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Structure-Activity Relationships for the Degradation Reaction of 1-β-O-Acyl Glucuronides. Part 2: Electronic and Steric Descriptors Predicting the Reactivity of 1-β-O-Acyl Glucuronides Derived from Benzoic Acids Tadao Yoshioka* and Akiko Baba Hokkaido Pharmaceutical UniVersity School of Pharmacy, 7-1 Katsuraoka-cho, Otaru, Hokkaido 047-0264, Japan ReceiVed March 7, 2009
Glucuronidation of carboxylic acid drugs has been found to be a metabolic activation pathway, possibly leading to covalent binding of the resultant 1-β-O-acyl glucuronides (βGAs) to proteins. Previous studies on the structure-activity relationships (SARs) of the degradation rate constants (k values) of βGAs have revealed that the electrophilicity of and steric hindrance around the 1-β-O-acyl linkages cause the diversity and complexity of the observed k values. To evaluate these effects and ultimately predict the k values of structurally diverse βGAs, we derived further SARs for k values of 18 1-β-O-benzoyl glucuronides with o-, m-, and p-substituents (BAGAs). In single regression analyses of 10 m- and p-substituted BAGAs, the log k values were well-predicted using an electronic parameter of Hammett’s σ constant, pKa, 1H NMR chemical shift (δCOOH), computed δCOOH, or computed partial atomic charge (HPAC or OPAC) of the parent benzoic acids. The log k values of eight o-substituted BAGAs, although showing a correlation with the 13C NMR chemical shift of the parent benzoic acids [δ(CdO)OH], were well-predicted using multiple regression analyses; some combinations of electronic (δCOOH, HPAC, or calculated pKa) and steric [δ(CdO)OH or Es] descriptors predicted the 18 observed k values with a high degree of certainty. The standard partial regression coefficients indicate that steric effects affected the k values as strongly as electronic effects, indicating that the k values increase as the acidity of the parent acids increases and as the steric bulkiness around the 1-β-O-acyl linkages decreases. These single and multiple regression equations, using different electronic and/or steric descriptors of the parent benzoic acids, are expected to be useful for predicting the k values of BAGAs. The applicability domain and mechanistic interpretation of the derived SAR models are also discussed together with the relevant toxicology of βGAs. Introduction Adverse drug reactions (ADRs), such as idiosyncratic druginduced liver injury and hypersensitivity, have long been of crucial importance from the standpoint of both clinical drug safety and industrial drug development (1-3). Metabolic activation of relatively inert functional groups of drugs into reactive electrophilic intermediates and subsequent covalent binding to proteins are considered to be toxicologically relevant to ADRs (4-9). Glucuronidation of carboxylic acid drugs, such as nonsteroidal anti-inflammatory drugs, has been found to be a metabolic activation pathway, possibly leading to covalent binding of the resultant 1-β-O-acyl glucuronides (βGAs) to cellular macromolecules (5, 7, 9). βGAs are potentially reactive electrophiles implicated in ADRs of the parent carboxylic acid drugs; hence, several comprehensive articles concerning the UDP-glucuronosyltransferases responsible for the formation of βGAs (10-13), the chemical reactivity of their 1-β-O-acyl linkages (9, 14-17), and the covalent binding to proteins responsible for the toxicological consequences (9, 18-20) have been reported, although the toxicological consequences remain largely unknown. As shown in Scheme 1, βGAs are labile at physiological pH and are known to undergo not only intramolecular acyl migration (major) and hydrolysis (minor) but also covalent binding to * To whom correspondence should be addressed. Tel: +81-134-62-1894. Fax: +81-134-62-5161. E-mail:
[email protected].
