enzimas

1. Biochemical Engineering Journal 71 (2013) 89–96
Contents lists available at SciVerse ScienceDirect
Biochemical Engineering Journal
journal homepage: www.elsevier.com/locate/bej
Regular article
Kinetic model of lipase-catalyzed conversion of ascorbic acid and oleic acid to
liposoluble vitamin C ester
Dejan Bezbradicaa,∗
, Marija Stojanovi´ca
, Duˇsan Veliˇckovi´cb
, Aleksandra Dimitrijevi´cb
, Milica Carevi´ca
,
Mladen Mihailovi´ca
, Nenad Milosavi´cb
a
Department of Biochemical Engineering and Biotechnology, Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia
b
Department of Biochemistry, Faculty of Chemistry, Studentski trg 12, University of Belgrade, 11000 Belgrade, Serbia
a r t i c l e i n f o
Article history:
Received 6 August 2012
Received in revised form 18 October 2012
Accepted 2 December 2012
Available online 10 December 2012
Keywords:
Ascorbyl oleate
Lipase
Candida antarctica
Kinetic parameters
Substrate inhibition
Production kinetics
a b s t r a c t
The kinetics of l-ascorbyl oleate synthesis catalyzed by immobilized lipase from Candida antarctica in ace-
tone was investigated. Significant inhibition of synthesis with an excess of ascorbic acid was observed.
Experimental data were successfully fitted with a ping–pong bi–bi kinetic model with substrate inhi-
bition, and related kinetic constants were determined. The kinetic study was performed at optimum
experimental factors (temperature, initial water content, and enzyme concentration), which were deter-
mined using response surface methodology. Then, a model for predicting product–time progress curves
was developed by expanding the obtained ping–pong model with terms describing ester hydrolysis.
Kinetic constants of the reverse reaction were determined, and good congruence between the model and
experimental data was achieved. Calculated kinetic constants revealed that lipase has the highest affin-
ity for ascorbyl oleate, slightly lower activity with ascorbic acid, and the lowest activity with oleic acid.
The obtained results are valuable for elucidating the reaction mechanism and represent an important
contribution for reaction optimization and creating strategies to increase the productivity of vitamin C
ester synthesis.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Vitamin C is well known for its antioxidative properties. Nev-
ertheless, the use of l-ascorbic acid in stabilizing fats and oils is
very scarce due to its hydrophilic nature [1]. On the contrary, fatty
acid ascorbyl esters are oil-soluble with the same or even enhanced
antioxidative properties compared to vitamin C. Mineral acids or
lipases can catalyze the esterification process between vitamin C
and fatty acid (or its methyl or vinyl ester). At the moment, despite
the numerous shortcomings, ascorbyl palmitate is being produced
industrially by chemical means [2]. On the other hand, there are
many advantages of the biosynthetic process, such as mild reaction
conditions, regioselectivity, and the possibility of using immobi-
lized enzymes, resulting in simpler downstream processing [3].
Additionally, obtaining a product in such a way allows it to be
labeled as natural and have a higher market value [4]. Although
lipase-catalyzed synthesis of ascorbyl esters has already been
described by many authors, long reaction times, bio-incompatible
solvents, and high price of the enzyme are still some of the main
obstacles in the commercialization of the process [5]. Ascorbyl
esters derived from unsaturated fatty acids are superior compared
∗ Corresponding author. Tel.: +381 11 3303727; fax: +381 11 3370387.
E-mail address: dbez@tmf.bg.ac.rs (D. Bezbradica).
to those with saturated hydrocarbon chains in terms of solubility,
free radical scavenging capacity and beneficial effects on human
nutrition [6]. Therefore, their biosynthesis, especially in GRAS (Gen-
erally Recognized as Safe) solvents, is of particular interest [5].
In regard to scale-up and process automation, it is necessary
to optimize operating parameters and establish adequate kinetic
models for the reactions. Additionally, the type of kinetic model
gives valuable information about the reaction mechanism and sub-
strate inhibition which helps in organizing enzymatic processes
in such a way as to avoid intrinsic limitations at the molecular
level. There are just a few reports of ascorbyl oleate synthesis cat-
alyzed by immobilized lipase from Candida antarctica [7–11]. On
the other hand, reports on the kinetics of aliphatic ester synthesis
are more frequent, but different kinetic models have been pro-
posed. In general, esterification reactions catalyzed by immobilized
C. antarctica lipase preparation occurs via acyl–enzyme interme-
diates and are most commonly being described by models based
on a ping–pong bi–bi or ordered bi–bi mechanism [12]. Addition-
ally, inhibition by one or both substrates was reported on several
occasions [13–17].
