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A simple method for calculating enantiomer ratio and equilibrium constants in biocatalytic resolutions
Tetrahedron: Asymmetry Vo|. 6, No. 12, pp. 3015-3022, 1995
Pergamon
Elsevier Science Ltd Printed in Great Britain 0957-4166/95 $9.50+0.00
0957-4166(95)00398-3
A SIMPLE METHOD FOR CALCULATING ENANTIOMER RATIO AND EQUILIBRIUM CONSTANTS IN BIOCATALYTIC RESOLUTIONS H e n r i k W. Anthonsen, a* Bard Helge Hoff and Thorleif A n t h o n s e n D e p a r t m e n t of Chemistry, The University of T r o n d h e i m N-7055 Trondheim, N o r w a y , Fax: +47 73596255 aMR-Centre, SINTEF-UNIMED, N-7030 Trondheim, N o r w a y , Fax: +47 73997708 Abstract: A c o m p u t e r p r o g r a m m e for d e t e r m i n a t i o n of equilibrium constant (K) a n d e n a n t i o m e r ratio (E) in biocatalytic resolutions has been d e v e l o p e d . The p r o g r a m m e utilises e x p e r i m e n t a l data, ees and eep m e a s u r e d at more than one conversion, a n d d e t e r m i n e s b o t h K and E no matter w h e t h e r the reaction is irreversible (K=0) or reversible (K>0). A n estimation of errors in the calculations indicates that errors in E does not show a Gaussian distribution, while errors in K does. The usefulness of the p r o g r a m m e has been tested in a lipase-catalysed transesterification of 1 - p h e n o x y - 2 - p r o p a n o l at v a r i o u s concentrations of acyl donor, with different solvents and at different water activities.
INTRODUCTION Racemate resolution is one of the most p o p u l a r w a y s to obtain homochiral b u i l d i n g blocks for synthesis of h o m o c h i r a l p h a r m a c e u t i c a l s . M a x i m u m chemical yield of a biocatalytic kinetic r e s o l u t i o n is 50% of each e n a n t i o m e r , i.e. w h e n one e n a n t i o m e r has r e a c t e d (product) and the other is left untouched (substrate). The result of the process is described by the enantiomeric excess of the p r o d u c t (eep), of the remaining substrate (ees) and the yield, which is related to the degree of conversion (c). A p a r a m e t e r that c o m p r i s e s both the enantiomeric excess and the degree of conversion, and thus the yield, is the e n a n t i o m e r ratio E. In biocatalytic resolutions it is defined as the ratio of k c a t / K M for the two enantiomers. While ee is a p r o p e r t y of the p r o d u c t , E is characteristic of a process. E describes the enantioselectivity or better the enantiospecificity, i.e. u n d e r p a r t i c u l a r p h y s i c a l conditions (solvent, t e m p e r a t u r e , pH, etc.), w i t h a certain
substrate and a specific enzyme, it is a constant parameter. For an irreversible process, such as a biocatalytic h y d r o l y s i s , s i m p l e calculations give E w h e n ees, eep and c is m e a s u r e d (Eqns. 1 and 2, K = 0). (E and K are defined according to Chen et al.1, 2) It is not strictly necessary to measure c since c = e e s / e e s + e e p . 1)
In(1 - (1 + K ) ( c + eel(1 - c))) = E ln(1 - (1 + K ) ( c - eel(1 - c))) 3015
H.W. ANTHONSENet al.
3016
ln(1 - (1 + K)c(1 + eep)) = E ln(1 - (1 + K)c(1 - eep))
2)
Since ees in this case is constantly increasing as the reaction proceeds towards 100% conversion, it is always possible to reach 100% enantiomeric excess of the unreacted substrate if a low yield can be accepted. It is important to emphasise that as opposed to asymmetric synthesis, in racemate resolution the quality of the product may be improved by sacrificing on the yield. It has been shown that a complete description of an irreversible process includes the equilibrium constant. (Eqns. 1 and 2, K > 0). 2 This relationship depends on the thermodynamic parameter K = (1-Ceq)/Ceq where Ceq is the equilibrium conversion. Since this definition of K does not include all participants in the reaction, it is often referred to as the "apparent equilibrium constant". In order to calculate E in this case, K has to be determined by allowing the faster reacting species to reach equilibrium and measure the concentrations of the product and the remaining substrate. Calculation of ees and eep values as a function of c for given values of K and E is not possible by separating the ees and eep (ees = f(c)K,E, eep = f(c)K,E). Previously different m e t h o d s for calculating ees and eep have been presented. These include numerical integration of the rate equations for both enantiomers 3 and parametric representation of the equations 1) and 2). 2 RESULTS
AND
DISCUSSION
The programme We have developed a method in order directly to calculate E and K using equations 1) and 2). In order to evaluate ees and eep as a function of c with constant K and E the algorithm finds values of ees and eep that minimises equations 3) and 4).
