Anal. Chem. 1996, 68, 2598-2604
Ionization Constants of Ginkgolide B in Aqueous Solution Oussama Zekri,† Philippe Boudeville,† Philippe Genay,‡ Bruno Perly,‡ Pierre Braquet,§ Philippe Jouenne,§ and Jean-Louis Burgot*,†
De´ partement de Physicochimie et Biocine´ tique des Pharmaco-syste` mes de l’Universite´ de Rennes I, 2 avenue du Professeur Le´ on-Bernard, 35043 Rennes Cedex, France, Laboratoire de RMN Haute Re´ solution du Commissariat a` l’Energie Atomique, Saclay, France, and IHB-IPSEN, 35 rue Spontini, 75116 Paris, France
The thermodynamic ionization constants (pKa1, pKa2, and pKa3) of ginkgolide B (9H-1,7a-(epoxymethano)-1H,6aHcyclopenta[c]furo[2,3-b]furo-[3′,2′:3,4]cyclopenta[1,2-d]furan-5,9,12-(4H)-trione, 3-tert-butylhexahydro-4,7b,11trihydroxy-8-methyl-) in aqueous solution have been settled by pH-metric and NMR studies. The three macroscopic pKa values as well as the water solubility and the water/n-octanol partition coefficient have been extracted from pH-metric data by means of a nonlinear regression methodology. NMR spectroscopy provided confirmation of the values of the macroscopic constants, information about the effective ionization pathways, and an estimation of the proportions of the various forms under physiologically relevant conditions. Ginkgolide B (Figure 1) is a natural compound extracted from the leaves of Ginkgo biloba L. trees. It has been the subject of many works in various fields,1 and the complete retrosynthesis has been performed by Corey et al.2 Ginkgolide B is endowed with significant pharmacological properties and exhibits potent antagonist activity against platelet-activating factor (PAF), which plays a key role in inflammatory processes. In vitro pharmacological studies have provided evidence that the efficiency of ginkgolide B is linked to pH and that its anti-PAF activity is enhanced in acidic medium.3a This result is clearly related to the existence of three lactone groups which may undergo hydrolysis, leading to the rings opening.3b These processes are reversible since, as reported by Braquet4 and confirmed by Plantefeve5 by means of HPLC studies, acidification of basic solutions of ginkgolide B invariably regenerates the original ginkgolide, without any alteration of the molecular structure. This important point will be further confirmed by NMR in the present work. Any attempt to relate biological properties to molecular structure(s) requires an unequivocal determination of the pH-dependent ionization state of ginkgolide B. †
Universite´ de Rennes I. Laboratoire de RMN Haute Re´solution. § IHB-IPSEN. (1) Braquet, P. Ginkgolides: chemistry, biology, pharmacology and clinical perspectives, Vols. 1 & 2; J. R. Prous Science Publishers: Barcelona, Spain, 1988. (2) Corey, E. J.; Kang, M. C.; Desai, M. C.; Ghosh, A. K.; Houpis, I. N. J. Am. Chem. Soc. 1988, 110, 649-651. (3) (a) Reference 1, Vol. 1, p XXVII. (b) Reference 1, Vol. 1, p 11. (4) Braquet, P.; Spinnewyn, B.; Braquet, M.; Bourgin, R. H.; Taylor, J. E.; Etienne, A.; Drieu, K. Ketsucki Myakkan 1985, 16, 558-572. (5) Plantefeve, J.-C. Beaufour-Ipsen internal communication. ‡
2598 Analytical Chemistry, Vol. 68, No. 15, August 1, 1996
Figure 1. Chemical structure of ginkgolide B (1), with atoms and rings numbered.
