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Kinetics of the hydrolysis of cellobiose catalysed by P-glucosidase
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Department of Chemistry, University of Ottawa, Ottawa, Ont., Canada K I N 9B4
Received June 5, 1984
Hsuanyu, Y. & Laidler, K. J. (1985) Kinetics of the hydrolysis of cellobiose catalysed by P-glucosidase. Can. J. Biochem.
Cell Biol. 63, 167- 175
The hydrolysis of cellobiose catalysed by P-glucosidase has been investigated by experimental techniques which allow the
course of reaction to be followed continuously. They involve assaying the product glucose by the use of ATP, hexokinase,
glucose-6-phosphate dehydrogenase, and nicotinamide adenine dinucleotide phosphate (NADP); the latter is converted into its
reduced form NADPH which absorbs strongly at 340 nm. Rates were measured at nine pH values varying from 5 to 6.9, at
substrate concentrations varying from 0.2 to 3.2 mM, and at temperatures varying from 10 to 37OC. The pH dependence revealed
pK values of 4.9 and 6.5 in the free enzyme at 24OC, and these are little changed on complex formation. The rates measured over a
range of temperature, as interpreted by Arrhenius plots, revealed an inflexion at 23OC, found consistently under all conditions.
The results are analyzed in terms of the mechanism
ES + ES' + E + products
It was found possible to obtain, for the four elementary reactions, activation energies and entropies of activation which explain
the inflexion at 23OC and the Arrhenius behavior above and below that temperature. Profiles are constructed showing the
variations of entropy and enthalpy during the course of an individual reaction.
Hsuanyu, Y. & Laidler, K. J. (1 985) Kinetics of the hydrolysis of cellobiose catalysed by P-glucosidase. Can. J. Biochem.
Cell Biol. 63, 167- 175
Nous avons examink l'hydrolyse du cellobiose catalysCe par la P-glucosidase grice a des techniques expkrimentales qui
permettent de suivre de fason continue le cours de la rkaction. Ces techniques comportent l'analyse du produit glucose par
l'emploi de I'ATP, de l'hexokinase, de la glucose-6-phosphate deshydrogknase et du nicotinamide addnine dinuclkotide
phosphate (NADP); ce dernier composk est transform6 en sa forme rCduite, le NADPH, qui absorbe fortement a 340 nm. Nous
avons mesurC les vitesses a neuf valeurs de pH allant de 5-6,9, a des concentrations du substrat variant de 0,2-3,2 mM et a des
tempkratures s'ktendant de 10-37°C. La dCpendance au pH rkvkle des valeurs de pK de 4,9 et 6,5 dans l'enzyme libre a 24°C et
ces valeurs changent peu lors de la formation du complexe. Les vitesses mesurCes a diffkrentes temperatures et interprCtCes par les
tracks d'Arrhknius rCvklent, a 23"C, une inflexion que l'on retrouve dans toutes les conditions. Nous avons analyst5 les rCsultats
en termes du mCcanisme
ES + ES' + E
+ produits
Pour les quatre rCactions ClCmentaires, nous avons pu obtenir les Cnergies d'activation et les entropies d'activation qui expliquent
l'inflexion a 23°C et le comportement ArrhCnius au-dessus et au-dessous de cette tempkrature. Nous avons construit des profils
montrant les variations d'entropie et d'enthalpie au cours d'une rCaction individuelle.
[Traduit par la revue]
The enzymic degradation of cellulose has important
practical implications from the standpoint of renewable
energy resources. The enzyme cellulase, used in the
degradation, has three major components (1,2): (i)
endo- p- l,4-glucanase, which randomly hydrolyzes cellulose chains; (ii) cellobiohydrolase, which splits cellobiose from the ends of cellulose chains; and (iii)
P-glucosidase, which catalyses the hydrolysis of cellobiose to glucose. Cellobiose is an inhibitor for celloABBREVIATIONS:
NADP, nicotinamide adenine dinucleotide phosphate; G-6-P, glucose 6-phosphate; G-6-PD, glucose6-phosphate dehydrogenase; UV, ultraviolet.
biohydrolase, the action of which is therefore inhibited
by products. The action of P-glucosidase on cellobiose
shows substrate inhibition.
