hydrolysis of lactose by free and immobilized ?-galactosidase from thermus sp. strain t2

Hydrolysis of Lactose by Free andImmobilized �-Galactosidase fromThermus sp. Strain T2

M. Ladero, M.T. Perez, A. Santos, F. Garcia-Ochoa

Departamento Ingenieria Quımica, Facultad CC. Quımicas, UniversidadComplutense, 28040 Madrid, Spain; telephone: +34-91-3944176; fax:+34-91-3944171; e-mail: [email protected]

Received 5 September 2001; accepted 19 June 2002

DOI: 10.1002/bit.10466

Abstract: The hydrolysis of lactose by a �-galactosidasefrom the thermophilic microorganism Thermus sp. strainT2, both in solution and immobilized on a commercialsilica-alumina, has been studied. The enzyme has beenpreviously produced by Escherichia coli JM101 harbor-ing the plasmid pBGT1, which contains the codifyinggene under the promoters lppP and lacPQ. The enzymewas immobilized on the support activated with tris-hydroxymethylphosphine (THP). Activity and stability ofthe free and the immobilized enzyme towards pH andtemperature were tested. To study the activity at differ-ent pH and temperature values, lactose was used as sub-strate. To check the stability, the enzyme was incubatedeither in buffer BP or in a solution of lactose in buffer BMat different pH and temperatures, being the remainingactivity tested by withdrawing samples and determiningtheir activity toward ONPG at 70°C in buffer BP. After-ward, runs were performed to obtain kinetic models ad-equate for the description of the hydrolysis of lactose bythe free and the immobilized enzyme. These data werefitted to the kinetic models proposed (all based on theMichaelis–Menten mechanism) by non-linear regression,being the models and their parameters compared to de-termine the effect of the immobilization on the kineticbehavior of the enzyme. Both the free and the immobi-lized enzyme are competitively inhibited by galactose,while glucose inhibited only the action of the free en-zyme, in an uncompetitive way. The immobilization stepseems to eliminate the inhibition by glucose. Moreover,the immobilization reduced to a half the inhibitory actionof galactose. In general, the immobilization reduced theactivity of the enzyme, but increased its thermal stability.Finally, a comparison between the kinetic behavior ofthis thermophilic enzyme and enzymes of mesophile mi-croorganisms previously studied by us (E. coli and K.fragilis) and by other authors (Aspergillus niger) is per-formed. © 2002 Wiley Periodicals, Inc. Biotechnol Bioeng81:241–252, 2003.Keywords: Keywords: lactose; hydrolysis; activity; im-mobilization; �-galactosidase; Thermus; kinetic model

INTRODUCTION

Lactose is the main carbohydrate contained in milk andwhey (at a concentration between 50 and 100 g L−1, de-

pending on the source of milk) (Ordonez et al., 1998). Theconsumption of foods with a high content of lactose is prob-lematic for almost a 70% of the world population, as theenzyme naturally present in the human intestine loses itsactivity during lifetime (Richmond et al., 1981). This fact,together with the relatively low solubility and sweetness oflactose, has lead to an increasing interest in the developmentof industrial processes to hydrolyze the lactose contained indairy products. Moreover, lactose has a high BOD, andalmost half of the quantity mobilized each year in industrialprocesses in dairy factories is not reutilized in either thefood or the pharmaceutical industries. Its disposal means thepollution of aquatic environments and the hydrolysis of thislactose is a way to recycle the whey, using it as a source toobtain additives for human or cattle feeding (Gekas andLopez-Leiva, 1985).

The hydrolysis of lactose can be performed by acids oracid resins or by enzymatic treatment. The use of acids isnot adequate to hydrolyze lactose in milk and whey due tothe generation of nasty flavors, odors, and colors during theprocess and the reduction in alimentary properties of milk.When the enzymatic treatment is performed with �-galac-tosidases as catalyst, the taste of milk is only changed to asweeter one (glucose and galactose are four times sweeterthan the lactose from which they come) and the develop-ment of lactose crystals in refrigerated products is avoided.A second advantage is the occurrence of a side reaction: thesynthesis of galacto-oligosaccharides, which are carbohy-drates able to promote the growth of beneficial bacteria inthe intestine (Mahoney, 1998). However, there are somedrawbacks such as the slower hydrolysis of the lactose andthe higher cost of the enzyme (Mooser, 1992).

Industrial enzymes are produced by microbial sources,although �-galactosidases are present in microorganismsand animal tissues. Usually, mesophilic sources are em-ployed: yeasts for the production of neutral enzymes andfungus for the production of enzymes active in a slightlyacid environment (more adequate for acid whey) (Sellekand Chaudhuri, 1999). The low stability of these enzymes isa technical problem that is usually overcome by injecting anCorrespondence to: F. Garcıa-Ochoa

© 2002 Wiley Periodicals, Inc.

enzyme dose in each brick containing milk and letting thehydrolysis proceed between the packing and the consump-tion of the milk. Continuous processes are still being studiedand developed (Gekas and Lopez-Leiva, 1985). To obtainhigher stabilities several approaches can be considered: theuse of enzymes produced by thermophilic microorganisms,the immobilization of the enzyme by a covalent method ableto stabilize the overall structure of the protein, and the ad-dition of salts of organic compounds with a stabilizing ef-fect on the enzyme (Coolbear et al., 1992; Guisan et al.,1997; Hernaiz et al., 1999). These procedures can be em-ployed together for the production of heterogeneous enzy-matic catalysts highly stable (Oswald et al., 1998). The useof thermophilic enzymes allows for higher operational tem-peratures, so the process of the hydrolysis can be performedin aseptic conditions and no microbial deactivation of thecatalyst should be expected (Coolbear et al., 1992). Theimmobilization of these enzymes and their application incontinuous processes can be carried out even during pas-teurization of milk, thus letting two operations to proceed atthe same time.

