kinetic model for synthesis of fructosyl-stevioside using suspended β-fructofuranosidase

Biochemical Engineering Journal 10 (2002) 207–215

Kinetic model for synthesis of fructosyl-steviosideusing suspended�-fructofuranosidase

Kentaro Suzuki, Takuya Fukumura, Naomi Shibasaki-Kitakawa, Toshikuni Yonemoto∗Department of Chemical Engineering, Tohoku University, Aoba-yama 07, Aramaki, Aoba-ku, Sendai 980-8579, Japan

Received 5 September 2001; accepted after revision 28 November 2001

Abstract

The synthesis experiments of fructosyl-stevioside were conducted under the various conditions of the initial concentrations of thesubstrates and the enzyme. The transfructosylation of stevioside with sucrose and the hydrolyses of sucrose and fructosyl-steviosidesimultaneously occurred. The fructosyl-stevioside synthesis was inhibited by the side products, glucose and fructose. A kinetic model wasconstructed by considering the Ping-Pong Bi Bi mechanism for the transfructosylation, the apparent Ordered Uni Bi mechanism for thehydrolysis and the competitive inhibition by the side products. The model constants were estimated by fitting the model equations withthe experimental results for the sucrose hydrolysis and the fructosyl-stevioside synthesis. The model can predict not only the appropriateconditions to efficiently synthesize the fructosyl-stevioside, but also the reaction time giving the maximum conversion. © 2002 ElsevierScience B.V. All rights reserved.

Keywords: Enzymes; Fructosyl-stevioside; Production kinetics; Modeling; Ping-Pong Bi Bi mechanism; Kinetic parameter

1. Introduction

Stevioside [1,2], the major sweet glycoside isolated fromthe leaves ofStevia rebaudiana, is commercially used [3,4]as a low calorie and a non-cariogenic [5] sweetener. Whilethis glycoside is about 140 times sweeter than sucrose atthe concentration of 0.025% [6–8], it has a slightly bittertaste and an aftertaste. In order to alleviate these concerns,many attempts have been studied regarding the enzymaticsaccharification of stevioside. Some researchers have in-vestigated the transglucosylation of stevioside with solublestarch using cyclodextringlucosyltransferase [9–11]. In thisenzymatic reaction, the transfer of one, two or more glucoseunits from the soluble starch to stevioside simultaneouslyoccurred to form complex products. Kitahata et al. [12,13]have studied the transgalactosylation of rubusoside, oneof the stevioside congeners, using�- and�-galactosidasesfrom various origins. They reported that the rubusoside con-versions were less than 20%. Ishikawa et al. [14] found thatthe�-fructofuranosidase fromArthrobacter sp., isolated byFujita et al. [15–18], transferred a fructosyl residue to stevio-side or rubusoside. They have investigated the effect of the

∗ Corresponding author. Tel.:+81-22-217-7255; fax:+81-22-217-7258.E-mail address: [email protected] (T. Yonemoto).

concentration of acceptor, stevioside or rubusoside, on thetransfructosylation. The mono-fructofuranosylated productswere obtained in a yield greater than 80% at a low acceptorconcentration.

In the fructosyl-stevioside synthesis, stevioside reactswith sucrose to form fructosyl-stevioside and glucose. Forsuch a reaction with two substrates and two products, the me-chanism is very complicated and the conventional Michaelis-Menten type mechanism cannot be applied. Furthermore,the side reactions are known to simultaneously occur in thissystem [15,17]. The kinetics is still not elucidated and theeffects of the operating factors on the fructosyl-steviosidesynthesis have hardly been discussed. In order to efficientlysynthesize fructosyl-stevioside, it is important to constructthe kinetic model which can quantitatively describe thereaction rates under the various conditions.

In this study, the synthesis experiments of fructosyl-stevioside were performed using�-fructofuranosidase.The effects of the initial concentrations of the substratesand the enzyme, and the side product addition on the re-action rates were investigated. A kinetic model for thefructosyl-stevioside synthesis was constructed. The modelconstants were estimated by fitting the model equationswith the experimental results for the sucrose hydrolysis andthe fructosyl-stevioside synthesis.