From a purely thermodynamic point of view, ring-opening of a lactone group with formation of an ionized alcohol-acid is quantified by the ionization constant Ka of the (in some cases) hypothetical lactone hydrate according to Ka
lactone, H2O y\z base-alcohol + H+
The constant Ka itself can be considered as the product of two equilibrium constants, Ka ) K′χa where K′ ) [alcohol-acid]/ [lactone] and χa ) [alcohol-base][H+]/[alcohol-acid]. Starting from the trilactone form 1 of ginkgolide B, three ionization pathways are conceivable (Figure 2). Three monoionized forms, 2, 3, and 4, may exist in the solution, as well as the three possible diionized ones, 5, 6, and 7. Eventually, a single triionized form, 8, should be considered. It is a well-known fact that only macroscopic constants can be obtained without ambiguity. The determination of microscopic constants requires, together with experimental data, additional extrathermodynamic assumptions about some physicochemical properties of the microspecies.6 The three macroscopic constants, Ka1, Ka2, and Ka3, are connected to the microscopic ones, Ki,j,k′ (Figure 3), by the following relations, (6) See, e.g.: Edsall, J. T.; Martin, R. B.; Hollingworth, B. R. Proc. Natl. Acad. Sci. U.S.A. 1958, 44, 505. Jaffe, H. H.; Orchin, M. Theory and applications of ultraviolet spectroscopy; John Wiley and Sons, Inc.: New York, 1966; p 561. S0003-2700(95)00939-5 CCC: $12.00
© 1996 American Chemical Society
Figure 2. Theoretical ionization pathways of ginkgolide B.
Figure 3. General ionization pathways for a tribasic acid: microscopic and macroscopic equilibria (the numbering of the microscopic constants is related to the released proton).
where β1, β2, and β3 are the overall macroscopic constants:
β1 ) Ka1 ) K1′ + K2′ + K3′ β2 ) Ka1Ka2 ) K1′K12′ + K1′K13′ + K2′K23′ ) K2′K21′ + K3′K31′ + K3′K32′ + ... β3 ) Ka1Ka2Ka3 ) K1′K12′K123′ ) K2′K21K123′ ) k2′K23′K231′ ) K1′K13′K132′ ) K3′K31′K132′ ) K3′K32′K231′
(1)
We report here the determination of the thermodynamic macroscopic ionization constants Ka1, Ka2, and Ka3 of ginkgolide B by potentiometry. We also describe in this paper the identifica-
tion by NMR spectroscopy of microscopic species which exist all along the ionization process. NMR spectroscopy allowed a rough estimation of the microscopic constants Ki,j,k′. Macroscopic constants were confirmed by independent determinations of solubility (S) in water and of the water/n-octanol partition coefficient (P) of 1. The choice of potentiometry was dictated by the fact that ginkgolide B lacks chomophore groups (absorbance is only significant under 220 nm) and electroactive groups in water. Moreover, owing to the low solubility of the trilactone in water (2.5 × 10-4 M), the variations of angular rotation of ginkgolide B with concentration are too low to be workable for our purpose; anyway, low concentration values are required to obtain pertinent thermodynamic data. Conductometry was also abandoned because of the lack of fundamental knowledge about molar conductivity values of the triionized form 8 and, of course, of the other ionized forms, 2-7. Study of variations of molar conductivities of “intermediate” species 2-7 with the ionic strength could not be performed independently because the forms 2-8 do not exist independently from each other in the solutions. This is due to the overlap of the three macroscopic ionization constants (see results below). Nevertheless, conductometry was used as a qualitative means to ascertain the state of equilibria, i.e., the end of opening or closing processes of the lactone groups. The solution conductivity did not vary any more when equilibrium was reached. Conductometry indicates that the slowest process is the monoionized forms opening to give the diionized forms. Under the lowest analytical concentration conditions, equilibrium was reached after 2 h for the opening process and 9 h for the closing process. To ensure that equilibrium was reached, all measurements were carried out after an overnight equilibration at 298 K. Analytical Chemistry, Vol. 68, No. 15, August 1, 1996
