an empirical rate equation for the fructooligosaccharide-producing

8/3/2019 An Empirical Rate Equation for the Fructooligosaccharide-Producing

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JOURNALOF FERMENTAT ION AND BIOENGINEERINGVol. 82, No. 5, 458-463. 1996

An Empirical Rate Equation for the Fructooligosaccharide-ProducingReaction Catalyzed by p-FructofuranosidaseMIN-HONG KIM,s3 MAN-JIN IN, HYUNG JOON CHA,2 AND YOUNG JE YO03*

R&D Center, Miwon Co. Ltd., Dobong-Ku, Seoul, KRIBB, Taeduk Science Town, Taejon,2 Department ofChemical Engineering, Seoul National University, Seoul,3 KoreaReceived 2 February 1996/Accepted 12 July 1996

An empirical rate equation having two parameters was proposed for the reaction catalyzed by ,&fructo-furanosidase (FFase) that was used for the production of fructooligosaccharides. The rate equation enabledthe estimation of FFase activity from the concentration of reducing sugar in the reaction product. The rateequation was applied to the case of immobilized FFase in a packed-bed reactor to determine the effects of linearvelocity on the performance of the reactor and to monitor the changes in activity during a 10-d operation. It wasconsidered that the proposed rate equation could be a valuable tool for quantitating the effects of variousparameters related to the process development of fructooligosaccharides.

[Key words: ,3-fructofuranosidase, fructooligosaccharides (FOS), enzyme reaction, kinetics, immobilizedenzyme]Fructooligosaccharides (FOS) have features of a low-calorie sweetener on the one hand and a bifidus growthfactor on the other (1, 2). FOS can be prepared fromsucrose through the transfructosylating action of en-zymes, that is, ;3-fructofuranosidase [FFase; EC 3.2.1.261 and ,%D-fructosyltransferase [EC 2.4.1.91 from micro-organisms and plants (3-6). FFase has both hydrolyticand transferring activities depending on the concen-tration of substrate. Glucose and fructose are the majorproducts at sucrose concentrations below 5 g/l, whileFOS and glucose predominate at sucrose concentrationsabove 200 g/l. Similar phenomena were observed for ,3-galactosidase when lactose was used as a substrate (7, 8).With the progress of reaction, FOS with a high degreeof polymerization are obtained. According to Jung et al.(9), FFase from Aureobasidium pull&am catalyzed thedisproportionation reaction shown in Eq. 1, where Gand F denote glucose and fructose, respectively, and thesubscript n denotes the number of fructose moleculesbound to glucose. When n equals 1, two moles of sucroseare converted to one mole each of kestose and glucose.

GF,+GF, - GF,. l+GF,+l (1)Rate equations based on this mechanism contain manyparameters and can only partially describe the progressof the reaction. Thus, it is necessary to formulate a sim-ple empirical rate equation for practical use. Kosugi andSuzuki proposed a 2-parameter empirical rate equation

for the lipase reaction that described the hydrolysis offat fairly well (10). The parameters could be determinedby experiment.In addition to the description of the progress of thereaction, it is important to estimate the enzyme activityfor determining and evaluating the performance of anenzyme reactor. Empirical approaches are available forestimating the changes in activity of the immobilizedenzyme in a packed-bed reactor (PBR). For immobilizedL-aspartate ,3-decarboxylase in PBR operation, Yamamotoet al. intermittently varied the operational flow rate (11).They were able to monitor the loss of activity during the* Corresponding author.

operation by correlating the activity of the immobilizedL-aspartate $decarboxylase with the conversion of thesubstrate at the reference flow rate. While this methodenabled them to estimate the changes in activity duringthe operation, time was needed for the reactor to reach asteady state after every change in the flow rate. For (Y-amylase, Kimura et al. investigated the empirical relation-ship between maltotetraose concentration in the effluentand the activity of cu-amylase (12). They calculated theremaining enzyme activity from the maltotetraose con-centration in the effluent during a continuous operation.Through use of empirical rate equations, it was possibleto select a reactor suitable for the immobilized glucoamy-lase, as was done by Cabral et al. (13).In this work, the mechanism of the reaction mediatedby FFase was discussed and a rate equation similar tothat proposed by Kosugi and Suzuki was formulated andapplied to the case of immobilized FFase in a PBR, forquantitating the effects of linear velocity and estimatingthe change in activity of immobilized FFase with time ina PBR.

