droplets are formed by the repetitive insertion and withdrawal of a 150 µm diameter glass needle into and out of a titrant reservoir. Titrations of samples ranging from 20 to 60 µL were described. Presumably the above instrumentation could be adapted to the determination of pKa values but this has not been reported. Diffusional microtitration has been employed to conduct acid-base titrations in samples ranging in size from microliters to femtoliters17-20 but, again, with endpoint detection as the primary aim. The determination of pKa values by diffusional microtitration may be complicated by the necessity to account for not only the diffusion of titrant but the back-diffusion of the titrated analyte species. Highly sensitive alternatives to potentiometric and spectrophotometric methods exist, such as capillary electrophoresis, which may be particularly useful in determining the pKa values of impure or poorly soluble compounds,21 but conventional titrimetry is generally preferred due to its simplicity, proven reliability, and costeffectiveness. The objective of this study was to adapt conventional techniques to a microscale for the determination of drug ionization constants and partition coefficients and, in so doing, determine the limitations of simply miniaturizing the devices ordinarily used in macroscale titrations. The microscale methods for pKa and equivalent weight were validated using a monofunctional weak acid (acetic acid) and weak base (tromethamine). Benzoic acid was used in
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Figure 1s(A) Schematic diagram of the experimental apparatus used in microscale titrimetry. (B) Schematic diagram of the experimental apparatus used in microscale spectrophotometry.
adapting the pH-metric method for pKa and Ko/w to a microscale method which was compared to a compoundsparing spectrophotometric method for obtaining the same quantities. The pKa values of an “unknown” diprotic acid were then determined using the microscale methods developed.
Materials and Methods Chemicals and ReagentssThe “unknown” diprotic acid [2-[(2mercaptobenzoyl)amino]-3-methylpentanoic acid; NSC 679825] was provided by the National Cancer Institute, National Institutes of Health (Bethesda, MD) and used as received. Glacial acetic acid and DILUT-IT HCl and NaOH standards were obtained from J. T. Baker (Phillipsburg, NJ). Tromethamine, benzoic acid, and 1-octanol were purchased from Aldrich Chemical Co. (Milwaukee, WI), Sigma (St. Louis, MO), and Fisher Scientific Co. (Fairlawn, NJ), respectively. All reagents were analytical grade and used without further purification. Microscale TitrimetrysApparatus DescriptionsA schematic diagram of the experimental apparatus is shown in Figure 1a. A three-branched conically shaped microvial was used as a titration vessel (length ∼ 45 mm; o.d. ∼ 6 mm; initial i.d. ∼ 4 mm tapering to ∼ 2 mm). A pH microelectrode (MI-412 Microcombination, glass; body diameter ∼ 2.5 mm; reading tip diameter ∼ 1.4 mm; Microelectrodes, Inc., Bedford, NH) was inserted through the middle opening. The supply lines, PE-10 tubing (polyethylene, o.d. ) 0.61 mm; i.d. ) 0.28 mm; Intramedic, Becton Dickinson, Sparks, MD) for the water-saturated nitrogen gas and a fused silica needle (o.d. ) 0.144 mm, i.d. ) 0.075 mm, length ) 17.5 cm; Polymicro Technologies, Phoenix, AZ) attached to a 10-µL gastight syringe (Hamilton Co., Reno, NV) for addition of titrant, were placed in the left and right sidearms, respectively. The
nitrogen supply line was placed in the bottom of the microtitration vial and the bubbling rate adjusted to ≈2 bubbles/s to provide solution mixing and protection from atmospheric CO2 without excessive bubbling/foaming. (A finer stream of bubbles can be obtained by using the fused silica line for the nitrogen supply.) The 10-µL gastight syringe was filled with titrant and inserted into a microinjection pump (CMA/100, CMA/Microdialysis; Acton, MA), the fused silica needle was placed in the titration vial (above the tip of the nitrogen line), and titrant aliquots were added at a fixed rate of 0.5 µL/min. The titration vessel solutions were maintained at 25 °C using a water-jacketed beaker with circulating water. Liquid evaporation was minimized by sealing the titration vial port openings with Parafilm which was punctured to allow passage of the titration lines. Experimental ProceduresAnalyte solutions of acetic acid, tromethamine, and benzoic acid (0.07-0.0007 M) and commercially prepared titrant standard solutions NaOH and HCl (0.01-1 M) were prepared in degassed, nitrogen-saturated sterile water. Initial volumes of analyte varied from 10 to 100 µL. The total volume of titrant typically added was 3.5-7.0 µL. A digital pH-meter (model 611, Orion Research Inc.; Boston, MA) was calibrated before and after each titration with commercially available National Bureau of Standards approved buffers chosen to cover the range of the titration curve. pH measurements were considered stable when the shift in pH was <0.01/min. In some cases, nitrogen gas was replaced with compressed air (breathable grade) to demonstrate the necessity for nitrogen flushing. The pKa, apparent purity, and Ko/w of benzoic acid were determined simultaneously using a 100 µL sample (0.007 M) by directly titrating the analyte with NaOH (0.1 M) to a pH at or near the equivalence point, adding water-saturated octanol (10 or 100 µL) to the ionized analyte solution, and back-titrating the octanol-aqueous mixture with HCl (0.1 M). Nitrogen saturated with both octanol and water was used in these experiments.
Journal of Pharmaceutical Sciences / 239 Vol. 87, No. 2, February 1998
The diprotic acid 2-[(2-mercaptobenzoyl)amino]-3-methylpentanoic acid (NSC 679825) (0.0015 M) was prepared in degassed, nitrogen-saturated water. A 100-µL sample was titrated as described above with a standard solution of NaOH (0.095 M), except that, in this case, titrant was dispensed by hand using a 1.0-µL Hamilton syringe. Standardization ProceduressPrimary stock solutions (10 mL) were standardized against the appropriate titrant standards using a semimicro ROSS combination pH electrode (model 8103; Orion Research Inc., Boston, MA). The pH microelectrode accuracy was verified via side-by-side comparisons of acetic acid’s pKa determined using the microelectrode with that determined using the semimicro pH electrode. The electrodes were connected to independent pH meters (ROSS connected to PHM82, radiometer, Copenhagen, Denmark; microelectrode connected to Model 611, Orion Research Inc., Boston, MA), standardized simultaneously in the same National Bureau of Standard buffers, placed in a 10mL solution containing acetic acid, and titrated with NaOH using a stream of nitrogen bubbles for mixing and protection from atmospheric CO2. Under these conditions, titrant delivery was accomplished with a 1.0-mL gastight Hamilton syringe using the microinjection pump. Analyte solutions were maintained at 25 °C using a water-jacketed beaker with circulating water. Data AnalysissEquations defining the hydrogen ion activity at various stages in the aqueous solution titrations were developed by inserting relationships for the species concentrations generated from mass balances and ionization constants into the charge balance equations as described by Butler.22 In two-phase (i.e., octanol-water) systems, a similar equation was derived with the additional assumption that only the neutral analyte species partitions into the organic phase as governed by the equilibrium constant Ko/w. Equations applicable to titrations in two-phase systems have been reported by several investigators.2-7 These equations were fitted to the pH (dependent variable) versus titrant volume (independent variable) curves by nonlinear regression analysis using commercially available computer software (Scientist; MicroMath Inc., Salt Lake City, UT) to determine simultaneously the parameters pKa, purity, p, and, in some cases, Ko/w. The implicit equations derived for hydrogen ion activity for each type of titration are shown in Appendix A. As is evident in these equations, ion activity coefficient corrections were included in the models. These were estimated from application of the Guntelberg equation for ion activity coefficients as a function of ionic strength23 (see definition of terms). Ionic strengths, which varied with titrant addition, were calculated iteratively along with pH. Microscale SpectrophotometrysApparatus DescriptionsA schematic diagram of the experimental apparatus is shown in Figure 1b. UV spectra were generated using a computer-assisted Cary 3E spectrophotometer (Varian Instruments, Palo Alto, CA) in which the temperature-controlled sample/reference chamber was modified such that a microelectrode (MI-412 Microcombination) and nitrogen supply lines (PE-10) could be placed in the 1-mL cuvettes for the duration of the experiment. This configuration allowed ready access for titrant delivery using a hand-held 1.0µL Hamilton syringe. The reference and sample cell solutions were mixed and protected from atmospheric CO2 by a fine stream of water-saturated nitrogen bubbles. The nitrogen lines were positioned near the bottom of the sample cell during titrant addition/mixing but raised to a level above the light path during scanning. Experimental ProceduresAfter the instrument was zeroed using sample solvent, analyte solution (6 µg benzoic acid in 600 µL of degassed, octanol-saturated, 0.001 M phosphoric acid, 8.28 × 10-5 M) was added to the sample cell and the micropH electrode was positioned in the sample cell above the light path. (Phosphoric acid, which contributes negligibly to the absorbance, was added to provide additional buffer capacity beyond that provided by the analyte of interest.) pH was recorded and the sample was scanned between 200 and 350 nm at a rate of 200 nm/min. After this baseline scan, equal volumes of titrant (2.5 M NaOH) were added to both cells, the pH was recorded, and a UV spectral scan was obtained. Titrations were performed at 25 °C. Total titrant volume added to the cuvettes was less than 1% of the sample volume, allowing volume changes due to titrant addition to be neglected. Simultaneous determinations of pKa and Ko/w were determined as described above by directly titrating the analyte with NaOH (2.5 M) to a pH at or near the equivalence point, adding water-
240 / Journal of Pharmaceutical Sciences Vol. 87, No. 2, February 1998
Figure 2sRepresentative pH−titration profiles obtained for the macroscale titration of a 10 mL volume (2) and microscale titration of 10 µL (O) and 100 µL (0) volumes of a solution of acetic acid (0.007 M). Total amounts of acetic acid titrated are 4.2 mg, 4.2 µg, and 42 µg, respectively. The solid lines are computer fits using eq 1.
