JOURNALOF FERMENTATION
ANDBIOENGINEERING
Vol. 86, No. 3, 324-331. 1998
The Kinetics and Mechanism of a Reaction Catalyzed by Bacillus
stearothermophilus Phosphoglucose Isomerase
ARIEF WIDJAJA,’ MASAHIRO SHIROSHIMA,’
TAKASHI OKA,’ MASAHIRO YASUDA,’ HIROYASU
KAZUTAKA
MIYATAKE,2 HIROSHI NAKAJIMA,3 AND HARUO ISHIKAWA’*
OGINO,’
Department of Chemical Engineering,’ Department of Applied Biological Chemistry,2 Osaka Prefecture University, 1-I
Gakuen-cho, Sakai, Osaka 599-8531 and Basic Technology Department, Research and Development
Center, Unitika Ltd., 23 Kozakura, Uji, Kyoto 611-0021,3 Japan
Received 6 April 199WAccepted 18 June 1998
The initial rates of isomerization between glucose 6-phosphate and fructose Q-phosphate catalyzed by Bacillus
stearothermophilus pbospboglucose isomerase (PGI) were measured in both the forward and reverse reactions.
Although B. stearothermophilus PGI is a tetrameric enzyme, the reaction rate vs substrate concentration
curves for both reactions exhibited Michaelis-Menten kinetic behavior. This was confirmed by the Hill plot
which gave the Hill coefficient of 1.0 for both reactions. Based on the above experimental results and another
experimental result that the number of substrate or product binding sites on the PGI molecule was 4, we propose
a reaction scheme which is able to explain Michaelis-Menten kinetic behavior of this oligomeric enzyme, and
determine the kinetic parameters.
[Key words:
kinetics,
fructose 6-phosphate]
mechanism,
tetrameric
enzyme,
Materials
from Unitika
isomerase,
glucose
6-phosphate,
SDS-polyacrylamide
gel electrophoresis
was purchased
from New England Biolabs, Inc. (Massachusetts,
USA),
and that for gel chromatography
was from Serva
Feinbiochemica
GmbH. & Co. (Heidelberg,
Germany).
Monosodium
salt of G6P and disodium salt of F6P were
purchased from Sigma (St. Louis, MO, USA), ~-[l-l~C]glucose 6-phosphate
from NEN (Tokyo), and glucose
6-phosphate
dehydrogenase
(G6PDH),
NADP+,
triethanolamine
(TEA), MgC12, and other chemicals from
Wako Pure Chemical Ind. Ltd. (Osaka).
Solutions were made up in 0.1 M TEA buffer solutions
containing
0.1 M HCl and adjusted to pH 8.0 using an
aqueous KOH solution.
Stability of B. stearothermophilus
PGI
To study
the stability of B. stearothermophilus
PGI, a solution
containing
2.1 x 1O-5 mM PGI in 0.1 M TEA buffer
(pH 8.0) was incubated at 30°C. After various incubation periods, 50,ul aliquots of the enzyme solution were
taken and each was added to 2950~1 of a reaction
mixture
containing
8.40 mM F6P, 1.0 mM NADP+,
2.0U/ml
G6PDH in 0.1 M TEA buffer (pH 8.0). The
activity of the enzyme was measured by determining the
rate of G6P formation
by the reverse reaction at 30°C
using the method described below.
Gel chromatography and SDS-polyacrylamide
gel electropboresis
Gel chromatography
experiments
were
performed using a Hiload 16/60 Superdex 200 p.g. gel
filtration
column which was equilibrated
with 10 mM
Tris-HCl buffer containing
150mM NaCl. Two ml of
1.32 x 10 4 mM PGI solution
was loaded onto the
column and was eluted at a rate of 1 ml/min at 4°C with
the same buffer. As a standard, a mixture containing the
marker proteins DNP-r.-alanine
(molecular mass: 0.255
kDa), cytochrome C (12.3 kDa), myoglobin (17.8 kDa),
chymotrypsinogen
A (25 kDa), egg albumin
(45 kDa),
bovine serum albumin (67 kDa), rabbit muscle aldolase
(160 kDa), bovine catalase (240 kDa), and horse spleen
ferritin (450 kDa) was applied to the same column.
SDS-polyacrylamide
gel electrophoresis was performed
Phosphoglucose
isomerase
(PGI: D-glucose 6-phosphate ketoisomerase;
EC 5.3.1.9) is widely distributed in
nature and catalyses the isomerization
reaction between
glucose 6-phosphate
(G6P) and fructose 6-phosphate
(F6P). PGI is physiologically
very important
as it is
an enzyme of the glycolytic pathway. Furthermore,
PGI
plays an important
role in the industrial production
of
fructose 1,6-diphosphate
(FDP), which is expected to be
useful for various medical applications,
from glucose
(1).