Because of these inhibiting effects, the accumulation
of cellobiose during cellulose degradation lowers the
glucose yield, which can be significantly improved by
addition of P-glucosidase (1-5). The kinetics of the
action of P-glucosidase is therefore a matter of considerable practical significance.
The present paper describes such a kinetic study,
which has included the effects of temperature and of pH.
It has been carried out using almond P-glucosidase,
on which there has been some previous work; some of
this has emphasized structural aspects (6,7) and activity
and kinetic aspects (8-1 1), and some work has been
concerned with the immobilized enzyme (12- 14). The
present work covers the kinetics in more detail than any
of the previous studies.
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Materials and Methods
Reactions catalysed by cellulase or P-glucosidase are
usually followed by assaying the amounts of glucose produced
after various periods of time. In the past this has been done by
stopping the reaction, either by heating the reaction system
(1,2) or by adding an inhibitor (3, 15- 18). The glucose
present is then measured spectrophotometrically using a
coupled glucose oxidase system or a coupled system containing glucose-6-phosphate dehydrogenase and NADP, or chemically (19). These methods are accurate and sensitive, but are
inconveniently laborious and time consuming for a kinetic
investigation. We therefore explored alternative methods
which would involve only one step and would allow the
reaction to be followed continuously. The method found to be
most satisfactory for assaying the glucose produced is based
on the following scheme:
Glucose + ATPADP + G-6-P
G-6-P + NADP-
6-Phosphogluconic acid
The NADPH formed, unlike the oxidized form NADP,
absorbs strongly at 340 nm, and its concentration can therefore
be determined spectrophotometrically at this wavelength.
The P-glucosidase (P-D-glucoside glucohydrolase,
EC3.2.1.2 1) , derived from almonds, was obtained in powder
form from the Sigma Chemical Co.; it had a reported specific
activity of 30 U mg-' with salicin as substrate at pH 5.0 and
37°C. The substrate D(+)-cellobiose (P-D(+)-cellobiose;
4- 0-P-D-glucopyranosyl-D-glucose)was also obtained from
The reagent for glucose determination, containing hexokinase and glucose-6-phosphate dehydrogenase, was that
provided by Sigma and to it was added 15.5 mL of water. The
resulting solution then contained the following: 2.0 mmol L-I
ATP, 1.O rnrnol L- NADP, 1600 U L- yeast hexokinase,
1000 U L- G-6-PDH (yeast), and 4.0 mmol L- M ~ * +to,
gether with buffers.
The enzyme solution and the substrate solution were both
prepared in 0.2 M acetate buffers at the pH values required.
The spectrophotometry was carried out using a double-beam
SP 1800 UV spectrophotometer connected to a Unicam AR 25
linear chart recorder. The sample chamber was thermostatted
by the use of a HAAKE refrigerated bath and an F3-C
Calibration curves were obtained with standard glucose
solution at different pH values and different temperatures; this
was done for each new batch of assay reagent. Standard
0.556 mM and 0.0556 mM glucose solutions were prepared
by diluting a standard glucose solution (containing 5.56 mM
glucose in saturated benzoic acid) with 0.2 M acetate buffer, at
a desired pH. A cuvette of 3-mL capacity and a light path of
1 cm was used to mix 1 mL of the assay reagent with an
appropriate amount of buffer solution at the desired pH. The
mixture was incubated at the temperature to be used in the
kinetic measurement. After 4min a certain aliquot of a
standard glucose solution was made up to a total volume of
3 mL, the final concentrations being between 2.97 mM and
37.1 pM or between 37.1 and 371 F M (for pH 5.0). The
absorbance at 340 nm, as compared with a glucose-free blank
solution, was automatically recorded as a function of time.
For pH values above 6.2, calibration curves were prepared
by plotting absorbance against concentration. For pH values
below 6.2, initial slopes of absorbance-time curves were
plotted against glucose concentration.
