Straathof1992

Biocafalysis, 1992, Vol. I , pp. 13-27
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KINETICS OF THE ENZYMATIC RESOLUTION
REACTIONS
OF RACEMIC COMPOUNDS IN BI-BI
A. J. J. STRAATHOF,* J. L. L. RAKELS and J. J. HEIJNEN
Department of Biochemical Engineering, Delft University of Technology,
Julianalaan 67, 2628 BC Delft, The Netherlands
(Received 17 July 1991;in final form 27 March 1992)
The course of the kinetic resolution of a racemic compound by an enantioselective enzyme can often
be described using Michaelis-Menten kinetics. This description (Chen et al., 1982, 1987) is formally
not correct for reactions with multiple substrates or products. Van To1 et al. (1992) showed for the
lipase-catalyzed resolution of glycidyl butanoate that the ping-pong kinetic mechanism has to be taken
into account. This paper systematically treats the deviations from the model of Chen that may occur
for bi-bi reactions obeying ping-pong or ternary complex kinetics. The course of the enantiomeric
excess as a function of the degree of conversion was found to be dependent on two or three kinetic
parameters (in contrast to the single E-value of Chen), on the thermodynamic equilibrium constant
and on the ratio of initial concentrations of the reactants. This ratio can be used to some extent to
manipulate the enantiomeric excess in a resolution process.
KEY WORDS Enantioselective enzymes, bi-bi reactions, ping-pong kinetics, ternary complex
kinetics, enantiomeric ratio.
NOTATION
E
ee
k
C
KV
Ki
Kln
r
V
a
E
Superscripts
R
S
Subscripts
0
1,2,. . .
-1, -2,. . .
A, B, P, Q
E
concentration
enantiomeric ratio, enantioselectivity
enantiomeric excess
rate constant
equilibrium constant
inhibition constant
Michaelis constant
rate of production
maximum rate
selectivity
degree of conversion of the racemic substrate
for the (R)-enantiomer
for the (S)-enantiomer
at zero time
of the forward reaction
of the reverse reaction
of compound A, B, P, Q
of the enzyme
13
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14 A. J. J. STRAATHOF, J. L. L. RAKELS AND J . J . HEIJNEN
INTRODUCTION
Enzymatic kinetic resolution is one of the most important methods for the
production of enantiomerically pure organic compounds. The knowledge about
suitable enzymes and substrates is growing rapidly. Many examples are known of
reactions that will yield products with an enantiomeric excess approximating
100%. When the enzyme shows no absolute enantioselectivity, optimization of
the yield or enantiomeric excess of the resolution process requires kinetic
knowledge of the enzymatic reaction. Usually the model of Chen et al. (1982,
1987) is assumed to be valid. However, van To1 et al. (1992) recently found
deviations from this model during their study of the lipase-catalyzed hydrolysis of
racemic glycidyl butanoate. They could explain this by considering the role of the
product glycidol in the kinetic mechanism. This inspired us to perform a formal
analysis of the kinetics of enzymatic resolution. Such an analysis is also required
in kinetic studies of complicated enzymatic resolution processes (Macfarlane,
Roberts and Turner, 1990; Straathof. Rakels and Heijnen, 1990).
We will consider a racemic substrate A, with an initial concentration cAo,
consisting of equal amounts of AR and AS. For the description of its kinetic
resolution, the following steps can be distinguished:
(a) Indicate which kind of mechanism will most probably be used by the
enzyme.
(b) Translate this into an adequate kinetic model, which enables the derivation
of a rate equation in which the rate of production r is given as a function of
the concentrations in the reactor.
(c) Find the ratio of rate equations of the enantiomers using the kinetic model
(rl&'r: =f(c0ncentrations)).
(d) incorporate this ratio in a ratio of macroscopic reactor balances. For a
batch, this ratio will equal dctldc; (but cf. Heijnen, Terwisscha van
Scheltinga and Straathof, 1991).
(e) Convert this equation, by incorporation of the stoichiometric balances and
by integration, into an expression which contains c t and c; as the only
concentrations.
(f) Convert this expression into a function of enantiomeric excess vs.
conversion. and plot this function.
(8) Experimental verification and parameter estimation.
When the course of the enantiomeric excess ee: of the remaining substrate is thus
known, the enantiomeric excess ee; of the formed product may be calculated
easily (Sih and Wu, 1989).
