Surface density of cellobiohydrolase on crystalline celluloses A critical parameter to evaluate enzymatic kinetics at a solid–liquid interface Kiyohiko Igarashi, Masahisa Wada, Ritsuko Hori and Masahiro Samejima Department of Biomaterials Sciences, Graduate School of Agricultural and Life Sciences, The University of Tokyo, Japan 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 gen- erally consists of a mixture of crystalline (cellulose I) and disordered amorphous regions. Cellulose I is fur- ther classified into two polymorphs, triclinic cellulose I a and monoclinic cellulose I b [1–3], whose detailed structures have been established recently through syn- chrotron X-ray and neutron fiber diffraction studies [4,5]. Cellulose I a is metastable, and is irreversibly con- verted into cellulose I b by hydrothermal treatment in alkaline solution [6]. To degrade cellulose, many organisms produce cellu- lases that hydrolyze b-1,4-glucosidic linkages of the polymer. Almost all cellulases can act at amorphous Keywords cellobiohydrolase; cellobiose dehydrogenase; crystalline cellulose; glycoside hydrolase; solid–liquid interface Correspondence 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 (Received 3 April 2006, revised 26 April 2006, accepted 2 May 2006) doi:10.1111/j.1742-4658.2006.05299.x 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 (q) 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 I a from Cladophora and cellulose I b from Halocynthia were compared, the maximum adsorption of the enzyme on cellulose I b was $1.5 times higher than that on cellulose I a , although the rate of cellobiose production from cellulose I b was lower than that from cellulose I a . This indicates that the specific activity (k) of Cel7A adsorbed on cellulose I a is higher than that of Cel7A adsorbed on cellulose I b . When k was plotted versus q, a dramatic decrease of the specific activity was observed with the increase of surface density (q-value), suggesting that overcrowding of enzyme molecules on a cellulose surface lowers their activ- ity. An apparent difference of the specific activity was observed between crystalline polymorphs, i.e. the specific activity for cellulose I a was almost twice that for cellulose I b . When cellulose I a was converted to cellulose I b by hydrothermal treatment, the specific activity of Cel7A decreased and became similar to that of native cellulose I b at the same q-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. FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS 2869 regions of cellulose, whereas only a limited number can hydrolyze crystalline cellulose [7]. Cellobiohydro- lase, 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 hydrolyz- ing 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-gly- cosylated 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 crys- talline 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 crys- talline cellulose is inhibited, even though the amount of bound enzyme is increased [22]. Although the kinetics of crystalline cellulose hydro- lysis 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 prep- arations. 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 cellu- lase, or whether the sample is indeed more susceptible to degradation. In the present study, we therefore investigated a novel approach to evaluate cellulase kin- etics 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 I a from Cladopho- ra and cellulose I b from Halocynthia and from hydro- thermally 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 micro- graphs are very similar, differences were observed in the synchrotron X-ray fiber diffraction diagrams (Fig. 1D– F). The diagrams of crystalline celluloses from Halocyn- thia (Fig. 1E) and hydrothermally treated Cladophora (Fig. 1F) were typical of resolved I b patterns, whereas that of Cladophora cellulose showed patterns of both cellulose I a and I b . The FT-IR spectra of the samples were different (Fig. 2). The characteristic peaks of cellu- lose I a (3240 cm )1 ) and cellulose I b (3270 cm )1 ) in the spectrum of Cladophora cellulose were consistent with a mixture of 70% cellulose I a and 30% cellulose I b (Fig. 2A), whereas only the peak at 3270 cm )1 was seen in the spectra of Halocynthia (Fig. 2B) and hydrother- mally treated Cladophora (Fig. 2C) celluloses. This is because the hydrothermal treatment converted Clado- phora cellulose I a to