1369-703X/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S1369-703X(01)00183-8

208 K. Suzuki et al. / Biochemical Engineering Journal 10 (2002) 207–215

Nomenclature

CE concentration of free enzyme (mol m−3)CE,0 initial concentration of free enzyme based

on unit of enzyme activity (units m−3)CE,Total total concentration of free enzyme in system

based on mole (mol m−3)CE·i concentration of enzyme-componenti

complex (mol m−3)Ci concentration of componenti (mol m−3)Ci ,0 initial concentration of component

i (mol m−3)k1–k12 rate constants for each elementary reactionKI,Fru inhibition constant by fructose (mol m−3)KI,Glu inhibition constant by glucose (mol m−3)Kmh Michaelis constant for sucrose hydrolysis

(mol m−3)K1–K5 kinetic constants for fructosyl-stevioside

synthesist reaction time (h)tmax maximum reaction time (h)Vmh maximum rate constant for sucrose

hydrolysis (mol m−3 h−1)

2. Materials and methods

2.1. Materials

All reagents were of analytical grade. Stevioside andsucrose (Wako Pure Chemical Industries, Ltd., Japan) wereused as the substrates.�-fructofuranosidase fromArthrobac-ter sp. was kindly donated by Bio Research Corporation ofYokohama, Japan. This enzyme is well known to catalyzenot only the transfructosylation of various materials havinga hydroxyl group (acceptor) with sucrose (donor) [15–18],but also the sucrose hydrolysis [15,17]. Thus, glucose andfructose formed by the latter reaction were the side productsin this system.

2.2. Fructosyl-stevioside synthesis

The synthesis experiments of fructosyl-stevioside wereperformed in a 5.0 × 10−4 m3 Erlenmeyer flask containinga 1.0× 10−4 m3 substrate solution. The flask was shaken in

Table 1Experimental conditions for fructosyl-stevioside synthesis

Run no. CSte,0 (mol m−3) CSuc,0 (mol m−3) CFru,0 (mol m−3) CGlu,0 (mol m−3) CE,0 (units m−3)

1 0.5 20 0 0 2.0 × 10−5

2 0.5 40 0 0 2.0 × 10−5

3 1.0 20 0 0 2.0 × 10−5

4 0.5 20 0 0 4.0 × 10−5

5 0.5 20 40 0 2.0 × 10−5

6 0.5 20 0 40 2.0 × 10−5

Table 2Experimental conditions for sucrose hydrolysis

Run no. CSuc,0

(mol m−3)CFru,0

(mol m−3)CGlu,0

(mol m−3)CE,0

(units m−3)

7 20 0 0 2.0 × 10−5

8 40 0 0 2.0 × 10−5

9 20 0 40 2.0 × 10−5

10 20 40 0 2.0 × 10−5

a water bath (313 K) at a well-mixed condition. The initialconcentrations of stevioside and sucrose were varied in therange 0.5–1.0 mol m−3 and 20–40 mol m−3, respectively.The initial enzyme concentration ranged from 2.0 × 105 to4.0× 105 units m−3. Here, “unit” denotes the enzyme activ-ity, and 1 unit is defined as the amount of enzyme required totransfer 1× 10−6 mol of the fructosyl residue from sucroseto xylose per minute. In order to investigate the effect of theside product addition, the synthesis experiments were alsoperformed under the condition in which 40 mol m−3 glu-cose or fructose was initially added to the reaction solution.The experimental conditions are summarized in Table 1.The condition of Run No. 1 was set to be the control one.

2.3. Sucrose hydrolysis

In order to estimate the kinetic constants for the sucrosehydrolysis, the experiments were performed in the sameway without stevioside. The initial concentrations of sucroseand the side products were varied in the range 20–40 and0–40 mol m−3, respectively. The experimental conditions aresummarized in Table 2.