The main goals of this study were to obtain an adequate
kinetic model for the enzymatic synthesis of ascorbyl oleate
(Scheme 1) in acetone, determine key kinetic constants, and
compare affinity of substrates towards lipase. To investigate inhi-
bition by excess of substrates, concentration was varied in a wide
1369-703X/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
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2. 90 D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89–96
Scheme 1. Formation of ascorbyl oleate in a reaction of ascorbic acid and oleic acid.
range from 0.05 to 1 M. Prior to kinetic studies, response surface
methodology (RSM) and 5-level-5-factor central composite rotat-
able design (CCRD) were employed to determine the effects of
key experimental parameters (initial water content, temperature,
ascorbic acid:oleic acid molar ratio, vitamin C concentration, and
enzyme content) on the initial rate of the vitamin C and oleic acid
esterification reaction, so the kinetic study was performed at opti-
mum conditions. Finally, it was shown that reaction kinetics can be
fitted throughout the reaction range with a model that also includes
the reverse reaction of ester hydrolysis, and the kinetic constants
of the reverse reaction were determined.
2. Materials and methods
2.1. Enzyme and chemicals
Novozym® 435 (lipase from C. antarctica, type B immobilized
on acrylic resin) was purchased from Novozymes (Bagsvaerd,
Denmark). Substrates were l-ascorbic acid (purity 99.7%, Zorka,
ˇSabac, Serbia) and oleic acid (Ph. Eur., NF pure purchased from
AppliChem, Darmstadt, Germany). Acetone was used as a reaction
medium (99.5%, JT Baker, USA). Substances used for the quantitative
HPLC analyses were methanol obtained from JT Baker (USA) and
phosphoric acid, purchased from Sigma–Aldrich (Chemie GmbH,
Steinheim, Germany); all were HPLC grade.
2.2. Procedure for the enzymatic synthesis
Experiments were carried out in 100 ml capped vials. The reac-
tion mixture consisted of different amounts of ascorbic acid, oleic
acid, enzyme, water, and acetone (amounts specified for each
experiment separately), so that the total volume was 10 ml. The
reactions were conducted in a shaker at 250 rpm and at a tempera-
ture in the range from 40 to 60 ◦C. All experiments were carried out
in duplicate, and average values are presented in Figs. All standard
deviations were less than 5%. Control samples (without enzyme)
were prepared by exposure to the same temperature treatment.
The product was not detected in control samples. In experiments
with the addition of molecular sieves, 80 mg of zeolite type sieves
were added per ml of the reaction medium.
2.3. Kinetic study
Kinetic studies were performed in accordance with experimen-
tal plans comprising of 64 experimental points of a matrix (8 × 8),
representing all possible pairs of ascorbic acid and oleic acid con-
centrations at following set of values: 0.05; 0.1; 0.15; 0.2; 0.3; 0.5;
0.75; 1.
The initial rate was determined as the slope of the reaction curve
tangent to the initial stage of the reaction. Because all experiments
were performed in duplicate, reaction curves were constructed
using average values of the reaction rate for each experimental
point. A linear portion of the reaction curve at various substrate
concentrations consisted of 4–6 experimental points, where the
number of experimental points included was determined by the
condition that correlation coefficients of the initial straight line
must be above 0.95.
2.4. HPLC analysis
For quantitative analysis of reactants and products, an Akta
Purifier HPLC system was used. A reverse phase column (Waters
Spherisorb ODS 2-C18, 250 mm × 4.6 mm, 5 ␮m) was employed.
The injection volume of the reaction mixture, diluted fifteen fold,
was 10 ␮l. Methanol/H3PO4, 100/0.1 (v/v), was used as eluent with
a flow rate of 1 ml/min. The product was detected by a UV detector
at 235 nm.