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EXPERIMENTAL SECTION Materials. Water used throughout this work was deionized on a set of ion exchanging columns (Bioblock Scientific) to F > 2 MΩ cm-1. Ginkgolide B (batch M 077222/CP 141005) was obtained from Beaufour-Ipsen Industrie. Potentiometric determinations were performed using a Tacussel LPH430T pH-meter calibrated with six buffers and using an Ingold 9811 (pH 0-14) glass electrode. All measurements were performed under nitrogen atmosphere (CO2 < 5 ppm) at 298 ( 0.1 K. All NMR spectra were collected using a Bruker AMX500 spectrometer operating at 500 and 125.7 MHz for 1H and 13C, respectively. Unless indicated otherwise, all experiments were performed at 298 ( 0.1 K. All buffers used were prepared in deuterium oxide (CEA, France). In all cases, the residual signal of the solvent was suppressed by low-power presaturation. Chemical shifts are given relative to external tetramethylsilane (TMS), calibration being performed using the residual solvent line as a secondary reference. Potentiometric Determinations. (A) Simultaneous pHMetric Determination of Ka1, Ka2, and Ka3. Solutions were prepared by dissolving known amounts of 1 and sodium hydroxide in known volumes of pure water, in such a way that solubility was not reached. pH was measured after equilibrium was reached. In these conditions, pH values of the resulting solutions are related to the overall ionization constants by the following relation:
[H+]5 + [H+]4(β1 + X) + [H+]3(β2 + β1(X - Y) - Kw) + [H+]2(β3 + β2(X - 2Y) - β1Kw) + [H+](β3(X - 3Y) - β2Kw) - β3Kw ) 0 (2) in which [H+] is the proton concentration, β1, β2, and β3 are derived from the macroscopic constants, and Kw is the ionic product of water. X and Y are defined by the following expressions: X ) CbVi/(V0 + Vi) Y ) C0V0/(V0 + Vi), where Cb and C0 are respectively the concentrations of added sodium hydroxide solution and of initial ginkgolide B solution, Vi is the added volume of sodium hydroxide solution, and V0 is the initial volume of ginkgolide B solution. Equation 2 is derived from the relations which rule the different equilibria and the mass and charge balances.7a The search for thermodynamic constants needed to take into account activity corrections; therefore, it resulted in some complexity in [H+] calculations. Proton concentration was calculated by a classical iterative process.7b For each set of chosen thermodynamic Ka1, Ka2, and Ka3 values, and thus β1, β2, and β3 values (and for each solution, i.e., for each Vi volume of titrant added), eq 2 was solved for [H+] several times. At the beginning of the process, a first estimation of [H+] was calculated by solving eq 2. At this step, the calculated [H+] value was neither an activity value nor a concentration one because of necessary initial mixing of activities (to which Ka1, Ka2, Ka3, and Kw values refer) with concentrations X and Y, to which equations of mass and charge balances pertained. However, this first obtained value of [H+] permitted the calculation of a first pseudo-ionic strength, which, in turn, allowed the estimation of a first set of activitiy coefficients of all (7) (a) Butler, J. N. Ionic equilibrium. A mathematical approach; Addison-Wesley Publishing Co.: Reading, MA, 1964; p 61. (b) Reference 7a, pp 440-458.
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species. With these activity coefficients, a set of equilibrium concentration constants Ka1, Ka2, Ka3, and Kw was therefore computed from the thermodynamic ones. A new value of [H+] was obtained, and the process was repeated until the the ionic strength was constant. During the whole process, Ka1, Ka2, Ka3, and Kw constants were hence successively thermodynamic and then, more and more, equilibrium concentration constants while [H+] became more and more a concentration value. After convergence of the ionic strength, the [H+] concentration was transformed back to {H+} activity with the help of the last activity coefficient of the proton. Activity coefficients used all along this process were computed through the extended Debye-Hu¨ckel8a,b relation,
-log γi ) Azi2(I)1/2/(1 + Ba(I)1/2)
or with the Davies8c relation when the ionic strength was over 0.01 M,
-log γi ) Azi2(I)1/2/(1 + (I)1/2) + 0.1zi2I)
