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Prediction of solvent effect on enzyme enantioselectivity
Fluid Phase Equilibria 450 (2017) 126e132
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Prediction of solvent effect on enzyme enantioselectivity Alexandra V. Chatzikonstantinou a, Giannis-Florjan Norra b, Haralambos Stamatis a, Epaminondas Voutsas b, * a
Laboratory of Biotechnology, Department of Biological Applications and Technologies, University of Ioannina, 45110 Ioannina, Greece Thermodynamics and Transport Phenomena Laboratory, Department of Chemical Engineering - Section II, National Technical University of Athens, Heroon Polytechniou 9, Zographos, GR-15780 Athens, Greece
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 April 2017 Received in revised form 25 July 2017 Accepted 25 July 2017 Available online 28 July 2017
Enantiomeric ratios for the esterification reaction of 2-phenylpropionic acid with 1-octanol catalyzed by immobilized Candida antarctica lipase B in sixteen organic solvents have been measured. Correlation equations that relate the enzyme enantioselectivity with the van der Waals volume (Vw), the van der Waals area (Aw), and the Hildebrand solubility parameters (d2) of the solvents were obtained, and they were compared with linear solvation energy relationship (LSER) correlation equations, which relates the enzyme enantioselectivity with polarity, acidity, basicity, and Hildebrand solubility parameters of the solvents. Statistical analysis of the experimental data for the esterification reaction investigated here as well as for seven other reactions taken from the literature showed that the pure solvent Vw, Aw and d2 parameters, sufficiently describe the dependence of enzyme enantioselectivity on the properties of the solvent, yielding better results than the LSER equations that use one more parameter. Furthermore, the enzyme enantioselectivity has been related to the infinite dilution activity coefficients of substrates in the solvent, which are predicted by the COSMO-RS model. It is shown that the predicted by COSMO-RS ratios of infinite dilution activity coefficients of the two enantiomers can be used to correlate satisfactorily the enantiomeric ratios. © 2017 Elsevier B.V. All rights reserved.
Keywords: Enantioselectivity Enzyme biocatalysis Lipase Activity coefficient COSMO-RS
1. Introduction The demand for enantiopure pharmaceuticals and agrochemicals has been growing continuously, especially due to the fact that different enantiomers can cause different biological effects [1,2]. Thus, the preparation of optically active products has become a major research area particularly in pharmaceutical and finechemical industry [3e5]. The use of biocatalysts in nonaqueous media has been proved to be a useful procedure for the preparation of optically pure compounds [6,7]. The activity and the enantioselectivity of enzymes have been found to be strongly dependent on the nature of the solvent used [8e11]. Several experimental, theoretical and simulation studies have been devoted to investigate the mechanisms by which solvents affect enzyme enantioselectivity and to define principles that can best guide the selection of the solvent in order to rationalize the phenomenon [9] [12e20].
* Corresponding author. E-mail address: [email protected] (E. Voutsas). http://dx.doi.org/10.1016/j.fluid.2017.07.016 0378-3812/© 2017 Elsevier B.V. All rights reserved.
The solvent could affect the enzyme conformation [16e18], or the active site of enzyme by binding in it or near it and thus affecting the molecular recognition process between enzyme and substrate [16,21]. On the other hand, Klibanov and coworkers proposed that solvent effects are due to differences in the energies of solvation of the substrates in their enzyme-bound transition states [8,14,22]. Ke et al. [14] determined the desolvated part of the substrate in the transition state using molecular modelling and dynamic simulations based on the crystalline structure of the enzymes, g-chymotrypsin and subtilisin, and then they used UNIFAC to predict the activity coefficients of the two enantiomers. Later, Colombo et al. [13] applied the same method in order to predict the solvent effect on the selectivity of lyophilized or cross-linked enzyme crystals of subtilisin in the resolution of secondary alcohols, but it was found that the theoretical model did not predict well the effect of the solvent. No clear consensus has yet emergent on which physicochemical properties of the solvent to use to describe the effect of the solvent on enzyme enantioselectivity. The most studied relations are those with solvent hydrophobicity [10] [23e28], measured as logP (P is the octanol-water partition coefficient), dielectric constant and
A.V. Chatzikonstantinou et al. / Fluid Phase Equilibria 450 (2017) 126e132
dipole moment [23,29], but the results are not always successful and, furthermore, no rationale for using them in a predictive way has been offered. The size of the solvent molecules, expressed through the van der Waals volume parameter, has also been suggested as a one of the parameters that govern solvent effect on enantioselectivity [12,19]. Except for the molecule size, functional group, location and structure of the carbon chains of organic solvents seem to effect the enantioselectivity of the enzyme [27]. Lee [30] has studied the application of a linear solvation energy relationship (LSER) that relates the enzyme enantioselectivity with the polarity, acidity, basicity and Hildebrand solubility parameters of the solvent. The objective of the present manuscript is two-fold. First, enantiomeric ratios for the esterification reaction of 2phenylpropionic acid with 1-octanol catalyzed by immobilized Candida antarctica lipase B, a commonly used industrial lipase with a very broad substrate specificity, in sixteen organic solvents have been measured. The second is to investigate the capability of predicting the effect of solvent and substrate on enzyme enantioselectivity in non-aqueous organic media. To this purpose two approaches were followed. In the first approach, the effect of solvent on enzyme enantioselectivity has been studied. To this purpose, a multiparameter regression analysis has been performed for the esterification reaction measured in this work, as well as for seven transesterification reactions, catalyzed by different lipases and proteases in various organic solvents, taken from the literature. The solvent parameters studied are, the van der Waals volume (Vw), the van der Waals area (Aw) and the Hildebrand solubility parameter (d2). These parameters were chosen on the basis that the enzyme enantioselectivity is a phenomenon driven by both entropic (combinatorial) effects and enthalpic effects [12,31,32]. Vw and Aw take into account entropic (combinatorial) effects and d2 takes into account enthalpic effects. For comparison, LSER correlation equations that relate the enzyme enantioselectivity with the polarity, acidity, basicity and Hildebrand solubility parameters of the solvent have been developed using also multiparameter regression analysis. In the second approach, the effect of solvent and substrate on enzyme enantioselectivity was investigated. To this purpose, the enzyme enantioselectivity is related to the infinite dilution activity coefficients of substrates in the various solvents, which are predicted with the COSMO-RS method.