There is a considerable work on mesophilic �-galactosi-dases, especially on the product of the lac-Z operon of Esch-erichia coli, including both the structure and the function ofthe enzymes (Wallenfelds and Weil, 1972; Gekas andLopez-Leiva, 1985; Mooser, 1992; Mahoney, 1998). Thereis a huge amount of kinetic studies over the activity ofmesophilic enzymes on lactose, mainly regarding the pro-teins produced by fungus (Wadiak and Carbonell, 1975;Chen et al., 1985; Yang and Okos, 1989; Bakken et al.,1991; Papayannakos et al., 1993; Carrara and Rubiolo,1996; Portaccio et al., 1998). However, few studies givekinetic information on the hydrolysis of lactose by thermo-philic �-galactosidases and data is usually obtained at agiven temperature (Pisani et al., 1990; Berger et al., 1997;Petzelbauer et al., 1999). Berger et al. (1997) isolated anenzyme from Thermus aquaticus YT-1, purifying it to ho-mogeneity, and studied some properties of the enzyme, in-cluding a kinetic study of the enzyme using lactose as sub-strate between 1 and 540 mM at 70°C and performing thekinetic runs in sodium phosphate 50 mM, pH 7. The reac-tion was well described in the conditions studied by a ki-netic model including competitive inhibition by galactose,although glucose proved to be a competitive inhibitor in thehydrolysis of ONPG, also studied by these authors. Theenzyme from S. solfataricus was isolated by Pisani et al.(1990), and a certain characterization was undertaken. Thekinetics of the hydrolysis of lactose were studied on sodiumphosphate 50 mM, pH 6.5 at 30°C, and a Michaelis–Mentenmodel without inhibition was selected. Petzelbauer et al.(1999) reported the possible application of the thermophilic�-galactosidases from S. solfataricus and P. furiosus for thehydrolysis of lactose at high temperature. In this case, themedium selected to carry out the reactions was a sodiumcitrate 20 mM, pH 5.5, and runs were made at 80°C, beingthe concentration of lactose selected between 16 and 680mM. The kinetic model proposed in both cases was a Mi-

chaelis–Menten model with competitive inhibition by ga-lactose.

In this work, the kinetics of the hydrolysis of lactosecatalyzed by a �-galactosidase from Thermus sp. strain T2over-expressed in E. coli is studied in depth, both with theenzyme in solution and covalently immobilized into a silica-alumina. Firstly, some preliminary research was carried outto determine the pH and temperature ranges in which thefree and immobilized enzyme forms are stable and the con-ditions where the chemical reaction was the controlling stepof the hydrolytic process. Secondly, kinetic studies havebeen performed in a wide range of temperatures (from me-sophilic to thermophilic conditions) and concentrations ofsubstrates and products. With the kinetic data obtained, thediscrimination of an adequate kinetic model was performedamong a considerable number of kinetic models, proposedby taking into account the overall effects of the operationalvariables on the initial reaction rates. Finally, the selectedkinetic models for each form of the enzyme are compared todetermine the effect of immobilization on the activity of theenzyme and an overall comparison with models describingthe kinetics of the hydrolysis of lactose with some meso-philic enzymes is performed.

EXPERIMENTAL PROCEDURES

Materials

The enzyme is produced by E. coli JM109 harboring plas-mid pBGT1, which contains the bgaA gene and the promot-ers lppP and lacPO (Vian et al., 1998). The enzyme is par-tially purified by heating at 70°C during 30 min, followedby a centrifugation step. By this procedure, a huge quantityof proteins from the mesophilic host is removed. The pro-tein thus obtained is conserved in a neutral sodium phos-phate buffer enriched with magnesium ion and mercapto-ethanol. The enzyme concentration is 0.8–2 g L−1, while thetotal protein concentration fluctuates between 6 and 8 g L−1.

The support is a commercial silica-alumina from Sudche-mie (KA-3). Its characteristics are shown elsewhere (Laderoet al., 2000). Silanization of the support was performed with�-aminopropyltriethoxysilane (�-APTES) of analyticalgrade. Lactose, galactose, and glucose, of reagent grade,were supplied from Riedel-deHaen. o-Nitrophenyl-�-D-galactoside (ONPG) was supplied by Sigma (St. Louis,MO). All other reactives used in the immobilization of theenzyme or in the preparation of buffers were analyticalgrade and supplied by Sigma.

Two different buffers have been employed. The buffercalled BP is a 50 mM phosphate buffer, pH 7.2 (K2HPO4

11.4 g L−1, KH2PO4 5.7 g L−1, 1 mM MgCl2 � 6H2O, 5 mMmercaptoethanol), being the medium selected for hydrolysisruns of ONPG (Santos et al., 1998; Ladero et al., 2001,2000). The buffer called BM is a citrate–phosphate pH 6.5buffer with added calcium, magnesium, potassium, and so-dium ions; it has a salt composition similar to that of milk,

242 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 81, NO. 2, JANUARY 20, 2003

and its detailed composition is shown elsewhere (Ladero etal., 2000). This buffer was used to study the hydrolysis oflactose. In the experiments performed to determine the sta-bility of the enzyme towards pH, a citrate–phosphate–carbonate buffer was employed (50 mM in each pair ofbuffer components and supplemented with magnesiumchloride and mercaptoethanol, as the BP buffer).

