Surface density of cellobiohydrolase on crystalline celluloses

A critical parameter to evaluate enzymatic kinetics at a solid–liquid interface

Authors


M. Samejima, Department of Biomaterials Sciences, Graduate School of Agricultural and Life Sciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113–8657, Japan
Fax: +81 3 58415273
Tel: +81 3 58415255
E-mail: amsam@mail.ecc.u-tokyo.ac.jp

Abstract

The enzymatic kinetics of glycoside hydrolase family 7 cellobiohydrolase (Cel7A) towards highly crystalline celluloses at the solid–liquid interface was evaluated by applying the novel concept of surface density (ρ) of the enzyme, which is defined as the amount of adsorbed enzyme divided by the maximum amount of adsorbed enzyme. When the adsorption levels of Trichoderma viride Cel7A on cellulose Iα from Cladophora and cellulose Iβ from Halocynthia were compared, the maximum adsorption of the enzyme on cellulose Iβ was ∼1.5 times higher than that on cellulose Iα, although the rate of cellobiose production from cellulose Iβ was lower than that from cellulose Iα. This indicates that the specific activity (k) of Cel7A adsorbed on cellulose Iα is higher than that of Cel7A adsorbed on cellulose Iβ. When k was plotted versus ρ, a dramatic decrease of the specific activity was observed with the increase of surface density (ρ-value), suggesting that overcrowding of enzyme molecules on a cellulose surface lowers their activity. An apparent difference of the specific activity was observed between crystalline polymorphs, i.e. the specific activity for cellulose Iα was almost twice that for cellulose Iβ. When cellulose Iα was converted to cellulose Iβ by hydrothermal treatment, the specific activity of Cel7A decreased and became similar to that of native cellulose Iβ at the same ρ-value. These results indicate that the hydrolytic activity (rate) of bound Cel7A depends on the nature of the crystalline cellulose polymorph, and an analysis that takes surface density into account is an effective means to evaluate cellulase kinetics at a solid–liquid interface.

Abbreviations
BMCC

bacterial microcrystalline cellulose

CBD

cellulose-binding domain

CD

catalytic domain

CDH

cellobiose dehydrogenase

FT-IR

Fourier transform infrared spectrometer

GH

glycoside hydrolase

TEM

transmission electron microscope

Cellulose degradation is one of the most important processes in the carbon cycle, since cellulose is the major component of the cell wall of plants and the most abundant polymer in nature. In addition to the cell wall of terrestrial plants, cellulose is found in marine algae, marine animals and bacteria, and it generally consists of a mixture of crystalline (cellulose I) and disordered amorphous regions. Cellulose I is further classified into two polymorphs, triclinic cellulose Iα and monoclinic cellulose Iβ[1–3], whose detailed structures have been established recently through synchrotron X-ray and neutron fiber diffraction studies [4,5]. Cellulose Iα is metastable, and is irreversibly converted into cellulose Iβ by hydrothermal treatment in alkaline solution [6].

To degrade cellulose, many organisms produce cellulases that hydrolyze β-1,4-glucosidic linkages of the polymer. Almost all cellulases can act at amorphous regions of cellulose, whereas only a limited number can hydrolyze crystalline cellulose [7]. Cellobiohydrolase, belonging to glycoside hydrolase (GH) family 7, is the major secreted protein of many cellulolytic fungi and is one of the best studied of the enzymes hydrolyzing crystalline cellulose to cellobiose [7–11]. These enzymes have a two-domain structure: a ∼50 kDa catalytic domain (CD) and a small (3 kDa) cellulose-binding domain (CBD) connected by a highly O-glycosylated linker region [12–15]. Loss of the CBD causes a significant decrease of crystalline cellulose decomposition, but has less effect on the hydrolysis of soluble or amorphous cellulose [16], suggesting that the adsorption of the enzyme on the surface via the CBD is important for the effective hydrolysis of crystalline cellulose [17–21]. However, if an excess amount of the enzyme is adsorbed, the CD is unable to bind appropriately to the cellulose chain owing to steric interference by other enzyme molecules. This is called nonproductive binding [15], and the hydrolysis of crystalline cellulose is inhibited, even though the amount of bound enzyme is increased [22].

