Mathematical model for enzymatic
production of fructo-oligosaccharides
from sucrose
Kyung Hoon Jung, Jong Won Yun, Kyung Rae Kang, Jai Yun Lim
and Jae Heung Lee
R & D Centre, Cheil Sugar & Co., Ltd., Kyonggi-Do, South Korea
The production of fructo-oligosaccharides by the action of fructosyltransferase was investigated at
55°C and pH 5.5. Enzyme kinetic studies with various substrates such as sucrose, 1-kestose, and
fructofuranosyl nystose revealed that the formation of fructo-oligosaccharides occurred from a
consecutive set of disproportionation reactions (viz. GF, + GF, ~ GF,_I + GF,+I). On the basis of
these experimental results, a mathematical model was proposed and computed. Although the data
points were scattered to some extent, good agreement was found between the model and experimental
results.
Keywords: Fructo-oligosaccharides; fructosyltransferase; disproportionation reactions; reaction mechanism; mathematical model
Introduction
Materials and methods
Fructo-oligosaccharides, ~ in which one to three fructose units are bound to the beta-2,1 position of sucrose, are mainly composed of 1-ketose (GFz), nystose
(GF3), and fructofuranosyl nystose (GF4). The fructooligosaccharides which may be used in so-called
health food are produced commercially from sucrose
by the action of a fructosyltransferase system. This
enzyme has been found in fungi such as Aspergillus
sp.,2 Fusarium sp. ,3,4 and Aureobasidium sp. 5
In our previous work, 6 conditions for the production of fructosyltransferase were studied. In the
present investigation, preliminary characterization of
this enzyme preparation was conducted. These included optimum reaction conditions in terms of pH
and temperature, determination of kinetic parameters
such as Km and Vmax values, and enzyme kinetic
studies with various substrates. Based on these experimental results, a possible reaction mechanism was
proposed and a mathematical model describing this
mechanism was compared with experimental data.
Substrates
Address reprint requests to Dr. Lee at the R & D Centre, Cheil
Sugar & Co., Ltd., 522-1 Dokpyung-Ri, Majang-Myon, Ichon-Kun,
Kyonggi-Do, South Korea
Received 16 January 1988; revised 9 August 1988
@1989 Butterworth Publishers
1-Kestose, nystose, and fructofuranosyl nystose were
purchased from Daichi Gakagu pharmaceutical company (Tokyo, Japan). Other chemicals used were
reagent grade.
Enzyme
The fructosyitransferase used in this study was prepared in this laboratory by growing Aureobasidium
pullulans. The procedure for this enzyme preparation
was described previously. 6
Enzyme assay
Unless otherwise specified, fructosyltransferase activity was determined by measuring the release of
glucose in the reaction mixture described below. One
fructosyltransferase unit is defined as the amount of
enzyme activity required to produce one micromole of
glucose per minute under the following conditionsS:
pH 5.5, temperature 55°C, and reaction mixture consisting of 7.5 ml of 80% (w/v) sucrose, 2.3 ml of 0.1 M
citrate buffer (pH 5.5), and 0.2 ml enzyme sample. The
enzyme reaction was stopped by heating at 100°C for
10 min and the released glucose was measured.
Enzyme Microb. Technol., 1989, vol. 11, August
491
Papers
Kinetic studies
100
Unless otherwise specified, enzyme reactions were
carried out for 1 h at 55°C and pH 5.5 in test tubes
containing 10 ml of reaction mixture as described
above. When other substrates instead of sucrose were
used, only the sucrose was replaced. Throughout the
course of this work, 5 units of enzyme per gram
substrate were employed. The enzyme reaction was
stopped by heating and the reaction products were
analyzed.
80
I
m
Ot
m
0
•
ti
I
Analytical method
Enzyme reaction products were analyzed by highpressure liquid chromatography (HPLC, Waters Associates Model 244, equipped with a differential refractometer RI-401 detector), using the Ix Bondapak carbohydrate column (0.4 x 30 cm). A mixture of
acetonitrile/distilled water (75:25, v/v) was used as
the mobile phase at a flow rate of 1.5 ml min -].
40
20
0
I
I
I
I
2
4
6
8
10
PH
Figure 2 Effect of pH on fructosyltransferase activity: phosphate buffer (ll) citrate buffer (O)
Results and discussion
Effect of temperature and pH
The influence of temperature on fructosyltransferase
activity was investigated by measuring activity in the
temperature range of 40 to 70°C. As shown in Figure
I, the curve of enzyme activity is fairly symmetrical
and maximum activity was measured at 55°C.