!
3)
mi_.._nn ln(1-(l+ K)(c +eG(1-c)))-E ~oE~ff(ln(1 -- (1 + K)(c - ees(1 - c)))
4)
min (ln(1-(l+K)c(l+eG)) ~ , ~ ~(ln(1 - (1 + K)c(1 - eep))
/2
E) 2
Currently we are doing this by the method of golden sectioning. 4 With the accuracy needed for this application the method is very fast and reliable. Using a 60 MHz PowerMacintosh 6100 more than 100 function-evaluations per second was generated.
Enantiomer ratio in biocatalytic resolutions
3017
Due to the nature of reversible reactions, there will be values of c w h e r e ees and eep is not d e f i n e d . I n s p e c t i o n of e q u a t i o n s 1) a n d 2) s h o w s t h a t the m a x i m u m constrained b y K for both ees and eep (Eqn. 5).
v a l u e of c is
1
5)
c _<- K+I
O b t a i n i n g K and E v a l u e s from a given set of (c, ees) and (c, eep) d a t a require a two d i m e n s i o n a l m i n i m i s a t i o n b y v a r y i n g K and E. The function to be m i n i m i s e d is a p e n a l t y function (often called "force-field") d e p e n d e n t on different p a r a m e t e r s chosen as i m p o r t a n t for description of " g o o d " values of K and E. We have used four objectives that are necessary for describing a " g o o d fit" of K and E to the data set. The first and second are that the values of K and E m u s t be in the allowed region, K > 0.0 and E > 1.0. If these objectives are violated there will be a large p e n a l t y , increasing w i t h the distance from the a l l o w e d region. In practice w e are using penalties so large that it is impossible to get these disallowed values in the final result. The third objective is not to allow values of c that are not consistent with equation 5. This p u n i s h m e n t h o w e v e r , m u s t be small e n o u g h to allow m i n o r violations. O t h e r w i s e one single o u t l y i n g p o i n t c o u l d influence the K v a l u e too much. The last objective is to m i n i m i s e the difference b e t w e e n the e x p e r i m e n t a l a n d calculated data. Values of K and E that give small differences are best. We have chosen to minimise the root mean square error b e t w e e n experimental and calculated points (Eqn. 6) N ~estl,mt~
6)
error
=
N,,pr~.,.t, - eeoxp ,) + ~(eG~.,0~ - eep
We chose the d o w n h i l l s i m p l e x m e t h o d 4 for the m i n i m i s a t i o n of the p e n a l t y function. This m e t h o d is relatively robust, it is easy to use, and it does not require calculation of derivatives. One d r a w b a c k is that it requires relatively m a n y e v a l u a t i o n s of the p e n a l t y function. This is not a serious p r o b l e m since a typical m i n i m i s a t i o n takes less than five seconds on a 60 M H z PowerMacintosh 6100. The d o w n h i l l simplex m e t h o d requires a N + I dimensional simplex as a starting point, for a t w o - d i m e n s i o n a l m i n i m i s a t i o n this is a triangle. D e p e n d i n g on the v a l u e of the p e n a l t y function at the p o i n t s describing the triangle, the triangle reflects, contracts and e x p a n d s t o w a r d s lower values for the p e n a l t y function. In o r d e r to obtain ees a n d eep values GLC-integrals of all four enantiomers in question are m e a s u r e d . W i t h this m e t h o d m a n y systematic errors b e c o m e self-compensating and thus the s t a n d a r d d e v i a t i o n s of the e r r o r s s m a l l e r . W e a s s u m e that e r r o r s of i n t e g r a l m e a s u r e m e n t s are in the o r d e r of 2% which in t u r n give an absolute s t a n d a r d deviation of 0.01 in the calculated ees and eep values.
H.W. ANTHONSENet al.
3018
In order to estimate errors in E and K we created one thousand new data sets for each measurement by adding Gaussian noise with a standard deviation of 0.01 to a data set with the same c-value as the original data set, and sets of ees and eep values according to the calculated E and K values.
Biocatalysis experiments To illustrate the use of the programme, we have chosen reversible transesterification with lipase B from Candida antartica as catalyst. The substrate, 1-phenoxy-2-propanol, was selected as a continuation of earlier work 5 and on basis of molecular m o d e l l i n g of s u b s t r a t e / l i p a s e interactions. 6 The reaction with 2chloroethyl butanoate as acyl donor showed reversibility, and was therefore well suited as a model reaction.
HOH O Ph O - . . ~ C H 3 + . , , , " ~ O
~C
H OCOC3H 7 H OH PhO.~c H3 + PhO,~c H3 R S
I
The absolute configurations of the products were established by comparison with (S)-Ip h e n o x y - 2 - p r o p a n o l which has been described p r e v i o u s l y . 7 T h e (R)-enantiomer was produced in a hydrolysis of the butanoate also catalysed by lipase B.