Scheme 1. Electrophilic Degradation Pathways and Protein Binding Mechanisms of βGAsa
a The glycation mechanism, proceeding at the stage of 3-O- and 4-Oacyl isomers, is illustrated with 4-O-acyl isomer.
proteins. Two mechanisms have been proposed to explain the process of covalent binding to proteins: a direct acylation mechanism by βGA itself (21) and a glycation mechanism via the formation of a Schiff base with 3-O- and/or 4-O-acyl-
10.1021/tx900092z CCC: $40.75 2009 American Chemical Society Published on Web 08/11/2009
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migrated isomers of βGA (22). As for the covalent binding to proteins, studies of structure-activity relationships (SARs) have shown a positive correlation between the extent of covalent binding of βGAs (to albumin or a peptide) and their degradation rate parameters (23-26). This indicates that more labile βGAs are more reactive to proteins. Although the number of substituents on the R-carbon to the carboxylic group of the parent drugs has been thought to affect the reactivity (23, 25), further studies, especially on the electronic and steric effects of the R group in Scheme 1, are required for the development and justification of SAR models. As for the SARs of the electronic effects on the spontaneous degradation (intramolecular acyl migration and hydrolysis) rate constant k (shown in Scheme 1), the log k values of 1-β-O-benzoyl glucuronides (BAGAs) with p-substituents showed a positive F value in the Hammett plot, indicating an increase in the k value by electronwithdrawing ring substituents (27). On the other hand, systematic SARs for the steric effects have not been published to date. The k value of the BAGA with an o-CF3 group was reported to be the lowest among o-, m-, and p-isomers of BAGAs with a CF3 substituent (28), whereas the k value of the BAGA with an o-F group is the largest among o-, m-, and p-isomers of BAGAs with a F substituent (29). These results indicate that not only electronic but also steric effects of ring substituents affect k values. From these findings, it is thought to be of great importance to derive and justify SARs for k values, which have been shown to be a valid parameter for predicting the biological reactivity of βGAs as mentioned above. Therefore, in our preceding paper (30), we synthesized 27 structurally diverse βGAs and then derived SARs for their k values using the 1H and 13C NMR chemical shifts of the parent carboxylic acids as descriptors. The observed diversity in the k values was found to depend largely on both the electrophilicity of the 1-β-O-acyl linkages and the steric hindrance around them. However, the effects on the k values of o-substituents of BAGAs, R-substituents of βGAs derived from 2-arylpropionic acids, and the stereochemistry at the R-position of 2-arylpropionyl groups have yet to be elucidated. In the present study, therefore, we focused on quantitative SARs [(Q)SARs] for the k values of BAGAs using both electronic and steric descriptors to clarify the effect of osubstituents. Recently, the Organisation for Economic Cooperation and Development (OECD) proposed a guidance document on the validation of (Q)SAR models, in which the OECD principles point out that (Q)SAR models should be associated with (i) a defined end point, (ii) an unambiguous algorithm, (iii) a defined domain of applicability, (iv) appropriate measures of goodness-of-fit, and (v) a mechanistic interpretation (31). Therefore, our SAR studies were conducted using 18 BAGAs including eight o-substituted ones, with their k values defined as the end point. Chemical descriptors such as NMR chemical shift and Taft’s Es parameter (32) as well as calculated chemical descriptors were examined for the development of SAR models, which would be applicable to BAGAs derived from not only existing but also theoretical benzoic acid derivatives (BAs). The statistical validation, the applicability domain, and the mechanistic interpretation of the derived SAR models are also discussed.
