Kinetic model for the esterification of ethyl caproate for reaction optimization

Article abstract of DOI:10.1016/j.molcatb.2013.12.012

The present work aims to achieve additional insight on a mechanism describing the fundamental steps involved in the esterification reactions catalyzed by cutinase. The synthesis of ethyl caproate has been used as a model system to obtain a suitable kinetic model to estimate the activation energies involved in the various steps of the reaction pathway. Kinetic measurements have been made for the enzymatic esterification of caproic acid with ethyl alcohol catalyzed by recombinant Fusarium solani pisi cutinase expressed in Saccharomyces cerevisiae SU50. Different temperature conditions, from 25 to 50 C, were tested for two different alcohol/acid molar ratios (R = 1 and R = 2). The third ordered Ping Pong Bi Bi mechanism with alcohol inhibition was shown to be able to describe the experimental results. The model shows that the productivity decreases as the reaction temperature increases.

Full text of DOI:10.1016/j.molcatb.2013.12.012

Journal of Molecular Catalysis B: Enzymatic 101 (2014) 16–22
Contents lists available at ScienceDirect
Journal of Molecular Catalysis B: Enzymatic
journal homepage: www.elsevier.com/locate/molcatb
Kinetic model for the esterification of ethyl caproate
for reaction optimization
Dragana P.C. de Barros∗, Fátima Pinto, Luís P. Fonseca, Joaquim M.S. Cabral, F. Lemos
Institute for Biotechnology and Bioengineering, Centre for Biological and Chemical Engineering, Instituto Superior Técnico, 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:
The present work aims to achieve additional insight on a mechanism describing the fundamental steps
involved in the esterification reactions catalyzed by cutinase. The synthesis of ethyl caproate has been
used as a model system to obtain a suitable kinetic model to estimate the activation energies involved in
the various steps of the reaction pathway.
Kinetic measurements have been made for the enzymatic esterification of caproic acid with ethyl
alcohol catalyzed by recombinant Fusarium solani pisi cutinase expressed in Saccharomyces cerevisiae
SU50. Different temperature conditions, from 25 to 50 ◦C, were tested for two different alcohol/acid
molar ratios (R = 1 and R = 2). The third ordered Ping Pong Bi Bi mechanism with alcohol inhibition was
shown to be able to describe the experimental results. The model shows that the productivity decreases
as the reaction temperature increases.
Received 20 September 2013
Received in revised form
13 December 2013
Accepted 21 December 2013
Available online 29 December 2013
Keywords:
Kinetic model
Enzymatic esterification
Organic solvent
Cutinase
© 2014 Elsevier B.V. All rights reserved.
Productivity
1. Introduction
aqueous solution but also suspended as a powder or immobi-
lized, have been reported [7–18]. Fundamental studies on the
Alkyl esters, an important part of aroma compounds, are com-
monly used in food, cosmetic and pharmaceutical industries. The
use of biocatalysis, using hydrolytic enzymes, for the synthesis of
aroma compounds of biological interest has gained a particular
interest during the last decades. Advantages of using the enzymatic
synthesis in non-aqueous media significantly expand the possibil-
ities for industrial applications [1–3].
There are several reasons for the use of enzymes, mainly lipases
and esterases, for the synthesis of short chain acid esters. Enzyme
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 have been considered as natural com-
ponents by food regulatory agencies [4,5].
hydrolysis of triglycerides [7] clarification of its mechanism
regarding stereo-selectivity and specificity [8], and studies of
esterification reactions [9–18] were performed with lyophilized
cutinase.
The sub-family of cutinases consists of about 20 members,
based on amino-acid sequence similarity, which display hydrolytic
activity on cutin polymers and efficiently hydrolyze soluble small
carboxylic esters and emulsified triacylglycerols.
Cutinase belongs to the family of serine hydrolases containing
its catalytic serine centre at the middle of a sharp turn between a
␤-strand and a ␣-helix [6]. The catalytic triad, Ser-120, Asp-175 and
His-188, is accessible to the solvent and can accommodate different
substrates. The esterification reaction was shown to follow a Ping-
Pong Bi Bi mechanism [15,16]. The serine in the active centre of the
enzyme is a very strong nucleophile, which attacks the carbonyl
group of the acid (Ac), forming a stable tetrahedral intermediate
acyl enzyme complex. The acyl enzyme complex is stabilized by
the oxyanion hole. Water is then released and the structure reverts
to the planar carbonyl flat plane acyl enzyme intermediate (EAc).
