A new mathematical method for determining the enantiomeric ratio in lipase-catalyzed reactions

Article abstract of DOI:10.1016/j.molcatb.2010.01.019

We present a new mathematical method for determining the enantiomeric ratio (E) during lipase-catalyzed kinetic resolutions. The method involves the fitting of a model to profiles of adimensionalized concentrations of the two enantiomers of the chiral substrate, plotted against degree of conversion. The model equations are presented for a reversible reaction involving bi-bi ping-pong kinetics in which the chiral substrate enters second and the chiral product leaves second. However, it is also shown that the method is easy to modify for analysis of resolutions involving other chiral substrate-product pairs and of resolutions in which the behavior of the system can be approximated by irreversible uni-uni kinetics. We show that our method retains several advantageous features of existing methods that help to ensure accuracy.

Full text of DOI:10.1016/j.molcatb.2010.01.019

Journal of Molecular Catalysis B: Enzymatic 64 (2010) 23–28
Contents lists available at ScienceDirect
Journal of Molecular Catalysis B: Enzymatic
journal homepage: www.elsevier.com/locate/molcatb
A new mathematical method for determining the enantiomeric ratio in
lipase-catalyzed reactions
David Alexander Mitchella,∗, Vivian Rotuno Mourea, Francisco de Assis Marquesb, Nadia Kriegerb
a Departamento de Bioquímica e Biologia Molecular, Universidade Federal do Paraná, Curitiba, Paraná, Brazil
b Departamento de Química, Universidade Federal do Paraná, Curitiba, Paraná, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history:
We present a new mathematical method for determining the enantiomeric ratio (E) during lipase-
catalyzed kinetic resolutions. The method involves the fitting of a model to profiles of adimensionalized
concentrations of the two enantiomers of the chiral substrate, plotted against degree of conversion. The
model equations are presented for a reversible reaction involving bi-bi ping-pong kinetics in which the
chiral substrate enters second and the chiral product leaves second. However, it is also shown that the
method is easy to modify for analysis of resolutions involving other chiral substrate-product pairs and
of resolutions in which the behavior of the system can be approximated by irreversible uni-uni kinetics.
We show that our method retains several advantageous features of existing methods that help to ensure
accuracy.
Received 26 September 2009
Received in revised form 22 January 2010
Accepted 23 January 2010
Available online 1 February 2010
Keywords:
Enantiomeric ratio
Lipase
Kinetic resolution
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
vary, depending on the reaction mechanism and on which of the
substrates is chiral.
The production of single enantiomers from racemates of chi-
ral intermediates is becoming of increasing importance in the
production of chiral agrochemicals and pharmaceuticals [1]. In
the pharmaceutical industry, enantiopure chiral drugs constitute
approximately 36% of the overall market [2,3]. At the turn of the
millennium, the size of the market for these drugs was increas-
ing by approximately 30% per year, with an estimated value of US
$151.9 billion in 2002 [4,5].
A kinetic resolution will be most successful, in terms of the enan-
tiomeric purity of the desired enantiomer (i.e. either a high ees or
a high eep), when the value of E is either much greater or much
smaller than unity. In order to screen enzymes for the purpose of
choosing the best one for the resolution of a particular racemate, it
is therefore necessary to have a reliable and easy to use method for
determining the value of E that each enzyme has for reaction with
the racemate.
One of the most commonly used methods for producing pure
enantiomers from racemates is enzymatic kinetic resolution. The
preference that an enzyme has for reacting with one enantiomer
over the other in this process is expressed by the enantiomeric
ratio E, which, for a uni-uni reaction (i.e. S → P), is defined by the
following ratio of specificity constants:
Lipases are very commonly used in enzymatic kinetic resolu-
tions, since they are able to catalyze various reactions with a range
of different types of substrates and, importantly, they often have
high preference for reacting with one of the enantiomers [6,7].