Experimental Procedures Chemicals. Furosemide, flufenamic acid and probenecid, and telmisartan were purchased from Tokyo Kasei Kogyo Co. Ltd., Wako Pure Chemical Industries, and Sigma, respectively. 2,4-
Yoshioka and Baba Dimethylbenzoic acid and o-trifluoromethylbenzoyl chloride were purchased from Wako Pure Chemical Industries and used without further purification. 2,4-Dimethylbenzoyl chloride was prepared from the corresponding acid according to the reported procedure (33). Benzyl 2,3,4-tri-O-benzyl-D-glucopyranuronate (34) was synthesized according to the reported procedure. All other chemicals used were analytical or reagent grade commercial products. 1H and 13 C NMR were recorded on a JNM-AL400 spectrometer (JEOL). Chemical shifts are presented as δ values in ppm in reference to the residual solvent signals (35) of DMSO-d6 (2.49 ppm for 1H and 39.50 ppm for 13C) or MeOH-d4 (3.30 ppm for 1H and 49.00 ppm for 13C). Preparation of 18 BAGAs Used for SAR Studies. Among 18 BAGAs, 16 compounds have been synthesized previously, and their analytical data have been reported (30, 36, 37). For the SAR studies, two o-substituted compounds, oCF3BAGA and 24DMBAGA, were newly synthesized according to reported procedures (30), as described below. Synthesis of 1-β-O-(o-Trifluoromethylbenzoyl)-D-glucuronide (oCF3BAGA). NEt3 (0.20 mL, 1.5 mmol) was added to a solution of benzyl 2,3,4-tri-O-benzyl-D-glucopyranuronate (90 mg, 0.16 mmol) in CH2Cl2 (2.0 mL, dried over Molecular Sieves 3 Å in advance), and stirring was maintained for 10 min at room temperature. o-Trifluorobenzoyl chloride (23 µL, 0.16 mmol) was then added in portions over 30 min. After it was stirred for 2 h, the reaction mixture was diluted with EtOAc (20 mL), and the organic layer was washed with saturated NaHCO3, 2.5% HCl, and finally saturated NaCl and then dried over Na2SO4. After removal of the organic solvent in vacuo, the crude product obtained was purified by a preparative silica gel TLC to give the product (104 mg, 88% yield). To deprotect the O-benzyl groups, the purified compound was dissolved in EtOAc-EtOH (3.0 mL, 2:1, v/v) and hydrogenated in the presence of Pd(OH)2/C (Aldrich, 10 mg) at atmospheric pressure for 1.5 h to yield the fully debenzylated product of oCF3BAGA in almost quantitative yield. 1H NMR (MeOH-d4): δ 8.01-7.99 (m, 1H), 7.84-7.82 (m, 1H), 7.77-7.69 (m, 2H), 5.72 (d, 1H, J ) 8.0 Hz), 3.99 (d, 1H, J ) 9.5 Hz), 3.60 (t, 1H, J ) 9.5 Hz), 3.54-3.50 (m, 2H). 13C NMR (MeOH-d4) δ: 172.0, 165.9, 133.3, 132.0, 131.3, 130.1 (JCF ) 33 Hz), 127.9 (JCF ) 5.0 Hz), 124.7 (JCF ) 273 Hz), 96.5, 77.5, 77.3, 73.6, 72.9. HRMS FABMS: calcd for C14H14F3O8 [M + H]+, m/z 367.0641; found, m/z 367.0661 (error +2.0 mmu). Synthesis of 1-β-O-(2,4-Dimethylbenzoyl)-D-glucuronide (24DMBAGA). According to the above procedure for the synthesis of oCF3BAGA, benzyl 2,3,4-tri-O-benzyl-D-glucopyranuronate (108 mg, 0.19 mmol) was treated with 2,4-dimethylbenzoyl chloride (31 mg, 0.18 mmol) in CH2Cl2 (2.0 mL) and NEt3 (0.20 mL, 1.5 mmol) to yield the desired product (100 mg, 81% yield) through a preparative silica gel TLC. After deprotection of the O-benzyl groups by catalytic hydrogenation for 1.5 h in EtOAc-EtOH (3.0 mL, 2:1, v/v) in the presence of Pd(OH)2/C (10 mg), 24DMBAGA was obtained in almost quantitative yield. 1H NMR (MeOH-d4): δ 7.93 (d, 1H, J ) 8.0 Hz), 7.11-7.08 (m, 2H), 5.70 (d, 1H, J ) 7.8 Hz), 3.98 (d, 1H, J ) 9.5 Hz), 3.62-3.49 (m, 3H), 2.56 (s, 3H), 2.34 (s, 3H). 