Step (a) may in principle yield numerous different mechanisms, but these can
be reduced to a relatively small number of kinetic models. Cleland (1963)
performed step (b) for many important cases. The actual rate equations thus
obtained are not required for deriving the ratios of step (c). Still they deserve
some attention, since the notation and method of derivation of these rate
equations should also be used in step (c). Then, the steady state parameters of
each of the enantiomers can directly be used in a model which describes the
resolution of the racemate, and no experiments with the racemate are required.
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KINETICS OF ENZYMATIC RESOLUTION 15
In this paper we will deal mainly with step (c). For some examples, step (d), (e)
and (f) will be performed. Firstly, uni-uni reactions, which yield the model of
Chen, will be treated, and then bi-bi reactions will be dealt with in a similar
manner. In this respect, the work of Langrand et al. (1986) should be mentioned.
They modelled some cases of bi-bi resolution, but found that their pseudo-
equilibrium assumption did not always hold. Therefore we will only use the
pseudo-steady state assumption according to the formalism of Briggs and Haldane
(1925).
UNI-UNI REACTIONS
Chen et al. (1982) modelled enzymatic kinetic resolution by irreversible uni-uni
reactions using Michaelis-Menten kinetics. Later, this model was extended to
reversible reactions. The reaction scheme that was used (Chen et al., 1987) is
AR 3pR
'k",
in which ARand ASare the chiral substrates and PRand Ps the chiral products.
the formation of reversible Michaelis complexes:
A mechanistically more structured reaction scheme would be one that includes
3+..- E R ~eE P ~
kR1
E E (3)
Since first-order isomerization steps are not detected by steady-state kinetics,
no rate constants need to be defined for the interconversion of the central
complexes (Cleland, 1963).
The rate equations for the above reactions with competing substrates are
and an equation for r i in which the R and S superscripts for the enantiomers
have been interchanged. The parameters V and K , are functions of the rate
constants k, to k2 (see Table 1). The equilibrium constant for a uni-uni reaction
is given by
Division of Equation (4) by the analogous equation for the (S)-enantiomer yields
the extended equation of Chen et al. (1987):
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16 A. J . J. STRAATHOF, J. L. L. RAKELS AND J. J. HEIJNEN
Table 1 Definitions of pseudo-steady state kinetic parameters for some mechanisms (Cornish-Bowden,
1979)
~~
Par Uni-unr Bi-bi sequential
ternary-complex
Bi-bi
ping-pong
The enantiomeric ratio (or enantioselectivity) E is defined by
Thus, the mechanistic model involving Michaelis complexes still supports the
result of Chen. For irreversible reactions (Keq= x ) , this equation simplifies to the
original relation of Chen et af. (1982):
R
(8)
'A- c- E S
c A
Although these relations will hold in many cases, one should realize that a
resolution reaction will generally involve more than one substrate or product. In a
hydrolysis reaction, for example, water is the second substrate. In this paper we
will reveal the possible role of the second substrate on the enantiomeric excess
that can be obtained. Even in cases where irreversible uni-uni kinetics seem to
be valid, since the second substrate is in large excess and the reaction is going to
completion, this role may be important (van To1 et al., 1992). Application of the
Michaelis-Menten model to irreversible uni-uni reactions may usually be
adequate for description of initial rates, but when the progression of a reaction is
to be modelled accurately, as in resolution processes, such a standard approach
often fails.
BI-BI REACTIONS
Many resolution reactions involve a chiral and a non-chiral substrate and a chiral
and a non-chiral product (bi-bi reactions). On kinetic grounds, different
mechanisms for bi-bi reactions can be distinguished, e.g. the ping-pong mechan-
ism, sequential ordered ternary complex mechanism and the random ordered
ternary complex mechanism. These lead to different functions of reaction rate vs.
time (Cleland, 1963). We will show below that the different mechanisms also lead
to different relations for the ratio of reaction rates of enantiomers in a racemic
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mixture. Therefore, at a certain degree of conversion, the enantiomeric excess
may depend on the mechanism (and, of course, on the kinetic parameters
involved). Here, we will deal with the sequential ordered ternary complex
mechanism and the ping-pong (substituted enzyme) mechanism.
For bi-bi reactions we sometimes use the term “going to completion.” This is
different from “irreversible” which will be used only when Ke, = 00. A resolution
reaction may be going to completion not only because it is irreversible, but also
because of a very large excess of the second substrate, or because the
concentration of one of the products is kept at zero by an independent process
which itself is practically irreversible (e.g. the deprotonation of a carboxylic acid
at pH 8, or the evaporation of a volatile alcohol).