Experimental Procedure

Immobilization of the Enzyme

The enzyme was immobilized according to the method de-scribed by Oswald et al. (1998). The support was acid-cleaned before treating it with a 10% �-aminopropyltrieth-oxysilane (�-APTES) solution in water at pH 3.5 for 3 h, asdescribed elsewhere (Ladero et al., 2000, 2001). The acti-vating reagent, THP (trihydroxyphosphine), was producedby mixing equimolar quantities of THPC (trihydroxyphos-phine chloride) and KOH and diluting it with distilled waterto a final concentration of 24 g L−1. Each gram of thesilanized support was treated with 15 mL of this solution for20 min at 25°C and rinsed with distilled water and BPbuffer. The activated support was mixed with a solution ofenzyme in buffer BP at a ratio of 1 g of support per 10 mLof solution (the concentration of enzyme in the solution was6 mg enzyme L−1). Protein and activity in the supernatantliquid were measured by the method of Bradford (1976) andusing ONPG as substrate, respectively, changing only thetemperature of the activity test with ONPG from 25 to 70°C(Lartillot, 1993; Santos et al., 1998). The activity of theimmobilized enzyme was also tested with ONPG dissolvedin buffer BP at 70°C (Ladero et al., 2001, 2000). In theseveral immobilization runs performed to obtain the bio-catalyst for the kinetic studies, all enzyme and protein wasimmobilized after the first 30 min of reaction and no proteinleakage was observed after continuous rinsing with a phos-phate buffer, pH 7.0, 50 mM with 3 M NaCl.

Kinetic Runs

The runs were carried out in a wide experimental range oftemperature and substrate, product, and enzyme concentra-tions. The experimental conditions for the runs both with thefree and the immobilized enzyme are detailed in Table I. Ascan be seen, a classical experimental design was performed;for instance, with the free enzyme, runs were performed atseven temperatures. At each temperature, runs were carriedout at five initial concentrations of lactose in the absence ofmonosaccharides at zero time. At initial concentrations oflactose of 50 and 100 g L−1, runs with 15 and 50 g L−1 asconcentrations at zero time of galactose and glucose werealso performed. So, at each temperature, seven runs weredone. All runs were carried out at a enzyme concentration of14 mg L−1. All in all, for the free enzyme, as many as 49runs were performed.

The hydrolysis runs were performed in closed vials, usedas batch reactors. When the enzyme was in solution, theruns were carried out in a thermostatic bath with a side-to-side agitation platform at 100 rpm. If the enzyme was im-mobilized, the agitation of the reacting media was providedby the same side-to-side agitation platform set at a speed of200 rpm. The reactors containing the carbohydrate solutionswere thermo stated in a bath coupled to a refrigeration unitat the reaction temperature. Afterward, enzyme was addedas a solution or as a wet solid (when immobilized) at zerotime. Then, samples were withdrawn at several reactiontimes and prepared for analysis as described in previouspapers (Santos et al., 1998; Ladero et al., 2001, 2000).

The agitation speed was chosen by performing a set ofruns where lactose was hydrolyzed by the immobilized en-zyme at 90°C changing this variable. In a similar way,another set of runs with support particles activated with avariable concentration of enzyme and a constant size of100–200 �m was performed to select the adequate enzymeconcentration in the solid to avoid diffusional hindrances.

Analytical Methods

The analysis of the carbohydrates (lactose, glucose, andgalactose) were carried out by HPLC with a silica-NH2

column as stationary phase, the eluent was a mixture ofacetonitrile and water in proportion 75:25 flowing at 1 mLmin−1, and a light-scattering detector was employed. For themeasuring of activity with ONPG as substrate the concen-tration of the product of the ONPG hydrolysis, o-nitrophenol, was determined by spectrophotometry at awavelength of 420 nm (Santos et al., 1998).

EXPERIMENTAL RESULTS

Preliminary Runs

The influence of temperature and pH over the stability andactivity of both the free and the immobilized enzyme wasstudied, allowing for the selection of the optimal pH andmaximum temperature to ensure the absence of any deac-

Table I. Experimental runs performed for the studies of the hydrolysis oflactose with free and immobilized �-galactosidase from Thermus sp.strain T2.

Enzyme Free Immobilized

T (°C) 30, 40, 50, 60, 70, 80,and 90

30, 40, 50, 60, 70,and 80

Clac 0 (g L−1) 25, 50*, 100*, 200, and 300 25, 50*, 100*, and 300Cgal 0 (g L−1) 0 and 15 0 and 15Cglu 0 (g L−1) 0 and 50 0 and 50CE (mg L−) 14 6 or 6.5Runs 49 36Data (Xlac vs. t) 309 297

*Runs with initial monosaccharides other than zero concentrations wereperformed only at these initial lactose concentrations.

LADERO ET AL.: HYDROLYSIS OF LACTOSE BY A �-GALACTOSIDASE FROM THERMUS SP. STRAIN T2 243

tivation phenomena that could be coupled to the hydrolysisreaction.

To know what effect on the kinetic efficiency of theenzyme has the immobilization process at several values ofthe pH, the activity of both forms of the enzyme was testedin a solution of lactose in buffer BM at a concentrationcommon in cow’s milk (Clac � 50 g L−1; T � 70°C),employing pH values between 4 and 9.5. To obtain the pHselected in each run, H2SO4 or NaOH was added to thebuffered solutions. Reaction rates were calculated by nu-merical differentiation of the concentration of products ver-sus time of reaction; values of reaction rates at zero timeversus pH are shown in Fig. 1. The optimum pH value forthe hydrolysis of lactose is around 6.5 for the free andimmobilized enzyme, so both enzymes are most active atthe pH usually found in milk.