FORMULATION OF THE EMPIRICAL RATEEQUATION

Batch reaction in a stirred tank reactor For monitor-ing of the time course of the reaction catalyzed by FFase,an empirical rate equation with two parameters wasproposed. The form of the proposed equation is similarto that of Eq. 2, where (Rs), (Rqeq and t denote theconcentration of reducing sugar at time t, equilibriumconcentration of reducing sugar and time, respectively.The time necessary to achieve half (RS),, is denotedby tm.

1 1 1m=$&, t+ (RS),, (2)

If Eq. 2 describes the reaction successfully, plottingof & vs. $ will give a straight line and (RS),, andt, will be obtained from the intercept and the slope.Differentiating Eq. 2 with respect to t leads to Eqs. 3

458


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VOL. 82, 1996 EMP IRICAL RATE EQUATION FOR ,3-FRUCT OFURANOSIDASE 459

and 4:d(R8 _ t (& [(Rf%- WI*dt m eq (3)at t=O, (RS)=O (4)

d(RS)At equilibrium, 7 equals zero and (RS) equals(Raeq. From Eqs. 3 and 4, the initial reaction rate isgiven by Eq. 5, where K, k and E are the concentrationof kestose, a correction factor and the activity of theenzyme per unit volume of reaction mixture, respectively.

WS) d(K)dt =-t I=0 dt at r=o= (Rtaeak.E (5)mSince equimolar kestose and glucose are formed fromsucrose in the early phase of the reaction, the activity de-termined in terms of the kestose formation rate wouldbe equivalent to that determined in terms of the glucose(reducing sugar) formation rate. It can be seen that theactivity of the enzyme is inversely proportional to theslope of the line which Eq. 2 represents. Multiplyingboth sides of Eq. 2 by (RS), substituting Eq. 5 and rear-ranging the resulting equation will give Eq. 6 which canbe used for more precise analysis in the high (RS)region.

(RS)=(RS),,- (Rp . e(Rii& and k can be calculated from the linear regressionof Eq. 6 for various reaction times and the activity ofthe enzyme. Once (R5& and k are known, E can becalculated from Eq. 7 through the measurement of (Rs)at time t.

E= W-ha . UW 1k (R&q - (Rs) 7

Continuous operation in a PBR For an immobi-lized enzyme reactor it is more convenient to use theenzyme activity based on unit weight of the enzyme ratherthan that based on unit volume of substrate solution.Equation 8 gives the relationship, where ET, Q and Tdenote total activity of the system, volumetric flow rateand residence time, respectively.E=ET/(Q.r) (8)

The enzyme activity per unit weight of a carrier can beobtained by dividing total activity, ET, by total weightof the carrier.Substituting Eq. 8 into Eq. 7 and replacing t with rgive Eq. 9.

E, _ Q. UWea WIk (R&q - (Rs) (9)MATERIALS AND METHODS

Microorganism used and culture conditions A. pul-luluns (KFCC 10754) was aerobically grown for 25 h at30C pH 6.8 in a 14-1 fermentor (New Brunswick Scien-tific, MF-214). The medium consisted of 20% sucrose,2% yeast extract, 0.5% K2HP04, 0.1% NaCl, 0.06%(NH4)*S04, and 0.05% MgS04. Final cell volume andthe activity of the enzyme were 20% (v/v) and 6OOU/g-wet cell.

