Kinetics and modeling of (R,S)-1-phenylethanol acylation over lipase

Article abstract of DOI:10.1002/kin.20504

The kinetics of the acylation of (R,S)-1-phenylethanol was investigated using lipase as a catalyst. The main parameters were temperature, reaction atmosphere, different acyl donors, and different amounts of acyl donor as well as the presence of some addit

Full text of DOI:10.1002/kin.20504

Kinetics and Modeling of
(R,S)-1-Phenylethanol
Acylation over Lipase
˚
¨
¨
¨
ALEXEY KIRILIN, SERAP SAHIN, PAIVI MAKI-ARVELA, JOHAN WARNA, TAPIO SALMI,
DMITRY YU. MURZIN
˚
˚
Process Chemistry Centre, Abo Akademi University, Abo/Turku, FI-20500, Finland
Received 6 February 2010; revised 21 February 2010; accepted 23 March 2010
DOI 10.1002/kin.20504
Published online 9 July 2010 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: The kinetics of the acylation of (R,S)-1-phenylethanol was investigated using lipase
as a catalyst. The main parameters were temperature, reaction atmosphere, different acyl
donors, and different amounts of acyl donor as well as the presence of some additives in the
reaction mixture. The initial reaction rate increased with increasing temperature and with a
decreasing amount of an acyl donor. The activated esters, such as isopropenyl- and vinyl acetate,
exhibited very high acylation rates for R-1-phenylethanol, whereas low rates were obtained with
ethyl acetate and 2-methoxyethyl acetate. The addition of water and acetophenone decreased
the acylation rate. A kinetic model was developed based on a sequential step mechanism, in
which enzyme was reacting in the first step with an acyl donor followed by the reaction of a
modified enzyme complex with the reactant, R-1-phenylethanol. Comparison with experimental
data obtained at different temperatures allowed simplification of this model, leading to a kinetic
equation with just one apparent parameter. The influence of the amount of acyl donor, ethyl
acetate, could be quantitatively described by taking into account the competitive inhibition
of the ethanol produced. The rate constants and apparent activation energy for experiments
performed under different temperatures and the amounts of acylation agent were determined.
The apparent activation energy was 24.5 kJ/mol. ꢀ 2010 Wiley Periodicals, Inc. Int J Chem Kinet
C
42: 629–639, 2010
cohols, which are important intermediates for synthesis
of pharmaceuticals.
INTRODUCTION
Kinetic resolution of secondary alcohols over li-
pases has been investigated intensively [1]. Enzymes
are active in apolar organic solvents, and the solvent
selection is of crucial importance when working with
lipases. It is known that enzyme conformation changes
with changing the polarity of the solvent, and some
residual water is needed for maintaining enzyme in its
active conformation [1a].
Kinetic resolution of racemic compounds is an im-
portant practical method to produce enantiomerically
pure alcohols, which are intermediates for synthesis
of pharmaceuticals. The drawback with this method is
the yield of the desired enantiomer, which is limited to
50% and separation of the enantiomers, typically with
chromatographic technique, is needed. The products,
optically active esters, can be easily transformed to al-
Typically, activated esters, such as vinyl acetate or
4-chlorophenyl acetate, have been used as acyl donors
in kinetic resolution of secondary alcohols [2,3]. This
is because the reaction rate is higher when the acylation
Correspondence to: Dmitry Yu. Murzin; e-mail: dmurzin@
abo.Þ.
c
ꢀ
2010 Wiley Periodicals, Inc.

630
KIRILIN ET AL.
is irreversible. The kinetic resolution with, e.g., vinyl
acetate is irreversible, because an unstable product,
vinyl alcohol, is formed in stoichiometric amounts and
quickly reacts further to form acetaldehyde via keto–
enol tautomerization [2]. When a saturated acyl donor,
such as ethyl acetate, is used, ethanol is formed as a
by-product and the reaction is reversible. The equilib-
rium can be shifted toward the desired ester via, e.g.,
using an excess of acyl donor. The reaction rate is,
however, quite slow in ethyl acetate [4], and ethanol
decreases the reaction rate further by increasing the
hydrophilicity of the reaction mixture [3].
synthesis of R-1-phenylethyl acetate from acetophe-
none [12–14].
