Kinetic cutinase-catalyzed esterification of caproic acid in organic solvent system

Article abstract of DOI:10.1016/j.molcatb.2010.06.005

Practical application of any chemical reaction requires the knowledge of its kinetics; in particular if one wishes to be able to describe a chemical reactor over an extended range of reaction conditions or if one intends to optimize the reaction conditions, a suitable kinetic model must be obtained. In order to ensure that the model is applicable over a wide range of experimental conditions it should be based on a mechanistic scheme describing the fundamental steps involved in the reaction; the development of these kind of models can also be used to provide insight into the processes that are taking place. A kinetic study, using experiments carried out in a batch stirred reactor, has been made for the enzymatic esterification of caproic acid with ethyl alcohol catalyzed by Fusarium solani pisi cutinase. Different acid and alcohol concentrations (whilst also varying the acid/alcohol molar ratio) were tested and the results were used to identify the best reaction scheme to describe the results obtained over an extended range of conditions. Several different approaches were used to identify the most adequate mechanistic model, namely by resorting to the quasi stationary state and the rate-limiting hypothesis. The main kinetic characteristics observed in esterification reaction were found to follow an ordered Ping-Pong Bi-Bi mechanism but different modifications were used o ensure that the kinetic model was applicable over the entire range of experimental conditions that were covered.

Full text of DOI:10.1016/j.molcatb.2010.06.005

Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
Contents lists available at ScienceDirect
Journal of Molecular Catalysis B: Enzymatic
journal homepage: www.elsevier.com/locate/molcatb
Kinetic cutinase-catalyzed esterification of caproic acid in organic solvent system
Dragana P.C. de Barros∗, Francisco Lemos, Luís P. Fonseca, Joaquim M.S. Cabral
IBB-Institute for Biotechnology and Bioengineering, Instituto Superior Técnico, Centre for Biological and Chemical Engineering, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
a r t i c l e i n f o
a b s t r a c t
Article history:
Practical application of any chemical reaction requires the knowledge of its kinetics; in particular if one
wishes to be able to describe a chemical reactor over an extended range of reaction conditions or if
one intends to optimize the reaction conditions, a suitable kinetic model must be obtained. In order to
ensure that the model is applicable over a wide range of experimental conditions it should be based on
a mechanistic scheme describing the fundamental steps involved in the reaction; the development of
these kind of models can also be used to provide insight into the processes that are taking place.
A kinetic study, using experiments carried out in a batch stirred reactor, has been made for the enzy-
matic esterification of caproic acid with ethyl alcohol catalyzed by Fusarium solani pisi cutinase. Different
acid and alcohol concentrations (whilst also varying the acid/alcohol molar ratio) were tested and the
results were used to identify the best reaction scheme to describe the results obtained over an extended
range of conditions. Several different approaches were used to identify the most adequate mechanis-
tic model, namely by resorting to the quasi stationary state and the rate-limiting hypothesis. The main
kinetic characteristics observed in esterification reaction were found to follow an ordered Ping-Pong
Bi–Bi mechanism but different modifications were used o ensure that the kinetic model was applicable
over the entire range of experimental conditions that were covered.
Received 14 March 2010
Received in revised form 31 May 2010
Accepted 10 June 2010
Available online 16 June 2010
Keywords:
Kinetic model
Enzymatic esterification
Cutinase
Ethyl caproate
Organic solvent
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
[25]. The cutinase was used in fundamental studies on the hydrol-
ysis of triglycerides [26], transesterification [15–17], in studies of
Studies of various enzymes (mostly lipases and esterases) in
enzymatic synthesis of short chain acid esters, compounds, which
have very significant application in cosmetic, pharmaceutical and
food industries, increased last few decades [1–4]. Enzyme catalyzed
esterification is an interesting option when compared to chemical
synthesis as it has the advantages of being able to be carried-out
under mild reaction conditions, and to ensure the high quality and
purity of the products; also enzymes have been considered as nat-
ural components by food regulatory agencies [5–7].
Fusarium solani pisi cutinase activity in hydrolysis, esterification
and transesterification has been extensively exploited in recent
years and several applications in different industrial fields have
been proposed [8]. Numerous report of using cutinases in dif-
ferent reaction media, often dissolved in aqueous solution but
also suspended as a powder or immobilized, have been reported
[8,9]. Immobilization has been commonly obtained by adsorption
onto solid supports [10–19] or encapsulation in reverse micelles
of sodium bis(2-ethylhexyl)sulfosuccinate (AOT) [20–23], phos-
phatidylcholine [24], or cetyltrimethylammonium bromide (CTAB)
esterification reactions [27–31] and in order to clarify cutinase
mechanism of reaction regarding stereo-selectivity and specificity
[32,33]. The understanding of the reaction kinetics is of impor-
tance not only to explain in the analysis of the mechanism of
the reaction, but also because the information about the rate of
product formation and changes in experimental system are essen-
tial for the design of appropriate reactor and later industrial scale
up.