Although the kinetics of crystalline cellulose hydrolysis by cellulases has been investigated intensively, it remains difficult to compare findings, because of the variability of cellulose samples. The main reason for this variability is the difference of surface area between celluloses from different sources and/or different preparations. When the hydrolytic activity of cellulase for one cellulose sample is higher than that for another, it is difficult to determine whether this is because the sample has a larger surface area available to the cellulase, or whether the sample is indeed more susceptible to degradation. In the present study, we therefore investigated a novel approach to evaluate cellulase kinetics on solid substrates by using the surface density of the enzyme (defined as the adsorbed amount of the enzyme divided by the maximum adsorption of the enzyme) as a parameter, in order to avoid the influence of heterogeneity of crystalline cellulose.

Results

Analysis of highly crystalline celluloses

Highly crystalline celluloses, cellulose Iα from Cladophora and cellulose Iβ from Halocynthia and from hydrothermally treated Cladophora, were characterized by transmission electron microscope (TEM), synchrotron diffraction, and Fourier transform infrared spectrometer (FT-IR). Electron micrographs (Fig. 1A–C) showed that cellulose microcrystals prepared by hydrochloric acid treatment appear as slender rods, more than 1 mm in length and about 20 nm wide. Although the micrographs are very similar, differences were observed in the synchrotron X-ray fiber diffraction diagrams (Fig. 1D–F). The diagrams of crystalline celluloses from Halocynthia (Fig. 1E) and hydrothermally treated Cladophora (Fig. 1F) were typical of resolved Iβ patterns, whereas that of Cladophora cellulose showed patterns of both cellulose Iα and Iβ. The FT-IR spectra of the samples were different (Fig. 2). The characteristic peaks of cellulose Iα (3240 cm−1) and cellulose Iβ (3270 cm−1) in the spectrum of Cladophora cellulose were consistent with a mixture of 70% cellulose Iα and 30% cellulose Iβ (Fig. 2A), whereas only the peak at 3270 cm−1 was seen in the spectra of Halocynthia (Fig. 2B) and hydrothermally treated Cladophora (Fig. 2C) celluloses. This is because the hydrothermal treatment converted Cladophora cellulose Iα to cellulose Iβ.

Figure 1.

 TEM pictures (top row) and synchrotron X-ray fiber diffraction diagrams (bottom row) of highly crystalline celluloses. Bar indicates 500 nm. (A) and (D) Cellulose Iα from Cladophora; B and E, cellulose Iβ from Halocynthia; C and F, cellulose Iβ from hydrothermally treated Cladophora. Circles in the bottom row indicate characteristic differences between cellulose Iα and cellulose Iβ.

Figure 2.

 FT-IR spectra of highly crystalline celluloses. A, cellulose Iα from Cladophora; B cellulose Iβ from Halocynthia; C, cellulose Iβ from hydrothermally treated Cladophora. Dotted line shows characteristic peaks of cellulose Iα and cellulose Iβ at 3240 cm−1 (right) and 3270 cm−1 (left), respectively.

Adsorption of Cel7A on crystalline celluloses

The enzyme concentration dependence of adsorbed Cel7A was estimated at various time points of incubation. Figure 3A shows the results at 120 min of incubation and Fig. 3B is the Scatchard plot (A-A/[F]) of the data in Fig. 3A. Cellulose Iβ from Halocynthia showed the highest adsorption of Cel7A, which was approximately 1.5 times higher than that of cellulose Iα from Cladophora at all Cel7A concentrations tested. Since the Scatchard plots (Fig. 3B) for the three cellulose samples were all nonlinear, the binding of Cel7A cannot be fitted to a simple Langmuir equation; instead, a two-binding site model (Eqn 1) should be employed for simulation. The adsorption parameters obtained by simulation using Eqn 1 are summarized in Table 1. Although the adsorption constants for high-affinity binding (Kad1) varied among substrates, those for low-affinity binding (Kad2) were all quite similar. The hydrothermal treatment, which converts cellulose Iα to cellulose Iβ, decreased Kad1 and increased A1, but had no effect on Kad2 or A2. The maximum amount of adsorbed enzyme (Amax) for cellulose Iβ from Halocynthia was 3.2 ± 0.4 nmol·mg cellulose−1, which was 1.5 times higher than that for cellulose Iα from Cladophora (2.2 ± 0.2 nmol·mg cellulose−1).