13C NMR (MeOH-d4) δ: 172.1, 167.1, 144.8, 142.3, 133.5, 132.3, 127.6, 126.8, 95.7, 77.6, 77.2, 73.7, 73.0, 21.9, 21.4. HRMS FAB-MS: calcd for C15H19O8 [M + H]+, m/z 327.1080; found, m/z 327.1089 (error +0.9 mmu). Measurement of Degradation Rate Constants (k values) of ΒΑGAs and SAR Analyses. Degradation Reaction Conditions and HPLC Measurement. Measurement of the k value was performed under physiological conditions as reported in our preceding paper (30), that is, in 100 mM sodium phosphate buffer at pH 7.40 and 37 °C. The k values of 16 BAGAs, other than the newly synthesized oCF3BAGA and 24DMBAGA, are taken from the preceding paper (30). The k values of oCF3BAGA and 24DMBAGA were determined under the same conditions using the reversed-phase HPLC method described previously (30). Within the limits of observation, decreases in the HPLC peak area of the starting BAGAs obeyed pseudo first-order reaction kinetics. The
SAR for the ReactiVity of Aromatic Acyl Glucuronides concentrations of CH3CN in the HPLC mobile phase for the analysis of oCF3BAGA and 24DMBAGA were 20 and 30% (v/v), respectively. Measurements of 1H and 13C NMR Spectra of BAGAs and Their Parent Carboxylic Acids. As descriptors for our SARs, δCdO values of oCF3BAGA and 24DMBAGA were measured in MeOHd4, while δ(CdO)OH and δCOOH values of the corresponding carboxylic acids were measured in DMSO-d6, where δCdO, δ(CdO)OH, and δCOOH correspond to the chemical shifts of 13C for the ester carbonyl carbons of the βGAs, 13C for the carbonyl carbons of the parent carboxylic acids, and 1H for the hydrogens of the carboxylic groups of the parent carboxylic acids, respectively. The δ(CdO)OH and δCOOH values of probenecid, furosemide, flufenamic acid, salicylic acid, and telmisartan were also measured. The concentration of these BAs in DMSO-d6 was around 90 mM since no effects of concentration (19, 58, and 115 mM) on δCOOH and δ(CdO)OH values were observed using BA as a model carboxylic acid. Computational Chemistry. Calculations were performed with a semiempirical model (with AM1 and PM3 models), Hartree-Fock model (with 3-21G and/or 6-31G* basis sets), and density functional model (with B3LYP/6-31G*) using Spartan ’06 and/or ’08 (Wave function, Inc., Irvine, CA) to obtain the lowest unoccupied molecular orbital (LUMO) energy levels, partial atomic charges (natural, electrostatic, and Mulliken), calculated δCOOH, δCdO, and δ(CdO)OH values, and maximum values of the electrostatic potential. Some chemical parameters such as atomic charge and NMR chemical shift were also calculated using the SM8 solvation model applicable to the Hatree-Fock and density functional models. The semiempirical and Hartree-Fock calculations were preceded by geometry optimization using the MMFF94 method and AM1 model (within the program), respectively. All calculations were performed with initial structures of the unionized form of BAs (in neutral form) and ionized BAGAs (in anion form) using default convergence. The pKa values of the BAs and both the molar volume (MV) and the molar refractivity (MR) of the o-substituents on the phenyl ring were calculated using ACD/pKa DB and ACD/Sigma, Version 12.0 (Advanced Chemistry Development Inc., Toronto, ON, Canada), respectively. Statistical Analyses and Evaluations. Single and multiple linear regression analyses were performed for the log k values of BAGAs with various descriptors. A weighted least-squares method was not used since the effect of using estimated weights on the results of the regression analyses is difficult to assess. For evaluation of the performance of the derived SAR models, the number of BAGAs used (n), the regression coefficient that was assessed the statistical significance with a t test, the standard partial regression coefficient, the coefficient of determination (R2), the cross-validated coefficient of determination (Q2), the externally validated coefficient of determination (Qext2), the standard deviation of residuals (s), the F value, and the P value were used.