3. Theory and calculations
3.1. Ping–pong bi–bi model
The ping–pong bi–bi mechanism illustrates alternate binding of
substrates and release of products in a bi-substrate reaction with
two products formed. It is the most frequently postulated reaction
mechanism in lipase-catalyzed esterifications [13–19]. The first
stage of the reaction is the binding of the acyl-donor (Ol, oleic acid),
resulting in the formation of an acyl–enzyme complex. In the next
step, the first product (water) is released. Then, the acyl acceptor
(AA, ascorbic acid) binds, and in the final step, ester (AOl) is released
[18].
Nevertheless, basic ping–pong mechanisms can rarely ade-
quately describe lipase-catalyzed esterifications because inhibition
by excess of one of the substrates was frequently reported [14–19].

3. D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89–96 91
Table 1
Coded levels and corresponding actual values of variables.
Factors Level
−2 −1 0 1 2
Water content, X1 (%, v/v) 0 0.05 0.1 0.15 0.2
Temperature, X2 (◦
C) 40 45 50 55 60
Enzyme amount, X3 (%, w/v) 0.2 0.4 0.6 0.8 1.0
Oleic acid/ascorbic acid molar ratio, X4 1:3 1:6 1:9 1:12 1:15
Vitamin C concentration, X5 (M) 0.02 0.07 0.12 0.17 0.22
Substrate inhibition occurs due to the formation of an inactive
“dead-end complex”. In a case of acyl donor inhibition, the inac-
tive complex with two molecules of the acyl donor attached to the
enzyme is formed [15]. When inhibition by an excess of acyl accep-
tor occurs, such as in our reaction, an inactive enzyme-acceptor
complex is formed that cannot be subsequently transformed into a
product [14]. The ping–pong bi–bi kinetic model with ascorbic acid
inhibition is described by Eq. (1).
es =
Vm,es[Ol][AA]
[Ol][AA] + KAA[Ol] + KOl[AA] + (KOl/Ki,AA)[AA]2
(1)
In Eq. (1), ves is the initial reaction rate; KAA and KOl are the
Michaelis constants of ascorbic and oleic acid, respectively; Vm,es
is the maximum reaction rate; and Ki,AA is the inhibition constant
for ascorbic acid. The term Vm,es is the product of the rate constant
(kcat) of the final reaction step and the initial enzyme concentra-
tion ([E]0). Kinetic constants were determined using a non-linear
regression fit of the results obtained in the experiment described in
Section 2.3. Goodness of fit was evaluated by calculating the corre-
lation coefficient. Specificity constants for each of reaction species
were calculated by dividing kcat by the Michaelis constant of the
compound. The reaction progress was simulated, and parameters
of the reverse (hydrolysis) reaction were estimated using Matlab
software.
3.2. Experimental design and statistical analysis
A 5-level-5-factor CCRD, including 32 experimental points (16
factorial, 10 axial, and 6 center points), was employed in this study.
Table 1 shows the coded and actual variable levels. All 32 runs
were performed in random order so that systematic errors would
be avoided.
Experimental data were analyzed by a response surface regres-
sion (RSREG) method to fit the second-order polynomial equation:
Y = ˇk0 +
5
i=1
ˇkiXi +
5
i=1
ˇkiiX2
i
+
4
i=1
5
j=i+1
ˇkijXiXj (2)
where Y is response (initial reaction rate), ˇk0, ˇkt, ˇktt and ˇkij
are constant regression coefficients, Xi and Xj are uncoded inde-
pendent variables, and k is the number of single factors. The
least-squares method was employed for the response function
coefficients calculation and their statistical significance evaluation.
Only the significant terms (p ≤ 0.05) were considered for the final
reduced model. Adequacy of the obtained model was determined
by the Fisher test. Student distribution was used to evaluate the
significance of the coefficients. The significance of all regression
coefficients was evaluated by comparing their calculated t-values
(Table 2) with the standard t-value of the degree of freedom of
applied experimental design, which was equal to 2.08.