To determine the effect of pH on the stability of theenzyme, both free and immobilized, the enzyme was incu-bated in buffer BP for 3 h at different pH values between 3and 13. Samples of the enzyme were withdrawn at severaltimes, and their activity was tested with ONPG dissolved inbuffer BP (CONPG � 0.5 g L−1; T � 70°C); and the re-maining activity was calculated as:

aR =r0�tinc = t�

r0�tinc = 0�. (1)

The stability of both forms of enzyme is compared in Fig. 2.As can be seen, immobilization increases the stability of theenzyme in acid and basic media, while the behavior of theenzyme remains the same at neutral pH. This stabilizationcan be of interest taking into account that basic compoundssuch as amines and hydroxide solutions are employed assanitizers in industrial reactors where enzymes are used ascatalysts. It seems that immobilization hinders the interac-

tion of protonated species of water with the active center,avoiding to a certain extent the denaturation of the enzyme.

The stability of the immobilized enzyme toward tempera-ture was checked by incubating the enzyme in a 50 g L−1

solution of lactose in buffer BM at relatively high tempera-tures (60–90°C). The remaining activity is also given by Eq.(1) and results are shown in Fig. 3. Deactivation of theenzyme is not observed at temperatures of 90°C during, atleast, 2 h and for 6 h at 80°C, so kinetic runs were per-formed at temperatures equal or lower than 90°C consider-ing the above limits for reaction time. As can be seen in Fig.3, immobilization seems to improve considerably the sta-bility of the enzyme at all the temperatures tested (by afactor of 2.5 at 90°C or by a factor of 3 at 60°C). Taking intoaccount the multimeric nature of the enzyme and the highactivation of the surface of the support by THP, multiplebonds between the enzymatic conglomerate and the supportcould be established and a certain increase in the rigidity ofthe overall structure of the enzyme could issue by immobi-lization. Moreover, cross-linking between subunits isknown to have an important effect of stabilization on theoverall structure. Natural cross-linking leads, in thermo-philic enzymes, to active aggregates of an especially highstability (Sellek and Chaudhuri, 1999). Multimeric immo-bilization of these enzymes can only add to this stability. Inconclusion, considering the overall tendencies of deactiva-tion data at all the temperatures tested, although a singlefirst-order deactivation reaction could account for the re-sults obtained at 60°C, grace period behavior is observed at70°C and an initial activating reaction previous to the de-

Figure 1. Influence of pH on the activity of free and immobilized �-ga-lactosidase from Thermus sp. strain T2. Operational conditions: T � 70°C,CE � 6 mg L−1, Clac � 50 g L−1.

Figure 2. Effect of pH on the stability of free and immobilized �-galac-tosidase from Thermus sp. strain T2. Activity test carried out in buffer BPunder the following conditions: CONPG 0 � 0.5 g L−1; T � 70°C.


activation itself can cope with deactivation data at 80 and90°C. Further studies on the stability of the enzyme towarda variety of deactivation agents is currently under course.

In addition to the pH and temperature conditions wherethe enzyme kinetics should be tested, selected with the pre-viously mentioned runs, other preliminary studies were per-formed to ensure that the chemical reaction was the phe-nomena controlling the overall transformation rate. Whenthe enzyme is used as a homogeneous catalyst, solved in thebuffered media where the reaction happens, the chemicalreaction is always the controlling step. However, if the en-zyme is immobilized, there are mass transfer phenomena inthe outer film and inside the pores of the support. With theimmobilized enzyme, the agitation has to be enough for theexistence of a fast external film mass transfer and the en-zyme content in the particle, together with a small particlesize, has to be low enough so that the mass transfer insidethe pores of the support is faster than the reaction in theinner surface of the pores, where the enzyme is immobi-lized. When the reaction itself is the slowest step, it is thecontrolling step. In Fig. 4, it can be seen that the higherconversion per unit enzyme concentration and time is ob-tained at agitation speeds higher than 180 rpm and enzyme

concentrations in the solid lower than 2.5 mg enzyme pergram of support. That implies that, in those conditions, thereaction catalyzed by the immobilized enzyme is the stepcontrolling the overall rate of the hydrolytic process and themaximum catalyst efficiency is attained. All runs in thekinetic study of the hydrolysis reaction with the immobi-lized enzyme were performed at 200 rpm and at a concen-tration of enzyme in the solid of 0.06 mg g−1, with a supportwhose particle size was 100–200 �m.

Kinetic Runs

The kinetic runs were carried out in a very wide experimen-tal range, with a total of 85 runs performed. The detailedexperimental conditions are reported in Table I for eachenzyme form. To determine the trend of the reaction ratewith the initial concentrations of the substrate and the prod-ucts, the obtained experimental data (shown as conversionof lactose vs. tCE) were fitted with a double-exponentialdecay function and reaction rates were calculated by differ-entiating this function and substituting the time values. Inthe case of the free enzyme, as well as with the immobilizedenzyme, the reaction rates are hyperbolic functions of theinitial concentrations of substrate at all the temperatures,

Figure 3. Effect of temperature on the stability of free and immobilized�-galactosidase from Thermus sp. strain T2. Activity test carried out inbuffer BP under the following conditions: CONPG 0 � 0.5 g L−1; T � 70°C.