Figure 3.

 Enzyme concentration dependence of the amount of adsorbed Cel7A (A) and Scatchard plot (B). ▪, cellulose Iα from Cladophora; ○, cellulose Iβ from Halocynthia; •, cellulose Iβ from hydrothermally treated Cladophora. The adsorption of Cel7A was measured after incubation for 120 min with 1 mg·mL−1 of crystalline cellulose at 30 °C as described in Experimental procedures. The lines represent fitting the data to Eqn 1 in Experimental procedures.

Table 1.   Adsorption parameters of highly crystalline celluloses for Cel7A. The adsorption parameters were calculated by nonlinear fitting of the data after incubation for 120, 180, 240, 320 min to Eqn 1.
 Kad1aKad2aA1bA2bAmaxb
  1. a μM−1, b nmol·mg cellulose−1.

Cladophora8.5 ± 0.70.44 ± 0.040.22 ± 0.022.0 ± 0.22.2 ± 0.2
Halocynthia3.2 ± 0.20.43 ± 0.020.80 ± 0.082.4 ± 0.33.2 ± 0.4
Hydrothermally treated Cladophora4.7 ± 0.40.43 ± 0.040.58 ± 0.032.1 ± 0.32.6 ± 0.3

Hydrolysis of highly crystalline celluloses

The time course of changes in cellobiose concentration was monitored for various concentrations of Cel7A using highly crystalline celluloses as substrates. Figure 4 shows the degradation of cellulose Iα from Cladophora as a representative result. The hydrolysis of the crystalline cellulose was well fitted by the double exponential plot versus time (Eqn 7), which shows an initial rapid increase followed by constant production of cellobiose. The cellobiose production increased with increase of total Cel7A concentration up to 2.2 µm (Abs280 ∼0.2), but decreased at higher concentrations. The velocities of cellobiose production were estimated by differentiation of cellobiose concentration in the reaction mixture, as described in Experimental procedures, then plotted versus Cel7A concentration. Figure 5 shows the results obtained at the incubation time of 120 min. As expected from the time course of cellobiose concentration, cellobiose production by Cel7A from cellulose Iα increased with increasing enzyme concentration, reaching a maximum value (0.56 µmol·min−1) at a free enzyme concentration, [F], of 1.3 µm, and then decreasing with further increase of enzyme concentration to 0.42 µmol·min−1 at [F] = 6.9 µm. Similar patterns were obtained using cellulose Iβ from Halocynthia and hydrothermally treated Cladophora as substrates, although the concentration providing maximum cellobiose production was lower ([F] ∼0.5 µm) than in the case of cellulose Iα from Cladophora.

Figure 4.

 Time course of cellobiose production from Cladophora cellulose by Cel7A. The total concentration of Cel7A in the reaction mixture was as follows: ▪, 0.40 µm; •, 0.84 µm; bsl00066, 1.3 µm; □, 2.2 µm; ○, 4.3 µm; bsl00084, 8.6 µm. The cellobiose concentration in the reaction mixture was measured with a CDH–cytochrome c redox system as described in Experimental procedures.

Figure 5.

 Free enzyme concentration dependence of cellobiose production by Cel7A after incubation for 120 min. ▪, cellulose Iα from Cladophora; ○, cellulose Iβ from Halocynthia; •, cellulose Iβ from hydrothermally treated Cladophora. The rate of cellobiose production was estimated by the fitting the time course of cellobiose concentration to Eqn 7, and by calculation using Eqn 8.

