J. Phys. Chem. B 2006, 110, 14507-14514
14507
Characterization of Ester Hydrolysis in Terms of Microscopic Rate Constants Be´ la Nosza´ l,* Do´ ra Visky, and Ma´ rta Kraszni Semmelweis UniVersity, Department of Pharmaceutical Chemistry, Research Group for Abuse Drugs and Dopings, Hungarian Academy of Sciences Ho˜ gyes E. u. 9, H-1092 Budapest, Hungary ReceiVed: March 31, 2006; In Final Form: May 30, 2006
Hydroxide-catalyzed ester hydrolysis for molecules of coexisting species is quantitated in terms of microscopic rate constants, a new, species-specific physicochemical parameter. Relationships between the overall and component reactions, as well as the macroscopic and microscopic rate constants are deduced. Experimental techniques, evaluation methods, and feasibility are discussed. Species-specific, pH-independent rate constants of four coexisting, differently hydrolyzing microspecies are determined for the first time. Protonation of an R-amino and β-imidazolyl site in amino acid esters has been found to accelerate the hydroxide-catalyzed hydrolysis by factors of 120 and 7.5, respectively, whereas they jointly exert a nearly 3000-fold acceleration. A total of 20 microscopic protonation equilibrium constants, as component parameters in the rate equations, have also been determined. The species-specific rate constants have been found to correlate with the site- and species-specific basicity of the leaving group and the NMR chemical shift of an adjacent proton. Individual contributions of the various microforms to the overall hydrolysis rate are depicted in microscopic reaction fraction diagrams.
Introduction Ester hydrolysis, one of the most frequent biotransformations takes place on such fundamental biomolecules as ATP, ADP, AMP, and acetylcholine, as well as on acetylsalicylic acid, the oldest and best-known prodrug. The kinetics and equilibrium of ester hydrolysis have extensively been studied as a function of extramolecular factors such as temperature, pH, solvent, and ionic strength.1-4 The intramolecular environment also influences the process of ester hydrolysis, but the role of the adjacent moieties has been the subject of much fewer systematic studies.5,6 Quantitation of the intramolecular effects is especially valuable information for ester group-containing bio- and drug molecules. Their typical biotransformation pathway is hydrolysis, resulting usually in loss of the biological activity. In other cases (e.g., prodrugs), however, hydrolysis produces the active substance.7 The most frequent mechanism of ester hydrolysis is the bimolecular, hydroxide-catalyzed one.8,9 This reaction takes place via nucleophilic attack.10 Its rate is therefore sensitive to the electron density at the ester site. It was observed, for example, that insertion of a permanent cationic moiety into ethyl-acetate causes a 200-fold acceleration of the base-catalyzed hydrolysis.11 Charge-dependent rate constants have also been reported for a number of compounds, the side-chain of which contains a protonating/deprotonating site near the ester group.12-22 The typical molecules in such studies were amino acid esters, since their amino site is located near the ester moiety, and the amino protonation takes place in the pH range of the hydroxide-catalyzed ester hydrolysis. Thus, the protonated/deprotonated status of the amino site can cause a switching effect on the hydrolysis propensity of the ester. Some of the compounds (esters of lysine,17 ornithine,17 histidine,18 cysteine18) possess two protonating/deprotonating sites in the side chain, assuming multiple switching effects, and the concomitant rate constant of each. Unfortunately, many of the reported rate constants are conflict* To whom correspondence should be addressed. E-mail: nosbel@ hogyes.sote.hu. Fax: (+36)-1-2170891.