The kinetic runs were carried out in cuvettes, 1 mL of the
assay reagent being mixed with 0.5 mL of 0.6 mg m ~ - 'of
enzyme solution and with an appropriate aliquot of 0.2 M
acetate buffer to make the final volume 3 mL after adding
substrate solution. Addition of the appropriate amount of
5.99 mM substrate solution started the reaction, which was
followed by recording, as a function of time, the changes of
absorbance at 340nm; a mixture of 1 mL assay reagent,
0.5 mL enzyme solution, and 1.5 mL buffer was used as a
At pH values above 6.2 the reaction between the assay
reagent and the glucose is very fast, being essentially complete
in 2-2.5 min as shown in curve A of Fig. 1a . The initial rates
for the P-glucosidase reaction were therefore calculated from
the initial slopes of the corresponding absorbance-time
curves, use being made of the conventional calibration curves
with the absorbance plotted against the glucose concentration.
In what follows this method is referred to as the glucoseconcentration method.
At pH values below 6.2 it was observed from the records of
absorbance against time (Fig. 16) that there was a lag phase, of
length dependent upon pH; later the absorbance varied linearly
with time. The lag phase is due to the fact that the reaction of
the assay reagent is slow at pH values below 6.2, as shown in
curve B of Fig. 1a . At the beginning of the reaction, the
quantities of glucose produced are too small for reaction with
the assay reagent to occur sufficiently rapidly. After glucose
has accumulated sufficiently during the lag phase, the assay
reagent reacts with the glucose at a constant rate which is equal
to the rate of glucose formation. In this situation the rate would
be seriously underestimated if it were obtained from the
calibration curve of absorbance against glucose concentration.
The method employed was to obtain an average rate after a
time that is sufficiently short that it is very close to the initial
rate. The glucose concentration at point 0 (Fig. 16) was first
determined; it was given by the slope of the straight portion of
the curve, use being made of a calibration curve of slope
against the glucose concentration. The average rate was then
obtained by dividing the glucose concentration so determined
by the length of the lag phase; this procedure involves the
approximation, which introduces negligible error, of neglecting the glucose that has reacted with the assay reagent during
the lag phase. In the remainder of this paper, the term
glucose-slope method will be used to describe this procedure.
Results and discussion
Experiments were first carried out to establish the
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FIG. 2. Lineweaver-Burk plot for the system. [P-Glucosidase] = 0.1 mg m I - T = 24°C; pH 5.32. The plot leads to
V , = 950 nM s-'; K , = 5.8 mM.
FIG. 1. (a) Absorbance-time curves for the reaction between glucose and the assay reagent; the glucose concentra- and A is the product which is determined spectrotions are shown. (A) pH 6.48; (B) pH 5.35; T = 24.0°C. ( b ) photometrically at 340 nm.
Absorbance-time c u k e for the enzyme-catalyzed reaction.
[P-Glucosidase] = 0.1 mg m I - ; [cellobiose] = 0.699 mM; The glucose-concentration method
T = 24.0°C; pH 5.35.
At pH values greater than 6.2, the cellobiose hydro-
validity of the kinetic procedures employed in this
investigation. The reaction system contains not only
P-glucosidase and cellobiose, but also the assay reagent
which contains two additional enzymes (hexokinase and
G-6-PD), ATP, and NADP. The system is therefore
kinetically complicated, and it was necessary to investigate whether the assay reagent interferes with the
P-glucosidase system and whether either the P-glucosidase or cellobiose interferes with the glucose determination. The first effect was shown to be unimportant
by using assay concentrations much larger than used in
the kinetic experiments; the change in absorbance was
barely detectable. The second possibility was eliminated
by use of very high enzyme and cellobiose concentrations, which brought about a negligible change in
The reaction sequence employed can be expressed in
simplified form as follows:
E + S+G-A
( +reagent
where E is P-glucosidase, S is cellobiose, G is glucose,
lysis is the slow step (kA/ks > 100); the rate of this
reaction is therefore given directly by the rate of change
of absorbance.
