Biochemical Engineering Journal 43 (2009) 327–332
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Synthesis of ethyl butyrate in organic media catalyzed by Candida rugosa lipase immobilized in polyurethane foams: A kinetic study P. Pires-Cabral a,c , M.M.R. da Fonseca b , S. Ferreira-Dias c,∗ a
Escola Superior de Tecnologia, Universidade do Algarve, Campus da Penha, 8000 Faro, Portugal Instituto Superior Técnico, Centro de Engenharia Biológica e Química, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal c Instituto Superior de Agronomia, Centro de Estudos de Engenharia Rural, Technical University of Lisbon, Tapada da Ajuda, 1349-017 Lisboa, Portugal b
a r t i c l e
i n f o
Article history: Received 3 July 2008 Received in revised form 31 October 2008 Accepted 1 November 2008 Keywords: Biocatalyst preparation Enzyme Immobilized Kinetics Lipase Polyurethane foams
a b s t r a c t A kinetic study on the synthesis of ethyl butyrate in n-hexane, catalyzed by Candida rugosa lipase immobilized in two hydrophilic polyurethane foams (“HYPOL FHP 2002” and “HYPOL FHP 5000”) was performed. With the “FHP5000” foams, esterification rates and conversion were always higher than those obtained with “FHP2002”. For both immobilized preparations, BA did not cause any inhibition on the enzymatic activity, in the range of concentration tested (0.078–0.7 M) at an initial ethanol concentration of 0.105 M. Michäelis–Menten kinetics was observed: a plateau being reached at the initial bulk BA concentration of 0.40 M and 0.45 M, corresponding to microenvironmental concentrations of 0.851 M and 0.329 M, respectively with the lipase in “FHP2002” and “FHP5000” foams. Inhibition by EtOH was observed for initial bulk concentrations higher than 0.15 M, corresponding to microenvironmental concentrations of 0.426 M and 0.256 M, for the lipase in “FHP2002” and “FHP5000” foams, respectively. Kinetic data could be well described by the substrate-inhibition model, considering the initial bulk or microenvironmental ethanol concentrations as inhibitory. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Short-chain esters with fruity notes are widely used in the food industry as flavouring compounds. The direct extraction of these esters from plant materials involves rather expensive and low yield processes [1]. Thus, the production of these flavours has been currently carried out by chemical synthesis. However, biotechnological processes have clear environmental advantages and seem to be a competitive alternative toward chemical methods, because of the mild reaction conditions used, the high catalytic efficiency and the inherent selectivity of natural catalysts. Also, the product can be labelled as “natural” [2–5]. Lipases have been successfully used to catalyse esterification [1–16] and interesterification reactions [4,8,17,18] aimed at the production of flavouring esters for food, pharmaceutical and cosmetics purposes. Among a wide variety of immobilization supports, polyurethane foams have been tested for the immobilization of enzymes and cells, to be used in aqueous or in non-conventional organic media [5,6,19–36].
∗ Corresponding author. Tel.: +351 21 3653540; fax: +351 21 3653200. E-mail address:
[email protected] (S. Ferreira-Dias). 1369-703X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.bej.2008.11.002