I O0 80
4o
20 0
I
0
20
40
60
80
I
I
I
I O0
Conversion, % Figure 1. Effect of variation of solvent in transesterification of 1phenoxy-2-propanol with 2-chloroethyl butanoate (5x excess). Circles toluene, squares hexane, filled symbols p r o d u c t fraction, open symbols remaining substrate fraction.
Enantiomer ratio in biocatalytic resolutions
3019
When the resolution was performed in two different solvents, hexane and toluene, the Kvalues were virtually the same, 0.29 and 0.31 respectively. However, there was a significant change in the enantioselectivity on going from hexane (E=149) to toluene (E=75.3) (Figure 1). It seems reasonable that the two unpolar solvents do not influence the thermodynamics of the reaction in a different way. The catalytic properties of the enzyme, however, may be altered by different solvents. When the relative molar amount of acyl donor was increased from 1.5 times the amount of substrate, to 3 and finally 5, the K-value naturally increased (Figure 2, Table 1). This just reflects the fact that the equilibrium is shifted towards the product side. The E-value, however, which was virtually constant for the two reactions with the smallest amount of acyl donor, E= 242 and 254 respectively, decreased drastically in the third experiment. We think that a five times excess of acyl donor may change the properties of the enzyme. We are currently investigating this observation.
100 80 60
\
20
)
o
X 0
20
40
Conversion,
i'''
60
80
100
%
Figure 2. Variation of relative concentrations of 2-chloroethyl butanoate in transesterification of 1-phenoxy-2-propanol. Circles 5x excess, squares 3x excess, triangles 1.5x excess. Filled symbols represent product fraction, open symbols remaining substrate fraction.
3020
H.W. ANTHONSENet aL
[Acyldonor] [substrate] 1.5
K
[Acyldonor] 0.066
242 (+47, -36)
0.71 (-+ 0.025)
0.131
254 (+240, -79)
0.44 (+ 0.014)
0.218
149 (+15, -12)
0.29 (+ 0.010)
Table 1. Effect of variation of concentration of acyl donor in transesterification. The solvent used was hexane, and the acyl donor 2-chloroethyl butanoate. Figures in parenthesis is standard deviation assuming +2% inaccuracy in measurements of GLC integrals.
It is well known that the amount of water in the organic solvent, best expressed as the water activity (aw), may influence the reaction. The water activity may easily be altered and kept at a constant level by introducing pairs of inorganic hydrate salts into the reaction vessel. 8 It has been reported that the water activity both influences the enantioselectivity 9 and that it does not. 10 For the present system we have monitored the reaction at three different levels of aw and we observe an increase of both E and K with increasing water activity. (Figure 3, Table 2)
1 O0 80 60
40
\
zo
0 0
20
40 60 Conversion, %
I''' 80
1 O0
Figure 3. Variation of water activity (aw) in hexane in transesterification
of 1-phenoxy-2-propanol with 2-chloroethyl butanoate (5x excess). Circles aw=0, squares aw=0.16, triangles aw=0.61. Filled symbols represent product fraction, open symbols remaining substrate fraction.
Enantiomer ratio in biocatalytic resolutions
aw 0 0.16 0.61
E 149 (+15, -12) 258 (+37, -27) 418 (+141, -90)
3021
K 0.29 (+ 0.010) 0.35 (+ 0.0087 0.69 (+ 0.010)
Table 2. V a r i a t i o n of w a t e r a c t i v i t y ( a w ) in h e x a n e in transesterification of 1 - p h e n o x y - 2 - p r o p a n o l w i t h 2-chloroethyl b u t a n o a t e (5x excess). F i g u r e s in p a r e n t h e s i s is s t a n d a r d d e v i a t i o n a s s u m i n g +2% inaccuracy in m e a s u r e m e n t s of GLC integrals. W h e n the w a t e r activity of the reaction m e d i u m increases, water will serve as a competing nucleophile and the reverse reaction will be m o r e favoured leading to an increasing K. It is very interesting to notice that the enantioselectivity also increases, however, the usefulness of o p e r a t i n g at an elevated water activity in order to obtain a high E-value is doubtful since K also increases. C o n c e r n i n g the e r r o r e s t i m a t i o n s , the E-value, as e x p e c t e d , d i d n o t s h o w G a u s s i a n distribution. The error values in Tables 1 and 2 represent a region covering 37% of the data counting in both directions of the calculated E. There is no evidence that K was not showing a Gaussian distribution, and errors in K are given as one s t a n d a r d deviation.
ACKNOWLEDGEMENT We are grateful to Dr. Martin Barfoed, N o v o - N o r d i s k , Bagsvaerd, DK for gift of enzymes.