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2. Materials and methods 2.1. Materials Immobilized lipase B from Candida antarctica was purchased from c-LEcta GmbH, Germany. All chemicals, R-()-2phenylpropionic acid, (S)-(þ)-2-phenylpropionic acid, racemic 2phenylpropionic acid, 1-hexanol and organic solvent used were purchased from Alfa Aesar, Fluka or Sigma-Aldrich and were of the highest available purity. The source and purities of the chemicals used are listed in Table 1. 2.2. Enzymatic reactions The enzymatic esterification of 2-phenylpropionic acid with 1octanol to octyl-2-phenylpropionate and water was carried out in sealed stirred round bottom flasks (10 mL) using various organic solvents. The reactants R-()-2-phenylpropionic acid or (S)-(þ)-2phenylpropionic acid (0.01 mmol) and 1-octanol (0.05 mmol) were dissolved in 2 mL of the organic solvent previously dried with 4 Å molecular sieves. The enzymatic esterification started by addition of 15 mg/mL of immobilized lipase. In all cases studied, the flasks were incubated in an orbital shaker at 240 rpm at 55 C. Reactions were carried out in the presence of 20 mg/mL of 4 Å molecular sieves. Control experiments were conducted without enzyme. Samples were withdrawn at various times and diluted with organic solvent. The reaction was terminated by removing the biocatalyst and the molecular sieves by filtration using a 0.45 mm nylon membrane filter. The reaction's progress was monitored by gas chromatography (GC). A Shimadzu 17A gas chromatographer was used, equipped with a flame ionization detector (FID) and a bDEX 120 column (Supelco), 30 m 0.25 mm x 0.25 mm. Helium was used as the carrier gas at a flow rate of 0.9 mL/min. The injector and detection port temperatures were set to 250 C and 300 C, respectively. The oven temperature was set at 150 C for 5 min and linearly increased to 180 C by 10 C/min. For the analysis of the alcohol substrate and the ester products, appropriate standard curves were used using n-decane as external standard. Reaction rates were calculated from the slope of the linear portion of plots of product (ester) concentration versus time and expressed as mmol h1 g1 of enzymatic preparation. All experiments were repeated at least 3 times. In order to determine the enantioselectivity E without
Table 1 Materials description. Chemical name
Source
Initial mole fraction purity
Purification method
Immobilized lipase B from Candida antarctica Water R-()-2-phenylpropionic acid (S)-(þ)-2-phenylpropionic acid (±)-2-Phenylpropionic acid 1-Hexanol (anhydrous) Acetonitrile (anhydrous) Acetone 2-Butanone Diethyl ether 2-Methyl-2-butanol tert-Butyl alcohol tert-Butyl methyl ether Methylene chloride Di-isopropylether Toluene Cyclohexane n-Hexane
c-LEcta GmbH Fisher Scientific Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Alfa Aesar Alfa Aesar Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich
Specific activity:> 9000 PLU/g dry beads HPLC gradient grade 97% 97% 97% >99% 99.8% HPLC gradient grade >99% Analytical standard 98% 99% 99.8% HPLC gradient grade Analytical standard 99.8% 99.5% Analytical grade
None None None None None None None None None None None None None None None None None None
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performing a compete kinetic study, the initial rates reaction rates vR and vS of the esterification reactions of R-()-2-phenylpropionic acid or (S)-(þ)-2-phenylpropionic acid respectively, were determined at low concentration of enantiomers (less than 0.5 of KM value) which ensures that the reaction is first order [33]. In this case, the ratio of the initial rates (vR/vS) of the esterification of two enantiomers is a good estimation of E i.e E z vR/vS ¼ (Vmax,R/KM,R)/ (Vmax,S/KM,S) were KM,R and KM,S are the Michaelis- Menten constants and Vmax,R and Vmax,S the maximum reaction rates for isomer R and S respectively. The enantioselectivity values E of the esterification reactions in various solvents of different polarity are presented in Table 2. 3. Results and discussion 3.1. Development of correlation equations of enantioselectivity with solvent physicochemical properties Regression analysis was performed to the enantioselectivity data measured in this work for the esterification of R-()-2phenylpropionic acid and (S)-(þ)-2-phenylpropionic acid with 1octanol catalyzed by immobilized C. antarctica lipase, as well as to seven enantiomeric ratio data sets for transesterification reactions catalyzed by various hydrolytic enzymes (lipases and protease) taken from the literature. The parameters studied in the multiparameter regression analysis of enantioselectivity data are: the van der Waals volume (Vw), the van der Waals surface area (Aw) and the Hildebrand solubility parameters (d2) of the solvent. These pure compound parameters were chosen on the basis of the knowledge that enzyme enantioselectivity is driven by entropic and enthalpic effects. Van der Waals (vdW) volume is a molecular parameter defined by Bondi [34] that is used to calculate the hard-core or closed-packed volume of a molecule, which is in fact the minimum volume that a molecule occupies if all molecules in the system were firmly packed in contact with each other, i.e. if they were closed-packed spheres. In an analogous way, Bondi defined the vdW area (Aw) as the area of the closed-packed sphere. Vw and Aw parameters are used for the calculation of the combinatorial contribution to the activity coefficient in models like UNIQUAC [35] or UNIFAC [36]. The solubility parameter (d2) was introduced by Hildebrand and Scott in the development of the regular solution theory [37]. The solubility
Table 2 Enantiomeric ratio (E) at atmospheric pressure of immobilized C. antarctica catalyzed esterification of 2-phenylpropionic acid with 1-octanol in various organic solvents. Reactions were carried out at 328.15 K and atmospheric pressure. Solvent
E ¼ vR/vS
Acetonitrile Acetone 2-Butanone Dielthylether 2-Methyl-2-butanol Tert butanol Tert butyl methyl ether Dichloromethane Isopropylether Toluene Cyclohexane Hexane Heptane Isooctane Decane Isobutyl methyl ketone
9.2 8.5 7.3 6.5 4.5 4.8 4.2 10.5 4.5 4.1 3.2 3.1 3 3 2.6 3.2
Standard uncertainties: u(T) ¼ ±0.1 K, u(P) ¼ ±0.1 kPa, ur(vR) ¼ ±0.03, ur(vS) ¼ ±0.03.