ing ones. For example, the literature values of ornithine methyl ester17 and phenylalanine methyl ester,21 both with +1 charge, differ by as many as 11 orders of magnitude. Also, the reported data for aspartyl-phenylalanine methyl ester21 and the two compounds above claim that protonation of a nearby site slows down, rather than accelerates the hydrolysis. Experimental errors cannot account for any such discrepancies. Furthermore, hydrolysis rate constants of esters with two basic sites in the side chain are not assigned to the appropriate species in solution. Difficulties stemming from enhanced complexity in cases of esters with more than one basic side-chain sites lie in the fact that the charge-dependent rate-modification can only be unambiguously assigned to any neighboring site, if the vicinity of the ester group contains one single basic site. If, however, more than one adjacent protonating sites of commensurable basicity constitute the vicinity of the ester group, the protonation-initiated rate-acceleration results from contributions of every such site. The extent of these contributions is not a priori known. When differently hydrolyzing species of isomeric side-chain protonation occur, the number of site-specific rate parameters can be postulated to increase exponentially with the number of sites. No paper provides information on the characterization of such systems, because of the lack of appropriate rate equations and evaluation methods. The thorough kinetic description of ester hydrolysis in species-specific detail necessitates the introduction of a new type of rate constant that takes into account the various protonation states of the basic site(s) adjacent to the ester group. Other species-specific physicochemical parameters that quantitate various properties of the reactive site with respect to the status of the intramolecular environment are acknowledged terms in chemistry, such as microscopic23,24 and rota-microscopic25,26 acid dissociation constants, proton-deuterium exchange rates,27 microscopic activation energy,28 and conformer-specific partition coefficients.29,30 These parameters specify not only the property, process, and site in question, but also the status of the participating species. Practical needs also necessitate the introduction and use of species-specific hydrolysis rate constants
10.1021/jp0620116 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/06/2006
14508 J. Phys. Chem. B, Vol. 110, No. 29, 2006 that exactly and thoroughly quantitate the hydrolysis kinetics of esters with two or more basic side-chain sites. Common examples are cocaine and heroine that contain two ester groups and one basic nitrogen. However, each of their intermediate hydrolysis products contains one ester group and two basic sites, providing subtly different alternative routes for binding and hydrolytic processes. Various enzymes also contain amino and ester loci, and their protonation-dependent interactions are indispensable preconditions of the enzyme activity.31 Thus, the species-specific rate constants of ester hydrolysis are important parameters to thoroughly understand biochemical reactions, to design drugs, prodrugs and ester-type polymers and to influence biological processes at the molecular level. Here we report the introduction and determination of microscopic rate constants of ester hydrolysis. This new physicochemical term quantitates the specific hydrolytic properties of microspecies, including the coexisting, unseparable protonation isomers. The number of alternative hydrolytic pathways is formulated, principles and limitations of the microscopic treatment are described, and the applicable experimental methods are surveyed. The feasibility and methodology are exemplified by a set of amino acid esters and their model compounds. The rate constants determined reflect the effects of phenyl, amino, ammonium, imidazole, imidazolium, and hydroxyl moieties in the side chain of the ester site. Contribution of the individual species to the overall hydrolytic process is depicted in microscopic reaction fraction diagrams, a new tool to visualize pHdependent simultaneous kinetics. Experimental Methods All experiments were performed at 298 K and the ionic strength was held constant at 0.2 m dm-3 using NaCl as the auxiliary electrolyte. Nonlinear parameter fitting was performed with STATISTICA 5.0 for Windows. Chemicals. Phenylalanine, histidine, potassium dihydrogen phosphate, sodium dihydrogen phosphate, disodium hydrogen phosphate, sodium chloride, and sodium hydroxide were obtained from Reanal Co. (Budapest, Hungary); phenylalanin methyl ester (PheOMe) and potassium tetraoxalate were obtained from Fluka (Buchs, Switzerland); histidine methyl ester (HisOMe) and Borax were from Sigma; potassium dihydrogen phthalate was from Merck (Darmstadt, Germany). Imidazolelactic acid methyl ester (ImlacOMe) was synthesized from imidazole lactic acid (Sigma, Steinheim, Germany). Bidistilled water was used in all experiments. Protonation Equilibria. Protonation macroconstants