8
Biochemical Engineering Journal 71 (2013) 89–96 Contents lists available at SciVerse ScienceDirect Biochemical Engineering Journal journa l h omepage: 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 Bezbradica a,, Marija Stojanovi ´ c a , Duˇ san Veliˇ ckovi ´ c b , Aleksandra Dimitrijevi ´ c b , Milica Carevi ´ c a , Mladen Mihailovi ´ c a , Nenad Milosavi ´ c b 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: [email protected] (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. http://dx.doi.org/10.1016/j.bej.2012.12.001

Ping pong model-for_lipases_2013

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Biochemical Engineering Journal 71 (2013) 89– 96

Contents lists available at SciVerse ScienceDirect

Biochemical Engineering Journal

journa l h omepage: www.elsev ier .com/ locate /be j

egular article

inetic model of lipase-catalyzed conversion of ascorbic acid and oleic acid toiposoluble vitamin C ester

ejan Bezbradicaa,∗, Marija Stojanovic a, Dusan Velickovic b, Aleksandra Dimitrijevic b, Milica Carevic a,laden Mihailovic a, Nenad Milosavic b

Department of Biochemical Engineering and Biotechnology, Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, SerbiaDepartment of Biochemistry, Faculty of Chemistry, Studentski trg 12, University of Belgrade, 11000 Belgrade, Serbia

r t i c l e i n f o

rticle history:eceived 6 August 2012eceived in revised form 18 October 2012ccepted 2 December 2012vailable online 10 December 2012

eywords:scorbyl oleate

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 optimumexperimental factors (temperature, initial water content, and enzyme concentration), which were deter-mined using response surface methodology. Then, a model for predicting product–time progress curveswas developed by expanding the obtained ping–pong model with terms describing ester hydrolysis.

ipaseandida antarcticainetic parametersubstrate inhibitionroduction kinetics

Kinetic constants of the reverse reaction were determined, and good congruence between the model andexperimental 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 importantcontribution for reaction optimization and creating strategies to increase the productivity of vitamin C

ester synthesis.

. Introduction

Vitamin C is well known for its antioxidative properties. Nev-rtheless, the use of l-ascorbic acid in stabilizing fats and oils isery scarce due to its hydrophilic nature [1]. On the contrary, fattycid ascorbyl esters are oil-soluble with the same or even enhancedntioxidative properties compared to vitamin C. Mineral acids oripases can catalyze the esterification process between vitamin Cnd fatty acid (or its methyl or vinyl ester). At the moment, despitehe numerous shortcomings, ascorbyl palmitate is being producedndustrially by chemical means [2]. On the other hand, there are

any advantages of the biosynthetic process, such as mild reactiononditions, regioselectivity, and the possibility of using immobi-ized enzymes, resulting in simpler downstream processing [3].dditionally, obtaining a product in such a way allows it to be

abeled as natural and have a higher market value [4]. Althoughipase-catalyzed synthesis of ascorbyl esters has already beenescribed by many authors, long reaction times, bio-incompatible

olvents, and high price of the enzyme are still some of the mainbstacles in the commercialization of the process [5]. Ascorbylsters derived from unsaturated fatty acids are superior compared

∗ Corresponding author. Tel.: +381 11 3303727; fax: +381 11 3370387.E-mail address: [email protected] (D. Bezbradica).

369-703X/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.bej.2012.12.001

© 2012 Elsevier B.V. All rights reserved.

to those with saturated hydrocarbon chains in terms of solubility,free radical scavenging capacity and beneficial effects on humannutrition [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 necessaryto optimize operating parameters and establish adequate kineticmodels for the reactions. Additionally, the type of kinetic modelgives valuable information about the reaction mechanism and sub-strate inhibition which helps in organizing enzymatic processesin such a way as to avoid intrinsic limitations at the molecularlevel. There are just a few reports of ascorbyl oleate synthesis cat-alyzed by immobilized lipase from Candida antarctica [7–11]. Onthe other hand, reports on the kinetics of aliphatic ester synthesisare more frequent, but different kinetic models have been pro-posed. In general, esterification reactions catalyzed by immobilizedC. antarctica lipase preparation occurs via acyl–enzyme interme-diates and are most commonly being described by models basedon a ping–pong bi–bi or ordered bi–bi mechanism [12]. Addition-ally, inhibition by one or both substrates was reported on severaloccasions [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, andcompare affinity of substrates towards lipase. To investigate inhi-bition by excess of substrates, concentration was varied in a wide
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90 D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89– 96