Results and Discussion BAGAs Used for This SAR Study. Among the 18 BAGAs used in this study, 16 BAGAs other than oCF3BAGA and 24DMBAGA have been previously synthesized (30, 36, 37), and their k values have been reported in our preceding paper (30). Figure 1 shows the 18 BAs used in this study, consisting of 10 BAs with m- and p-substituents and eight BAs with o-substituents. For the o-substituted BAs, Taft’s Es steric parameters (32) were not determined for the N-phenyl and N-(2,3-dimethyl)phenyl groups of AB and MF, respectively. Because the Es values of the o-substituents of oCF3BA and 24DMBA are known, the corresponding oCF3BAGA and 24DMBAGA were selected as the objects of this SAR study. 24DMBA was selected since the compound was an o,pdisubstituted BA, which is suitable for the assessment of the performance of the SAR models. Chemical Synthesis and Measurement of k Values of oCF3BAGA and 24DMBAGA. oCF3BAGA and 24DMBAGA
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Figure 1. o-, m-, and p-Substituted BAs used. Abbreviations are as follows: HBA, benzoic acid; 24DM, 2,4-dimethylbenzoic acid; AB, 2-anilinobenzoic acid; and MF, mefenamic acid.
Figure 2. Time courses of degradation reaction of HBAGA (O), oCF3BAGA (9), and 24DMBAGA (b) under physiological conditions (pH 7.40 and 37 °C).
were synthesized in good yields by the acyl chloride method as reported in our preceding paper (30). Their β-anomeric configuration was confirmed by the J values (8.0 and 7.8 Hz for oCF3BAGA and 24DMBAGA, respectively) of the anomeric protons in their 1H NMR spectra. This synthetic method was shown to give β-anomers exclusively since no signal attributed to the corresponding R-anomers was detected in the 1H NMR spectra of either crude product (data not shown). The k values were determined for oCF3BAGA and 24DMBAGA as well as for HBAGA (as a standard sample) under the physiological conditions used in the preceding paper (30), that is, in 100 mM sodium phosphate buffer (pH 7.40) at 37 °C. As shown in Figure 2, these BAGAs degraded according to first-order reaction kinetics with different k values. The k values obtained, together with those of other BAGAs cited from the preceding paper (30), are listed in Table 1. The k value of HBAGA was comparable to that determined previously (30). The k value of oCF3BAGA (0.234 h-1) was considerably smaller than that of pCF3BAGA (1.79 h-1) as reported previously (30). Similarly, the k value of 24DMBAGA (0.064 h-1) was smaller than those of oMeBAGA (0.123 h-1) and pMeBAGA (0.165 h-1) (30), indicating that the lower degradative activity of 24DMBAGA is possibly due to both the electron-donating p-Me and the sterically hindering o-Me groups (discussed again later). For both oCF3BAGA and
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Table 1. Measured k Values of 18 BAGAs and Their Electronic and Steric Parameters for SARs BA
k (h-1)
δCdOa
δ(CdO)OHb
δCOOHb
pKac
pKae
σf
Esi
HBA oClBA mClBA pClBA oMeBA mMeBA pMeBA 24DMBA oOMeBA pOMeBA oCF3BA pCF3BA pFBA oPhBA mPhBA pPhBA AB MF
0.35 ( 0.00 1.21 ( 0.13 1.27 ( 0.04 0.61 ( 0.00 0.123 ( 0.002 0.252 ( 0.072 0.165 ( 0.002 0.064 ( 0.001 0.146 ( 0.005 0.082 ( 0.003 0.234 ( 0.002 1.79 ( 0.08 0.38 ( 0.01 0.036 ( 0.001 0.45 ( 0.01 0.35 ( 0.01 0.082 ( 0.002 0.044 ( 0.001
166.54 165.19 165.25 165.62 167.19 166.68 166.61 167.10 166.05 166.34 165.93 165.28 165.51 168.09 166.51 166.29 168.14 168.62
167.26 166.65 165.98 166.38 168.59 167.33 167.23 168.47 167.24 166.94 167.81 166.04 166.28 169.60 167.19 167.09 169.87 170.13
12.98 13.35 13.24 13.17 12.82 12.88 12.78 12.62 12.61 12.67 13.55 13.48 13.04 12.75 13.11 12.98 13.08 12.99