The aim of the current work is to demonstrate a new mathemat-
ical method for the determination of E in lipase-catalyzed kinetic
resolutions.
kSR
kSS
kcRat/KMR
kcSat/KMS
E =
=
(1)
2. Materials and methods
For reactions that involve more than one substrate, the expres-
sion for E is similar, but the catalytic and saturation constants used
2.1. Case studies and reaction schemes
Lipase-catalyzed reactions occur by the ping-pong bi-bi mech-
anism, which involves a compulsory sequence of binding of
substrates and release of products. The second substrate to enter
and the second product to leave the active site are the chiral species
in both of the reactions used as case studies:
Abbreviations: E, enantiomeric ratio.
∗
Corresponding author at: Department of Biochemistry and Molecular Biology,
Federal University of Paraná, PO Box 19046 Centro Politécnico, Curitiba 81531-980
PR, Brazil. Tel.: +55 41 3361 1536; fax: +55 41 3266 2042.
E-mail addresses: davidmitchell@ufpr.br (D.A. Mitchell),
vivianmoure@hotmail.com (V.R. Moure), tic@quimica.ufpr.br (F.d.A. Marques),
nkrieger@ufpr.br (N. Krieger).
first substrate + second substrate → first product
+ second product
(2a)
1381-1177/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.molcatb.2010.01.019

24
D.A. Mitchell et al. / Journal of Molecular Catalysis B: Enzymatic 64 (2010) 23–28
Table 1
Model equations.
vinyl acetate + (R, S)-alcohol → acetaldehyde
+ (R, S)-alcohol acetate
(2b)
Description and equation
Eq. no.
(5)
Adimensionalized concentrationsa
R
S
]
[S
]
[S
[A]
[N]
SR
=
; SS
=
; A =
; N =
2-chloroethyl butyrate + (R, S)-1-phenoxypropan-2-ol
R
S
R
S
R
S
R
S
]
o
[S
]
+[S
]
[S
]
+[S
]
[S
]
+[S
]
[S
]
+[S
o
o
o
o
o
o
o
Relative fractions of enantiomers
→ 2-chloroethanol + (R, S)-1-phenoxypropan-2-yl butyrate
(2c)
S
R
S
R
S
S
P
P
S
FSS
=
R ; FR
=
R ; FS
=
R ; FR
=
(6)
S
S
S
R
S
P
P
S
+S
S
+S
P
+P
P
+P
Stoichiometric relationships between substrate and product
enantiomers
SR + PR = SoR; SS + PS = SoS
(7)
(8)
For this case, it is possible to show that the enantiomeric ratio is
given by an expression analogous to Eq. (1), where kcat is considered
for the forward direction of Eqs. (2a)–(2c) and KM is the saturation
constant for the chiral substrate.
Two reaction schemes are considered: the irreversible uni-uni
case and the reversible bi-bi ping-pong case where the second sub-
strate to enter and the second product to leave are chiral. In this
paper the chiral substrate and the chiral product will always be rep-
resented as S and P, respectively, with the appropriate superscript
to identify the enantiomer (either R or S). Non-chiral substrates
and products will be represented by letters without superscripts.
Using this notation, the irreversible uni-uni reaction scheme can be
written as:
Zero-time adimensionalized concentrations of the two enantiomers
SoS = SoR = 0.5
Adimensionalized concentrations as a function of measured relative
fractions
ꢀ
ꢀ
ꢁ ꢀ
ꢁꢁ
ꢀ ꢁ
S
S
R
P
S
S
S
R
F
F
F
F
SS = 0.5 1 − 1 −
/
1 −
·
; SR = SS
(9)
S
R
R
S
S
F
F
F
F
S
P
S
Degree of conversion
ꢀ = 1 − (SR + SS)
(10)
Differential equations for irreversible uni-uni scheme
R
R
S
S
dS
dꢀ
E.S
R
dS
dꢀ
S
R
= −
;
= −
(11)
(12)
(13)
S
S
E.S +S
E.S +S
General form of differential equations for reversible bi-bi ping-pong
scheme
R
R
S
S
r
+r
dS
dꢀ
r
dS
dꢀ
= −
;
= −
r
R
S
R
S
r
+r
SR → PR
SS → PS
(3a)
(3b)
Identities of reaction rates in Eq. (12) for the reaction shown in Eqs.
