Modelling the biokinetic resolution of diastereomers present in unequal initial amounts

Article abstract of DOI:10.1016/S0957-4166(02)00419-6

The enantiomeric ratio (E) is commonly used to evaluate enzyme-catalysed kinetic resolutions. Chen et al. (1982) proposed a model for the enantiomeric ratio, which relates the extent of substrate conversion and the enantiomeric excess. The model, however,

Full text of DOI:10.1016/S0957-4166(02)00419-6

TETRAHEDRON:
ASYMMETRY
Pergamon
Tetrahedron: Asymmetry 13 (2002) 1637–1643
Modelling the biokinetic resolution of diastereomers present in
unequal initial amounts
Carla C. C. R. de Carvalho, Frederik van Keulen and M. Manuela R. da Fonseca*
Centro de Engenharia Biolo´gica e Qu´ımica, Instituto Superior Te´cnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Received 7 June 2002; accepted 23 July 2002
Abstract—The enantiomeric ratio (E) is commonly used to evaluate enzyme-catalysed kinetic resolutions. Chen et al. (1982)
proposed a model for the enantiomeric ratio, which relates the extent of substrate conversion and the enantiomeric excess. The
model, however, does not apply to cases where the substrate initially contains unequal amounts of enantiomers. This paper
describes the adaptation of Chen’s model to cases where the reagent consists of a mixture of diastereomers present in unequal
initial amounts and gives product as a single diastereomer. Diastereomeric ‘resolutions’ of (+)-limonene-1,2-epoxide and of
(−)-carveol were used to validate this model. © 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction
conversion and the diastereomeric ratio was thus
developed.
Chiral building blocks, pharmaceutical or agrochemical
compounds and food additives are commercially con-
sidered as isolated enantiomers only when the enan-
tiomeric purity is very high (usually the enantiomeric
excess has to be greater than 98%) Thus, efforts to
obtain compounds in enantiomerically pure form and
models for processes in which enantiopure compounds
are produced are of increasing interest and importance.
The model that is presented herein was experimentally
validated in two case-studies involving the diastereose-
lective biotransformations of (+)-limonene-1,2-epoxide
to limonene-1,2-diol and of (−)-carveol to carvone,
both reactions being catalysed by whole cells of Rhodo-
coccus erythropolis DCL14.
1.1. Model
The enantiomeric ratio (E) is commonly used to evalu-
ate enzyme-catalysed kinetic resolutions. So far, the
methods described in the literature to determine the
enantiomeric ratio in enantioselective biocatalysis have
If A0 and B0 represent the concentration of each of the
isomers in the initial mixture and h and i the initial
fraction of the fast (A) and slow (B) reacting isomers in
an irreversible reaction with no inhibition by products,
then:
mainly focused on the resolution of
a racemic
substrate1–3 and to our knowledge, models describing
the resolution of substrates that contain unequal initial
amounts of enantiomers have not been developed as
yet.
h
A0= B0
(1)
i
The model presented in this work is based on the model
of Chen et al.,1 and takes into consideration the frac-
tion of each of the two diastereomers/isomers present in
the initial substrate, and thus the initial diastereomeric
excess. It is assumed that the diastereomeric selectivity
of a biocatalyst may be described in a similar way to
and
1
x
i
h
A0= (A0+B0)Ux=1+
(2)
(3)
1
h
B0= (A0+B0)Uy=1+
the enantioselectivity.
A
model correlating the
y
i
diastereomeric excess of the substrates, the rate of
where x and y are the reciprocal of the initial fractions
of A and B, respectively.
* Corresponding author. Tel.: +351-21-841 72 33; fax: +351-21-848 00
72; e-mail: mmrf@alfa.ist.utl.pt
The enantiomeric ratio (E) is defined as:
0957-4166/02/$ - see front matter © 2002 Elsevier Science Ltd. All rights reserved.