Figure 3sRepresentative pH−titrant volume profile obtained during microscale titration of tromethamine (85 µg in 100 µL) with 0.1 M HCl using air (0) or nitrogen (9) bubble mixing. The solid lines are computer fits using eq 2. saturated octanol (200 µL) to the ionized analyte solution, and back-titrating the octanol-layered solution with HCl (2.5 M). The titrations were performed as described above at 25 °C but with water-octanol saturated nitrogen gas for mixing. The diprotic acid 2-[(2-mercaptobenzoyl)amino]-3-methylpentanoic acid (NSC 679825) (0.0015 M) was prepared in degassed, nitrogen-saturated phosphoric acid (0.001M) and titrated as described above but at a volume of 1.2 mL with a standard solution of NaOH (0.095 M). Data AnalysessThe UV spectra were examined to determine the wavelength at which there was a maximum change in absorbance (λ∆max) as pH was varied. Absorbance (Abs) versus pH profiles were constructed at λ∆max. Ka and Ko/w were determined by fitting these profiles to the equations shown in Appenndix B using nonlinear regression analysis (Scientist, MicroMath Inc.).
Results and Discussion Microscale Titrimetric Determination of pKa and PuritysIn adapting conventional acid-base titrimetry to a microscale, several possible sources of error in the determination of ionization constants and purities were considered, including the accuracy/precision of the pH microelectrode, limitations due to analyte concentration, limitations due to solution volume, and the increased likelihood for significant errors due to contamination from atmospheric CO2. Side-by-side comparisons of the performance of the pH microelectrode and a conventional semimicro combination pH electrode routinely used in the authors’ laboratories were initially conducted by titrating acetic acid solutions (10 mL) ranging in concentration from 0.07 to 0.0007 M with both electrodes immersed in the solution. Though the
Table 1sMicroscale Determination of pKa and Apparent Purity (p) of Acetic Acid and Tromethamine acetic acid conditions concentration, M (volume ) 100 µL) 0.07 0.007 0.0007 volume, µL (concentration ) 0.007 M) 100 20 10 nitrogen vs air ([acetic acid] ) 0.0007 M [tromethamine] ) 0.007 M volume ) 100 µL) nitrogen air a
pKa ± SD (n)
a
tromethamine p ± SD
pKa ± SD (n)
a
p ± SD
4.74 ± 0.05 (6) 4.77 ± 0.02 (7) 4.90 ± 0.02 (3)
0.99 ± 0.02 1.01 ± 0.02 0.98 ± 0.02
8.11 ± 0.02 (3) 8.11 ± 0.01 (5) 8.01 ± 0.04 (6)
0.999 ± 0.004 1.00 ± 0.01 1.00 ± 0.03
4.77 ± 0.02 (7) 4.78 ± 0.01 (3) 4.77 ± 0.02 (4)
1.01 ± 0.02 0.986 ± 0.004 1.00 ± 0.01
8.11 ± 0.01 (5) 8.07 ± 0.02 (3) 8.04 ± 0.06 (3)
1.00 ± 0.01 0.993 ± 0.008 1.00 ± 0.02
4.90 ± 0.02 (3) 4.89 ± 0.01 (3)
0.98 ± 0.02 0.959 ± 0.002
8.11 ± 0.01 (5) 7.80 ± 0.05 (4)
1.00 ± 0.01 1.05 ± 0.08
n ) number of determinations.
results obtained using the microelectrode appeared to be slightly less precise, no significant difference could be detected in the pKa of acetic acid obtained by either electrode, with values of 4.75 ( 0.06 and 4.78 ( 0.04 (mean ( SD, n ) 6) determined using the microelectrode and conventional semimicroelectrode, respectively. These results were in excellent agreement with literature values for the pKa of acetic acid (4.74-4.761,24). Representative microscale titration curves obtained for acetic acid and tromethamine are shown in Figures 2 and 3, respectively. Figure 2 illustrates that equivalent results were obtained in the microscale (10-100 µL) and macroscale (10 mL) experiments. Best-fit parameters generated from such curves according to the equations described previously are listed in Table 1. The effect of analyte concentration was first explored using a total solution volume of 100 µL and concentrations of acetic acid or tromethamine ranging from 7 × 10-4 to 0.07 M, representing sample size ranges of 4.2-420 µg for acetic acid and 8.5-850 µg for tromethamine. As is evident in Table 1, close agreement with theory was obtained for both pKa and apparent purity except at the lowest concentrations. Thus, at concentrations of 0.007 M and higher, the pKa found for acetic acid (4.74-4.77) was within the range of literature values reported (4.744.761,24), while the value of 8.11 obtained for the pKa of tromethamine was also within the range of values in the literature (8.08-8.111,25). For reasons not fully understood, the results at the lowest analyte concentrations deviated from those obtained at higher concentrations, with the apparent pKa of acetic acid increasing to 4.90 and that for tromethamine decreasing to 8.01. Since similar deviations were not seen in titrations of 10 mL samples at the same analyte concentrations, these results may reflect errors resulting from miniaturizing the experiment. Two possible sources of error are (1) premature diffusive titrant delivery from the immersed tip of the fused silica delivery needle and (2) trace CO2 contamination due to less than complete protection from air at the slow flow rates of nitrogen utilized. Since the titrant molarity was scaled down with sample concentration, parasitic delivery of titrant due to diffusion should not have varied significantly at decreasing sample concentrations. Regardless, these results reinforce the observations of Steele and Hieftje16 that “the best approach to microtitration is usually to miniaturize the solution-dispensing apparatus and maintain reagents at their original concentration”.
The accuracy of the pKa values for both compounds at the lowest sample sizes titrated improved somewhat by maintaining a higher solution concentration (0.007 M) while decreasing the sample volume. Thus, as shown in the second part of Table 1 and by the overlay of profiles in Figure 2, there was no apparent difference in pKa determinations (n ) 3-7) over a 10-fold decrease in sample volume from 100 to 10 µL, representing sample size ranges of 4.2-42 µg for acetic acid and 8.5-85 µg for tromethamine. Although not statistically significant, a trend toward lower apparent pKa with decreasing sample amount was suggested in the tromethamine data, which may again reflect the sources of error listed above. Purity values displayed no apparent change with decreasing sample volume over the range of 10-100 µL. The effects of CO2 uptake in samples exposed to air are more pronounced on the microscale, particularly in the titration of weak bases. Thus, as shown in Table 1, the estimated pKa of acetic acid (4.2 µg/100 µL) in samples exposed to air was not significantly different from that determined with nitrogen bubbling. On the other hand, the pKa of tromethamine even at a larger sample size of 85 µg/100 µL deviated significantly when mixing was performed using air rather than nitrogen, from a value of 8.11 ( 0.01 (n ) 5) in nitrogen to a value of 7.80 ( 0.05 (n ) 4) in air-exposed samples. Macroscale titrations of tromethamine (10 mL of 0.007 M) in air (with mechanical stirring) yielded a pKa estimate of 8.10 ( 0.01 (n ) 3), suggesting that the combination of air exposure and the microscale of the titration magnifies the error. Microscale pH-metric Determination of pKa, Purity, and Ko/wsThe octanol-water partition coefficient, Ko/w, is a useful parameter in studying quantitative structure-activity relationships and in evaluating the permeability of drugs across membranes, which, in turn, is important in determining their oral bioavailability and delivery to tissues outside of the vascular space. The use of a dual-phase potentiometric titration technique for determining Ko/w and pKa values, referred to as the pHmetric technique, has been the subject of several recent reports.2-7 pH-metric methodology appears to be adaptable to the determination of thermodynamic inclusion constants of guest/cyclodextrin complexes as well.25 Typically, aqueous solution volumes in these experiments are 5-50 mL while the octanol volumes range from 2 to 10 mL. The present study explored the accuracy and precision of the pH-metric technique at aqueous volumes of 100 µL and octanol volumes varying from 10 to 100 µL. Benzoic acid Journal of Pharmaceutical Sciences / 241 Vol. 87, No. 2, February 1998
Figure 4sRepresentative microscale pH-metric determination of the pKa and Ko/w for benzoic acid (85 µg in 100 µL): phase 1, direct titration with NaOH (0.1 M) in the absence of octanol (9, lower axis); phase 2, back-titration with HCl (0.1 M) in the presence of octanol (10 µL) (0, upper axis). The solid lines are computer fits using eqs 1 and 4.