The effect of pH on enzyme activity was tested by
measuring the amount of 1-kestose produced in buffers
a t p H ranging from 3 to 8 because sucrose may be
hydrolyzed at lower pH values. The enzyme was
active above pH 5 but the optimum pH was found to
be 5.5 (Figure 2).
10o
A
60
N
E
~e
m
Determination of kinetic parameters
The effects of sucrose, l-kestose, or nystose concentration on fructosyltransferase activity were investigated at 55°C and pH 5.5. The Km and Vmax values for
each
substrate
were
determined using the
Lineweaver--Burk plot. As illustrated in Table 1,
increases in the number of fructose units in the substrate resulted in decreased Vmax and increased Km
values. These kinetic parameters obtained from experiments were used in later computer simulation studies.
In order to investigate any types of enzyme inhibition that may occur in the enzyme system, glucose in
the range 20--80 g 1-] was added to the reaction
system with sucrose as a substrate. In Figure 3, the
reaction rate with and without glucose is shown. The
competitive type of inhibition by glucose was evident
and the value of the inhibition constant K~ was
determined to be 30 g 1-1. Similar experiments were
also carried out to determine whether the enzyme
reaction might be inhibited by one of the other components such as sucrose, l-kestose, nystose, and
fructofuranosyl nystose. As a result, it was concluded
that the effect of inhibition caused by the other components was negligibly small.
50
Proposed mechanism for enzyme reaction
E
In order to investigate the enzyme reaction mechanism
involved in the production of fructo-oligosaccharides,
N
C
i
Table 1 Km and Vmaxvalues for various substrates
}/jr
I
40
I
I
l
I
50
60
70
80
Temperature
Figure 1
activity
492
Influence of temperature
(°C)
on fructosyltransferase
Enzyme Microb. Technol., 1989, vol. 11, August
Sub.rate
GF
GFF
GFFF
Vmax(gl l h 1)
Km (g 1-1 )
130
30
16
330
750
850
Mathematical model for production of fructo-oligosaccharides: K. H. Jung et al.
nystose were produced from 1-kestose, while 1kestose and fructofuranosyl nystose were formed from
nystose. Therefore, one can generally express the
enzyme reaction as follows:
GFn + GF, ~ GF,-1 + GF,+I
J=
m
4
If n is equal to 1, GF,-1 becomes equal to GF0 which
indicates glucose.
In Figure 4 an enzyme reaction mechanism network
is shown together with the molecular weights of substrates and products. The sucrose as a starting substrate undergoes a number of enzyme reaction steps to
yield 1-kestose, nystose, and fructofuranosyl nystose.
As shown in Figure 4, the enzyme reactions are
eventually accompanied by the liberation of glucose. It
is worthwhile to note that further enzyme reaction
with fructofuranosyl nystose as a substrate did not
occur in up to 50 h in a batch enzyme reaction system
at 55°C and pH 5.5, probably due to its small Wmax
value and its large Km value.
0
0
ql=
X
3
,'1>
1
4 °~
i
t /
-2
I
I
I
I
I
2
4
6
8
10
1 X103 ( i g _ l )
Development o f mathematical model
According to the proposed mechanism as shown in
Figure 4, 8 moles of sucrose disappear to form 4 moles
of glucose and 4 moles of 1-kestose. The rate of
sucrose disappearance may be written:
Figure 3 Lineweaver-Burk plots of enzyme reaction rates
using sucrose as a substrate with and without glucose or
1-kestose. Without glucose (©), 40 g 1-1 glucose supplemented
(B), 40 g 1-1 1-kestose supplemented (e)
dS
dt
enzyme reactions with various substrates were carried
out as illustrated in Table 2. When glucose plus
fructose were used as substrates, no enzyme reaction
occurred. When sucrose was employed as a substrate,
however, only both glucose and l-kestose were produced. The molar ratio of glucose to 1-kestose was
found to be about 1 : l, indicating that a disproportionation reaction mechanism was involved, i.e. sucrose
acts as either a donor or an acceptor so that 1 mole of
glucose and 1 mole of 1-kestose are formed simultaneously from 2 moles of sucrose:
GF+GF~G
2 × 342
Vmk"K
+ 4 × 50-----~ " (Kmk + K)
Substrate
+ GFF
dG
4 × 180
d---t = 8 × 342
Concentration
(g 1-1)
250
F
250
300
400
600
300
400
600
300
400
600
GFF
GFFF
Vms" S
[Kms + S + (Kms/Kig)G]
(2)
Data for enzyme reaction studies with various substrates
G
GF
(1)
where S indicates sucrose, G indicates glucose, K
indicates 1-kestose, Vms indicates Vma, for sucrose,
Vmk indicates Vmax for 1-kestose, Kms indicates the
Michaelis constant for sucrose, Kink indicates the
Michaelis constant for 1-kestose, and Kig indicates a
competitive inhibition constant for glucose.
