ABBS 2005,38(06): Estimation of Cellobiohydrolase I Activity by Numerical Differentiation of Dynamic Ultraviolet Spectroscopy

Abstract        1,4-b–D-glucan cellobiohydrolase
I (CBH I), p–nitrophenyl b–D–cellobioside, p–nitrophenol and cellobiose show
distinct ultraviolet spectra, allowing the design of an assay to track the
dynamic process of p–nitrophenyl b–D–cellobioside
hydrolysis by CBH I. Based on the linear relationship between p–nitrophenol formation in the hydrolysate
and its first derivative absorption curve of AUC340–400 nm (area under
the curve), a new sensitive assay for the determination of CBH I activity was
developed. The dynamic parameters of catalysis reaction, such as Vm and Kcat, can all be derived from this result. The
influence of b–glucosidase and endoglucanase in
crude enzyme sample on the assay is discussed in detail. This approach is useful
for accurate determination of the activity of CBHs.

Key words         cellobiohydrolase;
dynamic spectrum; area under the curve (AUC)

A fungal cellulase
system typically comprises three major classes of enzymes: 1,4–b–D-glucan cellobiohydrolase
or exoglucanase (CBH; EC The water-soluble
substrate p–nitrophenyl b–D–cellobioside
(PNPC) has been widely used to determine the catalytic activity of CBH [4,5]. At the reaction end of this assay, 10% Na2CO3 must be added to ensure the alkaline
environment to enable p–nitrophenol (PNP) to
fully develop a yellow color, then the absorbance at
410 nm is used to assess the presence of PNP.

Based on the two basic
hypotheses describing the dynamics of enzymatic action, the intermediate
complex hypothesis and the steady-state hypothesis, an assay for catalytic
enzyme activity requires that the reaction rate be determined by the
concentration of enzyme with all the other variables optimized. The essential purpose
is to determine the initial reaction rate at the highest substrate
concentration (>Km), because
only when the actual initial reaction rate is determined, are V and [E]t linearly
related [6–8]. However,
those PNPC assays belong to the end-point of titration, and the reaction
conditions (such as concentrations of enzyme and PNPC) and the reaction time
have to be empirically selected. Using this method, the dynamic properties of
catalytic reaction will not be estimated, and no accurate comparison among the
outcomes of different experiments is possible.

The dynamic spectrum
assay has been effectively applied in the studies of the structure and function
of various biomacromolecules [9–11]. For example, changes in the spectrum of p–nitrophenyl b–D–glucoside have been used to measure the activity of creatine phosphokinase [12]. It
is reported here the application of this approach to follow the hydrolysis of
PNPC by CBH I, and a new dynamic method for the sensitive determination of CBH
I activity is described.

Materials and Methods

Trichoderma pseudokoningii

Trichoderma
pseudokoningii S-38 was isolated [13], and CBH I was purified as previously described
[14]. Its molecular weight is approximately 66 kDa
and the molar extinction coefficient e=73,000. PNPC and p-PNP were purchased from
Sigma (

Smooth observed data and
statistical analysis

Enzyme assay as a matter
of course yields a series of points with an experimental error. Direct
numerical differentiation of these points or construction of a model will be
greatly influenced by the experimental error. Thus it should be useful for
smoothing progress curves before obtaining derivatives [15]. The spline interpolation approach is considered here. Smoothing
spline is a popular method for performing
nonparametric regression. It approaches a true function subinterval by
subinterval [16]. Microsoft Excel, graph software Prism 6.0 (2002) and software
TableCurve 2D version 5.0 (http://www.spssscience.com)
were used to treat the experimental data. Isosbestic points of derivative
absorption curves were used as an index to determine the concentration of PNP
formation during hydrolysis of PNPC by CBH I.

An isosbestic point
wavelength in the ultraviolet (UV) spectrum indicated the presence of
equilibrium between two absorbing species. At this wavelength, the absorbance
depended on the total molar concentration of the two absorbing species and not
their concentration. Isosbestic points of derivative spectra can be used for
quantitative determination of the two absorbing species in equilibrium [17–20].

