A. Vrsalović Presečki, Z. Findrik, Đ. Vasić-Rački: Mathematical modeling of amylase catalyzed starch …
Mathematical modeling of amylase catalyzed starch hydrolysis
Ana Vrsalović Presečki, Zvjezdana Findrik, Đurđa Vasić-Rački
Faculty of Chemical Engineering and Technology, University of Zagreb, Marulićev trg 19,
HR-10000 Zagreb, Croatia, Phone: +385 (1) 4597-157, Fax: +385 (1) 4597-133, E-mail:
[email protected]
The first step of starch hydrolysis, i.e. liquefaction process has been studied in this work. Two
commercial α-amylases from Bacilllus licheniformis, known as Termamyl and Liquozyme
have been used for this purpose. pH and temperature dependence of both enzymes activity has
been examined. Using the starch as the substrate, the kinetics of both enzymes has been
determined at optimal pH and temperature (pH 7, T = 80 °C). Impact of glucose and maltose
to the initial reaction rate was also studied. All kinetic data were collected by the initial
reaction rate method. Kinetics of both enzymes was described by Michaelis-Menten kinetics
with uncompetitive product inhibition. With the estimated kinetic parameters, mathematical
models were developed and validated in the repetitive batch and fed-batch reactor. Significant
enzyme deactivation was noticed in the starch hydrolysis catalyzed by Termamyl. By the
action of Termamyl, glucose and maltose yield was 7 % and 12 % respectively. In the
hydrolysis catalyzed by Liquozyme the yield of 16 % on glucose and of 22 % on maltose was
observed
Introduction
Enzymatic starch hydrolysis is one of the most important enzymatic reactions that is carried
out at an industrial scale (Baks et al. 2006). It is usually performed in a batch reactor by twostep procedure (Paolucci-Jeanjean et al. 2000). During the first step, so called liquefaction,
starch is dissolved in water and partially hydrolyzed to oligosaccharides with an α-amylase
(Figure 1). In the second step, so called saccharification, saccharifying enzymes
(glucoamylase, pullulanase) transform liquefied starch into final products which can be
specific oligosaccharides, glucose, maltose, or a mixture of hydrolysates named
maltodextrins.
α
α
α = α - amylase
α
α
starch
α
α
α
α
α
α
[pH 6.0; 95-105 °C; 90 min]
α
oligosaccharides
Figure 1. Starch hydrolysis – liquefaction
α-Amylases are endoglucanases that catalyze the hydrolysis of internal α-1,4-glycosidic
linkages of polysaccharides to yield dextrins, oligosaccharides, maltose and D-glucose. These
enzymes can be found in animals, plants, bacteria and fungi (Kazaz et al. 1998). They are
classified as the most important industrial enzymes and are used in different processes in
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A. Vrsalović Presečki, Z. Findrik, Đ. Vasić-Rački: Mathematical modeling of amylase catalyzed starch …
food, textile, pharmaceutical industries, etc. α-Amylases can hydrolyze both insoluble starch
and starch granules held in aqueous suspension (Apar & Özbek 2005).
Before designing a successful hydrolysis system catalyzed by α-amylase, besides information
of optimal reaction conditions (pH and temperature) it is necessary to describe phenomena
which affect the kinetics (Hill et al. 1997). This can be an important tool for developing the
process for the large scale production. The knowledge of enzyme kinetics provides us to
develop a mathematical model of the process (Vasić-Rački et al. 2003). Model can be used to
find optimal operation points and to enable identification of the most effective reactor mode
for performing the reaction (Vasić-Rački et al. 2003a).
Termamyl and Liquozyme, two commercial α-amylases were used for starch hydrolysis in
this work. Detailed kinetic study was performed in order to develop a mathematical model.
Developed model was validated in two types of reactor.
Materials and methods
Materials
Starch from maize, glucose, maltose and KH2PO4 were purchased from Fluka (Switzerland).
K2HPO4, was obtained from Kemika (Croatia). Two α-amylases with the commercial names
Liquozyme and Termamyl, used in this work, were purchased from Novozymes (Denmark).