It is worth noting that, because of the three Ka values and low solubility of 1, markedly different initial concentrations, C0, of ginkgolide B had to be used to ascertain them. As a matter of fact, it was necessary to work with very low C0 values to get the first constant, Ka1. Consequently, at these low C0 values, even the addition of 3 equiv of sodium hydroxide did not reach the pH range of the third ionization constant. On the other hand, the required C0 value to reach Ka3 led to a pH range which could not allow Ka1 determination. However, Ka2 was accessible at each analytical concentration used, and its value allowed us to check the reliability of Ka1 and Ka3 values. C0 concentrations used were respectively 10-4, 2.5 × 10-4, 10-2, and 2 × 10-2 M. For each Vi volume of titrant added, six solutions corresponding to the same C0 values were prepared in an absolutely independent manner. A nonlinear least-squares regression process was adopted to fit the calculated pH values to the corresponding experimental ones. The least-squares function was defined as n
UT )
m
∑∑W (pH i
calc i
- pHi,jexp)2
i)1 j)1
where n is the number of titration points treated, m the number of replicates (generally, m ) 6), i the running point, j the replicate considered at the i point, and Wi a weighting factor chosen as the inverse of variance σ2pHi taken over the m replicates for the same volume Vi. This UT function was compared to a theoretical minimum cost function U0, which only takes into account the random experimental errors: (8) (a) Harned, H. S.; Owen, B. B. The physical chemistry of electrolytic solutions; Chapman and Hall, Ltd.: London, 1958; p 66. (b) Tanford, C; Wawzonek, S. Physical methods of organic chemistry; Interscience Publishers, Inc.: New York, 1960; Vol 1, Part IV, p 2924. (c) Rossotti, F. J. C.; Rossotti, H. The determination of stability constants in solutions; McGraw-Hill Book Co., Inc.: New York, 1961; p 30.
n
U0 )
m
∑∑W (pH i
mean
i
- pHi,jexp)2
i)1 j)1
where pHimean is the mean of the m experimental pH values corresponding to the Vi titrant volume added. The ratio UT/U0 quantifies the lack of fit. Usually, the UT cost function must be within 1-3 times the U0 cost function value. The search for the physically convenient roots of eq 2 and the search for the set of thermodynamic constants Ka1, Ka2, and Ka3 which minimize the least-squares function were performed through a home-made algorithm. In this algorithm, the variancescovariances matrix, which takes place naturally during the search for the best set of parameters, allows the obtention of standard deviations of Ka1, Ka2, and Ka3. (B) Validation of the Method. To check the goodness of both the program and the potentiometric methodology, citric and orthophosphoric acids were titrated with the same experimental design. Results were in very good agreement with literature data when activity corrections were made. However, to gain further confirmations, two other pH-metric approaches were developed taking into account the water solubility (S) of ginkgolide B and its water/n-octanol partition coefficient (P). (C) Simultaneous pH-Metric Determination of the Product SKa1 (or Sβ1) and of Ka2 (β2/β1). Some solutions of ginkgolide B were prepared in such a way that an excess of solid form 1 was present once the ring-opening equilibria were reached. This was made by careful addition of different volumes of a hydrochloric solution to a known volume of a solution containing 1 equiv of ginkgolide B and 3 equiv of sodium hydroxide. In these conditions, [H+] is given by eq 3:
[H+]4 + (Y - X)[H+]3 - (Kw + Sβ1)[H+]2 2Sβ2[H+] - 3Sβ3 ) 0 (3) A difficulty was met in the computational phase of this determination because the constants S and Ka1 always appear as the product Sβ1 in eq 3. Therefore, only the product value SKa1 and the Ka2 constant value could be derived from the experimental data. These values were “mixed” activity-concentration ones, because the iterative computation of ionic strength could not be performed as in the previous section. Therefore, the Ka1 constant value is not rigorously known. (D) Simultaneous pH-Metric Determination of P, Ka1 (β1), and Ka2 (β2/β1). Samples of 50 mL of the solutions prepared in the same way as previously were left under shaking in the presence of 10 mL of n-octanol (in these cases, no solid form was observed). After equilibria were obtained (24 h of equilibriation), n-octanol was removed by centrifugation, and pH values of these solutions were compared to those computed from the following relation:
[H+]5(W + PVoct) + [H+]4(Wβ1 + (Y - X)(W + PVoct)) + [H+]3(Wβ2 + Wβ1(Y - X) - Kw(W + PVoct) - C0V0β1) + [H+]2(Wβ3 + Wβ2(Y - X) - Wβ1Kw - 2C0V0β2) + [H+](Wβ3(Y - X) - Wβ2Kw + 3C0V0β3) - WKwβ3 ) 0 (4) where W ) (V0 + Vi). n-Octanol has been chosen for practical9
Figure 4. Comparison of the partial 1H NMR spectra of ginkgolide B (298 K, 500 MHz) at pH 5.1 (a) and 8.0 (b).