were determined by potentiometric titration. The titrations were carried out using ABU91 Radiometer titrator equipped with a Radiometer PHC2406 combination pH electrode. Concentrations of 0.03-0.05 m dm-3 were used at all potentiometric experiments. All pH data are pH meter readings based upon NBS primary standards: 0.05 m potassium hydrogen phthalate (4.008), 0.025 m KH2PO4 + 0.025 m Na2HPO4 (6.865) and 0.01 m Borax (9.180), and 0.05 m potassium tetraoxalate buffer (1.780) (entries in brackets are buffer pH values at 298 K). Protonation microconstants of histidine methyl ester were calculated from protonation macroconstants of histidine using intramolecular interactivity parameter.28 Kinetic Studies. The progress of ester hydrolysis was quantified by capillary zone electrophoresis. Processes were followed in situ: the hydrolysis took place in the vial of the CE instrument, and sampling was carried out directly from here. Hydrolysis experiments were performed in buffer solutions containing 0.05 m KH2PO4 and 0.025 m Na2B4O7 at different
Nosza´l et al. pH values (see Table 3). Ester concentration of 0.005 mol dm-3 was performed for CE experiments. Appropriate pH was set by 2 m H3PO4 or 2 m NaOH. Capillary electrophoresis was performed using Crystal 310 CE system (Unicam) with automated sampling and thermostat. This apparatus was equipped with a 375 mm o.d. × 50 mm i.d. fused silica capillary of 80 cm total length and 65 cm effective length. The solution of 0.035 m KH2PO4 + 0.035 m Na2B4O7 (pH ) 7.5) was used as running buffer. A total of 180 mbar‚s of hydrodynamic injection was performed for all runs. A voltage of 20 kV was applied during the analysis, the current did not exceed 80 µA. On-column UV detection was employed with the wavelength set at 210 nm. The carousel was thermostated to 25 °C, and the capillary was thermostated to 28 °C by air. The detector signals were collected and analyzed using Unicam 4880 chromatography data handling system. The capillary was flushed with 0.1 m NaOH solution for 15 min at the start of each day. Then the running buffer was used to rinse the column to equilibrate for 15 min. The capillary was flushed with fresh buffer for 4 min between runs. NMR Studies. 1H NMR spectra of amino acid esters were recorded at 298 K at 599.9 and 200.1 MHz with Varian Unity Inova 600 and Bruker AM 200 NMR spectrometers. A concentration of 5 mg/mL in D2O was used; the pH of the solutions was set in the NMR tubes to three different values (pH ∼1, 5, and 11) for each ester compound. A 90° pulse was applied and the FID was digitized into 32000 data points. Typically 16 transients were coadded, and a 15 s repetition time was used. Chemical shifts were measured relative to internal tert-butyl alcohol (1.236 ppm). Results/Discussion Theory. Formulation and related theoretical background of hydrolysis kinetics for esters with two or more basic side-chain sites cannot be found in the literature. Also, the hydrolysis rate parametrization of monobasic esters needs a unified view for exact evaluation as evidenced by literature data cited above.12-22 We therefore first provide definition, relationships, feasibility, and methodical description for the microscopic treatment of ester hydrolysis kinetics. The Number of Distinct Rate Processes as a Function of Basic Sites in the Hydrolyzing Molecule. A basic moiety occurs in unprotonated and protonated forms, designated here as -B and -BH, respectively, where charges are omitted. Common, anionic basic moieties are the carboxylate, phenolate, thiolate, etc. sites, whereas examples of common, neutral, basic moieties are the amino, imidazolyl, etc. sites. No matter whether the basic site is anionic or neutral, its protonated form (-BH) is certainly more electron-withdrawing than the unprotonated one (-B). Thus, an ester group with a single adjacent basic site occurs in two states of electron density and the concomitant two states of hydrolytic propensity. With two basic sites (e.g., B and b), the molecule exists in four different forms (B,b; BH,b; B,bH; BH,bH). Each of these forms has its own, species-specific properties, including the rate constants of hydrolysis. In general, n basic sites result in 2n distinct molecular states of protonation, electron density, and hydrolysis properties of the ester group. Thus, molecules with B and b, the two proton-binding side-chain sites, species B,b, and BH,bH are the most basic and most acidic microspecies of increasing and decreasing concentration with pH, respectively. The monoprotonated BH,b and B,bH protonation isomers permanently coexist; they always provide composite analytical and physicochemical signals. Information on their concentration,23 and also their individual contribution to the overall rate of hydrolysis, can be obtained by indirect methods only.
Characterization of Ester Hydrolysis
J. Phys. Chem. B, Vol. 110, No. 29, 2006 14509 Integration and rearrangement yields
[e]init 1 + KIlm[H+]
ln
Figure 1. Acid-base equilibrium and hydrolysis processes of imidazolelactic acid methyl ester.