Most of the kinetic studies of reactions using immobilized enzymes as catalysts in organic solvents are based on the application of Michäelis–Menten assumptions. However, this model is only valid for simple enzymatic reactions. The Ping-Pong Bi-Bi model has been proposed to explain several experimental lipase-catalyzed reaction kinetics [18,37–54]. In the Ping-Pong Bi-Bi mechanism, the first step in the lipase-catalyzed reaction consists of the binding of the fatty acid to the enzyme. An acyl-enzyme intermediate is then formed and a water molecule is released. Subsequently, the alcohol binds to the acyl-enzyme complex and the ester is formed. After the release of the ester, another fatty acid can bind to the enzyme [38]. Ping-Pong kinetic model with competitive inhibition by the alcohol [38–43], by the acid [44] or by both substrates [45,46] was suggested in lipase-catalyzed esterification reactions. These studies have been carried out with enzymes from different origins and with substrates (acids and alcohols) of various chain-lengths and structures, either in solvent free systems or in the presence of an organic solvent. Since the majority of these studies were performed with immobilized lipases, the effects of partition of substrates and products between the bulk and the microenvironment of the biocatalyst on the kinetic models cannot be neglected. In fact, when immobilized preparations are used, the interactions between the support and the substrates and products will lead to different sub-
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2.3. Reagents Nomenclature BA butyric acid concentration (M) CmicroEtOH microenvironmental ethanol concentration (M) CmicroBA microenvironmental butyric acid concentration (M) ESTER ethyl butyrate concentration (M) EtOH ethanol concentration (M) “FHP2002” foamable hydrophilic polyurethane pre-polymer “Hypol FHP 2002TM ” from Dow Chemicals, UK “FHP5000” foamable hydrophilic polyurethane pre-polymer “Hypol FHP 5000TM ” from Dow Chemicals, UK KBA Ping-Pong constant for butyric acid (M) ethanol inhibition constant (M) KI,EtOH KEtOH Ping-Pong constants for ethanol (M) KM Michäelis–Menten constant of butyric acid (M) MR initial ethanol/butyric acid molar ratio in the organic medium U unit of enzyme activity, defined as the amount of enzyme that hydrolyses 1 mol of fatty acid in 1 min at 37 ◦ C and with a pH of 7.0 v initial esterification rate (mol/min U) vmax maximum esterification reaction rate (mol/min U) residual sum-of-squares between experimental S2 data points and the values estimated by the models
strate concentrations in the bulk solution and in the vicinity of the enzyme due to partition effects [6,31,55]. The focus of the present work is the kinetic study of ethyl butyrate (a banana/pineapple flavour ester) production by esterification, in n-hexane, catalyzed by Candida rugosa lipase immobilized in two biocompatible hydrophilic polyurethane foams. For each reaction system, the compositions of both lipase microenvironment and organic bulk medium, under partition equilibrium conditions, were estimated from the knowledge of initial organic medium composition, using polynomial model equations previously established for similar systems [31]. The inhibitory effect of both substrates (ethanol and butyric acid) on lipase activity was also investigated. The fit of substrate-inhibition and Ping-Pong Bi-Bi inhibition kinetic models to kinetic data using either (i) bulk or (ii) microenvironmental compositions was attempted. 2. Materials 2.1. Enzyme The lyophilised Candida rugosa lipase, presenting a hydrolytic activity of 32,400 U/g (lipase AY 30), was a generous gift from Amano Enzyme Europe Ltd., UK. According to the manufacturer, 1 U will hydrolyze 1.0 microequiv. of fatty acid from triglyceride in 1.0 h at pH 7.7 at 37 ◦ C. 2.2. Immobilization matrix The hydrophilic polyurethane pre-polymers (“Hypol FHP 2002TM ” and “Hypol FHP 5000TM ”), for lipase immobilization, were kindly donated by Dow Chemical Company Limited, UK. “Hypol FHP 2002TM ” is a toluene diisocyanate (TDI) pre-polymer and “Hypol FHP 5000TM ” contains diphenylmethane-4,4 -diisocyanate (4,4 MDI) groups. “Hypol FHP 2002TM ” and “Hypol FHP 5000TM ” foams have aquaphilicity values [54] of 3.2 and 2.6, respectively [31].