Surface density plot of Cel7A

To analyze the difference between the hydrolytic properties towards cellulose Iα and cellulose Iβ, the specific activity of adsorbed enzyme (k) was plotted versus surface density of Cel7A (ρ), as shown in Fig. 6. The specific activity towards all crystalline celluloses was high at low surface density, but decreased with increase of the ρ-value, suggesting that the crowding of Cel7A on the surface of crystalline celluloses causes a decrease of the activity. The specific activity for cellulose Iα from Cladophora was approximately twice that for cellulose Iβ from Halocynthia. Interestingly, hydrothermal treatment caused a significant decrease of specific activity for Cladophora cellulose, and the ρ–k curve became quite similar to that for cellulose Iβ from Halocynthia, although these celluloses had been prepared from different sources by different methods. This suggests that the surface density plot compensates for the different surface areas of crystalline celluloses, and reflects the specific activity of Cel7A for the crystalline polymorphs.

Figure 6.

 Surface density dependence of specific activity for adsorbed enzyme after incubation for 120, 180, 240, and 320 min. ▪, cellulose Iα from Cladophora; ○, cellulose Iβ from Halocynthia; •, cellulose Iβ from hydrothermally treated Cladophora. ρ- and k-values were estimated by using Eqns 3 and 9, respectively.

Cellobiose production and high- and low-affinity absorption were plotted versus surface density, as shown in Fig. 7. The cellobiose production reached maximum at ρ = 0.4 (cellulose Iα from Cladophora) and ρ = 0.3 (cellulose Iβ from Halocynthia and hydrothermally treated Cladophora), suggesting that sufficient space for another 1.5 or 2.3 enzyme molecules per adsorbed molecule must be left free in order to achieve optimum hydrolysis of crystalline cellulose. The surface density dependence at high- and low-affinity adsorption sites (solid and dashed lines, respectively) showed that the high-affinity curve almost reaches saturation at the ρ-value of 0.4 (cellulose Iα) or 0.3 (cellulose Iβ), whereas the low-affinity curve rises linearly with increase of ρ. Moreover, the cellobiose production increased at lower concentration, where the high-affinity adsorption was observed, whereas it declined with increase of low-affinity adsorption. These results may indicate that the high- and low-affinity binding curves represent the amounts of productive and nonproductive enzyme, respectively.

Figure 7.

 Surface density dependence of high- (solid line) and low-affinity (dashed line) adsorption of Cel7A with plot of cellobiose production. These lines are drawn using the parameters in Table 1, and the plots were obtained from the results after incubation for 120, 180, 240, and 320 min. A, cellulose Iα from Cladophora; B, cellulose Iβ from Halocynthia; C, cellulose Iβ from hydrothermally treated Cladophora.

Discussion

The hydrolysis of crystalline cellulose has generally been evaluated using microcrystalline cellulose [(Avicel), FMC Corp, Newark, DE] as a substrate, but heterogeneity of the substrate often causes variable results in the case of cellobiohydrolase [7,20]. To avoid this difficulty, bacterial microcrystalline cellulose (BMCC) has been used as a homogeneous crystalline cellulose substrate instead [22–24]. However, as we have shown, the properties of BMCC as a substrate of cellulase are strongly dependent on the preparation conditions [25]. In the present study, we wished to compare the highly crystalline celluloses from Cladophora and Halocynthia, and faced difficulties in evaluating their hydrolysis, presumably because of the differences of surface area and/or surface structure. There are several techniques to estimate the surface area of solid cellulose from the amounts of bound small molecular compounds, such as nitrogen, water or dye, but the results cannot be used to evaluate the surface area available to cellulases, since CBDs are adsorbed only on limited regions of crystalline cellulose, mainly hydrophobic surfaces, as demonstrated previously [26–29]. Therefore, we developed the novel concept of using surface density as a parameter to express the adsorption of cellobiohydrolase relative to the maximum amount of adsorption of the enzyme (Amax), in order to obtain the specific activity of Cel7A for crystalline cellulose.