EXPERIMENTAL General. Chiral analyses were p e r f o r m e d using a Varian 3400 gas c h r o m a t o g r a p h with a CPChiracil-DEX-CB from C h r o m p a c k . Lipase B (EC 3.1.1.3) from Candida antarctica (SP 435) N o v o - N o r d i s k , i m m o b i l i s e d on Lewatit, h a d specific activity of 19000 P L U / g . NMR spectra of 1-phenoxy-2-propanol and its butanoate conformed with their structures. 7
Transesterification. To solvent (3 mL), was a d d e d 1-phenoxy-2-propanol (0.131 mmol), and 2-chloroethyl butanoate (for a m o u n t see Tables 1 and 2). The reaction was started b y a d d i n g the lipase (20 mg) to the reaction mixture. The reactions w e r e p e r f o r m e d in a shaker incubator at 30 °C. The s a m p l e s w e r e filtrated to r e m o v e the i m m o b i l i s e d e n z y m e before analysis. The s u b s t r a t e alcohol a n d p r o d u c t ester w e r e b o t h a n a l y s e d directly on GLC w i t h o u t d e r i v a t i s a t i o n in the same run. Retention times for 1-phenoxy-2-propanol were 23 - 24 rain. and for the butanoates 39 - 40 min., temp. prog. 100 - 142 oC, l O / m i n . At various intervals ees and eep were d e t e r m i n e d and c was calculated from these as s h o w n above. In the experiments with v a r y i n g water activity a total of 0.4 g of salt h y d r a t e was used for each
H.W. ANTHONSENet al.
3022
experiment,
aw = 0.16 was obtained using equimolar amounts of N a 2 H P O 4 . 2 H 2 0 +
Na2HPO4-0H20 and for aw = 0.61 was used Na2HPO4.7H20 + Na2HPO4-2H20.
(R)-l-phenoxy-2-propanol was isolated by column c h r o m a t o g r a p h y after hydrolysis of racemic butanoate (2.5g) in phosphate buffer (100 mL) at pH 7.2 using lipase B (50mg), yield 0. 45g), [a] 22 = + 2.8 (c 1.8 EtOH). (For (S)-enantiomer see ref. 7)
The programme for calculation of E and K was written in ANSI C++ and compiled for the P o w e r M a c i n t o s h type of c o m p u t e r s by means of the C o d e W a r r i o r gold academic p r o g r a m m i n g environment, version 6. A copy of the program is available on request (E-mail: Thorleif.Anthonsen @avh.unit.no). Values of K and E that describe a given (c, ees) and (c, eep) data set were calculated by the minimisation of a penalty function. The penalty function was dependent on the root mean square error between experimental points and points calculated on the basis of given K and E values and also dependent on the values of K, E and c in order to keep the value of these parameters in their allowed region. The initial starting triangle was always at ((E,K)) (1.1, 0.0), (20.1, 0.0) and (1.1, 1.0), but it was not critical for the result. The minimisation gave K and E values which were used as input to another program that generated the (c, ees, eep) curves. Calculation of ees and eep values given K, E and c was done by minimisation of equations 1 and 2. Visualisation Kaleidagraph TM 3.0.
and d r a w i n g
of the curves was p e r f o r m e d
by
REFERENCES
1 2. 3. 4. 5.
Chen, C. S.; Fujimoto, Y.; Girdaukas, G.; Sih, C. J. J. Am. Chem. Soc., 1982, 104, 7294 7299. Chen, C.-S.; Wu, S.-H.; Girdaukas, G.; Sih, C. J. J. Am. Chem. Soc., 1987, 109, 2812-2817. van Tol, J. B. A. Doctoral Thesis, 1994, Delft University of Technology, Delft, The Netherlands, p. 32. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B.P. Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 1992. Hansen, T. V.; Waagen, V.; Partali, V.; Anthonsen, H. W.; Anthonsen, T. Tetrahedron:
Asymmetry, 1995, 6, 499 -504. 6.
Uppenberg, J.; Ohrner, N.; Norin, M.; Hult, K.; Patkar, S.; Waagen, V.; Anthonsen, T.; Alwyn Jones, T.; Abstract EU Bridge-T Lipase Meeting, Isle de Bendor, France, 1994.
7.
Waagen, V.; Partali, V.; Hollingsa~ter, I.; Soon Huang, M. S.; Anthonsen, T. Acta Chem. Scand., 1994, 48, 506 - 510. Kvittingen, L.; Sjursnes, B. J.; Anthonsen, T.; Halling, P. J. Tetrahedron, 1992, 48, 2793 - 2802. H6gberg, H.-E.; Edlund, H.; Berglund, P.; Hedenst6m, E. Tetrahedron: Asymmetry, 1993,
8. 9.
4, 2123 - 2126. 10. Bovara, R.; Carrea, G.; Ottolina, G.; Riva, S. Biotechnol. Lett., 1993, 15, 169 - 174.