Analytical methods
Starch concentration was determined using the iodine solution (5 mM I2 and 5 mM KI) on the
spectrophotometer at 580 nm. The test contained 0.9 mL of iodine solution and 0.1 mL of
sample. Absorbance was converted to starch concentration using the calibration chart
prepared each day.
HPLC (Shimadzu, Japan) with a C18 column (Carbohydrate Ca 2+, 300 x 6.5 mm, CSChromatographie service GmbH) and RI detector was used for determination of maltose and
glucose concentrations. The analysis was performed at 80 °C with the flow of mobile phase
(redistilled water) of 0.5 cm3 min. Before analysis, the samples were filtered using the
membrane filter with the pore size of the 0.2 µm (Chromafil CA 20-25 supplied by MachereyNagel) to remove amylase and starch from the reaction solutions. The retention times of
maltose and glucose were 7.5 and 10.0 min respectively.
α-amylase assay
Measurements of the α-amylase activity were carried out in a 5 cm3 reactor. The reactor was
thermostated at 80 ºC, and the enzyme concentration was 0.1 % (v/v). Samples were taken out
every minute in a total time of five minutes. Starch concentration was determined
immediately using the iodine solution as it was described above. Activity of amylase was
defined as mg of starch hydrolyzed per minute per cm3 of enzyme.
Reactor experiments
Starch hydrolysis catalyzed by α-amylase was performed in repetitive batch and fed-batch
mode at 80°C in the 0.1 M phosphate buffer pH 7.
Experiments performed in the repetitive batch mode were carried out in a 50 cm3 glass batch
reactor with the initial starch concentration of 20 g dm-3. The start of the experiment was
approximated by adding the amylase (0.1 % (v/v)). The sampling was continued at the regular
time intervals. When the substrate concentration dropped to approximately zero, fresh starch
was added. The product was not charged out of the reactor. Subsequent addition of starch was
repeated two or three times in each experiment.
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A. Vrsalović Presečki, Z. Findrik, Đ. Vasić-Rački: Mathematical modeling of amylase catalyzed starch …
Fed-batch experiments were carried out in a 500 cm3 reactor. Initial working volume was 100
cm3. The initial starch concentration was 20 g dm-3 and the concentration of amylase was 0.5
% (v/v). After initial amount of starch was hydrolyzed the reactor was put in the fed batch
mode. Starch concentration in the feed was 47 g dm-3 and flow on the peristaltic pump was set
at 0.51 cm3 min-1. In all experiments starch was diluted in a 0.1 mol dm-3 phosphate buffer pH
7.
Initial reaction rate measurements and data processing
The kinetic parameters of the Michaelis-Menten equations (Km, Vm and Ki) were estimated
from experimental data using the initial reaction rate method. Initial reaction rates were
defined as the decrease of starch concentration per minute during the first five minutes of
hydrolisys. The initial reaction rates as a function of starch concentration define the
Michaelis-Menten plots. From these plots kinetic parameters were estimated by non linear
regression analysis using the simplex or least squares method implemented in "Scientist"
software package. The numerical values of the parameters were evaluated by fitting the
Michaelis-Menten kinetic model (Table 1, Eq. (1)) to the experimental data. The calculated
data were compared with the experimental data, recalculated in the optimization routine and
fed again to the integration step until minimal error between experimental and integrated
values was achieved (built-in Scientist). The set of optimum parameters was used for the
simulation according to the model equations (Table 1, Eq (2)-(10)). The residual sum of
squares was defined as the sum of the squares of the differences between experimental and
calculated data. The "Episode" algorithm for stiff system of differential equations,
implemented in the "Scientist" software package, was used for the simulations. It uses
variable coefficient Adams-Moulton and Backward Differentiation Formula methods in the
Nordsieck form, treating the Jacobian matrix as full or banded (Scientist handbook).
