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Theoretical Prediction and Experimental Verification of ee s Versus Time in Biocatalytic Resolution and its Application in a Bioresolution-inversion Process

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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 de-veloped 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.
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*Corresponding author: xuyi@sit.edu.cn
1 INTRODUCTION
Preparation methods of optically active compounds
are classified into two broad categories: the optical
resolution of racemic compounds and the asymmetri-
zation of prochiral compounds. Biocatalysts are wide-
ly used in both cases. When the starting material is a
racemic mixture, the most popular enzymatic ap-
proach 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 ma-
terial (or product) has the wrong absolute configura-
tion 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 cen-
tre of the substrate (or product) after a biocatalytic res-
olution. For example, the lipase/Mitsunobu process of
secondary alcohol
[1-11]
or an acid hydrolysis/inversion
of the remaining epoxide in the epoxide hydro-
lase-catalysed enantiomeric hydrolysis of epoxide
[12-18]
.
By these methods, one can obtain the chiral compounds
with high optical purity at 100% theoretical yield. Alt-
hough pioneer works had been made before1 or 10, the
derivations were incomplete. In the following paragraph,
a complete derivation was made. Moreover, the possi-
bility for predicting the time (t
max
) which is needed to
reach the maximum enantiomeric excess of the final
product (ee
f
) was firstly explored.
2 EXPERIMENT
2.1 Generalization
All the chemicals and reagent were commercially
obtained and of analytical grade.
2.2 Enantioselective hydrolysis of 3-(2-nitrophenoxy)
propylene oxide (1a) by Trichosporon loubierii
ECU1040
Lyophilized yeast cells (3 g) were rehydrated in so-
dium 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/ isopropa-
nol (90/10, v/v) at a flow rate of 1.0 ml/min and de-
tected at 254 nm.
2.3 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 7.5 by Tris-HCl buffer). The reactions were carried
out at 30
o
C and 160 rpm in 100 ml flasks equipped
Theoretical Prediction and Experimental Verification of ee
s
Versus Time
in Biocatalytic Resolution and ts Application in a Bioresolution-
inversion Process
Yi Xu* & Dan Zhou
School of Chemical and Environmental Engineering, Shanghai Institute of Technology, Shanghai, China
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 interrela-
tionships among ee
f(max)
, conv.
(max)
, ee
p(max)
and ee
s(max)
were deduced. Furthermore, a simple equation was de-
veloped 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 resolu-
tion-inversion was developed.
Keywords: theoretical prediction; bioresolution-inversion; epoxide hydrolase; lipase
DOI: 10.1051/
C
Owned by the authors, published by EDP Sciences, 2015
/
00 ( 2015)
201conf
Web of Conferences
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MATEC Web of Conferences
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.
2.4 Enzymatic transesterification of (R,
S)-4-hydroxy-3-methyl-2-(2-propenyl)-2-cyclope
nten-1-one) [HMPC] with vinyl acetate catalyzed
by Lipase PS
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 tem-
perature, 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.
3 DERIVATION OF EQUATIONS
3.1 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 biocat-
alytic kinetic resolution-inversion process, supposing
that no racemization occurred in the whole course, we
can obtain equations 1~5
[19]
:
0
0
ln
ln
B
B
A
A
E
(1)
AB
AB
ee
s
(2)
QP
QP
ee
p
(3)
ps
s
eeee
ee
BA
QP
C
00
(4)
ps
ps
f
eeee
eeee
AQPB
AQPB
ee
2
)(
)()(
(5)
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
x
B
B
0
(6)
Then,
E
x
A
A
0
(7)
By substituting equations (6) and (7) into equations
2~5, we can obtain as follows:
22
1
E
xxC
(8)
E
E
s
xx
xx
ee
(9)
E
E
p
xx
xx
ee
2
(10)
E
f
xxee
(11)
Figure 1. Graphic plots of Conv. versus ee
f
at different
E-values
Figure 2. Graphic plots of ee
s
versus ee
f
at different E-values
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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.
Figure 3. Graphic plots of ee
p
versus ee
f
at different E-values
It is obvious that if
0
'
xf
ee
,
That is:

)1(
1
1
E
E
x
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:
 