Figure 4. Effect of agitation speed (�) and concentration of enzyme inthe solid (CEw) on the hydrolysis of lactose with �-galactosidase fromThermus sp. strain T2. Run conditions: T � 80°C; Clac 0 � 50 g L−1; Cgal

0 � Cglu 0 � 0 g L−1; CE ≈ 6.5 mg L−1.


which is the behavior expected for Michaelis–Menten ki-netics with no substrate inhibition. On the other hand, theaddition of glucose or galactose at the beginning of thereaction reduced the initial reaction rate when the enzyme insolution was the catalyst employed, while only galactoseacted as an inhibitor in the case of the immobilized enzyme.Inhibition due to glucose has been observed in enzymes ofmesophile microorganisms, as in the case of E. coli (Laderoet al., 2001) and K. fragilis (Chen et al., 1985), and inthermophilic enzymes, as the one produced by S. solfatari-cus (Pisani et al., 1990). Galactose is a common inhibitor for�-galactosidases, both from mesophile and thermophilesources, as previously reported (Berger et al., 1997; Portac-cio et al., 1998; Petzelbauer et al., 1999; Ladero et al., 2000,2001).

Kinetic Modeling

To obtain the kinetic model able to describe quantitativelythe hydrolysis reactions with the free and the immobilizedenzyme, experimental data of conversion of substrate versusthe product between the time of reaction and the enzymeconcentration (integral data) obtained at all the temperaturestested were fitted to several kinetic models, which areshown in Table II. The complexity of the kinetic modelstested increases from the simplest ones: first order and Mi-chaelis–Menten with two parameters, to those with differenttypes of inhibition due to the two products of the reaction.Models with a medium complexity supposed inhibition byone of the monosaccharides formed. Concerning the type ofinhibition, competitive inhibition was the one involving theactive center alone, uncompetitive inhibition that involves

Table II. Kinetic models proposed for the fitting of experimental data obtained in the hydrolysis oflactose.

Kinetic model Kinetic equation

First order r = k2 CE CS

Michaelis–Menten without inhibition r =k2 CE CS

KM + CS

Michaelis–Menten with uncompetitiveinhibition by substrate

r =k2 CE CS

KM + CS�1 +CS

KI�

Michaelis–Menten with competitiveinhibition by product

r =k2 CE CS

KM�1 +CP

KI� + CS

Michaelis–Menten with uncompetitiveinhibition by product

r =k2 CE CS

KM + CS�1 +CP

KI�

Michaelis–Menten with non-competitiveinhibition by product

r =k2 CE CS

�KM + CS��1 +CP

KI�

Michaelis–Menten with mixed inhibition byproduct

r =k2 CE CS

KM�1 +CP

KI� + CS�1 +

CP

K�I�

Michaelis–Menten with competitiveinhibition by both products

r =k2 CE CS

KM�1 +CP1

KI1

+CP2

KI2� + CS

Michaelis–Menten with uncompetitiveinhibition by both products

r =k2 CE CS

KM + CS�1 +CP1

KI1

+CP2

KI2�

Michaelis–Menten with noncompetitiveinhibition by both products

r =k2 CE CS

�KM + CS��1 +CP1

KI1

+CP2

KI2�

Michaelis–Menten with competitiveinhibition by one product anduncompetitive by the other

r =k2 CE CS

KM�1 +CP1 or 2

KI1 or 2

� + CS�1 +CP2 or 1

KI2 or 1

�Michaelis–Menten with competitive

inhibition by one product andnoncompetitive by the other

r =k2 CE CS

KM�1 +CP1 or 2

KI1 or 2

+CP2 or 1

KI2 or 1

� + CS�1 +CP2 or 1

KI2 or 1

�Michaelis–Menten with uncompetitive

inhibition by one product andnoncompetitive by the other

r =k2 CE CS

KM�1 +CP2 or 1

KI2 or 1

� + CS�1 +CP1 or 2

KI1 or 2

+CP2 or 1

KI2 and 1

�


the interaction of the product with the complex ES and theother two involve the two inhibition, the first one with iden-tical inhibition constants, the second one with different in-hibition constants. In summary, as many as twenty kineticmodels were considered during the discrimination step.

Data were fitted as in previous works (Santos et al., 1998;Ladero et al., 2001, 2000) by non-linear regression to all theproposed kinetic models, the temperature being a variable.Parameters are considered exponential functions of the tem-perature, following the Arrhenius equation, and these func-tions were substituted in the rate equation of each kineticmodel. Experimental data of conversion of lactose versusthe product enzyme concentration in the reactor per timewere fitted to each model using the algorithm of Marquardt–Levenberg, to which a numerical integration of each rateequation is coupled; thus assuming that conversion of lac-tose is the dependent variable, while the product time perconcentration of enzyme is the independent variable (as islogic because experimental error is mainly in sugar concen-tration or conversion data). For the selection of the mostappropriate kinetic model statistical and physical criteriahave been applied, according to the procedure described inprevious works for both enzymatic and non-enzymatic re-actions (Garcia-Ochoa et al., 1990; Garcia-Ochoa and San-tos, 1995; Santos et al., 1999; Ladero et al., 2001, 2000).Statistical criteria taken into account were the square re-sidual sum (SQR) of the model (the lower its value, thebetter the fit obtained with that model), the confidence in-