This approach has several advantages: (1) Amax provides a measure of the surface area of crystalline cellulose available as a substrate of cellulase. It is reported that cellulose Iβ from Halocynthia has a greater hydrophobic surface than cellulose Iα from Cladophora[30]. Indeed, in the present study, Amax of Cel7A on cellulose Iβ from Halocynthia was 1.5 times higher than that on cellulose Iα from Cladophora. (2) Generally, specific activity of cellulase is evaluated based on the amount of added enzyme. However, this is inappropriate for cellobiohydrolases, since only adsorbed enzyme represents ‘working enzyme’ which generates the product (cellobiose). Therefore, we should evaluate the specific activity of adsorbed enzyme. (3) During the hydrolytic process, the shape and surface area of the solid substrate should change with the reaction time. By using surface density as a parameter, however, we can monitor the changes of surface area and compensate for them, whether they arise from the nature of the cellulose preparations, or from changes during hydrolysis. In the present study, indeed, the Amax values decreased slightly with increasing incubation time, perhaps because of a reduction of the surface area owing to enzymatic degradation (data not shown). However, cellobiose production also decreased correspondingly with increasing incubation time, suggesting that the surface density plot can allow for the real-time changes of the substrate caused by the enzymatic reaction.

In nature, there are two crystalline polymorphs of cellulose, celluloses Iα and Iβ[1–3], and cellulose Iα has been reported to be degraded much faster than cellulose Iβ[31,32]. To analyze the differences in degradability in detail, we prepared three crystalline cellulose samples, Iα-rich crystalline cellulose from Cladophora, natural cellulose Iβ from Halocynthia, and cellulose Iβ generated by hydrothermal treatment of Cladophora cellulose, and we compared the hydrolysis of these samples by Cel7A. The ρ–k plot of Cel7A (Fig. 6) clearly indicates that the higher degradability of cellulose Iα is mainly due to a higher specific activity of the enzyme for this substrate than for cellulose Iβ, but is not due to a larger surface area. As hydrothermal treatment does not cause any change of shape of cellulose microfibrils [33], differences of specific activity should reflect differences in the arrangements of cellulose chains in the two crystalline polymorphs. Quite recently, the detailed structures of celluloses Iα and Iβ were solved by synchrotron X-ray and neutron fiber diffraction analyses [4,5]. The top views of the hydrophobic surfaces of celluloses Iα and Iβ are compared in Fig. 8. If cellulose chains of the first layer (colored cyan) are superimposed in the two crystalline polymorphs, the cellobiose units in the second layer of celluloses Iα (colored yellow) are completely opposed to those of cellulose Iβ (colored green). This suggests that Cel7A can distinguish this difference between the first and second layers of crystalline celluloses. A possible reason for this is that the structural difference may cause a difference of steric hindrance at CBD or CD, and thus may affect the processivity of Cel7A on the crystalline celluloses [8,22,34].

Figure 8.

 Views of the hydrophobic surfaces of cellulose Iα (left) and cellulose Iβ (right). The cellulose chains in the first layer are superimposed and colored cyan. The chains in the second layer are colored yellow (cellulose Iα) and green (cellulose Iβ). The structures are based on the results reported by Nishiyama et al. [4,5].

The enzyme concentration dependence of absorption ([F]–A plot; Fig. 3A) fitted well to the two-binding site equation reported by Ståhlberg et al. [16]. In addition, when the high- and low-affinity adsorption curves and cellobiose production were plotted versus surface density (Fig. 7), it appeared that cellobiose production increased in the high-affinity phase of adsorption, whereas it was apparently inhibited with increase of low-affinity binding. This may be because high-affinity adsorption involves both CD and CBD (productive binding), whereas low-affinity adsorption may involve only CBD (nonproductive binding). In Table 1, moreover, a higher Kad1-value was observed for cellulose Iα than cellulose Iβ, although Kad2 for all samples were quite similar to each other. This phenomenon might be explained by the different affinity of productive binding, i.e. CD of Cel7A may hold cellulose Iα more tightly than cellulose Iβ, resulting in higher cellobiose production from cellulose Iα than cellulose Iβ at same ρ-value. Since low affinity (nonproductive) binding contributes much more to the total amount of adsorbed enzyme than high-affinity (productive) binding, a drastic decrease of specific activity is observed with increase of ρ, as shown in Fig. 7. To elucidate the relationship between adsorption and hydrolysis, further experiments with mutant enzymes and detailed kinetic studies will be necessary.