Modeling of cutinase-catalyzed reaction for transesterification
[18,21,22] and esterificaton reaction [24] has been reported. A Ping-
Pong Bi–Bi mechanism with competitive inhibition by the alcohol
was proposed by Serralha et al. [18] for the alcoholysis of butyl
acetate with hexanol in isooctane catalyzed by cutinase immobi-
lized on NaY zeolite. Ping-Pong Bi–Bi mechanism was also proposed
for the same reaction in AOT/isooctane reverse micellar system by
Carvalho et al. [22] and by Sebastião et al. [21] and Pinto-Sousa
et al. [24] for the esterification reaction in phosphatidylcholine
reversed miccelar system. Although these representative examples
of research work focused on the kinetic analysis of cutinase-
catalyzed reaction, mostly performed on transesterification and
esterification reactions in reversed micellar systems, no detailed
kinetic model for esterification reaction in organic solvent, namely
in iso-octane, by lyophilized cutinase, was presented, despite the
catalytic potential of cutinase in organic solvent system. However,
∗
Corresponding author. Tel.: +351 21 8419065; fax: +351 21 8419062.
E-mail addresses: dragana 05@hotmail.com, dragana@ist.utl.pt
(D.P.C. de Barros).
1381-1177/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.molcatb.2010.06.005

286
D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
introduced in this model to improve the description of the reaction
Nomenclature
system with the aim of obtaining a model that can be used over a
sufficiently wide range of operating conditions so as to allow the
optimization of a bioreactor for this reaction.
As a model system the production of ethyl caproate from caproic
acid and ethanol has been used. Ethyl caproate is a flavour com-
pound that is incorporated in a wide range of aromas such as: apple,
apple green apple, banana, beer, butter, cognac, herbal, pineapple
and wine [37].
Ac
acid
Al
alcohol
Es
ester
E
free enzyme
[E]t
EAc
EAc2
total enzyme concentration (mM)
enzyme–acyl complex
enzyme–acyl complex with two bound acid
molecules
2. Materials and methods
EAc3
EAl
enzyme–acyl complex with three bound acid
molecules
enzyme–alcohol complex
2.1. Enzyme and chemicals
K
a1, Ka2, Ka3, Kb1, Kb2, Kb3 equilibrium constants
Ki inhibition coordination constant
a1, ka2, ka3, kb1, kb2, kb3 rate constants (mM−1 min−1
F. s. pisi cutinase wild-type was biosynthesized by recombinant
S. cerevisiae SU50 strain as described by Calado et al. [38].
k
)
Caproic acid (C6) (99.0%, Fluka, Germany) and ethanol abs.
(VWR, Germany) were used for ester synthesis, while iso-octane
(99.5%, Fluka, Germany) was used as organic solvent and n-decane
(VWR, Germany) was used as an internal standard for gas chro-
matography (GC). Sodium sulfate anhydride (Acros, Geel, Belgium)
was used to dry iso-octane as organic media before and after
esterification reactions. Saturated salt solution of sodium chloride
(Panreac, Spain) was used for equilibration of enzyme and sub-
strates. All other chemicals used were of analytical grade.
the development of a detailed kinetic model that is capable of
describing the reaction over an extended range of reactions condi-
tions is of paramount importance for practical applications, namely
for the optimisation of reaction systems.
Cutinases are a group of enzymes that can be considered as a
link between esterases and lipases. As small carboxylic ester hydro-
lases, the sub-family of cutinases consists of 20 members based
on amino-acid sequence similarity, which display hydrolytic activ-
ity on cutin polymers and efficiently hydrolyze soluble esters and
emulsified triacylglycerols. Cutinase belongs to the family of ser-
ine hydrolases containing its catalytic serine centre at the middle
of a sharp turn between a ␤-strand and a ␣-helix [14,34]. The F.
s. pisi catalytic triad, Ser-120, Asp-175 and His-188, is accessible to
the solvent and it can possibility to accommodate different sub-
strates. The Asp-175 hydrogen binds to His-188, thus promoting
the interaction of the imidazole ring with Ser-120. The histidine
acts as a base, deprotonating the serine to generate a very nucle-
ophilic alkoxide (–O–) group (Fig. 1). The serine in the active centre
of the enzyme is a very strong nucleophile, which attacks the car-
bonyl group of the acid, forming a stable tetrahedral intermediate
acyl–enzyme complex. The acyl–enzyme complex is stabilized by
the oxyanion hole [12]. Water is then released and the structure
reverts to the planar carbonyl flat plane acyl–enzyme intermedi-
ate. The alcohol acts afterwards as a new nucleophile and links
to the tetrahedral intermediate. Subsequently, as the final step,
the resolution of tetrahedral complex yields the ester and the free
enzyme. This reversible reaction was shown to follow a Ping-Pong
Bi–Bi mechanism [8,35].