The alcohol (Al) 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 (Es) and the free
enzyme (E).
Fusarium solani pisi (F.s.pisi) cutinase activity in hydroly-
sis, esterification and transesterification has been extensively
exploited in recent years and several applications in different
industrial fields have been proposed [6]. Numerous report of
using cutinases in different reaction media, often dissolved in
∗
Corresponding author at: Department of Bioengineering, IBB – Institute for
Biotechnology and Bioengineering, Centre for Biological and Chemical Engineering,
Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal.
Tel.: +351 218 419 065; fax: +351 218 419 062.
The industrial application of any chemical reaction requires the
knowledge of its kinetics, in particular by using a suitable kinetic
model, to allow the description of a chemical reaction and its
E-mail address: dragana@ist.utl.pt (D.P.C. de Barros).
1381-1177/$ – see front matter © 2014 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.molcatb.2013.12.012

D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 101 (2014) 16–22
17
Table 1
Experimental conditions for the set of experiments used in the fitting of the different
models.
Ac
acid
T, ◦
C
Al/Ac = 1
Al/Ac = 2
Al
alcohol
Es
E
[E]t
EAc
EAc2
ester
free enzyme
Ethanol,
mM
Caproic acid,
mM
Ethanol,
mM
Caproic acid,
mM
total enzyme concentration, mM
enzyme acyl complex
enzyme acyl complex with two bound acid
molecules
enzyme–acyl complex with three bound acid
molecules
25
30
35
40
45
50
208
231
211
216
214
213
205
214
199
219
213
197
217
210
210
204
203
210
121
117
110
114
119
117
EAc3
EAl
THC
enzyme–alcohol complex
tetrahedral intermediate acyl enzyme complex
All concentrations are given in mM. Enzyme concentration is equal to 0.1 mM in all
runs and the specific activity was 240 10 U ml−1 of reaction media.
Ka1, Ka2, Ka3, Kb1, Kb1, Kb1 equilibrium constants
240 10 U m−1 of reaction medium according the p-NPB method
[11].
Ki inhibition coordination constant
k
a1, k−a1, ka2, k−a2, ka3, k−a3, kb1, k−b1, kb1, k−b2, kb3, k
rate
−b3
constants, mM−1 min−1
2.2. Enzymatic esterification
optimization over an extensive range of reagents composition and
presence of inhibitors and concentrations, and reaction conditions
such as temperature, pH, pressure, etc.
The esterification of acid and alcohol by cutinase was carried
out in iso-octane as organic solvent, as previously explained [15].
The enzymatic ester synthesis was performed in an incubator (AGI-
TORB 16OE, Aralab, Portugal) at various temperatures (25–50 ◦C),
and cutinase concentration of 2 mg/ml of reaction mixture. Exper-
iments were performed at least in duplicate and the experimental
error was estimated less than 8%. Samples were withdrawn peri-
odically using a needle, without destroying the rubber cap, and
analyzed by GC. The reaction yield was calculated according to
the molar ratio between the ethyl ester and respective limiting
substrate, in this case acid.
In order to ensure that the model is applicable over a wide range
of experimental conditions it should be preferentially based on a
mechanistic scheme describing the fundamental steps involved in
the reaction. The development of this kind of models can also be
used to provide insight into the processes that are taking place.
From previous studies [12,15] F.s. pisi cutinase expressed in
Saccharomyces cerevisiae showed a significant potential for the
synthesis of short chain ethyl esters in isooctane. The kinetic
parameters of this system in terms of Ping Pong Bi Bi models were
estimated, under isothermal conditions, to improve the description
of the reaction system. However, the impact of different tempera-
ture regimes in the reaction progress is very important and requires
additional study. The impact of temperature in the ester yield and
rate is difficult to predict because it may affect reaction efficiency
in conflicting ways and this knowledge is required for system opti-
mization. On one hand a temperature raise will have a positive
effect on the reaction rates, as expected from the transition state
theory. On the other hand, higher temperatures may disrupt the
enzyme’s tertiary structure, causing it to lose its catalytic activity.
Therefore, the aim of this work was evaluation of activation
energy of the different steps of the cutinase catalyzed esterification
to analyze temperature impact in the production of ethyl caproate.
2.3. 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).