The glucose-slope method
At lower pH values the above is not true and the
absorbance-time curve shows a lag phase (Fig. 16). A
steady concentration of G is soon established and the
rate of formation of A is a measure of the rate of
formation of G; this rate is effectively the initial rate
except at pH values below 5. The typical LineweaverBurk plot in Fig. 2 shows that the procedure is selfconsistent.
The ks value is obtained by making use of the
- ---
where kT is the rate constant obtained from the slopes of
plots of the type shown in Fig. l b ; a typical slopesubstrate concentration plot is shown in Fig. 3. Since kA
is obtained from slope-glucose concentration plots, ks
values can be calculated from [I]. Some results are
given in Table 1.
The glucose-slope method is unsuitable at tempera-
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FIG. 3. Plots of slopes of absorbance-time curves (e.g.,
Fig. 1) against the substrate concentration. T = 18.0°C;
[P-glucosidase] = 0.1 mg rnL- l ; [cellobiose] = 0.2-3.2 mM;
the pH values are shown.
TABLE1. Rate constants kA and ks under different
FIG. 4. Plots of log l o V, against pH, at three temperatures.
therefore closely follow the Michaelis-Menten equation
Plots of loglo Vm against pH are shown in Fig. 4, and
plots of loglo (Vm/Km)against pH are shown in Fig. 5.
The theory of pH effects has been reviewed in various
places (20, 21). For a reaction obeying [2], the pH
dependence is usually given by
*The units of k, and ks are divisions per minute per micromolar concentration.
tures over 40°C, because of inactivation of the assay
reagent; it is also unsuitable at pH values below 5.0,
since then kA is too small. Otherwise it gives completely
self-consistent results and is much less time consuming
than taking samples at various times.
Influence of pH
By use of the procedures described above, rate constants for the enzyme-catalysed reaction were measured
at temperatures of 18, 24, and 3 1°C and at pH values
ranging from 5.0 to 6.9. Lineweaver-Burk plots, an
example of which is shown in Fig. 2, were all linear for
substrate concentrations from 0.2 to 4.8 rnM. The results
where the unprimed dissociation constants relate to the
free enzyme and the primed ones relate to the enzymesubstrate complex. Reliable values of the dissociation
constants cannot be obtained directly from the plots in
Figs. 4 and 5, although very approximate estimates can
be made and provide a useful check of the calculations
based on statistical procedures. Use was made of a
procedure of Hinberg and Laidler (22) that was modified
and improved by Mazid and Laidler (23); full details are
given in these publications. The values of the dissociation constant so obtained, at three temperatures, are
shown in Table 2.
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FIG.5. Plots of loglo (Vm/Km) against pH, at three
TABLE2. Dissociation constants obtained by use of statistical
- -
- -
Free enzyme
FIG. 6. Plots of loglou against 1IT, at pH 6.39 and at the
substrate concentrations shown.
Enzyme-substrate complex
The pKb values of about 5 suggest that a carboxyl
group is involved at the active center and that it is
catalytically active when in the basic form -COO- and
inactive in the protonated form -COOH. Since this
group undergoes little change when the enzymesubstrate complex is formed, it is probably not directly
involved in the binding, but only in the catalysis of the
splitting of the bond. The other group, corresponding to
the pKa values, is presumably an imidazole group,
active in its protonated form. Again the pKa values are
hardly changed on complex formation, suggesting that
the group is not involved in binding.
Injuence of temperature
Rates were measured at an enzyme concentration of
0.1 mg mL-' , at substrate concentrations ranging from
0.2 to 3.2 mM, and at 11 temperatures ranging from 10
to 37°C. Results obtained at pH 6.39 are shown in Fig. 6
as plots of loglo u against l/T. Such plots consistently
showed a change of slope at about 23°C. From Lineweaver-Burk plots at the 11 temperatures the values of
I O ~ K/ T
FIG.7. Plots of loglo Vm and of loglo (Vm/Km)against
1/T, at pH 6.39.