Note that lipase-catalyzed resolution for R,S-1-
phenylethanol has been commercialized [15,16]. Pre-
cise information about the type of acylation agent is not
available, and reactants such as succinic anhydride [15]
and vinyl esters [16] were described. In the latter case,
the reaction was considered [16] as irreversible since
the reaction product vinyl alcohol rapidly tautomerizes
into acetaldehyde. Despite commercial application of
R,S-1-phenylethanol, no information about concentra-
tion proÞles, values of kinetic constants, or reaction
rates is readily available. The current contribution is
aimed to Þll this apparent void.
The main parameters in the current work were tem-
perature, amount and type of acyl donor, reaction atmo-
sphere, and the presence of water and other substrates,
such as acetophenone. The kinetic model developed
in this study was based not on transformed data, such
as initial rates, but on primary data, i.e., concentration
proÞles. The kinetic parameters were determined for a
series of experiments performed at different tempera-
tures and concentrations of ethyl acetate.
The effect of temperature variations on the stereo-
chemistry of enzymatic reactions has been addressed
in the literature [5–9].
Dynamic kinetic resolution involves kinetic resolu-
tion together with the racemization of an undesired
enantiomer yielding more than 50% of the desired
product. An integrated catalytic reaction combining
three different reactions, i.e., hydrogenation, kinetic
resolution, and racemization in one step, is one-pot
synthesis of chiral acetates via acetophenone hydro-
genation to (R,S)-1-phenylethanol ((R,S)-1-PE) and
the acylation of its R-enantiomer with lipase. In this
reaction, homogeneous Ru-complex was used both as
a hydrogenation catalyst for acetophenone and as a
racemization catalyst for S-enantiomer [3]. Ethyl ac-
etate is used as an acyl donor, since vinyl acetate will
be hydrogenated immediately to ethyl acetate [3].
Kinetic modeling of lipase-catalyzed transesteriÞ-
cation has been demonstrated in a few publications
[2,10,11]. The modeling was based on a two-step se-
quence in the transesteriÞcation of 2-alkanol with vinyl
acetate, in which an acyl-enzyme complex was formed
in the Þrst step followed by its reaction between the R-
and S-1-phenylethanol in the second step [2]. The ini-
tial rates and the double reciprocal plots of inverse
rate versus inverse of either acyl donor or reactant
concentrations were taken as a basis for the earlier
models.
EXPERIMENTAL
Kinetic resolution of ( )-1-phenylethanol (Acros Or-
ganics, Fairlawn, NJ; >98% GC) was performed in a
glass reactor with the liquid phase volume of 50 mL.
The initial concentration of the racemic substrate
R,S-1-phenylethanol was 0.02 mol/L; thus the ini-
tial concentration of the respective enantiomers was
0.01 mol/L. Ethyl acetate (Sigma-Aldrich, Germany;
>99.5% GC), vinyl acetate (Sigma-Aldrich; >99+%),
2-methoxy ethyl acetate (Sigma-Aldrich; 98%), and
isopropenyl acetate (Sigma-Aldrich; >99%) were used
as acyl donors. Toluene (J. T. Baker, The Netherlands;
>99.5%, water content maximum 0.03%) or ethyl ac-
etate (Sigma-Aldrich; >99.5%; hydranal-composite 2,
water content <0.05%; Karl Fischer, Sigma-Aldrich)
was used as a solvent; and a lipase (Novozym 435, Can-
dida antarctica lipase immobilized on macroporous
polyacrylate resin beads, bead size 0.3–0.9 mm, S =
95.50 m2, average pore diameter 17.9 μm, bulk density
430 kg/m3, activity of 7000 PLU/g; Sigma-Aldrich)
[17,18], was applied as an acylation catalyst. The stir-
ring rate was 1000 rpm. The samples were taken after
different reaction times and analyzed by a gas chro-
matograph equipped with a chiral column CP Chirasil
Dex (250 μm × 0.250 μm × 25 m) and a ßame ioniza-
tion detector. The following temperature programme
was used for analysis: 100◦C (1 min)–0.30◦C/min-
To elucidate the reaction mechanism and to study
the kinetics in one-pot synthesis of R-1-phenylethyl
acetate, the kinetic resolution of (R,S)-1-PE (Fig. 1)
was separately investigated in the current work under
the analogous conditions as applied earlier in one-pot
OH
OH
OAc
EtOAc, Lipase
–EtOH
R,S–PE
R–PEAC
S–PE
Figure 1 Reaction scheme for kinetic resolution of (R,S)-
1-phenylethanol.