Results and Discussion
α-Amylases kinetics
In this work two α-amylases, commercial name Termamyl and Liquozyme, were investigated
in the reaction of starch hydrolysis. Before the kinetics measurements were performed, the
optimal temperature and pH was determined. For that purpose the activity of these enzymes in
the temperature interval from 40 °C to 80 °C and in pH range from 5.5 to 8.0 were measured.
Maximum activity of both enzymes was obtained at 80 °C and at pH 7. Further investigations
were carried out using these conditions.
α-Amylases kinetics was determined by the initial reaction rate method. Dependence of the
initial reaction rate on the starch concentration was determined. Product inhibition in the
reaction of starch hydrolysis was also investigated. Impact of the glucose and maltose on the
initial reaction rate was examined. The results suggested that both products inhibit the rate of
the reaction catalyzed with both biocatalysts. According to the literature, glucose and maltose
were found to act as the uncompetitve inhibitor to the α-amylases (Apar & Özbek 2007).
Hence, the kinetics of starch hydrolysis catalyzed by these enzymes was described by
Michelis-Menten kinetic model with uncompetitive product inhibition (Eq. (1)). Parameters of
the model (Table 1) were estimated from experimental data using the non-linear regression.
The estimated parameters show that α-amylase – Liquozyme has a higher activity in the
reaction of starch hydrolysis than the enzyme Termamyl. Assigned Km values point out that
Termamyl has more affinity toward starch as substrate. Values of inhibition constants show
that the both enzymes are more maltose inhibited than glucose. Also it could be seen that the
rate of starch hydrolysis catalyzed by Liquozyme is less product inhibited (higher Ki values)
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A. Vrsalović Presečki, Z. Findrik, Đ. Vasić-Rački: Mathematical modeling of amylase catalyzed starch …
Table 1. Kinetic parameters of starch hydrolysis catalyzed by α-amylases
Parameter
Value
α-amylase - Termamyl
Vm [mg cm-3 min-1]
5402.4 ± 464.2
Km [g dm-3]
17.1 ± 1.5
-3
glucose
Ki
[g dm ]
47.2 ± 4.1
K imaltose [g dm-3]
12.2 ± 1.1
α-amylase - Liquozyme
Vm [mg cm-3 min-1]
6230.4 ± 609.8
-3
Km [g dm ]
18.8 ± 1.4
-3
glucose
Ki
[g dm ]
101.0 ± 7.5
K imaltose [g dm-3]
34.7 ± 3.3
Mathematical model of starch hydrolysis catalyzed by α-amylases
The reaction rate of starch hydrolysis catalyzed by α-amylases was described using MichaelisMenten equations with uncompetitive product inhibition (Eqs. (1)):
r=
ϕ α −amylase ⋅Vm ⋅ cstarch

cglucose
c
K m + cstarch  1 + glucose + maltose
K imaltose
 Ki



(1)
The parameters of this equation have been determined by independent measurements.
The mass balances for the starch hydrolysis in the batch and fed batch reactor are based on the
following assumptions:
- the reactor contents are considered homogenous in axial and radial directions
- energy balance was not considered since effective temperature control was accomplished reactor was thermostated
Mass balances for the experiments performed in the batch or repetitive batch reactor, are
given by equations for starch, glucose and maltose (Eqs. (2)-(4)).
dcstarch
= −r
dt
dcglucose
= Yglucose/starch ⋅ r
dt
dcmaltose
= Ymaltose/starch ⋅ r
dt
(2)
(3)
(4)
Deactivation of the first order for α-amylase was incorporated in the mathematical model (Eq.
(5)).
dVm
= − kdα -amylase ⋅ Vm
(5)
dt
The parameters like yield and enzyme deactivation would be estimated directly from the
reactor experiments.
Assumed reactor model for the experiments carried out in the fed-batch-mode consist of the
balances for starch, glucose and maltose (Eqs. (6)-(8)).