e in a

rmakaeemfito

2

2

oDSAmHpS

2

taertidwT

ww

Scheme 1. Formation of ascorbyl oleat

ange from 0.05 to 1 M. Prior to kinetic studies, response surfaceethodology (RSM) and 5-level-5-factor central composite rotat-

ble design (CCRD) were employed to determine the effects ofey experimental parameters (initial water content, temperature,scorbic acid:oleic acid molar ratio, vitamin C concentration, andnzyme content) on the initial rate of the vitamin C and oleic acidsterification reaction, so the kinetic study was performed at opti-um conditions. Finally, it was shown that reaction kinetics can be

tted throughout the reaction range with a model that also includeshe reverse reaction of ester hydrolysis, and the kinetic constantsf the reverse reaction were determined.

. Materials and methods

.1. Enzyme and chemicals

Novozym® 435 (lipase from C. antarctica, type B immobilizedn acrylic resin) was purchased from Novozymes (Bagsvaerd,enmark). Substrates were l-ascorbic acid (purity 99.7%, Zorka,

ˇabac, Serbia) and oleic acid (Ph. Eur., NF pure purchased fromppliChem, Darmstadt, Germany). Acetone was used as a reactionedium (99.5%, JT Baker, USA). Substances used for the quantitativePLC analyses were methanol obtained from JT Baker (USA) andhosphoric acid, purchased from Sigma–Aldrich (Chemie GmbH,teinheim, Germany); all were HPLC grade.

.2. Procedure for the enzymatic synthesis

Experiments were carried out in 100 ml capped vials. The reac-ion mixture consisted of different amounts of ascorbic acid, oleiccid, enzyme, water, and acetone (amounts specified for eachxperiment separately), so that the total volume was 10 ml. Theeactions were conducted in a shaker at 250 rpm and at a tempera-ure in the range from 40 to 60 ◦C. All experiments were carried outn duplicate, and average values are presented in Figs. All standardeviations were less than 5%. Control samples (without enzyme)ere prepared by exposure to the same temperature treatment.

he product was not detected in control samples. In experiments

ith the addition of molecular sieves, 80 mg of zeolite type sievesere added per ml of the reaction medium.

reaction of ascorbic acid and oleic acid.

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 curvetangent to the initial stage of the reaction. Because all experimentswere performed in duplicate, reaction curves were constructedusing average values of the reaction rate for each experimentalpoint. A linear portion of the reaction curve at various substrateconcentrations consisted of 4–6 experimental points, where thenumber of experimental points included was determined by thecondition that correlation coefficients of the initial straight linemust be above 0.95.

2.4. HPLC analysis

For quantitative analysis of reactants and products, an AktaPurifier HPLC system was used. A reverse phase column (WatersSpherisorb 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 witha flow rate of 1 ml/min. The product was detected by a UV detectorat 235 nm.

3. Theory and calculations

3.1. Ping–pong bi–bi model

The ping–pong bi–bi mechanism illustrates alternate binding ofsubstrates and release of products in a bi-substrate reaction withtwo products formed. It is the most frequently postulated reactionmechanism in lipase-catalyzed esterifications [13–19]. The firststage of the reaction is the binding of the acyl-donor (Ol, oleic acid),resulting in the formation of an acyl–enzyme complex. In the nextstep, 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 inhibitionby excess of one of the substrates was frequently reported [14–19].

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D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89– 96 91

Table 1Coded 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 0.2Temperature, X2 (◦C) 40 45 50 55 60Enzyme amount, X3 (%, w/v) 0.2 0.4 0.6 0.8 1.0Oleic acid/ascorbic acid molar ratio, X4 1:3 1:6 1:9 1:12 1:15

0

S“tetcpi

Mif(trSlwcos

3

fTwb

s

Y

waplcOrbsc(a

to the mutual effect of the parameters, a significant interactionwas observed between the following variables: water content andenzyme amount, temperature and substrate molar ratio, vitaminC concentration and temperature, and substrate molar ratio and

Table 2Coefficients 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 1.16ˇ5 0.0905 1.27ˇ11 0.194 2.92a