Extraction of ,&fructofuranosidase from the cellsMicrobial cells were collected from the culture brothusing a centrifuge equipped with filter cloth. Wet cells(1 kg) thus obtained were suspended in 0.025 M, citratebuffer (pH 4, 10 I). A Dyno-mill (Typ KDL, Switzerland)was employed to rupture the cells in suspension. Theflow rate of the suspension to the Dyno-mill was 10 l/h.Cell debris was removed by centrifugation and the super-natant was filtered through filter paper (WhatmanGF/B). The filtrate was the enzyme solution and wasused for immobilization without further purification.The activity of the enzyme solution was 44,000 U/I.Enzyme immobilization HPA75 (Mitsubishi Chem-icals, Japan), a macroporous, strong anion exchangeresin, was employed as a carrier for the FFase. Theaverage diameter of the carrier was 0.35 mm. After beingwashed with 2 N hydrochloric acid (10 r) and water (10 r)consecutively, HPA75 (1 kg) was suspended in theenzyme solution (10 r) under mild agitation and at roomtemperature for 3 h. The suspension was filtered throughfilter cloth and the enzyme-resin complex was washedthoroughly with water. The enzyme-resin complex thusobtained after filtration was the immobilized FFase andits activity was 137 U/g.Substrate For the soluble enzyme, a predeterminedamount of sucrose was dissolved in 0.05 M citrate buffer(pH 5.5) such that the final concentration of sucrose was1.8 mol per liter of the reaction mixture that comprisedthe enzyme solution, while a predetermined amount ofsucrose was dissolved in distilled water such that theconcentration of sucrose was 1.8 mol per liter of the sub-strate for the immobilized FFase system. The intraparti-cle void volume of the ion exchange resin was about40% of the resin volume, which was taken into accountin adjusting the substrate concentration.Determination of ,&fructofuranosidase activity Cul-ture tubes with caps (25 x 150 mm, Corning, New York)were employed as reaction vessels for the determinationof the enzyme activity where every assay mixture con-tained 15 ml of the substrate solution and a predeter-mined amount of enzyme. In the case of soluble enzyme,0.5 ml of enzyme solution was added to the substratesolution which had been preincubated at 50C. Then, theassay mixture was shaken for 30 min at 150 strokes permin. The reaction was stopped by boiling in a micro-wave oven for 1.5 min. The boiled reaction mixture wasstored in the refrigerator until analysis. In the case ofimmobilized FFase, 0.1 g of the enzyme was added to 15ml of the substrate solution. After a predetermined timehad elapsed, the assay mixture was immediately filteredthrough a cartridge filter (0.22 pm, Millipore, MILLEX-GV) prior to microwave oven heat treatment in order toremove the immobilized enzyme particles. Shaking timevaried from 30 to 60min depending on the activity ofthe enzyme. All other conditions were the same as thosefor soluble enzyme. This activity will be called the mea-sured activity in contrast to the calculated activity whichwas obtained using Eq. 9. One unit is defined as theamount of enzyme that can produce one pmol of kestosefrom sucrose per min at 50C.Empirical rate equation Jacketed glass vessels(105 4 x 140 mm) equipped with 4 glass baffles were em-ployed for the enzyme reaction. Prior to the addition ofthe enzyme, the substrate solution in the reaction vesselwas agitated at 50C and 250 rpm for 30 min. Workingvolume was 500-600 ml for both soluble and immobi-


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460 KIM ET AL. J. FERMENT. BIOENG.,

lized FFase. The enzyme loading tested ranged from4,860 to 30,78OU/I-mixture for the soluble enzyme andranged from 1,740 to 17,640 U/I-substrate for the im-mobilized FFase. Samples (5 ml) were taken at intervalsafter a predetermined amount of enzyme was added.Duration of the reaction was limited to less than 12 h.PBR Jacketed glass columns (17.8 # x 300 mm) in-sulated with cotton wool were used as PBRs where theimmobilized FFase (31 g) was charged. Measured activityat the beginning was 137 U/g-carrier. Substrate solutionwas passed through the column at a flow rate of0.0441/h. During the 10d of operation, samples weretaken every day from the product stream in order to ana-lyze the composition of saccharides. After the 10d ofthe operation, the flow of substrate was stopped and allthe immobilized FFase was drawn out of the PBR care-fully without disturbing the relative position along thevertical direction. Samples of immobilized FFase weretaken along the vertical positions of the PBR and theiractivities were measured. In order to determine theaverage activity, the immobilized FFase drawn out of thePBR was mixed and its activity was measured.Other analytical methods The concentration ofreaction products was determined by high-performanceliquid chromatography (HPLC: Waters Assoc., USA).Kestose and nystose standards were purchased fromDaiichikagaku (Japan). Sugar-PAK (Waters Assoc.) wasused as a column with its temperature maintained at90C. Deionized water containing 50 mg/l Ca-EDTAwas used as a mobile phase with its flow rate set at 0.5ml/min. The refractive index of the eluate was detectedby a differential refractometer (R-401, Waters Assoc.).All chemicals were of reagent grade unless otherwisespecified.