PII: S0957-4166(02)00419-6

1638
C. C. C. R. de Car6alho et al. / Tetrahedron: Asymmetry 13 (2002) 1637–1643
A
A0
1−de
1−de0
ꢀ ꢁ
ꢂꢀ ꢁ n
ln
ln
ln
(1−x)
E=
(4)
D=
(8%)
(9%)
B
1+de
ꢀ ꢁ
ꢂꢀ ꢁ n
ln
(1−x)
1+de0
B0
and
By applying this definition to the situation under study,
in which both fast and slow reacting diastereomers
produce the same product, the diastereomeric ratio (D)
can be written as:
1
D-1
1−de
Æ ꢀ ꢁÇ
Ã
Ã
1−de0
x=1−Ã
DÃ
1+de
ꢀ ꢁ
Ã
Ã
È
É
< =
1+de0
x
x
2
:
:
A
;
;
(A+B)+ (A−B)
ln
ln
As with the kinetic resolution of a racemic mixture, in
this case the value of the diastereomeric ratio can also
be estimated from the measurements of conversion and
diastereomeric excess obtained during the course of the
biotransformation. Chen et al.1 proposed a model for
recycling processes in which they considered that the
resulting product, formed in the first step of the resolu-
tion (first cycle of the recycling process), may be trans-
formed into the initial reagents. The next step of the
recycling process would then start with a non-racemic
mixture. This model correlates the extent of conversion
with the enantiomeric ratio, the enantiomeric excess of
the initial antipodal mixture, and the enantiomeric
excess of the recycled product fraction. However, in our
case ‘the enantiomeric excess of the recycled product
fraction’ is zero (only one product) and the enan-
tiomeric excess of the initial antipodal mixture is con-
stant. Thus, if Chen’s model were used, the
enantiomeric ratio would depend on the conversion
only. This is a further reason why Eq. (9) is useful in
the estimation of de for the type of conversions
addressed in the current study.
2
A+B
A0+B0
1
x
·
(A0+B0)
A+B
D=
=
< =
y
y
2
(A+B)+ (B−A)
B
ln
2
A+B
A0+B0
ln
=
·
1
y
A+B
(A0+B0)
x
2
A−B A+B
A+B A0+B0
B−A A+B
A+B A0+B0
ꢂ ꢀ ꢁ n
ln
ln
1+
·
(5)
(6)
y
ꢂ ꢀ ꢁ n
1+
·
2
The extent of conversion, x, is given by
A+B
A0+B0
x=1−
and the diastereomeric excess, de, defined by analogy
with the enantiomeric excess, ee, as
B−A
de=
(7)
A+B
The substitution of Eqs. (6) and (7) in Eq. (5) gives:
Fig. 1 shows several plots of D obtained by the resolu-
tion of Eq. (9) for different initial ratios of the
diastereomers present in the mixture. These plots
provide a useful overview of the relationships between
de, x and D for a given h. It can be observed that for
a D of 50, for example, when the initial ratio of the fast
reactant is small, the reaction should be stopped at low
degrees of conversion to attain a high de. On the other
hand, when the initial amount of the fast reactant is
high, it is necessary to have high degrees of conversion
to obtain reasonable values of de, even for high values
of D. The plots for high values of D are much closer to
one another than their counterparts at low D values,
i.e. a D of 100 is almost as effective as a D=8, but a
significant difference to a D of 10 is observed. Never-
theless, even low D values can be exploited to obtain
products with high enantiomeric/diastereomeric excess.