4.20 2.94 3.83 3.99 3.91 4.24 4.34 4.05 4.09 4.47 -d -d 4.14 3.46 3.99 4.21 -d -d
4.20 2.97 3.83 3.97 3.95 4.27 4.37 4.18 4.09 4.47 3.20 3.69 4.14 3.46 4.14 4.19 3.43 3.73
0 -g 0.37 0.23 -g -0.07 -0.17 (-0.17)h -g -0.27 -g 0.54 0.06 -g 0.06 -0.01 -g -g
0 -0.97 -g -g -1.24 -g -g (-1.24)j -0.55 -g -2.4 -g -g -3.79 -g -g -d -d
a δCdO: 13C chemical shift of carbonyl carbon in the 1-β-O-acyl group of BAGAs measured in MeOH-d4. b δ(CdO)OH and δCOOH: 13C chemical shift of the carbonyl carbon and 1H chemical shift of the carboxylic hydrogen in parent BAs measured in DMSO-d6, respectively. c Values for parent BAs are from refs 42 and 43. d Values are unknown. e Calculated using ACD/pKa DB Ver. 12.0. f Values for ring substituents are from ref 44. g Values are not defined. h The value in parentheses is for the p-Me group. i Values for ring substituents are from ref 32. j The value in parentheses is for the o-Me group.
24DMBAGA, the intramolecular acyl migration is the predominant pathway (over 90% in ratio, data not shown) as reported for other βGAs (30, 38-41). Scatter Plots of the log k Values of 18 BAGAs. In Table 1, together with the k values of 18 BAGAs, some possible descriptors for predicting k values of these BAGAs are listed as follows: 1H and 13C NMR chemical shifts (δCOOH, δ(CdO)OH, and δCdO), reported (42, 43) and calculated pKa values, Hammett’s σ constants (44), and Taft’s Es values (32). Figure 3 shows the scatter plots of the k values versus the chemical shifts and calculated pKa values. Although there were no clear correlations between the 18 values of log k and each independent variable, as shown in Figure 3A,B, good positive correlations were observed between the log k values of the 10 m- and p-substituted BAGAs and their calculated pKa values (see also Table 2, line 3) and their δCOOH (see also Table 2, line 4), respectively. In both cases, log k values of the eight o-substituted BAGAs deviated downward from the regression lines. These data indicated that the pKa and δCOOH values were good electronic descriptors for the log k values of m- and p-substituted BAGAs and that the other factor(s) also affected log k values of o-substituted BAGAs. Figure 3C,D show the correlations between log k values and δ(CdO)OH and δCdO, respectively. Vanderhoeven et al. have first reported the correlations of the log k values of 10 p-substituted BAGAs with δ(CdO)OH (R2 ) 0.783) and δCdO (R2 ) 0.786) (27), whereas R2 values obtained for the 10 m- and p-substituted BAGAs dropped to lower values of 0.514 with δ(CdO)OH (Figure 3C and also Table 2, line 6) and 0.562 with δCdO (Figure 3D and also Table 2, line 8). Surprisingly, the R2 values obtained for the 18 BAGAs showed higher values of 0.707 with δ(CdO)OH and 0.715 with δCdO; furthermore, the R2 values obtained for the eight o-substituted BAGAs showed even higher values of 0.722 with δ(CdO)OH and 0.744 with δCdO. These results were in contrast to Figure 3A,B, where no correlation was observed for the eight o-substituted BAGAs (the corresponding R2 values of Figure 3A,B were 0.303 and 0.361, respectively), indicating that δ(CdO)OH and δCdO values might be used as descriptors for the log k values of BAGAs including o-substituted BAGAs. The δ(CdO)OH was thought to be a better descriptor since it is more readily available as compared to δCdO of the corresponding synthetically prepared BAGAs. The following eq 1 using δ(CdO)OH as a predictor could
be useful for predicting the k values of BAGAs including o-substituted BAGAs, although the accuracy of its predictions was only fair.