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A. Vrsalović Presečki, Z. Findrik, Đ. Vasić-Rački: Mathematical modeling of amylase catalyzed starch …
dcstarch − cstarch + c0,starch
=
qc0 − r
dt
V
dcglucose
cglucose
=−
qc0 + Yglucose/starch ⋅ r
dt
V
dcmaltose
c
= − maltose qc0 + Ymaltose/starch ⋅ r
dt
V
(6)
(7)
(8)
Since the main characteristic of this type of experiment is a constant increase of the reaction
media volume (Eq. (10)), a dilution of enzyme is included in the mathematical model (Eq.
(9)).
dϕ α-amylase
dt
=−
ϕ α-amylase
V
qc0
(9)
dV
= qc 0
dt
(10)
Equation for the α-amylase deactivation (Eq. (5)) is also considered for the experiments
carried out in the fed-batch mode.
Starch hydrolysis in the reactors
Kinetic measurements proved that the reaction catalyzed by both enzymes is not strongly
product inhibited. First the experiments were carried in the repetitive batch mode with three
or four starch addition and then in the fed-batch mode. In the both reactors product was not
charged out of the reactor. These experiments are useful to estimate the enzyme deactivation
during its long term use.
Repetitive batch reactor
Starch hydrolysis catalyzed by Termamyl and Liquozyme in the repetitive batch mode is
presented in the Figure 2.
30
30
enzyme addition:
ϕTermamyl = 0.001
A
20
starch
glucose
maltose
model
B
25
-3
c [g dm ]
-3
c [g dm ]
25
starch
glucose
maltose
model
15
10
5
20
15
10
5
0
0
0
50
100
150
200
t [min]
250
300
350
400
0
50
100
150
200
250
300
350
400
t [min]
Figure 2. Starch hydrolysis catalyzed by α-amylase in the repetitive batch experiment (T= 80
°C, 0.1 mol dm-3 phosphate buffer pH 7, Vreactor = 50 cm3): A) α-amylase – Termamyl
(φTermamyl0 = 0.001); B) α-amylase – Liquozyme (φLiquozyme0 = 0.00043)
During the experiment very fast deactivation of Termamyl was remarked in the first cycle
(Figure 2A). The deactivation was described by the first order kinetic (Eq. (5)) and the
deactivation constant was estimated from the experimental data ( kdTermamyl = 0.054 min-1).
Since the hydrolysis of starch in the second cycle was very slow, the fresh enzyme was added
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A. Vrsalović Presečki, Z. Findrik, Đ. Vasić-Rački: Mathematical modeling of amylase catalyzed starch …
at the time of 108 minute. The amount of added enzyme was as at the beginning of the
experiment. It enabled to hydrolyze cca 20 g/l starch for additional three times. The
subsequently added enzyme was less deactivated ( kdTermamyl = 0.012 min-1). In the experiment
with Liquozyme, enzyme deactivation was also noticed. The deactivation was lower
( kdLiquozyme = 0.0053 min-1) than in the experiment with Termamyl. Hence, with two times
lower initial Liquozyme concentration than it was in experiment with Termamyl, the starch
hydrolysis was successful in three cycles. From the experimental results glucose and maltose
yield was calculated and the values are given in the Table 2.
Table 2. Glucose and maltose yield in the starch hydrolysis catalyzed by α- amylase
Value
Parameter
Termamyl
Liquozyme
-1
Yglucose/starch [g g ]
0.07
0.12
-1
Ymaltose/starch [g g ]
0.16
0.22
With both enzyme yields of maltose are higher that those of the glucose. Higher maltose and
glucose concentration are obtained in the starch hydrolysis catalyzed by Liquozyme, but still
there are approximately 64 % of other oligosaccharides that was not hydrolyzed by this
amylase. It is evident that with these amylases it is not possible to produce glucose for the
ethanol production and that the second step of sacchariffication catalyzed by glucoamylase is
necessary (Roy & Gupta 2003).
As it could be seen the developed mathematical model (Eq (1)-(5)) with the estimated
deactivation constants and yields describes the experimental data well.
Fed-batch reactor
Results of the experiments that were carried out in the fed-batch reactor are presented in the
Figure 3.