Ping-pong Mechanism
The ping-pong mechanism is
E‘ is the substituted-enzyme complex. An example is the esterase-catalyzed
conversion of ethyl acetate (A) and water (B) to ethanol (P) and acetic acid (Q).
Then, E’ is the acetyl-enzyme complex. The convention says that A is the first
substrate to enter the active site of the enzyme and P is the first product to leave.
The rate equation for a reaction according to this mechanism can be written as
(CACB -cI’cQ/Keq)
VI
KiAKmB
The inhibition constants Ki and the other parameters are defined in Table 1.
For a resolution reaction by a ping-pong bi-bi mechanism, three different
situations exist. These will be called A-P resolution, A-Q resolution and B-Q
resolution, after the substrate-product pair in which the chirality resides.
A-P resolution
In this case a chiral substrate A is converted to a chiral product P. Substrate B
and product Q are not chiral. An example is the lipase-catalyzed conversion of
glycidyl butanoate (A) and water (B) to glycidol (P) and butanoic acid (a). The
reactions are
+B epR+Q
+B epS+Q
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18 A. J. J. STRAATHOF, J. L. L. RAKELS AND J. J. HEIJNEN
and the mechanistic scheme is
The rate of conversion of AKis, using the pseudo-steady state assumption:
(YK K[cA(cB + L~~C:/K,,)- cF/K,,(c, + CY~C~)]CEO
-rf: =
(14)
K,,
The general definitions of the kinetic parameters (Y' and asare:
Thus, like the enantiomeric ratio E , these parameters express the selectivity of an
enzyme for two substrates by the ratio of maximum rate and Michaelis constant
of each substrate (Fersht, 1985). For bi-bi reactions, E is defined for substrate
A' and AS,or B R and BS,depending on which substrate is chiral, but a is always
defined for A and Q. Therefore there are two a's when A is chiral (aRfor AR
and Q, and asfor As and Q).
It would also have been possible to define cy not for A and Q, but for A and P
or for B and Q, e.g. Then the equations would have looked a little different, but
their consequences would have been the same.
In the specific case of A-P resolution the superscripts of V-,/K,, in the
definitions may be deleted because this ratio is equal for the (R)- and
(Sj-enantiomers. Then, cyR/asequals E.
Division of Equation (14) by the analogous equation for AS yields
R R
(17)
_ -r t (Y [cA(cB+aScZ/K,,) - cp(cu + aSci)/K,,]
r: ( Y ~ [ C ; ( C ~+ aKcF/K,,) - c~(c, + aRc:)/K,,]
r t cf:(EcB+ cyKcE/K,,) - cF(Ec, + aKc;)/Krq
r% c:(c15 + cyRc~/K,,)- c$(cQ+ (Y~C:)/K,,
-
Now either a' or cys can be eliminated, yielding in the latter case
(18)
(19)
(20)
(211
(22)
_ --
Integration of this equation using the stoichiometric balances
K
C t I , - c: = c," - Cpg
c;li-Cs - s sA - c? - CPiI
CUII - CB = cQ -
K
C A ( , - c t f c i ( )- c; = CB()- CB
will yield curves of enantiomeric excess vs. conversion.
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1.o
0.8
0.6
ee,*
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
Conversion
Effect of K,, on the enantiomeric excess of the remaining substrate for reversible bi-biFigure 1
reactions, when the a’sare zero, E = 10 and cBn/cAn= 10. (Equation (23)).
When aR= 0 Equation (18) reduces to
This equation is the bi-bi analogue of equation 6. When it is incorporated in a
macroscopic balance for a batch reactor, only numerical integration is possible.
The plot of enantiomeric excess vs. conversion thus obtained (Figure 1)
qualitatively shows the same behavior as the reversible uni-uni case (Chen et al.,
1987). An enantiomeric excess of 100% is not reached unless the reaction will be
going to completion.
It is most interesting to consider positive values of the a’s. Then, when the
reaction is going to completion because K,, = or because the concentration of
B exceeds that of all the other components to a very large extent (e.g. in a
hydrolysis reaction in a diluted aqueous solution, where B is water), the kinetics
reduce to the irreversible uni-uni case. This case also will be found when cp is
kept at zero, by chemical or physical removal during the reaction. However,
when the reaction is going to completion because cQremains zero, the following
equation is obtained:
R
(24)
_ -r A C2(ECBKeq/ffR+c:) -c”,:-
r i cZ(c,K,,/aR +cF)-C ~ C ;
An example of such a reaction has been performed by van To1 et al. (1992). They
hydrolyzed chiral glycidyl butanoate by porcine pancreas lipase at pH 7.8. At this
pH-value, the butanoic acid which is liberated (product Q) will be deprotonated
to butanoate, thus cQ was practically zero and the reaction went to completion.