4. Results and discussion
4.1. The effect of operating parameters on initial esterification
rate
The optimization study was performed in accordance with the
experimental design with 5-factors and 5-levels with 32 exper-
imental points [20]. The adequacy of the model described by a
second-order polynomial equation (Eq. (2)) was analyzed using the
Fischer test, and the F-value was calculated to be 2.89, indicating
that the model properly describes experimental results. The Stu-
dent’s t-test was employed to analyze the significance of model
coefficients, and calculated t-values for each of the examined fac-
tors are listed in Table 2. A regression model (Eq. (3)) was developed
after eliminating insignificant coefficients, with the exception of
coefficients ˇ4 and ˇ44 because these are necessary for hierarchy
of the model due to the significant interactive effect of factor x4.
Y = 2.98 − 0.253X1 + 1.43X20.613X3 − 0.0829X4 + 0.19X2
1
+ 0.911X2
2 − 0.096X2
4 − 0.195X2
5 − 0.331X1X3 + 0.297X2X4
+ 0.191X2X5 − 0.854X4X5 (3)
Values of model coefficients indicated a statistical significance
of all varied factors, with quadratic terms of all variables except
enzyme amount, which was also included in the model. In regard
to the mutual effect of the parameters, a significant interaction
was observed between the following variables: water content and
enzyme amount, temperature and substrate molar ratio, vitamin
C concentration and temperature, and substrate molar ratio and
Table 2
Coefficients values and results of Student’s t-test analysis.
Coefficient Value t-Value
ˇ0 2.98 20.9a
ˇ1 −0.253 3.54a
ˇ2 1.43 20.0a
ˇ3 0.613 8.60a
ˇ4 −0.0829 1.16
ˇ5 0.0905 1.27
ˇ11 0.194 2.92a
ˇ22 0.911 13.9a
ˇ33 0.141 1.94
ˇ44 0.0964 1.58
ˇ55 0.195 2.99a
ˇ12 −0.0521 0.597
ˇ13 −0.331 3.77a
ˇ14 −0.0515 0.590
ˇ15 −0.0138 0.158
ˇ23 −0.0109 0.125
ˇ24 0.297 3.39a
ˇ25 0.191 2.18a
ˇ34 −0.0233 0.266
ˇ35 0.126 1.44
ˇ45 −0.854 9.74a
a
Significant coefficients.

4. 92 D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89–96
Fig. 1. Contour plot of ascorbic acid and molar ratio effects on initial reaction rate. Values of other factors: x1 = −2; x2 = 2; x3 = 2.
ascorbic acid concentration. In Figs. 1–3, only the most interesting
findings with impact on the following kinetic study are illustrated.
The effects of the substrate molar ratio and vitamin C concen-
tration, factors which showed the most intensive interaction, are
illustrated in Fig. 1. Both experimental factors had significant and
negative quadratic coefficients, so individual effects are described
by convex graphs with maximum values. Due to negative interac-
tions, the position of the local maxima of individual factors shifts
towards lower values with increases of other factors (Fig. 1). As a
result, high initial velocities were achieved when experiments were
conducted at high substrate molar ratios and low ascorbic acid con-
centrations or vice versa. Such trends should be discussed bearing
in mind the previous findings regarding mechanism of lipase-
catalyzed esterifications because it was univocally established that
the formation of the acyl–enzyme complex is the necessary first
step [14–16]. Consequently, at a low initial concentration of ascor-
bic acid, the local maximum of the initial rate was reached at the
highest oil/ascorbic acid molar ratios (even above 15), most likely
because the excess of oleic acid enables faster formation of the
acyl–enzyme complex. On the other hand, increases of ascorbic
acid concentrations led to the shift of local maxima toward lower
substrate ratios, even below 3 (Fig. 1). It is plausible that the main
cause of the initial reaction rate decrease is mass-transfer limita-
tions, which usually occur at higher reaction medium viscosity [21],
and these are reached at the highest values of both factors, mostly
due to extremely high oleic acid concentration.
A strong negative interaction was also observed between the
enzyme amount and water content (Fig. 2). The lipase loading
(X3) effect was described with only a linear coefficient; hence,
the initial reaction rate continuously increased with the increase
of enzyme concentration in our study. But due to the negative
interaction, slopes varied with the initial water concentration. At
low water concentrations, initial reaction rates increased steeply
when lipase loading was increased and reached maximum val-
ues, while at higher water concentration, slope becomes almost
negligible. The results obtained in our experiment shows that
the addition of water was not necessary for achieving a max-
imum initial reaction rate, indicating that the solvent contains
a sufficient amount of water for keeping enzymes in the open
conformation essential for providing its activity. It seems that a
higher amount of water in the media represents the hindrance
for the mass transfer, leading to lower initial reaction rates; oth-
erwise, the amount of water present in the solvent itself was
sufficient to provide lipases catalytic function. To investigate if
Fig. 2. Surface plot of the effects of enzyme and added water concentrations on initial reaction rates. Values of other factors: x2 = 2; x4 = 0; x5 = 0.