RESULTS AND DISCUSSIONParameters for empirical rate equation Kineticdata for various concentrations of soluble and immobi-lized FFase were fitted according to Eq. 6. From Fig. 1,it can be seen that the data for the immobilized FFasefell on the single straight line. From linear regression,the values of (RS& and k were obtained and are shownin Table 1. The equilibrium concentration of reducing

sugar, (RX&, was lower for the soluble enzyme than forthe immobilized one, suggesting that the soluble enzymemight have been deactivated. The correction factor, k,was very similar, suggesting that the catalytic mechanismwas the same for the two types of FFase.It was found from Fig. 1 that the rate equation wasvalid for the concentration range of reducing sugarabove 0.22 and below 1.22 mol/l. In order to determinethe valid range of the rate equation in terms of the FOScontent, the ratio of FOS content to total sugar contentvs. the concentration of reducing sugar is shown in Fig.2 where it can be seen that the ratio for the commercial-ly available product, 55x, corresponds to 0.88mol/l ofreducing sugar. However, caution should be paid asregards operating conditions since (RS& and k are func-

TABLE 1. Rate equation parameter valuesEnzyme formSoluble 1.305 17080/E 7.64 x lo-~5 0.99Immobilized 1.428 18040/E 7.92 x IO-5 0.99

1 . 4 -

1 . 2 -

1 . 0 -sg . 6

g . 6 -

. 4 -

0 1 2 3 4 5 6 7(RS)/E/f (xl O-5mol/U/h)

FIG. 1. Fitting of kinetic data to the proposed rate equation forimmobilized /3Sfructofuranosidase. The enzyme reaction was carriedout in a batch reactor. The enzyme loading E (U//-substrate) was 0,1740; q , 2400; n, 4800; 0, 9600; 0, 17640.tions of operational variables such as initial sucroseconcentration, temperature and pH.Equation 9 can be employed to estimate the activity ofthe immobilized FFase without the need for enzyme sam-pling and activity measurement provided that the reduc-ing sugar concentration in the reaction product and theflow rate of the substrate are known.Hydrolysis of FOS by /?-fructofuranosidase Themechanism of the reaction mediated by FFase fromAureobasidium pullulans is described by Eqs. 10, 11 and12 which are derived by applying n= 1, 2 and 3 to Eq. 1,respectively.

2. sucrose - kestose + glucose2. kestose tf nystose + sucrose2. nystose tf fructosylnystose + kestose

From Eqs. 10-12, we obtain Eqs. 13 and 14.3 .kestose - 2. nystose + glucose

(10)(11)(12)(13)

. 2 . 4 . 6 . 6 1 . 0 1 . 2 1 . 4Reducing sugar (mol//)

FIG. 2. Relationship of FOS content to the concentration ofreducing sugar.


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VOL. 82, 1996 EMPIRICAL RATE EQUATION FOR $-FRUCTOFURANOSIDASE 461

2. kestose - fructosylnystose +glucose (14)Equations 13 and 14 imply that total FOS content candecrease with the progress of the reaction, since glucoseis formed from kestose in addition to nystose and fruc-tosylnystose. It was reported that fructose was formedas a result of the hydrolysis of nystose according to Eq.