was chosen as a model compound for these studies because its ionization constant (pKa ) 4.20) and octanol-water partition coefficient (Ko/w ) 74)26 are well-determined and it is suitable for analysis by both the potentiometric and spectrophotometric methods (described in a later section). Figure 4 illustrates the pH-metric method applied on a microscale for benzoic acid (85 µg in 100 µL). In the first phase of the experiment (lower curve), the acid was titrated with NaOH (0.1M) to a pH at or near its equivalence point in the absence of octanol. In the second phase (upper curve), water-saturated octanol (10 µL) was added and the system was back-titrated with HCl (0.1 M). Previous investigators have shown that benzoate anion partitioning into octanol is barely detectable,5,6 so the equilibria model used to describe the octanol-water partitioning vs pH profile for benzoic acid assumed partitioning of only the un-ionized species. Varying the octanol volume from 10 to 100 µL did not significantly affect Ko/w (Ko/w ) 61 ( 5 at 10 µL; 70 ( 5 at 100 µL (mean ( SD; n ) 2-4)). For this reason, all results (six sets of curves) were fit simultaneously using the same shared parameters, resulting in a pKa of 4.24 ( 0.03, apparent purity of 100 ( 1%, and Ko/w of 64 ( 6, in reasonable agreement with literature values. While the volume of octanol used had no effect on Ko/w, the time required to reach apparent equilibrium (i.e., <0.01 pH unit change/min) was markedly dependent on octanol volume, with equilibration times increasing from 5 min in the presence of 10 µL of octanol to 15 min in the presence of 100 µL of octanol. These observations suggest the need for an improved method of mixing in the dual-phase experiments if a high throughput analytical method is the goal. Microscale Spectrophotometric Determination of pKa and Ko/wsConventional spectrophotometric methods require substantially less compound than conventional titrimetric techniques, providing that the compound’s molar extinction coefficient is sufficiently high. Therefore, the need to further miniaturize spectrophotometric methods for determining pKa and Ko/w is less compelling. Nevertheless, we have found that adapting some of the microscale methodology developed for titrimetry to the spectrophotometric determination of pKa and Ko/w in a single sample 242 / Journal of Pharmaceutical Sciences Vol. 87, No. 2, February 1998
Figure 5sUV spectra for benzoic acid (6 µg in 600 µL) as a function of pH: (A) direct titration with NaOH (2.5 M), (B) back-titration with HCl (2.5 M) after addition of 200 µL of octanol.
offers advantages both in terms of minimizing sample consumption and in ensuring precision of the measurements. Although smaller cell configurations could have been selected, these studies used a sample volume of 600 µL in a 1-mL cuvette fitted with a pH microelectrode and nitrogen line for sample mixing and protection from atmospheric CO2. Titrant concentrations were sufficiently high (e.g., 2.5 M) that the complete pH range of interest could be attained with the addition of <1 µL of titrant, so that sample dilution could be neglected. Figure 5 displays the spectra generated as a function of pH for a 6 µg sample of benzoic acid titrated with NaOH in the absence of octanol (A) and those obtained for the back-titration with HCl after addition of 200 µL of octanol (B). From these spectra, absorbance-pH profiles at 235 and 223 nm were generated (Figure 6) for the direct titrations and back-titrations, respectively, and computer fitted using eqs 5 and 7 to obtain estimates of pKa and Ko/w of 4.23 ( 0.06 and 63 ( 3, respectively (n ) 2). These values are nearly identical with those determined using the microscale pH-metric technique. Application of Microscale Methodology To Determine pKa Values for an “Unknown” Diprotic AcidsThe diprotic acid 2-[(2-mercaptobenzoyl)amino)]-3-methylpentanoic acid (NSC 679825), shown in Figure 7, is one of two decomposition products formed in a reversible reaction from L,L-isoleucine disulfide, a drug candidate under investigation by the National Cancer Institute as a potential anti-HIV agent.27 The pKa values for the phenylthiol and the carboxylic acid functional groups in this compound were of interest in interpreting the pH-degradation profiles of this reversible decomposition reaction. However, only milligram quantities of the degradation product were available, necessitating the use of microscale techniques. The pKa values were initially determined titrimetrically using a 40-µg sample in 100 µL, as depicted in Figure 8.
Figure 8sRepresentative pH (left axis)−titration profile obtained in the microscale titration of compound I (40 µg in 100 µL) with NaOH (0.095 M). The solid line is the computer fit using eq 3 while the dashed line is the first-derivative curve (pH′, right axis).
Figure 6sBenzoic acid absorbance vs pH profiles at λ∆max determined from the UV spectral changes as a function of pH: (A) direct titration with NaOH in the absence of octanol (λ∆max ) 235 nm), (B) back-titration with HCl in the presence of 200 µL of octanol (λ∆max ) 223 nm). The solid lines are computer fits using eqs 5 and 7.
Figure 7sChemical structure of the “unknown” diprotic acid [2-[(2-mercaptobenzoylamino)]-3-methylpentanoic acid (compound I, NSC 679825)].
As suggested by the two inflection points and by the firstderivative curve, the titration curve was fitted to a model containing two ionization constants with pK1 equal to 4.05 ( 0.04 and pK2 equal to 6.29 ( 0.06 (mean ( SD, n ) 2). Although an examination of the compound’s structure suggested that pK1 probably reflects the ionization of the carboxylic acid group, the titrimetric method does not provide such information unambiguously. Microscale spectrophotometry was employed to confirm the pKa value for the aromatic thiol. The UV spectrum for this compound at wavelengths above 200 nm reflects primarily the (2-mercaptobenzoyl)amino portion of the molecule, which would be expected to shift significantly on ionization of the thiol due to resonance delocalization of the negative charge into the aromatic ring. The absorption spectra obtained as a function of pH are shown in Figure 9A. Apparent isosbestic points at ∼220 and ∼300 nm indicate that the UV spectra are only sensitive to a single
Figure 9s(A) UV spectra of diprotic acid I (16 µg in 1.2 mL) vs pH (B) Absorbance vs pH profile of I at λ∆max ) 236 nm. The solid line is the computer fit using eq 6.