and pharmacochemical reasons.10 As before, only pH values in the range of pKa1 were processed to get a good assessment of P value. A Ka3 value could not be reached this way. NMR Investigations. NMR experiments were performed with a triple purpose: (i) to have a deeper insight into the effective pathways; (ii) to determine the microscopic constants from the ratios of the relative concentrations of the microscopic species; and (iii) to confirm the values of the ionization constants settled by pH-metric measurements through the calculation of the overall ionization constants according to relations 1. Owing to the low solubility of the trilactone form 1 of ginkgolide B in water, all literature data concerning NMR investigations of Ginkgolides relate to solutions in organic solvents.11 The improvement of the sensitivity of NMR spectrometers (due to the use of high fields and low-noise detection systems) allows good quality spectra of 1 (trilactone form) to be obtained in deuterium oxide. The complete assignment of resonance lines was performed using bidimensional experiments. The use of double-quantum correlations12 was preferred to the more classical COSY13 since it allows a clarification of the correlation map by intrinsic suppression of all singlet lines (tBu group and residual solvent signal). (A) Variation of NMR Spectra with pH. Figure 4 displays a comparison of the NMR spectra of ginkgolide B at two different pH values. Two conclusions can be derived from this observation. First, several molecular forms of the solute are clearly observed, and their proportions can be derived from integration of signals corresponding to the same proton. The signals from Me16 will be used mainly since they show limited overlap with other signals. All other signals can be assigned (starting from the Me signals using the double-quantum correlation method). Second, the (9) Levitan, H.; Barker, J. L. Science 1972, 176, 1423. (10) Smith, R. N.; Hansch, C.; Ames, M. J. Pharm. Sci. 1975, 64, 599. (11) Roumestand, C.; Perly, B.; Braquet, P. Reference 1, Vol. 1, pp 49-68. (12) Bodenhausen, G. Proc. Nucl. Magn. Reson. Spectrosc. 1981, 14, 137. (13) Bax, A.; Freeman, R. J. Magn. Reson. 1981, 44, 542.
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Figure 5. Contour plot of a double-quantum correlation experiment on a sample at pH 7.4 (500 MHz, 298 K). The dotted line represents the pseudo-diagonal in this experiment. Horizontal lines indicate correlated signals used for the assignement.
ionization process leads to species which interchange very slowly at the NMR time scale since separate signals (and not averaged ones) are obtained for the different ionized forms. This confirms the fact that equilibrium is reached slowly and that care should be taken to make sure that NMR observations are performed on samples having reached the thermodynamic equilibrium. To ensure reproducibility, all samples were prepared ahead of time (2 days), and spectra were run at different periods and eventually checked after 1 month. Slight variations were observed only for very high pH values, probably due to variations of the real pH resulting from slow absorption of carbon dioxide. This type of analysis was performed at 75 different pH values ranging from 5 to 13. (B) Assignment of the NMR Signals to the Various Possible Forms of Ginkgolide B. This analysis was performed using the pH dependence of the most relevant NMR signals. These shifts were derived from bidimensional experiments starting from the Me16 signals. Although it is expected that the opening of a given lactone ring will induce the largest variations of chemical shifts for the