In previous work made by de Barros et al. [30] F. s. pisi cutinase
expressed in Saccharomyces cerevisiae showed a high potential for
the synthesis of short chain ethyl esters in iso-octane, an organic
solvent recognized as a safe ingredient for use in the food and
beverage industrial processes by FDA. Among the advantages of
using the organic solvent media for enzymatic ester synthesis are
the increased solubility of non-polar substrates and products and
the shifting the thermodynamic equilibrium of the reaction to
favour ester synthesis over hydrolysis. Log P (the partition coeffi-
cient between water and 1-octanol) is generally used to describe
the solvent hydrophobicity. It has been reported that solvent with
intermediate log P (around 4) are suitable for esters synthesis [36].
Log P of iso-octane is 4.5 and by previous work it was shown that it
favours the esterification reaction, reason for which it was chosen
for this work.
2.2. Purification and lyophilization of cutinase
The isolation and purification of cutinase excreted by recom-
binant S. cerevisiae SU50 strain were carried out by expanded bed
adsorption (EBA) [39].
The pool of elution fractions exhibiting the highest cutinase
activity was firstly dialyzed against distilled water and then frozen
at −80 ◦C and lyophilized (B.BRAUN Biotech. International CHRIST
Alpha 2-4) overnight. Lyophilized cutinase preparations were char-
acterized by measuring the cutinase esterolytic activity and protein
content [40–42] and stored at −20 ◦C before used in esterification
reactions.
2.3. Characterization of the cutinase preparations
The cutinase estereolytic activity was assayed using a spec-
trophotometric method based on monitoring the hydrolysis of
p-nitrophenylbutyrate (p-NPB) to nitrophenol (p-NP), a yellow
compound easily identify and quantify by the absorbance at 400 nm
[40]. One unit of cutinase estereolytic activity was defined as the
amount of enzyme required to convert 1 ␮mol of p-NPB to p-NP
per 1 min, at 30 ◦C and pH 8. The extinction coefficient of p-NP was
consideredtobe1.84 × 104 (M−1 cm−1), asindicatedby the supplier
(Sigma).
The protein concentration was determined by the method of
PEARCE (BCA assay) with reference to a standard, the Bovine Serum
Albumin (BSA) (Merck) [42].
Specific activities of lyophilized cutinase preparations were of
170 U mg−1. These enzyme samples when loaded in SDS elec-
trophoresis gel showed a single band of 22 kDa [41].
2.4. Methods for monitoring substrate and ester concentrations
The concentrations of ethanol, caproic acid and ethyl caproate
were determined using a Hewlett-Packard model 5890 gas chro-
matograph, equipped with a flame ionization detector (FID).
Since mechanism based kinetic models are usually better for
interpolating and extrapolating purposes, the goal of this study is
to estimate the kinetic parameters of this system in terms of a Ping-
Pong Bi–Bi model and to analyse possible refinements that can be
A WCOT Fused Silica coating CP Chirasil-Dex CB column,
25 m × 0.25 mm, DF = 0.25 (Varian Inc.) was used to separate the
componentsin the reaction mixture. n-Decane was usedas aninter-
nal standard in the computation of ethyl caproate and respective

D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
287
Fig. 1. Schematized mechanism for the esterification catalyzed by cutinase.
substrates concentrations in the reaction media. Nitrogen was used
2.6. Kinetic model
as carrier gas. The oven temperature was held at 50 ◦C for 4 min
before being raised to 160 ◦C for 1.67 min at 15 ◦C min−1; the injec-
tor temperature was set at 200 ◦C and the detector temperature
was set at 250 ◦C.
The base Ping-Pong Bi–Bi mechanism was used as a starting
point and modifications have been introduced so as to improve the
descriptive ability of the model. For each kinetic model the material
balances for ethanol, caproic acid, ethyl caproate, water and, in the
case of the base model for the enzyme containing species, were
derived and the corresponding set of differential equations was
numerically solved using the Euler’s method. The model was fitted
to the experimental data (all the available experiments were used
simultaneously) by a least squares procedure where the objective
function consisted of the sum of the square of relative errors of the
concentrations of ethanol, caproic acid, ethyl caproate measured
in all experiments for all times; this corresponded to a total of 807
data points distributed over 18 different experiments with different
initial concentrations. The experimental conditions, for the set of
experiments used in the fitting procedure are given in Table 1. This
procedure was carried-out using a Microsoft Excel 2003 spread-
sheet and the estimation of the parameters was carried-out using
the Solver tool.