ionization, which is presumably that of the phenylthiol. A plot of absorbance at 236 nm vs pH fitted to eq 6, shown in Figure 9B, yielded an estimate for pK2 of 6.29 ( 0.06 (mean ( SD, n ) 2), identical with that determined titrimetrically. In conclusion, conventional techniques employed to determine drug ionization constants and octanol-water partition coefficients have been successfully adapted to a microscale. Using the miniaturized titrimetric methods described, reasonably precise and accurate values of pKa and Ko/w are obtainable using solvent volumes as low as 10-20 µL. Both titrimetric and spectrophotometric methods can be conveniently and reliably performed using only a few micrograms of drug per determination. Journal of Pharmaceutical Sciences / 243 Vol. 87, No. 2, February 1998
References and Notes 1. Serjeant, E. P. Chemical Analysis; John Wiley & Sons, Inc.: New York, 1984; Vol. 69. 2. Clarke, F. H. Ionization constants by curve fitting: Application to the determination of partition coefficients. J. Pharm. Sci. 1984, 73, 226-230. 3. Clarke, F. H.; Cahoon, N. Ionization constants by curve fitting: Determination of partition and distribution coefficients of acids and bases and their ions. J. Pharm. Sci. 1987, 76, 611-620. 4. Clarke, F.; Cahoon, N. M. Potentiometric determination of the partition and distribution coefficients of dianionic compounds. J. Pharm. Sci. 1995, 84, 53-54. 5. Clarke, F. H.; Cahoon, N. M. Partition coefficients by curve fitting: The use of two different octanol volumes in a dualphase potentiometric titration. J. Pharm. Sci. 1996, 85, 178183. 6. Avdeef, A. pH-metric log P. II: Refinement of partition coefficients and ionization constants of multiprotic substances. J. Pharm. Sci. 1993, 82, 183-190. 7. Slater, B.; McCormack, A.; Avdeef, A.; Comer, J. E. A. pHmetric log P. 4. Comparison of partition coefficients determined by HPLC and potentiometric methods to literature values. J. Pharm. Sci. 1994, 83, 1280-1283. 8. Tolg, G. Ultramicro Elemental Analysis; Wiley-Interscience: New York, 1970. 9. Williams, M. Organic analysis: Ultramicro methods. In Treatise on Analytical Chemistry; Williams, M., Ed.; Wiley-Interscience: New York, 1965; Vol. Part II, Vol. 11, pp 219-296. 10. Belcher, R. Submicro Methods of Organic Analysis; Elsevier: New York, 1966. 11. Keen, R. T.; Fritz, J. S. Microtitration of amines. Anal. Chem. 1952, 24, 564-566. 12. Pietrogrande, A.; Guerrato, A.; Bortoletti, B.; Fini, G. D. Automatic potentiometric microdetermination of basic nitrogen in organic compounds. Analyst 1984, 109, 1541-1543. 13. Wadhwa, A.; Verma, R. M. Iodimetric microdetermination of aliphatic acids by a potentiometric titration method and comparison with acid-base potentiometry. Analyst 1983, 108, 1022-1025. 14. Alerm, L.; Bartroli, J. Development of a sequential microtitration system. Anal. Chem. 1996, 68, 1394-1400. 15. Sweileh, J. A.; Dasgupta, P. K. Applications of in situ detection with an automated micro batch analyzer. Anal. Chim. Acta 1988, 214, 107-120. 16. Steele, A. W.; Hieftje, G. M. Microdroplet titration apparatus for analyzing small sample volumes. Anal. Chem. 1984, 56, 2884-2888. 17. Gratzl, M. Diffusional microtitration: A technique for analyzing ultramicrosamples. Anal. Chem. 1988, 60, 484-488. 18. Gratzl, M. Diffusional microtitration: stationary or nonstationary reagent delivery. Anal. Chem. 1988, 60, 2147-2152. 19. Gratzl, M.; Yi, C. Diffusional microtitration: Acid/base titrations in pico- and femtoliter samples. Anal. Chem. 1993, 65, 2085-2088. 20. Hui, K. Y.; Gratzl, M. Diffusional microtitration of 20 µL samples with optical indication. Anal. Chem. 1997, 69, 695698. 21. Ishihama, Y.; Oda, Y.; Asakawa, N. Microscale determination of dissociation constants of multivalent pharmaceuticals by capillary electrophoresis. J. Pharm. Sci. 1994, 83, 15001507. 22. Butler, J. N. Ionic Equilibrium. A Mathematical Approach; Addison-Wesley: Reading, MA, 1964. 23. Butler, J. N. In Ionic Equilibrium. A Mathematical Approach; Butler, J. N., Ed.; Addison-Wesley: Reading, MA, 1964; p 436. 24. Budavari, S. The Merck Index; eleventh ed.; Budavari, S., Ed.; Merck & Co.: Rahway, NJ, 1989; p 1606. 25. Boudeville, P.; Burgot, J.-L. A new pH-metric methodology for the determination of thermodynamic inclusion constants of guest/cyclodrextrin complexes. J. Pharm. Sci. 1995, 84, 1083-1089.
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26. Fujita, T.; Iwasa, J.; Hansch, C. A new substituent constant, π, derived from partition coefficients. J. Am. Chem. Soc. 1964, 86, 5175-5180. 27. Liu, K.; Anderson, B. D. Stabilization of L-L-isoleucine disulfide (NSC 672594) requires stabilization of its thiol degradation product. Pharm. Res. 1996, 13 (Suppl.), S-269.
Acknowledgments A portion of this work was performed under Contract NO1-CM27720 from the National Cancer Institute.
Glossary aH+ γ1, γ2 I
Ao, Bo Co Vo Va, Vb Voct Kw Ka K1, K2 Ko/w p Vo, Vw Ci HA, A-
H2A, HA-, A2-
hydrogen ion activity monovalent, divalent ion activity coefficients [log γ ) -0.51z2I1/2/(1 + I1/2)] ionic strength (I ) 1/2∑cizi2, where ci and zi are the concentration and charge of the ith species) molar concentrations of HCl and NaOH, respectively, in titrant solutions initial molar drug concentration initial sample volume (µL) volumes (µL) of HCl and/or NaOH titrant added, respectively volume of octanol (µL) ion product of water (1 × 10-14 at 25 °C) monoprotic acid dissociation constant diprotic acid dissociation constants octanol-water partition coefficient apparent compound purity (equiv found/theoretical equiv) the organic and aqueous solvent volumes, respectively initial molar (aqueous) concentration of drug molar extinction coefficients of the un-ionized and ionized monoprotic acid species, respectively, at λ∆max (λ∆max will not generally be the same wavelength in the presence and absence of organic solvent) molar extinction coefficients of the various diprotic acid species
Appendix A Equation for monoprotic acid titration (acetic acid and benzoic acid)
BoVb Kw Ka aH+ Vo pCo + ) + γ1 Vo + Vb aH+γ1 aH+γ1 + Ka Vo + Vb
(1)
Equation for base titration (tromethamine)
pCoVo Kw AoVa aH+ aH+ + ) + γ1 Vo + Va aH+ + Kaγ1 aH+γ1 Vo + Va
(2)
Equation for diprotic acid titration [2-[(2-mercaptobenzoyl)amino]-3-methylpentanoic acid]
Equation for Ka determination (monoprotic acid) from absorbance data
BoVb Kw aH+ + ) + γ1 Vo + Vb aH+γ1 K1aH+ aH+
Appendix B
Vo pCo + V γ1 + K1aH+ + K1K2γ1/γ2 o + Vb 2K1K2γ1 Vo pCo (3) 2 γ γ a + + γ K a + + K K γ Vo + Vb
Abs ) Ci
2
1 2 H
2
1 H
1
2 1
Equation for back-titration of monoprotic acid anion in the presence of octanol (benzoic acid)
(aH+HA + KaA- /γ1)
(5)
(aH+ + Ka/γ1)
Equation for Ka determination (diprotic acid) from absorbance data
Abs ) Ci
[
]
aH+2H2A + K1aH+HA- /γ1 + K1K2A2- /γ2 aH+2 + aH+K1/γ1 + K1K2/γ2
(6)
Equation for simultaneous Ka and Ko/w determination (monoprotic acid) from absorbance data
BoVb Kw Va Ao aH+ + ) + + γ1 Va + Vb + Vo aH+γ1 Va + Vb + Vo KaVo pCo (aH+γ1 + Ka)(Va + Vb + Vo) + aH+γ1VoctKo/w
(aH+HA + KaA- /γ1) aH+Ko/wVo aH+ + Ka/γ1 + Vw
(
Abs ) Ci
)
(7)
(4) JS970057S
Journal of Pharmaceutical Sciences / 245 Vol. 87, No. 2, February 1998
AND
BRADLEY D. ANDERSON*
Contribution from the Department of Pharmaceutics and Pharmaceutical Chemistry, College of Pharmacy, University of Utah, Salt Lake City, Utah 84124 Received February 6, 1997.
Accepted for publication November 19, 1997.
Abstract 0 This study describes the adaptation of conventional titrimetric and spectrophotometric techniques to a microscale for the determination of drug ionization constants (pKa) and partition coefficients (log P). The apparatus for determining pKa and compound purity (or equivalent weight) consists of a three-port conical glass microvial maintained at 25 °C, a pH microelectrode, and a microinjection pump equipped with a 10 µL gastight syringe for titrant delivery. Sample mixing and protection from atmospheric CO2, which is particularly important at the microscale, is accomplished using a fine stream of water-saturated N2 bubbles. Simple titrimetric procedures combined with ionic equilibria models which allow the accurate determination of pKa and purity (or equivalent weight) using sample sizes in the microgram range and solution volumes of 10−100 µL were developed and validated using acetic acid and tromethamine. Simultaneous determinations of pKa, purity or equivalent weight, and octanol/water partition coefficient were shown to be possible from a single sample of a test solute by adapting the pH-metric technique to a microscale. Using benzoic acid as a model compound, a pKa of 4.24 and octanol/water partition coefficient of 64 were obtained, in close agreement with the literature values. The principles employed in titrimetric analysis were also applied to demonstrate the spectrophotometric determination of benzoic acid’s pKa and partition coefficient using only 6 µg of compound. The microscale titration method was then used to determine the two pKa values of an “unknown” diprotic acid containing a carboxyl and an aromatic SH group. The phenyl thiol pKa was confirmed using the microscale spectrophotometric procedure.