15. On the other hand, hydrolysis of sucrose or kestoseaccording to Eqs. 16 and 17 was negligible since concen-trations of sucrose and kestose were above 5% for mostof the reaction time (14).nystose - kestose + fructose (15)sucrose - glucose + fructose (16)kestose - sucrose+ fructose (17)

Thus, the formation of fructose is mainly due to thehydrolysis of nystose and not to the hydrolysis of su-crose and kestose. The concentration of reducing sugarincreased with the reaction time. However, FOS contentshowed a maximum of about 60% of total sugar con-tent. The decrease in FOS content at high concentrationsof reducing sugar was attributed to the formation ofglucose according to Eqs. 13 and 14 and the hydrolysisof nystose according to Eq. 15.Some of the data employed for constructing Fig. 1were analyzed for the product compositions and theresults appear in Table 2. Table 2 shows that the ratio ofthe reducing sugar produced to the sucrose consumedincreased with increasing conversion of sucrose. The netresult of the enzyme reaction was the hydrolysis of su-crose to reducing sugar without changes in FOS content,when A(RS)/A(S) was equal to - 1.9, at a sucrose conver-sion of 0.85. As A(Rs)/A(s) became less than -1.9,FOS content began to decrease.It is evident from Fig. 2 and the mechanism of thereaction that the FOS content does not adequatelyrepresent the extent of reaction, especially when the ex-tent of reaction is as high as that in the commerciallyoperating range. Also, it is expected that theoretical rateequations that do not take into account the hydrolysisof FOS would not fully describe the progress of thereaction.Effect of linear velocity Linear velocity of sub-strate solution and flow patterns inside a bioreactor areimportant factors influencing its performance. With in-creasing linear velocity, the boundary layer around im-mobilized enzyme beads is expected to be thinner, result-ing in lesser external mass transfer resistance. From Fig.3, it can be seen that the effect of linear velocity on the

TABLE 2. Changes in the compositions of saccharides and theirdifferentials during the enzyme reaction=

Conversior+ (0 (0 A(Rs)/A(s) FOWtotaI sugar(-) (mol/l) (moI/l) (moI/mol) (g/g)0.2816 0.3062 0.0198 -0.7347 0.2210.3982 0.4409 0.0241 -0.6412 0.3340.5485 0.6034 0.033 1 -0.6583 0.4450.6993 0.7750 0.0439 -0.7255 0.5280.7900 0.8781 0.0521 -0.6110 0.5620.8329 0.9456 0.0644 - 1.4786 0.5770.8722 1.0528 0.0906 -2.5264 0.5890.8956 1.1351 0.1175 -3.0269 0.574

a The operator A means the differential change in the concentrationof the component.b The conversion of sucrose is defined as [(s)O-((s)]/(s)O, where(s),= 1.8 mol/l.

I I I I 10 2 4 6 a 10 12 1 4 1 6

v - ' (h/m)FIG. 3. Effect of linear velocity on the activity of ,%fructo-furanosidase in a packed-bed reactor.

activity was less than 20% at most in the operatingrange investigated here, suggesting that the system waskinetically controlled. The activity of the system wascalculated using Eq. 9.Continuous operation of a PBR During a continu-ous operation of a PBR, FOS content of the effluent wasmeasured and remaining activity of the immobilizedFFase was calculated using Eq. 9. No loss of the activitywas noted for up to two days of continuous operationand then logarithmic loss of the activity was observed,as shown in Fig. 4. The loss of activity of the immobi-lized FFase during the continuous operation of the PBRwas thought to have been caused by two main factors:thermal deactivation and dissociation of the ionicallybound enzyme from the carrier. Although the data arenot shown, the enzyme activity was sharply decreasedwhen ionic species such as sodium chloride or calciumchloride were added to the substrate solution. The ioniccharacter of the interaction between the enzyme and thecarrier is shown in Fig. 5 where the remaining activitiesalong the vertical position of the PBR were not uniformand were higher as the immobilized enzyme was locatednearer the bottom of the PBR. This suggested that the

.1 1 I I 1 0 . 00 2 4 6 6 10

Time (d)FIG. 4. Changes in calculated activities and FOS contents duringa 10-d operation of a packed-bed reactor: 0, fractional remaining

activity estimated from Eq. 9; 0, ratio of FOS to total sugar content.