2.5. Enzymatic esterification
The esterification of acid and alcohol by cutinase was carried out
in iso-octane as organic solvent. Unless otherwise stated a typical
esterification reaction for ethyl esters synthesis was carried out in
7 ml of working volume inside a 10 ml flasks capped with rubber
(EPDM stoppers, black, Sigma-Aldrich, Germany) so as to minimize
the evaporation or loss of volatile compounds. Reaction medium
and enzyme were pre-equilibrated separately at 30 ◦C, for 72 h,
inside closed vessels containing saturated NaCl aqueous solution
to control water activities (aw = 0.75). Alcohol, acid and n-decane
were mixed thoroughly in iso-octane before the addition of enzyme
(lyophilized form). The first sample (zero point of the reaction) was
collected before enzyme addition. The enzymatic ester synthesis
was performed in an incubator (AGITORB 16OE, Aralab, Portugal)
at 30 ◦C and cutinase activity of 240 10 U ml−1 reaction mixture
(r.m.). The experimental setup enabled us to run multiple parallel
experiments using a multiple magnetic stirrer (S.B.S. Instruments
A-23) and the simultaneous operation of 6–12 reactors. A control
run, for each set of experimental conditions, was performed using at
least one blank experiment (without the enzyme) running in paral-
lelfor eachenzymatic estersynthesis. Experiments wereperformed
at least in duplicate and the experimental error was estimated as
less than 8%. The calibration curves that were obtained allowed
us to estimate accurately the concentration of caproic acid above
30 mM; bellow this value there is a significant error in the deter-
mination. However, the experimental caproic acid concentration
were usually above 30 mM. The fact that the calibration curve is
not accurate below 30 mM may explain why the model has more
difficult in fitting experiments with low caproic acid concentra-
tions. During the reaction, a magnetic stirring set at 300 rpm was
used. Samples were withdrawn periodically using a needle, with-
out destroying the rubber cap. The reaction yield was calculated
according to the molar ratio between the ethyl ester and respective
limiting substrate, alcohol or acid.
3. Results and discussion
3.1. Base kinetic model
The esterification of caproic acid by ethanol catalyzed by
cutinase is an enzymatic reaction system which involves two reac-
Table 1
Experimental conditions for the set of experiments used in the fitting of the differ-
ent models. All concentrations are given in mM. Enzyme concentration is equal to
0.1 mM in all runs.
Run
Ethanol
conc.
Carpoic acid
conc.
Run
Ethanol
conc.
Carpoic acid conc.
1
2
3
4
5
6
7
8
9
99
188
204
201
214
202
232
216
105
87
196
175
140
127
100
74
10
11
12
13
14
15
16
17
18
104
165
160
167
122
110
92
99
197
178
164
172
181
183
106
95
45
196
229
121

288
D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
Table 2
and somewhat overestimated when the concentration of alcohol
was in the range from 175 to 200 mM. This implied that, in order to
have a better description of the reaction under all conditions cov-
ered by the experiments some modifications should be introduced
in the overall scheme.
Kinetic constant obtained for the synthesis of ethyl caproate catalyzed by cutinase.
Complete
model
Quasi stationary
state model
Rate limiting
step model
ka1 (mM−1 min−1
(mM−1 min−1
)
1.67
0.876
2.42
k
)
)
0.022
However, working with this set of equations posed a series of
issues that had to be dealt with. Since the concentrations of the var-
ious species have different orders of magnitude, in particular since
the enzyme concentration is much smaller than that of the other
species present, and since the reactions proceed at different speed,
the numerical integration of Eqs. (3)–(8) requires a relatively small
integration step and, consequently, very lengthy integrations. In
order to circumvent this difficulty we have tried to apply a set of
approximating assumptions that would allow us to obtain a global
reaction rate law. Although using a global reaction law has the
disadvantage of not allowing us to compute the individual steps
separately, it has the distinct advantage of giving a more concise
description of the reactor and being easier to adapt for the final
goal of optimising reaction conditions in a bioreactor.
−a1
Ka1
kb1 (mM−1 min−1
(mM−1 min−1
76a
0.36a
0.39
)
0.274
7.12
302,053
0.026
0.0020
226,802
0.024
0.073
207,729
k
−b1
Objective function
aComputed as Ka1 = ka1/k
.
−a1
tants and two products. As most of the kinetic studies on the
cutinase-catalyzed synthesis of esters have described the reaction
as following a Ping-Pong Bi–Bi kinetic mechanism with inhibition
by the substrates, this reaction mechanism was taken as the basis
for this work. Taking into account that for this reaction it is neces-
sary that an acyl–enzyme bond is formed, the first step will be the
formation of the active enzyme–substrate complex between cuti-
nase and the caproic acid. The sequence of steps involved in the
reaction can be schematized as in Fig. 1.