Purification of PGI has been achieved from mesophilic
sources, such as human erythrocyte (2, 3), spinach leaves
(4), brewer’s yeast (5, 6), and rabbit muscle (7), as well
as from thermophilic sources, such as Bacillus caldotenax
(8) and Bacillus stearothermophilus
(9). For analytical
or industrial
applications
thermophilic
PGI is suitable
due to its high thermostability.
There is some information available concerning the kinetics and mechanism of
the reaction catalyzed by the mesophilic PGI, however
almost none exists concerning the kinetics and mechanism
of the reaction catalyzed by the thermophilic PGI.
In the present work, the initial rates of both the forward and reverse reactions of the isomerization
between
G6P and F6P catalyzed by PGI of the thermophilic
organism B. stearothermophilus at pH 8.0 and 30°C under
various G6P or F6P concentration
conditions,
and the
time courses of the increase in the G6P concentration
produced by the reverse reaction were measured. Furthermore, experiments concerning the molecular mass of the
enzyme and the number of substrate or product binding
sites per molecule were performed. Based on these experimental results, we propose a reaction mechanism.
MATERIALS
phosphoglucose
AND METHODS
B. stearothermophilus
PGI was obtained
Ltd. (Osaka). The protein marker kit for
* Corresponding author.
324
VOL. 86, 1998
REACTION MECHANISM OF B. STEAROTHERMOPHKUS
at 10 mA for 4 h according to the method of Weber and
Osborn (10) at a 7% gel concentration.
As a standard, a
mixture containing the marker proteins MBP-/3-galactosidase (175 kDa), MBP-paramyosin
(83 kDa), glutamic
dehydrogenase
(62 kDa), aldolase (47.5 kDa) and triosephosphate isomerase (32.5 kDa), was used.
The number of substrate or product binding sites on
The number of substrate
B. stearothermophilus PGI
or product binding sites on PGI was measured by the
dialysis equilibrium
method (11). The experiments were
carried out in a dialysis equilibrium
apparatus consisting
of two jacketed acrylic resin cells each with a working
volume of 0.7 ml. Temperature-regulated
water was circulated inside the jackets to maintain the temperature
at
30°C. A Teflon-coated magnetic stirrer bar was placed in
each of the cells to stir the liquid inside the cells. One of
the compartments
(compartment
I) was filled with 0.1 M
TEA buffer (pH 8.0) containing
52 PM PGI, while the
other (compartment
II) was filled with 0.1 M TEA buffer
containing
0.15-10mM
G6P which contained
D-[l14C]-G6P. The ratio of the labeled G6P molar concentration to the total G6P molar concentration
ranged from
0.00021 to 0.19 when the buffers containing labeled G6P
were prepared.
As in previous investigations,
Visking
Cellophane dialysis tubing was used as a membrane for
separating
the two compartments.
Twenty-five
~1 of
liquid sample was taken from each compartment
for determination
of the concentration
of labeled G6P using a
liquid scintillation
counter (Wallac 1409 model, Pharmacia). In the present experiment, the total concentrations
of D-[~-‘~C]-G~P and D-[~-‘~C]-F~P, and of G6P and
F6P were measured because F6P was produced by the
catalytic action of the enzyme. When equilibrium
was
attained between the solutions in the two compartments,
the next run was carried out by replacing the solution
in compartment
II with fresh ligand (G6P) solution of a
different concentration.
A small amount of the enzyme
solution was added to compartment
I to compensate for
the sample withdrawn for analysis. The time required to
attain the equilibrium state was 4 d. The total concentration of ligands (G6P and F6P) bound to the enzyme was
determined
by the difference in concentrations
between
the two compartments.
The initial rates of the forward reaction
To obtain
the initial rates of the forward reaction of the isomerization between G6P and F6P (the reaction in which G6P is
the substrate and F6P is the product), the F6P concentrations
were measured
by the calorimetric
method
described by Roe (12). A 10 ml-volume vial, with a jacket
in which temperature-regulated
water at 30°C was circulated, was used as the reactor. Fiveml of a substrate
solution
containing
0.3-25 mM G6P in 0.1 M TEA
buffer (pH 8.0) was stirred with a Teflon-coated magnetic
stirrer bar. After the solution temperature reached 30°C
100/d of the enzyme solution (the final concentration
was 1.97 x lo- 7 mM PGI) was added to the solution to
initiate the reaction. At appropriate time intervals, liquid
samples of 1 ml each were taken and mixed immediately
with 4 ml of a 0.01 M HsP04 solution (pH 1.6) to stop
the reaction. The analytical procedure was as follows: (i)
0.4 ml of ethanol containing
0.5% wt. resorcinol and
1Oml of 36% HCl were added to 5 ml of the sample
solution,
and the mixture was stirred vigorously.
(ii)
The mixture was heated in a water bath at 80°C for 8
min, and then cooled to 25°C. (iii) Using a Shimadzu
UV-2100 spectrophotometer
(Shimadzu Co. Ltd., Kyoto)
PGJ
325
the absorbance was measured at 405 nm to determine the
F6P concentration.
