Theoretical Prediction and Experimental Verification of ees Versus Time in Biocatalytic Resolution and ts Application in a Bioresolution-inversion Process

A systematic theoretical derivation of bioresolution-inversion process was made. An equation was derived between the maximum ee value of final product (eef(max)) and enantiomeric ratio (E) of a reaction. The corresponding equations of conv.(max), eep(max), ees(max) versus E-value were also derivative and the interrelationships among eef(max), conv.(max), eep(max) and ees(max) were deduced. Furthermore, a simple equation was developed to predict the enantiomeric excess of substrate (ees) at any other time of the whole reaction course based on the ees value which was determined at a certain reaction time. This equation of ees versus time was verified by three different experiments. Based on the equation of ees versus time, a new equation for predicting the time (t(max)) needed to reach the maximum enantiomeric excess of the final product (eef (max)) after the resolution-inversion was developed.


INTRODUCTION
Preparation methods of optically active compounds are classified into two broad categories: the optical resolution of racemic compounds and the asymmetrization of prochiral compounds.Biocatalysts are widely used in both cases.When the starting material is a racemic mixture, the most popular enzymatic approach to obtaining the optically active compounds is kinetic resolution.However, the maximum theoretical yield is limited to 50% and the tedious procedures for the separation of the recovered starting material and the product are inevitable and half of the starting material (or product) has the wrong absolute configuration for certain purposes.
To overcome these drawbacks, several methods have been offered, such as the dynamic kinetic resolution.Another method is the inversion of the stereogenic centre of the substrate (or product) after a biocatalytic resolution.For example, the lipase/Mitsunobu process of secondary alcohol [1][2][3][4][5][6][7][8][9][10][11] or an acid hydrolysis/inversion of the remaining epoxide in the epoxide hydrolase-catalysed enantiomeric hydrolysis of epoxide [12][13][14][15][16][17][18] .By these methods, one can obtain the chiral compounds with high optical purity at 100% theoretical yield.Although pioneer works had been made before1 or 10, the derivations were incomplete.In the following paragraph, a complete derivation was made.Moreover, the possibility for predicting the time (t max ) which is needed to reach the maximum enantiomeric excess of the final product (ee f ) was firstly explored.

Generalization
All the chemicals and reagent were commercially obtained and of analytical grade.

Enantioselective hydrolysis of 3-(2-nitrophenoxy) propylene oxide (1a) by Trichosporon loubierii ECU1040
Lyophilized yeast cells (3 g) were rehydrated in sodium phosphate buffer (90 ml, 100 mm, pH 7.0) for 30 min on a shaker (160 rpm, 30 o C).Then 10 ml DMSO containing 500 mg of the substrate was added and the mixture was agitated at 30 o C. Samples were taken at different time.The ee value of epoxide was directly determined by HPLC analysis through using Chiralcel OD column.The mobile phase was hexane/ isopropanol (90/10, v/v) at a flow rate of 1.0 ml/min and detected at 254 nm.

Enantioselective hydrolysis of trans-3-(4-methoxyphenyl)glycidic acid methyl ester (MPGM) by Serratia sp. lipase
Experiments were performed through using a substrate concentration of 50 mm in 10 ml toluene solution and 10 ml culture supernatant (the pH value was adjusted to 7.

Jianbo Chen
College of Life and Environment Science, Shanghai Normal University, Shanghai, China ABSTRACT: A systematic theoretical derivation of bioresolution-inversion process was made.An equation was derived between the maximum ee value of final product (ee f(max) ) and enantiomeric ratio (E) of a reaction.The corresponding equations of conv.(max) , ee p(max) , ee s(max ) versus E-value were also derivative and the interrelationships among ee f(max) , conv.(max) , ee p(max) and ee s(max) were deduced.Furthermore, a simple equation was developed to predict the enantiomeric excess of substrate (ee s ) at any other time of the whole reaction course based on the ee s value which was determined at a certain reaction time.This equation of ee s versus time was verified by three different experiments.Based on the equation of ee s versus time, a new equation for predicting the time (t (max) ) needed to reach the maximum enantiomeric excess of the final product (ee f (max) ) after the resolution-inversion was developed.with tight plugs.Samples were taken at different time for the determination of ee value of MPGM.The ee value was determined by HPLC with a chiral column (Chiralcel OJ, 25×4.6 cm, Daicel Chemical Industries, Tokyo, Japan) and elution by hexane/isopropanol (60: 40, v/v; 0.8 ml/min) and detection at 254 nm.The retention time was respectively 13.5 and 15.7 min for (2S, 3R)-MPGM and (2R, 3S)-MPGM.