To obtain a global reaction rate some additional assumptions
have to be made. On one hand we tried the quasi stationary state
assumption and on the other hand we used the rate-limiting step
hypothesis.
According to this scheme, and assuming that the first two steps
occur rapidly, we can write the general mechanism by following
reaction steps.
We will start by considering that a quasi stationary state
approach can be used and, thus the derivatives of the species involv-
ing the intermediates (Eqs. (3) and (8)) are zero. This assumption
is usually adequate when the intermediate species are very reac-
tive and, looking at the reaction rate constants that were estimated
using the complete model, this might not be the case since the reac-
tion rate constant for the second reaction is actually smaller than
for the first one. It should be noted that the relative rate of the two
reactions cannot be ascertained just by looking at the values of the
kinetic rate constants, since all of these reactions are the second
order and the concentrations of the various species are quite dif-
ferent. In fact for this hypothesis to be applicable it is sufficient that
the concentration of the intermediate is kept sufficiently low during
the course of the reaction, so that its derivative can be taken as zero.
Thus, albeit bearing in mind the inherent and possible limitations of
this approach, the advantages of having a global kinetic rate law are
significant and we will see what the application of this assumption
provides in terms of the overall fitting to the experimental data.
From the quasi stationarystate assumption therelationbetween
the enzyme–acyl concentration and the concentration of the free
enzyme can be computed.
k
a1
E + Ac ꢀ EAc + H2O
(1)
k
−a1
k
b1
EAc + Al ꢀ Es + E
(2)
k
−b1
where ka1, k−a1, kb1, k
are the rate constants for the different
−b1
steps.
Assuming that these reactions have simple order kinetics and
since all reactions were carried-out in closed vessels (thus allowing
us to neglect evaporation of any of the components in the mixture),
the material balances for each of the species involved were written,
leading to the following set of differential equations:
d[E]
dt
= −ka1[E][Ac] + k−a1[EAc][H2O] + kb1[EAc][Al] − k−b1[E][Es]
(3)
d[Ac]
dt
= −ka1[E][Ac] + k−a1[EAc][H2O]
(4)
(5)
(6)
(7)
d[H2O]
k
a1[E][Ac] + k−b1[E][Es]
kb1[Al] + k−a1[H2O]
= ka1[E][Ac] − k−a1[EAc][H2O]
[EAc] =
(9)
dt
d[Al]
dt
= −kb1[EAc][Al] + k−b1[E][Es]
= kb1[EAc][Al] − k−b1[E][Es]
Taking into account that the total amount of enzyme that was added
to the reaction mixture is fixed we can obtain a relation between
the concentrations of the two enzyme species and the total enzyme
concentration
d[Es]
dt
ꢀ
ꢁ
d[EAc]
dt
k
a1[Ac] + k−b1[Es]
= ka1[E][Ac] − k−a1[EAc][H2O] − kb1[Ac][Al] + k−b1[E][Es]
(8)
Et = 1 +
[E]
(10)
kb1[Al] + k−a1[H2O]
As a first step the complete model described by these equations,
and the relevant initial conditions for each of the runs that were
performed, was fitted, using the four kinetic rate constants as the
fitting parameters, to the experimental data available. The param-
eters obtained by the fitting are presented in Table 2.
The model was found to provide a reasonable description of the
data but presented significant deviations in the runs where either
the acid or the alcohol concentrations were near 200 mM.
In particular, the reaction rate seemed to be underestimated
when the acid concentration was in the range from 160 to 200 mM
where Et is the concentration of enzyme that was added. From Eqs.
(9) and (10) we can obtain
kb1[Al] + k−a1[H2O]
[E] =
Et
(11)
k
a1[Ac] + k−b1[Es] + kb1[Al] + k−a1[H2O]
and
k
a1[Ac] + k−b1[Es]
[EAc] =
Et
(12)
k
a1[Ac] + k−b1[Es] + kb1[Al] + k−a1[H2O]

D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
289
A global rate equation can be obtained.
a1kb1[Ac][Al] − k−a1k−b1[Es][H2O]
a1[Ac] + k−b1[Es] + kb1[Al] + k−a1[H2O]
According to this model a global reaction stoichiometry was used
and the concentrations of the various species were computed
according to the rate equation given in Eq. (10).
The model was solved for all experimental conditions that were
used, as before, and the estimated kinetic parameters are, again,
shown in Table 2.
k
r =
Et
(13)
k
The data on Table 2 shows that the rate limiting step approxi-
mation provides a better description of the reaction, as shown by
the fact that its objective function is around 10% lower that for the
quasi-steady state one. The rate limiting approximation, however,
does not allow the simultaneous estimation of ka1 and k−a1, since
the first step is considered to be in equilibrium. However, compar-
ing the values of Ka1 for quasi stationary state model (Ka1 = 0.36)
and rate limiting step model assumption Ka1 = 0.39 we can see that
the constants that were estimated are quite similar (Table 2).