Butyric acid, ethanol, ethyl butyrate, n-hexane and 4-methyl2-penthanol (used as internal standard) were analytical grade and obtained from various commercial sources. 3. Methods 3.1. Preparation of immobilized lipase Hydrophilic polyurethane foams were prepared by mixing the polyurethane pre-polymer (0.60 g of “Hypol FHP 2002TM ” or 0.35 g of “Hypol FHP 5000TM ”) with the aqueous phosphate buffer solution (0.020 M KH2 PO4 + 0.027 M Na2 HPO4 ; pH 7.0), containing lipase powder (0.35 g or 0.30 g for “Hypol FHP 2002TM ” and “Hypol FHP 5000TM ” foams, respectively), in a ratio of 1:1 (w:w), as previously described [28]. 3.2. Time-course of esterification experiments The “FHP5000” or “FHP2002” foams containing immobilized lipase molecules were cut in cuboids (∼0.07 cm3 ) and immersed in 12 cm3 of n-hexane solution containing 0.078 M of butyric acid and 0.105 M of ethanol. The esterification reactions were carried out at 30 ◦ C in a thermostated-capped cylindrical glass vessel under magnetic stirring at 1400 rev/min. Along the 24-h reaction, samples of 500 L of organic medium were taken and assayed for ethanol (EtOH), butyric acid (BA) and ethyl butyrate (ESTER) content. These samples were added to equal volumes of 0.4 M 4methyl-2-penthanol (internal standard) in n-hexane, prior to the analysis by gas chromatography, as previously described [31]. The conversion into ester was calculated as the ratio of ethyl butyrate concentration and the initial concentration of the limiting substrate (butyric acid, in this case). 3.3. Effect of substrate concentrations on esterification rate The effect of substrate concentration on the esterification of butyric acid with ethanol was investigated by performing two sets of experiments of 6 h duration each: (i) set I, where the initial concentration of BA varied between 0.078 M and 0.7 M, while the initial concentration of EtOH was kept constant at 0.105 M and (ii) set II, where the initial concentration of EtOH varied from 0.020 M to 0.6 M, and the initial BA concentration was fixed at 0.105 M. Along the reaction, samples of 500 L of organic medium were taken and assayed for substrates and product as previously described (cf. Section 3.2). Initial rates were calculated by linear regression on these data-points (time, ester concentration) and were expressed as mol of ethyl butyrate per minute and per enzyme activity unit (U). 3.4. Microenvironment substrate concentrations For each set of experiments (cf. Section 3.3), the respective microenvironmental substrate concentrations were estimated by using the first order or second order polynomial model equations previously established for both systems [31]. 3.5. Data analysis and fit of kinetic models The following kinetic models were tested: (i) Michäelis–Menten (Eq. (1)), (ii) substrate inhibition (Eq. (2)) and (iii) Ping-Pong Bi-Bi with alcohol inhibition mechanisms (Eq. (3)) [37–43]:
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Fig. 1. Time-course of the production of ethyl butyrate (triangles) by the esterification of ethanol (filled circles) with butyric acid (open circles), catalyzed by C. rugosa lipase immobilized in “FHP2002” foam (A) and “FHP5000” foam (B).
v= v= v=
vmax [S]
(1)
KM + [S]
vmax 1 + KEtOH /[EtOH] + [EtOH]/KI,EtOH
vmax [EtOH][BA] KBA [EtOH](1 + [EtOH]/KI,EtOH ) + KEtOH [BA] + [EtOH][BA]
(2)
(3)
These kinetic models were tested using (i) initial substrate concentrations in bulk media (cf. Section 3.3) and also (ii) the respective predicted microenvironmental substrate concentrations, after the partition equilibrium was attained, upon the addition of the immobilized biocatalyst to the organic medium (cf. Section 3.4). The fit of the models to experimental data was carried out using “Solver” add-in from Excel for Windows, version 8.0 SR2, by minimizing the residual sum-of-squares between the experimental data points and those estimated by the respective model and considering the following options: Newton method; 10,000 iterations, precision of 10−7 ; 2% of tolerance and 10−4 convergence. The kinetic constants were obtained by this non-linear regression analysis for the above-mentioned models. 4. Results and discussion 4.1. Time-course of esterification experiments The time-course of substrates consumption and product formation for the esterification of ethanol with butyric acid catalyzed by the C. rugosa lipase immobilized in “FHP2002” or “FHP5000” foams is shown in Fig. 1. In these experiments, where a low acid concentration (0.078 M) and an excess of ethanol (0.105 M) were used, the reaction equilibrium was attained in about 15 h and in less than 10 h, with a conversion into ester of 74.4% and 97.1%, respectively when the lipase was immobilized in “FHP2002” or