terval of each kinetic parameter (the narrower the confi-dence interval, the better, and, of course, it must not includethe zero value) and Fischer’s F parameter (the higher, thebetter and, for given numbers of data and parameters, it hasto be over a certain value for the model to be statisticallysignificant). Physical criteria are those imposed to the val-ues or variation of the parameters with temperature; in thiscase, the activation energy of k2 has to be positive (it is akinetic constant). This methodology has been already usedin kinetic studies involving non-enzymatic and enzymaticreactions (Garcıa-Ochoa et al., 1990; Garcıa-Ochoa andSantos, 1995; Santos et al., 1998; Ladero et al., 2000, 2001)and is able to avoid the mathematical manipulation of dataand smooth the experimental error associated. Thus, nu-merical differentiation of data and any kind of linearization(mathematic or graphic) are not needed and the manipula-tion error imposed by those methodologies is avoided. Inthis way, data with experimental errors higher than 5% canbe employed to discriminate the correct kinetic model(HPLC data can have experimental errors higher than 10%in some cases).

The discrimination performed among all models for thetwo forms of the enzyme is summarized in Table III. Forevery kinetic model tested, the activation energy of the cata-lytic kinetic constant k2 was positive, so the physical crite-rion was fulfilled by all models. Considering the resultsobtained for both the free and the immobilized enzyme, onlythe model with uncompetitive inhibition due to the substrate

Table III. Results achieved in the discrimination among the several kinetic models employed forthe fitting of experimental data.*

Kinetic model

Free enzyme Immobilized enzyme

Non-validparameters F value SQR

Non-validparameters F value SQR

First order 0/2 738 6.18 0/2 926 3.38MM without inhibition 0/4 837 3.00 2/4 1307 1.32MM IU lac NC – – NC – –MM IC glu 2/6 734 2.34 2/6 870 1.32MM IU glu 0/6 688 2.46 2/6 871 1.31MM INC glu 2/6 712 2.39 2/6 871 1.31MM IM glu NC – – 4/8 648 1.31MM IC gal 0/6 1251 1.37 0/6 5449 0.21MM IU gal 2/6 906 1.88 1/6 3872 0.30MM INC gal 1/6 1125 1.52 1/6 5000 0.23MM IM gal 2/8 935 1.37 0/8 4634 0.19MM IC glu IC gal 0/8 2,257 0.56 – – –MM IC glu IU gal 8/8 1,413 0.90 – – –MM IC glu INC gal 1/8 2,104 0.61 – – –MM IU glu IC gal 0/8c 2,879 0.45 – – –MM IU glu IU gal 8/8 1,264 1.01 – – –MM IU glu INC gal 1/8 2,646 0.49 – – –MM INC glu IC gal 1/8 2,960 0.44 – – –MM INC glu IU gal 8/8 1,414 0.90 – – –MM INC glu INC gal 0/8 2,515 0.51 – – –

*Abbreviations: MM, Michaelis–Menten; IC, competitive inhibition; IU, uncompetitive inhibition;INC, no competitive inhibition; IM, mixed inhibition.

anumber of non-acceptable parametersbtotal parameters of the modelcboldface models � selected models.


did not converge, which was logical considering that noinhibition due to the lactose has been observed.

With the free enzyme and when only glucose was con-sidered as an inhibitor, the model able to pass the statisticalcriteria was the one which considered uncompetitive inhi-bition due to this product. In all the models consideringinhibition by glucose, the residue is less than the simpleMichaelis-Menten with two parameters. This is reasonable,as glucose has been proven to be an inhibitor. The samehappened when the inhibition due to galactose was takeninto account. As this inhibition is stronger than the one dueto glucose, the SQR value was considerably reduced wheninhibition by galactose was considered. In this case, only themodel with competitive inhibition by galactose has validkinetic parameters (no parameter included zero value in itsconfidence interval). Finally, when both products were con-sidered as inhibitors, a final and drastic reduction in theSQR value was achieved. Only three models passed thestatistical criterion concerning the confidence of the kineticparameters. One supposed competitive inhibition due toboth products; the second, competitive inhibition due togalactose and uncompetitive inhibition by glucose and thelast one took into account non-competitive inhibition by thetwo monosaccharides. The second model is the one with theminor value of SQR and the higher value of F. Moreover,the results for the models with only one inhibition due toproduct suggest this model too.

When the catalyst is the immobilized enzyme, it wasfound that, in the wide experimental range employed, theeffect of the glucose is negligible. This was observed wheninitial glucose concentrations other than zero were used: noeffect over the reaction rate was observed. Moreover, nobetter fitting issues when using the models that involveinhibition by glucose compared to the Michaelis–Mentenmodel with no inhibition. Another reason to mention is thefact that several kinetic parameters in models with inhibi-tion of glucose included zero value in their confidence in-tervals. On the other hand, galactose inhibition has beenconfirmed by the results obtained in the fitting to modelswhich take into account inhibition due to this sugar: ingeneral, a better fitting is obtained comparing to the moresimple Michaelis–Menten model with no inhibition. Thefitting with models including galactose as an inhibitor hasthe highest values of F, so, from a statistical point of view,these models are the best to describe the reaction data con-sidered. Only the models considering competitive andmixed inhibition by galactose have parameters with suffi-ciently narrow confidence intervals. To discriminate be-tween then, one should considered the F value, as the SQRvalues are both very low and similar. The mixed inhibitionmodel includes the competitive inhibition one, mathemati-cally and physically. If the effect of an uncompetitive inhi-bition due to galactose was real, then the F value of the mostcomplex model would be the highest. This does not happen,so the simpler model (competitive inhibition due to galac-tose) is the selected one (the model with the highest value ofF). To add to this selection, mixed inhibition was a non-

eligible model in the case of the free enzyme, as it hasnon-valid parameters from a statistical point of view.