Introduction The development of quantitative microscale methods for determining various physicochemical properties of new drug candidates is becoming increasingly important as preformulation and formulation scientists become involved at earlier stages in the overall drug discovery/development process, as only limited quantities of drug are usually available in the early phases of development. Among the properties routinely determined early in the drug evaluation and candidate selection process are apparent purity as assessed by equivalent weight and other means, acid dissociation constants (pKa values), and lipophilicity, which is typically estimated by the compound’s octanol-water partition coefficient (Ko/w). Potentiometric titration is the most common technique employed in the determination of compound pKa values and * Corresponding author. Telephone: (801) 581-7216. Fax: (801) 5853614. E-mail: [email protected]. † Present address: Aradigm Corp., 26219 Eden Landing Road, Hayward, CA 94545.
238 / Journal of Pharmaceutical Sciences Vol. 87, No. 2, February 1998
in estimating apparent purity or equivalent weight of ionizable drugs.1 More recently, pH-metric procedures for simultaneously determining both pKa and Ko/w have gained in popularity.2-7 However, conventional titration methods typically utilize volumes of >5 mL and require several milligrams of compound per determination. In many cases, several milligrams of drug may represent a significant fraction of the total compound available for investigation at the early stages of evaluation. Ideally, therefore, methods for determining these physicochemical properties are needed which involve negligible compound consumption (e.g., microgram quantities). A recent survey of the literature by the authors revealed that, though several laboratories have developed compound sparing titrimetric methods,8-14 most studies have focused on reliable end-point detection without regard for pKa, and for the most part, the amount of compound consumed per determination in these reports has exceeded 1 mg. Sweileh and Dasgupta15 described an automated microbatch analyzer in which the sample is loaded into a loop injector and blown into a 1.5 mL reaction chamber by compressed gas. Various reagents are delivered to the chamber from pressurized reservoirs using high-speed valves under microcomputer control for precise delivery of microliter aliquots. Steele and Hieftje16 introduced a computer-controlled, automatic titrator in which titrant droplets are formed by the repetitive insertion and withdrawal of a 150 µm diameter glass needle into and out of a titrant reservoir. Titrations of samples ranging from 20 to 60 µL were described. Presumably the above instrumentation could be adapted to the determination of pKa values but this has not been reported. Diffusional microtitration has been employed to conduct acid-base titrations in samples ranging in size from microliters to femtoliters17-20 but, again, with endpoint detection as the primary aim. The determination of pKa values by diffusional microtitration may be complicated by the necessity to account for not only the diffusion of titrant but the back-diffusion of the titrated analyte species. Highly sensitive alternatives to potentiometric and spectrophotometric methods exist, such as capillary electrophoresis, which may be particularly useful in determining the pKa values of impure or poorly soluble compounds,21 but conventional titrimetry is generally preferred due to its simplicity, proven reliability, and costeffectiveness. The objective of this study was to adapt conventional techniques to a microscale for the determination of drug ionization constants and partition coefficients and, in so doing, determine the limitations of simply miniaturizing the devices ordinarily used in macroscale titrations. The microscale methods for pKa and equivalent weight were validated using a monofunctional weak acid (acetic acid) and weak base (tromethamine). Benzoic acid was used in
S0022-3549(97)00057-9 CCC: $15.00 Published on Web 01/07/1998
© 1998, American Chemical Society and American Pharmaceutical Association
Figure 1s(A) Schematic diagram of the experimental apparatus used in microscale titrimetry. (B) Schematic diagram of the experimental apparatus used in microscale spectrophotometry.
adapting the pH-metric method for pKa and Ko/w to a microscale method which was compared to a compoundsparing spectrophotometric method for obtaining the same quantities. The pKa values of an “unknown” diprotic acid were then determined using the microscale methods developed.
Materials and Methods Chemicals and ReagentssThe “unknown” diprotic acid [2-[(2mercaptobenzoyl)amino]-3-methylpentanoic acid; NSC 679825] was provided by the National Cancer Institute, National Institutes of Health (Bethesda, MD) and used as received. Glacial acetic acid and DILUT-IT HCl and NaOH standards were obtained from J. T. Baker (Phillipsburg, NJ). Tromethamine, benzoic acid, and 1-octanol were purchased from Aldrich Chemical Co. (Milwaukee, WI), Sigma (St. Louis, MO), and Fisher Scientific Co. (Fairlawn, NJ), respectively. All reagents were analytical grade and used without further purification. Microscale TitrimetrysApparatus DescriptionsA schematic diagram of the experimental apparatus is shown in Figure 1a. A three-branched conically shaped microvial was used as a titration vessel (length ∼ 45 mm; o.d. ∼ 6 mm; initial i.d. ∼ 4 mm tapering to ∼ 2 mm). A pH microelectrode (MI-412 Microcombination, glass; body diameter ∼ 2.5 mm; reading tip diameter ∼ 1.4 mm; Microelectrodes, Inc., Bedford, NH) was inserted through the middle opening. The supply lines, PE-10 tubing (polyethylene, o.d. ) 0.61 mm; i.d. ) 0.28 mm; Intramedic, Becton Dickinson, Sparks, MD) for the water-saturated nitrogen gas and a fused silica needle (o.d. ) 0.144 mm, i.d. ) 0.075 mm, length ) 17.5 cm; Polymicro Technologies, Phoenix, AZ) attached to a 10-µL gastight syringe (Hamilton Co., Reno, NV) for addition of titrant, were placed in the left and right sidearms, respectively. The
nitrogen supply line was placed in the bottom of the microtitration vial and the bubbling rate adjusted to ≈2 bubbles/s to provide solution mixing and protection from atmospheric CO2 without excessive bubbling/foaming. (A finer stream of bubbles can be obtained by using the fused silica line for the nitrogen supply.) The 10-µL gastight syringe was filled with titrant and inserted into a microinjection pump (CMA/100, CMA/Microdialysis; Acton, MA), the fused silica needle was placed in the titration vial (above the tip of the nitrogen line), and titrant aliquots were added at a fixed rate of 0.5 µL/min. The titration vessel solutions were maintained at 25 °C using a water-jacketed beaker with circulating water. Liquid evaporation was minimized by sealing the titration vial port openings with Parafilm which was punctured to allow passage of the titration lines. Experimental ProceduresAnalyte solutions of acetic acid, tromethamine, and benzoic acid (0.07-0.0007 M) and commercially prepared titrant standard solutions NaOH and HCl (0.01-1 M) were prepared in degassed, nitrogen-saturated sterile water. Initial volumes of analyte varied from 10 to 100 µL. The total volume of titrant typically added was 3.5-7.0 µL. A digital pH-meter (model 611, Orion Research Inc.; Boston, MA) was calibrated before and after each titration with commercially available National Bureau of Standards approved buffers chosen to cover the range of the titration curve. pH measurements were considered stable when the shift in pH was <0.01/min. In some cases, nitrogen gas was replaced with compressed air (breathable grade) to demonstrate the necessity for nitrogen flushing. The pKa, apparent purity, and Ko/w of benzoic acid were determined simultaneously using a 100 µL sample (0.007 M) by directly titrating the analyte with NaOH (0.1 M) to a pH at or near the equivalence point, adding water-saturated octanol (10 or 100 µL) to the ionized analyte solution, and back-titrating the octanol-aqueous mixture with HCl (0.1 M). Nitrogen saturated with both octanol and water was used in these experiments.
