A new kinetic model proposed for enzymatic hydrolysis of lactose by a -galactosidase from Kluyveromyces fragilis

Enzyme and Microbial Technology 31 (2002) 300–309<br /> <br /> A new kinetic model proposed for enzymatic hydrolysis of lactose<br /> by a ␤-galactosidase from Kluyveromyces fragilis<br /> E. Jurado∗ , F. Camacho, G. Luzón, J.M. Vicaria<br /> Departmento Ingenier´ıa Qu´ımica, Facultad Ciencias, Universidad de Granada, Granada 18 071, Spain<br /> Received 3 January 2002; accepted 21 March 2002<br /> <br /> Abstract<br /> We study the enzymatic hydrolysis of lactose by a commercial enzyme from a selected strain of Kluyveromyces fragilis. The variables<br /> analyzed were: temperature (25–40 ◦ C), enzyme concentration (0.1–3.0 g l−1 ), lactose concentration (0.0278–0.208 M), and initial galactose<br /> concentration (0.0347 M). On the basis of the data analyzed, both published and in the present work, we propose a Michaelis–Menten<br /> kinetic model with inhibition by the product (galactose), which reveals that the substrate (lactose) and the product (galactose) present<br /> similar affinity for the active site of the enzyme.<br /> © 2002 Elsevier Science Inc. All rights reserved.<br /> Keywords: Lactose hydrolysis; Kluyveromyces fragilis; Kinetic model; ␤-Galactosidase<br /> <br /> 1. Introduction<br /> Enzymatic hydrolysis of lactose is one of the most important biotechnological processes in the food industry because<br /> of the potentially beneficial effects on the assimilation of<br /> foods containing lactose, as well as the possible technological and environmental advantages of industrial application,<br /> including:<br /> 1. Elimination of lactose intolerance (3–70% depending on<br /> the populational group [1]), encouraging the utilization<br /> of lactose as an energy source, as well as calcium and<br /> magnesium assimilation from milk.<br /> 2. Formation of galacto-oligosaccharides during lactose hydrolysis to favor the growth of intestinal bacterial microflora. The presence of these compounds is considered<br /> desirable in foods [2,3].<br /> 3. Improvement in the technological and sensorial characteristics of foods containing hydrolyzed lactose from<br /> milk or whey [4–7] such as: increased solubility (avoidance of lactose crystallization and the grainy aspect of<br /> ice creams and condensed or powdered products); greater<br /> sweetening power and thus lower caloric content of the<br /> products (glucose and galactose monosaccharides have<br /> greater sweetening power than does lactose); formation<br /> of monosaccharides, which are easier to ferment in cer∗<br /> <br /> Corresponding author.<br /> E-mail address: ejurado@ugr.es (E. Jurado).<br /> <br /> tain products such as yogurt [8]; lower freezing point of<br /> ice creams (increasing softness and creaminess); and reduction of the Maillard reaction.<br /> 4. Greater biodegradability of whey in which the lactose<br /> has been hydrolyzed [9].<br /> The commercial enzymes used for lactose hydrolysis are<br /> ␤-galactosidases of diverse origins [5,6,10]. Yeast and fungal enzymes have the greatest commercial interest. Many<br /> studies have been made with ␤-galactosidases obtained from<br /> Escherichia coli, although their use is not viable for products intended for human consumption [11–15].<br /> The optimal operating conditions are described in Table 1.<br /> Fungal enzymes are usually used to hydrolyze lactose from<br /> products with acidic pH values, such as whey. Yeast enzymes<br /> are habitually used for products with neutral pH values [16]<br /> such as milk and sweet whey.