(4a)–(4c)
ꢂ
ꢃ
ꢂ
ꢃ
S
S
P
˛
E.N
S
rR = SR E.A +
− PR
− PS
+
;
R
R
K
˛
R
EQ
ꢂ
ꢃ
ꢂ
ꢃ
R
P
N
S
rS = SS A +
+
˛
while the scheme for each of the reactions presented in Eq. (2) can
be represented as a set of three reactions:
R
R
K
˛
EQ
Expressions, in terms of SR and SS, for other variables that appear in
Eq. (13)
A + SR ↔ N + PR
A + SS ↔ N + PS
PR + SS ↔ SR + PS
(4a)
(4b)
(4c)
A = AO − (1 − SR − SS); N = 1 − SR − SS; PR = 0.5 − SR; PS = 0.5 − SS
(14)
(15)
Objective function for curve fittingb
n
n
ꢄ
ꢄ
2
2
SSR =
(SeRi − SpRi
)
+
(SeSi − SpSi
)
i=1
i=1
The reaction described by Eq. (4c) is not desirable, but may occur.
a
Zero-time concentrations are indicated by the subscript “o”.
b
The subscript “ei” represents the ith experimental data point and the subscript
2.2. Mathematical method
“pi” represents the corresponding model prediction.
The model is based on Eqs. (5)–(14), which are presented in
Table 1. Eq. (5) defines the adimensionalized concentrations used
in the model. The data obtained experimentally are the fractions
of the two enantiomers of the chiral substrate (denoted as FSS and
FSR) and the relative fractions of the two enantiomers of the chi-
ral product (denoted as FPS and FPR), which are defined by Eq. (6).
The adimensionalized concentrations of the substrate and product
enantiomers are related, according to the stoichiometry of the reac-
tion, by Eq. (7). It is assumed that the original substrate mixture is
racemic and there is no product at time zero. In this case, the zero-
time adimensionalized concentrations of the two enantiomers (SoS
and SoR) are given by Eq. (8). Eqs. (6)–(8) can be used to derive Eq.
(9), which expresses SS and SR in terms of the originally measured
relative fractions of the enantiomers.
given by Eq. (14). After substitution of Eqs. (13) and (14) into Eq.
(12), the final differential equation set for the reversible bi-bi ping-
pong case contains two dependent variables, SR and SS, and three
parameters, the enantiomeric ratio (E), the equilibrium constant for
the reaction (Keq) and the selectivity factor ˛R.
For given values of parameters (either E alone or E, Keq and
˛R), the FORTRAN subroutine DRKGS [11], which uses a 4th order
Runge-Kutta algorithm with automatic step size adjustment, was
used to integrate the equation set (either Eq. (11) or Eq. (12)) to
obtain values of SR and SS as functions of ꢀ. When parameter esti-
mation was undertaken, the sum of squares of residuals (SSR), given
by Eq. (15) in Table 1, was minimized.
The mathematical analysis is based on a method that can be
applied to any system of sequential and parallel reactions catalyzed
by the same enzyme. The deduction of the equations has been
described in detail previously [8–10]. The equations use the degree
of conversion (ꢀ) as the independent variable; if the starting reac-
tion mixture contains a racemate of the chiral substrate and no
chiral product, the degree of conversion is given by Eq. (10). When
the analysis is applied to the irreversible uni-uni scheme shown in
Eqs. (3a) and (3b), the final equation set is that given by Eq. (11).
On the other hand, when the analysis is applied to the reversible
bi-bi ping-pong scheme shown in Eqs. (4a)–(4c), the final equation
set is given by Eq. (12), where the expressions for the individual
rates are those given by Eq. (13). It is possible to express all other
concentrations that appear in Eq. (13) as functions of SR and SS, as
2.3. Cultivation to produce lipase
Burkholderia cepacia LTEB11 was cultivated in a 125 mL Erlen-
meyer flask containing 50 mL Luria Bertani (LB) Miller broth (NaCl
10 g/L, bacteriological tryptone 10 g/L, yeast extract 5 g/L) at 37 ◦C
and 150 rpm for 8 h. 1 mL of the culture broth was then inoculated
into a 500 mL Erlenmeyer flask containing 150 mL of a medium con-
taining (in g/L): KNO3 3.54, K2HPO4 1.0, MgSO4·7H2O 0.5, NaCl 0.38,
FeSO4·7H2O 0.01, yeast extract 5.0 and 1% (v/v) commercial olive
oil (Gallo brand). After incubation for 72 h at 37◦C and 150 rpm, the
medium was centrifuged at 12,500 × g for 20 min at 4 ◦C.