To measure
The initial rates of the reverse reaction
the initial rates of the reverse reaction of the isomerization between G6P and F6P (the reaction in which F6P is
the substrate and G6P is the product), the G6P formed
was converted to a stoichiometrically
equivalent amount
of NADPH according to the following reaction:
G6P+NADP+G=
glucono-&lactone
6-phosphate
+NADPH
(1)
Then, the formation
of G6P was followed indirectly
by measuring
the absorbance
change due to NADPH
formation
at 340nm (~~~=6220 M ~‘.crn~ ‘) using the
Shimadzu
UV-2100 spectrophotometer.
The reactions
were carried out at 30°C in total volume 3.0 ml of 0.1 M
TEA buffer (pH 8.0) containing
0.05-7.0mM
F6P,
2.0U/ml
G6PDH,
and 5.26~ 10 ’
1.0 mM NADP+,
mM PGI.
Time courses of the increase in G6P concentration
produced by the reverse reaction
To measure the
time courses of the G6P concentration
produced by the
reverse reaction, 100 ,nl of the enzyme solution (the final
concentration
was 5.26x lop6 mM PGI) was added to
the reactor containing
2- 10mM F6P in 0.1 M TEA
buffer (pH 8.0) to start the reaction. At appropriate time
intervals, 200ml aliquots of liquid samples were taken
and each was mixed promptly
with 0.8 ml of HjPOd
(pH 1.6) to stop the reaction. Then, to these solutions
NADP+ and G6PDH were added (the final concentrations were 1 mM and 0.1 U/ml, respectively),
and the
concentrations
of G6P produced
were measured by following the absorbance
change due to NADPH formation at 340 nm using the spectrophotometer.
RESULTS AND DISCUSSEON
Stability of B. stearothermophilus PGI
Figure 1
shows the experimental
results as a plot of the relative
remaining activity vs the incubation
period on a semilogarithmic scale. As shown in the figure, the experimental results were correlated well with a straight line generated by the linear regression method. The slope of the
straight line gave the inactivation
rate constant of the
enzyme, kd=1.76x
lop4 hh’, which was equivalent to a
half-life of 164 d. This result assured us that the effect of
enzyme inactivation
on the isomerization
reaction was
negligible in all the reaction experiments
because the
measurements
of the time courses of the G6P or F6P
concentration
were always completed
within 90 min.
However, 3.7% inactivation
of PGI may have occurred
during the dialysis equilibrium
experiments
where the
longest experimental period was 12 d. We do not believe
that this inactivation
led to significant errors in the determination of the number of binding sites of the enzyme.
Gel chromatography and SDS-polyacrylamide
gel electrophoresis
The experimental
elution
volumes
of
DNP-L-alanine,
cytochrome
C, myoglobin,
chymotrypsinogen A, egg albumin, bovine serum albumin,
rabbit
muscle aldolase, bovine catalase, and horse spleen ferritin
were 126.2, 98.0, 94.4, 91.8, 82.0, 75.4, 67.4, 65.8, and
44.0 ml, respectively.
These experimental
results are
well described by the following equation:
In m=17.7078-0.0842
I’,,
(2)
326
WIDJAJA
ET AL.
J. FERMENT. BIOENG.,
kDa
._:
140.”
d
”
0
1’
100
”
83
200
Time (d)
FIG. 1. Stability of B. stearothermophilus PGI. The experimental relative remaining activity was plotted against the length of incubation period. A solution containing 2.1 x 10ds mM PGI (1.58 U/ml)
in 0.1 M-TEA buffer (pH 8.0) was incubated at 30°C. After various
incubation periods, 50 ,ul aliquots of the enzyme solution were taken
and each was added to 2950~1 of a reaction mixture containing
8.4OmM F6P, l.OmM NADP+, 2.0U/ml G6PDH in 0.1 M TEA
buffer (pH 8.0). The activity of the enzyme was measured by determining the rate of G6P formation by the reverse reaction at 30°C
using the method described in the experimental section.
62
--
47.5
32.5
where m and Vel represent the molecular mass [Da] and
the elution volume [ml], respectively. In correlation analysis, the data for DNP-L-alanine
and horse spleen ferritin were excluded because their molecular masses are too
small and too large, respectively, compared with that of
the enzyme PGI. When PGI was applied to the column,
the elution volume was 66 ml. Therefore, the molecular
mass of PGI was determined to be 189 kDa using Eq. 2.
This value was in good agreement with the values reported by Unitika (200 kDa; Enzymes, p. 73, a brochure
published by Unitika) and by Muramatsu
and Nosoh
(172 kDa) (9). The concentration
of the enzyme PGI expressed throughout
this paper was calculated based on
the molecular mass of I89 kDa.