◦
130◦C–15 C/min–200◦C (10 min). The temperature
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KINETICS AND MODELING OF (R,S)-1-PHENYLETHANOL ACYLATION OVER LIPASE
of the injector and split ratio were 280◦C and 100:1,
respectively.
631
Effect of Reaction Atmosphere
The effect of hydrogen and argon was investigated
to elucidate the effect of the reaction atmosphere on
lipase activity in the acylation of R-1-phenylethanol.
In one-pot synthesis of R-1-phenylethyl acetate, the
reaction atmosphere is hydrogen and there is no knowl-
edge of the effect of the reaction atmosphere on lipase.
The results revealed the kinetic resolution of (R,S)-
1-phenylethanol was faster in hydrogen than in argon
(Fig. 2; Table I, entries 1, 2, and 4–6). The reason
behind these results requires further investigation.
RESULTS AND DISCUSSION
Enantioselectivity
In all experiments conducted with (R,S)-1-
phenylethanol, only (R)-1-phenylethanol was reac-
tive independent of temperature, reaction atmosphere,
or acyl donor type. Therefore within the precision
of chiral GC analysis, it can be stated that (S)-1-
phenylethanol was completely unreactive, leading to
more than 99% enantioselectivity. As expected, no re-
action was obtained starting from (S)-1-phenylethanol,
in perfect agreement with the literature as it is generally
known that the apparent rate constant in acylation of
S-enantiomer is four to six orders of magnitude lower
thanthat of R-enantiomer for conventional lipases [1b].
Effect of the Amount of Acyl Donor
The effect of the amount of acyl donor—ethyl
acetate—was studied using one, two, or three equimo-
lar amounts of ethyl acetate in the kinetic resolu-
tion of (R,S)-1-phenylethanol in toluene as a solvent
(Table II). The initial rates and the conversions in-
creased, as expected, with increasing amount of ethyl
acetate, and the equilibrium was shifted toward the
formation of the desired product. The initial reaction
rate was, however, much slower with ethyl acetate in
large excess (Table I, entry 4). The conversion of R-
1-phenylethanol after 300 min in ethyl acetate was
23%, which was lower than with equimolar amounts
or in a slight excess of acyl donor. This result can be
explained by the fact that the enzyme conformation
changes depending on liquid-phase composition, and
usually lower activities were achieved in more polar
solvents than in nonpolar solvents (see later).
Effect of Reaction Temperature
The kinetic resolution of (R,S)-1-phenylethanol was
performed under an argon atmosphere in a tempera-
ture range of 40–70◦C in ethyl acetate as a solvent. The
initial acylation rates of R-1-phenylethanol (no trans-
formation of S-1-phenylethanol was observed) were
calculated as
ꢀCR-1-PE
ꢀt
gcat
racylation
=
(1)
Effect of Acyl Donor
CR-1-PE, t, and gcat are the concentration of R-1-
phenylethanol, time, and catalyst amount, respectively.
The initial acylation rates increased with increasing
temperature (Table I, entries 1–4.). The initial acyla-
tion rate and the conversion after 1500 min increased,
as expected, with increasing temperature. The apparent
activation energy was determined by kinetic modeling
(see the section Reaction Mechanism and Kinetics).
The effect of the acyl donor was investigated at 70◦C in
toluene using three equimolar amounts of an acyl donor
in the kinetic resolution of (R,S)-1-phenylethanol
(Table III; Fig. 3). The following compounds were
applied as acyl donors: ethyl acetate, vinyl acetate,
2-methoxy-ethyl acetate, and isopropenyl acetate. The
initial acylation rates and conversions after 300 min are
Table I Kinetic Data from the Acylation of R-1-Phenylethanol over Lipase at Different Temperatures and under
Hydrogen or Argon Atmosphere
Entry
Atmosphere
Temperature (◦C)
Initial Acylation Rate (mmol/min/gcat.
)
Conversion after 1000 min (%)
1
2
3
4
5
6
Ar
Ar
Ar
Ar
H2
H2
40
55
63
70
55
70
0.002
0.0026
0.004
0.006
0.006
0.010
31
34
52
70
47
62
Ethyl acetate was used as a solvent and as an acyl donor.