log k ) -0.329((0.053) × δ(CdO)OH + 54.55((8.88) (1) where n ) 18, R2 ) 0.707, s ) 0.279, F ) 38.6, and P < 0.001. To derive SAR models with improved predictive accuracy, regression analyses of the log k values were further performed using several electronic and steric descriptors. m- and p-Substituted BAGAs: Single Regression Analyses Using Electronic Descriptors. As previously reported by Vanderhoeven et al. (27) and Baba et al. (30), the Hammett plot (44) produced a good positive correlation between the log k values and the σ constants (see also Table 2, line 1). However, the σ constants are not known for all m- and p-substituents, and the Hammett plot is not usually applicable to the corresponding o-substituted derivatives due largely to steric effects of the o-substituents. Therefore, to find good electronic descriptors as alternatives to the σ constants, single regression analyses using possible electronic descriptors were performed. The criteria of the statistical significance used were the significance (P < 0.05 by t statistics) of individual SAR term as well as the R2 value, a measure of the goodness-of-fit. On the basis of statistical parameters including the cross-validated correlation coefficient (Q2) for assessment of robustness and estimation of the predictive accuracy of the models (Table 2), both measured and calculated pKa values (lines 2 and 3, respectively) as well as both measured and calculated δCOOH values (lines 4 and 5, respectively) were found to be quite suitable electronic descriptors for predicting not only existing but also theoretical BAGAs with m- and p-substituents. Both δ(CdO)OH (line 6) and δCdO (line 8) yielded acceptable results. Among the calculation methods used for the chemical shifts, the Hartree-Fock model with the 3-21G basis set (in vacuum) and with the 6-31G* basis set (in water) were the best for δCOOH (line 5) and δ(CdO)OH (line 7), respectively. The LUMO energy levels (lines 9-12) and the maximum values of the electrostatic potentials (EPmax) (lines 13-16) of the parent BAs also yielded acceptable results. The EPmax is a possible additional measure of relative acid strength.
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Figure 3. Scatter plots of log k values of 18 BAGAs (A) vs the calculated pKa of parent BAs, (B) vs δCOOH of parent BAs, (C) vs δ(CdO)OH of parent BAs, and (D) vs δCdO of BAGAs. Symbols (b) and (O) represent 10 m- and p-substituted BAGAs (a-j) and eight o-substituted BAGAs, respectively. Solid lines in panels A-D are regression lines (Table 2; lines 3, 4, 6, and 8, respectively) for m- and p-substituted BAGAs. (a) pCF3BAGA, (b) mClBAGA, (c) pClBAGA, (d) mPhBAGA, (e) pFBAGA, (f) HBAGA, (g) pPhBAGA, (h) mMeBAGA, (i) pMeBAGA, and (j) pOMeBAGA. Single correlation coefficient (R2) values observed for log k values of eight o-substituted BAGAs were 0.303 with pKa, 0.361 with δCOOH, 0.722 with δ(CdO)OH, and 0.744 with δCdO.