The simple analytical method used in the present study, i.e. measuring the adsorption of the enzyme and the concentration of products in the same reaction mixture, makes it possible to evaluate the enzyme kinetics at a solid–liquid interface. This approach not only provides novel insights into cellulose–cellulase interaction, but also should be relevant to many other enzymes acting on insoluble substrates having a limited surface area.

Experimental procedures

Cellulose and enzyme preparations

Cellulose samples from green alga Cladophora sp. and tunicate Halocynthia roretzi were used in this study. They were purified by repeated treatments with 5% KOH and 0.3% NaClO2 solutions [35], then broken into small fragments using a double-cylinder type homogenizer. The Cladophora cellulose was further hydrothermally treated in 0.1 m NaOH solution at 260 °C [33]. The cellulose samples thus obtained were hydrolyzed with 4 m HCl solution at 80 °C for 6 h, and then suspensions of cellulose microcrystals dispersed in water were prepared as reported previously [36].

Cel7A from Trichoderma viride (formerly known as cellobiohydrolase I) was purified from a commercial cellulase mixture, Meicelase (Meiji Seika Kaisha Co., Ltd, Tokyo, Japan) as described previously [25,37]. Recombinant cellobiose dehydrogenase (CDH) was produced by Pichia pastoris and purified from the culture filtrate as described previously [38]. The purity of these enzymes was confirmed by SDS/PAGE. No detectable contamination of β-glucosidase or hydroxyethylcellulose-degrading activity was observed in Cel7A or CDH.

Analysis of highly crystalline celluloses

Dilute suspensions of crystalline celluloses were dropped on carbon-coated copper grids, allowed to dry, and observed with a JEOL 2000EX TEM (Jeol Ltd., Tokyo, Japan), operating at 200 kV under diffraction contrast in the bright-field mode [39].

For the X-ray fiber diffraction analysis, oriented films of cellulose microcrystals were prepared as previously reported [40]. The X-ray fiber patterns were obtained on a flat imaging plate, R-AXIS IV++ (Rigaku Corporation, Tokyo, Japan), at room temperature using synchrotron radiation with a wavelength of 0.1 nm in beam line BL40B2 at the SPring-8 facility in Japan.

Dilute suspensions were cast on glass plates and the dried films were analyzed with a JASCO FT-IR 615 spectrometer (JASCO Corporation, Tokyo, Japan) in the region of 4000–400 cm−1; 64 scans of 4 cm−1 resolution were signal-averaged and stored.

Adsorption of Cel7A on crystalline celluloses

Crystalline cellulose (0.1% w/v) was incubated with various concentrations of enzymes (total concentration, Abs280 ∼0.04–1.6) in 1 mL of 50 mm sodium acetate buffer, pH 5.0, at 30 °C using an end-over-end mixer (12 r.p.m.). The mixture was centrifuged (15 000 g × 30 s) to terminate the reaction after incubation for 15, 30, 60, 120, 180, 240, and 320 min, and the supernatant (900 µL) was collected. The absorbance at 280 nm of the supernatant was measured after the termination of the enzymatic reaction, and the concentration of free enzyme [F] (µm) was determined based on an absorption coefficient at 280 nm of 88 250 m−1·cm−1 for T. viride Cel7A, estimated from the amino acid sequence of the enzyme [41]. The amount of adsorbed enzyme (A, nmol·mg cellulose−1) was calculated by subtraction of the amount of free enzyme from the amount of added enzyme, as described previously [16,22,23,42]. The amount of adsorbed enzyme was plotted versus free enzyme concentration, based on a two-binding-site model for Cel7A analysis [16], using the following equation:

image(1)

where A1 and A2 are the adsorption maxima of high- and low-affinity binding (nmol/mg-cellulose); Kad1 and Kad2 are the adsorption constants of the high- and low-affinity binding sites (µm−1). The maximum amount of adsorbed enzyme (Amax, nmol·mg cellulose−1) and the surface density (ρ) of Cel7A were defined according to the following equations:

image(2)
image(3)