<br /> The mechanism of enzymatic hydrolysis of lactose by<br /> ␤-galactosidase applied to different substrates (lactose<br /> solutions, whey and skim-milk) under different experimental conditions has been studied by several authors.<br /> Table 2 presents the kinetic models proposed by different<br /> researchers, showing that most propose a Michaelis–Menten<br /> kinetic model, with competitive inhibition by galactose.<br /> However, there is great dispersion of the values of the<br /> kinetic constants proposed (see Table 3).<br /> The present work provides a survey of the models proposed by different authors, presents an experimental study of<br /> enzymatic hydrolysis in a stirred tank with ␤-galactosidase<br /> <br /> 0141-0229/02/$ – see front matter © 2002 Elsevier Science Inc. All rights reserved.<br /> PII: S 0 1 4 1 - 0 2 2 9 ( 0 2 ) 0 0 1 0 7 - 2<br /> <br /> E. Jurado et al. / Enzyme and Microbial Technology 31 (2002) 300–309<br /> <br /> Nomenclature<br /> E<br /> L<br /> Ga<br /> Gl<br /> EL<br /> EGa<br /> k<br /> KM<br /> KI<br /> r<br /> e<br /> x<br /> R<br /> Ea<br /> (−
Hf )a<br /> T<br /> <br /> concentration of free enzyme present in the<br /> reaction medium (g enzyme preparation l−1 )<br /> concentration of monohydrate lactose (M)<br /> concentration of galactose (M)<br /> concentration of glucose (M)<br /> concentration of the enzyme–lactose<br /> complex<br /> concentration of the enzyme–galactose<br /> complex<br /> rate constant of Eq. (2) (mol g−1 h−1 )<br /> Michaelis–Menten constant (M)<br /> equilibrium constant of Eq. (3) (M)<br /> reaction rate (mol g−1 h−1 )<br /> concentration of total active<br /> enzymatic complex (g l−1 )<br /> conversion (adimensional)<br /> constant of the ideal gases (cal K−1 mol−1 )<br /> activation energy (kcal mol−1 )<br /> enthalpy of formation (kcal mol−1 )<br /> temperature (K)<br /> <br /> Subscripts<br /> 0<br /> initial concentrations<br /> <br /> from Kluyveromyces fragilis, and proposes a simplified<br /> kinetic model for the action of the enzyme.<br /> <br /> 2. Materials and methods<br /> The chemical products used (PRS quality) are glucose,<br /> citric acid, K2 HPO4 , KCl, trichloroacetic acid (supplied<br /> <br /> 301<br /> <br /> by Panreac), MgCl2 ·6H2 O (Prolabo), monohydrate lactose<br /> (Scharlau), and galactose (Across).<br /> The enzyme used was a commercial ␤-galactosidase, lactozym 3000L HP-G [EC.3.2.1.23], which has a protein content of 35 g l−1 , supplied by Novo Nordisk, derived from a<br /> selected strain of the yeast K. fragilis, ρ = 1.2 g ml−1 , with a<br /> declared activity of 3000 LAU ml−1 (1 LAU = commercial<br /> enzyme which can obtain 1 ␮mol glucose min−1 in standard conditions: 4.7% lactose concentration, pH 6.5, 30 ◦ C,<br /> 30 min, standard milky buffer [4]). This enzyme satisfies the<br /> specifications recommended for food enzymes.<br /> The glucose was analyzed applying the GOD-Perid<br /> method proposed by Werner et al. [36] using a commercial reagent (Böehringer Mannheim Gmbh). The galactose<br /> and lactose present in the medium had no influence on the<br /> glucose determination.<br /> As the reaction medium, lactose solutions were prepared<br /> on a buffer of 0.01 M K2 HPO4 , 0.015 M KCl, and 0.012 M<br /> MgCl2 ·6H2 O at pH 6.75 adjusted with citric acid.<br /> The enzymatic activity was measured in test tubes at 30 ◦ C<br /> in the following way: 1 ml of 50 g l−1 monohydrate lactose<br /> solution prepared on the buffer indicated was added to 1 ml<br /> of 10 g l−1 enzyme solution prepared on the same buffer.