Derivation of equations for resolution-inversion process
If we define the enantiomeric excess of the final product (after the biocatalytic resolution and inversion) as ee f , the value of ee f would be directly dependent upon the conversion ratio and the enantioselectivity of biocatalyst, E-value.For a simple irreversible biocatalytic kinetic resolution-inversion process, supposing that no racemization occurred in the whole course, we can obtain equations 1~5 [19] : In this equation, A and B refer to the fast-and slow-reacting enantiomers of the substrate; P and Q refer to the corresponding enantiomers of the product; ee s and ee p are respectively the enatiomeric excess of the substrate and the product; E is the enantiomeric ratio.
If we define By substituting equations ( 6) and ( 7) into equations 2~5, we can obtain as follows: By combination of equations 8~11, we can get plots of C versus ee f (Figure 1), ee s versus ee f (Figure 2) and ee p versus ee f (Figure 3).From Figures 1~3, we can see that there is a maximum ee f value (ee f(max) ) for a fix 'E' and the ee f(max) varies with the change of E-value.
One can get the maximal ee f value: ee f (max) and the corresponding conv., ee p , ee s are defined as conv.(max), ee p (max), ee s (max).By substituting the x value into equations 8~11, we can get the following equations: From equations 12~15, we can clearly know the maximum ee f and corresponding conv., ee p and ee s .
For example, if E-value equals 200, we can get the maximum ee f value 96.9% at 51.1% conversion or at 94.9% ee p or at 99.0% ee s .In practical process, the chemical inversion (y) is not always 100%, perhaps 90% or others in some cases.Considering the above mentioned condition, some modifications should be made for an incompletely chemical inversion.In fact, only equation 12 should be changed to equation 16 and others are kept unchanged (y is the efficiency of chemical inversion): Figure 4 shows the curves of ee f(max) , ee s(max) , ee p(max) and Conv.(max) vs. E.It is interesting to see that the ee f(max ) value is always larger than ee s(max) value, but smaller than ee p(max) value.Now, a question arises.How to predict the time for the reaction to stop at appropriate moment to reach ee f(max) ?

Prediction of the time-dependant changes in enantiomeric excess of substrate (ee s ~ t)
According to Chen et al. [20] and Lu et al. [21] , for a simple irreversible kinetic resolution, the E-value is shown as follows: This indicates that the distinction between two competing enantiomers (A and B) by an enzyme is equal to a constant E. Equation 1 can be re-written as follows: Then the equation 17 can be derived to: It is at a low initial substrate concentration according to Lu's derivation and Michaelis-Menten equation (if the substrate concentration is low enough and relative to Km, the reaction is the first order).Here, A 0 and B 0 are initial concentrations of the fast-and slowreacting enantiomers, k is the rate constant for the fast-reacting enantiomer.For the kinetic resolution of a racemate (A 0 =B 0 =0.5S 0 ), it is known that: By substituting equation 18 and equation 19 into equation 2, we can write as follows: Considering that both k and E are constants, we can acquire as follows: ee s1 and ee s2 are respectively ee s values at t 1 and t 2 .Equation 21 can be written as follows: It can be concluded from equation 22 that if we know ee s1 at t 1 , then we can theoretically predict the ee s value at another time (t 2 ) in the same reaction mixture.
By substituting equation 15 into equation 22, we can get: It can be seen from Figure 5 that for the first example, , both of the theoretical curves (the curves were respectively plotted according to equation 22 and ee s values at 30 min and 60 min) fit the experimental data quite well in the resolution of 3-(2-nitrophenoxy) propylene oxide by epoxide hydrolase of Trichosporon loubierii ECU1040 [22].This enables one to stop the reaction at a proper time (e.g.ee s > 98%) to get both high optical purity and high yield of the epoxide.And this will also simplify the work of measurement.The second example is related to enzymatic resolution of MPGM.(2R, 3S)-MPGM, a very important intermediate in the synthesis of Diltiazem Hydrochloride, can be prepared according to enantioselective hydrolysis of the racemic MPGM catalyzed by Serratia sp.Lipase [23] .So it is necessary to stop the reaction when the ee s value was enough high so that we can get (2R, 3S)-MPGM at both high yield and optical purity.It can be seen from Figure 6 that the theoretical curves fit the experimental data quite well.This enables one to stop the reaction at a proper time (e.g.ee s t 98%) to get both high optical purity and high yield of the MPGM.Chiral HMPG and its ester are very important agricultural intermediates.Figure 7 showed the time course of ee s value in transesterification of (R, S)-HMPC with vinyl acetate which is catalyzed by the Lipase PS.The theoretical curve was plotted based on equation 22 and the ee s at 3h.The theoretical curves fit the experimental data quite well.The t (max) value can be also calcultated from equation 23.This enables one to stop the reaction at a suitable time to obtain high ee value and yield of the substrate ((S)-HMPC) and product ((R)-HMPC acetate).And the highest yield and ee value of final product ((R)-HMPC acetate) can be obtained after the bioresolution/chemical inversion.Calculated with the ees at t = 3 h.