Evaluation of the Rate Constants. Equations of the evaluation process depend on the number of ester groups and basic moieties in the molecule. Molecules of one ester group and one protonating side-chain site are phenylalanine methyl ester and imidazolelactic acid methyl ester in this study. The acid-base equilibria and hydrolysis kinetics of imidazolelactic acid methyl ester are shown in a unified scheme in Figure 1. If e0 and e+ stand for the basic and acidic forms of imidazolelactic acid methyl ester, respectively, KIlm, the protonation constant is given as
KIlm ) [e+]([e0][H+])-1
[e]t
-
t[OH ]
) k0 + k+KIlm[H+]
(8)
where [e]init and [e]t are the unhydrolyzed ester concentrations after zero and t second in the course of hydrolysis, respectively. If KIlm, the protonation equilibrium constant has previously been determined, [e]init and a series of [e]t values are obtained by an appropriate analytical technique, k0 and k+ can be determined in a set of experiments at various pH values and a subsequent, nonlinear parameter fitting. A fraction of eq 8, ln([e]init[e]t-1)t-1, the observed rate, directly depends on pH because OH- is a reactant in the bimolecular hydrolysis process. On the other hand, it also has an indirect pH-dependence caused by changes in the protonation state(s) of basic side chain(s). Because of the latter effect, the observed hydrolysis rates of esters with basic side chain(s) are not linear functions of pH or pOH. Molecules of one ester group and two protonating side-chain sites exist in 4 forms of protonation. Such molecules therefore undergo 4 types of hydrolysis, as shown in Figure 2 on histidine 0 + methyl ester. The symbols e00, e+ 0 , e+, and e+ indicate the forms A of histidine methyl ester, kA, kIm, kIm, and kIm A are the micro0 + scopic protonation equilibrium constants, and k00, k+ 0 , k+ and k+ are the species-specific rate constants of ester hydrolysis. The overall rate is the sum of the species-specific rates:
(1)
Mole fraction of the basic and acidic forms of the molecule are expressed respectively in eqs 2 and 3:
R e0 ) Re+ )
[e0] [e0] + [e+] [e+] [e0] + [e+]
)
)
[e0] [e] [e+] [e]
)
)
1 1 + KIlm[H+] KIlm[H+] 1 + KIlm[H+]
(2)
(3)
If k0 and k+ are the specific rate constants of species e0 and e+, respectively, the species-specific second-order rate equations are as follows:
d[e0] ) k0[e0][OH-] dt d[e+] ) k+ [e+ ][OH-] dt -
(4) (5)
where t is time. The observed, overall rate equation is the sum of the above component equations:
-
d[e] ) k0[e0][OH-] + k+ [e+][OH-] dt
(6)
Introducing eqs 2 and 3 into eq 6 yields
-
d[e] 1 [e][OH-] + ) k0 dt 1 + KIlm[H+] KIlm[H+] k+ [e][OH-] (7) 1 + KIlm[H+]
Figure 2. Protonation and hydrolysis scheme of histidine methyl ester.
14510 J. Phys. Chem. B, Vol. 110, No. 29, 2006
-
Nosza´l et al.
d[e] + 0 0 ) k00[e00][OH-] + k+ 0 [e0 ][OH ] + k+[e+][OH ] + dt + k+ + [e+][OH ] (9)
Equation 9 can be transformed into a relationship of reduced complexity, if microscopic and macroscopic protonation constants and protonation mole fractions are introduced. The microscopic protonation constants in terms of speciesconcentrations are shown in eqs 10-13.
[e+ 0]
kA ) kIm ) kAIm ) kIm A )
(10)
[e00][H+] [e0+]
(11)
[e00][H+] [e+ +]
(12)
[e0+][H+] [e+ +]
(13)
+ [e+ 0 ][H ]
Mole fractions of the microspecies are as follows:
Re 0 ) 0
[e00] [e00]
Re + ) 0
Re 0 ) +
Re
+
+
)
+
[e+ 0]
+
[e0+]
+
)
[e+ +]
[e+ 0]
1 1 + β1[H ] + β2[H+]2 (14)
)
0 + [e00] + [e+ 0 ] + [e+] + [e+]
[e0+]
)
0 + [e00] + [e+ 0 ] + [e+] + [e+]
[e+ +] 0 + [e00] + [e+ 0 ] + [e+] + [e+]
)
+
kA[H+] 1 + β1[H+] + β2[H+]2 (15) kIm[H+] 1 + β1[H+] + β2[H+]2 (16) β2[H+]2 1 + β1[H+] + β2[H+]2 (17)
Im A where β1 ) kA + kIm and β2 ) kAkIm A ) k kIm, the relationships between the protonation macro- and microconstants. The concentration of the four microscopic forms can be expressed as the product of [e], the total ester concentration, and R, the respective mole fraction:
[e00] ) Re 0[e]
(18)
[e+ 0 ] ) Re0+[e]
(19)
[e0+] ) Re 0[e]
(20)
[e+ +] ) Re +[e]
(21)
0
+
+
Introducing eqs 18-21 into eq 9, the rate equation can be rewritten as
-
d[e] 0 + ) [e](k00Re 0 +k+ 0 Re + + k+Re 0 +k+Re +)[OH ] (22) dt 0 0 + +
Integration, unwrapping of the R values, and rearrangement yield
ln
[e]init 1 + β1[H+] + β2[H+]2 [e]t
) t[OH-] Im 0 + + 2 + k00 + (kAk+ 0 + k k+)[H ] + k+β2[H ] (23)