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
components in the reaction mixture. n-Decane was used as an inter-
nal standard in the quantification of ethyl esters and respective
substrates concentrations in the reaction media. Nitrogen was used
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.
2. Materials and methods
2.4. Kinetic model
2.1. Enzyme and chemicals
The base model development was described in a previous
work [15] where it was applied to data at a single temperature.
To implement the different models the appropriate differential
and equilibrium equations were written for each kinetic model
and an approximate global reaction rate was obtained using the
quasi-steady-state approximation. This rate equation was used
to compute the time-course evolution of the different species
involved by numerical integration of the material balances using
the Euler method.
The model was fitted to the experimental data (all the avail-
able 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 ethanol, caproic acid and
ethyl caproate concentrations measured in all experiments. The
experimental conditions, for the set of experiments used in fit-
ting procedure are given in Table 1. This procedure was carried-out
using a Microsoft Excel 2003 spreadsheet and the estimation of the
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 of esterification reac-
tions. Saturated salt solution of sodium chloride (Panreac, Spain)
was used to control water activities of enzyme and substrates. All
other chemicals used were of analytical grade.
Fusarium solani pisi cutinase wild-type was biosynthesized by
recombinant S. cerevisiae SU50 strain as described by Calado et al.
[19]. The isolation and purification and characterization of cutinase
excreted by recombinant S. cerevisiae SU50 strain was carried out
by according to previous published protocols [12,15]. Lyophilized
pure cutinase was stored at −20 ◦C before used in esterification
reactions. Activities of lyophilized cutinase preparations were of

18
D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 101 (2014) 16–22
kb
1
EAc + Al ꢀ E + Es Kb
=
(3)
(4)
(5)
(6)
1
k
−b
1
ka
2
EAc + Ac ꢀ EAc2 + H2O Ka
=
2
k
−a
2
kb
2
EAc2 + Al ꢀ EAc + Es Kb
=
2
k
−b
2
ka
3
EAc2 + Ac ꢀ EAc3 + H2O Ka
=
3
k
−a
3
kb
3
EAc3 + Al ꢀ EAc2 + Es Kb
=
(7)
(8)
3
k
−b
3
Fig. 1. Effect of the temperature on esterification yield for alcohol/acid molar ratio
R1 = 1 and R2 = 2 (ethanol = 0.2 M) at the end of the reaction (6 h).
[E]t = [E] + [EAc] + [EAc2] + [EAc3
]
Given that all reactions were carried-out in closed vessels we
have considered that the evaporation of all the components in the
mixture is negligible, the volume was considered to be constant.
With this assumption the material balances for a batch reactor, for
all the species involved, can be described by the following set of
differential equations:
parameters was carried-out using the Solver tool, as in the previous
work [15].
3. Results and discussion
d[E]
dt
= −ka [E][Ac] + k
[EAc][H2O] + kb [EAc][Al] − k 1 [E][Es]
−a
−b
1
1
1
3.1. Effect of temperature
(9)
The effect of temperature on esterification yield was observed
for two different alcohol/acid molar ratios (R = 1 and R = 2), for tem-
perature range from 25 ◦C to 50 ◦C, with increment of 5 ◦C (Fig. 1).
A different yield profile was observed for two different molar
ratios. In the case of the R = 1 the ester yield decrease with the
temperature raise from 25 to 50 ◦C. For molar ratio R = 2, esteri-
fication yield increase from 67% to 71%) if temperature increased
from 25 to 30 ◦C and then a significant yield decay was observed
for temperature above 30 ◦C (52% for 35 ◦C).
d[Ac]
dt
= −ka [E][Ac] + k 1 [EAc][H2O]
(10)
(11)
(12)
(13)
−a
1
d[H2O]
dt
= ka [E][Ac] − k 1 [EAc][H2O]
−a
1
d[Al]
dt
= −kb [EAc][Al] + k 1 [E][Es]
−b
1
Lower esterification yield observed for R = 1, independently of
the temperature value, may be due to the alcohol inhibitory effect
already observed by previous work [12].
d[Es]
dt
= kb [EAc][Al] − k 1 [E][Es]
−b
1
3.2. Base kinetic model
d[EAc]
dt
= ka [E][Ac] − k
[EAc][H2O] − kb [Ac][Al] + k 1 [E][Es]
−b
−a
1
1
1
The esterification of caproic acid with ethanol was catalyzed by
cutinase F.s. pisi in iso-octane.