in “FHP5000” foams. Esterification rates of 62.7 × 10−6 mol/min U and 272.8 × 10−6 mol/min U were observed for experiments carried out with lipase immobilized in “FHP2002” or “FHP5000” foams, respectively. Along the first hour of reaction, initial bulk concentrations of ethanol (0.105 M) and butyric acid (0.078 M) decreased to about 0.04 M and 0.05 M, respectively when FHP 2002 and FHP 5000 foams were used as immobilization supports. This fast decrease in both the initial ethanol and acid concentrations is due to the partition of the substrates from the bulk organic media toward the microenvironment, leading to their accumulation in the vicinity of the lipase [30,31]. In addition, the better performance observed with “FHP5000” foam can be ascribed to its lower hydrophilicity, leading to lower and non-inhibitory concentrations of both substrates (butyric acid, BA, and ethanol, EtOH) in the microenvironment of enzyme. 4.2. Effect of substrate concentrations on esterification kinetics In a kinetic study, the presence of possible inhibition on the enzymatic activity, caused by the substrates or products involved in the reaction has to be investigated. The extent of inhibition depends on several factors, namely the type of enzyme, the immobilization matrix used, the reaction medium composition and the operating conditions. Fig. 2A shows the effect of the initial BA concentration in bulk organic medium, for an initial EtOH concentration of 0.105 M, on the initial esterification rate, catalyzed by both lipase preparations. The observed kinetics can be well described by the Michäelis–Menten model with no inhibition by the butyric acid. The effect of the initial ethanol concentration in bulk, at a fixed initial BA concentration of 0.105 M, on the esterification kinetics is presented in Fig. 2B. The increase in the initial ethanol concentration, up to 0.15 M, is accompanied by an increase in the esterification rate, followed by a smooth and a sharp decrease,
Fig. 2. Effect of initial bulk (A) butyric acid (at a fixed initial ethanol concentration of ethanol 0.105 M) and (B) ethanol (at a fixed initial butyric acid concentration of 0.105 M) concentrations, on the initial esterification rate, catalyzed by C. rugosa lipase immobilized in “FHP2002” (triangles) and “FHP5000” (circles) foams.
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Fig. 3. Effect of microenvironmental (A) butyric acid and (B) ethanol concentrations on the initial esterification rate, catalyzed by C. rugosa lipase immobilized in “FHP2002” (triangles) and “FHP5000” (circles) foams.
respectively when the lipase immobilized in “FHP2002” (triangles) or “FHP5000” foams (circles), was used. This indicates that ethanol exerted an inhibition at initial concentrations higher than 0.15 M. At 0.15 M EtOH and 0.105 M BA, corresponding to a molar ratio ethanol/butyric acid of 1.4, maximum esterification rates of 69.3 × 10−6 mol/min U and 444.8 × 10−6 mol/min U were observed when the lipase was immobilized in “FHP2002” or “FHP5000”, respectively. During lipase-catalyzed esterification, the first step consists of the preferential binding of the acid molecule to the enzyme [41]. The acyl transfer is affected by the concentration of free alcohol available. Maximum esterification rates were observed at a molar ratio ethanol/acid of 1.4; this is probably the situation where maximum acyl transfer occurs. At higher molar ratios, the large increase in alcohol concentration may promote the binding of alcohol molecules to the lipase, during the first reaction step, competing with the acid. As a result, a decrease in the amount of bound acid occurs. This situation will lead to a decrease in the reaction rates, since the reaction will be limited by the amount of acid in the vicinity of the enzyme. With C. rugosa lipase immobilized in “FHP5000” foams, the esterification rates were always higher than those obtained when the lipase in “FHP2002” foams was used (Figs. 1 and 2). This may be ascribed to the lower hydrophilicity of “FHP5000” [31], leading to lower and non-inhibitory concentrations of both substrates in the vicinity of the biocatalyst, as compared to the “FHP2002” case in media of similar initial composition. In fact, with initial BA and EtOH concentrations of 0.105 M and 0.15 M, which led to maximum esterification rates, the corresponding microenvironmental concentrations were: 0.358 M BA and 0.256 M EtOH, for the immobilized lipase in “FHP5000” foams, and 0.497 M BA and 0.426 M EtOH, when “FHP2002” lipase preparation was used. The loss of activity of the biocatalyst may be mainly due to (i) a dehydration effect of ethanol on protein molecules and/or to (ii) a modification of the protonation state by the acidic or basic species in the microenvironment [56]. However, in a previous study on the esterification of ethanol with butyric acid in n-hexane, catalyzed by the C. rugosa lipase immobilized in “FHP2002” polyurethane foams, both substrates presented an inhibitory effect on enzyme activity: (i) above 0.5 M for butyric acid, and (ii) above 0.3 M for ethanol, respectively when 0.3 M ethanol or 0.3 M butyric acid were used [6]. In this study, the variation range for the initial BA concentration (0.078–0.7 M) was similar to the range tested in the previous work, but the initial ethanol concentration was about three times lower. In fact, the inhibition of the biocatalyst depends on the concentration of inhibitory species in its vicinity, i.e. in its microenvironment. The composition of the microenvironment of the lipase in PU foams