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462 KIM ET AL. J. FERMENT. BIOENG.,

60 TO P2.a ,

01 I I I I0 3 6 9 12 15 16Vert ical pos i t ion (cm)

FIG. 5. Remaining activity of ;Y-fructofuranosidase along verticalpositions of a packed-bed reactor after 10 d. The substrate solutionwas passed from the top to the bottom of the reactor.

ionic binding between the enzyme and the carrier wascleaved and the enzyme leaked out of the carrier due tothe cleavage, because if thermal deactivation were thesole cause, the remaining activities would be uniform.The constancy of the activity in the initial period of oper-ation was attributed to the gradual expression of internalenzyme activity which was suppressed by the internalmass transfer resistance (15). It is noteworthy that FOScontent decreased from 55.7% of total sugar content to53% after 7 days operation while the remaining activitywas 50% of the initial activity. It is evident from theproposed kinetics and Fig. 2 that the total FOS contentcould be kept above 55% even if the enzyme activity wasdecreasing. For example, Eq. 9 predicts that FOS con-tent remains approximately constant at 55% of totalsugar content [(Rs)=O.88 mol/l] until the remaining ac-tivity reaches approximately 50% of the initial activitywhen the concentration of reducing sugar at the start ofa PBR operation was 1.1 i mol/l which corresponds to aFOS content of 57%. Constancy of the total FOS con-tent in terms of productivity was also observed for asystem of alginate-encapsulated FFase at 50C (16).Although productivity or conversion was often chosen asan indirect representation of the enzyme activity as inthe cases of invertase (17), n-galactosidase (18), andcyclodextrin glucanotransferase (19), it is obvious thatproductivity or conversion may not be suitable forrepresenting the activity. Such unsuitability was noted byCabral ef al. for glucoamylase (13).The knowledge of the activity of the immobilizedenzyme in a reactor enabled us to quantitate the reactorefficiency which was defined as the ratio of the calculatedactivity of the immobilized FFase in a PBR to the mea-sured activity. The reactor efficiency was found to beabout 70% as shown in Table 3.Figure 5 shows the remaining activity of immobilizedFFase along the vertical position of the PBR. Interesting-ly, the activities were not uniform; i.e., the immobilizedFFase located nearer the top of the PBR exhibited thelower remaining activity. Nonuniformity of the activitywas attributed to the gradual elution of the enzyme fromthe top of the PBR caused by the ionic impurities con-tained in the substrate solution. This phenomenon is

TABLE 3. Fractional remaining activity and the reactor efficiencyduring a 10-d operation of a packed-bed reactor

Point of Activity (U/g-carrier) Reactor efficiencymeasurement Measured Calculatedb (Calculated/Measured)Initial 137 100 0.7310 day 45c 34 0.67

a Measured activity is the activity measured according to the assayconditions.

b Calculated activity is the activity estimated according to Eq. 9.u All the immobilized FFase was drawn out of the PBR after the 10

days operation and was mixed well. The activity of the mixed samplewas measured.

very similar to the case in which the protein ionicallybound to the ion exchange resin was eluted using theappropriate buffer.The empirical approach to deriving the rate equationwas considered to be very useful compared to themechanistic approach for cases in which the reactioninvolved complicated mechanisms or in which activitiesalong the PBR were not uniform such as in this study.The empirical rate equation enabled the quantitation ofthe effects of parameters such as the linear velocity forthe reactor design and could be a valuable tool for theprocess development of FOS.

NOMENCLATURE; : residence time in a packed-bed, h: enzvme loading. U/I

ttmV1.2.3.

4.

5.

6.

7.

total activity ofFFase in a reactor, Uconcentration of fructose, mol//concentration of glucose, mol/lconcentration of kestose, mol/lcorrection factor, mol/(U. h)flow rate of substrate, I/hcorrelation coefficientconcentration of reducing sugar, mol/fequilibrium concentration of reducing sugar,mol/lconcentration of sucrose, mol/linitial concentration of sucrose, mol/freaction time in a batch reaction, htime necessary to achieve half (RS),,, h: linear velocity, m/h

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an empirical rate equation for the fructooligosaccharide-producing

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