x
1
i
ꢂ n ꢂ ꢀ ꢁ n
ln (1−de)(1−x)
ln
1+ (1−de)(1−x)
2
y
2
2
1
h
D=
=
(8)
h
ꢂ n ꢂ ꢀ ꢁ n
ln (1+de)(1−x)
ln
1+ (1+de)(1−x)
2
i
Rearrangement of Eq. (8) results in:
1
ÇD-1
x
Æ
Ã
(1−de)
Ã
2
x=1−Ã
Ã
=
D
y
ꢀ ꢁ
(1+de)D
Ã
Ã
È
É
2
1
Æ
ÇD-1
1
2
i
ꢀ ꢁ
1+ (1−de)
Ã
Ã
h
1−Ã
Ã
(9)
D
1
2
h
ꢀ ꢀ ꢁꢁ
(1+de)D
Ã
Ã
1+
È
É
i
2. Results and discussion
The initial fractions of the fast and slow reacting iso-
mers can also be used for calculating the initial
diastereomeric excess, de0, defined as
2.1. Biotransformation of limonene-1,2-epoxide
R. erythropolis DCL14 cells contain a highly active
limonene epoxide hydrolase (LEH) when grown on
monoterpenes. According to van der Werf et al.,4 the
hydrolysis of (+)- and (−)-limonene-1,2-epoxide
catalysed by the pure enzyme resulted in respectively
(+)-(1S,2S,4R)- and (−)-(1R,2R,4S)-limonene-1,2-diol
B0−A0
de0=
A0+B0
In this case, Eqs. (8) and (9) can be expressed, respec-
tively, as

C. C. C. R. de Car6alho et al. / Tetrahedron: Asymmetry 13 (2002) 1637–1643
1639
Figure 1. Diastereomeric excess versus degree of conversion, with the diastereomeric ratio (D) as parameter, for different relative
initial amounts (h) of the fast reacting isomer.
as products. When LEH was added to a mixture of cis-
and trans-limonene-1,2-epoxide, the sequential degrada-
tion of the (1R,2S)- and then the (1S,2R)-diastereomer
was observed.4
By analogy with Eq. (7), we defined ‘diastereomeric
excess’ as:
trans−cis
de=
(10)
trans+cis
Inthepresentwork, R. erythropoliscellswereusedtocarry
out the hydrolysis of (+)-limonene-1,2-epoxide (Fig. 2).
The purpose of the reaction can be two-fold: (i) produc-
tion of the diol from (+)-limonene-1,2-epoxide and (ii)
diastereomericresolutionofmixturesofcis/transepoxide.
The (+)-limonene epoxide used in this work was a mixture
of 42.2% of the cis- and 55.7% of the trans-epoxide.
Substituting the values of h and i in Eqs. (2) and (3),
we obtain 2.32 and 1.76 for x and y, respectively. The
introduction of these values in Eq. (8) gives:
Figure 2. Conversion of (+)-limonene-1,2-epoxide by whole cells of R. erythropolis DCL14.

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C. C. C. R. de Car6alho et al. / Tetrahedron: Asymmetry 13 (2002) 1637–1643
ln[1.16 (1−de)(1−x)]
ln[0.88 (1+de)(1−x)]
With the mean value of D from Table 1, Eq. (11) was
D=
(11)
solved using the Solver function of Microsoft Excel,
version 7.0. The diastereomeric excess predicted by the
model is plotted in Fig. 3 as a function of substrate
conversion.
Rearrangement of Eq. (11) similar to that performed
with Eq. (8) (which resulted in Eq. (9)) was used to
estimate the values of D for the ‘whole cell’ biotransfor-
mation using experimental results on diastereomeric
excess and degree of conversion. The data were
obtained in two configurations of biphasic reactors: (i)
mechanically stirred with direct-phase contact (at two
initial substrate concentrations) and (ii) membrane
reactor (Table 1). The values were fitted using the
program TableCurve™2D from Jandel Scientific and
confirmed by the Solver function of Microsoft Excel,
version 7.0 for Windows 95.
When the degree of conversion of limonene-1,2-epoxide
reached the value of 0.43, the de was higher than 0.99.
This is an indication that this process is suitable for the
production of trans-limonene epoxide (Fig. 3). The
model was able to fit well with the experimental results.