2.4. Analysis

The sample solution was withdrawn at a specific timeinterval and heated at 373 K for 5 min to inactivate the en-zyme. Afterwards, the solution was filtered using an ultrafil-ter (USY-1, Toyo Roshi Kaisha, Ltd., Japan) to remove theenzyme and was analyzed using an HPLC system (L-6200,Hitachi, Ltd., Japan) with an amino column (NH2P-50 4E,Showa Denko K.K., Japan). The concentrations of steviosideand the saccharides in the sample were determined by a UVdetector (210 nm) and a refractive index detector, respec-tively. The mobile phase was acetonitrile:water= 75:25 and

K. Suzuki et al. / Biochemical Engineering Journal 10 (2002) 207–215 209

the flow rate was 1.67× 10−8 m3 s−1. The standard reagentof fructosyl-stevioside is not commercially available. In thechromatogram of the sample, there were only two peaksfor stevioside and fructosyl-stevioside. The stevioside wasconsidered to be transformed into only fructosyl-stevioside.On the basis of the material balance of stevioside, therefore,the fructosyl-stevioside concentration was calculated usingthe following equation:

CFSte= CSte,0 − CSte (1)

Here,Ci is the concentration of componenti. Ste and FSterepresent stevioside and fructosyl-stevioside, respectively.The subscript 0 denotes the initial value.

Fig. 1. Effects of initial concentrations of substrates and enzyme on time courses of the respective component concentrations in fructosyl-steviosidesynthesis: (a)CSte,0 = 0.5 mol m−3, CSuc,0 = 20 mol m−3, CE,0 = 2.0×105 units m−3 (control condition); (b)CSte,0 = 0.5 mol m−3, CSuc,0 = 40 mol m−3,CE,0 = 2.0× 105 units m−3; (c) CSte,0 = 1.0 mol m−3, CSuc,0 = 20 mol m−3, CE,0 = 2.0× 105 units m−3; (d) CSte,0 = 0.5 mol m−3, CSuc,0 = 20 mol m−3,CE,0 = 4.0× 105 units m−3. (�) Stevioside, (�) fructosyl-stevioside, (�) sucrose, (�) fructose, (�) glucose. Solid lines, the calculated values by modelfor fructosyl-stevioside synthesis, Eqs. (13)–(17).

3. Results and discussion

3.1. Effects of initial concentrationsof substrates and enzyme

Figure 1 shows the effects of the initial concentrationsof the substrates and the enzyme on the time courses ofthe respective component concentrations. The ordinates ofthe upper figure denote the concentrations of steviosideand fructosyl-stevioside, and those of the lower figure, theconcentrations of the saccharides. In Fig. 1(a), the exper-imental stevioside concentration, indicated by the circlesymbol, decreased for 24 h and then gradually increased.The change of the fructosyl-stevioside concentration,


indicated by the square symbol, was opposite to that ofthe stevioside concentration and the maximum value wasobtained at 24 h. On the other hand, the sucrose concen-tration decreased and reached almost 0 after 24 h. Theconcentrations of glucose and fructose increased up to24 h and then asymptotically approached constant values.Therefore, the transfructosylation of stevioside and thesucrose hydrolysis were confirmed to occur in this sys-tem. In addition, the hydrolysis of fructosyl-stevioside wasfound to occur [19] and this reaction became dominantafter the depletion of sucrose. As the initial sucrose con-centration increased to 40 mol m−3 (Fig. 1(b)), the periodin which sucrose existed in the system was longer andthe maximum concentration of fructosyl-stevioside becamehigher. This is because the amount of the fructosyl-donor,sucrose, increased. When the initial stevioside concentra-tion increased to 1.0 mol m−3 (Fig. 1(c)), the maximumconcentration of fructosyl-stevioside became higher. How-ever, the depletion time of sucrose hardly changed. Thisis because the initial stevioside concentration was muchlower (1/40 to 1/20) than that of sucrose. When the ini-tial enzyme concentration increased to 4.0 × 105 units m−3

(Fig. 1(d)), the consumption rates of stevioside and sucrosebecame faster. However, the maximum concentration offructosyl-stevioside did not change. This is because therewas no difference in the amounts of the fructosyl-donor, su-crose, and acceptor, stevioside, between this condition andthe control one. The lines in the figure will be discussedlater.

Fig. 2. Effects of side-product addition on time courses of substratesin fructosyl-stevioside synthesis: circle, stevioside; diamond, sucrose;all lines, calculated values by model for fructosyl-stevioside synthesis,Eqs. (13)–(27).