(14)
Ac + Al = Es + H2O
(1)
Combining all these equations and assuming that the quasi sta-
tionary state assumption can be applied for, Eqs. (9) and (14), the
global reaction rates for the first, second and third order, respec-
tively, for the systems without inhibition were obtained as it was
described in a previous work [15]:
All of these schemes were changed so as to incorporate the pos-
sibility of reversible inhibition by the alcohol binding to the enzyme
site (Eq. (15)) and adequate reaction rate equation is given by Eq.
(16):
The accepted mechanism for this reaction Ping-Pong Bi-Bi
kinetic mechanism with inhibition by the substrates [15] was taken
as the basis for the reaction esterification of caproic acid by ethanol
catalyzed by cutinase (Eq. (1)). Taking into consideration that for
this reaction it is essential that an acyl–enzyme bond is formed, the
first step will be the formation of the active enzyme–acyl complex
between cutinase and the caproic acid and the second step will be
reaction of the enzyme–acyl complex with the alcohol end ester
formation. Following the procedure used in the previous work [15]
the rate limiting step approximation was applied. The reaction rate
will be limited by the rate of the second reaction. The model was
further extended to consider that up to three acid molecules could
bind to the enzyme (Eqs. (2)–(7)), following previous observations,
where it was observed that for the hydrolysis of triglycerides, the
enzyme was able to bind up to 3 of products molecules [20].
E + Al = EAl
(15)
[EAl] = Ki[E][Al]
kb [E]t((Ka (([Ac][Al])/[H2O]) − [Es])/K 1 ) + · · ·
1 + K [Al] + Ka ([Ac]/H2O) + · · ·b
1
1
r =
(16)
(17)
i
1
A total enzyme amount is given by expression:
ka
1
E + Ac ꢀ EAc + H2O Ka
=
(2)
[E]t = [E] + [EAc] + [EAc2] + [EAc3] + [EAl]
1
k
−a
1

D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 101 (2014) 16–22
19
Table 2
Values of kinetic and equilibrium constants with and without alcohol inhibition for the thermodynamically consistent model.
Constant
Order
1st
2nd
3rd
1sti
2ndi
3rdi
Ka1
Ka2
Ka3
Kb1
Kb2
Kb3
kb1
kb2
kb3
Ki
1.54E+05
–
–
2.31E+04
2.42E+04
4.14E−11
1.55E+08
7.24E−05
4.23E+10
1.13E−08
5.58E−02
1.45E+00
2.54E−02
–
4.72E+04
–
–
2.39E+04
3.62E−02
–
9.34E−05
6.25E+01
–
5.47E−02
3.27E−02
–
2.14E+04
2.51E+00
1.01E+00
1.24E−03
1.06E+01
2.30E+01
5.71E−01
4.32E−01
1.67E−02
2.12E+04
8.14E−02
–
1.07E−05
7.63E−05
3.48E−05
–
–
2.16E+01
–
–
–
4.41E−02
5.62E−02
4.41E−02
–
–
–
2.55E−02
–
–
–
–
1.33E−08
1.07E+02
Fobj
33 366
26 869
26 704
33 349
24 197
20 097
1st, 2nd, 3rd – without alcohol inhibition, 1sti, 2ndi, 3rdi – with alcohol inhibition.
Rate constants unites kb1, kb2, kb3 are mM−1 min−1
.
The dependence of rates on temperature manifests in the tem-
perature dependence of the rate constant ki.
model (decrease the Fobj 19.5%), but further order increase did not
improve significantly the data description (less than 1%).
On the other hand inclusion of inhibition for the 1st order model
does not produce any significant improvement in description of
the experimental data but nevertheless influence of the inhibition
effect for the 2nd order model (Fobj reduce 10%) and specially for
the 3rd order model (Fobj reduce 25%) is significant. In models with
inhibition the higher positive impact of the high order inclusion
was observed too. Fobj from 1st to 2nd order model reduce 27% and
from 2nd to 3rd order 17%.
The apparent equilibrium constant for the 3rd ordered model
with inhibition Ka1 > Ka2 > Ka3, which indicates that enzyme is much
less receptive for the binding of a second and third acid molecules.