2.2. Biotransformation of carveol
According to van der Werf et al.,5 R. erythropolis
DCL14 cells contain a carveol dehydrogenase (CDH)
which allows for the stereoselective oxidation of (+)-cis-
carveol to (+)-carvone and of (−)-trans-carveol to (−)-
carvone. The conversion of the respective diastereomers
by CDH was not observed by these authors.
Table 1. ‘Resolution’ selectivity of a mixture of cis- and
trans-limonene-1,2-epoxide carried out by whole cells of
R. erythropolis DCL14 with activity in limonene epoxide
hydrolase, evaluated by the diastereomeric ratio
Reactor
D
When a mixture of diastereomeric, cis- and trans-(−)-
carveol, was subjected to biotransformation with whole
cells, the (−)-trans-carveol was converted to (−)-car-
vone. Two products were obtained: (i) (−)-carvone and
(ii) diastereomerically resolved (−)-cis-carveol6 (Fig. 4).
Direct-phase contact, 2.5 mM
Direct-phase contact, 50 mM
Membrane, 75 mM
86.1
86.4
86.5
Figure 3. Diastereomeric excess of trans-limonene epoxide (ꢀ and "—experimental values obtained in a direct-phase contact
reactor at an initial epoxide concentration of 2.5 and 50 mM, respectively; ꢁ—experimental values obtained in a membrane
reactor; --- model, obtained by resolution of Eq. (11) for D=86.3).
Figure 4. Conversion of (−)-carveol by whole cells of R. erythropolis DCL14.

C. C. C. R. de Car6alho et al. / Tetrahedron: Asymmetry 13 (2002) 1637–1643
1641
However, we could detect the transformation of the
cis-diastereomer when the concentration of trans-
carveol reached rather low levels.7
grown on limonene only, cyclohexanol only and on
both substrates were 67.0, 67.0 and 67.2, respectively.
Biotransformation runs using cells grown under the
above three sets of conditions were carried out to assess
the effect on selectivity of cofactor dependence. No
significant differences in CDH selectivity were observed
(Fig. 5) and the experimental values correlate well with
the model (Fig. 5).
The (−)-carveol used in this experiments was a mixture
of 38% (−)-cis- and 62% (−)-trans-carveol. The amount
of the fast reacting diastereomer, (−)-trans, being higher
than that of the slow reacting, gives rise to negative
diastereomeric excess values before the two quantities
become equal. Straathof and Jongejan3 considered ee as
being always positive, i.e. they included a modulus in its
definition. However, in the present case, the amount of
the fast reacting diastereomer, which is higher in the
beginning, decreases during the biotransformation and
is even smaller than the amount of the slow reacting
isomer at the end. If we introduced the modulus in the
de definition, the curves of de versus degree of conver-
When trans-carveol consumption was almost complete
(at ca. 96% conversion), degradation of cis-carveol
started to occur. From this time onwards, the cis-iso-
mer was consumed at a higher rate than the remaining
trans-carveol, although at a much lower rate than the
initial consumption of trans-carveol (0.789 and 32.77
nmol carvone/min mgprot, respectively). At this point, the
de obtained was only 0.9 (Fig. 5), although the isomeric
ratio during this period was 67.1 (mean value for the
three situations). According to Eq. (12), the value of de
decreases as the cis-diastereomer is converted. If we
take into consideration the fact that the slow reacting
diastereomer is now trans-carveol, then the value of de
will increase, but all the values will be negative. At the
switch point there were 4.9 and 95.1% of trans- and
cis-carveol, respectively. Hence the equation used was:
sion would take
a
less common shape. The
diastereomeric excess was thus calculated as:
cis−trans
de=
(12)
trans+cis
Substituting the values of h and i in Eqs. (2) and (3),
the x and y values obtained are 1.61 and 2.63, respec-
tively. Substituting for x and y in Eq. (8) gives:
ln[0.526 (1−de)(1−x)]
ln[10.24 (1+de)(1−x)]
ln[0.81 (1−de)(1−x)]
ln[1.32 (1+de)(1−x)]
D=
(14)
D=
(13)
CDH activity and co-factor dependence vary with the
carbon source used for R. eryhtropolis growth.5 The
values of D obtained (using TableCurve™2D from
Jandel Scientific) for the CDH resolutions with cells
During this later period, the values of D, calculated
using the software referred to above, were 2.45, 1.95
and 2.00 for the CDH resolutions with cells grown on
limonene, cyclohexanol and on both substrates, respec-
Figure 5. Diastereomeric excess during the conversion of (−)-carveol. For conversion degrees lower than 0.6 there is a
diastereomeric excess of cis-carveol. For conversion degrees higher than 0.6 there is a diastereomeric excess of trans-carveol (ꢂ,
ꢃ and ꢀ—experimental values obtained with cells grown on limonene+cyclohexanol, cyclohexanol and limonene, respectively, as
carbon source; direct-phase contact reactor with a carveol concentration of 50 mM; --- model, for D=67.1; · · · model, for
D=2.1).