cellulose I b . Adsorption of Cel7A on crystalline celluloses The enzyme concentration dependence of adsorbed Cel7A was estimated at various time points of incuba- tion. Figure 3A shows the results at 120 min of incuba- tion and Fig. 3B is the Scatchard plot (A-A ⁄ [F]) of the data in Fig. 3A. Cellulose I b from Halocynthia showed the highest adsorption of Cel7A, which was approxi- mately 1.5 times higher than that of cellulose I a 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 (K ad1 ) varied among substrates, those for low-affinity binding (K ad2 ) were all quite similar. The hydrothermal treat- ment, which converts cellulose I a to cellulose I b , decreased K ad1 and increased A 1 , but had no effect on K ad2 or A 2 . The maximum amount of adsorbed enzyme (A max ) for cellulose I b from Halocynthia was 3.2 ± 0.4 nmolÆmg cellulose )1 , which was 1.5 times higher than that for cellulose I a from Cladophora (2.2 ± 0.2 nmolÆmg cellulose )1 ). 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 I a from Cladophora as a representative result. The hydrolysis of the crystalline cellulose was well fitted by the double expo- Surface density of GH family 7 cellobiohydrolase K. Igarashi et al. 2870 FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS nential 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 lm (Abs 280 $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 proce- dures, 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 I a increased with increasing enzyme concentration, reaching a maximum value (0.56 lmolÆmin )1 ) at a free enzyme concentration, [F], of 1.3 lm, and then decreasing with further increase of enzyme concentration to 0.42 lmolÆmin )1 at [F] ¼ 6.9 lm. Similar patterns were obtained using cellulose I b from Halocynthia and hydrothermally treated Cladopho- ra as substrates, although the concentration provid- ing maximum cellobiose production was lower ([F] $0.5 lm ) than in the case of cellulose I a from Cladophora. Surface density plot of Cel7A To analyze the difference between the hydrolytic properties towards cellulose I a and cellulose I b , the specific activity of adsorbed enzyme (k) was plotted versus surface density of Cel7A (q), as shown in Fig. 6. The specific activity towards all crystalline celluloses was high at low surface density, but decreased with increase of the q-value, suggesting that the crowding of Cel7A on the surface of crys- talline celluloses causes a decrease of the activity. The specific activity for cellulose I a from Cladophora was approximately twice that for cellulose I b from Halocynthia. Interestingly, hydrothermal treatment caused a significant decrease of specific activity for Cladophora cellulose, and the q–k curve became quite similar to that for cellulose I b from Halocynthia, although these celluloses had been prepared from different sources by different methods. This suggests that the surface density plot compensates for the dif- ferent surface areas of crystalline celluloses, and reflects the specific activity of Cel7A for the crystal- line polymorphs. Fig. 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 I a from Cladophora; B and E, cellulose I b from Halocynthia; C and F, cellulose I b from hydrothermally treated Cladophora. Circles in the bottom row indicate characteristic differences between cellulose I a and cellulose I b . K. Igarashi et al. Surface density of GH family 7 cellobiohydrolase FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS 2871 Cellobiose production and high- and low-affinity absorption were plotted versus surface density, as shown in Fig. 7. The cellobiose production reached maximum at q ¼ 0.4 (cellulose I a from Cladophora) and q ¼ 0.3 (cellulose I b from Halocynthia and hydro- thermally treated Cladophora), suggesting that suffi- cient 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-affin- ity adsorption sites (solid and dashed lines, respect- ively) showed that the high-affinity curve almost reaches saturation at the q-value of 0.4 (cellulose I a )or 0.3 (cellulose I b ), whereas the low-affinity curve rises linearly with increase of q. 