The left-hand side of eq 23 is a known quantity, since β1 and β2 are constants from independent equilibrium experiments. The values for [e]init and [e]t are provided by the analytical method that monitors the progress of hydrolysis in the actual kinetic study. The enhanced complexity and nonlinearity of ln([e]init[e]t-1)t-1, the observed rate are also shown by eq 23. From data taken at a series of pH values, nonlinear parameter fitting produces the k00 and k+ + microscopic rate constants, and Im 0 the coefficient of [H+]. Latter is kAk+ 0 + k k+ ) A, a composite parameter. The composition of A indicates that k+ 0 and k0+, the microspecies-specific hydrolysis rate constants of the protonation isomers cannot be elucidated from the kinetic experiments directly. Even if kA and kIm, the microscopic protonation constants, are available from separate determina0 tions, the individual values of k+ 0 and k+, the microscopic rate constants, necessitate the introduction of one more independent information. Such information can be obtained from derivative compounds of close similarity but reduced complexity. In this study we introduced two compounds and related pieces of information, one for the calculations, another one for the assessment of the results. Concerning histidine methyl ester, one of its close derivatives is imidazolelactic acid methyl ester, an isoelectronic, isosteric compound, in which the amino site of the parent compound is replaced by a hydroxyl moiety. Imidazolelactic acid methyl ester protonates therefore at the imidazolyl site only. Introducing the hydrolysis rate constant of the cationic species of imidazolelactic acid methyl ester into the corresponding k0+ value of histidine methyl ester would be an obvious choice, since the two related species are isoelectronic, iso-Coulombic, and utmost isosteric. Nevertheless, such introduction would bear dissimilarities between electron densities and hydrolysis propensities of the two ester moieties, owing to differences between the -NH2 and -OH moieties. To further minimize the effects of this dissimilarity, we introduced the formula below:
k+Ilm
k0+ ) k00
k0Ilm
(24)
Equation 24 contains the only assumption that an imidazole protonation accelerates the ester hydrolysis identically at both analogue compounds. This treatment eliminates the need of directly imported microscopic rate constants even from a very close derivative. In fact, the above formula is the kinetic version of the interactivity conservation principle for analogous moieties in related compounds,32 which allowed the analysis of highly complex or correlated microequilibrium systems.33 The microscopic hydrolysis rate constant of the aminoprotonated histidine methyl ester, k0+ can then be calculated as Im 0 A -1 k+ 0 ) (A - k k+)(k )
(25)
An analogous calculation would have been feasible using the hydrolysis accelerating factor of the amino site as well, taking its value as the k+/k0 ratio of phenylalanine methyl ester, another close derivative of histidine methyl ester. This calculation, however, would have been inferior to the one based on imidazolelactic acid methyl ester, for the following reason: if
Characterization of Ester Hydrolysis
J. Phys. Chem. B, Vol. 110, No. 29, 2006 14511
TABLE 1: Protonation Macroconstants of the Compounds Studied this work compound
literature data
log K1
log K2
phenylalanine phenylalanine methyl ester
9.23 ( 0.02 7.22 ( 0.02
2.20 ( 0.03
imidazolelactic acid imidazolelactic acid methyl ester histidine
7.48 ( 0.02 6.84 ( 0.03 9.17 ( 0.01
3.07 ( 0.02 6.14 ( 0.01
histidine methyl ester
7.33 ( 0.01
5.41 ( 0.02
log K3
1.78 ( 0.03
log K1
log K2
9.1134 7.1115 7.0535
2.1834
9.1736 9.1718 9.2234 7.2336 7.3018
6.1018 6.0234
log K3
1.734
5.0136 5.3518
TABLE 2: Microscopic Protonation Constants of Phenylalanine, Imidazole Lactic Acid, Histidine-Methyl Ester, and Histidine compound
constant
phenylalanine imidazole lactic acid histidine methyl ester histidine
log ) 9.23 log kIm ) 7.48 log kA ) 7.28 log kA ) 9.17 log kIm ) 7.0 log kC ) 4.4
log k ) 4.2 log kC ) 3.7 log kIm ) 6.4 log kAIm ) 8.4 log kIm A ) 6.14 log kCA ) 2.5
kA
C
log kAC ) 7.2 log kIm C ) 6.8 log kAIm ) 6.4 log kAC ) 7.3 log kIm C ) 6.4 log kCIm ) 3.7
log kCA ) 2.20 log kCIm ) 3.07 log kIm A ) 5.46 A log kIm,C ) 6.4 log kIm A,C ) 5.5 log kCA,Im ) 1.78
TABLE 3: Observed Rate (kobs) Values phenylalanine methyl ester
imidazole lactic acid methyl ester
histidine methyl ester
pH
kobs (10-6 sec-1)
pH
kobs (10-6 sec-1)
pH
kobs (10-6 sec-1)
6.86 7.22 7.51 7.68 7.99 8.27 8.59 9.04
6.96 ( 0.24 8.58 ( 0.08 11.0 ( 0.10 13.3 ( 0.24 15.6 ( 0.20 17.4 ( 0.27 20.4 ( 0.41 24.7 ( 0.54
5.61 5.95 6.35 6.72 7.11 7.46 7.89 8.31
0.79 ( 0.09 1.74 ( 0.09 3.01 ( 0.10 5.49 ( 0.09 10.5 ( 0.21 18.4 ( 0.18 30.2 ( 0.29 39.1 ( 0.33
5.70 6.00 6.29 6.77 7.13 7.53 8.05 8.33 9.48 10.04
4.32 ( 0.11 5.19 ( 0.11 6.68 ( 0.15 7.36 ( 0.17 9.26 ( 0.21 13.1 ( 0.59 17.3 ( 0.35 18.1 ( 0.32 40.0 ( 2.22 96.8 ( 3.84
k+ 0 , the anticipated major kinetic microconstant had been calculated first, by a (24)-type, “proportionation” relationship, then k0+, the minor one, by a (25)-type, “subtractive” relationship, the value of k0+ would have inherently born a higher relative error, since minor components are more vulnerable to uncertainties of large parent numbers in subtractive operations. For testing purposes, however, the species-specific hydrolysis rate constants of phenylalanine methyl ester, k0 and k+ and their k+/k0 ratio were then used to assess the corresponding histidine methyl ester constants. Protonation Constants. Equations 8-23 show that speciesspecific rate constants can be obtained if appropriate protonbinding equilibrium constants are known. Latters have been
Figure 3. Protonation microequlibria of histidine.