(Received in UK 14 September 1995)
Pergamon
Elsevier Science Ltd Printed in Great Britain 0957-4166/95 $9.50+0.00
0957-4166(95)00398-3
A SIMPLE METHOD FOR CALCULATING ENANTIOMER RATIO AND EQUILIBRIUM CONSTANTS IN BIOCATALYTIC RESOLUTIONS H e n r i k W. Anthonsen, a* Bard Helge Hoff and Thorleif A n t h o n s e n D e p a r t m e n t of Chemistry, The University of T r o n d h e i m N-7055 Trondheim, N o r w a y , Fax: +47 73596255 aMR-Centre, SINTEF-UNIMED, N-7030 Trondheim, N o r w a y , Fax: +47 73997708 Abstract: A c o m p u t e r p r o g r a m m e for d e t e r m i n a t i o n of equilibrium constant (K) a n d e n a n t i o m e r ratio (E) in biocatalytic resolutions has been d e v e l o p e d . The p r o g r a m m e utilises e x p e r i m e n t a l data, ees and eep m e a s u r e d at more than one conversion, a n d d e t e r m i n e s b o t h K and E no matter w h e t h e r the reaction is irreversible (K=0) or reversible (K>0). A n estimation of errors in the calculations indicates that errors in E does not show a Gaussian distribution, while errors in K does. The usefulness of the p r o g r a m m e has been tested in a lipase-catalysed transesterification of 1 - p h e n o x y - 2 - p r o p a n o l at v a r i o u s concentrations of acyl donor, with different solvents and at different water activities.
INTRODUCTION Racemate resolution is one of the most p o p u l a r w a y s to obtain homochiral b u i l d i n g blocks for synthesis of h o m o c h i r a l p h a r m a c e u t i c a l s . M a x i m u m chemical yield of a biocatalytic kinetic r e s o l u t i o n is 50% of each e n a n t i o m e r , i.e. w h e n one e n a n t i o m e r has r e a c t e d (product) and the other is left untouched (substrate). The result of the process is described by the enantiomeric excess of the p r o d u c t (eep), of the remaining substrate (ees) and the yield, which is related to the degree of conversion (c). A p a r a m e t e r that c o m p r i s e s both the enantiomeric excess and the degree of conversion, and thus the yield, is the e n a n t i o m e r ratio E. In biocatalytic resolutions it is defined as the ratio of k c a t / K M for the two enantiomers. While ee is a p r o p e r t y of the p r o d u c t , E is characteristic of a process. E describes the enantioselectivity or better the enantiospecificity, i.e. u n d e r p a r t i c u l a r p h y s i c a l conditions (solvent, t e m p e r a t u r e , pH, etc.), w i t h a certain
substrate and a specific enzyme, it is a constant parameter. For an irreversible process, such as a biocatalytic h y d r o l y s i s , s i m p l e calculations give E w h e n ees, eep and c is m e a s u r e d (Eqns. 1 and 2, K = 0). (E and K are defined according to Chen et al.1, 2) It is not strictly necessary to measure c since c = e e s / e e s + e e p . 1)
In(1 - (1 + K ) ( c + eel(1 - c))) = E ln(1 - (1 + K ) ( c - eel(1 - c))) 3015
H.W. ANTHONSENet al.
3016
ln(1 - (1 + K)c(1 + eep)) = E ln(1 - (1 + K)c(1 - eep))
2)
Since ees in this case is constantly increasing as the reaction proceeds towards 100% conversion, it is always possible to reach 100% enantiomeric excess of the unreacted substrate if a low yield can be accepted. It is important to emphasise that as opposed to asymmetric synthesis, in racemate resolution the quality of the product may be improved by sacrificing on the yield. It has been shown that a complete description of an irreversible process includes the equilibrium constant. (Eqns. 1 and 2, K > 0). 2 This relationship depends on the thermodynamic parameter K = (1-Ceq)/Ceq where Ceq is the equilibrium conversion. Since this definition of K does not include all participants in the reaction, it is often referred to as the "apparent equilibrium constant". In order to calculate E in this case, K has to be determined by allowing the faster reacting species to reach equilibrium and measure the concentrations of the product and the remaining substrate. Calculation of ees and eep values as a function of c for given values of K and E is not possible by separating the ees and eep (ees = f(c)K,E, eep = f(c)K,E). Previously different m e t h o d s for calculating ees and eep have been presented. These include numerical integration of the rate equations for both enantiomers 3 and parametric representation of the equations 1) and 2). 2 RESULTS
AND
DISCUSSION
The programme We have developed a method in order directly to calculate E and K using equations 1) and 2). In order to evaluate ees and eep as a function of c with constant K and E the algorithm finds values of ees and eep that minimises equations 3) and 4).
!