Measurement of cellobiose formation

The concentration of cellobiose formed in the supernatant was estimated from the amount of cytochrome c reduced by CDH, as follows. The supernatant (after incubation for 15, 30, 60, 120, 180, 240, and 320 min) was kept at 4 °C for 18 h to allow the anomeric configuration to reach equilibrium. The supernatant (100 µL) was then incubated for 3 min with 200 nm recombinant CDH and 50 µm cytochrome c (bovine heart, Wako Pure Chemical Industries, Ltd, Osaka, Japan) in 50 mm sodium acetate buffer, pH 4.0, at 30 °C, and the absorbance at 525.6 (Abs525.6: isosbestic point of oxidized and reduced cytochrome c) and 550.0 nm (Abs550.0) were measured. The reduced cytochrome c concentrations were calculated using the following equations

image(4)
image(5)
image(6)

where inline image (= 7.80 mm−1·cm−1) and inline image (= 25.8 mm−1·cm−1) are the absorption coefficients at 550.0 nm for oxidized and reduced cytochrome c, respectively; ε525.6 (= 10.2 mm−1·cm−1) is the absorption coefficient of cytochrome c at 525.6 nm; [Cox] and [Cred] are the concentrations of oxidized and reduced cytochrome c, respectively. The proportion of β-anomer in cellobiose was estimated to be 64.9 ± 0.4% at the temperature employed in the present study, and it was assumed that two moles of cytochrome c is reduced by one mole of β-anomeric cellobiose. Examination of the cellobiose concentration after 18 h incubation at 4 °C indicated that further hydrolysis was minimal (< 2 µm), and this was confirmed by comparison of the cellobiose concentrations in reaction mixtures containing supernatant with and without ultrafiltration. Since precipitation prevented the measurement of cellobiose concentration at the highest enzyme concentration (Abs280 ∼1.6), these data was eliminated from the results.

Analysis of the rate of cellobiose production from crystalline celluloses

The rate of cellobiose production at various time points was estimated from fitting of cellobiose concentrations in the reaction mixtures to the following equation based on Väljamäe et al. [22]:

image(7)

where P(t) is the cellobiose concentration (µm); t is time (min); and a, b, c, and d are empirical constants. The rate of cellobiose production (v) was calculated by the differentiation of Eqn 7 as follows:

image(8)

Thus, the specific activity of adsorbed enzyme k (min−1) was defined as follows:

image(9)

In order to evaluate the steady-state reaction of Cel7A, the rate of cellobiose production and the specific activity were calculated from the data points after incubation for 120, 180, 240, and 320 min. It must be pointed out that we have used Eqns 7 and 8 only for estimating the rate of cellobiose production at each time point. We do not include any physical interpretation to the equations or the constants since they are empirical.

Acknowledgements

The authors are grateful to Professor Gunnar Johansson (Department of Biochemistry, University of Uppsala) for valuable discussions about the kinetics of cellobiohydrolases. We thank Dr K. Noguchi (Tokyo University of Agriculture and Technology, Tokyo, Japan) for his help during the synchrotron radiation experiments, which were performed at BL40B2 in SPring-8 with the approval of the Japan Synchrotron Research Institute (JASRI) (Proposal no. 2002A0435-NL2-np). This research was supported by a Grant-in-Aid for Scientific Research to MS (no. 17380102) from the Japanese Ministry of Education, Culture, Sports and Technology, and a Research Fellowship to RH from the Japan Society for the Promotion of Science.

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