Still, eeA never reached 100%. This was explained by taking into account
enantioselective product inhibition by both enantiomers of glycidol.
Figure 2 shows the course of a reaction according to a numerical integration.
The model also indicates that a higher ratio of cB0to cAo will improve the final
enantiomeric excess (Figure 3).
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1.o
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.0 1.0
Conversion
Figure 2 Effect of K,,/aR on the enantiomeric excess of the remaining chiral substrate for A-P
resolution, according to Equation 24, with co = 0, E = 10 and cso/cA,~= 10.
A-Q resolution
In this case a chiral substrate A is converted into a chiral product Q. Substrate B
and product P are not chiral. An example is the esterase-catalyzed conversion of
methyl 2-chloropropanoate (A) and water (B) into methanol (P) and 2-
chloropropanoic acid (a).The reactions are
+ B -P + Q~ (25)
(26)A~+B T= P +Q~
eeAs
1.o
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
Conversion
Figure 3 Effect of ceo/ca,, on the enantiomeric excess of the remaining chiral substrate for A-P
resolution, according to Equation 24, with co = 0, E = 10, and Keq/aR= 0.1.
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E E
The rate equations for ARand ASare not shown here. Their ratio is
R
(28)-rA -- (ctcB-cPcg/Keq) (asc,/Keq +c g )
6 (cSACB -cpc~/K,,) (aRcp/Ke,+cB)
Now V-,/K,A differs for the (R)-and (S)-enantiomer, and neither aRnor ascan
be eliminated. Description of this system therefore requires three selectivity
parameters.
When aRand asare zero, the bi-bi case of Figure 1is obtained. When the a’s
have a positive value, A-Q resolution has been evaluated for some special cases.
For Keq=m, cB= m , or cp=O, it reduces to the irreversible uni-uni case. For
cQ= 0, the equation obtained is
For several parameter values, this equation has been numerically integrated for a
batch system. The plots of enantiomeric excess vs. conversion thus obtained show
some interesting features (Figures 4-5): 100% enantiomeric excess is reached at a
lower conversion than for the irreversible uni-uni case when aR/aS<1 and at a
higher conversion when aR/aS>1.The smaller cBo/cA0,the larger the difference
with the uni-uni case. Since it is hardly possible to estimate aR/aSa priori, it
might be interesting in some cases to experiment at very low values of CB,,/CAO.
eeAs
1.o
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
Conversion
Figure 4 Effect of K,,ImR on the enantiomeric excess of the remaining chiral substrate for A-Q
resolution, according to Equation 29, with cQ= 0, E = 10, K,,/aS = 1 and cBo/cAo= 1.5.
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ee,*
1.o
0.0
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
Conversion
Figure 5 Effect of the a's on the enantiomeric excess of the remaining chiral substrate for A-Q
resolution, according to Equation 29. with c,, = 0, E = 10. and K,, = 1 and cBI,/cA,,= 1. The dashed
line shows the results for cBII/cA0= 100; then for both sets of a's the lines are similar to the
irreversible uni-uni case.
Positive deviations of the uni-uni case might occur, and increased amounts of a
100% enantiomerically pure compound may be obtained.
A further modification of the uni-uni-curve of enantiomeric excess vs.
conversion might be obtained by adding some non-chiral product P at the start of
the reaction. Figure 6 shows that a high ratio of cpl~/cAoenhances the effect of a
low ratio of cB,,/cAlj.An example is the enzymatic hydrolysis of chiral methyl
2-chloropropanoate at a high concentration at pH 7, in the presence of methanol.
Conversion
Figure 6 K,,= 1 and
cRJcAII= 1. The solid lines are for aR= 0.1 and as= 1 and the dashed lines for aR= 1 and as= 0.1.
For the same conditions without addition of P the graphs are shown in Figure 5.
Effect of cA,/cAII on ping-pong A-Q resolution with co=O, E = 10,
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The enantiomeric excess of the remaining substrate significantly decreased upon
addition of 1mol/l of methanol. Equal volumes of non-reacting solvents did not
show such an effect. (Rakels et al., preliminary results).