3.2. Effects of side product addition

Figure 2 shows the time courses of the substrate con-centrations obtained under the conditions with and withoutthe side product addition. In the presence of fructose, theconcentrations of stevioside and sucrose decreased moreslowly than those without the side products. In the presenceof glucose, the consumption rates of both substrates weresignificantly lower. The synthesis of fructosyl-steviosidewas considered to be inhibited by glucose as was the casefor the transfructosylation of sucrose [20–22]. In addition,the reaction was found to be slightly suppressed by fructose.The lines will be discussed later.

4. Construction of kinetic model

4.1. Derivation of model equations

Chambert et al. [23–25] reported that the transfructosy-lation of levan with sucrose followed the Ping-Pong Bi Bimechanism [26]. The transfructosylation of stevioside withsucrose was considered to follow the same mechanism asschematically shown in Fig. 3(a). The free enzyme, E, reactswith sucrose, Suc, to form the first complex, E·Suc. Glucose,Glu, is then released from E·Suc to form the second com-plex, E·Fru. This complex reacts with stevioside to form thethird complex, E·FSte, and then FSte is released. In this sys-tem, not only the transfructosylation, but also the hydrolysisreactions of sucrose and fructosyl-stevioside simultaneously

Fig. 3. Schematic diagram of Ping-Pong Bi Bi mechanism for eachreaction: (a) fructosyl-stevioside synthesis; (b) sucrose hydrolysis; (c)fructosyl-stevioside hydrolysis.


Fig. 4. Conceptual scheme of overall reaction mechanism forfructosyl-stevioside synthesis.

occurred as described in the section of the experimental re-sults. Such hydrolysis reactions, which have the Ping-PongBi Bi mechanism with water as the second substrate, areknown to give the apparent Ordered Uni Bi kinetics [26]. Inthis system, the hydrolysis reactions were assumed to followthe mechanisms as shown in Fig. 3(b) and (c). In addition,the synthesis of fructosyl-stevioside was suppressed by notonly glucose but also fructose as described in the sectionof the experimental results. It is necessary to take into ac-count the competitive inhibition by glucose and fructose.The conceptual scheme of the overall reaction mechanismis shown in Fig. 4. Here,k1 to k12 denote the rate constantsof the respective elementary reactions. The complexes ofthe enzyme and the side products, E·Glu and E·Fru∗, wereconsidered to be inactive. The time derivatives of the con-centrations of the respective components are given as

dCSte

dt= −k4CSteCE·Fru + k5CE·FSte (2)

dCFSte

dt= k6CE·FSte− k7CECFSte (3)

dCSuc

dt= −k1CECSuc+ k2CE·Suc (4)

dCGlu

dt= k3CE·Suc− k9CECGlu + k10CE·Glu (5)

dCFru

dt= k8CE·Fru − k11CECFru + k12CE·Fru∗ (6)

Here,Ci andCE·i denote the concentrations of componentiand enzyme-componenti complex, respectively. Assuming apseudo-steady-state for the respective concentrations of theenzyme complexes gives the following equations:

dCE·Suc

dt= 0 = k1CECSuc− k2CE·Suc− k3CE·Suc (7)

dCE·Fru

dt= 0 = k3CE·Suc− k4CE·FruCSte

+k5CE·FSte− k8CE·Fru (8)

dCE·FSte

dt= 0 = k4CE·FruCSte− k5CE·FSte

+k6CE·FSte− k7CECFSte (9)

dCE·Glu

dt= 0 = k9CECGlu − k10CE·Glu (10)

dCE·Fru∗

dt= 0 = k11CECFru − k12CE·Fru∗ (11)

The total concentration of the enzyme in the system is

CE,Total = CE + CE·Suc+ CE·Fru + CE·FSte

+CE·Glu + CE·Fru∗ (12)

Rearranging Eqs. (7)–(12) and substituting them intoEqs. (2)–(6) gives the following model equations:

dCSte

dt= −K1VmhCSteCSuc+ K5VmhCFSte

σ(13)

dCFSte

dt= K1VmhCSteCSuc− K5VmhCFSte

σ(14)

dCSuc

dt= −K1VmhCSteCSuc− VmhCSuc

σ(15)

dCGlu

dt= K1VmhCSteCSuc+ VmhCSuc

σ(16)

dCFru

dt= VmhCSuc+ K5VmhCFSte

σ(17)