Also, from the fittings of the model to the experimental data, we
can see that both models are able to describe in a reasonable way
the experimental data although some significant discrepancies are
observed, again, as for the complete model, namely for the cases
where either the acid or the alcohol concentrations are higher. As
explained above we will introduce some refinements in the model
may be required to describe the experimental data over the entire
range of experimental conditions that were used. We will now dis-
cuss these refinements. Since the quasi stationary state assumption
and the rate limiting step approximation give comparable results,
and since deriving global rate equations for more complex models
is significantly easier within the rate limiting step approximation
and this has also provided a better fitting to the experimental data,
we will use the latter hereafter.
Ac + Al → Es + H2O
The fitting of this model to all experimental data, as it was done for
the complete model, estimates a set of parameters that are given
in Table 2.
(14)
Looking at the parameters in Table 2 we can see that the
approximate model actually provides a better description of the
experimental data, as seen by the fact that the objective function
is around 2/3 of the objective function for the complete model.
This fact may be explained by at least to reasons: on one hand the
complete model is probably more prone to errors in the numer-
ical integration procedure, since it generates to a rather stiff set
of differential equations and, on the other hand, the approxima-
tion involved in the quasi steady state approximation may actually
compensate for some of the shortcomings of the base model.
Another possible approach to develop a global reaction rate
equation is to use the rate-limiting step assumption. This alter-
native approach has the advantage of supplying equations that are
usually much simpler than the ones that are obtained by the quasi
stationary state assumption and is easier to apply to more elaborate
reaction schemes.
Under this approach we will consider that the first step of the
overall reaction (described by Eq. (1)) is very fast when compared
to the second step and can always be assumed to be in equilibrium.
Looking at the kinetic rate constants estimated by the complete
model we can see that, although it seems likely that the second step
is the rate limiting one (depending, of course, on the actual concen-
trations of the various species), since the reaction rate constant for
the first step is larger than for the second one, the reverse reaction
rate constant for the first step is not particularly high, which might
limit the applicability of this assumption, although it would seem
better that quasi stationary state.
3.2. Refinements of the model
We will address the discrepancies observed for higher alcohol
and acid concentrations in two different ways.
On one hand, according to previous studies for the cutinase-
catalyzed esterification reaction [18] the alcohol can react with
enzyme and form dead-end a complex which is unable to partic-
ipate in the reaction. Thus, the rate-limiting global reaction rate
was modified to take into account the reversible formation of an
enzyme–alcohol complex, which was taken as being totally inactive
for the reaction at hand.
On the other hand, it has been observed, for the hydrolysis of
triglycerides, that the enzyme was able to bind up to 3 of product
molecules (which can be assumed to be the free acid molecules)
[43]. In the case of the hydrolysis, the binding of product molecules
implied a certain degree of product inhibition; however, in this
work, if the enzyme is, in fact, able to bond additional reactant
molecules this could imply an increase in the apparent order of
the reaction in relation to the reactant in question. Again the rate
limiting step approximation was used to obtain global reaction rate
equations.
Under these assumption the reaction rate will be limited by the
rate of the second reaction
kb1
r = kb1(([EAc][Al]) − ([E][Es]/Kb1)); Kb1
=
(15)
k
−b1
And the concentrations of the species involving the enzyme can
be computed using the equilibrium condition for the first reaction
step
[E][Ac]
[H2O]
ka1
[EAc] = Ka1
;
Ka1
=
(16)
k
−a1
As above, the overall balance to the enzyme that was added to the
reactor
3.2.1. Second order approximation
ꢂ
ꢃ
Using the assumption that two molecules of acid could be bound
to the active site of the enzyme we can write the following equa-
tions:
[Ac]
[H2O]
[E]t = [E] + [EAc] = [E] 1 + Ka1
(17)
(18)
[E]t
[E] =
ka1
1 + Ka1([Ac]/[H2O])
E + Ac → EAc + H2O; Ka1
=
(20)
(21)
(22)
(23)
k
−a1
Combining all these equations leads to the following global reaction
rate equation
ka2
EAc + Ac → EAc2 + H2O; Ka2
=
k
−a2
kb1[E]t(Ka1([Ac][Al]/[H2O]) − ([Es]/Kb1))
r =
1 + Ka1([Ac]/[H2O])
kb1
EAc + Al → E + Es; Kb1
=
k
kb1[E]t(Ka1[Ac][Al] − [Es][H2O]/Kb1
)
−b1
=
(19)
[H2O] + Ka1[Ac]
kb2
Again the complete model will involved computing the transient
material balances for the relevant species using this rate equation.