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632
KIRILIN ET AL.
Figure 2 Concentration dependence of R-1-phenylethanol as a function of time in kinetic resolution of (R,S)-1-phenylethanol
over lipase in ethyl acetate as an acyl donor. Symbols: experiments performed under ( ) H at 70◦C, (ꢁ) Ar at 70◦C, (×) H at
ꢀ
2
2
55◦C, and (ꢂ) Ar at 55◦C.
Table II Kinetic Data from the Acylation of R-1-Phenylethanol over Lipase with Different Amounts of Acyl Donor,
Ethyl Acetate, under Argon Atmosphere at 70◦C
Entry
Solvent (Added Substrate)
Initial Acylation Rate (mmol/min/gcat.
)
Conversion after 300 min (%)
1
2
3
Toluene/3 equiv EtOAc
Toluene/2 equiv EtOAc
Toluene/1 equiv EtOAc
0.2
0.1
0.06
90
48
38
given in Table III. The following decreasing order of
the initial rates and conversions was achieved for differ-
ent acyl donors: isopropenyl acetate > vinyl acetate >
ethyl acetate > 2-methoxy ethyl acetate. The acylation
of R-1-phenylethanol exhibited the highest rate with
isopropenyl acetate. Analogous results were achieved
in the transesteriÞcation of 2-heptanol in chloroben-
zene at 80◦C, in which the conversion of the alkanol
after 240 min was 35% and 18% with isopropenyl ac-
etate and ethyl acetate, respectively [19]. The activated
esters, i.e., those containing unsaturated groups or elec-
tronegative functional groups, are known to react faster
than ethyl acetate as an acyl donor [3], and this was
also the case in the current study, in which a 2.4 times
higher initial acylation rate was achieved in toluene
using 3 equiv of isopropenyl acetate (Table III, entry
2) compared to the case using 3 equiv of ethyl acetate
in toluene (Table III, entry 4). The initial acylation
rate in 2-methoxyethyl acetate was, as expected, lower
than in ethyl acetate, since the methoxy group delo-
calizes the charge and thus 2-methoxy ethyl acetate
releases an acyl group more slowly than ethyl acetate.
An irreversible acylation occurred in the case of iso-
propenyl acetate and vinyl acetate [20,21] (Fig. 3). Un-
stable enols were formed and tautomerized rapidly to
the corresponding ketone with unsaturated acyl donors.
When vinyl acetate and isopropenyl acetate are used
as acyl donors, either vinyl alcohol [2] or isopropenyl
alcohol [4] is formed in the Þrst step; thereafter these
enols are converted via keto–enol tautomerization to
corresponding ketones, i.e., acetaldehyde or acetone,
respectively.
Table III Kinetic Parameters in the Acylation of R-1-Phenylethanol in Toluene over Lipase under Argon Atmosphere
at 70◦C Using Different Acyl Donors
Entry
Solvent (Added Substrate)
Initial Acylation Rate (mmol/min/gcat.
)
Conversion after 300 min (%)
1
2
3
4
Toluene/3 equiv vinyl acetate
0.32
0.48
0.08
0.2
97
100
70
Toluene/3 equiv Isopropenylacetate
Toluene/3 equiv 2-methoxyethyl acetate
Toluene/3 equiv ethyl acetate
90
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KINETICS AND MODELING OF (R,S)-1-PHENYLETHANOL ACYLATION OVER LIPASE
633
Figure 3 Concentration dependence of R-1-phenylethanol as a function of time in kinetic resolution of (R,S)-1-phenylethanol
over lipase at 70◦C under argon atmosphere. Symbols: ( ) in toluene and 3 equiv of ethyl acetate, (ꢂ) in toluene and 3 equiv
ꢀ
of 2-methoxyethyl acetate, (ꢁ) in toluene and 3 equiv of vinyl acetate, and (×) 3 equiv of isopropenyl acetate.
effects on enzyme activities is the octanol/water par-
tition coefÞcient; if its value, log P, is larger than
four, biocatalysts are known to be active [26]. The
inßuence of acetophenone is relevant, if one-pot syn-
Effect of Additives
The acylation of (R,S)-1-phenylethanol in the presence
of either water or acetophenone was investigated. The
initial acylation rates with different reaction mixtures
thesis of R-1-phenylethyl acetate would be studied.