Vm and Km were obtained, and Fig. 7 shows plots at
pH 6.39 of loglo (V,/K,)
and of loglo V, against 1/T.
These plots also show the inflexion at 23°C. Some
previous studies with almond P-glucosidase have also
given changes of slope; Miyairi et al. (14) obtained an
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200 -
0 -
FIG.8. Plots of the activation energies against the pH. The
subscript "e"refers to temperatures below 23°C and " h refers
to those above. The first subscript "0" refers to values obtained
from rates when [S] << K,; the subscript "c" relates to [S]
>> K,.
FIG.9. Plots of entropies of activation A'S against pH.
inflexion at 27OC, Weber and Fink (10) at 24OC, and
Venardos et al. (2) at 45OC.
Similar measurements were made at eight other pH
values ranging from 5.0 to 6.9, and the activation
energies obtained are plotted against pH in Fig. 8. The
values designated Ec are those obtained from the plots of
loglo Vm against 1/T; Ec,e, is for the lower temperature
range and Ec ,h is for the higher. The Eo,e and Eo,hvalues
are those obtained from the loglo(Vm/Km)plots. It is to
be seen that Eo,h and Ec,h do not vary much with the pH,
but that the Eo,e and Ec,e values pass through a minimum
at around pH 6.
Using a molecular weight of 85 000 for P-glucosidase
(6), entropies of activation A'S were calculated on the
basis of the transition-state equation
The values are plotted against pH in Fig. 9. Again there
is little dependence of A'soph and A'Scyh on pH, but the
A'Sove and A'Sc,e values pass through a minimum at
around pH 6. Since the actual rates show a maximum, it
follows that in the case of the results at the lower
temperatures this is largely due to the variations in
activation energy, but that there is a partly compensating
variation in the entropies of activation. This compensation effect is shown in the plots in Fig. 10.
FIG. 10. Plots of A'S against energy of activation E, for
different pH values, showing the compensation effect.
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The existence of the inflexion at 23OC, found at both
low and high substrate concentations, is satisfactorily
and most simply explained (20, 24) in terrns of a
mechanism involving a second intermediate:
E +
k- 1
Application of the steady-state treatment (20) leads to
+ k2
+ [A]
where [Elo is the total enzyme concentration. The rate in
the limit of high substrate concentrations is therefore
while that at low substrate concentrations is
The complex form of the coefficients, involving the sum
of two rate constants in each case, provides an interpretation of an inflexion in the Arrhenius plot. This will
now be analyzed quantitatively with respect to one set of
data, shown as an Arrhenius plot in Fig. 7.
These results correspond to a pH of 6.4 and to
saturation by substrate; they are thus interpreted in terrns
of [6]. If k is a rate coefficient, the experimental activation energy E, is defined (25) as
Since, by [6], k
In k
k2k3/(k2 + k3),
In k2 + In k3 - In (k2 + k3)
and therefore
d In k2
-=-+R T ~ d~
d l n k3 d In (k2 + k3)
k3 d l n k2
k2+k3 dT
+--k 2k2+ k 3 d ldnTk3
The temperature dependencies of the rate constants k2
and k3 are given by
The observed activation energy at any temperature is
thus the weighted mean of the values E2 and E3, the
weighting factors being k3/(k2 + k3) and k2/(k2 + k3),
Since the expression k2k3/(k2 + k3) which appears in
[6] is symmetrical in k2 and k3, as far as this analysis
alone is concerned it is immaterial which reaction has
the higher activation energy. By a method of successive
approximations we have found that the two activation
energies 28.5 and 67.5 kJ mol- ' give excellent agreement with the results for this particular case; the line
drawn in Fig. 7 in fact corresponds to these values. For
reasons to be explained later, the values are assigned as
E2 = 67.5 k~ mol-' and E3 = 28.5 k~ mol-'. For there
to be an inflexion at 23OC, it follows that the preexponential factor ratio A2/A3 = 7.6 x lo6. The actual
A values may be obtained by making use of the fact that
k2 = k3 at 23"C, so that, from [6],
Use of the value of V , at 23OC then gives A2 = 9.43 x
10" s-' and A3 = 1.25 x lo5 s-l.