5. D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89–96 93
Fig. 3. The effect of temperature on the initial reaction rate. (a) Surface plot of ascorbic acid and temperature effects. Values of other factors: x1 = −2; x3 = 2; x4 = 0; (b) surface
plot of substrate molar ratio and temperature effects. Values of other factors: x1 = −2; x3 = 2; x5 = 2.
reaction rates can be increased with further reduction of water
concentration, two additional experiments were performed: one in
acetone previously dehydrated by molecular sieves and the other
in untreated acetone. Other experimental factors were kept at opti-
mum conditions in both experiments. It was revealed that a higher
initial rate was achieved in acetone (15.8 mM h−1) than in dehy-
drated acetone (14.2 mM h−1), indicating that removal of water
present in acetone is not advantageous because it reduced lipase
activity.
The effect of temperature is depicted in Fig. 3. In previous stud-
ies, when the incubation temperature was optimized from the
aspect of ester yield, the positive effect of temperature increase
was reported [7]. Within the initial reaction rate optimization in our
research, the same influence of reaction temperature was observed,
and therefore, the best results were achieved at 60 ◦C. Slight pos-
itive interaction effects between ascorbic acid concentration and
temperature (ˇ25 = 0.191) caused a shift of local maxima from low
towards moderate ascorbic acid concentrations (Fig. 3a). At lower
temperatures, the rate of substrate interchange at the active site
and diffusion of substrates and products are significantly lower,
so high ascorbic acid concentrations are futile. With the increase of
reaction temperature, the acceleration of interchange and diffusion
leads to higher rates at higher initial ascorbic acid concentrations.
A similar trend was observed with the effects of temperature and
substrate molar ratio, where positive interaction between factors
(ˇ24 = 0.297) led to a reduced decrease of the initial rate with the
increase of molar ratio at higher reaction temperatures (Fig. 3b).
This result could also be ascribed to the increased diffusion of
both substrates or to the reduction of reaction medium viscosity,
which becomes significantly higher at a higher molar ratio due to
increased concentrations of viscous oleic acid. Notably, higher reac-
tion temperatures could not be investigated because the boiling
point of the initial reaction mixture is slightly greater than 60 ◦C,
even for high substrate(s) concentration mixtures, due to the high
volatility of acetone.
Findings, which had been obtained in a previous optimization
study, were applied in the subsequent kinetic study findings. Fur-
ther kinetic experiments were performed at 60 ◦C, with 1% (w/v)
of immobilized enzyme and without addition of water to the reac-
tion medium. Moreover, the goodness of the model prediction was
confirmed by an experiment performed at 0.22 M of ascorbic acid
and molar ratio 1:3 (and optimum values of other factors), where
the initial rate of 15.6 mM h−1 was achieved, which is only a 3.2%
deviation from the predicted value.

6. 94 D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89–96
Fig. 4. The effects of both substrates on initial reaction rate. Reaction temperature 60 ◦
C; initial lipase concentration 1% (w/v); without addition of water.
4.2. Initial rate analysis
To correlate initial reaction rates with substrates concentra-
tions in the kinetic model, a set of experiments was carried
out. Initial velocities for the ascorbyl oleate biosynthesis were
evaluated for the ascorbic and oleic acid concentrations in the
range of 0.05–1 mol/dm3. The experimental data that represents
the mutual effect of ascorbic and oleic acid concentrations on
the initial reaction velocity are represented with a 3D graph in
Fig. 4. It was observed that the maximum value of the initial
rate (16.7 mmol h−1) was achieved in an experiment with a high
oleic acid concentration (0.75 M) and a relatively low ascorbic acid
concentration (0.1 M). Significant increases in the initial rate of
comparison with the experimental design could be ascribed to the
fact that three factors have extreme optimum values, and the exper-
imental plan does not include the experiments with more than one
extreme value of experimental factors.