are given in Table IV. The following order of the de-
This order can be interpreted partially with solvent hy-
creasing initial rates was achieved: toluene (3 equiv
drophobicities, in which log P—partition coefÞcient
ethyl acetate) > toluene (3 equiv ethyl acetate and
in octanol/water—is one quantiÞcation tool. The log
acetotophenone) > toluene (3 equiv ethyl acetate and
P values for different solvents are reported in Table V.
water). Typically, the effect of water on enzyme activ-
When comparing the log P values with the initial
ity is given as a function of water activity (aw) [22]
and the reactants were preequilibrated to perform the
investigations with known water amounts [23]. When
a polar solvent would be used together with enzymes,
the critical water content, i.e., with which an optimal
enzyme activity can be achieved, is higher than in a
nonpolar solvent due to the fact that water exhibits
higher afÞnity to a polar solvent compared to a non-
polar one. Thus polar solvents can strip the essential
water from the enzyme [24].
Table V Partition Coefficients for Different Solvents
(Octanol/Water)
Solvent
Log P
Reference
Toluene
2.5
1.14
[1]
Acetophenone
Ethyl acetate
Ethanol
[33]
[34]
[35]
[34]
0.67
−0.31
Another tool to investigate the hydrophobic-
ity/hydrophilicity of organic solvents [25] and their
Water
−1.15
Table IV Kinetic Results in the Acylation of R-1-Phenylethanol over Lipase Using Three Equivalents of Ethyl Acetate
as an Acyl Donor and Adding Water and Acetophenone in the Reaction Mixture
Entry
Solvent (Added Substrate)
Initial Acylation Rate (mmol/min/gcat.
)
Conversion after 300 min (%)
1
2
3
Toluene/3 equiv EtOAc
Toluene/3 equiv EtOAc/AP
Toluene/3 equiv EtOAc/H2O
0.2
0.18
0.0016
90
66
44
Reaction performed under argon atmosphere at 70 ◦C.
AP is acetophenone.
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634
KIRILIN ET AL.
Figure 4 Concentration dependence of R-1-phenylethanol as a function of time in kinetic resolution of (R, S)-1-phenylethanol
over lipase. Symbols: ( ) in toluene and 3 equiv of ethyl acetate, (ꢁ) in toluene and 3 equiv ethyl acetate, 0.5 g water added,
ꢀ
and (×) in toluene and 3 equiv of ethyl acetate, 20 mg acetophenone added.
acylation rates, it turned out that the initial acylation
rate decreased with increasing solvent polarity. One
exception was found in this series, namely the log P
value for acetophenone was higher than that of ethyl
acetate and still an addition of acetophenone slightly
decreased the initial acylation rate.
The conversions after prolonged reaction time fol-
lowed the same order as the initial rates, and the ki-
netics is depicted in Fig. 4. The results thus showed
that the presence of acetophenone slowed the rate of
transesteriÞcation of R-1-phenylethanol.
It is assumed that the acyl donor, ethyl acetate (B),
binds Þrst with the free enzyme (E) and forms a
noncovalent enzyme-acyl complex, which releases a
modiÞed enzyme (EQ). The reactant, R-1-phenylethyl
alcohol (A), combines with EQ, which subsequently
relinquishes the R-phenylethyl acetate (P). Ethanol (I)
was formed as a stoichiometric product.
The derivation of a two-step sequence with an irre-
versible second step is [29]
k1k2CACB
r =
(2)
k1CA + k2CB + k
−1
which after dividing the numerator and denominator
by k−1 gives
REACTION MECHANISM AND KINETICS
The kinetics of the resolution of (R,S)-1-phenylethanol
was investigated using lipase as a catalyst. Acyl-
enzyme complexes are crucial intermediates in all
lipase-catalyzed reactions [27]. From the mechanistic
point of view, it has been suggested that the lipase Þrst
forms an acyl-enzyme complex with the acyl donor
[28]. A sequential step mechanism was applied for en-
zymatic kinetic resolution of R-1-phenylethyl alcohol
to R-phenylethyl acetate over immobilized lipase un-
der Ar, using ethyl acetate as an acyl donor and solvent.