3)
mi_.._nn ln(1-(l+ K)(c +eG(1-c)))-E ~oE~ff(ln(1 -- (1 + K)(c - ees(1 - c)))
4)
min (ln(1-(l+K)c(l+eG)) ~ , ~ ~(ln(1 - (1 + K)c(1 - eep))
/2
E) 2
Currently we are doing this by the method of golden sectioning. 4 With the accuracy needed for this application the method is very fast and reliable. Using a 60 MHz PowerMacintosh 6100 more than 100 function-evaluations per second was generated.
Enantiomer ratio in biocatalytic resolutions
3017
Due to the nature of reversible reactions, there will be values of c w h e r e ees and eep is not d e f i n e d . I n s p e c t i o n of e q u a t i o n s 1) a n d 2) s h o w s t h a t the m a x i m u m constrained b y K for both ees and eep (Eqn. 5).
v a l u e of c is
1
5)
c _<- K+I
O b t a i n i n g K and E v a l u e s from a given set of (c, ees) and (c, eep) d a t a require a two d i m e n s i o n a l m i n i m i s a t i o n b y v a r y i n g K and E. The function to be m i n i m i s e d is a p e n a l t y function (often called "force-field") d e p e n d e n t on different p a r a m e t e r s chosen as i m p o r t a n t for description of " g o o d " values of K and E. We have used four objectives that are necessary for describing a " g o o d fit" of K and E to the data set. The first and second are that the values of K and E m u s t be in the allowed region, K > 0.0 and E > 1.0. If these objectives are violated there will be a large p e n a l t y , increasing w i t h the distance from the a l l o w e d region. In practice w e are using penalties so large that it is impossible to get these disallowed values in the final result. The third objective is not to allow values of c that are not consistent with equation 5. This p u n i s h m e n t h o w e v e r , m u s t be small e n o u g h to allow m i n o r violations. O t h e r w i s e one single o u t l y i n g p o i n t c o u l d influence the K v a l u e too much. The last objective is to m i n i m i s e the difference b e t w e e n the e x p e r i m e n t a l a n d calculated data. Values of K and E that give small differences are best. We have chosen to minimise the root mean square error b e t w e e n experimental and calculated points (Eqn. 6) N ~estl,mt~
6)
error
=
N,,pr~.,.t, - eeoxp ,) + ~(eG~.,0~ - eep
We chose the d o w n h i l l s i m p l e x m e t h o d 4 for the m i n i m i s a t i o n of the p e n a l t y function. This m e t h o d is relatively robust, it is easy to use, and it does not require calculation of derivatives. One d r a w b a c k is that it requires relatively m a n y e v a l u a t i o n s of the p e n a l t y function. This is not a serious p r o b l e m since a typical m i n i m i s a t i o n takes less than five seconds on a 60 M H z PowerMacintosh 6100. The d o w n h i l l simplex m e t h o d requires a N + I dimensional simplex as a starting point, for a t w o - d i m e n s i o n a l m i n i m i s a t i o n this is a triangle. D e p e n d i n g on the v a l u e of the p e n a l t y function at the p o i n t s describing the triangle, the triangle reflects, contracts and e x p a n d s t o w a r d s lower values for the p e n a l t y function. In o r d e r to obtain ees a n d eep values GLC-integrals of all four enantiomers in question are m e a s u r e d . W i t h this m e t h o d m a n y systematic errors b e c o m e self-compensating and thus the s t a n d a r d d e v i a t i o n s of the e r r o r s s m a l l e r . W e a s s u m e that e r r o r s of i n t e g r a l m e a s u r e m e n t s are in the o r d e r of 2% which in t u r n give an absolute s t a n d a r d deviation of 0.01 in the calculated ees and eep values.
H.W. ANTHONSENet al.
3018
In order to estimate errors in E and K we created one thousand new data sets for each measurement by adding Gaussian noise with a standard deviation of 0.01 to a data set with the same c-value as the original data set, and sets of ees and eep values according to the calculated E and K values.
Biocatalysis experiments To illustrate the use of the programme, we have chosen reversible transesterification with lipase B from Candida antartica as catalyst. The substrate, 1-phenoxy-2-propanol, was selected as a continuation of earlier work 5 and on basis of molecular m o d e l l i n g of s u b s t r a t e / l i p a s e interactions. 6 The reaction with 2chloroethyl butanoate as acyl donor showed reversibility, and was therefore well suited as a model reaction.
HOH O Ph O - . . ~ C H 3 + . , , , " ~ O
~C
H OCOC3H 7 H OH PhO.~c H3 + PhO,~c H3 R S
I
The absolute configurations of the products were established by comparison with (S)-Ip h e n o x y - 2 - p r o p a n o l which has been described p r e v i o u s l y . 7 T h e (R)-enantiomer was produced in a hydrolysis of the butanoate also catalysed by lipase B.