ˇ22 0.911 13.9a

ˇ33 0.141 1.94ˇ44 0.0964 1.58ˇ55 0.195 2.99a

ˇ12 −0.0521 0.597ˇ13 −0.331 3.77a

ˇ14 −0.0515 0.590ˇ15 −0.0138 0.158ˇ23 −0.0109 0.125ˇ24 0.297 3.39a

ˇ25 0.191 2.18a

Vitamin C concentration, X5 (M) 0.02

ubstrate inhibition occurs due to the formation of an inactivedead-end complex”. In a case of acyl donor inhibition, the inac-ive complex with two molecules of the acyl donor attached to thenzyme is formed [15]. When inhibition by an excess of acyl accep-or occurs, such as in our reaction, an inactive enzyme-acceptoromplex is formed that cannot be subsequently transformed into aroduct [14]. The ping–pong bi–bi kinetic model with ascorbic acid

nhibition 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 theichaelis constants of ascorbic and oleic acid, respectively; Vm,es

s the maximum reaction rate; and Ki,AA is the inhibition constantor ascorbic acid. The term Vm,es is the product of the rate constantkcat) of the final reaction step and the initial enzyme concentra-ion ([E]0). Kinetic constants were determined using a non-linearegression fit of the results obtained in the experiment described inection 2.3. Goodness of fit was evaluated by calculating the corre-ation coefficient. Specificity constants for each of reaction species

ere calculated by dividing kcat by the Michaelis constant of theompound. The reaction progress was simulated, and parametersf the reverse (hydrolysis) reaction were estimated using Matlaboftware.

.2. Experimental design and statistical analysis

A 5-level-5-factor CCRD, including 32 experimental points (16actorial, 10 axial, and 6 center points), was employed in this study.able 1 shows the coded and actual variable levels. All 32 runsere performed in random order so that systematic errors would

e avoided.Experimental data were analyzed by a response surface regres-

ion (RSREG) method to fit the second-order polynomial equation:

= ˇk0 +5∑

i=1

ˇkiXi +5∑

i=1

ˇkiiX2i +

4∑

i=1

5∑

j=i+1

ˇkijXiXj (2)

here Y is response (initial reaction rate), ˇk0, ˇkt, ˇktt and ˇkijre constant regression coefficients, Xi and Xj are uncoded inde-endent variables, and k is the number of single factors. The

east-squares method was employed for the response functionoefficients calculation and their statistical significance evaluation.nly the significant terms (p ≤ 0.05) were considered for the final

educed model. Adequacy of the obtained model was determinedy the Fisher test. Student distribution was used to evaluate the

ignificance of the coefficients. The significance of all regressionoefficients was evaluated by comparing their calculated t-valuesTable 2) with the standard t-value of the degree of freedom ofpplied experimental design, which was equal to 2.08.

.07 0.12 0.17 0.22

4. Results and discussion

4.1. The effect of operating parameters on initial esterificationrate

The optimization study was performed in accordance with theexperimental design with 5-factors and 5-levels with 32 exper-imental points [20]. The adequacy of the model described by asecond-order polynomial equation (Eq. (2)) was analyzed using theFischer test, and the F-value was calculated to be 2.89, indicatingthat the model properly describes experimental results. The Stu-dent’s t-test was employed to analyze the significance of modelcoefficients, and calculated t-values for each of the examined fac-tors are listed in Table 2. A regression model (Eq. (3)) was developedafter eliminating insignificant coefficients, with the exception ofcoefficients ˇ4 and ˇ44 because these are necessary for hierarchyof the model due to the significant interactive effect of factor x4.

Y = 2.98 − 0.253X1 + 1.43X20.613X3 − 0.0829X4 + 0.19X21

+ 0.911X22 − 0.096X2

4 − 0.195X25 − 0.331X1X3 + 0.297X2X4

+ 0.191X2X5 − 0.854X4X5 (3)

Values of model coefficients indicated a statistical significanceof all varied factors, with quadratic terms of all variables exceptenzyme amount, which was also included in the model. In regard

ˇ34 −0.0233 0.266ˇ35 0.126 1.44ˇ45 −0.854 9.74a

a Significant coefficients.

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92 D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89– 96

n initi

afi

tinbttrccictsbhbaas

Fig. 1. Contour plot of ascorbic acid and molar ratio effects o

scorbic acid concentration. In Figs. 1–3, only the most interestingndings with impact on the following kinetic study are illustrated.