CONCLUSIONS
A systematic theoretical derivation of bioresolution-inversion process was made.An equation was derived between the ee f(max) and E-value of a reaction.The corresponding equations of conv.(max) , ee p(max) , ee s(max) versus E-value were also derived and the interrelationships among ee f(max) , conv.(max) , ee p(max) and ee s(max) were deduced.Furthermore, a simple equation was developed to predict the enantiomeric excess of substrate (ee s ) at any other time of the whole reaction course based on the ee s value which was determined at a certain reaction time.This equation of ee s versus time was verified by three different experiments.
Based on the equation of ee s versus time, a new equation for predicting the time (t (max) ) needed to reach the maximum enantiomeric excess of the final product (ee f (max) ) after the resolution-inversion which was developed.The current work will be beneficial to the biocatalytic resolution-inversion study.
Keywords: theoretical prediction; bioresolution-inversion; epoxide hydrolase; lipase DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, 2015 50 mm (R, S)-HMPC dissolved in vinyl acetate was added to the lipase PS, and the reaction was conducted at 30 o C, 160 rpm.Samples were taken at different time for the determination of ee value HMPC.The enantiomeric excess of substrate (ee s ) and product (ee p ) was determined by GLC using β-DEXTM 120 column (oven temperature, 150 o C; injector and detector temperature, 280 •C).The retention time was respectively 15.4, 16.1, 20.6 and 21.2 min for (R)-HMPC acetate, (S)-HMPC acetate, (S)-HMPC and (R)-HMPC.

Figure 1 .Figure 2 .
Figure 1.Graphic plots of Conv.versus eef at different E-values

Figure 3 .
Figure 3. Graphic plots of eep versus eef at different E-values

Figure 4 .
Figure 4. Theoretical plots of eef (max), ees(max), eep(max) and conv(max) as a function of E according to equations (12) -(15) the ee s value at t 1 and the E-value, he can calculate the time which is needed to reach the maximum ee f according to equation 23.4 EXPERIMENTAL VERIFICATION OF TIME-DEPENDANT CHANGES IN ENANTI-OMERIC EXCESS OF SUBSTRATE (EES ~ T)The equation 22 was verified by three different biocatalytic kinetic resolution experiments.

02003-p. 4 EMME 2015 Figure 6 .
Figure 6.Variation of ees in the resolution of racemic MPGM by by Serratia sp.lipase.Symbols:Measured; Calculated with the ees at t = 1.5 h.

Figure 7 .
Figure 7. Time course of ees value in transesterification of (R, S)-HMPC with vinyl acetate catalyzed by Lipase PS.Measured;Calculated with the ees at t = 3 h.