Here,σ in Eqs. (13)–(17) is

σ =Kmh

{K1K2CSteCSuc+K1

(1+ CGlu

KI,Glu+ CFru

KI,Fru

)CSte

+CSuc

Kmh+ K3CFSte+ K4CSteCFSte

+1 + CGlu

KI,Glu+ CFru

KI,Fru

}(18)

The nine constants in Eqs. (13)–(18) are

Vmh = k3k8

k3 + k8CE,Total (19)

Kmh = k8

k1

k2 + k3

k3 + k8(20)

KI,Glu = k10

k9(21)

KI,Fru = k12

k11(22)

K1 = k4k6

k8(k5 + k6)(23)

K2 = k1

k6

k3 + k6

k2 + k3(24)

K3 = k7

k8

k5 + k8

k5 + k6(25)

K4 = k4k7

k8(k5 + k6)(26)

K5 = k5k7

k1k3

k2 + k3

k5 + k6(27)


Fig. 5. Flowchart for calculation procedure of model constants.

SubstitutingCSte = 0 andCFSte = 0 into the model equa-tions, Eqs. (13)–(17), gives the following equations:

dCSuc

dt= −VmhCSuc

CSuc+ Kmh(1 + CFru/KI,Fru + CGlu/KI,Glu)

(28)

dCGlu

dt= VmhCSuc


(29)

dCFru

dt= VmhCSuc


(30)

These equations describe the sucrose hydrolysis and thereare four unknown constants,Vmh, Kmh, KI,Glu andKI,Fru.

4.2. Estimation of model constants

The four constants for the sucrose hydrolysis were es-timated by fitting the experimental results for the sucrosehydrolysis with Eqs. (28)–(30).Vmh depends on the totalconcentration of free enzyme in the system based on mole,CE,Total. However, it is difficult to determineCE,Total. By in-troducing an imaginary initial concentration of free enzymebased on unit of enzyme activity,CE,0, Vmax(=Vmh/CE, 0)

(mol unit−1 h−1) was estimated instead ofVmh.

A flowchart for the calculation procedure of the constantsis shown in Fig. 5. Using an arbitrary set of constants, thesimultaneous differential equations were numerically solvedby means of the Runge–Kutta method. The time step forthe numerical calculation was set at 0.01 h. The best fittedvalues of the constants were determined using the Simplexmethod [27] by minimizing the squared-sum of the relativeerrors between the calculated values and the four sets of theexperimental data obtained under the various conditions asshown in Table 2.

The other constants,K1–K5, are estimated by fitting theexperimental results for the fructosyl-stevioside synthesiswith Eqs. (13)–(17) using the estimated values of the con-stants for the sucrose hydrolysis. The calculation procedurewas the same as that mentioned above. The six sets of theexperimental results as shown in Table 1 were used.

4.3. Application of the model

4.3.1. Sucrose hydrolysisThe experimental and the fitted results for the sucrose

hydrolysis under the various conditions are shown in Fig. 6.Under all conditions, the calculated lines are in agreementwith the experimental results. For the initial sucrose con-centration of 40 mol m−3 (Fig. 6(b)), however, there was aslight difference in the concentrations of glucose and fruc-tose between the experimental and the calculated results.One possibility for this discrepancy was that isomerizationfrom fructose to glucose occurred [28].


Fig. 6. Experimental and fitted results for sucrose hydrolysis: (a)CSuc,0 = 20 mol m−3; (b) CSuc,0 = 40 mol m−3; (c) CSuc,0 = 20 mol m−3,CGlu,0 = 40 mol m−3; (d) CSuc,0 = 20 mol m−3, CFru,0 = 40 mol m−3. (�) Sucrose, (�) fructose, (�) glucose. Solid lines, the calculated values by modelfor sucrose hydrolysis, Eqs. (28)–(30).

Table 3Estimated values of constants for sucrose hydrolysis

Constant Estimated value Literature value [15]

Vmax (mol unit−1 h−1) 1.23×10−4 –Kmh (mol m−3) 10.2 9.1KI,Fru (mol m−3) 0.198 –KI,Gru (mol m−3) 1.25 –

The estimated values of the constants are listed in Table 3.The estimated value of the Michaelis constant for the sucrosehydrolysis,Kmh, of 10.2 mol m−3 was close to the literaturevalue of 9.1 mol m−3 [15]. There were no literature valuesfor the other constants.