We showed experimentally
an isosbestic point on the UV spectrum curve, which was observed of hydrolysate during PNPC hydrolysis progress by CBH I. Such
wavelength changes of isosbestic point were also observed in the mixture
solutions consisting of different concentrations of PNPC and PNP. A linear
relationship could be established between the PNP concentration and the first
derivative curve area in the range of 340–400 nm. It could then be used to calculate the PNP
formation during hydrolysis progress of PNPC by CBH I.

For estimation of the
total area under curve (AUC) of UV spectra, AUC during hydrolysis to express
the effects of time or enzyme concentration, a statistical moment of the Michaelis-Menten elimination kinetic method was used. It is
a common nonlinear method used in pharmacokinetics, and the area can be
directly calculated by definite integral [21–23]. If concentration values Ci are measured at time ti (i=1,¼,n), the numerical
integration method might be written as a summation over n–1 intervals, as shown in Equation 1:

Eq. 1

In the present study,
the wavelength was used instead of ti, and absorbance used instead of C,
therefore, AUC is the total intensity of absorbance in the range of n
to n1 wavelength.

Results

UV-spectrophotometric
properties of CBH I, PNPC, PNP and cellobiose in
acetate buffer

The UV spectra of CBH I,
PNPC, PNP and cellobiose are shown in Fig. 1(A).
The absorbance of PNPC was higher than that of PNP between 250 and 300 nm, and
it was lower than that between 300 and 400 nm. One isosbestic point was
observed at 305 nm for both PNPC and PNP, and the cellobiose
and CBH I had no absorbance beyond the range 240–300 nm. Those spectrophotometric
properties could be used to estimate the PNP formation during hydrolysis by CBH
I.

The CBH I drives
hydrolysis of each PNPC molecule to generate one PNP and one cellobiose molecule which can be illustrated as follows:

The cleavage of the gluconic bond between PNP and cellobiose
generates a distinct spectrum in the 200–400 nm range between the substrate (PNPC) and the product
(PNP). Thus it is possible to use spectral patterns to quantitatively determine
the amounts of substrate and hydrolysis product at any time point during the
progress of the reaction. The effect of cellobiose on
the absorbance in the wavelength 250–400 nm was
small enough to be ignored.

Comparison of the
isosbestic points of PNPC and PNP mixture solution on UV spectra curves in
acetate buffer

Although one isosbestic
point was observed at 305 nm for both PNPC and PNP, the position for each
mixture solution depended on the molar ratio of PNPC and PNP (data not shown).
Similar phenomena were also observed in the time progress of PNPC hydrolysis by
CBH I. Thus, this result used as an index for determination of PNP might lead
to errors. This problem could be resolved using its first order derivative
curve, as shown in Fig. 1(B,C).

Using this method, it
clearly indicated that, for the mixture solutions consisting of different composite
ratios of PNPC and PNP, and for the PNPC hydrolysate
products hydrolyzed by CBH I at different time points, their isosbestic points
were both at 3401 nm. As described above, AUC, a symmetry peak in the range of
340–400 nm, can be used as
an index to express the catalytic activity of CBH I in hydrolysis of PNPC [Fig.
1(D)].

Design of assay
conditions to obtain accurate catalysis rate in enzyme assay

The favorable conditions
for CBH I catalysis reaction are well known: a pH level of 4.8 and temperature
of 50 篊 [4,5,7,14], and used in present studies. To
obtain an accurate record of the reaction progress, the highest substrate
concentration (>Km) is needed
and the conversion is within 10% [7,8]. The
measurement time must be maintained for a considerable period, during which the
reaction rate might appear linear [8]. The behaviors of time progress expressed
by UV spectra during the hydrolysis of PNPC catalyzed by CBH I was shown in Fig.
1(A–C) and Fig.
2. It was carried out as follows: 0.8 ml of 250 礛 PNPC, 0.1 ml
of 1 礛 CBH I and 0.1 ml 100 礛 sodium acetate buffer, pH 4.8, incubation at 50 篊 for more
than 20 min in the scanning dynamic UV spectra (250400 nm) at 5 min intervals.

During the first 10 min
of hydrolysis, PNP formation, as calculated by the increase of AUC340–400 nm, was linearly correlated with the time of
hydrolysis (Fig. 2), however, the virtual
linearity of the instantaneous rate of this reaction is within 5 min. Thus, to
accurately determine the catalytic rate of PNPC hydrolysis, the reaction time
must be within 5 min.