determined under circumstances identical with the kinetic experiments, and the macroscopic ones are collected in Table 1. Related data of nonester compounds and corresponding literature values are also listed. Comments and conclusions related to the protonation constants are as follows: (a) The constants bear low uncertainty, since most moieties of the molecules protonate in ranges of reliable pH measurement. Agreement with corresponding literature data is good, taking into account that solution circumstances (ionic strength, auxiliary electrolyte, and temperature) have typically been different in the literature studies.
Figure 4. Species-specific rate constants of ester hydrolysis (lg k) plotted against the carboxylate basicity of the leaving group (lg k).
14512 J. Phys. Chem. B, Vol. 110, No. 29, 2006
Nosza´l et al.
TABLE 4: Species-Specific Rate Constants of Ester Hydrolysis and Related Data: Site-Specific Basicity of the Hydrolyzing Species (log k) and Carboxylate Basicity (log kC) of the Leaving Group
(b) Esterification of the carboxylate site causes approximately 2 units decrease in those macroconstants that largely reflect amino protonations (log K1 in phenylalanine and histidine) and 0.7 units decrease in those macroconstants that refer mainly to imidazole basicity (log K1 in imidazolelactic acid and log K2 in histidine). Esterification transforms anionic carboxylates into neutral, electron-withdrawing moieties in the vicinity of the basic amino or/and imidazol sites. These transformations account for the sign of the log K changes. Their magnitudes can also be interpreted in terms of the number of bonds separating the ester and the basic loci.
To interpret the species-specific rate constants in terms of site- and species-specific basicities of the leaving group, microscopic protonation constants have also been determined. The microscopic protonation of histidine methyl ester is part of Figure 2. Equilibrium microconstants are shown along the double arrows, whereas single arrows indicate the kinetic processes. Histidine microequilibria are symbolized in Figure 3. The microspeciation schemes of phenylalanine and imidazolelactic acid are analogous with that of histidine methyl ester. Superscripts indicate the protonating site, subscripts stand for the group having been protonated. Abbreviations A, Im, and C
Characterization of Ester Hydrolysis
Figure 5. Hydroxide-catalyzed ester hydrolysis rate of histidine methyl ester microspecies.
stand for amino, imidazole and carboxylate, respectively. The microconstant values are compiled in Table 2. Estimated uncertainty of the microconstants is in the range of 0.03-0.15 log k units, with relatively small and large error of those constants that belong to the major and minor protonation pathway, respectively, which is also indicated in the number of decimals. Data in Table 2 indicate that values of the “core” microconstants (when none of the other groups is protonated) show
J. Phys. Chem. B, Vol. 110, No. 29, 2006 14513 significant diversity for the imidazole and carboxylate groups, whereas the amino sites retain a nearly uniform log kA ) 9.2 value in all the compounds. Further conclusions will be drawn along with the microscopic rate constants. Rate Constants. Observed rates are listed in Table 3. Nonlinear parameter fittings provided k0 and k+ values, based upon eq 8, and k00, k+ + and A values, based upon eq 23. The composite parameter A was found to be 1.671 × 109 0 and could be then decomposed to obtain k+ 0 and k+, the microscopic rate constants of the isomeric species, as shown in eqs 24-25. All the pH-independent rate constants and related parameters are assigned to species in Table 4. Those three species-specific rate constants that belong to the most basic species are directly comparable. There is striking agreement between k0 of PheOMe and k00 of HisOMe, parallel with the highly similar basicities of the analogously located amino sites. These data also show the virtually identical effects of the aromatic phenyl and imidazolyl sites. The corresponding k0 value of ImlacOMe is some 40-fold larger since the electronwithdrawing effect of the adjacent hydroxyl moiety is stronger than that of an amino, as shown also by the carboxylate basicity of the leaving group. Protonation of a nearby basic site accelerates the hydrolysis. The magnitude of the effect, however,
Figure 6. (top) Distribution diagram of histidine methyl ester protonation forms; (bottom) microscopic ester hydrolysis reaction fraction chart of histidine methyl ester protonation forms.