parameter of a molecule i, which is equal to square root of its cohesive energy density, is calculated form the following equation:
d2i
¼
DUi ViL
! ¼
DHvap RT
! (1)
ViL
where DUi is the energy required isothermally to evaporate the liquid i from the saturated liquid to ideal gas, DHvap is the molar enthalpy of vaporization of pure liquid i at temperature T, and VLi is the liquid molar volume of the molecule. In addition, correlations with logP and with the LSER method of Lee [30] were also examined. For the LSER method four solvent parameters were included in the regression analysis: polarity (p*), acidity (a), basicity (b) and solubility parameter (d2). Vw, Aw and d2 parameter values were taken from the DIPPR database [38], logP values from EPI Suite [39], while p*, a and b parameters were taken from Lee [30]. In fact, the multiparameter regression analysis revealed that the inverse of Vw (moles per unit volume) and the inverse of Aw (moles per unit area) are better descriptors than Vw and Aw. Multiparameter regression analysis results are presented in Tables 3e10, which include the correlation coefficient (r2), the F-test value that determines whether this relationship is statistically significant, the pvalue that represents the level of marginal significance within a statistical hypothesis test, the residual sum of squares
Table 3 Multiparameter regression analysis results for the immobilized C. antarctica lipase catalyzed esterification of 2-phenylpropionic acid with 1-octanol. Experimental enantiomeric ratio data were measured in this work (Table 1). Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.817 0.624 0.466 0.640 0.821 0.830 0.859
62.7 52.9 12.2 24.9 29.7 19.6 16.8
1.55E-06 4.05E-06 3.58E-03 1.98E-04 1.41E-05 6.37E-05 1.19E-04
0.101 0.119 0.303 0.202 0.101 0.090 0.080
12.08 11.81 9.96 10.69 14.11 16.25 18.60
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 4 Multiparameter regression analysis results of immobilized C. antarctica lipase catalyzed transesterification of 3-methyl-2-butanol with vinyl octanoate in organic solvents. Experimental enantiomeric ratio data were taken from Ref. [12]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.707 0.787 0.729 0.621 0.808 0.826 0.885
14.5 22.1 16.2 9.8 10.5 6.4 5.8
8.88E-03 3.33E-03 6.89E-03 2.03E-02 1.63E-02 5.31E-02 9.09E-02
0.011 0.008 0.01 0.014 0.007 0.006 0.005
12.33 12.42 12.33 12.36 14.47 16.47 18.62
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 5 Multiparameter regression analysis results of the Aspergillus oryzae protease transesterification of N-acetyl-phenylamine-2-chloroethylester with 1-propanol in 18 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [34]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.438 0.371 0.755 0.626 0.477 0.821 0.746
12.5 9.4 49.3 26.7 6.87 21.5 9.6
2.74E-03 7.33E-03 2.88E-06 9.27E-05 7.63E-03 1.67E-05 7.74E-04
2.186 2.452 0.955 1.459 2.001 0.695 0.986
6.23 5.99 7.41 6.91 8.59 13.09 14.03
d2 LogP 1/Vw,1/Aw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
A.V. Chatzikonstantinou et al. / Fluid Phase Equilibria 450 (2017) 126e132 Table 6 Multiparameter regression analysis results of lyophilized subtilisin catalyzed transesterification of sec-phenethyl alcohol with vinyl butyrate in 9 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [13]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.728 0.543 0.601 0.261 0.830 0.843 0.748
18.7 8.3 10.5 2.5 14.6 9.0 3.0
3.44E-03 2.36E-02 1.42E-02 1.58E-01 4.90E-03 1.87E-02 1.58E-01
0.118 0.199 0.174 0.322 0.074 0.068 0.11
7.02 6.81 6.87 6.47 9.12 11.07 13.06
d
2
LogP 1/Vw,1/Aw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 7 Multiparameter regression analysis results of subtilisin Carlsberg transesterification of sec-phenethyl alcohol with vinyl butyrate in 8 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [53]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.706 0.482 0.801 0.424 0.899 0.916 0.931
14.3 5.8 24.1 4.4 22.0 14.5 10.2
9.09E-03 5.62E-02 2.68E-03 8.07E-02 3.33E-03 1.29E-02 4.28E-02
0.535 0.941 0.361 1.047 0.185 0.153 0.124
5.84 5.32 6.26 5.40 8.49 10.65 11.99
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 8 Multiparameter regression analysis results of lyophilized chymotrypsin catalyzed transesterification of 2-(3,5-dimethoxybenzyl)-1,3 propanediol with vinyl acetate in 10 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [14]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.743 0.848 0.819 0.602 0.882 0.901 0.830
23.2 45.0 36.2 12.1 26.2 18.3 6.2
1.33E-03 1.51E-04 3.16E-04 8.29E-03 5.60E-04 2.02E-03 3.61E-02
0.090 0.053 0.064 0.14 0.041 0.035 0.059
7.35 7.38 7.37 7.23 9.45 11.45 13.32
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
PNdat
exp
129
pred
RSS ¼ i¼1 ðyi yi Þ2 , where Ndat is the number of data points, yexp is the ith experimental value of the variable and ypred is i i the corresponding predicted value, and the Akaike information criterion (AIC) that is a measure of the relative quality of statistical models for a given set of data, i.e. when model fits are ranked according to their AIC values, the model with the lowest AIC value being considered the ‘best’. The following comments summarize our conclusions on the obtained results: 1. The inverse van der Waals volume and area parameters (1/Vw and 1/Aw) and, especially, their combination describe most of the variation of the experimental data. This suggests that entropic effects on enantioselectivity can be satisfactorily taken into account by these parameters. 2. The solubility parameter gives in most cases satisfactory correlation results suggesting that enthalpic effects on enantioselectivity can be taken into account from this parameter. 3. Correlation with logP, which is the most widely used parameter in the literature to relate enzyme enantioselectivity with solvent characteristics, does not always leads to successful results that is in agreement with the findings of other publications [16,40]. 4. Combination of 1/Vw, 1/Aw and d2 leads to a successful correlation of the enantioselectivity data and can be used to describe sufficiently the dependence of enzyme enantioselectivity on the properties of the solvent. Some typical comparisons between predicted enantiomeric ratios, using Vw, Aw and d2 parameters, and the experimental ones are shown graphically in Fig. 1. 5. Correlations using 1/Vw, 1/Aw and d2 are comparable or even better than those obtained with the LSER method, which, however, involves one more parameter. It should be also noted that Vw and Aw parameters, unlike the solvatochromic parameters p*, a and b, are easily available for the vast majority of the organic solvents or can be calculated through a group contribution method like UNIFAC [36]. Moreover, the higher F-test values, the smaller p-values values and the smaller AIC values obtained with the correlations using 1/Vw, 1/Aw and d2 in comparison with the LSER method parameters indicate that the relationship of the enantiomeric ratios with the 1/Vw, 1/Aw and d2 parameters is statistically more significant than the one with p*, a, b and d2 parameters.
Table 9 Multiparameter regression analysis results of lipase Pseudomonas sp. catalyzed transesterification of 6-methyl-5-hepten-2-ol with trifluoroethyl butyrate in 10 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [19]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.432 0.635 0.121 0.090 0.850 0.863 0.740
6.1 13.9 1.1 0.8 20.0 12.5 3.5
3.89E-02 5.79E-03 3.24E-01 3.99E-01 1.28E-03 5.38E-03 9.88E-02
0.141 0.091 0.219 0.226 0.037 0.034 0.065
7.15 7.32 6.94 6.94 9.46 11.46 13.38
d
2
LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 10 Multiparameter regression analysis results of lyophilized subtilisin catalyzed transesterification of sec-phenethyl alcohol with vinyl acetate in 7 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [13]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.397 0.303 0.558 0.071 0.437 0.832 0.929
3.3 2.2 6.3 0.4 1.5 4.9 6.6
1.29E-01 2.00E-01 5.67E-02 5.65E-01 3.16E-01 1.11E-01 1.36E-01
0.207 0.239 0.152 0.319 0.193 0.058 0.024
6.26 6.16 6.32 5.96 8.30 10.66 12.68
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Fig. 1. Predicted versus experimental enantiomeric ratios. Predicted enantiomeric ratios were obtained from the correlations using 1/Vw, 1/Aw and d2.