The effects of the substrate molar ratio and vitamin C concen-ration, factors which showed the most intensive interaction, arellustrated in Fig. 1. Both experimental factors had significant andegative quadratic coefficients, so individual effects are describedy convex graphs with maximum values. Due to negative interac-ions, the position of the local maxima of individual factors shiftsowards lower values with increases of other factors (Fig. 1). As aesult, high initial velocities were achieved when experiments wereonducted at high substrate molar ratios and low ascorbic acid con-entrations or vice versa. Such trends should be discussed bearingn mind the previous findings regarding mechanism of lipase-atalyzed esterifications because it was univocally established thathe formation of the acyl–enzyme complex is the necessary firsttep [14–16]. Consequently, at a low initial concentration of ascor-ic acid, the local maximum of the initial rate was reached at theighest oil/ascorbic acid molar ratios (even above 15), most likelyecause the excess of oleic acid enables faster formation of the

cyl–enzyme complex. On the other hand, increases of ascorbiccid concentrations led to the shift of local maxima toward lowerubstrate ratios, even below 3 (Fig. 1). It is plausible that the main

Fig. 2. Surface plot of the effects of enzyme and added water concentration

al reaction rate. Values of other factors: x1 = −2; x2 = 2; x3 = 2.

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, mostlydue to extremely high oleic acid concentration.

A strong negative interaction was also observed between theenzyme 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 increaseof enzyme concentration in our study. But due to the negativeinteraction, slopes varied with the initial water concentration. Atlow water concentrations, initial reaction rates increased steeplywhen lipase loading was increased and reached maximum val-ues, while at higher water concentration, slope becomes almostnegligible. The results obtained in our experiment shows thatthe addition of water was not necessary for achieving a max-imum initial reaction rate, indicating that the solvent containsa sufficient amount of water for keeping enzymes in the openconformation essential for providing its activity. It seems that ahigher 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 wassufficient to provide lipases catalytic function. To investigate if

s on initial reaction rates. Values of other factors: x2 = 2; x4 = 0; x5 = 0.

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D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89– 96 93

F bic acp 2; x3 =

rcaimidpa

iawraitttasr

ig. 3. The effect of temperature on the initial reaction rate. (a) Surface plot of ascorlot of substrate molar ratio and temperature effects. Values of other factors: x1 = −

eaction rates can be increased with further reduction of wateroncentration, two additional experiments were performed: one incetone previously dehydrated by molecular sieves and the othern untreated acetone. Other experimental factors were kept at opti-

um conditions in both experiments. It was revealed that a highernitial rate was achieved in acetone (15.8 mM h−1) than in dehy-rated acetone (14.2 mM h−1), indicating that removal of waterresent in acetone is not advantageous because it reduced lipasectivity.

The effect of temperature is depicted in Fig. 3. In previous stud-es, when the incubation temperature was optimized from thespect of ester yield, the positive effect of temperature increaseas reported [7]. Within the initial reaction rate optimization in our

esearch, the same influence of reaction temperature was observed,nd therefore, the best results were achieved at 60 ◦C. Slight pos-tive interaction effects between ascorbic acid concentration andemperature (ˇ25 = 0.191) caused a shift of local maxima from lowowards moderate ascorbic acid concentrations (Fig. 3a). At lower

emperatures, the rate of substrate interchange at the active sitend diffusion of substrates and products are significantly lower,o high ascorbic acid concentrations are futile. With the increase ofeaction temperature, the acceleration of interchange and diffusion

id and temperature effects. Values of other factors: x1 = −2; x3 = 2; x4 = 0; (b) surface 2; x5 = 2.

leads to higher rates at higher initial ascorbic acid concentrations.A similar trend was observed with the effects of temperature andsubstrate molar ratio, where positive interaction between factors(ˇ24 = 0.297) led to a reduced decrease of the initial rate with theincrease of molar ratio at higher reaction temperatures (Fig. 3b).This result could also be ascribed to the increased diffusion ofboth substrates or to the reduction of reaction medium viscosity,which becomes significantly higher at a higher molar ratio due toincreased concentrations of viscous oleic acid. Notably, higher reac-tion temperatures could not be investigated because the boilingpoint of the initial reaction mixture is slightly greater than 60 ◦C,even for high substrate(s) concentration mixtures, due to the highvolatility of acetone.