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C. C. C. R. de Car6alho et al. / Tetrahedron: Asymmetry 13 (2002) 1637–1643
tively. The diastereomeric ratio was thus much lower
than that obtained during the fast trans-carveol con-
sumption period. Model fitting to the experimental data
was not as good as in the previous examples.
Chemicals: The terpenes used were (R)-(+)-limonene
(97%), (+)-limonene oxide (97%), (−)-carveol (97%) and
(R)-(−)-carvone (98%), from Aldrich Chemicals.
4.1. Limonene-1,2-epoxide biotransformation
In a 500 mL mechanically stirred reactor, complete
consumption of trans-carveol could be achieved.8 By
adding substrate every time the organic phase was
depleted in trans-carveol, several ‘initial’ trans/cis ratios
were obtained. Fig. 6 shows how well the model fits the
data obtained at the different ‘initial’ substrate ratios.
Growth: Cells were grown at 30°C and 400 rpm in a 2.0
L fermenter containing 1.5 L of mineral medium.9 The
growth substrate, (R)-(+)-limonene, was continuously
fed via the gas phase by bubbling the inlet air, at 100
ml/min, through the sintered glass sparger of a glass
bottle containing limonene. Growth was followed by
measuring the O.D. (600 nm); when the value was
higher than 1.5, 2/3 of the fermentation broth was
removed and cells were harvested by centrifugation
(7000 rpm, 10 min). The fermenter was refilled with
fresh medium.
3. Conclusions
There are large numbers of methods available for the
accurate determination of E values.2 However, non-
racemic substrates and isomeric/diastereomeric resolu-
tions with a single product obtained from both
diastereomers have not, to our knowledge, been
addressed. The extension to Chen’s model, which is
presented in this work is intended at reducing this gap.
Reactions: Assays were carried out in a 500 mL reactor
(containing 300 mL of 50 mM phosphate buffer, pH
7.0, 60 ml of organic phase, defined concentrations of
epoxide and about 50 mg, d.w., of cells) and in a
membrane reactor (600 mL of aqueous phase; the
substrate was recirculated through a silicone tube with
149.4 cm2, acting as a membrane). Reactors were
mechanically stirred at 200 rpm and operated at room
temperature. Reactions were followed by monitoring
the diol accumulation in the aqueous phase and the
substrate consumption in the organic phase.
Two case-studies were discussed, regarding the
diastereomeric resolution of (+)-limonene-1,2-epoxide
and of (−)-carveol, both catalysed by whole cells of R.
erythropolis DCL14. It was shown that the proposed
extension to the model satisfactorily describes this type
of kinetic ‘resolutions’. These two sets of experimental
data thus validate the model.