Hydrolysis of PNPC by
different concentrations of CBH I

To study the effect of
CBH I concentration on the hydrolysis of PNPC, reaction conditions were as
follows: 0.05–0.80 礛 CBH I (0.1 ml) was mixed with 250 礛 PNPC (0.8 ml)
and As shown in Fig. 3(B),
the virtual linearity between the concentration of CBH
I and the catalysis velocities, calculated by the first order derivative of AUC340–400 nm, was obtained. However, the AUC value shows only
relative activities of CBH I. Based on the standard curve of AUC340–400 nm for PNP [Fig.
1(D)], CBH I activity shown as PNP concentration can be easily transformed.
Using crude cellulase as the enzyme sample, the value of PNP formation by a
certain volume of crude cellulase can also be evaluated.

Evaluation of the Kcat

Evaluation of
the Kcat is very important to achieve a detailed analysis
of catalysis reaction of an enzyme. It has been defined as 搕urnover number or 搈olecular activity,
which means the number of moles of substrate transformed per minute per mol of
enzyme, expressed as 礛 product/ml by 礛 enzyme per min [6]. The
value of Kcat can be obtained through Equation 2:

Kcat=Vmax/[E]t  2

However, there are many
difficulties in calculating the Vmax using the Michaelis-Menten equation [24–27].

In the present study,
the Vmax and [E]t can be directly observed
from the plot of instantaneous rate of CBH I activities versus different
concentrations of CBH I (Fig. 4) and the smooth data (the insert in Fig.
4). Thus, the Kcat can be easily obtained by simple calculation
through Equation 2.

Using Equation 2,
the Kcat is calculated to be approximately 2756.3 nM PNP formation per nM CBH I in
1 min at 50 篊 in acetate buffer, pH 4.8. Using this method, it
is unnecessary to measure the initial rate to determine Vmax and Kcat, and they do not depend on the Michaelis-Menten assumption.

Discussion

The widely used PNP
assay method [4,5] is unsuitable for the kinetic study, as mentioned above, and
the molecular extinction coefficient of PNP is also lower (el 410 nm=0.0008120 礛), whereas
the e of PNP expressed as the
first derivative AUC340400 nm is 5.2 times higher [Fig. 1(D)]. It is
suggested that the method of first derivative absorbance curve based on
isosbestic points could provide better resolution and higher sensitivity. Many P/O-NPC-like
compounds, such as p–nitrophenyl b–D–glucoside,
O-NPG (-galactoside) and O-NPF (-fucoside),
are widely used in enzyme assay. The method proposed here might also be useful
in these fields.

    In general, the catalytic rate is
calculated by three approaches.

First, using the integrated
Michaelis-Menten equation, as shown in Equation 3:

DP/t=Vm(1+Km/S0)-DPVmKm/[2(Km+S0)2]     3

By this
method, the intercept at P0 of the resulting curve is necessarily dP/dt0 the initial rate [21]. Because of the complexities
of the integrated rate equation, this method has not gained wide acceptance.

Second, evaluation of
the initial rate is defined as the reaction rate at the early phase of
enzymatic catalysis, which equals the rate near the beginning of the reaction.
However, the slope at the origin of the progress curve has the highest rate of
change that is even more unreliable than that expected, and lacks predication
power for the entire reaction mechanism [16,17]. In
practice, the catalytic rate is measured in certain interval-time at a fixed
temperature as other factors are maintained, then
calculated using some kinetic equations. Under this condition, the obtained
catalysis rate might depend on the timescale and temperature range used in the
measurement and the selected equation. In fact, most of the experimental data
lie in the range of the slower reaction period. For many enzymes, the progress
curves monitored by product or substrate consumption and enzyme inactivation
are non-linear. The kinetic behavior of enzymes can be described in terms of a
hyperbolic or sigmoid relationship between measured response and controlled
variable [24]. Under these conditions, estimation of initial rate based on the Michaelis-Menten assumption is a subjective and inexact progress
[25–27].