The reaction sequence is depicted as follows:
(k1/k−1)k2CACB
k1CA/k−1 + k2CB/k−1 + 1
r =
(3)
The equation can be simpliÞed for the low concen-
tration domain of A; i.e., k1CA/k ꢁ k2CB/k−1 + 1.
−1
The simpliÞed model is written as follows:
k2K1CACB
ꢀ
ꢁ
r =
(4)
k2
1 +
CB
k
−1
It should be noted that CB was assumed to be constant
in this series.
Acylation reactions were carried out at temperatures
at 40, 55, and 70◦C in an excess of acylation agent,
k1
−→
E + B
EQ
←−
k
−1
k2
EQ + A −→ E + P + I
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KINETICS AND MODELING OF (R,S)-1-PHENYLETHANOL ACYLATION OVER LIPASE
635
k2
The temperature dependence of the lumped kinetic
ethyl acetate; thus it can be assumed that
leading to
CB ꢁ 1,
k
−1
constant kꢂ is evaluated by the ꢂArrhenius equation.
ꢃ
E
1
T
1
mean
ai
−
kiꢂ = k0 × e−
(11)
r = kꢂCA
(5)
(6)
R
T
k1
kꢂ =
k2
The activation energy and the rate constants were deter-
mined by estimation of the parameters via minimiza-
tion of the residual sum of the squares
k
−1
where r is the rate of reaction and CA and kꢂ are the
concentration of R-1-phenylethyl alcohol and the ap-
peared reaction rate constant, respectively.
The effect of the amount of acyl donor, ethyl acetate,
was investigated in another series at 70◦C. The exper-
imental set was conducted using 0.5, 1, and 3 equiv
molar amounts of ethyl acetate and modeled with the
following equation:
ꢄ ꢄ
Q =
(ci,t,exp − ci,t, mod el)2 wi,t
(12)
t
i
where ci,t,exp, ci,t,model, and w are the experimentally
recorded concentrations, the concentrations predicted
by the model, and the weight factors, respectively. The
weight factor w was set to 1 for all experimental points.
The software Modest was used for minimizing the
objective function and the rate constants were esti-
mated with the simplex method and then switched to
Levenberg–Marquardt method [31]. The ordinary dif-
ferential equations (ODE) describe the reactor model
by the backward difference method. The equations for
the reaction kinetic model are ODEs and were inte-
grated starting from the initial conditions.
r = k2K1CACB = kꢂꢂCACB
(7)
which is obtained from Eq. (3) when 1 ꢃ
(k1/k−1)CA + (k2/k−1)CB. It should be noted that
since the rate constants of enzymatic reactions are sig-
niÞcantly inßuenced by the reaction environment (sol-
vent) the apparent rate constants kꢂand kꢂꢂ are solvent
dependent and thus are not equal to each other.
Since deactivation was observed in the acylation
step and it is known from the literature [30] that li-
pase can be deactivated in the presence of ethanol, it
was assumed that formed ethanol can act as a compet-
itive inhibitor, leading to a conventional description of
competitive inhibition
MODELING RESULTS
The Þt of the model depicted by Eq. (6) to the experi-
mental data performed under different reaction temper-
atures is presented in Fig. 5. The degree of explanation
for this model was 99.21%. The estimated rate constant
(kꢂ) and the activation energy (Ea) are listed in Table
VI. The experimental data were very well described
with the model according to Eq. (6) as can be seen
from Fig. 5.
Equation (7) describes the effect of using differ-
ent amounts of acyl donor, 0.5, 1, and 3 equiv molar
amounts of ethyl acetate. The comparison of the esti-
mated and measured data using different amounts of
acyl donor demonstrated poor description (not shown).
The reason for this is that lipase was deactivated in the
presence of ethanol. An adequate Þt of the model was
kꢂꢂCACB
r =
(8)
(1 + KICI)
where KI is the binding constant of ethanol and CI is
the concentration of the formed ethanol. In a special
case of strong inhibition, 1 ꢁ KICI, Eq. (8) can be
rewritten as
kꢂꢂCACB
KICI
CACB
CI
r =
= kꢂꢂꢂ
(9)
where kꢂꢂꢂ = kꢂꢂ/KI.