is dictated by the initial concentration of both substrates in the organic medium and results from the partition effects between the bulk organic solution and the microenvironment [6,30,31]. Thus, the apparently opposite results are most probably explained by the composition of the reaction medium in the biocatalyst microenvironment. 4.3. Effect of microenvironmental substrate concentrations on esterification kinetics For each experiment, the concentrations of substrates in the microenvironment were estimated by previously established polynomial equations, from the knowledge of the initial bulk composition (prior to the addition of the biocatalyst) [31]. The concentrations of BA in the microenvironment were higher than those in the initial bulk medium, for all the experiments performed with the lipase in “FHP2002” foams and for the experiments with molar ratios ethanol/butyric acid above 0.26, when “FHP5000” lipase preparation was used (data not shown). For both immobilized preparations, the dependence of the esterification rate on the microenvironmental concentrations of substrates is presented in Fig. 3. In the system with the immobilized lipase in “FHP2002” foams, Michäelis–Menten kinetics is also observed when the initial BA concentrations were replaced by the corresponding concentration values estimated for the microenvironment. For this system, the esterification rate increased with BA microenvironmental concentration up to 0.851 M reaching a plateau thereafter (Fig. 3A). Also, a decrease in ethanol concentration in the microenvironment occurs as both the initial bulk BA and microenvironmental BA concentrations increase (data not shown). Concerning the system with the lipase in “FHP5000” foams, a completely different kinetic profile was observed when the microenvironmental BA concentrations were used instead of the initial values in bulk reaction media. For this biocatalyst, the increase in the initial BA concentration in the organic medium, from 0.078 M to 0.701 M, is accompanied by a slight decrease in the microenvironmental acid concentration from 0.358 M to 0.297 M, i.e. the BA concentration near the lipase remains approximately constant. Therefore, it seems that all these experiments were performed at a maximum BA microenvironmental concentration of about 0.3 M. The esterification rate reached a maximum value of 675.266 × 10−6 mol/min U, decreasing thereafter with the increase in ethanol concentration in the microenvironment (from 0.102 M to 0.426 M), conversely to what happens in the microenvironment of the lipase in “FHP2002” foams (data not shown). This situation may be explained by an inhibitory effect of ethanol on lipase activity.
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Table 1 Estimated kinetic parameters for esterification of ethanol with butyric acid in n-hexane, catalyzed by Candida rugosa lipase immobilized in “FHP2002” and “FHP5000” polyurethane foams, using different kinetic models fitted to experimental data of initial substrate concentrations in the bulk media or to microenvironment substrate concentrations data and the respective residual sum-of-squares between these experimental data points and those estimated by the models (S2 ). Parameter
Butyric acid Michäelis–Menten “FHP2002”
Initial bulk concentration
S2
vmax × 106 (mol/min U) KM (M) KEtOH (M) KI,EtOH (M) KBA (M) Microenvironmental concentration
S2
vmax × 106 (mol/min U) KM (M) KEtOH (M) KI,EtOH (M) KBA (M)