The binding affinity of second and third acid molecule is quite sim-
ilar.
ki = k(ti), ti = 25 ◦C, 30 ◦C, 35 ◦C, 40 ◦C, 45 ◦C, 50 ◦C
(18)
The quantitative relationship between the rate constant and
temperature was expressed by the Arrhenius equation, written as:
ꢀ
ꢁ
ꢂꢃ
EA
R
1
Ti
1
Tref
ki = kref exp
−
(19)
where kref, represent the kinetic constant at a reference tem-
perature Tref = 303.17 K, Ti = 273.17 + ti and R is the universal gas
constant.
The kinetic model indicates that all the species with bound
substrate molecules are active for the synthesis reaction and
with kinetic rate constants that decrease as the number of sub-
strate molecules bound increases, as it can be seen by the order
By application of van’t Hoff equation the relationship between
the equilibrium constants Ka and Kb with the apparent standard
j
j
enthalpy change ꢀHa and ꢀHb (j = 1, 2, 3 present reaction order).
j
j
k
b1 > kb2 > kb3 in Table 2.
Inclusion of alcohol inhibition shows important improvement
ꢄ
ꢅ
ꢁ
ꢂ
ꢀHa ,b
1
Ti
1
Tref
j
j
Ka ,b = Kref exp
−
(20)
on the quality of fitting obtained, so we can conclude that the
change in the temperature regime, studied in this work, under-
lines more alcohol inhibition then it was the case with isothermic
system observed by previous work [15].
Table 3 summarizes the values of activation energies and
enthalpies for the 3rd ordered reaction with alcohol inhibition sys-
tems, obtained from the Eq. (19) and Eq. (20).
An evaluation of the error on the estimated kinetic parameters
was obtained using a “bootstrap technique” [22]. In this procedure,
1/3 of original data points were randomly replaced by other data
points in the same set and a new optimization procedure was per-
formed. This procedure was repeated 20 times and the reported set
j
j
R
where Kref, represent the equilibrium constant at a reference tem-
perature Tref = 303.17 K, Ti = 273.17 + ti (ti = 25, 30, 35, 40, 45, 50 ◦C)
and R is the universal gas constant.
The model was solved for all experimental conditions that were
used, as explained above. The consistency between chemical kinetic
and thermodynamics plays an important role (Eq. (21)) [21]. So,
the refinement of the third order model with alcohol inhibition
was performed and the equilibrium constant and rate constant was
obtained.
Ka Kb = Ka Kb = Ka Kb
(21)
1
2
3
1
2
3
Table 3
The third order model with alcohol inhibition was confirmed to
Kinetic constants, enthalpies and activation energies for the 3rd ordered reaction
with alcohol inhibition systems (3rdi).
provide a better description of the experimental results, as shown
by the fact that its objective function (Fobj) decreases by rise of the
reaction order and inclusion of the alcohol inhibition (Table 2) and
it was used to study the temperature influence for two different
molar ratios. The estimated kinetic parameters for all models that
were tested are shown in Table 2.
Constants
Energies, kJ mol−1
Ka1
Ka2
Ka3
Kb1
Kb2
Kb3
kb1
kb2
kb3
Ki
(21.4 1.78)E+03
(2.51 0.313)E+00
(1.01 0.552)E+00
(1.24 0.723)E−03
(1.06 0.248)E+01
(2.30 1.56)E+01
(0.571 0.338)E+00
(4.32 0.447)E−01
(1.67 0.264)E−03
(2.12 0.431)E+04
ꢀHa
ꢀHa
ꢀHa
ꢀHb
ꢀHb
ꢀHb
ꢀEb1
ꢀEb2
ꢀEb3
ꢀHi
−141 3.88
1
2
3
1
2
3
−494 11.4
−672 16.0
−70 9.19
0
Ka1, Ka2, Ka3, Kb1, Kb2, Kb3, Ki are equilibrium constants and kb1
,
kb2, kb3 are rate constants. The rate limiting approximation does
−527 21.3
182 11.8
149 15.4
48 11.2
−26 12.6
not allow the simultaneous estimation of ka and k−a, since the first
step is considered to be in equilibrium.
It was observed (Table 2) that the inclusion of higher order coor-
dination of the acid molecules for the systems without inhibition
improve the description of the experimental data only for 2nd order
Rate constants unites kb1, kb2, kb3 are mM−1 min−1
.

20
D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 101 (2014) 16–22
Fig. 2. Experimental results for alcohol/acid molar ratio R = 1, [Alcohol] = 200 mM. Ethanol (triangle), caproic acid (diamond), ethyl caproate (square). Lines correspond to the
kinetic model.
of parameters, for a 90% confidence level, was computed from the
distribution of parameter values obtained. Table 3 summarizes the
values of kinetic constants, activation energies and enthalpies for
the 3rd ordered reaction with alcohol inhibition systems.
experimental results and can be used with confidence within the
range of experimental conditions that was covered by this study.