Journal of Pharmaceutical Sciences / 239 Vol. 87, No. 2, February 1998
The diprotic acid 2-[(2-mercaptobenzoyl)amino]-3-methylpentanoic acid (NSC 679825) (0.0015 M) was prepared in degassed, nitrogen-saturated water. A 100-µL sample was titrated as described above with a standard solution of NaOH (0.095 M), except that, in this case, titrant was dispensed by hand using a 1.0-µL Hamilton syringe. Standardization ProceduressPrimary stock solutions (10 mL) were standardized against the appropriate titrant standards using a semimicro ROSS combination pH electrode (model 8103; Orion Research Inc., Boston, MA). The pH microelectrode accuracy was verified via side-by-side comparisons of acetic acid’s pKa determined using the microelectrode with that determined using the semimicro pH electrode. The electrodes were connected to independent pH meters (ROSS connected to PHM82, radiometer, Copenhagen, Denmark; microelectrode connected to Model 611, Orion Research Inc., Boston, MA), standardized simultaneously in the same National Bureau of Standard buffers, placed in a 10mL solution containing acetic acid, and titrated with NaOH using a stream of nitrogen bubbles for mixing and protection from atmospheric CO2. Under these conditions, titrant delivery was accomplished with a 1.0-mL gastight Hamilton syringe using the microinjection pump. Analyte solutions were maintained at 25 °C using a water-jacketed beaker with circulating water. Data AnalysissEquations defining the hydrogen ion activity at various stages in the aqueous solution titrations were developed by inserting relationships for the species concentrations generated from mass balances and ionization constants into the charge balance equations as described by Butler.22 In two-phase (i.e., octanol-water) systems, a similar equation was derived with the additional assumption that only the neutral analyte species partitions into the organic phase as governed by the equilibrium constant Ko/w. Equations applicable to titrations in two-phase systems have been reported by several investigators.2-7 These equations were fitted to the pH (dependent variable) versus titrant volume (independent variable) curves by nonlinear regression analysis using commercially available computer software (Scientist; MicroMath Inc., Salt Lake City, UT) to determine simultaneously the parameters pKa, purity, p, and, in some cases, Ko/w. The implicit equations derived for hydrogen ion activity for each type of titration are shown in Appendix A. As is evident in these equations, ion activity coefficient corrections were included in the models. These were estimated from application of the Guntelberg equation for ion activity coefficients as a function of ionic strength23 (see definition of terms). Ionic strengths, which varied with titrant addition, were calculated iteratively along with pH. Microscale SpectrophotometrysApparatus DescriptionsA schematic diagram of the experimental apparatus is shown in Figure 1b. UV spectra were generated using a computer-assisted Cary 3E spectrophotometer (Varian Instruments, Palo Alto, CA) in which the temperature-controlled sample/reference chamber was modified such that a microelectrode (MI-412 Microcombination) and nitrogen supply lines (PE-10) could be placed in the 1-mL cuvettes for the duration of the experiment. This configuration allowed ready access for titrant delivery using a hand-held 1.0µL Hamilton syringe. The reference and sample cell solutions were mixed and protected from atmospheric CO2 by a fine stream of water-saturated nitrogen bubbles. The nitrogen lines were positioned near the bottom of the sample cell during titrant addition/mixing but raised to a level above the light path during scanning. Experimental ProceduresAfter the instrument was zeroed using sample solvent, analyte solution (6 µg benzoic acid in 600 µL of degassed, octanol-saturated, 0.001 M phosphoric acid, 8.28 × 10-5 M) was added to the sample cell and the micropH electrode was positioned in the sample cell above the light path. (Phosphoric acid, which contributes negligibly to the absorbance, was added to provide additional buffer capacity beyond that provided by the analyte of interest.) pH was recorded and the sample was scanned between 200 and 350 nm at a rate of 200 nm/min. After this baseline scan, equal volumes of titrant (2.5 M NaOH) were added to both cells, the pH was recorded, and a UV spectral scan was obtained. Titrations were performed at 25 °C. Total titrant volume added to the cuvettes was less than 1% of the sample volume, allowing volume changes due to titrant addition to be neglected. Simultaneous determinations of pKa and Ko/w were determined as described above by directly titrating the analyte with NaOH (2.5 M) to a pH at or near the equivalence point, adding water-
240 / Journal of Pharmaceutical Sciences Vol. 87, No. 2, February 1998
Figure 2sRepresentative pH−titration profiles obtained for the macroscale titration of a 10 mL volume (2) and microscale titration of 10 µL (O) and 100 µL (0) volumes of a solution of acetic acid (0.007 M). Total amounts of acetic acid titrated are 4.2 mg, 4.2 µg, and 42 µg, respectively. The solid lines are computer fits using eq 1.
Figure 3sRepresentative pH−titrant volume profile obtained during microscale titration of tromethamine (85 µg in 100 µL) with 0.1 M HCl using air (0) or nitrogen (9) bubble mixing. The solid lines are computer fits using eq 2. saturated octanol (200 µL) to the ionized analyte solution, and back-titrating the octanol-layered solution with HCl (2.5 M). The titrations were performed as described above at 25 °C but with water-octanol saturated nitrogen gas for mixing. The diprotic acid 2-[(2-mercaptobenzoyl)amino]-3-methylpentanoic acid (NSC 679825) (0.0015 M) was prepared in degassed, nitrogen-saturated phosphoric acid (0.001M) and titrated as described above but at a volume of 1.2 mL with a standard solution of NaOH (0.095 M). Data AnalysessThe UV spectra were examined to determine the wavelength at which there was a maximum change in absorbance (λ∆max) as pH was varied. Absorbance (Abs) versus pH profiles were constructed at λ∆max. Ka and Ko/w were determined by fitting these profiles to the equations shown in Appenndix B using nonlinear regression analysis (Scientist, MicroMath Inc.).
Results and Discussion Microscale Titrimetric Determination of pKa and PuritysIn adapting conventional acid-base titrimetry to a microscale, several possible sources of error in the determination of ionization constants and purities were considered, including the accuracy/precision of the pH microelectrode, limitations due to analyte concentration, limitations due to solution volume, and the increased likelihood for significant errors due to contamination from atmospheric CO2. Side-by-side comparisons of the performance of the pH microelectrode and a conventional semimicro combination pH electrode routinely used in the authors’ laboratories were initially conducted by titrating acetic acid solutions (10 mL) ranging in concentration from 0.07 to 0.0007 M with both electrodes immersed in the solution. Though the
Table 1sMicroscale Determination of pKa and Apparent Purity (p) of Acetic Acid and Tromethamine acetic acid conditions concentration, M (volume ) 100 µL) 0.07 0.007 0.0007 volume, µL (concentration ) 0.007 M) 100 20 10 nitrogen vs air ([acetic acid] ) 0.0007 M [tromethamine] ) 0.007 M volume ) 100 µL) nitrogen air a
pKa ± SD (n)
a
tromethamine p ± SD
pKa ± SD (n)
a
p ± SD
4.74 ± 0.05 (6) 4.77 ± 0.02 (7) 4.90 ± 0.02 (3)
0.99 ± 0.02 1.01 ± 0.02 0.98 ± 0.02
8.11 ± 0.02 (3) 8.11 ± 0.01 (5) 8.01 ± 0.04 (6)
0.999 ± 0.004 1.00 ± 0.01 1.00 ± 0.03
4.77 ± 0.02 (7) 4.78 ± 0.01 (3) 4.77 ± 0.02 (4)
1.01 ± 0.02 0.986 ± 0.004 1.00 ± 0.01
8.11 ± 0.01 (5) 8.07 ± 0.02 (3) 8.04 ± 0.06 (3)
1.00 ± 0.01 0.993 ± 0.008 1.00 ± 0.02
4.90 ± 0.02 (3) 4.89 ± 0.01 (3)
0.98 ± 0.02 0.959 ± 0.002
8.11 ± 0.01 (5) 7.80 ± 0.05 (4)
1.00 ± 0.01 1.05 ± 0.08
n ) number of determinations.
results obtained using the microelectrode appeared to be slightly less precise, no significant difference could be detected in the pKa of acetic acid obtained by either electrode, with values of 4.75 ( 0.06 and 4.78 ( 0.04 (mean ( SD, n ) 6) determined using the microelectrode and conventional semimicroelectrode, respectively. These results were in excellent agreement with literature values for the pKa of acetic acid (4.74-4.761,24). Representative microscale titration curves obtained for acetic acid and tromethamine are shown in Figures 2 and 3, respectively. Figure 2 illustrates that equivalent results were obtained in the microscale (10-100 µL) and macroscale (10 mL) experiments. Best-fit parameters generated from such curves according to the equations described previously are listed in Table 1. The effect of analyte concentration was first explored using a total solution volume of 100 µL and concentrations of acetic acid or tromethamine ranging from 7 × 10-4 to 0.07 M, representing sample size ranges of 4.2-420 µg for acetic acid and 8.5-850 µg for tromethamine. As is evident in Table 1, close agreement with theory was obtained for both pKa and apparent purity except at the lowest concentrations. Thus, at concentrations of 0.007 M and higher, the pKa found for acetic acid (4.74-4.77) was within the range of literature values reported (4.744.761,24), while the value of 8.11 obtained for the pKa of tromethamine was also within the range of values in the literature (8.08-8.111,25). For reasons not fully understood, the results at the lowest analyte concentrations deviated from those obtained at higher concentrations, with the apparent pKa of acetic acid increasing to 4.90 and that for tromethamine decreasing to 8.01. Since similar deviations were not seen in titrations of 10 mL samples at the same analyte concentrations, these results may reflect errors resulting from miniaturizing the experiment. Two possible sources of error are (1) premature diffusive titrant delivery from the immersed tip of the fused silica delivery needle and (2) trace CO2 contamination due to less than complete protection from air at the slow flow rates of nitrogen utilized. Since the titrant molarity was scaled down with sample concentration, parasitic delivery of titrant due to diffusion should not have varied significantly at decreasing sample concentrations. Regardless, these results reinforce the observations of Steele and Hieftje16 that “the best approach to microtitration is usually to miniaturize the solution-dispensing apparatus and maintain reagents at their original concentration”.