The selected models for each enzyme form and reactionare highlighted in Table III and their kinetic equations, to-gether with the kinetic parameters, are shown in Table IV.They are as follows:

(a) Hydrolysis of lactose with free enzyme: Michaelis–Menten with competitive inhibition due to galactose anduncompetitive inhibition by glucose [Eq. (2) in TableIV].

(b) Hydrolysis of lactose with immobilized enzyme: Mi-chaelis–Menten with competitive inhibition by galac-tose (Eq. [3] in Table IV).

The effects of temperature and initial concentrations of lac-tose and both mono-saccharides on the reaction are shownin Fig. 4. Experimental data are drawn as scattered pointsand the simulations with the selected kinetic models aredrawn as discontinuous (free enzyme) or continuous lines(immobilized enzyme). The kinetic models selected are ableto fit the data obtained at all the temperatures and the pa-rameters of these models behaved similarly to those ob-tained for enzymes from mesophilic organisms.

DISCUSSION

Considering the kinetic behavior of both forms of the en-zyme in the hydrolysis of lactose, a comparison between thekinetic models is possible.

Firstly, the values of the catalytic constant k2 for the freeenzyme is 10–20 times higher than those observed whenlactose is hydrolyzed by the immobilized enzyme, so thecatalytic activity is much lessened by the immobilizationprocess. Moreover, the activation due to temperature ishigher in the free enzyme. This is logical if the immobilizedenzyme is more rigid (as the higher stability of this form ofthe enzyme means) and this rigidity affects negatively themobility in the active center during the reaction step.

Regarding the Michaelis–Menten constant, the free andthe immobilized enzyme shows the same affinity for thelactose at 30°C. However, as the temperature rises, the af-finity of the immobilized enzyme for the substrate is gradu-ally higher than the one of the free enzyme. At 90°C, theaffinity of the immobilized enzyme for the lactose is 10times higher than that of the free enzyme. This means thatthe rigidity imposed by the immobilization does not disturbthe chemisorption of the substrate in the active center. Infact, it promotes the equilibrium toward the enzyme–substrate complex.

The inhibition constant for galactose in the case of thefree enzyme is twice the same constant for the immobilizedenzyme at all temperatures from 30 to 90°C. The immobi-lization process means a reduction of the inhibition by ga-lactose to half of that present during the hydrolysis of lac-tose with the free enzyme.

The inhibition due to glucose is higher at high tempera-tures, while the one due to galactose is reduced as the tem-perature rises. At temperatures of 70°C or lower the inhi-


bition by galactose is more acute than the one by glucose. Attemperatures higher than 70°C both inhibitory effects aresimilar.

Finally, the turnover number remains the same regardlessof the temperature for the immobilized enzyme, approxi-mately 43,000 �mol of substrate converted per minute and�mol of enzyme (considering one active center per subunit),while it decreases gradually from 180,000 at 30°C to100,000 �mol of lactose per minute and �mol of enzyme at90°C in the case of the free enzyme. This involves that theimmobilized enzyme is more efficient at high temperature,with a yield of 43% compared to the free enzyme, than atlow temperatures, where the yield, at 30°C, is 24%.

Some deviations from the Michaelian behavior for ther-mophile enzymes have been pointed out by some authors(Vian et al., 1998; Pisani et al., 1990), but it seems that otherreactions competing with hydrolysis should be taken intoaccount for the enzymes studied in those works or a closeror more complete study of the kinetics should be performed.Here, the production of galacto-oligosaccharides (GOS) isnegligible; even at high concentrations of lactose (300 gL−1), the concentration of GOS does not rise over 5–6% ofthe total carbohydrates, in any case. This was further provedby the fact that concentrations of glucose and galactose overthe entire reaction progress are similar, even if the twopeaks were not perfectly separated and quantification bypeak height was the obligated method to quantify the twomonosaccharides produced during the hydrolysis. This en-

zyme is an even better hydrolytic enzyme that the one fromK. fragilis—a good hydrolytic enzyme industrially used forthe hydrolysis of lactose in milk—as the selectivity of thisenzyme to hydrolysis is higher than that of the yeast enzyme(comparing transgalactosylation and hydrolysis, which arecompetitive reactions). This is strange if results from otherauthors are taken into account (Berger et al., 1997; Petzel-bauer et al., 1999): from those results, a general impressionthat with thermophilic enzymes—P. furiosus, T. aquati-cus—a higher selectivity toward transgalactosylation reac-tions issues.

If the kinetics of the hydrolysis of lactose with this �-ga-lactosidase and with the mesophilic enzymes studied in pre-vious works (Santos et al., 1998; Ladero et al., 2001) arecompared, little difference is observed in the models ob-tained. The activation energies (shown as the ratio betweenthe activation energy and the constant R) for all the param-eters fluctuate between 5,000 and 12,000 K, regardless ofthe source of the enzyme (E. coli, K. fragilis, or Thermus sp.strain T2). Similarly, the activation energies of the enzymefrom the �-galactosidase of A. niger in the hydrolysis oflactose at pH 3.5 vary between 3,500 and 8,500 K (Papay-annakos et al., 1993).