D.A. Mitchell et al. / Journal of Molecular Catalysis B: Enzymatic 64 (2010) 23–28
25
2.4. Free and immobilized lipase preparations
is not surprising, since the initial concentration of the non-chiral
substrate (vinyl-acetate) was 44-fold greater than the initial con-
centration of the racemate of the secondary allylic alcohol. With
such a large excess of the non-chiral substrate, the reversible bi-bi
equation system described by Eq. (12) is very closely approximated
by the irreversible uni-uni equation system described by Eq. (11)
[17].
To produce ‘free lipase’, the culture supernatant was frozen
and subsequently lyophilized. ‘Immobilized lipase’ was produced
according to [12]. Accurel MP 1000® powder was wetted with
ethanol for 30 min and then washed twice with ethanol–water
(50:50, v/v) and once with water. It was then added to the culture
supernatant in the proportion of 1 g of Accurel for every 25 mg of
protein, determined according to [13], in order to obtain maximal
adsorption [14]. The mixture was left overnight at 25 ◦C at 200 rpm.
The liquid phase was removed by filtration through Qualy® fil-
ter paper, and the solid support was then delipidated: 20 mL of
a solution of chloroform:butanol (9:1) was added per gram of solid
material, the mixture was stirred at 200 rpm for 10 min at 25 ◦C
and the solids were recovered by filtration. This procedure was
repeated until the organic phase separated by filtration did not con-
tain free fatty acids or triglycerides, as determined by thin-layer
chromatography, using hexane:diethyl-ether:acetic acid (7:3:0.1)
as the mobile phase. The immobilized enzyme was then dried in a
desiccator for 16 h at 4 ◦C and stored at 4 ◦C.
3.2. Fit of the model to literature data
The model, represented by Eq. (12), was applied to litera-
ture data [18] for the resolution of (R,S)-1-phenoxypropan-2-ol, as
described by Eq. (2c). This reaction also follows the scheme given
in Eqs. (4a)–(4c). The authors undertook reactions with four dif-
ferent initial adimensionalized concentrations of the non-chiral
acyl donor (Ao = 1.5, 3, 5 and 10). With a single set of parameters,
obtained by fitting all four data sets simultaneously, good fits were
obtained for all profiles (Fig. 2). A notable feature of these graphs
is that SR, after initially decreasing, begins to increase as the reac-
tion nears equilibrium. This occurs because the high values of PR
and SS that occur during the kinetic resolution favor the reaction
described by Eq. (4c). The tendency of this side reaction to occur
depends on the value of ˛R.
2.5. Determination of lipase activity
The pNPP (p-nitrophenyl palmitate, Sigma) method in aque-
ous solution was used [15]. 1 mL of solution A (3 mg of pNPP in
1 mL of 2-propanol) was added to 9.0 mL of solution B (50 mM
pH 7 phosphate buffer, Triton X-100, 0.44%, gum arabic 0.11%,
w/v), dropwise, with intense stirring. For free lipase, 0.9 mL of this
mixture was then transferred to a cuvette and a 0.1 mL sample
containing the enzyme was mixed in. For immobilized lipase, the
reaction was initiated by adding 1 mg of immobilized enzyme to
the 10 mL of reaction medium. The mixture was stirred at 200 rpm,
with samples being removed at intervals. The molar absorptivity
coefficient of p-nitrophenol (pNP) at pH 7.0 was determined as
9.8 × 103 L/(mol cm) at 410 nm. A unit of activity was defined as
the liberation of 1 ␮mol/min of pNP (p-nitrophenol).