EAc2 + Al → EAc + Es; Kb2
=
k
−b2

290
D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
With this reaction scheme the overall reaction rate will be given by
the summation of the contributions of the two different reactions
r = kb1(([EAc][Al]) − ([E][Es]/Kb1)) + kb2(([EAc2][Al])
− ([EAc][Es]/Kb2))
(24)
Assuming again, that both the reactions involving the formation of
enzyme–acyl complexes, Eqs. (22) and (23) can be assumed to be
near equilibrium we can write
[E][Ac]
[H2O]
[EAc] = Ka1
(25)
[EAc][Ac]
[H2O]
[E][Ac]2
[H2O]2
ꢀ
[EAc2] = Ka2
= Ka1Ka2
(26)
ꢁ
[Ac]
[H2O]
[Ac]2
[H2O]2
[E]t = [E] + [EAc] + [EAc2] = [E] 1 + Ka1
+ Ka1Ka2
(27)
[E]t
[E] =
(28)
(1 + Ka1([Ac]/[H2O]) + Ka1Ka2([Ac]2/[H2O]2))
Substituting Eqs. (25)–(28) into Eq. (24) the following expression
for the global rate law is obtained:
kb1[E] (Ka1([Ac][Al]/[H2O]) − [Es]/Kb1) + kb2[E] (Ka1Ka2([Ac]2[Al]/[H2O]2)
t
t
−Ka1([Ac][Es]/[H2O])/Kb2
)
r =
1 + Ka1([Ac]/[H2O]) + Ka1Ka2([Ac]2/[H2O]2)
(29)
and
where
K
a1 = ka1/k
,
K
a2 = ka2/k
,
K
b1 = kb1/k
,
−a1
−a2
−b1
Kb2 = kb2/k
are equilibrium constants for Eqs (20)–(23).
−b2
3.2.2. Third order approximation
This model was further extended to consider that up to three
acid molecules could bind to the enzyme, as described by the equa-
tions below
ka1
E + Ac → EAc + H2O; Ka1
=
(30)
(31)
(32)
(33)
(34)
(35)
k
−a1
ka2
EAc + Ac → EAc2 + H2O; Ka2
=
k
−a2
ka3
EAc2 + Ac → EAc3 + H2O; Ka3
=
k
−a3
kb1
EAc + Al → E + Es; Kb3
=
k
−b1
kb2
EAc2 + Al → EAc + Es; Kb1
=
k
−b2
kb3
EAc3 + Al → EAc2 + Es; Kb3
=
k
−b3
Following the same procedure as above the final rate equation is
obtained as
kb1[E] (Ka1([Ac][Al]/[H2O]) − [Es]/Kb1) + kb2[E] (Ka1Ka2([Ac]2[Al]/[H2O]2)
t
t
−Ka1([Ac][Es]/[HlO])/Kb2) + kb3[E] (Ka1Ka2Ka3([Ac]3[Al]/[H2O]3)
t
−Ka1Ka2([Ac]2[Es]/[H2O]2)/Kb3
)
r =
1 + Ka1([Ac]/[H2O]) + Ka1Ka2([Ac]2/[H2O]2) + Ka1Ka2Ka3([Ac]3/[H2O]3)
(36)
where Ka1 = ka1/k−a1, Ka2 = ka2/k−a2, Ka3 = ka3/k−a3, Kb1 = kb1/k
,
−b1
K
b2 = kb2/k−b2, and Kb3 = kb3/k−b3, are equilibrium constants for Eqs.
(30)–(35).

D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
291
Fig. 2. Experimental results for different alcohol/acid (R) molar ratio, obtained using a fixed concentration of caproic acid (200 mM) at a different concentration of alcohol.
ꢀ, ethanol; ꢁ, ethyl caproate;♦, caproic acid. Lines correspond to the kinetic model.
3.2.3. Alcohol inhibition
Each of these schemes was changed so as to incorporate the
possibility of reversible inhibition by the alcohol, according to
[E]t
[E] =
(40)
(41)
1 + kI[Al] + Ka1([Ac]/[H2O]) + · · ·
kb1[E]t(K1([Ac][Al]/[H2O]) − [Es]/Kb1) + · · ·
r =
1 + Ki[Al] + Ka1([Ac]/[H2O]) + · · ·
(i) E + Al → EAl;
[EAl] = Ki[E][Al]
(37)
(38)
where Kt is inhibition coordination constant.
As it can be seen, this kind of inhibition leads only to the
inclusion, in the denominator or the reaction rate law of the corre-
sponding term.
ꢂ
ꢃ
Table 3 summarizes the values of kinetic and equilibrium con-
stants for the six models that were tested.
The first observation that can be made is that the inclusion of
the alcohol inhibition in the first order model does not produce
[Ac]
[H2O]
[E]t = [E] + [EAl] + [EAc] + · · · = [E] 1 + Ki[Al] + Ka1
+ · · ·
(39)
Fig. 3. Experimental results for different alcohol/acid (R) molar ratio, obtained using a fixed concentration of ethanol (200 mM) at a different concentration of caproic acid.