14514 J. Phys. Chem. B, Vol. 110, No. 29, 2006 depends on the number, distance, and type of the basic moiety. An R-amino protonation causes 2 orders of magnitude increase in the rate constant (a factor of 148 in phenylalanine k+/k0), the β-imidazolyl protonation enhances the rate by 1 order of magnitude (k+/k0 ) 7.5 in ImlacOMe), and the mutual effect is 0 in the range of 3 orders of magnitude (k+ +/k0 ) 2880 for HisOMe). Concerning rate constants of the two monoprotonated HisOMe species, the k0+ value is, as a matter of necessity, 7.5 times larger than k00, owing to its derivative origin. The value of k+ 0 , which serves as a probe of decomposition of A, is approximately 120-times larger than k00. The agreement between this value and k+/k0 ) 148, found for PheOMe, is excellent on the scale of kinetic studies, especially if uncertainties are taken into account. 0 0 0 The k+ 0 /k0 and k+/k0 ratios quantitate acceleration of the hydrolysis upon the first protonation of HisOMe at the amino and imidazole site, respectively. The second, protonationinitiated, site-specific accelerations can also be quantitated by 0 + + the k+ +/k+ and k+/k0 ratios. The calculated, respective, amino-, and imidazole-specific acceleration values are 380 and 24. Even if the estimated 30% ambiguity is taken into consideration, these values show a significant, 3-fold extra acceleration, as compared to the corresponding k+/k0 ratios found for the first protonations of PheOMe and ImlacOMe. These microscopic data have been proved to be reproducible and are in agreement with Martin’s pioneer work, which found a 466-fold hydrolysis rate enhancement upon the second side-chain protonation at the macroscopic level. The synergistic effect can be interpreted in terms of the enhanced hydrophilicity and hydroxide-attractivity of the dicationic species, the increased electron-depletion, and the concomitant, higher vulnerability of the ester moiety to nucleophilic attacks. Hydrolysis rate constants and carboxylate basicities of the leaving group are known to be correlating quantities. Such correlation at the microscopic level, however, has not been reported before. The correlation between microscopic rate constants and carboxylate basicities is obvious, with r ) 0.923 (Figure 4). The off-line rate constants of ImlacOMe are larger than expected, indicating some extra capacity of the adjacent hydroxyl moiety. Such capacity can be its enhanced hydroxidebinding capability, which promotes hydrolysis, beyond its electron-withdrawing effect through the connecting bonds. Correlation has also been sought between species-specific rate constants and 1H NMR chemical shifts, a third quantity that depends on electron density. To serve as NMR reference nucleus, the R-proton has been selected instead of the even closer carbons, since 13C NMR chemical shifts show disproportionate distance-dependence of the site of protonation.37 The correlation coefficient, r ) 0.919, indicates unambiguous codependence but also that factors other than electron density also influence at least one of the two quantities. The individual pH-dependent contribution of the four HisOMe microspecies to the overall hydroxide-catalyzed hydrolysis rate is shown in Figure 5. Values in the vertical axis are products of the microscopic rate constant, the microspecies concentration, and hydroxide ion concentration, assuming 1 M ester total concentration. This representation of the reaction fractions shows that contribution of the four HisOMe microspecies to the overall hydrolysis is commensurable at pH ) 8 ( 1. Outside this pH range, the nonprotonated or the dicationic species highly predominates the overall hydrolysis. Crossover pH of the e00 and e+ + species on the reaction fraction diagram is 8.10,