Findings, which had been obtained in a previous optimizationstudy, 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 acidand molar ratio 1:3 (and optimum values of other factors), wherethe initial rate of 15.6 mM h−1 was achieved, which is only a 3.2%deviation from the predicted value.
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94 D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89– 96

peratu

4

toerttFroccfie

ocpocaori

cfitcc[i

vafakpseb

biosynthesis in n-hexane [13,14]. The inhibition mechanism withan excess of alcohol was most thoroughly elaborated by Yadav andLathi [14]. Because it is generally accepted that the formation ofthe acyl–enzyme complex is the first step of the reaction, it seems

Fig. 4. The effects of both substrates on initial reaction rate. Reaction tem

.2. Initial rate analysis

To correlate initial reaction rates with substrates concentra-ions in the kinetic model, a set of experiments was carriedut. Initial velocities for the ascorbyl oleate biosynthesis werevaluated for the ascorbic and oleic acid concentrations in theange of 0.05–1 mol/dm3. The experimental data that representshe mutual effect of ascorbic and oleic acid concentrations onhe initial reaction velocity are represented with a 3D graph inig. 4. It was observed that the maximum value of the initialate (16.7 mmol h−1) was achieved in an experiment with a highleic acid concentration (0.75 M) and a relatively low ascorbic acidoncentration (0.1 M). Significant increases in the initial rate ofomparison with the experimental design could be ascribed to theact that three factors have extreme optimum values, and the exper-mental plan does not include the experiments with more than onextreme value of experimental factors.

In graphic analyses of kinetic experiments, the effect of oleic acidn the initial rate resembles a classic Michaelis–Menten-shapedurve (Fig. 5a). However, the effect of ascorbic acid is far more com-lex than this pattern because the increase of initial rates can bebserved only up to 0.2 M, and further increases in ascorbic acidoncentration led to the decrease of initial rates (Fig. 5b). Such

trend indicates that inhibition with an excess of ascorbic acidccurs, while inhibition with oleic acid does not. Therefore, theesults were fitted with a ping–pong bi–bi model with ascorbic acidnhibition (Eq. (1)).

The goodness of fit was very high (R2 = 0.979), and the 3D-ongruence between model and results is illustrated in Fig. 6;tting of the effects of individual substrates at a fixed concentra-ion of other substrate is depicted in Fig. 5; and calculated kineticonstants are listed in Table 3. The inhibition constant is signifi-antly higher than previously reported in similar kinetic models14,19], indicating that ascorbic acid is not a very strong lipasenhibitor.

In previous studies of synthesis of esters with C. antarctica lipase,arious models with inhibition by different substrates or withoutny substrate inhibition were postulated. For example, in a studyocused on citronellol laurate synthesis, an ordered bi–bi mech-nism with acid inhibition was proposed [15]. An ordered bi–biinetic model with competitive inhibition by both reactants and

roducts was reported by Garcia et al. for the isopropyl palmitateynthesis in an organic solvent [16]. On the other hand, in sugarster synthesis, a ping–pong bi–bi mechanism without inhibitiony any substrate was established [17].

re 60 ◦C; initial lipase concentration 1% (w/v); without addition of water.

Ping–pong bi–bi models with alcohol inhibition, such as the oneproposed in our study, were previously reported for the synthe-sis of tetrahydrofurfuryl butyrate in heptane and butyl isobutyrate

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.

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D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89– 96 95

F ascorba

teCitaofsiaacha

4

atcowtaoook

TD

ig. 6. The surface plot of the obtained ping–pong bi–bi model with inhibition by

ddition of water.

hat alcohol inhibition occurs due to the formation of inactive “deadnd” complex between alcohol (in our reaction, this role is vitamin) and enzyme. Discrepancies between reported kinetic models

ndicate that size, branching and abundance of hydroxy groups inhe side chains of both substrates strongly affect the reaction mech-nism. C. antarctica B has been previously classified into the groupf lipases with a funnel-like active site, which is the main reasonor their higher affinity towards short- and medium-chain acid sub-trates and steep decreases in affinity for C14 acids [22]. Therefore,nhibition by an excess of vitamin C could be ascribed to an easierpproach of vitamin C than the sterically hindered approach of oleiccid, which resulted in the more frequent formation of an inactiveomplex than produces the acyl–enzyme complex. A significantlyigher (approximately 28 times) specificity constant for ascorbiccid (Table 3) confirms this higher affinity.