ꢀ, ethanol; ꢁ, ethyl caproate; ♦, caproic acid. Lines correspond to the kinetic model.

292
D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
Fig. 4. Experimental results for different alcohol/acid (R) molar ratio, obtained using a concentration lower than 120 mM of alcohol and acid. ꢀ, ethanol; ꢁ, ethyl caproate;
♦, caproic acid. Lines correspond to the kinetic model.
any significant improvement in the description of the experimental
data.
The importance of role of water from a kinetic point of view
in organic microaqueous media was reported by Monot et al. [44].
It has been found that distribution of water was in organic sol-
vent very small, then the other part of water was adsorbed by the
enzyme and for the greatest part it contributed to the formation
of a discrete water phase. However, water removal had a little
effect on the final yield of esterification. In fact by the study of
Monet et al. showed the basically similar mechanism for the reac-
tion carried out with solid hydrated enzyme in organic solvent
system with no discrete aqueous phase (system described in this
work) and for biphasic aqueous enzyme solution/organic solvent
system.
On the contrary, inclusion of higher order coordination of the
acid molecules always improved the description of the experimen-
tal data, as it can be seen by the improvements in the objective
function which measures the deviation between the experimental
and the computed data points. In fact, the inclusion of the sec-
ond order term produced a decrease of the objective function of
around 5% and a further inclusion of a third order term reduced the
objective function around 1%.
The apparent equilibrium constants for the various reaction
steps were fitted as the inverse of the equilibrium constant for rea-
sons related to the minimization process. It can be seen that the
esterification involving the enzyme with only a single acid molecule
bound is very much displaced towards the products, since 1/Kb1 is
always very small, regardless of the model being used. However,
as the number of acid molecules bound to the enzyme increase the
reaction seems to be increasingly displaced towards the reactants.
The fittings also show that Ka2 < Ka1, which indicates that
enzyme is much less receptive for the binding of a second acid
molecule and that the binding of a third molecule is even less
favourable.
Inclusion of the inhibition by alcohol shows that only a marginal
improvement on the quality of the fitting is obtained, although this
improvement is close to 0.5% in the case when the starting model
is the one with the third order kinetic term. We can then conclude
that, for the more detailed mechanism some alcohol inhibition
does, in fact, occur. This inhibition is described as a competitive
binding of alcohol to enzyme decrease the number of position
where acid could react and form enzyme–acyl complex and in these
way less for product formation.
3.3. Effect of alcohol/acid molar ratio
The quality of the fittings was checked by looking at two of the
series of experiments that were carried out at different alcohol/acid
molar ratio. Fig. 2 shows the results of the fitting of the third order
model with alcohol inhibition. A good fitting was achieved despite
some deviations that are observed in relation to the alcohol con-
centration and which can be attributed to some evaporation of the
alcohol during the experiment, a fact that was not taken in account
by the model.
A set of experimental data for fixed alcohol concentration is
depicted in Fig. 3.
In some cases it was noticed that if the concentration of alco-
hol was lower than 100 mM there is deviation in model predicting
and experimental data (Fig. 4). The similar behavior was explained
by Carvalho et al. [8] in cutinase-catalyzed transesterification with
small concentration of hexanol due to the cutinase deactivation and
denaturation.
In view of these results the third order model with alcohol inhi-
bition was accepted as the better model and it was applied to
studies of the alcohol/acid molar ratio.
The most significant deviations between the model compu-
tations and the experimental data were observed for higher
concentration of the substrates.
It should be noted that all the modelling was performed
assuming a pseudo-homogeneous system. Although the reaction
proceeds with the formation of water, which is not mixable with
the organic solvent and may induce the appearance of an aque-
ous phase, the amount of water produced is relatively small and,
although it may segregate in the isooctane, the enzyme is still
fully dispersed in the organic medium and no complications due
to the formation of an aqueous phase were expected nor were
observed.
As it can be seen in Fig. 5, after 15 min a sharp decrease in the
reaction rate is observed. This may be due to the high concentra-
tion of acid, active site of enzyme could be saturated with acid
molecules, that could change microenvironment of the enzyme
and lead to inhibition effect [21,24,25] and it was not completely
accounted for by the kinetic model that was used.
The inhibition effect of hexanoic (caproic) acid above 150 mM
was referred for reverse micellar system [25] in reaction esterifica-
tion.

D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 66 (2010) 285–293
293
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of conditions and may be useful for reactor design and optimization,
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of substrates.
Acknowledgements
Dragana P.C. de Barros acknowledges Fundac¸ ão para a Ciência e
a Tecnologia (Portugal) for financial support in the form of the PhD
grants SFRH/BD/24703/2005.
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