4.3.2. Fructosyl-stevioside synthesisThe fitted results for the fructosyl-stevioside synthesis are

shown in Figs. 1 and 2 by the lines. The estimated valuesof the constants are listed in Table 4. For the concentrationsof stevioside and fructosyl-stevioside, the fitted lines were

Table 4Estimated values of constants for fructosyl-stevioside synthesis

Constant Estimated value

K1 (m3 mol−1) 0.0982K2 (m3 mol−1) 0.233K3 (m3 mol−1) 0.0138K4 (m6 mol−2) 0.135K5 (–) 0.690

in good agreement with the experimental results under allconditions. On the other hand, the fitted lines for the su-crose concentration decreased slower than the experimentalones and those for the concentrations of glucose and fruc-tose increased slower. Thus, the hydrolysis rate of sucrosecalculated by the model was less than that obtained in theexperiments. This is because the estimation of model con-stants were conducted in two stages as described in Section4.2. The constants for sucrose hydrolysis were obtained bythe fitting with the experimental results for sucrose with noaddition of stevioside. In the presence of the surface-activeagents, the hydrolysis rates of the saccharides, such as cel-lulose [29–33] and xylose [34], were reported to becomelarger than those without the surface-active agents. Stevio-side has both hydrophilic and hydrophobic structures [1,2],as is the case for the common surface-active agents. There-fore, the surface-active effect of stevioside was consideredto contribute to the increase in the hydrolysis rate of su-crose. The effect of stevioside was not taken into accountin the constants for sucrose hydrolysis, so that the simu-lated lines cannot strictly describe the hydrolysis behaviorof sucrose in Figs. 1 and 2, where stevioside was added.

The calculated and experimental values for the maximumconversion of stevioside are listed in Table 5. The reactiontime giving the maximum value is also shown in the table.The calculated value for the maximum conversion becamehigher with an increase in the initial sucrose concentration.The reaction time giving the maximum value became shorterby increasing the initial enzyme concentration. These ten-dencies were in agreement with those in the experiments,


Table 5Maximum conversion of stevioside and reaction time for obtaining maximum value

CSte,0 (mol m−3) CSuc,0 (mol m−3) CE,0 (units m−3) Calculated Experimental

Maximumconversion (−)

Reactiontime (h)

Maximumconversion (−)

Reactiontime (h)

0.5 20 2.0 × 10−5 0.514 19.4 0.56 240.5 40 2.0 × 10−5 0.709 27.6 0.75 361.0 20 2.0 × 10−5 0.514 20.2 0.51 240.5 20 4.0 × 10−5 0.522 10.2 0.55 12

although the experimental value for the reaction time hada error of about±6 h due to the sampling interval. Thus,the model can predict not only the appropriate conditionsto efficiently synthesize the fructosyl-stevioside but also thereaction time giving the maximum conversion.

5. Conclusions

The synthesis experiments of fructosyl-stevioside wereconducted under various conditions of the initial concen-trations of substrates and enzyme. The transfructosylationof stevioside and the sucrose hydrolysis were confirmedto occur in this system. In addition, the hydrolysis offructosyl-stevioside was found to simultaneously occur.The fructosyl-stevioside synthesis was inhibited by the sideproducts, glucose and fructose. The kinetic model was con-structed by considering the Ping-Pong Bi Bi mechanismfor the transfructosylation, the apparent Ordered Uni Bimechanism for the hydrolysis and the competitive inhibitionby the side products. The model constants were estimatedby fitting the model equations with the experimental re-sults for the sucrose hydrolysis and the fructosyl-steviosidesynthesis. The model can predict not only the appropriateconditions to efficiently synthesize the fructosyl-steviosidebut also the reaction time giving the maximum conversion.

Acknowledgements

The authors wish to thank Dr. K. Fujita of Bio Re-search Corporation of Yokohama, Japan, for donating�-fructofuranosidase.

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kinetic model for synthesis of fructosyl-stevioside using suspended β-fructofuranosidase

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