Finally, the catalytic
rate continuously changes during reaction progress based on the chemical
kinetics. Mathematically, those changes can be expressed as its instantaneous
rate or rate and can be easily evaluated by the changes in the slope of a
tangent line at any point on the reaction curve, which is not affected by the
curve抯 shape and only depends on its position on the
curve [28–30].

Waley [31]
proposed an easy method for the determination of the initial rate that is based
on the differentiation rule. The rate near the beginning of an enzyme-catalyzed
reaction can be found accurately from the slope of a chord joining two points
on the progress curve. The instantaneous rates of enzyme reaction can be found
accurately from the slope of a chord joining points on the progress curve [26–30], which can be shown as Equation 4:

-DCA/Dt|t=to=(CA2–CA1)/(t2–t1)      4

Where CA is the concentration of substrate, k is the
reaction constant, and t is the time.

This approach has been generally
used and further developed to the kinetic analysis of the entire reaction
progress rather than the initial rate [24,32,33].

Building on those
studies and some modifications, a new approach in our study is: (1) smoothing
experimental data by the spline interpolation method
for permitting the determination of instantaneous rates; (2) the use of
isosbestic points of derivative absorbance curves as an index to determine the
concentration of PNP; (3) from the plot of first derivative AUC340–400 nm versus
concentrations of CBH I, evaluation of a suitable reaction time, in which a
linear relationship would be established between enzyme concentration and
catalytic activity; and (4) at the selected reaction time, using a higher
concentration of PNPC as the substrate hydrolyzed by a series of different
concentrations of CBH I or a series of diluted crude cellulase samples. The Vmax and [E]t can be
directly observed from the plot of the instantaneous rate of CBH I activities
versus different concentrations of CBH I. Then Kcat can be
obtained by simple calculation.

Our assay
procedures were very good not only for pure CBH I preparation but also for
crude cellulase preparation, as they take into account any interference from EG
and b–glucosidases
[5]. As EG has no catalysis capacity for PNPC [2,4,5],
the possibility of influence from it is ruled out. Also, although PNPC can, in
some degree, be hydrolyzed by b–glucosidases, its content in crude cellulase is much lower
than that in CBHs. For typical cellulolytic
fungi, such as Trichoderma spp, Penicillium spp and Phanerochaete chrysosporium,
the moles/unit in crude enzyme preparation of b–glucosidases is lower,
covering one or two orders of magnitude, than that of CBHs
[13,14,34,35].

We found that the CBH I
activities did not change when D-glucono-1,5–d-lactose was added to the crude cellulase of T.
pseudokoningii S-38 to overcome the influence of b–glucosidases, as suggested by Deshpande et al. [5] (data not shown). But the CBH I
activity was increased using samples from Aspergillus
 

Acknowledgement

We acknowledge the
contribution of Dr. Robert KOEBNER (Department of Crop Genetics,

References

 1    Lynd LR, Weimer
PJ, van Zyl WH, Pretorius
IS. Microbial cellulose utilization: Fundamentals and biotechnology. Microbiol Mol Biol Rev 2002, 66:
506–577

 2    Sharrock KR.
Cellulase assay method: A review. J Biochem Biophys Methods 1988, 17: 81–105

 3    Day DF, Workman WE. A
kinetic assay for cellulases. Anal Biochem
1982, 126: 205–207

 4    Wood TM, Bhat KM.
Methods for cellulase activities. In:  5    Deshpande MV,
Eriksson KE, Pettersson LG. An assay for selective
determination of exo-1,4,-b-glucanases in a mixture of cellulolytic
enzymes. Anal Biochem 1984, 138: 481–487

 6    Segel IH. Enzyme Kinetics.  7    Valjamae P, Sild V, Pettersson G, Johansson
G. The initial kinetics of hydrolysis by cellobiohydrolases
I and II is consistent with a cellulose surface-erosion model. Eur J Biochem 1998, 253: 469–475

 8    Purich DL. Practical consideration in the design of initial velocity enzyme
rate assay. In: Purich DL, ed. Methods in Enzymology V63.  9    Sporlein S, Carstens H, Satzger H, Renner C, Behrendt R, Moroder L, Tavan P et al. Ultrafast
spectroscopy reveals subnanosecond peptide
conformational dynamics and validates molecular dynamics simulation. Proc Natl Acad Sci
USA 2002, 99: 7998–8002