In the experiments where the initial bulk ethanol concentration varied from 0.020 M to 0.60 M, the corresponding EtOH concentrations in the microenvironment were always higher than those in the initial bulk medium either when the lipase was immobilized in “FHP2002” (up to 3.35 M) or in “FHP5000” foams (up to 1.39 M). This can be explained by the fact that ethanol is considerable more soluble in the aqueous phase near the enzyme than in the organic medium, leading to high concentrations in the microenvironment of the enzyme, particularly in the most hydrophilic foam used (“FHP2002”). In addition, the BA concentration in the microenvironment (i) also increased from 0.414 M to 1.755 M, for the systems with the lipase in “FHP2002” foams, while (ii) remained approximately constant (from 0.352 M to 0.379 M) for the system with the lipase in “FHP5000” foams. The esterification rate increased with the microenvironmental concentration of EtOH up to 0.426 M and 0.256 M, respectively when the lipase immobilized in “FHP2002” and “FHP5000” foams was used (Fig. 3B). This behaviour confirms the inhibitory effect of ethanol previously observed. 4.4. Fit of kinetic models The Michäelis–Menten model (two parameters), the substrateinhibition model (three parameters) and the Ping-Pong Bi-Bi with alcohol inhibition model (four parameters) were tested on the experimental kinetic data (i) using the initial bulk medium composition and also (ii) the predicted microenvironmental composition data, after partition equilibrium was attained. The estimated parameters and the mean sum of squares (the sum of the square residuals divided by the number of degrees of freedom) for Michäelis–Menten and substrate-inhibition models are shown in Table 1. Concerning the fit of Ping-Pong Bi-Bi with alcohol inhibition model, the negative values estimated for the kinetic parameters showed the lack of fit of this model (data not shown). A very good fit of the Michäelis–Menten model to the experimental data obtained with C. rugosa lipase immobilized in both polyurethane foams, is observed when the initial BA concentration in bulk medium, prior the addition of the biocatalyst, was used (Fig. 2A, Table 1). The estimated vmax for the systems with the lipase in “FHP5000” foams is almost four times higher than the value expected for the other counterpart. Also, the KM in the organic medium, for the lipase in “FHP2002” foams is about 1.4 times the value of KM for the lipase in “FHP5000” foams. Apparently, a higher affinity of the lipase for BA is expected when “FHP5000” foams are used as immobilization support.
1,094.37 196.31 0.129
Ethanol Substrate-inhibition “FHP5000” 17,658.51 774.28 0.092
“FHP2002”
“FHP5000”
256.48 6,672.33
12,883.52 1,104.01
8.80 0.003 4,079.78 221.02 0.50
78,851.83 209.15 −0.21
61.56 104.44 0.078 1.35
0.069 0.091 845.36 5,223.37 0.72 0.032
When the microenvironmental concentrations of BA were used, the kinetic behaviour can also be well described by the Michäelis–Menten model, for the lipase in “FHP2002” foams (Fig. 3A, Table 1). The estimated vmax is similar to the value predicted using the initial BA concentrations in the organic medium, but the KM in the microenvironment of the lipase (0.50 M) is 3.9 times the value predicted for initial bulk concentrations. This is expected due to the migration of butyric acid from the organic medium to the aqueous microenvironment of the lipase. However, for the system with the immobilized lipase in “FHP5000” foams, a lack of fit of the Michäelis–Menten model was found, since a negative value for KM in the microenvironment was estimated (Fig. 3A, Table 1). The effect of ethanol concentration on the esterification kinetics can be very well described by the substrate-inhibition model, both when initial bulk or microenvironmental ethanol concentrations were considered, whatever the biocatalyst used (Figs. 2B and 3B; Table 1). 5. Conclusions The analysis of the kinetic data showed that the esterification of ethanol with butyric acid catalyzed by C. rugosa, immobilized in “FHP2002” and “FHP5000” polyurethane foams, follows an ethanol–substrate-inhibition model for initial bulk concentrations over 0.15 M, corresponding to microenvironmental concentrations above 0.426 M and 0.256 M, respectively. Butyric acid did not cause any inhibition on both lipase preparations, in the range of concentrations (0.078–0.7 M) tested. The knowledge and understanding of esterification reaction kinetics is of great importance, not only to elucidate the reaction mechanism, but also for the design of bioreactors and industrial scale-up. References [1] M. Liaquat, R.K. Owusu, Synthesis of the low molecular weight flavour esters using plant seedling lipases in organic media, Food Chem. Toxicol. 65 (2000) 295–299. [2] D.W. Armstrong, H. Yamazaki, Natural flavours production: a biotechnological approach, Trends Biotechnol. 4 (1986) 264–268. [3] B. Gilles, H. Yamazaki, D.W. Armstrong, Production of flavour esters: immobilized lipase, Biotechnol. Lett. 9 (1987) 709–714. [4] G. Langrand, C. Triantaphylides, J. Baratti, Lipase catalyzed formation of flavour esters, Biotechnol. Lett. 10 (1988) 549–554. [5] P. Pires-Cabral, M.M.R. da Fonseca, S. Ferreira-Dias, Modelling the production of ethyl butyrate catalysed by Candida rugosa lipase immobilized in polyurethane foams, Biochem. Eng. J. 33 (2007) 148–158.
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