The accuracy of the pKa values for both compounds at the lowest sample sizes titrated improved somewhat by maintaining a higher solution concentration (0.007 M) while decreasing the sample volume. Thus, as shown in the second part of Table 1 and by the overlay of profiles in Figure 2, there was no apparent difference in pKa determinations (n ) 3-7) over a 10-fold decrease in sample volume from 100 to 10 µL, representing sample size ranges of 4.2-42 µg for acetic acid and 8.5-85 µg for tromethamine. Although not statistically significant, a trend toward lower apparent pKa with decreasing sample amount was suggested in the tromethamine data, which may again reflect the sources of error listed above. Purity values displayed no apparent change with decreasing sample volume over the range of 10-100 µL. The effects of CO2 uptake in samples exposed to air are more pronounced on the microscale, particularly in the titration of weak bases. Thus, as shown in Table 1, the estimated pKa of acetic acid (4.2 µg/100 µL) in samples exposed to air was not significantly different from that determined with nitrogen bubbling. On the other hand, the pKa of tromethamine even at a larger sample size of 85 µg/100 µL deviated significantly when mixing was performed using air rather than nitrogen, from a value of 8.11 ( 0.01 (n ) 5) in nitrogen to a value of 7.80 ( 0.05 (n ) 4) in air-exposed samples. Macroscale titrations of tromethamine (10 mL of 0.007 M) in air (with mechanical stirring) yielded a pKa estimate of 8.10 ( 0.01 (n ) 3), suggesting that the combination of air exposure and the microscale of the titration magnifies the error. Microscale pH-metric Determination of pKa, Purity, and Ko/wsThe octanol-water partition coefficient, Ko/w, is a useful parameter in studying quantitative structure-activity relationships and in evaluating the permeability of drugs across membranes, which, in turn, is important in determining their oral bioavailability and delivery to tissues outside of the vascular space. The use of a dual-phase potentiometric titration technique for determining Ko/w and pKa values, referred to as the pHmetric technique, has been the subject of several recent reports.2-7 pH-metric methodology appears to be adaptable to the determination of thermodynamic inclusion constants of guest/cyclodextrin complexes as well.25 Typically, aqueous solution volumes in these experiments are 5-50 mL while the octanol volumes range from 2 to 10 mL. The present study explored the accuracy and precision of the pH-metric technique at aqueous volumes of 100 µL and octanol volumes varying from 10 to 100 µL. Benzoic acid Journal of Pharmaceutical Sciences / 241 Vol. 87, No. 2, February 1998
Figure 4sRepresentative microscale pH-metric determination of the pKa and Ko/w for benzoic acid (85 µg in 100 µL): phase 1, direct titration with NaOH (0.1 M) in the absence of octanol (9, lower axis); phase 2, back-titration with HCl (0.1 M) in the presence of octanol (10 µL) (0, upper axis). The solid lines are computer fits using eqs 1 and 4.
was chosen as a model compound for these studies because its ionization constant (pKa ) 4.20) and octanol-water partition coefficient (Ko/w ) 74)26 are well-determined and it is suitable for analysis by both the potentiometric and spectrophotometric methods (described in a later section). Figure 4 illustrates the pH-metric method applied on a microscale for benzoic acid (85 µg in 100 µL). In the first phase of the experiment (lower curve), the acid was titrated with NaOH (0.1M) to a pH at or near its equivalence point in the absence of octanol. In the second phase (upper curve), water-saturated octanol (10 µL) was added and the system was back-titrated with HCl (0.1 M). Previous investigators have shown that benzoate anion partitioning into octanol is barely detectable,5,6 so the equilibria model used to describe the octanol-water partitioning vs pH profile for benzoic acid assumed partitioning of only the un-ionized species. Varying the octanol volume from 10 to 100 µL did not significantly affect Ko/w (Ko/w ) 61 ( 5 at 10 µL; 70 ( 5 at 100 µL (mean ( SD; n ) 2-4)). For this reason, all results (six sets of curves) were fit simultaneously using the same shared parameters, resulting in a pKa of 4.24 ( 0.03, apparent purity of 100 ( 1%, and Ko/w of 64 ( 6, in reasonable agreement with literature values. While the volume of octanol used had no effect on Ko/w, the time required to reach apparent equilibrium (i.e., <0.01 pH unit change/min) was markedly dependent on octanol volume, with equilibration times increasing from 5 min in the presence of 10 µL of octanol to 15 min in the presence of 100 µL of octanol. These observations suggest the need for an improved method of mixing in the dual-phase experiments if a high throughput analytical method is the goal. Microscale Spectrophotometric Determination of pKa and Ko/wsConventional spectrophotometric methods require substantially less compound than conventional titrimetric techniques, providing that the compound’s molar extinction coefficient is sufficiently high. Therefore, the need to further miniaturize spectrophotometric methods for determining pKa and Ko/w is less compelling. Nevertheless, we have found that adapting some of the microscale methodology developed for titrimetry to the spectrophotometric determination of pKa and Ko/w in a single sample 242 / Journal of Pharmaceutical Sciences Vol. 87, No. 2, February 1998
Figure 5sUV spectra for benzoic acid (6 µg in 600 µL) as a function of pH: (A) direct titration with NaOH (2.5 M), (B) back-titration with HCl (2.5 M) after addition of 200 µL of octanol.
offers advantages both in terms of minimizing sample consumption and in ensuring precision of the measurements. Although smaller cell configurations could have been selected, these studies used a sample volume of 600 µL in a 1-mL cuvette fitted with a pH microelectrode and nitrogen line for sample mixing and protection from atmospheric CO2. Titrant concentrations were sufficiently high (e.g., 2.5 M) that the complete pH range of interest could be attained with the addition of <1 µL of titrant, so that sample dilution could be neglected. Figure 5 displays the spectra generated as a function of pH for a 6 µg sample of benzoic acid titrated with NaOH in the absence of octanol (A) and those obtained for the back-titration with HCl after addition of 200 µL of octanol (B). From these spectra, absorbance-pH profiles at 235 and 223 nm were generated (Figure 6) for the direct titrations and back-titrations, respectively, and computer fitted using eqs 5 and 7 to obtain estimates of pKa and Ko/w of 4.23 ( 0.06 and 63 ( 3, respectively (n ) 2). These values are nearly identical with those determined using the microscale pH-metric technique. Application of Microscale Methodology To Determine pKa Values for an “Unknown” Diprotic AcidsThe diprotic acid 2-[(2-mercaptobenzoyl)amino)]-3-methylpentanoic acid (NSC 679825), shown in Figure 7, is one of two decomposition products formed in a reversible reaction from L,L-isoleucine disulfide, a drug candidate under investigation by the National Cancer Institute as a potential anti-HIV agent.27 The pKa values for the phenylthiol and the carboxylic acid functional groups in this compound were of interest in interpreting the pH-degradation profiles of this reversible decomposition reaction. However, only milligram quantities of the degradation product were available, necessitating the use of microscale techniques. The pKa values were initially determined titrimetrically using a 40-µg sample in 100 µL, as depicted in Figure 8.
Figure 8sRepresentative pH (left axis)−titration profile obtained in the microscale titration of compound I (40 µg in 100 µL) with NaOH (0.095 M). The solid line is the computer fit using eq 3 while the dashed line is the first-derivative curve (pH′, right axis).
Figure 6sBenzoic acid absorbance vs pH profiles at λ∆max determined from the UV spectral changes as a function of pH: (A) direct titration with NaOH in the absence of octanol (λ∆max ) 235 nm), (B) back-titration with HCl in the presence of 200 µL of octanol (λ∆max ) 223 nm). The solid lines are computer fits using eqs 5 and 7.
Figure 7sChemical structure of the “unknown” diprotic acid [2-[(2-mercaptobenzoylamino)]-3-methylpentanoic acid (compound I, NSC 679825)].