The kinetic parameters for the enzymes of K. fragilis, E.coli, and Thermus sp. strain T2 at several temperatures arecompared in Fig. 6. The values for the catalytic constant k2

are comparable if 30–40°C is the temperature of choice forthe enzyme of K. fragilis and 60–70°C is the working tem-

Table IV. Selected kinetic models (and their parameters) for the hydrolysis of lactose with free and immobilized �-galactosidase from Thermus sp.strain T2.*

Form of theenzyme Selected kinetic model Parameter values of the model

Free

r =k2CEClac

KM�1 +Cgal

KIgal� + Clac�1 +

Cglu

KIglu�

k2 = 3.8 � 109 exp�−10116

T �KM = 5.51 � 1013 exp�−

11210

T �KIgal = 9.79 � 107 exp�−

7933

T �KIglu = 5.59 � 10−8 exp�4272

T �Immobilized

r =k2CEClac

KM�1 +Cgal

KIgal� + Clac

k2 = 3.21 � 105 exp�−7830

T �KM = 5.58 � 108 exp�−

7851

T �KIgal = 5.88 � 107 exp�−

7505

T �*Note: error in parameters fluctuated between 6% and 34%.


perature of the thermophilic �-galactosidase. The enzymefrom E. coli is much less efficient over lactose as substratethan the other two because its catalytic constant is an orderof magnitude lower than the ones for the other enzymes.The affinity of the thermophilic enzyme for lactose is com-parable to that of the enzymes from the yeast and E. coli, butat temperatures from 5 to 40°C, where its catalytic constantis much lower. At its working temperature is 10 timesslower for forming the enzyme–substrate complex. Both theenzymes from the yeast and the thermophile are inhibited bygalactose. The inhibition by galactose is more acute in thethermophilic enzyme than in the enzyme of K. fragilis, evenif temperatures at which k2 is similar in both enzymes arecompared. The inhibition due to glucose is low with boththe enzymes of Thermus and E. coli and the inhibition con-stant is 1 order of magnitude higher than that of galactose.

In conclusion, the thermophilic enzyme seems to have thesame behavior as the mesophilic enzymes during the for-mation of the enzyme–substrate complex. If rigidity, as is

assumed in the comparison between the free and the immo-bilized enzyme from Thermus, is the key to explain thereduction in catalytic efficiency, this same reason can beapplied when the free thermophilic enzyme is compared tothe enzymes from the mesophile microorganisms. The lowvalue of its catalytic constant compared to the one of theenzyme from the yeast can be due to a higher rigidity,which, in turn, is the reason of its higher stability. However,the general rigidity of the enzymes is not the only featurethat can affect their activity. Comparing the two mesophilicenzymes is obvious that both have similar affinities for lac-tose, while the enzyme from K. fragilis have a much highervalue of the catalytic constant and, because of this, of theturnover number: this enzyme is much more active than theone from E. coli toward lactose, and they have similar sta-bility.

Finally, a comparison of the magnitude of the Michaelis–Menten constants for the previously mentioned enzymesand that of A. niger suggests that the interaction of lactose

Figure 5. Data of conversion versus the product time per enzyme concentration during the hydrolysis of lactose with the free and the immobilized enzymefrom Thermus sp. strain T2. (a) At temperatures from 40 to 60°C, with the following initial concentrations: Clac 0 � 50 g L−1; Cgal 0 � Cglu 0 � 0 g L−1.(b) At temperatures from 70 to 80°C, with the following initial concentrations: Clac 0 � 50 g L−1; Cgal 0 � Cglu 0 � 0 g L−1. (c) At several initialconcentrations of lactose, with the following initial concentrations: Cgal 0 � Cglu 0 � 0 g L−1, and T � 60°C. (d) At several initial concentrations ofproducts, with the following initial concentration: Clac 0 � 50 g L−1 and T � 60°C.


with the thermophilic enzyme and with the fungus enzymeare similar and 10 times weaker than in the other enzymes(at their working temperatures: 70, 50, and 40°C, respec-tively). The same comparison regarding the inhibition con-stant of galactose (a competitive inhibitor in all cases, ex-cept with E. coli enzyme) shows that the inhibition is similarat 50°C in the enzyme from Thermus at 70°C and five timesthat in the enzyme of K. fragilis at 40°C (Flaschel et al.,1982).

We thank Dr. Jose Luis Garcia Lopez, from the CIB-CSIC, andDr. Alfonso Carrascosa and Dr. Benevides C.C. Pessela, from theIFI (both research institutes of the CSIC) for the many usefuladvices given and for the kind supply of the enzyme of Thermusexpressed in E. coli. We also thank Novo-Nordisk for the kindsupply of enzyme from K. fragilis.

LIST OF SYMBOLS

aR remaining activityCE enzyme concentration in solution (mg L−1)CEw enzyme concentration in the solid (mg g−1)Cgal galactose concentration (mol L−1)Cglu glucose concentration (mol L−1)Clac lactose concentration (mol L−1)CONPG ONPG concentration (mol L−1)CP product concentration (mol L−1)CS substrate concentration (mol L−1)Ea activation energy (J mol−1)F Fischer’s F parameter

KI inhibition equilibrium constant (mol L−1)KM Michaelis–Menten constant (mol L−1)k2 kinetic constant (L mg−1 min−1)ONP o-nitrophenolONPG o-nitrophenol-�-D-galactosideR ideal gas constant (J mol−1 K−1 or cal mol−1 K−1)r reaction rate (mol L−1 min−1)SQR sum of square residualsT temperature (°C or K)t time (min)X conversion

Greek Symbols

� agitation speed (rpm)

Subscripts

0 initial conditionsinc incubation conditions

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hydrolysis of lactose by free and immobilized ?-galactosidase from thermus sp. strain t2

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