To check for the extrapolation capabilities of the model
obtained, it was used on a different set of experimental data without
further optimization of the model parameters.
The values of apparent enthalpy change for the formation of
enzyme–acyl complex ꢀHa show favourable energies for the bind-
j
ing of 3rd acid molecule.
3.3. Evaluation of the model fitting to the experimental data
The results have shown that the overall reaction rate increases
with temperature, resulting in apparent positive overall activation
energy.
It should, however, be noted that the parameters obtained can-
not be viewed as true kinetic or thermodynamic parameters but
they only describe the mechanistic approach that was used. Never-
theless the results obtained describe with very good accuracy the
The quality of fittings was checked by looking at 6 series of
experiments that were carried out at different temperature, 30, 35,
40 and 45 ◦C testing two molar alcohol/acid (R) molar ratio: R = 1
(Fig. 2) and R = 2 (Fig. 3).
A set of experimental data for molar ratio R = 1 is depicted in
Fig. 2.
Fig. 3. Experimental results for alcohol/acid molar ratio R = 2, [Alcohol] = 200 mM. Ethanol (triangle), caproic acid (diamond), ethyl caproate (square). Lines correspond to the
kinetic model.

D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 101 (2014) 16–22
21
Fig. 4. Productivity for the systems with different alcohol/acid molar ratio for temperature range 25–50 ◦C.
A very good quality of the model was obtain for the molar ratio
R = 1 (Fig. 2). The higher prediction esterification yield, observed
in the model for the reaction time above 2 h, may be due to the
inhibition effects of the substrates during the time course of the
reaction, already observed by previous work of the authors [12,15].
The prediction quality of the esterification yield was improved
for the molar ratio R = 2 (Fig. 3).
molar ratios R = 3 and R = 4 the productivity declines to 45.5%, and
for R = 0.3 the productivity decreases to 25%.
It means that lower temperatures favour the reaction esterifi-
cation, and the alcohol inhibition has significant influence on the
productivity.
4. Conclusions
As it can be seen the model was able to describe the experimen-
tal data within a good margin of accuracy.
From the results presented and the fittings obtained we can
conclude that the kinetic of synthesis of ethyl caproate catalyzed
by cutinase follows a complex scheme and that, as previously
observed, the cutinase can bind up to three substrate molecules.
The results also indicate, as expected, that alcohol inhibits the
reaction. Although we cannot conclude that all three bound acid
molecules can be activated, the kinetic model indicates that all the
species with bound substrate molecules are active for the synthesis
reaction and with kinetic rate constants that decrease as the num-
ber of substrate molecules bound increases, as it can be seen by the
order kb1 > kb2 > kb3 in Table 3.
3.4. Optimization of the system
The model was applied for different alcohol/acid molar ratio
(R = 0.3; 0.5; 1, 2, 3 and 4, respectively) in all temperature range
(25–50 ◦C), for the initial alcohol concentration from 10 to 250 mM,
and the time when esterification yield reaches 50% of equilibrium
value was observed (Fig. 4).
The model shows that productivity decreases as the temper-
ature increases for all alcohol/acid molar ratios. The fall in pro-
ductivity is specially emphasized for high alcohol concentrations
(Table 4). For the initial alcohol concentration of 250 mM and for
The development of a kinetic model has enabled us to analyze
the impact of the various operating parameters in the production of
ethyl caproate and conclude that the reaction is better carried-out
a low temperature.
Table 4
Difference in productivity (mM min−1), for temperature increase from 25 to 30 ◦
for different alcohol/acid molar ratio.
C
[Al], mM
R
Acknowledgement
0.3
0.5
1
2
3
4
Dragana P.C. de Barros acknowledges Fundac¸ ão para a Ciência
e a Tecnologia (Portugal) for financial support in the form of the
grant SFRH/BPD/70409/2010.
50
150
250
0.054
0.166
0.285
0.055
0.188
0.341
0.065
0.261
0.412
0.083
0.301
0.458
0.089
0.314
0.474
0.090
0.316
0.473

22
D.P.C. de Barros et al. / Journal of Molecular Catalysis B: Enzymatic 101 (2014) 16–22
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