)1()1(
1
(max)
11
E
E
E
f
EE
ee
(12)
 
2
11
1.
)1()1(
1
(max )
E
E
E
EE
Conv
(13)
 
 
)1()1(
1
)1()1(
1
(max )
11
2
11
E
E
E
E
E
E
p
EE
EE
ee
(14)
 
 
1
1
11
11
)1()1(
1
)1()1(
1
(max )
E
E
EE
EE
ee
E
E
E
E
E
E
s
(15)
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):
 
)1()1(
1
(max )
11
E
E
E
f
EE
yee
(16)
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.
Figure 4. Theoretical plots of ee
f (max)
, ee
s(max)
, ee
p(max)
and
conv
(max)
as a function of E according to equations (12) - (15)
Now, a question arises. How to predict the time for
the reaction to stop at appropriate moment to reach
ee
f(max)
?
3.2 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:
0
0
ln
ln
B
B
A
A
E
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:
02003-p.3
MATEC Web of Conferences
E
kt
kt
B
B
A
A
0
0
ln
ln
(17)
Then the equation 17 can be derived to:
)exp(
0
ktAA
(18)
)exp(
0
E
kt
BB
(19)
It is at a low initial substrate concentration accord-
ing to Lu’s derivation and Michaelis-Menten equation
(if the substrate concentration is low enough and rela-
tive to Km, the reaction is the first order). Here, A
0
and B
0
are initial concentrations of the fast- and slow-
reacting 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:
AB
AB
ee
s
By substituting equation 18 and equation 19 into
equation 2, we can write as follows:
s
e
s
e
ee
t
E
k
A
B
1
1
ln)
1
1()ln(
(20)
Considering that both k and E are constants, we can
acquire as follows:
2
2
21
1
1
1
1
ln
1
1
1
ln
1
s
e
s
s
e
s
e
ee
te
ee
t
(21)
ee
s1
and ee
s2
are respectively ee
s
values at t
1
and t
2
.
Equation 21 can be written as follows:
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
t
t
s
s
t
t
s
s
s
ee
ee
ee
ee
ee
(22)
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:
1
1
1(max )
1
1
ln
ln
s
e
s
e
ee
E
tt
(23)
If one knows 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 bio-
catalytic kinetic resolution experiments.
It can be seen from Figure 5 that for the first exam-
ple, , 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 Tricho-
sporon 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.
Figure 5 Variation of ee
s
in the resolution of racemic 1 by
lyophilized cells of Trichosporn loubierii ECU1040 (100
g/L). Symbols: Ƶ Measured; ũű Calculated with the
ee
s
at t = 30 min (10 mM) and 60 min (10 mM), respectively.
The second example is related to enzymatic resolu-
tion of MPGM. (2R, 3S)-MPGM, a very important
intermediate in the synthesis of Diltiazem Hydrochlo-
ride, can be prepared according to enantioselective
hydrolysis of the racemic MPGM catalyzed by Serra-
tia 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
98%) to
get both high optical purity and high yield of the
MPGM.
02003-p.4
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Figure 6. Variation of ee
s
in the resolution of racemic MPGM
by by Serratia sp. lipase. Symbols: Ƶ Measured; ũ
Calculated with the ee
s
at t = 1.5 h.
Chiral HMPG and its ester are very important agri-
cultural 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 in-
version.
Figure 7. Time course of ee
s
value in transesterification of (R,
S)-HMPC with vinyl acetate catalyzed by Lipase PS. Ʒ
Measured; ũCalculated with the ee
s
at t = 3 h.
5 CONCLUSIONS
A systematic theoretical derivation of bioresolu-
tion-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 in-
terrelationships 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 equa-
tion 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.
ACKNOWLEDGEMENT
This work was supported by the Shanghai Committee
of Science and Technology (No. 13430503400), the
Science Foundation of Shanghai Institute of Technol-
ogy (YJ2010-04, YJ2011-54), the Scientific Research
Foundation for the Returned Overseas Chinese Schol-
ars, State Education Ministry (No. ZX2012-05) and
the Innovation Program of Shanghai Municipal Edu-
cation Commission (No. 11YZ227).
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