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3.2. A thermodynamic approach for the prediction of solvent dependence on enzyme enantioselectivity
screening charge density between s and s þ ds. The representative s profile of a mixture is the concentration weighted average of the pure s profiles. The s profile of a component needs to be calculated
The empirical correlation equations investigated in the previous section describe only the dependence of enzyme enantioselectivity on solvent properties, not taking into account the presence of substrates and their interactions with the solvent. A method that takes into account thermodynamics of substrate solvation on enzyme selectivity has been proposed by Ke et al. [14]. In this model the enzyme enantioselectivity, E, is related to the thermodynamic activity coefficients (g) of the desolvated substrate moieties in the transition state for the S- and R-enantiomers. Ke et al. firstly determined the desolvated part of the substrate in the transition state using molecular modelling and molecular dynamic simulations based on the crystalline structure of the enzyme, and then they used the UNIFAC model to predict the activity coefficients of the desolvated part of two enantiomers. Later, Colombo et al. [13] applied the same methodology. In a previous publication [41] we have shown that the initial reaction rates of enzyme esterification reactions, which are used for the determination of the enantiomeric ratios, are very well correlated with the initial activities of the substrates. For a simple firstorder kinetics reaction: A þ B4C þ D, the initial reaction rate,voA , is given through the following expression:
only once. Aside from the electrostatic interactions, other intermolecular forces such as dispersive and repulsive interactions and hydrogen bonds also occur in fluid mixtures. They are merged in an energy concept within the COSMO-RS model. As a result, a COSMORS calculation provides the chemical potential or the activity coefficient of component i in the mixture [45]. The standard procedure that is also described in more details in Refs. [46,47] was applied for COSMO-RS calculations. The structures of the various molecules were designed using HyperChem Professional (Version 8.0) and were initially optimized using the Geometry Optimization tool of the same program. Then, a conformational analysis was performed for each molecule placed in vacuum, using the Mm þ method to calculate the potential energies. From the conformers that occurred, a selection was made excluding the ones that had similar dihedral angles and energies with the ones selected. Quantum chemical COSMO calculations were then performed for the selected structures on the density functional theory (DFT) level, utilizing the BP functional [48e50] with RI (resolution of identity) approximation and a triple-z valence polarized basis set (TZVP) [51,52]. Calculations were done using the TURBOMOLE program package. Finally, the infinite dilution activity coefficients of the R- and S- enantiomers in each solvent were calculated using COSMOtherm program (Version C2.1 Release 01.11) with the BP_TZVP_C21_0111 parameterization [44]. Correlations of logE with log(g∞S/g∞R), with g∞S and g∞R values predicted by COSMO-RS, for three reactions already investigated with the empirical correlations are presented in Figs. 2e4. For the reaction of Fig. 2, 2-methyl-2-propanol, 2-methyl-2-butanol and dichloromethane have been excluded from the correlation and the same was done for the reaction of Fig. 3 for dichloromethane. This was done since for these solvents the results do not correlate well with those of the other solvents. Similar problems with COSMO-RS predictions for tertiary alcohols and chlorohydrocarbons have been observed by Voulgaris et al. [47]. Apart from the above mentioned exceptions, the results, although not in all cases satisfactory, indicate that this thermodynamic approach can be used for predicting the effect of substrate on enzyme enantioselectivity and help to the proper design of enantioselective reactions.
voA ¼ kaoA aoB
(2)
where A and B refer to the S- and R-enantiomers, k is the rate constant and a is the thermodynamic activity: a ¼ x*g, where x is the concentration in mole fraction basis and g the activity coefficient. Superscript o stands for the initial condition. Considering that the enzyme enantioselectivity (E) is the ratio of the initial reaction rates of the S- and R-enantiomers and applying some simple algebra, the following expression is derived:
log E ¼ log
0 gS þK gR
(3)
where gS and gR are the activity coefficients of the S- and R-enantiomers and K0 is a constant. Ke et al. have used a similar equation to Eq. (3) but instead of the whole activity coefficient only that of the desolvated substrate moieties in the transition state for the S- and R-enantiomers have been considered. In order to investigate if there is a correlation between log E and log ggS , gS and gR values were predicted by the COSMO-RS method R that is able to differentiate the two enantiomers. Furthermore, since the mole fractions of the substrates in the solvent for all reactions are very small, only the infinite dilution activity coefficients are required. It should be noted that UNIFAC, which is a popular model for activity coefficient predictions, is not able to differentiate among isomers predicting, thus, the same activity coefficients for the two enantiomers. COSMO-RS is an efficient method for a priory prediction of thermophysical data of liquid mixtures on the basis of unimolecular quantum chemical calculations for the individual molecules that provide the necessary information for the evaluation of molecular interactions in liquids [42e44]. In the COSMO-RS model, a liquid is considered to be an ensemble of almost closely packed ideally screened molecules. Each piece of surface is characterized by its value of screening charge density (s). The interaction energy of the ensemble is then obtained by a statistically correct consideration of all possible pairs of pieces of surface. The composition of the ensemble that is needed to apply this procedure is delivered by the distribution function p(s). This function that is called as the s profile, describes the amount of surface in the ensemble having a
Fig. 2. Correlation between log E and log gS =gR for the reaction of Table 2. gS and gR values are the infinite dilution activity coefficients of the two enantiomers predicted by the COSMO-RS method. 2-methyl-2-propanol, 2-methyl-2-butanol and dichloromethane have been excluded from the correlation.
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that could influence the binding of substrates on enzyme active site and thus the stereoselectivity of the biocatalyst. The results of the first approach indicate that the van der Waals volume, the van der Waals area and the Hildebrand solubility parameter represent three parameters that sufficiently describe the dependence of enzyme enantioselectivity on the properties of the solvent, yielding better results than the LSER correlation equations that use one more solvent parameter (polarity, acidity, basicity, and Hildebrand solubility parameter). The preliminary results of the second approach clearly show that the use of the activity coefficients predicted from COSMO-RS, excluding tertiary alcohols and chloromentane, is a promising approach for the prediction of the effect of both substrates and solvent on the enzyme enantioselectivity, and suggest that further investigation is needed in order to make this method fully predictive. References
Fig. 3. Correlation between log E and log gS =gR for the reaction of Table 3. gS and gR values are the infinite dilution activity coefficients of the two enantiomers predicted by the COSMO-RS method. Dichloromethane has been excluded from the correlation.
Fig. 4. Correlation between log E and log gS =gR for the reaction of Table 6. gS and gR values are the infinite dilution activity coefficients of the two enantiomers predicted by the COSMO-RS method.