<br /> The test tube was incubated at 30 ◦ C for 10 min, after which<br /> 1 ml was extracted. The reaction was stopped by mixing with<br /> 1 ml of 0.1N trichloroacetic acid. Afterwards, the glucose<br /> concentration was measured by the GOD-Perid method. The<br /> enzymatic activity remained constant for the entire period<br /> of use.<br /> The enzymatic reaction took place in a 200 ml stirred<br /> tank reactor with pH and temperature controls. For a maximum period of 2 h, samples were extracted from the reactor. The enzyme was denatured with 0.1N trichloroacetic<br /> acid and the glucose concentration was measured by the<br /> GOD-Perid method. The variables tested are shown in<br /> Table 4.<br /> <br /> Table 1<br /> Experimental conditions of the most used enzymes<br /> Enzyme source<br /> <br /> pH (optimal)<br /> <br /> T (◦ C) (optimal)<br /> <br /> Cofactors<br /> <br /> Fungal (Aspergillus niger)<br /> Fungal (A. oryzae)<br /> Yeast (K. fragilis)<br /> Yeast (K. lactis)<br /> <br /> 3.0–4.0<br /> 5.0<br /> 6.6<br /> 6.9–7.3<br /> <br /> 55–60<br /> 50–55<br /> 37<br /> 35<br /> <br /> Mn2+ , Mg2+ , K+<br /> Mn2+ , Na+<br /> <br /> Table 2<br /> Kinetic models proposed by different authors for enzymatic hydrolysis of lactose<br /> Kinetic model proposed<br /> <br /> References<br /> <br /> Michaelis–Menten first order<br /> Michaelis–Menten without inhibition by product (galactose) (with enzyme–lactose complex formation)<br /> Michaelis–Menten with competitive inhibition by product (total galactose)<br /> Michaelis–Menten with competitive inhibition by product (␣- and ␤- galactose)<br /> Michaelis–Menten with competitive inhibition by product (glucose)<br /> Di-, tri- and tetra-saccharides formation<br /> <br /> [17]<br /> [18]<br /> [9,11,12,18–31]<br /> [32,33]<br /> [24]<br /> [34]<br /> <br /> 302<br /> <br /> E. Jurado et al. / Enzyme and Microbial Technology 31 (2002) 300–309<br /> <br /> Table 3<br /> Kinetic constants proposed by different authors for the enzymatic hydrolysis of lactose<br /> References<br /> <br /> Enzyme source<br /> <br /> pH<br /> <br /> T ( ◦ C)<br /> <br /> KM (M)<br /> <br /> KI (M)<br /> <br /> [19]<br /> <br /> A.<br /> A.<br /> A.<br /> A.<br /> <br /> 4.5<br /> 4.5<br /> 6.5<br /> 6.5<br /> <br /> 50<br /> 50<br /> 50<br /> 50<br /> <br /> 0.112<br /> 0.122<br /> 0.178<br /> 0.160<br /> <br /> 0.0095<br /> 0.0105<br /> 0.0025<br /> 0.0045<br /> <br /> oryzae<br /> oryzae<br /> oryzae<br /> oryzae<br /> <br /> (sol.)<br /> (imm.)<br /> (sol.)<br /> (imm.)<br /> <br /> [35]<br /> <br /> A. oryzae (sol.)<br /> <br /> [32]<br /> <br /> A. niger (sol.)<br /> <br /> [11]<br /> <br /> E.<br /> E.<br /> E.<br /> E.<br /> E.<br /> <br /> coli1 (imm.)<br /> coli2 (imm.)<br /> coli3 (imm.)<br /> coli4 (imm.)<br /> coli5 (imm.)<br /> <br /> [20]<br /> <br /> 50<br /> <br /> 0.0357<br /> <br /> 0.0201<br /> <br /> 50<br /> <br /> 0.0539<br /> <br /> 0.00092 (␣), 0.0118 (␤),<br /> 0.0109 (complex)<br /> <br /> 7.0<br /> <br /> 21<br /> <br /> 0.00298<br /> 0.00346<br /> 0.00434<br /> 0.00332<br /> 0.00373<br /> <br /> 0.035<br /> 0.034<br /> 0.082<br /> 0.039<br /> 0.034<br /> <br /> A. oryzae (sol.)<br /> A. oryzae (imm.)<br /> <br /> 4.5<br /> <br /> 50<br /> 50<br /> <br /> 0.0469<br /> 0.0490<br /> <br /> 0.0200<br /> 0.0200<br /> <br /> [21]<br /> <br /> A. niger (imm.)<br /> <br /> 4.5<br /> <br /> 30<br /> 40<br /> 50<br /> <br /> 0.0536<br /> 0.0519<br /> 0.0533<br /> <br /> 0.0321<br /> 0.0055<br /> 0.0946<br /> <br /> [22]<br /> <br /> K. fragilis (sol.)