With regard to calculated partial atomic charges, Vanderhoeven et al. have reported the correlations between the log k and the charges of the carbonyl carbons of both the BAGAs and the parent BAs (27). Hanai has reported that the charges of hydrogens of carboxylic acids were suitable for predicting the pKa values of the acids (45). Therefore, we performed calculations of the partial atomic charges of the hydrogen, oxygen (connected to the hydrogen), and carbon of the carboxylic group in the 18 BAs. Table 3 summarizes the results of the regression analyses for log k values of m- and p-substituted BAGAs with the calculated atomic charges. On the basis of the R2 values, the best correlations were obtained with the partial atomic charges (natural type) of the hydrogen (HPAC) (R2 ) 0.937 and Q2 ) 0.901) and the oxygen (OPAC) (R2 ) 0.949 and Q2 ) 0.937); both of the atomic charges were calculated using the B3LYP/6-31G* density functional model (in water) with the SM8 solvation model. Because Hammett’s σ constants have been reported to correlate linearly with the summation of partial atomic charges calculated by the AM1 method (46, 47), this
method was also examined. The R2 value of the correlation between the log k values and the sum of the partial atomic charges (natural type calculated by the AM1 method) of the hydrogen and the two oxygens of the carboxylic acid moiety of the parent BAs was 0.891 (data not shown), indicating that HPAC and OPAC calculated using the density functional model were suitable descriptors. Considering all results together, Hammett’s σ constant, pKa (both measured and calculated), δCOOH (both measured and calculated), and the calculated partial atomic charges HPAC and OPAC were selected as the electronic descriptors for successfully predicting the log k values of m- and p-substituted BAGAs. For a multiple regression analysis of the log k values of the eight o-substituted BAGAs, four descriptors other than Hammett’s σ constant, namely, pKa, δCOOH, HPAC, and OPAC, were examined as leading candidates for the electronic descriptors. o-Substituted BAGAs: Regression Analyses Using Electronic and/or Steric Descriptors. Prior to a multiple regression analysis of the log k values of the eight o-substituted BAGAs, single
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Table 2. Statistical Parameters for Single Regression Analyses Using Electronic Parameters for log k Values of BAGAs Derived from m- and p-Substituted BAs line
descriptor used
regression coefficient
const.
R2a
Q2b
sc
F
P
nd
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
σ pKa pKa (calcd)e δCOOH δCOOH (calcd)f δ(CdO)OH δ(CdO)OH (calcd)g δCdO ELUMO(AM1)h ELUMO(PM3)h ELUMO(HF)h ELUMO(DF)h EPmax (AM1)i EPmax (PM3)i EPmax (3-21G)i EPmax (6-31G*)i
1.57 ( 0.11 -1.67 ( 0.16 -1.62 ( 0.10 1.64 ( 0.12 3.03 ( 0.27 -0.52 ( 0.18 -0.25 ( 0.04 -0.51 ( 0.16 -0.013 ( 0.004 -0.013 ( 0.004 -0.010 ( 0.002 -0.014 ( 0.002 0.034 ( 0.008 0.038 ( 0.010 0.018 ( 0.004 0.023 ( 0.005
-0.52 6.47 6.28 -21.78 -16.53 86.33 41.20 83.92 -1.24 -1.29 -1.71 -2.33 -5.16 -5.13 -5.75 -6.66
0.965 0.942 0.972 0.960 0.938 0.514 0.849 0.562 0.617 0.587 0.694 0.808 0.687 0.636 0.683 0.692
0.942 0.923 0.957 0.937 0.915 -j 0.803 -j -j -j -j -j -j -j -j -j
0.078 0.087 0.069 0.083 0.103 0.290 0.161 0.275 0.257 0.267 0.230 0.182 0.233 0.251 0.234 0.231
219 113 280 191 122 8.45 45.1 10.3 12.9 11.4 18.2 33.7 17.5 14.0 17.3 18.0