B-Q resolution
In this case a chiral substrate B is converted into a chiral product Q. Substrate A
and product P are not chiral. An example is the lipase-catalyzed conversion of
propenyl acetate (A) and menthol (B) into propenol (P) and menthyl acetate
(a).The reactions are
A + B"--,P +Q~
A + ~~eP + as
This case is symmetrical with respect to A-P resolution. V,/K,A is equal for the
(R)- and (S)-enantiomer. Therefore asequals E .a",and can be eliminated from
the ratio of reaction rates, yielding
Of course, the definition of the enantiomeric ratio should now be applied to B
instead of A.
When aR= 00 the bi-bi case of Figure 1is obtained. For positive values of aR
the following simplified cases can be considered: When cA= 00 or cg = 0, B-Q
resolution reduces to the irreversible uni-uni resolution. For K,, = m or cp= 0,
one obtains
Because of the analogy to Equation 24 numerical integration of this equation
leads to graphs like Figure 2 and 3; a" is the variable instead Keq/aR,and the
letters B and Q have to be interchanged by A and P, respectively. Now,
situations may occur in which the enantiomeric excess does not reach loo%,
although the reaction is going to completion because of two reasons: The
equilibrium constant is infinite and the concentration of product P is kept at zero.
The larger the larger are the deviations from the irreversible uni-uni
case.
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Sequential Ordered Ternary Complex Mechanism
The sequential ordered ternary complex mechanism is
(35)
% k3c-H k i k
E +.- EA -t EAB r EPQ -EQ A E
k l k ?
An example is the lactate dehydrogenase-catalyzed oxidation of lactate (B) by
NAD+ (A).
Steady state kinetics cannot distinguish between the ternary EAB and EPQ
complexes, so no rate constants need to be defined for their interconversion. The
rate equation for the above reaction is:
. I
KIA K I A KmB KtAKrnB K t Q KrnP KiQ
+--+---+---CP CO KmQ c A cP KmA cB cQ
K m P K ~ Q K ~ QKtA KmP K,A KmB K ~ Q
K,A KmB K ~ BKmP KiQ
The kinetic parameters are defined in Table 1.
substrate and Q the chiral product, the reactions are
During kinetic resolution, two such reactions occur; e.g.,when A is the chiral
+ B eP + Q ~
A ~ +B eP + Q’
The rate equation for ARresembles Equation 36 but is much larger. Division by
the analogous equation for AS yields
(40)
! L E ( c ~ c ,- c p c G / K , , ) (cB + a’Cp/K,, +K%%B/Kk,)
r i (c”,~ - CpC:/Kt,) (CB + aRcp/Kcq+K $ K E B / K k A )
This is an extended form of the equation for A-Q resolution by ping-pong
kinetics, and similar deviations from the uni-uni case will occur.
Since the ternary complex mechanisms yield such complex equations and seem
to be of relatively low importance for resolution processes, we will not discuss
A-P, B-P and B-Q resolution here.
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COMPARISON OF ENANTIOMERIC RATIO OF FORWARD AND
REVERSE REACTION
The enantiomeric ratio of a reverse reaction should be defined in an analogous
fashion to that of the forward reaction according to Equation 7, using K , of the
chiral product and V-,.
For uni-uni reactions, Chen et al. (1987) showed that the enantiomeric ratio of
the forward and reverse reaction are identical, because of the thermodynamic
restriction of Equation 5 (though they properly remarked that in practice there
will be a difference since the experimental conditions of the forward and reverse
reaction will be different).
For bi-bi reactions, we also compared the enantiomeric ratio of the forward and
reverse reaction. These were identical for the B-P ternary complex and A-P and
B-Q ping-pong mechanisms, but not identical for the A-P, A-Q and B-Q ternary
complex and A-Q ping-pong mechanisms.
Below the comparison will be illustrated for ping-pong A-Q resolution. The
definitions of kinetic parameters of Table 1have been used.
Vp K:A kpk," (k?,+ks)
KEA Vs (kR,+k,") kskz
vR, ~k~ kR3kR4 (k?, +k:)
--
Eforward --~ -
-Ereverse = K:Q V?,
(kR3+k:) k?,k?,
After incorporation of the thermodynamic restriction
the definitions of the forward and reverse enantiomeric ratios remain different in
this example.
The pathway via which an (R)-enantiomer is converted sometimes has a large
part in common with the @)-pathway;e.g., for ping-pong A-P resolution k3, kP3,
k4 and k-4 are equal for the (R)- and (S)-enantiomer, as can be seen from the
mechanistic scheme. Then the enantiomeric ratios of forward and reverse
reactions are found to be equal.