<br /> K. fragilis (imm.)<br /> <br /> 6.9<br /> <br /> 43<br /> <br /> 0.0436<br /> 0.1370<br /> <br /> 0.0519<br /> 0.2340<br /> <br /> [23]<br /> <br /> A. niger (imm.)<br /> <br /> 4.0<br /> <br /> 25<br /> 30<br /> 35<br /> 40<br /> 45<br /> 50<br /> 55<br /> 60<br /> <br /> 0.0797<br /> 0.0764<br /> 0.0733<br /> 0.0705<br /> 0.0679<br /> 0.0656<br /> 0.0635<br /> 0.0615<br /> <br /> 0.0000613<br /> 0.0000620<br /> 0.0000627<br /> 0.0000633<br /> 0.0000640<br /> 0.0000646<br /> 0.0000652<br /> 0.0000658<br /> <br /> [26]<br /> <br /> K. fragilis (imm.)<br /> A. niger (imm.)<br /> <br /> 5.2<br /> <br /> 23<br /> 37<br /> <br /> 0.006<br /> 0.0286<br /> <br /> 0.012<br /> 0.0024<br /> <br /> [33]<br /> <br /> A. oryzae (imm.)<br /> <br /> 4.5<br /> <br /> 30<br /> <br /> 0.052<br /> <br /> 0.00022 (␣), 0.042(␤)<br /> <br /> [27]<br /> <br /> A. niger (sol.) (Model 1)<br /> <br /> 4.0<br /> <br /> 8<br /> 30<br /> 40<br /> 45<br /> 50<br /> 55<br /> 60<br /> <br /> 0.0833<br /> 0.0809<br /> 0.0799<br /> 0.0795<br /> 0.079<br /> 0.0786<br /> 0.0782<br /> <br /> 0.000472<br /> 0.000528<br /> 0.000553<br /> 0.000565<br /> 0.000578<br /> 0.00059<br /> 0.000601<br /> <br /> A. niger (sol.) (Model 2)<br /> <br /> 4.0<br /> <br /> 8<br /> 30<br /> 40<br /> 45<br /> 50<br /> 55<br /> 60<br /> <br /> 0.1019<br /> 0.0995<br /> 0.0986<br /> 0.0982<br /> 0.0977<br /> 0.0973<br /> 0.0969<br /> <br /> 0.000527<br /> 0.000584<br /> 0.000609<br /> 0.000622<br /> 0.000634<br /> 0.000646<br /> 0.000658<br /> <br /> K. marxianus (sol.)<br /> <br /> 6.6<br /> <br /> K. marxianus (imm.)<br /> <br /> 6.6<br /> <br /> 28<br /> 35<br /> 28<br /> 35<br /> <br /> 0.021<br /> 0.0278<br /> 0.0544<br /> 0.0365<br /> <br /> 0.0292<br /> 0.0316<br /> 0.0869<br /> 0.0114<br /> <br /> K. fragilis (sol.)<br /> <br /> 6.5–7.2<br /> <br /> 5<br /> 25<br /> 40<br /> <br /> 0.0004<br /> 0.0046<br /> 0.023<br /> <br /> 0.00041<br /> 0.0036<br /> 0.0153<br /> <br /> [28]<br /> <br /> [9]<br /> <br /> 4.5<br /> <br /> E. Jurado et al. / Enzyme and Microbial Technology 31 (2002) 300–309<br /> <br /> 303<br /> <br /> Table 3 (Continued )<br /> References<br /> <br /> Enzyme source<br /> <br /> pH<br /> <br /> T ( ◦ C)<br /> <br /> KM (M)<br /> <br /> KI (M)<br /> <br /> [30]<br /> <br /> K. marxianus (imm.)<br /> <br /> 6.6<br /> <br /> 10<br /> 15<br /> 20<br /> 22.5<br /> 25<br /> 27.5<br /> 30<br /> 32.5<br /> 35<br /> 37.5<br /> <br /> 0.0154<br /> 0.0183<br /> 0.0219<br /> 0.0239<br /> 0.0248<br /> 0.0275<br /> 0.0317<br /> 0.0330<br /> 0.0379<br /> 0.0383<br /> <br /> 0.0247<br /> 0.0370<br /> 0.0561<br /> 0.0695<br /> 0.0801<br /> 0.0969<br /> 0.1097<br /> 0.1351<br /> 0.1620<br /> 0.2008<br /> <br /> The variation in the glucose concentration over time can<br /> be defined as:<br /> <br /> Table 4<br /> Variables tested in the hydrolysis experiments performed<br /> T (◦ C)<br /> <br /> L0 (×102 M)<br /> <br /> Ga0 (×102 M)<br /> <br /> e0 (g l−1 )<br /> <br /> 25<br /> <br /> 2.78<br /> 6.94<br /> 13.9<br /> 20.8<br /> <br /> 0<br /> 0<br /> 0<br /> 0<br /> <br /> 0.5<br /> 0.1, 0.5, 1.0, 3.0<br /> 0.1, 0.5, 1.0, 3.0<br /> 0.5<br /> <br /> 2.78<br /> 3.47<br /> 6.94<br /> 13.9<br /> 20.8<br /> <br /> 0<br /> 3.47<br /> 0<br /> 0<br /> 0<br /> <br /> 0.1,<br /> 0.5<br /> 0.1,<br /> 0.1,<br /> 0.1,<br /> <br /> 2.78<br /> 6.94<br /> 13.9<br /> 20.8<br /> <br /> 0<br /> 0<br /> 0<br /> 0<br /> <br /> 0.5<br /> 0.1, 0.5, 1.0, 3.0<br /> 0.1, 0.5, 1.0, 3.0<br /> 3.0<br /> <br /> 30<br /> <br /> 40<br /> <br /> 0.5, 1.0<br /> 0.5, 1.0<br /> 0.5, 1.0<br /> 0.5, 1.0<br /> <br /> L0<br /> <br /> (k/KM )Le<br /> dx<br /> =<br /> dt<br /> 1 + (L/KM ) + (Ga/KI )<br /> kL0 (1 − x)e<br /> =<br /> KM + L0 (1 − x) + (KM /KI )(Ga0 + L0 x)<br /> <br /> Separating variables and integrating, we would arrive at<br /> an expression of the following type:<br />