4. Conclusions New experimental enantioselectivity data for the esterification reaction of 2-phenylpropionic acid with 1-octanol catalyzed by immobilized Candida antarctica lipase B in various organic solvents of different polarity are presented. The enantiomeric ratio values do not change very much and vary from about 3 in alkanes to about 10 in dichloromethane. Two different approaches for predicting the effect of solvents and substrates on enzyme enantioselectivity in non-aqueous organic media were investigated. The first one is an empirical correlation of the enzyme enantioselectivity with pure solvent properties, and the second is based on a semi-theoretical method that relates the enzyme enantioselectivity with the activity coefficients of substrates in the reaction media (solvent), where the activity coefficients were predicted by the COSMO-RS model. It must be noted that both approaches used do not take into consideration the effect of the solvents on the protein flexibility
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Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Prediction of solvent effect on enzyme enantioselectivity Alexandra V. Chatzikonstantinou a, Giannis-Florjan Norra b, Haralambos Stamatis a, Epaminondas Voutsas b, * a
Laboratory of Biotechnology, Department of Biological Applications and Technologies, University of Ioannina, 45110 Ioannina, Greece Thermodynamics and Transport Phenomena Laboratory, Department of Chemical Engineering - Section II, National Technical University of Athens, Heroon Polytechniou 9, Zographos, GR-15780 Athens, Greece
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 April 2017 Received in revised form 25 July 2017 Accepted 25 July 2017 Available online 28 July 2017
Enantiomeric ratios for the esterification reaction of 2-phenylpropionic acid with 1-octanol catalyzed by immobilized Candida antarctica lipase B in sixteen organic solvents have been measured. Correlation equations that relate the enzyme enantioselectivity with the van der Waals volume (Vw), the van der Waals area (Aw), and the Hildebrand solubility parameters (d2) of the solvents were obtained, and they were compared with linear solvation energy relationship (LSER) correlation equations, which relates the enzyme enantioselectivity with polarity, acidity, basicity, and Hildebrand solubility parameters of the solvents. Statistical analysis of the experimental data for the esterification reaction investigated here as well as for seven other reactions taken from the literature showed that the pure solvent Vw, Aw and d2 parameters, sufficiently describe the dependence of enzyme enantioselectivity on the properties of the solvent, yielding better results than the LSER equations that use one more parameter. Furthermore, the enzyme enantioselectivity has been related to the infinite dilution activity coefficients of substrates in the solvent, which are predicted by the COSMO-RS model. It is shown that the predicted by COSMO-RS ratios of infinite dilution activity coefficients of the two enantiomers can be used to correlate satisfactorily the enantiomeric ratios. © 2017 Elsevier B.V. All rights reserved.
Keywords: Enantioselectivity Enzyme biocatalysis Lipase Activity coefficient COSMO-RS
1. Introduction The demand for enantiopure pharmaceuticals and agrochemicals has been growing continuously, especially due to the fact that different enantiomers can cause different biological effects [1,2]. Thus, the preparation of optically active products has become a major research area particularly in pharmaceutical and finechemical industry [3e5]. The use of biocatalysts in nonaqueous media has been proved to be a useful procedure for the preparation of optically pure compounds [6,7]. The activity and the enantioselectivity of enzymes have been found to be strongly dependent on the nature of the solvent used [8e11]. Several experimental, theoretical and simulation studies have been devoted to investigate the mechanisms by which solvents affect enzyme enantioselectivity and to define principles that can best guide the selection of the solvent in order to rationalize the phenomenon [9] [12e20].
* Corresponding author. E-mail address: [email protected] (E. Voutsas). http://dx.doi.org/10.1016/j.fluid.2017.07.016 0378-3812/© 2017 Elsevier B.V. All rights reserved.
The solvent could affect the enzyme conformation [16e18], or the active site of enzyme by binding in it or near it and thus affecting the molecular recognition process between enzyme and substrate [16,21]. On the other hand, Klibanov and coworkers proposed that solvent effects are due to differences in the energies of solvation of the substrates in their enzyme-bound transition states [8,14,22]. Ke et al. [14] determined the desolvated part of the substrate in the transition state using molecular modelling and dynamic simulations based on the crystalline structure of the enzymes, g-chymotrypsin and subtilisin, and then they used UNIFAC to predict the activity coefficients of the two enantiomers. Later, Colombo et al. [13] applied the same method in order to predict the solvent effect on the selectivity of lyophilized or cross-linked enzyme crystals of subtilisin in the resolution of secondary alcohols, but it was found that the theoretical model did not predict well the effect of the solvent. No clear consensus has yet emergent on which physicochemical properties of the solvent to use to describe the effect of the solvent on enzyme enantioselectivity. The most studied relations are those with solvent hydrophobicity [10] [23e28], measured as logP (P is the octanol-water partition coefficient), dielectric constant and
A.V. Chatzikonstantinou et al. / Fluid Phase Equilibria 450 (2017) 126e132
dipole moment [23,29], but the results are not always successful and, furthermore, no rationale for using them in a predictive way has been offered. The size of the solvent molecules, expressed through the van der Waals volume parameter, has also been suggested as a one of the parameters that govern solvent effect on enantioselectivity [12,19]. Except for the molecule size, functional group, location and structure of the carbon chains of organic solvents seem to effect the enantioselectivity of the enzyme [27]. Lee [30] has studied the application of a linear solvation energy relationship (LSER) that relates the enzyme enantioselectivity with the polarity, acidity, basicity and Hildebrand solubility parameters of the solvent. The objective of the present manuscript is two-fold. First, enantiomeric ratios for the esterification reaction of 2phenylpropionic acid with 1-octanol catalyzed by immobilized Candida antarctica lipase B, a commonly used industrial lipase with a very broad substrate specificity, in sixteen organic solvents have been measured. The second is to investigate the capability of predicting the effect of solvent and substrate on enzyme enantioselectivity in non-aqueous organic media. To this purpose two approaches were followed. In the first approach, the effect of solvent on enzyme enantioselectivity has been studied. To this purpose, a multiparameter regression analysis has been performed for the esterification reaction measured in this work, as well as for seven transesterification reactions, catalyzed by different lipases and proteases in various organic solvents, taken from the literature. The solvent parameters studied are, the van der Waals volume (Vw), the van der Waals area (Aw) and the Hildebrand solubility parameter (d2). These parameters were chosen on the basis that the enzyme enantioselectivity is a phenomenon driven by both entropic (combinatorial) effects and enthalpic effects [12,31,32]. Vw and Aw take into account entropic (combinatorial) effects and d2 takes into account enthalpic effects. For comparison, LSER correlation equations that relate the enzyme enantioselectivity with the polarity, acidity, basicity and Hildebrand solubility parameters of the solvent have been developed using also multiparameter regression analysis. In the second approach, the effect of solvent and substrate on enzyme enantioselectivity was investigated. To this purpose, the enzyme enantioselectivity is related to the infinite dilution activity coefficients of substrates in the various solvents, which are predicted with the COSMO-RS method.