As suggested by the two inflection points and by the firstderivative curve, the titration curve was fitted to a model containing two ionization constants with pK1 equal to 4.05 ( 0.04 and pK2 equal to 6.29 ( 0.06 (mean ( SD, n ) 2). Although an examination of the compound’s structure suggested that pK1 probably reflects the ionization of the carboxylic acid group, the titrimetric method does not provide such information unambiguously. Microscale spectrophotometry was employed to confirm the pKa value for the aromatic thiol. The UV spectrum for this compound at wavelengths above 200 nm reflects primarily the (2-mercaptobenzoyl)amino portion of the molecule, which would be expected to shift significantly on ionization of the thiol due to resonance delocalization of the negative charge into the aromatic ring. The absorption spectra obtained as a function of pH are shown in Figure 9A. Apparent isosbestic points at ∼220 and ∼300 nm indicate that the UV spectra are only sensitive to a single
Figure 9s(A) UV spectra of diprotic acid I (16 µg in 1.2 mL) vs pH (B) Absorbance vs pH profile of I at λ∆max ) 236 nm. The solid line is the computer fit using eq 6.
ionization, which is presumably that of the phenylthiol. A plot of absorbance at 236 nm vs pH fitted to eq 6, shown in Figure 9B, yielded an estimate for pK2 of 6.29 ( 0.06 (mean ( SD, n ) 2), identical with that determined titrimetrically. In conclusion, conventional techniques employed to determine drug ionization constants and octanol-water partition coefficients have been successfully adapted to a microscale. Using the miniaturized titrimetric methods described, reasonably precise and accurate values of pKa and Ko/w are obtainable using solvent volumes as low as 10-20 µL. Both titrimetric and spectrophotometric methods can be conveniently and reliably performed using only a few micrograms of drug per determination. Journal of Pharmaceutical Sciences / 243 Vol. 87, No. 2, February 1998
References and Notes 1. Serjeant, E. P. Chemical Analysis; John Wiley & Sons, Inc.: New York, 1984; Vol. 69. 2. Clarke, F. H. Ionization constants by curve fitting: Application to the determination of partition coefficients. J. Pharm. Sci. 1984, 73, 226-230. 3. Clarke, F. H.; Cahoon, N. Ionization constants by curve fitting: Determination of partition and distribution coefficients of acids and bases and their ions. J. Pharm. Sci. 1987, 76, 611-620. 4. Clarke, F.; Cahoon, N. M. Potentiometric determination of the partition and distribution coefficients of dianionic compounds. J. Pharm. Sci. 1995, 84, 53-54. 5. Clarke, F. H.; Cahoon, N. M. Partition coefficients by curve fitting: The use of two different octanol volumes in a dualphase potentiometric titration. J. Pharm. Sci. 1996, 85, 178183. 6. Avdeef, A. pH-metric log P. II: Refinement of partition coefficients and ionization constants of multiprotic substances. J. Pharm. Sci. 1993, 82, 183-190. 7. Slater, B.; McCormack, A.; Avdeef, A.; Comer, J. E. A. pHmetric log P. 4. Comparison of partition coefficients determined by HPLC and potentiometric methods to literature values. J. Pharm. Sci. 1994, 83, 1280-1283. 8. Tolg, G. Ultramicro Elemental Analysis; Wiley-Interscience: New York, 1970. 9. Williams, M. Organic analysis: Ultramicro methods. In Treatise on Analytical Chemistry; Williams, M., Ed.; Wiley-Interscience: New York, 1965; Vol. Part II, Vol. 11, pp 219-296. 10. Belcher, R. Submicro Methods of Organic Analysis; Elsevier: New York, 1966. 11. Keen, R. T.; Fritz, J. S. Microtitration of amines. Anal. Chem. 1952, 24, 564-566. 12. Pietrogrande, A.; Guerrato, A.; Bortoletti, B.; Fini, G. D. Automatic potentiometric microdetermination of basic nitrogen in organic compounds. Analyst 1984, 109, 1541-1543. 13. Wadhwa, A.; Verma, R. M. Iodimetric microdetermination of aliphatic acids by a potentiometric titration method and comparison with acid-base potentiometry. Analyst 1983, 108, 1022-1025. 14. Alerm, L.; Bartroli, J. Development of a sequential microtitration system. Anal. Chem. 1996, 68, 1394-1400. 15. Sweileh, J. A.; Dasgupta, P. K. Applications of in situ detection with an automated micro batch analyzer. Anal. Chim. Acta 1988, 214, 107-120. 16. Steele, A. W.; Hieftje, G. M. Microdroplet titration apparatus for analyzing small sample volumes. Anal. Chem. 1984, 56, 2884-2888. 17. Gratzl, M. Diffusional microtitration: A technique for analyzing ultramicrosamples. Anal. Chem. 1988, 60, 484-488. 18. Gratzl, M. Diffusional microtitration: stationary or nonstationary reagent delivery. Anal. Chem. 1988, 60, 2147-2152. 19. Gratzl, M.; Yi, C. Diffusional microtitration: Acid/base titrations in pico- and femtoliter samples. Anal. Chem. 1993, 65, 2085-2088. 20. Hui, K. Y.; Gratzl, M. Diffusional microtitration of 20 µL samples with optical indication. Anal. Chem. 1997, 69, 695698. 21. Ishihama, Y.; Oda, Y.; Asakawa, N. Microscale determination of dissociation constants of multivalent pharmaceuticals by capillary electrophoresis. J. Pharm. Sci. 1994, 83, 15001507. 22. Butler, J. N. Ionic Equilibrium. A Mathematical Approach; Addison-Wesley: Reading, MA, 1964. 23. Butler, J. N. In Ionic Equilibrium. A Mathematical Approach; Butler, J. N., Ed.; Addison-Wesley: Reading, MA, 1964; p 436. 24. Budavari, S. The Merck Index; eleventh ed.; Budavari, S., Ed.; Merck & Co.: Rahway, NJ, 1989; p 1606. 25. Boudeville, P.; Burgot, J.-L. A new pH-metric methodology for the determination of thermodynamic inclusion constants of guest/cyclodrextrin complexes. J. Pharm. Sci. 1995, 84, 1083-1089.
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26. Fujita, T.; Iwasa, J.; Hansch, C. A new substituent constant, π, derived from partition coefficients. J. Am. Chem. Soc. 1964, 86, 5175-5180. 27. Liu, K.; Anderson, B. D. Stabilization of L-L-isoleucine disulfide (NSC 672594) requires stabilization of its thiol degradation product. Pharm. Res. 1996, 13 (Suppl.), S-269.
Acknowledgments A portion of this work was performed under Contract NO1-CM27720 from the National Cancer Institute.
Glossary aH+ γ1, γ2 I
Ao, Bo Co Vo Va, Vb Voct Kw Ka K1, K2 Ko/w p Vo, Vw Ci HA, A-
H2A, HA-, A2-
hydrogen ion activity monovalent, divalent ion activity coefficients [log γ ) -0.51z2I1/2/(1 + I1/2)] ionic strength (I ) 1/2∑cizi2, where ci and zi are the concentration and charge of the ith species) molar concentrations of HCl and NaOH, respectively, in titrant solutions initial molar drug concentration initial sample volume (µL) volumes (µL) of HCl and/or NaOH titrant added, respectively volume of octanol (µL) ion product of water (1 × 10-14 at 25 °C) monoprotic acid dissociation constant diprotic acid dissociation constants octanol-water partition coefficient apparent compound purity (equiv found/theoretical equiv) the organic and aqueous solvent volumes, respectively initial molar (aqueous) concentration of drug molar extinction coefficients of the un-ionized and ionized monoprotic acid species, respectively, at λ∆max (λ∆max will not generally be the same wavelength in the presence and absence of organic solvent) molar extinction coefficients of the various diprotic acid species
Appendix A Equation for monoprotic acid titration (acetic acid and benzoic acid)
BoVb Kw Ka aH+ Vo pCo + ) + γ1 Vo + Vb aH+γ1 aH+γ1 + Ka Vo + Vb
(1)
Equation for base titration (tromethamine)
pCoVo Kw AoVa aH+ aH+ + ) + γ1 Vo + Va aH+ + Kaγ1 aH+γ1 Vo + Va
(2)
Equation for diprotic acid titration [2-[(2-mercaptobenzoyl)amino]-3-methylpentanoic acid]
Equation for Ka determination (monoprotic acid) from absorbance data
BoVb Kw aH+ + ) + γ1 Vo + Vb aH+γ1 K1aH+ aH+
Appendix B
Vo pCo + V γ1 + K1aH+ + K1K2γ1/γ2 o + Vb 2K1K2γ1 Vo pCo (3) 2 γ γ a + + γ K a + + K K γ Vo + Vb
Abs ) Ci
2
1 2 H
2
1 H
1
2 1
Equation for back-titration of monoprotic acid anion in the presence of octanol (benzoic acid)
(aH+HA + KaA- /γ1)
(5)
(aH+ + Ka/γ1)
Equation for Ka determination (diprotic acid) from absorbance data
Abs ) Ci
[
]
aH+2H2A + K1aH+HA- /γ1 + K1K2A2- /γ2 aH+2 + aH+K1/γ1 + K1K2/γ2
(6)
Equation for simultaneous Ka and Ko/w determination (monoprotic acid) from absorbance data
BoVb Kw Va Ao aH+ + ) + + γ1 Va + Vb + Vo aH+γ1 Va + Vb + Vo KaVo pCo (aH+γ1 + Ka)(Va + Vb + Vo) + aH+γ1VoctKo/w
(aH+HA + KaA- /γ1) aH+Ko/wVo aH+ + Ka/γ1 + Vw
(
Abs ) Ci
)
(7)
(4) JS970057S
Journal of Pharmaceutical Sciences / 245 Vol. 87, No. 2, February 1998