closest protons, it should be kept in mind that signals from protons far away from the considered ring can also be affected, owing to structural and conformational variations. A stepwise analysis at the vicinity of the expected pKa values allows, however, a clear and unambiguous determination of the successively involved lactone groups. Figure 5 shows a partial contour plot of the double-quantum correlation experiment performed on 1, along with selected scalar pathways used for the stepwise assignment of proton signals. The signals of the correlated Me16 and H14 protons were used as starting points and will play a key role in the pH-dependent analysis of NMR spectra. Another confirmation is provided by a stepwise NMR investigation starting from the fully ionized form at very high pH. A stepwise decrease of pH showed the apparition of essentially one diionized form, which, on the basis of 1H and 13C experiments, could be assigned unequivocally to the species in which only ring E remains closed. 2602
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Table 1. Relative Proportions (in %) of the Various Forms of Ginkgolide B as a Function of pH Determined by NMR (Chosen among 75 pH Samples) form pH
1
2
3
4
5
6
8
5.0 6.0 6.5 7.0 7.5 8.0 9.0 10.0 11.0 12.0 13.0
100 100 93 67 37 17 0 0 0 0 0
0 0 0 17 36 47 22 0 0 0 0
0 0 0 12 15 20 12 2 0 0 0
0 0 7 4 9 7 2 1 1 0 0
0 0 0 0 0 5 57 90 95 90 61
0 0 0 0 0 2 5 2 1 0 0
0 0 0 0 0 0 0 1 3 10 39
A complete analysis of all samples at 75 pH values allowed both the assignment of the signals from the various forms and the determination of the proportions of these forms at any pH value. Results at some pH values are presented in Table 1. In the present case, the signals from the Me16 group were used for identification. Other protons can be used, but they give less accurate results owing to a more severe overlapping of signals corresponding to the different species. (C) Microscopic Ionization Constants Determination from NMR Data. Given the above conditions of the determination of the relative proportions of species 1-6, and 8, only an estimation of the microscopic equilibrium concentration constants Ki,j,k′ was accessible. They were determined by fitting calculated ratios with the corresponding experimental ones (some of which are given in Table 1) through a nonlinear regression. For example, K1′ was obtained starting from the relation
K1′/{H+} ) [2]/[1] where the experimental ratios [2]/[1] were calculated from the
Table 2. pKa1, pKa2, and pKa3 Values from pH Measurements C0 (mol L-1)
Uf/U0a
pKa1b
pKa2b
pKa3b
1 × 10-4 2.5 × 10-4 1 × 10-2 2 × 10-2
1.71 1.28 1.17 1.23
7.41 (7.38-7.45)c 7.18 (7.15-7.22)c
8.13 (7.99-8.36)c 8.48 (8.42-8.54)c 8.70 (8.70-8.71)c 8.76 (8.74-8.78)c
11.84 (11.82-11.85)c 11.93 (11.91-11.95)c
a Goodness of fit criterion. U is the minimal cost function obtained at the end of the fitting process, and U is the theoretical cost function f 0 which would be obtained with no lack of fit (only experimental errors being taken into account). b Average value of seven constants values. Each one is obtained by processing 31 pH values chosen at random among the six replicates. c The 95% confidence limits on the true average value are given by -log(Ka ( 2.447σn-1/n1/2) according to Student’s table.
Table 3. SKa1, pKa1, pKa3, and log P Values from pH-Solubility Measurementsa and pH-Partitioning Measurements experiment pH-solubility pH-partitioning a
C0 (mol L-1) 2.5 × 1 × 10-3
10-2
SKa1 3.66 ×
10-11
(2.3 ×
10-11-5
×
pKa1
pKa2
log P
6.95 (6.87-7.06)
8.35 (8.18-8.62) 8.31 (8.29-8.34)
1.72 (1.62-1.80)
10-11)
Processed without activity corrections (see text).