127
2. Materials and methods 2.1. Materials Immobilized lipase B from Candida antarctica was purchased from c-LEcta GmbH, Germany. All chemicals, R-()-2phenylpropionic acid, (S)-(þ)-2-phenylpropionic acid, racemic 2phenylpropionic acid, 1-hexanol and organic solvent used were purchased from Alfa Aesar, Fluka or Sigma-Aldrich and were of the highest available purity. The source and purities of the chemicals used are listed in Table 1. 2.2. Enzymatic reactions The enzymatic esterification of 2-phenylpropionic acid with 1octanol to octyl-2-phenylpropionate and water was carried out in sealed stirred round bottom flasks (10 mL) using various organic solvents. The reactants R-()-2-phenylpropionic acid or (S)-(þ)-2phenylpropionic acid (0.01 mmol) and 1-octanol (0.05 mmol) were dissolved in 2 mL of the organic solvent previously dried with 4 Å molecular sieves. The enzymatic esterification started by addition of 15 mg/mL of immobilized lipase. In all cases studied, the flasks were incubated in an orbital shaker at 240 rpm at 55 C. Reactions were carried out in the presence of 20 mg/mL of 4 Å molecular sieves. Control experiments were conducted without enzyme. Samples were withdrawn at various times and diluted with organic solvent. The reaction was terminated by removing the biocatalyst and the molecular sieves by filtration using a 0.45 mm nylon membrane filter. The reaction's progress was monitored by gas chromatography (GC). A Shimadzu 17A gas chromatographer was used, equipped with a flame ionization detector (FID) and a bDEX 120 column (Supelco), 30 m 0.25 mm x 0.25 mm. Helium was used as the carrier gas at a flow rate of 0.9 mL/min. The injector and detection port temperatures were set to 250 C and 300 C, respectively. The oven temperature was set at 150 C for 5 min and linearly increased to 180 C by 10 C/min. For the analysis of the alcohol substrate and the ester products, appropriate standard curves were used using n-decane as external standard. Reaction rates were calculated from the slope of the linear portion of plots of product (ester) concentration versus time and expressed as mmol h1 g1 of enzymatic preparation. All experiments were repeated at least 3 times. In order to determine the enantioselectivity E without
Table 1 Materials description. Chemical name
Source
Initial mole fraction purity
Purification method
Immobilized lipase B from Candida antarctica Water R-()-2-phenylpropionic acid (S)-(þ)-2-phenylpropionic acid (±)-2-Phenylpropionic acid 1-Hexanol (anhydrous) Acetonitrile (anhydrous) Acetone 2-Butanone Diethyl ether 2-Methyl-2-butanol tert-Butyl alcohol tert-Butyl methyl ether Methylene chloride Di-isopropylether Toluene Cyclohexane n-Hexane
c-LEcta GmbH Fisher Scientific Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Alfa Aesar Alfa Aesar Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich Sigma -Aldrich
Specific activity:> 9000 PLU/g dry beads HPLC gradient grade 97% 97% 97% >99% 99.8% HPLC gradient grade >99% Analytical standard 98% 99% 99.8% HPLC gradient grade Analytical standard 99.8% 99.5% Analytical grade
None None None None None None None None None None None None None None None None None None
128
A.V. Chatzikonstantinou et al. / Fluid Phase Equilibria 450 (2017) 126e132
performing a compete kinetic study, the initial rates reaction rates vR and vS of the esterification reactions of R-()-2-phenylpropionic acid or (S)-(þ)-2-phenylpropionic acid respectively, were determined at low concentration of enantiomers (less than 0.5 of KM value) which ensures that the reaction is first order [33]. In this case, the ratio of the initial rates (vR/vS) of the esterification of two enantiomers is a good estimation of E i.e E z vR/vS ¼ (Vmax,R/KM,R)/ (Vmax,S/KM,S) were KM,R and KM,S are the Michaelis- Menten constants and Vmax,R and Vmax,S the maximum reaction rates for isomer R and S respectively. The enantioselectivity values E of the esterification reactions in various solvents of different polarity are presented in Table 2. 3. Results and discussion 3.1. Development of correlation equations of enantioselectivity with solvent physicochemical properties Regression analysis was performed to the enantioselectivity data measured in this work for the esterification of R-()-2phenylpropionic acid and (S)-(þ)-2-phenylpropionic acid with 1octanol catalyzed by immobilized C. antarctica lipase, as well as to seven enantiomeric ratio data sets for transesterification reactions catalyzed by various hydrolytic enzymes (lipases and protease) taken from the literature. The parameters studied in the multiparameter regression analysis of enantioselectivity data are: the van der Waals volume (Vw), the van der Waals surface area (Aw) and the Hildebrand solubility parameters (d2) of the solvent. These pure compound parameters were chosen on the basis of the knowledge that enzyme enantioselectivity is driven by entropic and enthalpic effects. Van der Waals (vdW) volume is a molecular parameter defined by Bondi [34] that is used to calculate the hard-core or closed-packed volume of a molecule, which is in fact the minimum volume that a molecule occupies if all molecules in the system were firmly packed in contact with each other, i.e. if they were closed-packed spheres. In an analogous way, Bondi defined the vdW area (Aw) as the area of the closed-packed sphere. Vw and Aw parameters are used for the calculation of the combinatorial contribution to the activity coefficient in models like UNIQUAC [35] or UNIFAC [36]. The solubility parameter (d2) was introduced by Hildebrand and Scott in the development of the regular solution theory [37]. The solubility
Table 2 Enantiomeric ratio (E) at atmospheric pressure of immobilized C. antarctica catalyzed esterification of 2-phenylpropionic acid with 1-octanol in various organic solvents. Reactions were carried out at 328.15 K and atmospheric pressure. Solvent
E ¼ vR/vS
Acetonitrile Acetone 2-Butanone Dielthylether 2-Methyl-2-butanol Tert butanol Tert butyl methyl ether Dichloromethane Isopropylether Toluene Cyclohexane Hexane Heptane Isooctane Decane Isobutyl methyl ketone
9.2 8.5 7.3 6.5 4.5 4.8 4.2 10.5 4.5 4.1 3.2 3.1 3 3 2.6 3.2
Standard uncertainties: u(T) ¼ ±0.1 K, u(P) ¼ ±0.1 kPa, ur(vR) ¼ ±0.03, ur(vS) ¼ ±0.03.