Analysis: At regular intervals the aqueous phase was
sampled to follow diol production. The diol in the
samples was extracted with ethyl acetate (1:1), which
was analysed by gas chromatography (GC) on a
Hewlett Packard 5890 gas chromatograph with a FID
detector, connected to a HP3394 integrator. The capil-
lary column was a SGE HT5, 25 m in length and with
internal and external diameters of 0.22 and 0.33 mm,
respectively. The oven temperature was 150°C and the
4. Experimental
Microorganism: R. erythropolis DCL14 was supplied by
the Division of Industrial Microbiology of the
Wageningen Agricultural University, Wageningen, The
Netherlands, in the context of the European Project
BIO4-CT95-0049.
Figure 6. Diastereomeric excess observed during conversion of (−)-carveol by whole cells of R. erythropolis DCL14 in a direct
contact stirred reactor. Values of D calculated by the model for each curve.

C. C. C. R. de Car6alho et al. / Tetrahedron: Asymmetry 13 (2002) 1637–1643
1643
temperature of the injector and detector was 250°C.
Organic-phase samples were taken whenever it was
important to follow epoxide consumption. These were
injected without any previous treatment and analysed
for their epoxide content. The oven temperature of the
gas chromatograph was 150°C and that of the injector
and detector was 250°C. To separate the epoxide iso-
mers the oven temperature was 90°C, while the injector
and detector were at 250°C.
column was a SGE HT5, 25 m in length and with
internal and external diameters of 0.22 and 0.33 mm,
respectively. The oven temperature was 140°C and the
injector and detector were at 200 and 250°C,
respectively.
Error analysis: The error associated with the GC analy-
sis of samples of the organic phase was 6% and that of
the aqueous phase, extracted with ethyl acetate prior to
injections, was 8%. The errors were calculated based
on the standard deviation and sample mean of seven
repeated injections and are quoted for a confidence
interval of 95%. Biomass concentration measurements
(O.D.) had an associated error of 8% based on the
standard deviation and sample mean of eight repeated
samples, quoted for a confidence interval of 95%.
4.2. Carveol biotransformation
Growth: Cells were grown at 28°C and 400 rpm in a 2.0
L fermenter containing 1.5 L of mineral medium.9 The
inlet air flow was 200 mL/min. Limonene was supplied
through the air stream, as previously described. For
cells grown on cyclohexanol, a solution of cyclohexanol
(0.2 mM) was added at a flow rate of 6.3 mL/h. When
cells were grown in both limonene and cyclohexanol,
limonene was added through the air stream and a
solution of cyclohexanol was added to the fermenter, as
described for the single carbon source situations. In all
cases, cells where harvested when the O.D. value was
higher than 4.
Acknowledgements
This study was supported by a Ph.D. grant (PRAXIS
XXI/BD/21574/99) awarded to Carla da C. C. R. de
Carvalho by Fundac¸a˜o para a Cieˆncia e a Tecnologia,
Portugal.
Reactions: Activity assays were carried out, at least in
duplicate, in 60 mL flasks closed with rubber bungs,
containing 20 mL of 50 mM phosphate buffer (pH 7.0),
20 mL of organic phase and defined substrate concen-
trations. After the addition of a concentrated suspen-
sion of whole cells of R. erythropolis DCL14, the flasks
were incubated at 28°C and 200 rpm. Reactions were
followed by monitoring carvone accumulation in the
organic phase.
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Mechanically stirred reactor: Assays were carried out in
a 500 mL reactor containing 300 mL of 50 mM phos-
phate buffer pH 7.0, 60 mL of organic solvent (n-dode-
cane), 50 mM of (−)-carveol (referred to the organic
phase) and an initial O.D. (measured at 600 nm) of 0.8.
The reactor was mechanically stirred and operated at
room temperature. Every time the organic phase was
depleted in trans-carveol, 0.49 mL of (−)-carveol was
added.
Analysis: At regular intervals the organic phase was
sampled and the carveol and carvone were subsequently
analysed by gas chromatography (GC) on a Hewlett
Packard 5890 gas chromatograph with a HP3394 inte-
grator, without any previous treatment. The capillary
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