.3. Model for progress curve

To develop an efficient enzymatic process of ester synthesis anddequate reactor design, it is crucial to obtain a good fit betweenhe kinetic model and (product concentration)–(reaction time)urve throughout the reaction range. Therefore, the kinetic modelbtained in this study, which is based on initial reaction rates,as tested on reaction curves and was further adjusted to obtain

he best fit for the experimental results. Typical results, obtainedt an initial concentration of 0.1 M vitamin C and a molar ratio

f 1:5, are depicted in Fig. 7. It can be seen that the simulationf the model (dotted line) fits the experimental results (circles)nly during the initial 90 min of the reaction. Because obtaining ainetic model is suitable only if the reverse reaction does not occur

able 3etermined values of the model kinetic constants.

Esterification

Kinetic constant (unit) Calculated value

Vm,es (mmol h−1 dm−3) 21.9

KAA (mol dm−3) 0.0111

KOl (mol dm−3) 0.309

Ki,AA (mol dm−3) 0.864KS,AA (dm3 h−1 g−1) 0.197KS,Ol (dm3 h−1 g−1) 0.00709

ic acid. Reaction temperature 60 ◦C; initial lipase concentration 1% (w/v); without

[12], the discrepancy between the modeled and the experimen-tal results can be attributed to the onset of intensive hydrolysis ofthe formed ester. This hypothesis was tested by adding molecularsieves 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 presenceof sieves, the linear increase of product concentration is prolongeduntil approximately the 4th hour of the reaction, indicating that theonset of hydrolysis is delayed by the removal of water. Neverthe-less, hydrolysis occurred most likely when the adsorbent capacityhad 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 modelthat describes a complete product–time curve (Eq. (4)). Esterhydrolysis was fit with a lumped rate expression that resemblesa Michaelis–Menten equation (Eq. (5)) because it has been widelyapplied for lipase-catalyzed hydrolysis [24]. In Eq. (5), Vm,h repre-sents the maximum initial rate of hydrolysis and KAOl the Michaelisconstant of ascorbyl oleate.

The determined values of unknown parameters in Eq. (5) arelisted in Table 3, and the simulation of the reaction described byEq. (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 beapplied for estimating the reaction course after introducing a term

Hydrolysis

Kinetic constant (unit) Calculated value

KAOl (mol dm−3) 0.00963Vm,h (mmol h−1 dm−3) 16.9KS,AOl (dm3 h−1 g−1) 0.175

Page 8: Ping pong model-for_lipases_2013

96 D. Bezbradica et al. / Biochemical Engineering Journal 71 (2013) 89– 96

F tions

m tion; d(

dfitte

5

oaIbaiaial

dcirppsboof

A

M1

R

[

[

[[

[

[

[

[

[

[

[

[

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ig. 7. Fitting of experimental results with different kinetic models. Initial concentraolecular sieve addition; crosses: results of experiment with molecular sieve addi

Eq. (3)); solid line: the simulation of model including ester hydrolysis (Eq. (4)).

escribing the reverse reaction. Additionally, the determined speci-city constant for ester as a substrate (KS,AOl) is approximately 25imes higher than the specificity constant for oleic acid, indicatinghat the removal of at least one of the reaction products (water orster) is necessary for reaching high product yields.

. Conclusions

The aim of this study was to thoroughly examine the kineticsf ascorbyl oleate synthesis, to describe the reaction mechanismnd establish a model that accurately describes the reaction flow.t was revealed that the ping–pong bi–bi model with inhibitiony excess of ascorbic acid fitted experimental results with highccuracy. Comparing the obtained values of specificity constantsndicates that lipase has a significantly stronger affinity towardsscorbic acid. These findings were also valuable for explaining thenhibition mechanism because inhibition by an acyl acceptor is usu-lly based on the formation of an inactive complex, which is mostikely promoted with a strong affinity towards ascorbic acid.

After extending the ping–pong bi–bi model with a termescribing the reverse hydrolysis of ester and determining theorresponding kinetic constants, an adequate model for predict-ng product concentration was obtained. Good prediction of theeach of the reaction is of utmost importance for further enzymaticrocess development, especially when performed in conditionsreviously optimized by RSM, as was the case in this study. Inummary, the results of this study may present an important contri-ution for elucidating the mechanism of lipase-catalyzed synthesisf vitamin C esters and a novel, simplified approach to the devel-pment of a model that successfully predicts the dependence oformed product concentration and reaction time.

cknowledgement

The authors are grateful for financial support from the Serbianinistry of Science (projects III 46010 and 451-03-00605/2012-

6/51).

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