percentage values of 2 and 1 in Table 1. We then searched for the K1′ value which minimized the cost function U ) ∑ (K1′/{H+}i - [2]i/[1]i)2. It is clear that Ki′ is only a “mixed” constant14 because of the intervention of concentrations [2]i and [1]i and the activity, {H+}i, in the two last relations. To get a satisfactory accuracy for the Ki′ values, regression has been performed in an iterative way. First, all of the data of interest for the considered constant were processed. Then, experimental ratios which were too far away from the calculated ones were rejected. With the remaining data, a new regression was performed, and so on. Finally, the iterative process was stopped when no outlier was found. The adopted criterion of rejection was a difference between the experimental and calculated ratios greater than 1.96 times the square root of the ratio of the cost function and of the freedom degree: 1.96(U/(n - 1))1/2. “Mixed” macroscopic constants were determined in an analogous manner by processing all of the experimental ratios of interest. RESULTS AND DISCUSSION Ginkgolide B’s thermodynamic macroscopic ionization constants obtained from regression analysis of pH-metric titration curves at different concentrations are given in Table 2. Despite some weak discrepancies, these results are clearly reliable. The noticeable discrepancy is the lack of overlap of confidence limits for the different analytical concentrations used. However, it is worth noting that the corresponding confidence limits are close to each other. A first explanation of this discrepancy, which is valuable for the weakest analytical concentrations, is the unavoidable presence of carbon dioxide in the solutions, in spite of our experimental precautions. The carbonic acid concentration was estimated as ∼2 × 10-5-3 × 10-5 M (from conductometric measurements and a calculation considering an average CO2 concentration in the laboratory atmosphere of 600 ppm (v/v)), while the analytical concentration of ginkgolide B was 1 × 10-4 M. Moreover, the variability of carbonic acid concentration in the different replicates is the major cause of the range of uncertainties in pKa values for the weakest analytical concentration used. For higher analytical concentrations, the discrepancy is (14) Albert, A.; Serjeant, E. P. The determination of ionization constants; Chapman and Hall: London, 1971, p28.
probably due to the activity coefficients values, as it is a wellknown fact that the relations allowing their estimation deal more efficiently with 1:1 and 1:2 electrolytes than with 1:3 electrolytes.15 For these reasons, we decided to select the pKa values obtained at the intermediary concentrations 2.5 × 10-4 and 10-2 M. As there are two values for pKa2 (8.48 and 8.70), we imposed the mean value (8.60) to new regression analyses of the pH data corresponding to the intermediary concentrations 2.5 × 10-4 and 10-2 M. The resulting pKa1 and pKa3 values were 7.14 and 11.89, respectively. So, the definitive ginkgolide B’s pKa1, pKa2, and pKa3 thermodynamic values are 7.14, 8.60, and 11.89. It is relevant to note that the values of pKa1 and pKa3 obtained through these last minimizing processes are very close to those given in Table 2. Macroscopic ionization constants, S, and log P values obtained from solubility and partitioning measurements are given in Table 3. The pKa2 value issuing from solubility measurements is in good agreement with those given in Table 2, despite the fact that activity corrections could not be carried out. A solubility estimation by a fully independent means16 gave the value of total solubility of ginkgolide B at pH 7.4, St ) 7.07 × 10-4 M. Handling the expression St ) S(1 + β1/[H+] + β2/[H+]2 + β3/[H+]3) with the definitive overall constants gives the following value for the solubility of the fully closed form 1: S ) 2.4 × 10-4 M. This value is the same as the one we estimated at the beginning of this work by rough determinations at pH 4 by observing the appearance of a precipitate (2.5 × 10-4 M). Constants issuing from pH-partitioning measurements are in good compliance with the preceding ones. To our knowledge, the value of log P (1.72) is the first published one for ginkgolide B. The good compliance of Table 3’s pKa values with those of Table 1 emphasizes the goodness of our determinations. Unfortunately, the complexity of ginkgolide B’s structure precludes any credible a priori calculation of its log P value through the usual methods17 for the sake of comparison. (15) Butler, J. N. Reference 7a, pp 428-437. (16) Plantefeve, J.-C. Beaufour-Ipsen internal communication. (17) Hansch, C.; Leo, A. Substituent constants for correlation analysis in chemistry and biology; John Wiley and Sons: New York, 1979.