Table VI Estimated Parameters for Different
Temperatures
REACTOR AND PARAMETER ESTIMATION
Parameter
Value
Error (%)
The mass balances for a liquid-phase component (i) in
a batch reactor were written as
kꢂ
1.322 × 10−4 dm3/(g min)
1.8
5.0
Ea
24.5 kJ/mol
dci
The degree of explanation for the experiments was 99.21%.
Tmean = 55◦C.
= ri
(10)
dt
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636
KIRILIN ET AL.
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0
200
400
600
800
1000
1200
1400
1600
1800
0
500
1000
1500
Time (min)
Time (min)
(a)
(b)
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0
200
400
600
800
1000
1200
Time (min)
(c)
Figure 5 Comparison of the estimated and measured kinetic data. (a) 40◦C, (b) 55◦C, (c) 70◦C; ( ) R-1-phenylethyl alcohol;
◦
(∇) R-1-phenylethyl acetate. Mass of enzyme 62.5 mg.
achieved by introducing the competitive inhibition of
ethanol into the model (Eq. (8)). It turned out, however,
that parameters kꢂꢂ and KI were highly correlating; thus
Eq. (9) is able to describe the experimental data reason-
ably well. The estimated kinetic parameter kꢂꢂꢂ for the
experiments performed with 0.5, 1, and 3 equiv mo-
lar amounts of ethyl acetate is 1.642 × 10−3 dm3/min
g with a standard error of 7.5%. The residual sum of
squares was 0.2717 × 10−4; the degree of explanation
was 90.25%, and the model Þts the experimental data
rather well as demonstrated in Fig. 6.
means that there is no correlation at all, and −1.000
stands for a perfect negative correlation. The correla-
tion matrix of experiments performed under different
temperatures (Table VII) shows that there is a very low
positive correlation between parameters Ea and kꢂ.
The estimated kinetic constants were identiÞed by
parameter sensitivity analysis plots using the Markov
chain Monte Carlo (MCMC) method (Fig. 7). The dis-
tribution of the parameters showed how well the param-
eters were identiÞed [30]. The prediction distributions
The correlation matrix of estimated kinetic param-
eters is presented in Table VII for experiments carried
out under different temperatures. The correlation ma-
trix describes the correlation among kinetic parame-
ters. The diagonal elements of the correlation matrix
are always equal to 1.000 since they show the correla-
tion of a column with itself. Correlation on a scale with
1.000 indicates a perfect positive correlation; 0.000
Table VII Correlation Matrix of the Parameters for
Different Temperatures
kꢂ
Ea
kꢂ
1.000
0.048
Ea
1.000
International Journal of Chemical Kinetics DOI 10.1002/kin

KINETICS AND MODELING OF (R,S)-1-PHENYLETHANOL ACYLATION OVER LIPASE
637
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0
50
100
150
200
250
300
350
400
450
0
50
100
150
200
250
300
350
400
Time (min)
Time (min)
(a)
(b)
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0
50
100
150
200
250
300
350
400
450
Time (min)
(c)
Figure 6 Comparison of the estimated and measured kinetic data using different amounts of acyl donor in one-pot synthesis of
R-1-phenylethyl acetate. (a) 0.5 equiv of ethyl acetate at 70◦C, (b) 1 equiv of ethyl acetate at 70◦C, (c) 3 equiv of ethyl acetate
at 70◦C; ( ) R-1-phenylethyl alcohol; (∇) R-1-phenylethyl acetate. Mass of enzyme 25 mg.
◦
Figure 7 Parameter sensitivity analysis plots for experiments performed under different temperatures (2D and 1D marginal
posterior distribution plots Ea and kꢂ parameters).
International Journal of Chemical Kinetics DOI 10.1002/kin

638
KIRILIN ET AL.
revealed to which extent the parameter uncertainty is
relevant with respect to the model predictions. The
estimation of the model parameters was performed ac-
cording to the Bayesian paradigm. All of the model-
ing parameters were treated as statistical distributions
to obtain the optimum range of the estimated values.
MCMC plots for experiments performed under differ-
ent temperatures given in Fig. 7 reveal that the optimum
values of kinetic parameters, Ea and kꢂ, were identiÞed.
ing into account competitive inhibition by the ethanol
product. The kinetic model described the experimental
data well.
û
This work is part of the activities at the Abo Akademi Univer-
sity Process Chemistry Centre within the Finnish Centre of
Excellence Program (2000-2011) appointed by the Academy
of Finland.
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