4. Discussion
This paper presents a new mathematical method for determin-
ing the enantiomeric ratio (E) from data obtained during a kinetic
resolution. The proposed method has several of the advantages of
the methods reviewed by Straathof and Jongejan [19]. It is also eas-
ier to apply than the method described by Anthonsen et al. [18] for
determining E in reversible bi-bi reactions. In addition, it is readily
adaptable to situations other than those shown in the case studies.
These points are discussed separately below.
4.1. Advantages of the proposed method for determination of E
2.6. Resolution of secondary allylic alcohols
The proposed method shares the advantages of several of the
methods for determining E that were reviewed by Straathof and
Jongejan [19]. Although the methods reviewed were for the deter-
mination of E in uni-uni reactions, the advantages discussed below
apply to both uni-uni and bi-bi reactions.
The first advantage is that, experimentally, it is simply neces-
sary to determine the relative fractions of the two enantiomers of
the chiral substrate (i.e. FSS and FSR) and the relative fractions of the
The reaction medium contained 450 U of pNPP-hydrolyzing
activity, 0.5 mmol of a racemate of the secondary allylic alco-
hol, 22 mmol vinyl-acetate (Acros Organics, Belgium) and 7 mL
of hexane (Vetec, Brazil). The reaction was carried out at 37 ◦C
in an orbital shaker at 180 rpm. The racemates of the secondary
allylic alcohols were obtained by chemical synthesis according to
[16].
two enantiomers of the chiral product (i.e. FPS and FPR). This avoids
the need for quantitative handling of samples and calibration, thus
eliminating a potential source of error [19].
2.7. Determination of relative fractions of enantiomers
Substrates and products were separated on a gas chromato-
graph (Varian model 3800) with a ␤-cyclodextrin chiral column.
Analysis conditions were: 1 ␮L sample, flame ionization detector
at 280 ◦C, carrier gas He at 5.5 mL/min, temperature gradient from
40 to 170 ◦C at 2 ◦C/min. The relative fractions of the enantiomers
(FSS and FSR, FPS and FPR) were calculated from the relative peak areas.
The second advantage is that the proposed method is based
on the removal of multiple samples, taken at various degrees of
conversion. This leads to estimates of E that are statistically more
reliable than those obtained when simple equations, such as the
Chen equation [20], are used with data obtained at a single degree
of conversion. Further, if the multiple data points are collected over
a wide range of ꢀ values, then it is possible to detect systematic devi-
ations between the data profile and the best-fitting curve. Possible
causes of such systematic deviations will be discussed later.
The third advantage is that, since the proposed method is based
on the degree of conversion, it is not affected by interfering phe-
nomena that are common in kinetic resolutions, such as enzyme
deactivation and substrate or product inhibition. Although these
phenomena do slow the reaction, when the degree of conversion is
used as the independent variable, the variables and parameters that
describe their effects cancel out of the equation system [8–10,19].
3. Results
3.1. Fit of the model to experimental data for the resolution of
secondary alcohols
The irreversible uni-uni model represented by Eq. (11) was used
to fit data obtained during the resolution of racemates of several
secondary alcohols, as described by Eq. (2b). Although the reaction
follows the reversible bi-bi ping-pong scheme described by Eqs.
(4a)–(4c), good fits were obtained in all cases (Fig. 1). The good fit

26
D.A. Mitchell et al. / Journal of Molecular Catalysis B: Enzymatic 64 (2010) 23–28
Fig. 1. Experimental results for kinetic resolutions of secondary allylic alcohols. Also shown are the best-fitting model curves and the values of E obtained by the fitting
procedure. The different plots are for the resolution of: (a) (R,S)-1-phenylprop-2-en-1-ol; (b) (R,S)-1-(4-chlorophenyl)prop-2-en-1-ol; (c) (R,S)-1-(3-methoxyphenyl)prop-2-
en-1-ol; and (d) (R,S)-5-methylhex-1-en-3-ol with Burkholderia cepacia lipase immobilized on Accurel and (e) (R,S)-1-phenylprop-2-en-1-ol; and (f) (R,S)-p-chlorophenylprop-
2-en-1-ol with lyophilized free B. cepacia lipase. Key: (᭹) SS; (ꢀ) SR; (—) best-fitting curve.