Figure 2 shows the result of the SDS-polyacrylamide
gel electrophoresis
of B. steurothermophilus PGI. Only
one band corresponding
to a molecular mass of 50 kDa
appeared.
From this result and that of the molecular
mass, we conclude
that B. stearothermophilus PGI
consists of four subunits of identical molecular mass.
Takama and Nosoh (8) found that B. caldotenax PGI
consists of four identical subunits based on the results
of dansylation
and cyanogen bromide cleavage of the
enzyme. Furthermore,
they found that it shares many
common
properties
with B. stearothermophilus PGI.
The experimental
results obtained in the present work
are in good agreement with their findings.
The number of substrate or product binding sites of
In order to clarify the mechanism of the isomeriPGI
zation reaction between G6P and F6P, it is very important to know the number of substrate or product
binding sites of B. stearothermophilus PGI.
The number of binding sites on a protein for ligands
(small molecules or ions) can be determined
using the
following equation (13, 14).
[Fl@WW[Bl
=Kd
(3)
Here, Kd represents the dissociation
constant,
[F] the
concentration
of free ligand, [B] the concentration
of
bound ligand per total protein concentration
and n the
number of binding sites. By plotting the experimental
results as [B]/[F] vs [B], the number of binding sites and
FIG. 2. SDS-polyacrylamide gel electrophoresis of B. sfearothertnophilus PGI. SDS-polyacrylamide gel electrophoresis was performed at 10 mA for 4 h at a 7% gel concentration. As a standard
(lane 3) a mixture containing the marker proteins MBP+galactosidase (175 kDa), MBP-paramyosin (83 kDa), glutamic dehydrogenase
(62 kDa), aldolase (47.5 kDa) and triosephosphate isomerase (32.5
kDa), was used. The single band (lanes 1 and 2) obtained corresponds
to the molecular mass of 50 kDa.
the dissociation constant can be obtained from the intercept of the abscissa and the slope of the straight line,
respectively.
This method is valid in principle when small molecules
or ions bind to proteins without any catalytic action by
the proteins after binding. However, several investigators
(11, 15, 16) successfully used this method to determine
the number of substrate or product binding sites of an
enzyme.
There are three possibilities concerning the number of
the binding sites of the tetrameric enzyme PGI. First,
there are four binding sites per molecule. In this case,
the enzyme works as a tetrameric enzyme as it consists
of four active units. Second, there are two binding sites,
and the enzyme works as a dimer-like enzyme. Third,
there is only one binding site so that the tetrameric PGI
works as a monomer-like
enzyme.
The results of the dialysis equilibrium
experiments are
given in Table 1. The values of [B] and [F] calculated
from the data are shown in Fig. 3 as a plot of [B]/[F] vs
[B]. The largest experimental
[B] value was 3.1. It is
clear that the number of the binding sites on the enzyme
is neither one nor two. The figure shows that the data
points may be correlated by a straight line or a convex
downward curve. The straight line which correlates the
data points intersects the abscissa at a [B] value of about
3.4. However, a convex downward curve will intersect at
a [B] value which is greater than 3.4. Because there is no
possibility that the number of the binding sites is 3, it
can be concluded that the number of the binding site on
B. stearothermophilus PGI is four, that is, one binding
site per subunit.
REACTION MECHANISM OF B. STEAROTHERMOPHIL
VOL. 86, 1998
TABLE 1.
Run no.
1
2
3
4
5
6
Total amount of ligandsb
in compartments 1 and 11
Wmol)
6.93
I.37
0.646
0.357
0.180
0.108
US PGI
327
Results of dialysis equilibrium experiments
Total count in
compartment 1
(dpm)
8.00X 104
6.98 x lo5
3.32 X 10’
5.99 x 105
2.99 x 105
1.30x 106
Total count in
compartment II
(dpm)
7.75 x IO”
6.22 x lo5
2.85 X lo5
4.85% 105
2.37~ lo5
9.91 )r 105
Total concentration of
ligandsb in compartment 1
(M)
5.03 x 10-j
1.03x10 J
4.97 x 10 4
2.82- 10 4
1.44* 10 ‘I
8.72~ 10m5
Total concentration of
ligandsb in compartment Ii
(M)
4.87:t 10 3
9.22,, 10 j
4.26:. 10 -I
2.28 ‘<10 4
1.14:. 10 4
6.68 10 5
a dpm=disintegrations
per minute.
b ligands=both the substrate G6P and the product F6P.