In graphic analyses of kinetic experiments, the effect of oleic acid
on the initial rate resembles a classic Michaelis–Menten-shaped
curve (Fig. 5a). However, the effect of ascorbic acid is far more com-
plex than this pattern because the increase of initial rates can be
observed only up to 0.2 M, and further increases in ascorbic acid
concentration led to the decrease of initial rates (Fig. 5b). Such
a trend indicates that inhibition with an excess of ascorbic acid
occurs, while inhibition with oleic acid does not. Therefore, the
results were fitted with a ping–pong bi–bi model with ascorbic acid
inhibition (Eq. (1)).
The goodness of fit was very high (R2 = 0.979), and the 3D-
congruence between model and results is illustrated in Fig. 6;
fitting of the effects of individual substrates at a fixed concentra-
tion of other substrate is depicted in Fig. 5; and calculated kinetic
constants are listed in Table 3. The inhibition constant is signifi-
cantly higher than previously reported in similar kinetic models
[14,19], indicating that ascorbic acid is not a very strong lipase
inhibitor.
In previous studies of synthesis of esters with C. antarctica lipase,
various models with inhibition by different substrates or without
any substrate inhibition were postulated. For example, in a study
focused on citronellol laurate synthesis, an ordered bi–bi mech-
anism with acid inhibition was proposed [15]. An ordered bi–bi
kinetic model with competitive inhibition by both reactants and
products was reported by Garcia et al. for the isopropyl palmitate
synthesis in an organic solvent [16]. On the other hand, in sugar
ester synthesis, a ping–pong bi–bi mechanism without inhibition
by any substrate was established [17].
Ping–pong bi–bi models with alcohol inhibition, such as the one
proposed in our study, were previously reported for the synthe-
sis of tetrahydrofurfuryl butyrate in heptane and butyl isobutyrate
biosynthesis in n-hexane [13,14]. The inhibition mechanism with
an excess of alcohol was most thoroughly elaborated by Yadav and
Lathi [14]. Because it is generally accepted that the formation of
the acyl–enzyme complex is the first step of the reaction, it seems
Fig. 5. The representative kinetic model curves at fixed concentrations of one sub-
strate: (a) 0.3 M ascorbic acid; (b) 1 M oleic acid.

7. D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89–96 95
Fig. 6. The surface plot of the obtained ping–pong bi–bi model with inhibition by ascorbic acid. Reaction temperature 60 ◦
C; initial lipase concentration 1% (w/v); without
addition of water.
that alcohol inhibition occurs due to the formation of inactive “dead
end” complex between alcohol (in our reaction, this role is vitamin
C) and enzyme. Discrepancies between reported kinetic models
indicate that size, branching and abundance of hydroxy groups in
the side chains of both substrates strongly affect the reaction mech-
anism. C. antarctica B has been previously classified into the group
of lipases with a funnel-like active site, which is the main reason
for their higher affinity towards short- and medium-chain acid sub-
strates and steep decreases in affinity for C14 acids [22]. Therefore,
inhibition by an excess of vitamin C could be ascribed to an easier
approach of vitamin C than the sterically hindered approach of oleic
acid, which resulted in the more frequent formation of an inactive
complex than produces the acyl–enzyme complex. A significantly
higher (approximately 28 times) specificity constant for ascorbic
acid (Table 3) confirms this higher affinity.
4.3. Model for progress curve
To develop an efficient enzymatic process of ester synthesis and
adequate reactor design, it is crucial to obtain a good fit between
the kinetic model and (product concentration)–(reaction time)
curve throughout the reaction range. Therefore, the kinetic model
obtained in this study, which is based on initial reaction rates,
was tested on reaction curves and was further adjusted to obtain
the best fit for the experimental results. Typical results, obtained
at an initial concentration of 0.1 M vitamin C and a molar ratio
of 1:5, are depicted in Fig. 7. It can be seen that the simulation
of the model (dotted line) fits the experimental results (circles)
only during the initial 90 min of the reaction. Because obtaining a
kinetic model is suitable only if the reverse reaction does not occur
[12], the discrepancy between the modeled and the experimen-
tal results can be attributed to the onset of intensive hydrolysis of
the formed ester. This hypothesis was tested by adding molecular
sieves after 2 h of reaction because the rate of hydrolysis is influ-
enced by the concentration of free water in a reaction mixture [23].