10   Lu HP. Single-molecule spectroscopy studies
of conformational change dynamics in enzymatic reactions. Curr
Pharm Biotechnol 2004, 5:
261–269

11   Kim JE, Pan D, Mathies
RA. Picosencond dynamics of G-protein coupled
receptor activation in rhodopsin from time-resolved
UV resonance Raman spectroscopy. Biochemistry 2003, 42: 5169–5175

12   Aminlari M, Vaseghi T. A new colorimetric method for
determination of creatine phosphokinase.
Anal Biochem 1987, 164: 397–404

13   Ma DB, Gao
PJ, Wang ZN. Preliminary studies on the mechanism of
cellulose formation by Trichoderma pseudokoningii S-38. Enzyme Microb Technol 1990, 12: 631–635

14   Yan BX, Sun YQ, Gao PJ. Intrinsic
fluorescence in endoglucanase and cellobiohydrolase
from Trichoderma reesei disrupting the
structure of cellulose. J Protein Chem 1997,
18: 681–688

15   Schumaker LL. Spline Functions (Pure and Applied Mathematics). 16   Lee TCM. Improved smoothing
spline regression by combining estimates of different
smoothness. Stat Probab Lett
2004, 67: 133–140

17   Berlett BS, Levine
RL, Stadtman ER. Use of isosbestic
point wavelength shifts to estimate the fraction of a precursor that is
converted to a given product. Anal Biochem
2000, 287: 329–333

18   Wahbi AA, Hassan EM, Gazy AA. Use of
isosbestic points of derivative absorption curves: The dissolution rate
determination of aspirin. J Pharma Biomed Anal 1994, 12: 951–954

19   Hoxter G. Suggested
isosbestic wavelength calibration in clinical analysis. Clin
Chem 1979, 25: 143–146

20   O’Leary MA, Malik
J. Kinetics and mechanism of the binding of pyridixal
5‘-phosphate to apoglutamate decarboxylase. J Biol Chem 1972, 247: 7097–7105

21   Perrier MGD. Pharmacokinetics.
2nd ed. 22   Rescigno A. Area
under the curve and bio-availability. Pharma Res 2000, 42: 539–540

23   Purves RD. Optimum
numerical integration methods for estimation of area-under-the-curve (AUC) and
area-under-the-moment-curve (AUMC). J Pharmacakinet Biopharm 1992, 20: 211–226

24   Bardsley WG, Wright
AJ. A new approach to the measurement of sigmoid curves with
enzyme kinetic and ligand binding data. J Mol Biol 1983, 165: 163–182

25   Duggleby RG.
Estimation of the initial velocity of enzyme-catalysed
reactions by non-linear regression analysis of progress curves. Biochem J 1985, 228: 55–60

26   Huang C. Derivation and initial velocity and
isotope exchange rate equation. Methods Enzymol 1979,
63: 54–84

27   Allison PD, Purich
DL. Practical considerations in the design of initial velocity enzyme rate
assay. Methods Enzymol 1979, 63: 3–22

28   Petersen LC. Determination of Michaelis parameters from differentials of progress curves.
Biochem J 1983, 215: 589–595

29   Boeker EA. Initial
rates. A new plot. Biochem J
1982, 203: 117–123

30   Wahl RC. The calculation of initial velocity
from product progress curves when [s]<<[Km]. Anal Biochem 1994, 219: 383–384

31   Waley SG. An easy method for the determination of initial rates. Biochem J 1981, 193: 1009–1012

32   Duggleby RG. Progress-curve analysis in enzyme kinetics. Numerical solution of integrated rate equations. Biochem J 1986, 235: 613–615

33   Koerber SC, Fink
AL. The analysis of enzyme progress curves by numerical differentiation
including competitive product inhibition and enzyme reaction. Anal Biochem 1987, 165: 75–87

34   Klyosov AA. Trends in biochemistry and enzymology of
cellulose degradation. Biochemistry 1990, 29: 10577–10585

35 Wang
D, Qu YB, Gao
PJ. Primary studies on several cellulase components with special
characteristics purified from Trichoderma pseudokoniningii
S38. Biotechnol Appl Biochem 1997, 25: 181–187