Columns 3 and 4 show the total counts [dpm] for the labeled ligands in compartments 1 and II, respectively. Column 5 shows the total concentration of the free and bound ligands in compartment I. Column 6 shows the total concentration of the free ligands in compartment II. From
the experimental results of Run no. 1, the values of [B] and [F] can be calculated as follows: as the working volume of each compartment was
0.7 ml, the total concentration of the ligands in compartment 1 is calculated as
(8.00x 104/(8.00X 104+7.75X 104)X6.93)/0.7/1000=5.03x
10m3M
The total concentration of the ligands in compartment 11, which is equal to [F], is calculated in the same way. The total concentration of ligands
bound to the enzyme is given by the difference between the concentrations shown in columns 5 and 6. Using an enzyme concentration of 52 PM,
[B] is calculated as:
[B]=(5.03 x 10m~3-4.87 % 10m3)/52x IO- 6=3.1
For other runs, the values of [B] and [F] can be calculated in the same way.
Initial reaction rates of the forward and reverse reactions
Figure 4 shows the experimental
forward reaction rates as a plot of the reaction rate v vs the G6P
concentration
[G6P], and Fig. 5 the experimental reverse
reaction rates as a plot of -v vs the F6P concentration
[F6P]. The lines in these figures are the theoretical ones
and will be explained later. Both the figures show that
the Iv I -[S] curves are hyperbolic, indicating that both
the reactions exhibit Michaelis-Menten
kinetic behavior.
To check Michaelis-Menten
kinetic behavior,
the data
shown in Figs. 4 and 5 were replotted as I v I /(v,,/ v I)
vs [F6P] or [G6P] on a logarithmic
scale in Figs. 6
and 7, respectively.
In both figures, the data could be
correlated well with a straight line. From the slopes of
the straight lines, the Hill coefficients were determined to
be 1.0 in both the cases. This demonstrates
that the
I v I -[S] curves of the forward and reverse reactions
exhibit Michaelis-Menten
kinetic behavior despite the fact
that B. stearothermophifus
PGI is a tetrameric enzyme,
each of the subunits having one substrate or product
binding site.
Time courses of the increase in G6P concentration of
the reverse reaction
Figure 8 shows the time courses
of the increase in the G6P concentration
formed by the
_r
6000 -
E
g
4000 -
reverse reaction. As can be seen in the figure, the higher
the initial concentration
of F6P, the longer it takes to
reach equilibrium.
However,
90min
was a sufficient
period of time for the four initial F6P concentrations
tested to reach equilibrium.
The lines appearing in the figure are the theoretica
values which will be explained later.
Mechanism
As shown above, B. stearothermophilus PGI is a tetrameric enzyme consisting of four subunits, each of which has one binding site for substrate
or product.
Furthermore,
the Iv ~-[S] curves of the
forward and reverse reactions of isomerization
between
G6P and F6P catalyzed by B. stearothermophilus
PGI
exhibited Michaelis-Menten
kinetic behavior. This was
confirmed by the Hill plots which give the Hill coefficient of 1.0 for both the reactions.
The v- [S] curves of the reactions catalyzed by oligomerit enzymes usually exhibit sigmoidal behavior and
sometimes
exhibit Michaelis-Menten
kinetic behavior.
The sigmoidal behavior of the v- [S] curves of the reactions catalyzed by oligomeric enzymes was fully analyzed
by Monod et al. (17) and Koshland et a/. ( 18). However,
.
0
0
a
E
a
2000 -
0
0
~‘~~I~,~~I~,*~‘~“’
0
I
2
3
IBl (-)
W[Fl
vs [Bl.
WPI
4
FIG. 3. Plot of [B]/[F] vs [B] to determine the number of binding
sites of B. steurothermophilus PGI. The dialysis equilibrium experiments were carried out to determine the number of substrate or
product binding sites on PGI. The values of [B] and [F] were calculated from the data shown in Table 1 and are shown as a plot of
0.01
FIG. 4.
0.02
0.03
(M)
Initial rates of the forward reaction catalyzed by B.
sfearothermophilus PGI. The initial rates of the forward reaction were
measured at 30°C in 0.1 M TEA buffer (pH 8.0) containing 0.325 mM G6P and 1.97 x 10 -’ mM PGI. F6P concentration was determined by the calorimetric method described by Roe. The detailed
procedure is described in the experimental section. The solid line was
calculated using Eq. 6 and the kinetic parameters kl and KS listed
in Table 2.
328 WIDJAJA ET AL.
J. FERMENT.BIOENG.,
.
0
I
I
I
0.002
0.004
0.006
lF6PJ
I
0.008
(M)
FIG. 5. Initial rates of the reverse reaction catalyzed by B.
sfeurothermophilus PGI. The initial rates of the reverse reaction were
measured at 30°C in a total volume of 3.0ml of 0.1 M TEA buffer
@H 8.0) containing 0.05-7.0 mM F6P, 1.OmM NADP c, 2.0 U/ml
G6PDH, and 5.26 x lo-’ mM PGI. The formation of G6P was followed indirectly by measuring the absorbance change due to NADPH
formation at 340nm (&s@=6220 Mm1.crn--‘) using a Shimadzu UV2100 spectrophotometer. The solid line was calculated using Eq. 7 and
the kinetic parameters k, and KP listed in Table 2.