parameter of a molecule i, which is equal to square root of its cohesive energy density, is calculated form the following equation:
d2i
¼
DUi ViL
! ¼
DHvap RT
! (1)
ViL
where DUi is the energy required isothermally to evaporate the liquid i from the saturated liquid to ideal gas, DHvap is the molar enthalpy of vaporization of pure liquid i at temperature T, and VLi is the liquid molar volume of the molecule. In addition, correlations with logP and with the LSER method of Lee [30] were also examined. For the LSER method four solvent parameters were included in the regression analysis: polarity (p*), acidity (a), basicity (b) and solubility parameter (d2). Vw, Aw and d2 parameter values were taken from the DIPPR database [38], logP values from EPI Suite [39], while p*, a and b parameters were taken from Lee [30]. In fact, the multiparameter regression analysis revealed that the inverse of Vw (moles per unit volume) and the inverse of Aw (moles per unit area) are better descriptors than Vw and Aw. Multiparameter regression analysis results are presented in Tables 3e10, which include the correlation coefficient (r2), the F-test value that determines whether this relationship is statistically significant, the pvalue that represents the level of marginal significance within a statistical hypothesis test, the residual sum of squares
Table 3 Multiparameter regression analysis results for the immobilized C. antarctica lipase catalyzed esterification of 2-phenylpropionic acid with 1-octanol. Experimental enantiomeric ratio data were measured in this work (Table 1). Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.817 0.624 0.466 0.640 0.821 0.830 0.859
62.7 52.9 12.2 24.9 29.7 19.6 16.8
1.55E-06 4.05E-06 3.58E-03 1.98E-04 1.41E-05 6.37E-05 1.19E-04
0.101 0.119 0.303 0.202 0.101 0.090 0.080
12.08 11.81 9.96 10.69 14.11 16.25 18.60
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 4 Multiparameter regression analysis results of immobilized C. antarctica lipase catalyzed transesterification of 3-methyl-2-butanol with vinyl octanoate in organic solvents. Experimental enantiomeric ratio data were taken from Ref. [12]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.707 0.787 0.729 0.621 0.808 0.826 0.885
14.5 22.1 16.2 9.8 10.5 6.4 5.8
8.88E-03 3.33E-03 6.89E-03 2.03E-02 1.63E-02 5.31E-02 9.09E-02
0.011 0.008 0.01 0.014 0.007 0.006 0.005
12.33 12.42 12.33 12.36 14.47 16.47 18.62
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 5 Multiparameter regression analysis results of the Aspergillus oryzae protease transesterification of N-acetyl-phenylamine-2-chloroethylester with 1-propanol in 18 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [34]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.438 0.371 0.755 0.626 0.477 0.821 0.746
12.5 9.4 49.3 26.7 6.87 21.5 9.6
2.74E-03 7.33E-03 2.88E-06 9.27E-05 7.63E-03 1.67E-05 7.74E-04
2.186 2.452 0.955 1.459 2.001 0.695 0.986
6.23 5.99 7.41 6.91 8.59 13.09 14.03
d2 LogP 1/Vw,1/Aw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
A.V. Chatzikonstantinou et al. / Fluid Phase Equilibria 450 (2017) 126e132 Table 6 Multiparameter regression analysis results of lyophilized subtilisin catalyzed transesterification of sec-phenethyl alcohol with vinyl butyrate in 9 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [13]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.728 0.543 0.601 0.261 0.830 0.843 0.748
18.7 8.3 10.5 2.5 14.6 9.0 3.0
3.44E-03 2.36E-02 1.42E-02 1.58E-01 4.90E-03 1.87E-02 1.58E-01
0.118 0.199 0.174 0.322 0.074 0.068 0.11
7.02 6.81 6.87 6.47 9.12 11.07 13.06
d
2
LogP 1/Vw,1/Aw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 7 Multiparameter regression analysis results of subtilisin Carlsberg transesterification of sec-phenethyl alcohol with vinyl butyrate in 8 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [53]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.706 0.482 0.801 0.424 0.899 0.916 0.931
14.3 5.8 24.1 4.4 22.0 14.5 10.2
9.09E-03 5.62E-02 2.68E-03 8.07E-02 3.33E-03 1.29E-02 4.28E-02
0.535 0.941 0.361 1.047 0.185 0.153 0.124
5.84 5.32 6.26 5.40 8.49 10.65 11.99
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 8 Multiparameter regression analysis results of lyophilized chymotrypsin catalyzed transesterification of 2-(3,5-dimethoxybenzyl)-1,3 propanediol with vinyl acetate in 10 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [14]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.743 0.848 0.819 0.602 0.882 0.901 0.830
23.2 45.0 36.2 12.1 26.2 18.3 6.2
1.33E-03 1.51E-04 3.16E-04 8.29E-03 5.60E-04 2.02E-03 3.61E-02
0.090 0.053 0.064 0.14 0.041 0.035 0.059
7.35 7.38 7.37 7.23 9.45 11.45 13.32
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
PNdat
exp
129
pred
RSS ¼ i¼1 ðyi yi Þ2 , where Ndat is the number of data points, yexp is the ith experimental value of the variable and ypred is i i the corresponding predicted value, and the Akaike information criterion (AIC) that is a measure of the relative quality of statistical models for a given set of data, i.e. when model fits are ranked according to their AIC values, the model with the lowest AIC value being considered the ‘best’. The following comments summarize our conclusions on the obtained results: 1. The inverse van der Waals volume and area parameters (1/Vw and 1/Aw) and, especially, their combination describe most of the variation of the experimental data. This suggests that entropic effects on enantioselectivity can be satisfactorily taken into account by these parameters. 2. The solubility parameter gives in most cases satisfactory correlation results suggesting that enthalpic effects on enantioselectivity can be taken into account from this parameter. 3. Correlation with logP, which is the most widely used parameter in the literature to relate enzyme enantioselectivity with solvent characteristics, does not always leads to successful results that is in agreement with the findings of other publications [16,40]. 4. Combination of 1/Vw, 1/Aw and d2 leads to a successful correlation of the enantioselectivity data and can be used to describe sufficiently the dependence of enzyme enantioselectivity on the properties of the solvent. Some typical comparisons between predicted enantiomeric ratios, using Vw, Aw and d2 parameters, and the experimental ones are shown graphically in Fig. 1. 5. Correlations using 1/Vw, 1/Aw and d2 are comparable or even better than those obtained with the LSER method, which, however, involves one more parameter. It should be also noted that Vw and Aw parameters, unlike the solvatochromic parameters p*, a and b, are easily available for the vast majority of the organic solvents or can be calculated through a group contribution method like UNIFAC [36]. Moreover, the higher F-test values, the smaller p-values values and the smaller AIC values obtained with the correlations using 1/Vw, 1/Aw and d2 in comparison with the LSER method parameters indicate that the relationship of the enantiomeric ratios with the 1/Vw, 1/Aw and d2 parameters is statistically more significant than the one with p*, a, b and d2 parameters.
Table 9 Multiparameter regression analysis results of lipase Pseudomonas sp. catalyzed transesterification of 6-methyl-5-hepten-2-ol with trifluoroethyl butyrate in 10 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [19]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.432 0.635 0.121 0.090 0.850 0.863 0.740
6.1 13.9 1.1 0.8 20.0 12.5 3.5
3.89E-02 5.79E-03 3.24E-01 3.99E-01 1.28E-03 5.38E-03 9.88E-02
0.141 0.091 0.219 0.226 0.037 0.034 0.065
7.15 7.32 6.94 6.94 9.46 11.46 13.38
d
2
LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Table 10 Multiparameter regression analysis results of lyophilized subtilisin catalyzed transesterification of sec-phenethyl alcohol with vinyl acetate in 7 organic solvents. Experimental enantiomeric ratio data were taken from Ref. [13]. Parameters
R2
F
p-value
RSS
AIC
1/Vw 1/Aw
0.397 0.303 0.558 0.071 0.437 0.832 0.929
3.3 2.2 6.3 0.4 1.5 4.9 6.6
1.29E-01 2.00E-01 5.67E-02 5.65E-01 3.16E-01 1.11E-01 1.36E-01
0.207 0.239 0.152 0.319 0.193 0.058 0.024
6.26 6.16 6.32 5.96 8.30 10.66 12.68
d2 LogP 1/Aw,1/Vw 1/Aw,1/Vw, d2 LSER (p*, a, b, d2)
Fig. 1. Predicted versus experimental enantiomeric ratios. Predicted enantiomeric ratios were obtained from the correlations using 1/Vw, 1/Aw and d2.