SS + B ↔ PS + Q
SR + PS ↔ PR + SS
(16b)
(16c)
The fourth advantage of the proposed method is that it is pos-
sible to obtain good estimates from a single experiment involving
a racemate. One method for determining E involves independent
determination of Vmax and KM for experiments undertaken with
pure preparations of each enantiomer, but this method is highly
susceptible to error if the supposedly pure preparations of each
enantiomer are in fact contaminated with traces of the other enan-
tiomer [19].
The reaction described by Eq. (16c) is undesirable, but may
occur.
In this case, the equations for rR and rS will be [17]:
ꢅ
ꢆ
˛R.PS
Keq
PR(E.Q + ˛R.SS)
rR = SR E.B +
−
(17a)
(17b)
Keq
ꢅ
ꢆ
4.2. Flexibility of the proposed method for determining E
˛R.PR
PS(Q + ˛R.SR)
rS = SS B +
−
Keq
Keq
We have demonstrated the proposed method for the reversible
bi-bi ping-pong mechanism in which the chiral substrate enters
second and the chiral product leaves last and also for a situation
in which the simplification of irreversible uni-uni kinetics applies.
It is easy to adapt the equation set for lipase-catalyzed resolutions
involving different chiral substrate-product pairs. In such cases, Eq.
(12) will be used, but the expressions for rR and rS will be different.
When the chiral substrate enters first and the chiral product
leaves first, then the reaction scheme is as follows:
When a chiral substrate enters first and the chiral product leaves
second, then the reaction scheme is as follows:
SR + B ↔ N + PR
SS + B ↔ N + PS
(18a)
(18b)
In this case, the equations for rR and rS will be [17]:
ꢅ
ꢆꢅ
ꢆ
N.PR
Keq
˛SN
Keq
rR = E SR.B −
+ B
(19a)
SR + B ↔ PR + Q
(16a)

D.A. Mitchell et al. / Journal of Molecular Catalysis B: Enzymatic 64 (2010) 23–28
27
Fig. 2. Fit of the reversible bi-bi ping-pong model to the experimental results of Anthonsen et al. [18] for the transesterification of (R,S)-1-phenoxypropan-2-ol using 2-
chloroethyl butyrate as the acyl donor. Four different initial adimensionalized concentrations of chloroethyl butyrate (Ao) were used. They are indicated on the individual
graphs. Key: (᭹) SS; (ꢀ) SR; (—) best-fitting curves, corresponding to E = 174, Keq = 0.319 and ˛R = 98.1, obtained by simultaneously fitting all four data sets using the method
proposed in the current work; (- - -) curves corresponding to the parameter sets obtained by Anthonsen et al. [18], who fitted each data set individually. Their parameter
values were: for Ao = 1.5, E = 151, Keq = 0.366 and ˛R = 480; for Ao = 3, E = 259, Keq = 0.317 and ˛R = 940; for Ao = 5, E = 130, Keq = 0.358 and ˛R = 0.6; for Ao = 10, E = 133, Keq = 0.259
and ˛R = 740.
ꢅ
ꢆꢅ
ꢆ
N.PS
Keq
˛RN
Keq
techniques for stiff equation sets. Although such integration tech-
niques are available, our proposed method simplifies the task by
avoiding the need to use them. This is possible because changes in
SR and SS are described by separate differential equations and the
degree of conversion is used as the independent variable.
rS
=
SS.B −
+ B
(19b)
Note that in this case there are two selectivity factors, ˛R and ˛S.
Of course, it is necessary to deduce an appropriate set of relation-
ships amongst the adimensionalized concentrations, equivalent to
those shown in Eq. (14), such that the final equations are expressed
only in terms of SR and SS.