Michaelis-Menten
behavior of the reactions catalyzed by
oligomeric enzymes has not yet been analyzed in full.
Ishikawa et al. (19) studied the effects of the reaction
schemes and the kinetic parameters on the co-operativity
of the reaction catalyzed by a dimeric enzyme. For the
reaction StiP catalyzed by a dimeric enzyme, the reaction schemes were considered on the basis of the KNF
model (18). The rate equation for each of the possible
schemes was derived on the basis of the combined
steady-state
and rapid-equilibrium
assumptions.
They
found that even if interaction
occurred between the distinct protomers or subunits, the sigmoidal rate behavior
was not necessarily observed. On the other hand, the
deviation
of the V- [S] curve from the hyperbola
associated with Michaelis-Menten
kinetic behavior could
be observed even if there was no interaction between the
distinct protomers
or subunits.
Thus, they found that
Michaelis-Menten
kinetic behavior could be observed to
occur even for a reaction catalyzed by an oligomeric
100
k
0.0001
0.00001
0.001
W’l
0.01
(MI
FIG. 7. Hill plot of the initial rates of the reverse reaction catalyzed by B. stearothermophilus PGI. The data shown in Fig. 5 were
replotted as 1v //(v,,/vi) vs [F6P]. The data in the region where
O.l< /vl/(v,,1v I)< 10 were correlated by a straight line using
the linear regression method. From the slope of the straight line, the
Hill coefficient was determined to be 1.O.
enzyme.
Based on the above theoretical analysis, Ishikawa et
al. (20) clarified the kinetics and mechanism of the ATP
regeneration reaction catalyzed by B. stearothermophilus
acetate kinase, which consists of four subunits but can
be treated as a dimer-like enzyme because its functional
unit consists of two subunits (21). The rate equation
derived based on the Random Bi Bi mechanism and on the
KNF model offered a good explanation of the experimental Iv 1- [S] curves in which the forward reaction exhibited Michaelis-Menten
behavior while the reverse reaction exhibited sigmoidal behavior. We believe that this
was the first investigation
which clarified wholly the
kinetics and mechanism of a reversible reaction catalyzed
by an oligomeric enzyme.
0.008
,
1
I
I
0.006
_j
E
ii;
0.004
Z
0.002
0
I
0
20
I
I
I
40
60
,
I
80
,
100
Time (min)
WPI Of)
FIG. 6. Hill plot of the initial rates of the forward reaction catalyzed by B. stearothermophilus PGI. The data shown in Fig. 4 were
replotted as v/(v,,,- v) vs [G6P]. The data in the region where
0.1< V/(Y,, -v)< 10 were correlated by a straight line using the
linear regression method. From the slope of the straight line, the
Hill coefficient was determined to be 1.O.
FIG. 8. Time courses of the increase in G6P concentration. The
time courses of the increase in G6P concentration produced by the
reverse reaction were measured at 30°C in 0.1 M TEA buffer (pH 8.0)
containing 5.26 X 10m6mM PGI. F6P concentrations were 2 mM (A),
3 mM ( n ), 5 mM (+) and 10 mM (0). At appropriate time intervals,
200 ~1 aliquots of the liquid samples were taken and each was mixed
promptly with 0.8 ml of HXPOI (pH 1.6) to stop the reaction. Then,
to these liquid samples NADP+ and G6PDH were added (the final
concentrations were 1 mM and 0.1 U/ml, respectively), and the concentrations of G6P produced were measured spectrophotometrically
by following the absorbance change due to NADPH formation at
340 nm.
VOL. 86, 1998
REACTION
In the present work, efforts were made to find a plausible reaction
scheme that could
explain
MichaelisMenten kinetic behavior of the isomerization
reaction
between G6P and F6P catalyzed by B. stearothermophilus
PGI, a tetrameric enzyme. According to Ishikawa et al.
(19), the rate equations
for the single substrate-single
product/dimeric
enzyme system reduced to the Michaelis-Menten rate equation under some special conditions
if the reaction scheme did not include the reaction step
between the complexes ESS and EPP. Therefore, a similar approach was adopted in this single substrate-single
product/tetrameric
enzyme system. Figure 9 shows a
simplified scheme in which the reactions between the
complexes ESS and EPP, ESSS and EPPP, and ESSSS
and EPPPP are neglected. In the scheme, E represents
a tetrameric enzyme consisting of four subunits, each of
which has one binding site for S or P, and S and P are
the substrate (G6P) and the product (F6P), respectively.
ES and EP represent complexes in which one of the
subunits
is bound to S and to P, respectively.
ESP
represents a complex in which one of the subunits is
bound to S and another one is bound to P.