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3.2. A thermodynamic approach for the prediction of solvent dependence on enzyme enantioselectivity
screening charge density between s and s þ ds. The representative s profile of a mixture is the concentration weighted average of the pure s profiles. The s profile of a component needs to be calculated
The empirical correlation equations investigated in the previous section describe only the dependence of enzyme enantioselectivity on solvent properties, not taking into account the presence of substrates and their interactions with the solvent. A method that takes into account thermodynamics of substrate solvation on enzyme selectivity has been proposed by Ke et al. [14]. In this model the enzyme enantioselectivity, E, is related to the thermodynamic activity coefficients (g) of the desolvated substrate moieties in the transition state for the S- and R-enantiomers. Ke et al. firstly determined the desolvated part of the substrate in the transition state using molecular modelling and molecular dynamic simulations based on the crystalline structure of the enzyme, and then they used the UNIFAC model to predict the activity coefficients of the desolvated part of two enantiomers. Later, Colombo et al. [13] applied the same methodology. In a previous publication [41] we have shown that the initial reaction rates of enzyme esterification reactions, which are used for the determination of the enantiomeric ratios, are very well correlated with the initial activities of the substrates. For a simple firstorder kinetics reaction: A þ B4C þ D, the initial reaction rate,voA , is given through the following expression:
only once. Aside from the electrostatic interactions, other intermolecular forces such as dispersive and repulsive interactions and hydrogen bonds also occur in fluid mixtures. They are merged in an energy concept within the COSMO-RS model. As a result, a COSMORS calculation provides the chemical potential or the activity coefficient of component i in the mixture [45]. The standard procedure that is also described in more details in Refs. [46,47] was applied for COSMO-RS calculations. The structures of the various molecules were designed using HyperChem Professional (Version 8.0) and were initially optimized using the Geometry Optimization tool of the same program. Then, a conformational analysis was performed for each molecule placed in vacuum, using the Mm þ method to calculate the potential energies. From the conformers that occurred, a selection was made excluding the ones that had similar dihedral angles and energies with the ones selected. Quantum chemical COSMO calculations were then performed for the selected structures on the density functional theory (DFT) level, utilizing the BP functional [48e50] with RI (resolution of identity) approximation and a triple-z valence polarized basis set (TZVP) [51,52]. Calculations were done using the TURBOMOLE program package. Finally, the infinite dilution activity coefficients of the R- and S- enantiomers in each solvent were calculated using COSMOtherm program (Version C2.1 Release 01.11) with the BP_TZVP_C21_0111 parameterization [44]. Correlations of logE with log(g∞S/g∞R), with g∞S and g∞R values predicted by COSMO-RS, for three reactions already investigated with the empirical correlations are presented in Figs. 2e4. For the reaction of Fig. 2, 2-methyl-2-propanol, 2-methyl-2-butanol and dichloromethane have been excluded from the correlation and the same was done for the reaction of Fig. 3 for dichloromethane. This was done since for these solvents the results do not correlate well with those of the other solvents. Similar problems with COSMO-RS predictions for tertiary alcohols and chlorohydrocarbons have been observed by Voulgaris et al. [47]. Apart from the above mentioned exceptions, the results, although not in all cases satisfactory, indicate that this thermodynamic approach can be used for predicting the effect of substrate on enzyme enantioselectivity and help to the proper design of enantioselective reactions.
voA ¼ kaoA aoB
(2)
where A and B refer to the S- and R-enantiomers, k is the rate constant and a is the thermodynamic activity: a ¼ x*g, where x is the concentration in mole fraction basis and g the activity coefficient. Superscript o stands for the initial condition. Considering that the enzyme enantioselectivity (E) is the ratio of the initial reaction rates of the S- and R-enantiomers and applying some simple algebra, the following expression is derived:
log E ¼ log
0 gS þK gR
(3)
where gS and gR are the activity coefficients of the S- and R-enantiomers and K0 is a constant. Ke et al. have used a similar equation to Eq. (3) but instead of the whole activity coefficient only that of the desolvated substrate moieties in the transition state for the S- and R-enantiomers have been considered. In order to investigate if there is a correlation between log E and log ggS , gS and gR values were predicted by the COSMO-RS method R that is able to differentiate the two enantiomers. Furthermore, since the mole fractions of the substrates in the solvent for all reactions are very small, only the infinite dilution activity coefficients are required. It should be noted that UNIFAC, which is a popular model for activity coefficient predictions, is not able to differentiate among isomers predicting, thus, the same activity coefficients for the two enantiomers. COSMO-RS is an efficient method for a priory prediction of thermophysical data of liquid mixtures on the basis of unimolecular quantum chemical calculations for the individual molecules that provide the necessary information for the evaluation of molecular interactions in liquids [42e44]. In the COSMO-RS model, a liquid is considered to be an ensemble of almost closely packed ideally screened molecules. Each piece of surface is characterized by its value of screening charge density (s). The interaction energy of the ensemble is then obtained by a statistically correct consideration of all possible pairs of pieces of surface. The composition of the ensemble that is needed to apply this procedure is delivered by the distribution function p(s). This function that is called as the s profile, describes the amount of surface in the ensemble having a
Fig. 2. Correlation between log E and log gS =gR for the reaction of Table 2. gS and gR values are the infinite dilution activity coefficients of the two enantiomers predicted by the COSMO-RS method. 2-methyl-2-propanol, 2-methyl-2-butanol and dichloromethane have been excluded from the correlation.
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131
that could influence the binding of substrates on enzyme active site and thus the stereoselectivity of the biocatalyst. The results of the first approach indicate that the van der Waals volume, the van der Waals area and the Hildebrand solubility parameter represent three parameters that sufficiently describe the dependence of enzyme enantioselectivity on the properties of the solvent, yielding better results than the LSER correlation equations that use one more solvent parameter (polarity, acidity, basicity, and Hildebrand solubility parameter). The preliminary results of the second approach clearly show that the use of the activity coefficients predicted from COSMO-RS, excluding tertiary alcohols and chloromentane, is a promising approach for the prediction of the effect of both substrates and solvent on the enzyme enantioselectivity, and suggest that further investigation is needed in order to make this method fully predictive. References
Fig. 3. Correlation between log E and log gS =gR for the reaction of Table 3. gS and gR values are the infinite dilution activity coefficients of the two enantiomers predicted by the COSMO-RS method. Dichloromethane has been excluded from the correlation.
Fig. 4. Correlation between log E and log gS =gR for the reaction of Table 6. gS and gR values are the infinite dilution activity coefficients of the two enantiomers predicted by the COSMO-RS method.
4. Conclusions New experimental enantioselectivity data for the esterification reaction of 2-phenylpropionic acid with 1-octanol catalyzed by immobilized Candida antarctica lipase B in various organic solvents of different polarity are presented. The enantiomeric ratio values do not change very much and vary from about 3 in alkanes to about 10 in dichloromethane. Two different approaches for predicting the effect of solvents and substrates on enzyme enantioselectivity in non-aqueous organic media were investigated. The first one is an empirical correlation of the enzyme enantioselectivity with pure solvent properties, and the second is based on a semi-theoretical method that relates the enzyme enantioselectivity with the activity coefficients of substrates in the reaction media (solvent), where the activity coefficients were predicted by the COSMO-RS model. It must be noted that both approaches used do not take into consideration the effect of the solvents on the protein flexibility
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