DISCUSSION
When bi-bi resolution reactions are considered their kinetics should be treated
using the pseudo-steady state assumption. In doing so, many cases are found
which differ from uni-uni resolution reactions with respect to the enantiomeric
excess obtainable. In contrast to the conventional opinion, it is not always
possible to reach 100% enantiomeric excess for the remaining substrate when the
reaction is going to completion. The course of the enantiomeric excess as a
function of the conversion depends on the ratio of initial concentrations. The
higher the concentration of the chiral substrate and one of the products, the
larger the deviations from conventional kinetics. Of course, deviations may also
occur because of thermodynamic non-idealty, but non-idealty is not considered in
this paper.
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26 A. J. J. STRAATHOF, J. L. L. RAKELS AND J . J. HEIJNEN
Table 2 Overview of equations to be used to model enzymatic resolution processes.
uni-uni not going to completion
ping-pong A-P a R = O o r aS=O
going to completion
bi-bi
others
A-Q a K = O a n d d = O
others
ternary complex A-P
bi-hi A-Q
B-Q
B-P
Eq. (6)
Eq. (8)
no completion Eq. (23)
to completion Eq. (8)
co = 0 Eq. (24)
others Eq. (18)
co=o Eq. (29)
others Eq. (28)
K,,==or cp=O Eq. (34)
others Eq. (33)
Eq. (40)
K,, = = or cB= = or cp = 0 Eq. (8)
no completion Eq. (23)'
K,, =
no completion Eq. (231'.'
cA= 50 or cQ = 0
or cB= z or cp = 0 Eq. (8)
Eq.
not evaluated
not evaluated
not evaluated
'Repbcc P by 0and 0 hy P
Replace A hy B and B by A
Table 2 shows an overview of the equations which should be used to evaluate a
resolution process. Equation 6 (Chen et af., 1987) is not recommended in any of
the bi-bi cases. When the wrong model is used, an apparent E-value will be found
which may differ from the real value. Then incorrect conc!usions may be drawn
about the enantioselectivity of the enzyme. Table 3 shows some examples of
apparent E-values which were calculated from the enantiomeric excess at 50%
conversion, incorrectly assuming that irreversible uni-uni kinetics were valid. In
some cases the deviation from the real value (10 in this example) is larger. The
apparent value of E may subsequently be used to calculate the degree of
conversion at which ee = 99% is to be expected according to the wrong model.
Sometimes the enantiomeric excess which will be measured at this conversion will
be much lower than 99% according the model simulations (see Table 3).
Table 3 Apparent enantiomeric ratio and the enantiomeric excess that will be
measured when ping-pong bi-bi models apply but the model of Chen et al. (1982)
is used. K,, = 10, cBII/cA,,= 10. as= 1 and (for A-Q resolution) aR= 100.
Model E(,,',,, E(.pparmr) ee: ("rm<dul) ee:, (mruTtmd)
._ _ _ ~ ~-.. -~ _--__
A-P resolution cp = 0 10 10 099 0 990
C" = 0 10 9 52 0 99 0 979
A-Q resolution c p = 0 10 10 0 99 0 990
B-Q resolution cp = 0 10 7 47 0 99 0 881
co=O 10 10 0 99 0 990
c,=0 10 7 53 0 99 0 975
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When the enantiomeric excess is measured at ca. 50% conversion only, these
phenomena may be difficult to predict. At higher degrees of conversion the
amount of product present in the reaction mixture will be larger, and deviation
from uni-uni kinetics will be more obvious.
References
Briggs, G. E. and Haldane, J. B. S. (1925) A note on the kinetics of enzyme action. Biochem. J., 19,
338-339
Chen, C. S., Fujimoto, Y., Girdaukas, G. and Sih, C. J. (1982) Quantitative analysis of biochemical
kinetic resolutions of enantiomers. J. Am. Chem. SOC.,104, 7294-7299
Chen, C. S., Wu, S. H., Girdaukas, G. and Sih, C. J. (1987) Quantitative analysis of biochemical
kinetic resolutions of enantiomers. 2. Enzyme-catalyzed esterifications in water-organic solvent
biphasic systems. J. Am. Chem. SOC., 109,2812-2817
Cleland, W. W. (1963) The kinetics of enzyme-catalyzed reactions with two or more substrates and
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