I O0 80
4o
20 0
I
0
20
40
60
80
I
I
I
I O0
Conversion, % Figure 1. Effect of variation of solvent in transesterification of 1phenoxy-2-propanol with 2-chloroethyl butanoate (5x excess). Circles toluene, squares hexane, filled symbols p r o d u c t fraction, open symbols remaining substrate fraction.
Enantiomer ratio in biocatalytic resolutions
3019
When the resolution was performed in two different solvents, hexane and toluene, the Kvalues were virtually the same, 0.29 and 0.31 respectively. However, there was a significant change in the enantioselectivity on going from hexane (E=149) to toluene (E=75.3) (Figure 1). It seems reasonable that the two unpolar solvents do not influence the thermodynamics of the reaction in a different way. The catalytic properties of the enzyme, however, may be altered by different solvents. When the relative molar amount of acyl donor was increased from 1.5 times the amount of substrate, to 3 and finally 5, the K-value naturally increased (Figure 2, Table 1). This just reflects the fact that the equilibrium is shifted towards the product side. The E-value, however, which was virtually constant for the two reactions with the smallest amount of acyl donor, E= 242 and 254 respectively, decreased drastically in the third experiment. We think that a five times excess of acyl donor may change the properties of the enzyme. We are currently investigating this observation.
100 80 60
\
20
)
o
X 0
20
40
Conversion,
i'''
60
80
100
%
Figure 2. Variation of relative concentrations of 2-chloroethyl butanoate in transesterification of 1-phenoxy-2-propanol. Circles 5x excess, squares 3x excess, triangles 1.5x excess. Filled symbols represent product fraction, open symbols remaining substrate fraction.
3020
H.W. ANTHONSENet aL
[Acyldonor] [substrate] 1.5
K
[Acyldonor] 0.066
242 (+47, -36)
0.71 (-+ 0.025)
0.131
254 (+240, -79)
0.44 (+ 0.014)
0.218
149 (+15, -12)
0.29 (+ 0.010)
Table 1. Effect of variation of concentration of acyl donor in transesterification. The solvent used was hexane, and the acyl donor 2-chloroethyl butanoate. Figures in parenthesis is standard deviation assuming +2% inaccuracy in measurements of GLC integrals.
It is well known that the amount of water in the organic solvent, best expressed as the water activity (aw), may influence the reaction. The water activity may easily be altered and kept at a constant level by introducing pairs of inorganic hydrate salts into the reaction vessel. 8 It has been reported that the water activity both influences the enantioselectivity 9 and that it does not. 10 For the present system we have monitored the reaction at three different levels of aw and we observe an increase of both E and K with increasing water activity. (Figure 3, Table 2)
1 O0 80 60
40
\
zo
0 0
20
40 60 Conversion, %
I''' 80
1 O0
Figure 3. Variation of water activity (aw) in hexane in transesterification
of 1-phenoxy-2-propanol with 2-chloroethyl butanoate (5x excess). Circles aw=0, squares aw=0.16, triangles aw=0.61. Filled symbols represent product fraction, open symbols remaining substrate fraction.
Enantiomer ratio in biocatalytic resolutions
aw 0 0.16 0.61
E 149 (+15, -12) 258 (+37, -27) 418 (+141, -90)
3021
K 0.29 (+ 0.010) 0.35 (+ 0.0087 0.69 (+ 0.010)
Table 2. V a r i a t i o n of w a t e r a c t i v i t y ( a w ) in h e x a n e in transesterification of 1 - p h e n o x y - 2 - p r o p a n o l w i t h 2-chloroethyl b u t a n o a t e (5x excess). F i g u r e s in p a r e n t h e s i s is s t a n d a r d d e v i a t i o n a s s u m i n g +2% inaccuracy in m e a s u r e m e n t s of GLC integrals. W h e n the w a t e r activity of the reaction m e d i u m increases, water will serve as a competing nucleophile and the reverse reaction will be m o r e favoured leading to an increasing K. It is very interesting to notice that the enantioselectivity also increases, however, the usefulness of o p e r a t i n g at an elevated water activity in order to obtain a high E-value is doubtful since K also increases. C o n c e r n i n g the e r r o r e s t i m a t i o n s , the E-value, as e x p e c t e d , d i d n o t s h o w G a u s s i a n distribution. The error values in Tables 1 and 2 represent a region covering 37% of the data counting in both directions of the calculated E. There is no evidence that K was not showing a Gaussian distribution, and errors in K are given as one s t a n d a r d deviation.
ACKNOWLEDGEMENT We are grateful to Dr. Martin Barfoed, N o v o - N o r d i s k , Bagsvaerd, DK for gift of enzymes.