Other adaptations are possible. For example, when the substrate
is a racemic ester, it can decompose during storage or handling,
meaning that chiral product is present at time zero [19]. This can
be taken into account by measuring how much chiral product is
present in the zero-time sample and formulating Eqs. (10) and (14)
appropriately. Also, if the enantiomers of the chiral substrate are
initially present in different amounts, which can happen if the start-
ing material has been previously processed [19], then this is taken
into account by using the real zero-time values of SoR and SoS, instead
of simply substituting them with 0.5.
Our approach has another advantage over that used by Anthon-
sen et al. [18]. They generated a table of output at evenly spaced
degrees of conversion (ꢀ) and then used cubic spline interpola-
tion to estimate the substrate and product concentrations at other
degrees of conversion. Our approach is simpler: we avoid the need
for interpolation by obtaining output from the numerical integra-
tion for each degree of conversion obtained experimentally.
Finally, Anthonsen et al. [18] carried out the same reaction with
several different initial concentrations of the non-chiral substrate.
In this case, our strategy of estimating a single set of parameter
values from the combined data is statistically sounder than is their
strategy of determining a separate parameter set for each differ-
ent reaction and then estimating each parameter by averaging the
values obtained for that parameter from the various different fits.
4.3. Comparison with the model of Anthonsen et al.
4.4. Causes of systematic deviations
The method proposed in the current work has similarities with
that proposed by Anthonsen et al. [18] but is somewhat easier to
use. For the reaction scheme described by Eqs. (4a)–(4c), they used
numerical integration to integrate the following equation directly:
It is possible for systematic deviations to occur between the
experimental profiles for SR and SS and the best-fitting curves
obtained by the analysis. There are two possible reasons for such
deviations.
Firstly, deviations will occur if the model equations are not
appropriate for the mechanism being analyzed. For example, the
irreversible uni-uni equation can be applied to determine E for bi-
bi reactions only under specific conditions [17,19]. It is important
to note that when these conditions are not met, if one were to apply
the Chen equation [20] to data obtained from a single sample, the
[SR](E[A] + [PS]/˛R) − [PR](E[N]/KEQ + [SS]/˛R)
[SS]([A] + [PR]/˛R) − [PS]([N]/KEQ + [SR]/˛R)
d[PR]
d[PS]
=
(20)
When E is large, then initially [PR] will change rapidly for very small
changes in [PS]; once PR is almost completely consumed, [PR] will
change very slowly for large changes in [PS]. This creates difficulty
for the numerical integration of Eq. (20), it being necessary to use

28
D.A. Mitchell et al. / Journal of Molecular Catalysis B: Enzymatic 64 (2010) 23–28
value obtained for E would be erroneous, but it would be impossi-
ble to detect this error. Deviations will only be visible if multiple
samples are obtained, as in the current method.
References
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Secondly, the value of E might change during the reaction. In
some cases the medium properties can change to such a degree
that they affect the enantioselectivity of the enzyme [21]. How-
ever, such effects are highly complex and at the moment we simply
do not have sufficient knowledge to incorporate them into model
equations.
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5. Conclusions
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Our method can be used to analyze reaction profiles to deter-
mine the enantiomeric ratio (E) during lipase-catalyzed kinetic
resolutions. It applies to reversible reactions involving bi-bi
ping-pong kinetics, with different rate expressions being used,
depending on the order in which the chiral substrate and chiral
product enter and leave the active site. It can be modified for reso-
lutions in which the behavior of the system can be approximated by
irreversible uni-uni kinetics. Our method combines several advan-
tages of previously proposed methods and is easy to use.
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Acknowledgements
[19] A. Straathof, J. Jongejan, Enzyme Microb. Technol. 21 (1997) 559–571.
[20] C. Chen, Y. Fujimoto, G. Girdaukas, J. Sih, J. Am. Chem. Soc. 104 (1982)
7294–7299.
[21] E.E. Jacobsen, E. Hellemond, A.R. Moen, L.C.V. Prado, T. Anthonsen, Tetrahedron
Lett. 22 (2003) 8453–8455.
David Mitchell, Vivian Moure and Nadia Krieger thank CNPq
(Conselho Nacional de Desenvolvimento Científico e Tecnológico),
a Brazilian Government Agency for the advancement of science and
technology, for research scholarships.