<br /> <br />
<br /> <br /> S0<br /> KM<br /> KM 1 +<br /> [−ln(1 − x)] + 1 −<br /> L0 x<br /> KI<br /> KI<br />  t<br /> = k e dt<br /> (8)<br /> 0<br /> <br /> where:<br /> S0 = L0 + Ga0<br /> <br /> 3. Results and discussion<br /> 3.1. Kinetic model of enzymatic hydrolysis with<br /> competitive inhibition of galactose<br /> The widely accepted kinetic model to explain enzymatic<br /> lactose hydrolysis is competitive inhibition by the product<br /> (galactose):<br /> E + L ↔ EL<br /> k<br /> <br /> EL→EGa + Gl<br /> KI<br /> <br /> EGa↔E + Ga<br /> <br /> (1)<br /> (2)<br /> (3)<br /> <br /> The lactose, galactose, and glucose concentrations were<br /> defined as a function of the conversion:<br /> L = L0 (1 − x)<br /> <br /> (4)<br /> <br /> Ga = Ga0 + L0 x<br /> <br /> (5)<br /> <br /> Gl = Gl0 + L0 x<br /> <br /> (6)<br /> <br /> considering the concentrations of the enzymatic complexes<br /> EL and EGa to be negligible.<br /> <br /> (7)<br /> <br /> (9)<br /> <br /> In the case that the enzymatic deactivation does not occur<br /> in the hydrolysis process, the active enzyme concentration<br /> would remain constant throughout the experimental period,<br /> giving e = e0 , and thus:<br />
<br /> <br />
<br /> <br /> S0<br /> KM<br /> KM 1 +<br /> [−ln(1 − x)] + 1 −<br /> L0 x = ke0 t<br /> KI<br /> KI<br /> (10)<br /> an expression that enables the fit of the experimental data<br /> by a linear regression according to:<br /> <br />
<br /> e0 t<br /> KM<br /> S0 [−ln(1 − x)]<br /> (1 − (KM /KI ))<br /> =<br /> 1+<br /> + L0<br /> x<br /> k<br /> KI<br /> x<br /> k<br /> [−ln(1 − x)]<br /> =A<br /> +B<br /> (11)<br /> x<br /> an expression previously proposed by several authors [27].<br /> As an example, Fig. 1 shows the linearization of the<br /> experimental results at 30 ◦ C, applying Eq. (11). All the experiments performed at the same substrate concentration and<br /> different enzyme concentrations were aligned, indicating<br /> that, during the reaction period and under the experimental<br /> conditions, no enzymatic denaturing occurred (Fig. 1). Similarly, in the experiments in which the sum of the initial molar concentrations of galactose and lactose were the same,<br /> <br /> 304<br /> <br /> E. Jurado et al. / Enzyme and Microbial Technology 31 (2002) 300–309<br /> <br /> Fig. 1. Experiments of lactose hydrolysis at T = 30 ◦ C; e0 t/x vs. [−ln(1 − x)]/x.<br /> <br /> the data were fitted to the same line (experiment made with<br /> 0.0347 M initial galactose concentration). Nevertheless, the<br /> kinetic constants resulting from the application of Eq. (11)<br /> did not lead to completely satisfactory results, prompting us<br /> to reconsider the kinetic model proposed. The result is due<br /> to the fact that the fitting used, Eq. (11), is not appropriate to<br /> <br /> calculate the KM /KI relationship, because it implies extrapolation distant from the experimental interval, and an experimental deviation can heavily influence the KM /KI value<br /> (for conversions ranging between 0 and 0.95 the value of<br /> [−ln(1−x)]/x fluctuates between 1 and 3, far from the origin<br /> axis).<br /> <br /> Fig. 2. Representation of the kinetic constants KM and KI proposed by different authors.<br /> <br />