25
starch
glucose
maltose
model
B
starch
glucose
maltose
model
20
-3
c [g dm ]
enzyme addition:
ϕTermamyl = 0.0045
20
-3
c [g dm ]
25
A
15
fed-batch
started
10
5
15
fed-batch
started
10
5
0
0
0
100
200
300
t [min]
400
500
600
0
100
200
300
400
500
600
t [min]
Figure 3. Starch hydrolysis catalyzed by α-amylase in the fed-batch experiment (T= 80 °C,
0.1 mol dm-3 phosphate buffer pH 7, Vreactor0 = 100 cm3, cstarch,feed = 47.2 g dm-3, qfeed = 0.51
cm3min-1): A) α-amylase – Termamyl (φTermamyl0 = 0.005); B) α-amylase – Liquozyme
(φLiquozyme0 = 0.005)
These experiments were started as a batch and the starch feed began after all initial amount of
starch was hydrolyzed (18 minutes).
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A. Vrsalović Presečki, Z. Findrik, Đ. Vasić-Rački: Mathematical modeling of amylase catalyzed starch …
In the experiment with Termamyl (Figure 3A), enzyme lost its activity very fast ( kdTermamyl =
0.032 min-1). Therefore fresh amount of enzyme was added at the time of 257 minute as it is
indicate in the Figure 3A. The new amount of enzyme was deactivated with the similar rate
( kdTermamyl = 0.023 min-1).
In the starch hydrolysis catalyzed by Liquozyme (Figure 3B) enzyme has also been
deactivated ( kdLiquozyme = 0.0067 min-1) but slowlier than in the case of Termamyl. The
conversion of starch was always more than 90 % during the experimental time of 510 minute.
The results of the fed-batch experiments have also been described well with the proposed
mathematical model (Eq. (1), (5)-(10)). It is necessary to mention that the yield of maltose
and glucose are the same as the one calculate in the repetitive batch experiments (Table 2).
By comparing these two enzymes in two types of reactors, a few remarks could be drawn. αAmylase – Liquozyme is a better catalyst for starch hydrolysis than Termamyl because it
shows a higher stability at the optimal conditions (T = 80 °C, pH 7). Also by this enzyme a
higher yield on maltose and glucose is achieved, which means that starch hydrolysate
produced by Liquozyme posses a lower concentration of higher oligosaccharides. The
oligosaccharides should be hydrolyzed by the action of some saccharifying enzymes. More
concentrated product is obtained by hydrolysis performed in the repetitive batch than in the
fed batch mode. The reason is relatively low starch concentration in feed and high flow rate
which result with a significant dilution of product and enzyme as well. The feed concentration
is limited by starch insolubility in the water. Flow rate is determined by the pump
characteristic. Hence the optimal way to hydrolyze starch according to the results is to use αamylase - Liquozyme and the reactor in the repetitive batch mode.
Conclusion
Detailed kinetic study of the starch hydrolysis catalyzed by α-amylases at the optimal
conditions, Termamyl and Liquozyme, enabled us to develop a mathematical model. The
developed model described with high accuracy the experimental data from repetitive batch, as
well as from fed-batch reactor mode. Remarkably strong enzyme deactivation was noticed in
the experiments with Termamyl. Higher concentrations of maltose and glucose were obtained
in the starch hydrolysate produced by Liquozyme
List of symbols
c
kd
ki
Km
q
r
t
T
V
Vm
Y
φ
concentration, g dm-3
deactivation constant, g dm-3
inhibition constant, g dm-3
Michaelis-Menten constant, g dm-3
flow rate, cm3 min-1
reaction rate, g dm-3 min-1
time, min
temperature, °C
reactor volume, dm3
maximal activity, mg cm-3 min-1
yield, volume ratio, cm3cm-3
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A. Vrsalović Presečki, Z. Findrik, Đ. Vasić-Rački: Mathematical modeling of amylase catalyzed starch …
Acknowledgment
This research was supported by the Croatian Ministry of science, education and sport by grant
125-1252086-2793. The authors gratefully acknowledge Novo Nordisk A/S (Denmark) for
the gift of Termamyl and Liquozyme.
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