As in the case of the single substrate-single
product/
dimeric enzyme system (19), further simplifications
were
introduced in order to reduce the number of kinetic constants to the same as or less than that of the experimentally obtainable kinetic parameters: The binding rates of
the substrate to both the free enzyme and the enzyme
complex, and the dissociation rates of the product from
the enzyme complex are much faster than those of the
reactions in which a change in the molecular structure of
the substrate or the product occurs. Therefore the rapidequilibrium
assumption
was applied to steps l-20, and
the steady state assumption
was applied to steps 21-30
in the scheme shown in Fig. 9.
The rate equation for the scheme can be derived by
the method
of King and Altman
(22) or others.
However, because of the number of reaction steps in the
scheme proposed in the present work, the use of a computer program developed by the present authors, which
is an advanced version of the previous program (23), is
necessary. The rate equation derived was as follows.
v= -d[S]/dt==d[P]/dt
MECHANISM
ESSS
ESSSSFIG. 9.
OF B. STEAROTHERMOPHILUS
r-,
ESSP N-%
ESSSP A
ESPP dh
ESSPP +%
PGI
329
EPPP
ESPPP @+
EPPPP
A scheme of the reaction
catalyzed by B. stearothermophilus PGI. A simplified scheme was proposed to explain the
isomerization reaction catalyzed by B. stearothemophilus PGI. E
represents a tetrameric enzyme consisting of four subunits, each of
which has one binding site for S or P, and S and P are the substrate
(G6P) and product (F6P), respectively. ES and EP are the complexes
in which one of the subunits is bound to S and to P, respectively.
ESP is the complex in which one of the subunits is bound to S and another one is bound to P. Other symbols are defined in a similar manner.
+ indicates the steps to which the rapid-equilibrium assumption
was applied, and - indicates the steps that the steady-state assumption was applied.
stants as described by Segel (24). As the enzyme consists
of four subunits, there are four sets of the intrinsic constants, that is, one for each of the four subunits.
However, if the active sites are identical and completely
independent
of each other, the presence of a substrate or
a product at one site will have no effect on the binding
properties of the other sites (24). In this special case, it
is sufficient to use only one set of the four intrinsic constants, kf, k,, KS and KP. The effective constants KTi-,
o=l-lo),
Kzj o=l-lo),
kfj u=21-30)
and ki u=21-30)
were related to the intrinsic constants KS, KP, kf and
k,, respectively, by a similar method to that reported by
Segel (24), and the relationships
obtained were substituted into Eq. 4 to give the following equation.
v= -d[S]/dt=d[P]/dt
(4&~f[~l-4~Pk[pI)
= x [U +~s~~l~3~~~+~~~~I~3+~~sK~~~l~~1~~-t~~~~l+~s~~I~IIlElo
(I +&lW+(I
+&lP1)4+
I2KsK,lPllSl
t lX&[P]*[S] t 1X~~p[P][S]2t6K~~;[P]z[S]2
t 4K$p[P])[s] t 4@p[P] [S]3- 1
(5)
Equation 5 has only two rate constants kf and k, and
two equilibrium
constants KS and KP. However, it is
noteworthy that the rate equation derived in the present
work is quite different from that for a reversible reaction
catalyzed by a monomeric
enzyme (25). When [P]=O,
Eq. 5 reduces to the Michaelis-Menten
rate equation as
given by:
(4)
In Eq. 4, there are 20 equilibrium
constants Kj (j= l20) for steps l-20, and 20 rate constants consisting of 10
rate constants
kfj U=21-30)
for the forward
reactions
and 10 rate constants krj 0=21-30)
for the reverse reaction
of steps 21-30. The rate constants and the equilibrium
constants used in Eq. 4 are the effective
constants
and
can be related to the intrinsic rate and equilibrium
con-
v= -d[S]/dt=
;‘;p$l”s’l
s
Similarly,
when [S]=O, the
reduces to the Michaelis-Menten
lows:
rate equation
rate equation
5 also
as fol-
(7)
330
J. FERMENT.BIOENG.,
WIDJAJA ET AL.
TABLE 2.
Kinetic parameters determined by using the data
shown in Figs. 4 and 5
kr =8.46x UYs-l
~s=4.9Ox102M--’
k, =1.83x l@s-’
K,, =4.90x 10’ M-’
TABLE 3. The experimental equilibrium concentrations of G6P
and the equilibrium concentration ratios obtained from
the data in Fig. 8
The kinetic parameters were determined by fitting the experimental
initial reaction rates shown in Figs. 4 and 5 to the rate equations given
by Eqs. 6 and 7 using a non-linear regression procedure (the Pawell
method).
At equilibrium,
ship.
[PI,_ _- K&f
Isle
K&r
Eq.
5 yields
the following
relation-
(8)
The intrinsic kinetic parameters kf, k,, KS and Kp were
determined
by fitting the experimental
initial reaction
rates shown in Figs. 4 and 5 to the rate equations given
by Eqs. 6 and 7 using a non-linear
regression procedure
(the Pawell method). The parameters
thus determined
are listed in Table 2.