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Table 4. Microscopic, Macroscopic, and Overall Equilibrium Constants of Ginkgolide B macroscopic constants
overall constants
ionization step
microscopic constants
NMRa
1
K1′ ) 3.0 × 10-8 K3′ ) 1.6 × 10-8 K2′ ) 2.2 × 10-9 K12′ ) 6.0 × 10-11 K13′ ) 2.0 × 10-9 K31′ ) 3.9 × 10-9 K21′ ) 5.0 × 10-9 K123′ ) 7.0 × 10-11 K132′ ) 2.0 × 10-13
pKa1 ) 7.32
pKa1 ) 7.14
β1 ) 4.82 × 10-8
β1 ) 7.20 × 10-8
pKa2 ) 8.84
pKa2 ) 8.60
β2 ) 6.95 × 10-17
β2 ) 14.4 × 10-17
pKa3 ) 12.05
pKa3 ) 11.89
β3 ) 2.30 × 10-28
β3 ) 1.86 × 10-28
2
3 a
pH-metric
NMRb
pH-metricc
Calculated from the overall constants. b Calculated from the microscopic constants. c Calculated from the definitive macroscopic constants.
Figure 6. Distribution diagram of microscopic species of ginkgolide B versus pH. Percentage values were obtained from calculations using the corresponding pKi,j,k values of Table 4.
It is worth noting that, contrary to pH measurements, pHsolubility and pH-partitioning measurements were carried out to establish equilibria starting from basic solutions and acidification. Reliability of all results is a very strong support for the goodness of the model and, in particular, for the full reversibility of the whole process. It also indicates the very good accuracy of the results. NMR spectra showed the absence of form 7. This rules out the corresponding ionization pathway. The mixed microscopic equilibrium constants obtained from Table 1 data are given in Table 4. The calculated values of overall constants through relations 1 are reported in Table 4, along with the resulting macroscopic constants. As shown in Table 4, pKa values issuing from NMR data are also in full agreement with the ones obtained from pH-metric studies. Actually, from a rigorous standpoint, they cannot be exactly equal because NMR results were obtained with no activity corrections and because these determinations were carried out in deuterium oxide instead of water. The difference between pH values in water and in deuterium oxide induces differences in pKa values. On the molar concentration scale, the pH difference pD - pH ) 0.41 is well established.18 (18) Bates, R. Determination of pH. Theory and practice; John Wiley and Sons: New York, 1973; p 375.
2604 Analytical Chemistry, Vol. 68, No. 15, August 1, 1996
The microscopic ionization constants allow the plotting of the distribution diagram of the different species versus the pH (Figure 6). Obviously, it is of utmost importance from the pharmacological standpoint to know the occurrence of the different species versus the pH values. NMR investigations were performed under physiologically meaningful conditions to derive the proportions of the various forms. 1H NMR spectra were obtained in a saline non-hemolytic buffer at pH 7.40. To correlate with the previously determined proportions, experiments were first run at 298 K, and further determinations were performed at 310 K. Results are 37, 41, 16, and 6% at 25 °C and 34, 37, 24, and 5% at 37 °C for species 1, 2, 3, and 4, respectively. The distribution at 25 °C is in full compliance with the values predicted from the ionization constants. From the purely biological point of view, it is, however, important to note that, under physiological pH conditions, an equilibrated sample of ginkgolide B contains only 34% of the trilactone form 1. Another important contribution of the NMR study concerns the reversibility of the opening of the lactone groups. Several NMR observations were performed by adjusting the pH to the desired value starting from either acidic (pH 4.7) or basic (pH 13) solutions. As long as the sample is allowed to reach thermodynamic equilibrium, the proportions of the various species did not differ significantly in the two samples. Moreover, acidification of several samples to pH 3 and isolation of the recrystallized material showed (NMR spectra in DMSO) that the recovered samples are strictly identical to an authentic sample of ginkgolide B. CONCLUSION To summarize, a pH-metric study followed by a specially designed computational proceeding allowed us to solve such a difficult problem as that presented by the determination of the three overlapping thermodynamic macroscopic ionization constants of ginkgolide B. This work also demonstrates that NMR studies nicely complete the pH-metric determination of macroscopic constants, since they provide a means to estimate the relevant microscopic ones.
Received for review September 18, 1995. Accepted April 17, 1996.X AC950939G X
Abstract published in Advance ACS Abstracts, June 1, 1996.