The rate of glucose production can be expressed:
Similar reaction patterns were found with other substrates such as 1-kestose and nystose. Sucrose and
Table 2
Vms" S
[Kms + S + (Kms/Kig)G]
Products a
GF._I (g 1-1)
GFn+I (g 1-1)
Molar ratio
(GF._I/GFn.I)
10.3
11.8
13.4
1.7
2.5
4.0
1.0
1.9
3.5
29.2
34.7
29.5
4.3
6.6
9.0
1.7
2.8
6.1
0.98
0.96
1.26
0.78
0.84
0.86
1.23
1.10
0.94
Enzyme reactions were carried out for 20 min instead of 1 h at 55°C and pH 5.5
Enzyme Microb. Technol., 1989, vol. 11, August
49:3
Papers
8 x 342
600
8GF4
I
500
4 G F2 •
4 x 504
A
400
•
•
300
GF
2 x 666
2o0
2
100
1-kestose.
4 x 504
Vr~s" S
8 X 342
[Kms + S + (Kms/Kig)G]
Vmk " K
504
+ - (Kink+K)
2 x666
-
=
-
2 x 666
4 x 504
-
Vmn " N
(Km.+N)
(3)
Vmk " K
(Kmk+ K)
Vmn " N
(Km. + N)
(4)
Finally, the rate of fructofuranosyl nystose production is given by:
dP
828
Vmn " N
d--~- = 66------~
2 x
" (Kin, + N)
(5)
where P indicates fructofuranosyl nystose.
The simultaneous integration of the differential
equations describing the proposed mechanism was
carried out using a digital computer with a fixed step
size of 0.1 h. As illustrated by Figure 5, which shows
the computer curve and the experimental data, good
agreement was found between the model and the
experimental results, although the data points were
scattered to some extent. Therefore, it appears that
494
40
50
10
20
30
40
50
the production of fructo-oligosaccharides by the action
of fructosyltransferase occurs from a consecutive set
of disproportionation reactions. It should be mentioned that small amounts of fructose (below 1%) were
also accumulated slowly as the enzyme reaction progressed. The production of fructose is most likely due
to the action of another enzyme such as invertase as a
contaminant in the fructosyltransferase enzyme preparation.
Nomenclature
where N indicates nystose, Vm~ indicates Vmax for
nystose, and Kmn indicates the Michaelis constant for
nystose.
With respect to the production of nystose, 2 moles
of nystose are produced from 4 moles of 1-kestose and
the nystose formed is removed to form 1 mole of
fructofuranosyl nystose and 1 mole of 1-kestose.
dt
30
ical model at 55°C and pH 5.5. (A) 50% sucrose, (B) 65% sucrose.
Glucose (O), sucrose (Q), 1-kestose (A), nystose (IlL fructofuranosyl nystose (~)
The rate of 1-kestose production is complicated: 4
moles of 1-kestose are produced from 8 moles of
sucrose and 1 mole of 1-kestose is formed from 2
moles of nystose. Simultaneously 2 moles of nystose
and 2 moles of sucrose are also formed from 4 moles of
dN
20
Figure 5 Comparison of experimental data with the mathemat-
Figure 4 Network of the proposed reaction mechanism
-
10
Tlmelh)
1 GF 4
!
'.
dK
dt
•
0
O F2
4 x 828
•
Enzyme Microb. Technol., 1989, vol. 11, August
F
G
K
fructose concentration (g 1-~)
glucose concentration (g l -J)
1-kestose concentration (g 1-~)
competitive inhibition constant for glucose
Kig
(g 1-1)
Kink
Krnn
Krns
N
P
S
t
Vmk
Vms
Michaelis constant for 1-kestose (g 1-l)
Michaelis constant for nystose (g 1-l)
Michaelis constant for sucrose (g 1-l)
nystose concentration (g 1-l)
fructofuranosyl nystose concentration (g l-l)
sucrose concentration (g 1-1)
time (h)
maximum velocity for 1-kestose (g 1-l h l)
maximum velocity for nystose (g 1-l h -l)
maximum velocity for sucrose (g 1-1 h -1)
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1
2
3
4
5
6
Hidaka, H., Eida, T., Adachi, T. and Saitoh, Y. Nippon
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Gupta, A. K. and Bhatia, I. S. Phytochemistry 1982, 21,
1249-1253
Smith, J. A., Grove, D., Luenser, S. J. and Park, L. G. US Pat.
4 309 505 (1982)
Jung, K. H., Lira, J. Y., Yoo, S. J., Lee, J. H. and Yoo, M. Y.
Biotechnol. Lett. 1987, 9, 703-708