Nosza´l et al. whereas that on the mole fraction diagram is pH ) 6.37 which can be seen in Figure 6. The 8.10-6.37 = 1.7 shift toward the higher pH values is a visual quantitative representation of the fact that protonated species take a larger portion of the hydrolysis than could be expected on the basis of their concentration. Conclusion Microscopic rate constants of ester hydrolysis represent the individual decomposition propensity of inseparable, coexisting species in solution. This new physicochemical parameter is not only of theoretical interest, but also it has considerable capacity in drug design: The insertion of protonating/deprotonating group(s) into the molecule near the ester site allows a set of pH-dependent, subtle switching effects on the rate of ester hydrolysis. Acknowledgment. This work was supported by OTKA T 43579 and ETT 535/2003 grants. Valuable contributions of Ildiko´ Ko´czia´n-Pothorszky are greatly appreciated. References and Notes (1) Talbot, R. J. E. In ComprehensiVe Chemical Kinetics Section 4. Ester Formation and Hydrolysis and Related Reactions, Vol. 10; Bamford, C. H., Tipper, C. F. H., Eds.; Elsevier: Amsterdam, The Netherlands, 1972; p 146. (2) Skrabal, A.; Zahorka, A. Monatsh. Chem. 1929, 53, 562. (3) Nolan, G. J.; Amis, E. S. J. Phys. Chem. 1956, 65, 1556. (4) Humffray, A. A.; Ryan, J. J. J. Chem. Soc. B 1968, 468. (5) Hammett, L. P. Physical Organic Chemistry; McGraw-Hill: New York, 1970. (6) Taft, R. W. In Steric Effects in Organic Chemistry; Newman, M. S., Ed.; Wiley: New York, 1956. (7) Testa, B.; Mayer, J. M. Hydrolysis in Drug and Prodrug Metabolism: Chemistry, Biochemistry and Enzymology; Wiley-VCH: Weinheim, Germany, 2003. (8) Ingold, C. K. Structure and Mechanism in Organic Chemistry; Cornell University Press: Ithaca, NY, 1969. (9) Pratt, R. F.; Bruice, T. C. J. Am. Chem. Soc. 1970, 92, 5956. (10) Jencks, W. P. Chem. ReV. 1972, 72, 705. (11) Bell, R. P.; Lindars, F. J. Nature, 1954, 4601. (12) Robson, M. Nature 1965, 208, 265. (13) Robson Wright, M. J. Chem. Soc. B 1967, 1265. (14) Robson Wright, M. J. Chem Soc. B 1968, 548. (15) Hay, R. W.; Porter, L. J.; Morris, P. J. Aust. J. Chem. 1966, 19, 1197. (16) Hay, R. W.; Morris, P. J. J. Chem. Soc. B 1970, 1577. (17) Hay, R. W.; Morris, P. J. J. Chem. Soc., Perkin Trans. 2 1972, 1021. (18) Conley, H. L., Jr.; Martin, R. B. J. Phys. Chem. 1965, 69, 2923. (19) Blinkovsky, A. M.; Galaev, I. Y.; Sˇ Vedas, V. K. J. Chem. Soc., Perkin Trans. 2 1986, 1537. (20) Roy, A. K.; Guillory, J. K. Int. J. Pharm. 1995, 120, 169. (21) Skwierczynski, R. D.; Connors, K. A. Pharm. Res. 1993, 10, 1174. (22) Visky, D.; Kraszni, M.; Hosztafi, S.; Nosza´l, B. HelV. Chim. Acta 2000, 83, 364. (23) Nosza´l, B. In Biocoordination Chemistry. Coordination Equilibria in Biologically ActiVe Systems; Burger, K., Ed.; Ellis Horwood: New York, 1990. (24) Szaka´cs, Z.; Nosza´l, B. J. Math. Chem. 1999, 26, 139. (25) Fujiwara, S.; Ishizuko, H.; Fudano, S. Chem. Lett. 1974, 1281. (26) Nosza´l, B.; Sa´ndor, P. Anal. Chem. 1989, 61, 2631. (27) Nosza´l, B.; Scheller-Krattinger, V.; Martin, R. B. J. Am. Chem. Soc. 1982, 104, 1078. (28) Nosza´l, B.; Rabenstein, D. L. J. Phys. Chem. 1991, 95, 4761. (29) Nosza´l, B.; Kraszni, M. J. Phys. Chem. B 2002, 106, 1066. (30) Kraszni M.; Ba´nyai I.; Nosza´l B. J. Med. Chem. 2003, 46, 2241. (31) Williams, F. M. Clin. Pharmacokinet. 1985, 10, 392. (32) Nosza´l, B. J. Phys. Chem. 1986, 90, 6345. (33) Nosza´l B.; Szaka´cs Z. J. Phys. Chem. B 2003, 107, 5074. (34) Smith, R. M.; Martell, A. E. Critical Stability Constants, Plenum Press: New York, London 1985. (35) Hay, R. W.; Porter, L. J. J. Chem. Soc. B 1967, 1261. (36) Li, N. C.; Manning, R. A. J. Am. Chem. Soc. 1955, 77, 5225. (37) Suprenant, H. L.; Sarneski, J. E.; Key, R. R.; Byrd, J. T.; Reilley, C. T. J. Magn. Reson. 1980, 40, 231.