EXPERIMENTAL General. Chiral analyses were p e r f o r m e d using a Varian 3400 gas c h r o m a t o g r a p h with a CPChiracil-DEX-CB from C h r o m p a c k . Lipase B (EC 3.1.1.3) from Candida antarctica (SP 435) N o v o - N o r d i s k , i m m o b i l i s e d on Lewatit, h a d specific activity of 19000 P L U / g . NMR spectra of 1-phenoxy-2-propanol and its butanoate conformed with their structures. 7
Transesterification. To solvent (3 mL), was a d d e d 1-phenoxy-2-propanol (0.131 mmol), and 2-chloroethyl butanoate (for a m o u n t see Tables 1 and 2). The reaction was started b y a d d i n g the lipase (20 mg) to the reaction mixture. The reactions w e r e p e r f o r m e d in a shaker incubator at 30 °C. The s a m p l e s w e r e filtrated to r e m o v e the i m m o b i l i s e d e n z y m e before analysis. The s u b s t r a t e alcohol a n d p r o d u c t ester w e r e b o t h a n a l y s e d directly on GLC w i t h o u t d e r i v a t i s a t i o n in the same run. Retention times for 1-phenoxy-2-propanol were 23 - 24 rain. and for the butanoates 39 - 40 min., temp. prog. 100 - 142 oC, l O / m i n . At various intervals ees and eep were d e t e r m i n e d and c was calculated from these as s h o w n above. In the experiments with v a r y i n g water activity a total of 0.4 g of salt h y d r a t e was used for each
H.W. ANTHONSENet al.
3022
experiment,
aw = 0.16 was obtained using equimolar amounts of N a 2 H P O 4 . 2 H 2 0 +
Na2HPO4-0H20 and for aw = 0.61 was used Na2HPO4.7H20 + Na2HPO4-2H20.
(R)-l-phenoxy-2-propanol was isolated by column c h r o m a t o g r a p h y after hydrolysis of racemic butanoate (2.5g) in phosphate buffer (100 mL) at pH 7.2 using lipase B (50mg), yield 0. 45g), [a] 22 = + 2.8 (c 1.8 EtOH). (For (S)-enantiomer see ref. 7)
The programme for calculation of E and K was written in ANSI C++ and compiled for the P o w e r M a c i n t o s h type of c o m p u t e r s by means of the C o d e W a r r i o r gold academic p r o g r a m m i n g environment, version 6. A copy of the program is available on request (E-mail: Thorleif.Anthonsen @avh.unit.no). Values of K and E that describe a given (c, ees) and (c, eep) data set were calculated by the minimisation of a penalty function. The penalty function was dependent on the root mean square error between experimental points and points calculated on the basis of given K and E values and also dependent on the values of K, E and c in order to keep the value of these parameters in their allowed region. The initial starting triangle was always at ((E,K)) (1.1, 0.0), (20.1, 0.0) and (1.1, 1.0), but it was not critical for the result. The minimisation gave K and E values which were used as input to another program that generated the (c, ees, eep) curves. Calculation of ees and eep values given K, E and c was done by minimisation of equations 1 and 2. Visualisation Kaleidagraph TM 3.0.
and d r a w i n g
of the curves was p e r f o r m e d
by
REFERENCES
1 2. 3. 4. 5.
Chen, C. S.; Fujimoto, Y.; Girdaukas, G.; Sih, C. J. J. Am. Chem. Soc., 1982, 104, 7294 7299. Chen, C.-S.; Wu, S.-H.; Girdaukas, G.; Sih, C. J. J. Am. Chem. Soc., 1987, 109, 2812-2817. van Tol, J. B. A. Doctoral Thesis, 1994, Delft University of Technology, Delft, The Netherlands, p. 32. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B.P. Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 1992. Hansen, T. V.; Waagen, V.; Partali, V.; Anthonsen, H. W.; Anthonsen, T. Tetrahedron:
Asymmetry, 1995, 6, 499 -504. 6.
Uppenberg, J.; Ohrner, N.; Norin, M.; Hult, K.; Patkar, S.; Waagen, V.; Anthonsen, T.; Alwyn Jones, T.; Abstract EU Bridge-T Lipase Meeting, Isle de Bendor, France, 1994.
7.
Waagen, V.; Partali, V.; Hollingsa~ter, I.; Soon Huang, M. S.; Anthonsen, T. Acta Chem. Scand., 1994, 48, 506 - 510. Kvittingen, L.; Sjursnes, B. J.; Anthonsen, T.; Halling, P. J. Tetrahedron, 1992, 48, 2793 - 2802. H6gberg, H.-E.; Edlund, H.; Berglund, P.; Hedenst6m, E. Tetrahedron: Asymmetry, 1993,
8. 9.
4, 2123 - 2126. 10. Bovara, R.; Carrea, G.; Ottolina, G.; Riva, S. Biotechnol. Lett., 1993, 15, 169 - 174.
(Received in UK 14 September 1995)