The results (indicated by crosses in Fig. 7) show that in the presence
of sieves, the linear increase of product concentration is prolonged
until approximately the 4th hour of the reaction, indicating that the
onset of hydrolysis is delayed by the removal of water. Neverthe-
less, hydrolysis occurred most likely when the adsorbent capacity
had been exceeded.
d[AOl]
dt
= es − h (4)
h =
Vm,h[AOl]
KAOl + [AOl]
= es − h (5)
Therefore, it seems unavoidable to include hydrolysis in a model
that describes a complete product–time curve (Eq. (4)). Ester
hydrolysis was fit with a lumped rate expression that resembles
a Michaelis–Menten equation (Eq. (5)) because it has been widely
applied for lipase-catalyzed hydrolysis [24]. In Eq. (5), Vm,h repre-
sents the maximum initial rate of hydrolysis and KAOl the Michaelis
constant of ascorbyl oleate.
The determined values of unknown parameters in Eq. (5) are
listed in Table 3, and the simulation of the reaction described by
Eq. (4) is depicted in Fig. 7 (solid line). Strong congruence between
ascorbyl oleate synthesis and the model were observed (R2 = 0.943),
indicating that the kinetic model established at initial conditions,
in addition to elucidating the reaction mechanism, can also be
applied for estimating the reaction course after introducing a term
Table 3
Determined values of the model kinetic constants.
Esterification Hydrolysis
Kinetic constant (unit) Calculated value Kinetic constant (unit) Calculated value
Vm,es (mmol h−1
dm−3
) 21.9 KAOl (mol dm−3
) 0.00963
KAA (mol dm−3
) 0.0111 Vm,h (mmol h−1
dm−3
) 16.9
KOl (mol dm−3
) 0.309 KS,AOl (dm3
h−1
g−1
) 0.175
Ki,AA (mol dm−3
) 0.864
KS,AA (dm3
h−1
g−1
) 0.197
KS,Ol (dm3
h−1
g−1
) 0.00709

8. 96 D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89–96
Fig. 7. Fitting of experimental results with different kinetic models. Initial concentrations were: 0.1 M ascorbic acid and 0.5 M oleic acid. Circles: results of experiment without
molecular sieve addition; crosses: results of experiment with molecular sieve addition; dotted line: the simulation of ping–pong bi–bi model with ascorbic acid inhibition
(Eq. (3)); solid line: the simulation of model including ester hydrolysis (Eq. (4)).
describing the reverse reaction. Additionally, the determined speci-
ficity constant for ester as a substrate (KS,AOl) is approximately 25
times higher than the specificity constant for oleic acid, indicating
that the removal of at least one of the reaction products (water or
ester) is necessary for reaching high product yields.
5. Conclusions
The aim of this study was to thoroughly examine the kinetics
of ascorbyl oleate synthesis, to describe the reaction mechanism
and establish a model that accurately describes the reaction flow.
It was revealed that the ping–pong bi–bi model with inhibition
by excess of ascorbic acid fitted experimental results with high
accuracy. Comparing the obtained values of specificity constants
indicates that lipase has a significantly stronger affinity towards
ascorbic acid. These findings were also valuable for explaining the
inhibition mechanism because inhibition by an acyl acceptor is usu-
ally based on the formation of an inactive complex, which is most
likely promoted with a strong affinity towards ascorbic acid.
After extending the ping–pong bi–bi model with a term
describing the reverse hydrolysis of ester and determining the
corresponding kinetic constants, an adequate model for predict-
ing product concentration was obtained. Good prediction of the
reach of the reaction is of utmost importance for further enzymatic
process development, especially when performed in conditions
previously optimized by RSM, as was the case in this study. In
summary, the results of this study may present an important contri-
bution for elucidating the mechanism of lipase-catalyzed synthesis
of vitamin C esters and a novel, simplified approach to the devel-
opment of a model that successfully predicts the dependence of
formed product concentration and reaction time.
Acknowledgement
The authors are grateful for financial support from the Serbian
Ministry of Science (projects III 46010 and 451-03-00605/2012-
16/51).
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