The analysis of the rates at low substrate concentration proceeds similarly. According to [7] the rate
constant is now klk2/(k-l + k2), and an analogous
procedure to that in [8] to [14] leads to
A successive approximation procedure now led to
E l = 41.0 kJ mol-' and E l + E2 - E P 1 = 90.5kJ
mol-'. Use of the E2 value obtained previously then
gave E- = 18.0 kJ mol- . The upper curve shown in
Fig. 7 is plotted on the basis of these values and is seen
to pass very well through the experimental points. The
preexponential factors were again calculated from the
rate at the inflexion, and were found to be Al = 2.6 x
lo9 dm3 mol-' s-I and A-1 = 1.75 x lo3 s-l.
The analysis of the results at high substrate concentrations led to the two activation energies 67.5 and 28.5 kJ
mol- ' , but a decision could not immediately be made as
to which was E2 and which E3. Similarly, the values of
4 1.0 and 90.5 kJ mol- ' could have been assigned in
either way to E l and E l + E2 - E- When the two sets
of results are considered together, only the one assignment that we have chosen leads to a reasonable interpretation; for example, one alternative assignment led
to a large negative value of E- another to impossibly
high values of A and A -
TABLE3. Kinetic parameters obtained from analysis of the temperature dependence (pH 6.4)
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factor (A)
(1)E + S + ES
2.62 X
(-1) E S + E + S
1.75 x
(2) ES + ES'
9.43 X
(3) ES' + E + Y + Z 1.25 X
(E)/kJ mol-I
A' G (23"C)/
lo9 dm3mol-'s-'
lo3 s-'
10" s-'
lo5 s-'
- #++#\\\\J\,
FIG. 1 1. Reaction profiles, showing the variations of Gibbs
energy, entropy, and enthalpy during the course of the process
The kinetic parameters obtained are summarized in
Table 3, which also includes the Gibbs energies of
activation, the entropies of activation, and the enthalpies
of activation. Figure 1 1 shows these quantities represented as reaction profiles.
General Discussion
It must be emphasized at the outset that there can
never be a unique mechanistic interpretation of kinetic
results. The present work has shown that the results now
available can be interpreted satisfactorily in terms of an
extended Michaelis-Menten mechanism in which there
are two intermediates. This is undoubtedly the simplest
mechanism that will explain the results, but more
complicated schemes could do so also.
kJ mol-'
A*S/J K-' mol-I
A*H/kJ mol-'
- 191.1
- 155.7
The analysis has shown that the enzyme-substrate
addition complex ES is formed by a process having a
small enthalpy of activation (38.5 kJ mol-I). The
complex is formed endothermically, but the process of
complex formation is helped by a substantial entropy
increase (1 18 J K- ' mol- I); this indicates some loosening of the enzyme structure as the substrate becomes
attached to it.
The conversion of ES into the second intermediate ES'
has a much more substantial enthalpy of activation (65.1
kJ mol-'), and there is a small entropy loss in forming
the activated state. The final breakdown of ES' to form
products has a much lower enthalpy of activation (26.1
kJ mol- I ) , but now the entropy of activation (- 155.7 J
K-' mol -') is much more negative. The net result is that
the Gibbs energies of activation and, therefore, the rates
are very close to one another for reactions 2 and 3,
throughout the temperature range investigated; they are
in fact identical at 23"C, the temperature at which there
is the inflexion.
The enthalpy-entropy compensations (Fig. 10) found
in the present study are very striking. They are to be
attributed (26) to structural effects accompanied by
changes in vibrational frequencies and restricted rotations in the enzyme molecules. A pH change that brings
about a loosening of the enzyme structure, for example,
and which therefore gives an entropy increase, will at
the same time produce an enthalpy increase because of
the necessity for the breaking of secondary bonds such
as hydrogen bonds.
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