Equation 8, which was derived from the rate equation
for the proposed scheme, implies that the value of [PI,/
[S], must be constant irrespective of the initial concentrations
of P (F6P) or S (G6P). Substitution
of the
experimental kinetic parameters listed in Table 2 into Eq.
8 gives the [P],/[S], value of 0.46. Table 3 lists the
experimental [P],/[S], values which were directly calculated
from the equilibrium
concentrations
of F6P and G6P
determined from the time courses of [G6P] shown in Fig.
8. The [P],/[S], values were found to be constant at an
average value of 0.45 irrespective of the initial F6P concentrations.
Since this average value was in close agreement with the above value of 0.46, the reaction scheme
proposed in the present work was demonstrated
to offer
an adequate
explanation
of Michaelis-Menten
kinetic
behavior of isomerization between G6P and F6P catalyzed
by B. stearothermophilus PGI.
The solid line in Fig. 4 shows the theoretical line calculated based on the rate equation Eq. 6, with the kinetic
parameters listed in Table 2. The initial rate data in this
figure were obtained
using solutions
containing
only
G6P as the substrate. Similarly, the solid line in Fig. 5
shows the theoretical line calculated based on Eq. 7 and
is compared with the data obtained by using solutions
containing
only F6P as the substrate.
Agreement
between the theoretical lines and experimental data is satisfactory in both the figures.
Using the kinetic parameters
shown in Table 2, the
theoretical values of the time courses of the increase in
the G6P concentration
formed by the reverse reaction
were calculated based on Eq. 5 using the Runge-Kutta
method. In Fig. 8, the theoretical values are shown as
solid lines and are compared with the experimental time
courses of the G6P concentration.
All the data were
obtained using solutions containing both G6P and F6P,
though the solutions initially contained only F6P. The
theoretical lines and experimental
data are also in good
agreement in this figure.
From the above experimental results, we can conclude
that despite the fact that B. stearothermophilus PGI is a
tetrameric enzyme, its kinetic behavior can be explained
by the Michaelis-Menten
rate equation.
In the present work, we clarified the kinetics and the
mechanism of a single substrate-single
product reaction
wm
lG@l,
(mM)
10
5
3
2
(mM)
6.88
3.44
2.06
1.42
Experimental [FSP],/[GSP],
(-)
0.454
0.454
0.457
0.415
av. 0.45
The experimental equilibrium concentration ratios were directly
calculated from the equilibrium concentrations of F6P and G6P determined from the time courses of the increase in G6P concentration
shown in Fig. 8.
catalyzed by a tetrameric enzyme. To the best of our
knowledge, the present study was the second investigation that wholly clarified the kinetics and mechanism of
a reversible reaction catalyzed by an oligomeric enzyme.
We believe that the present study contributes to the analysis of the kinetics and mechanism of reactions catalyzed
by other oligomeric enzymes and the rational design of
a reactor for the enzymatic production
of FDP from
glucose.
NOMENCLATURE
PI
: concentration
of bound substrates or ligands per
total protein concentration,
E
: enzyme
[Elo : initial enzyme concentration, M
ES, ESS, ESSS, ESSSS, EP, EPP, EPPP,
EPPPP,
ESP, ESSP, ESSSP, ESPP, ESPPP, ESSPP
: complexes of enzyme and one or more substrates
(S) and/or products (P)
Fl : concentration of free molecules or ligands, M
kf : intrinsic rate constant of the forward reaction of
the slow steps, s-l
k, : effective rate constant for the forward reaction of
slow step j Q=21-30), s-l
k, : intrinsic rate constant of the reverse reaction of
the slow steps, ssl
kr, : effective rate constant for the reverse reaction of
slow step j (j=21-30),
s-r
constant of rapid step j (j=
K, : effective equilibrium
l-20) (for example, Kl = [ES]/[E][S],
K2= [EP]/
[EIPI, . ..A IV-’
kd : inactivation rate constant of enzyme, h-l
: dissociation constant, M
: intrinsic equilibrium constant of
the product binds or dissociates,
KS : intrinsic equilibrium constant of
the substrate binds or dissociates,
m : molecular mass, Da
n
: number of substrate or product
enzyme, P
: product (F6P)
PI : concentration of product, M
S
: substrate (G6P)
PI : concentration of substrate, M
t
: reaction time, s
V
: reaction rate, M. s-l
VCI : elution volume, ml
v,, : maximum reaction rate, M .s- I
Kli
KP
the steps in which
M-r
the steps in which
M-t
binding
sites of
REACTION MECHANISM OF B. STEAROTHERMOPHILUS
VOL. 86, 1998
ACKNOWLEDGMENTS
This work was partially supported by a Grant-in-Aid for Developmental Scientific Research @lo. 06555250) from the Japanese Ministry of Education, Science, Sports and Culture. The authors express
their thanks for its support.
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