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. Discussion The hydrolysis of crystalline cellulose has generally been evaluated using microcrystalline cellulose [(Avicel), FMC Corp, Newark, DE] as a substrate, but heterogen- eity 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 proper- ties 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 crystal- line celluloses from Cladophora and Halocynthia, and faced difficulties in evaluating their hydrolysis, presuma- bly because of the differences of surface area and ⁄ or sur- face structure. There are several techniques to estimate the surface area of solid cellulose from the amounts of A B Fig. 3. Enzyme concentration dependence of the amount of adsorbed Cel7A (A) and Scatchard plot (B). n, cellulose I a from Cladophora; s, cellulose I b from Halocynthia; d, cellulose I b from hydrothermally treated Cladophora. The adsorption of Cel7A was measured after incubation for 120 min with 1 mgÆmL )1 of crystalline cellulose at 30 °C as described in Experimental procedures. The lines represent fitting the data to Eqn 1 in Experimental procedures. A B C Fig. 2. FT-IR spectra of highly crystalline celluloses. A, cellulose I a from Cladophora; B cellulose I b from Halocynthia; C, cellulose I b from hydrothermally treated Cladophora. Dotted line shows charac- teristic peaks of cellulose I a and cellulose I b at 3240 cm )1 (right) and 3270 cm )1 (left), respectively. Surface density of GH family 7 cellobiohydrolase K. Igarashi et al. 2872 FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS 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 previ- ously [26–29]. Therefore, we developed the novel con- cept of using surface density as a parameter to express the adsorption of cellobiohydrolase relative to the maxi- mum amount of adsorption of the enzyme (A max ), in order to obtain the specific activity of Cel7A for crystal- line cellulose. This approach has several advantages: (1) A max pro- vides a measure of the surface area of crystalline cellu- lose available as a substrate of cellulase. It is reported that cellulose I b from Halocynthia has a greater hydro- phobic surface than cellulose I a from Cladophora [30]. Indeed, in the present study, A max of Cel7A on cellu- lose I b from Halocynthia was 1.5 times higher than that on cellulose I a from Cladophora. (2) Generally, specific activity of cellulase is evaluated based on the amount of added enzyme. However, this is Fig. 5. Free enzyme concentration dependence of cellobiose pro- duction by Cel7A after incubation for 120 min. n, cellulose I a from Cladophora; s, cellulose I b from Halocynthia; d, cellulose I b from hydrothermally treated Cladophora. The rate of cellobiose produc- tion was estimated by the fitting the time course of cellobiose con- centration to Eqn 7, and by calculation using Eqn 8. Fig. 6. Surface density dependence of specific activity for adsorbed enzyme after incubation for 120, 180, 240, and 320 min. n, cellu- lose I a from Cladophora; s, cellulose I b from Halocynthia; d, cellu- lose I b from hydrothermally treated Cladophora. q-andk-values were estimated by using Eqns 3 and 9, respectively. 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. K ad1 a K ad2 a A 1 b A 2 b A max b Cladophora 8.5 ± 0.7 0.44 ± 0.04 0.22 ± 0.02 2.0 ± 0.2 2.2 ± 0.2 Halocynthia 3.2 ± 0.2 0.43 ± 0.02 0.80 ± 0.08 2.4 ± 0.3 3.2 ± 0.4 Hydrothermally treated Cladophora 4.7 ± 0.4 0.43 ± 0.04 0.58 ± 0.03 2.1 ± 0.3 2.6 ± 0.3 a lM )1 , b nmolÆmg cellulose )1 . Fig. 4. Time course of cellobiose production from Cladophora cellu- lose by Cel7A. The total concentration of Cel7A in the reaction mix- ture was as follows: n, 0.40 lM; d, 0.84 lM; m,1.3lM; h, 2.2 lM; s,4.3l M; n,8.6lM. The cellobiose concentration in the reaction mixture was measured with a CDH–cytochrome c redox system as described in Experimental procedures. K. Igarashi et al. Surface density of GH family 7 cellobiohydrolase FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS 2873 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 A max values decreased slightly with increas- ing 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 I a and I b [1–3], and cellulose I a has been reported to be degraded much faster than cellu- lose I b [31,32]. To analyze the differences in degrada- bility in detail, we prepared three crystalline cellulose samples, I a -rich crystalline cellulose from Cladophora, natural cellulose I b from Halocynthia , and cellulose I b generated by hydrothermal treatment of Cladophora cellulose, and we compared the hydrolysis of these samples by Cel7A. The q–k plot of Cel7A (Fig. 6) clearly indicates that the higher degradability of cellu- lose I a is mainly due to a higher specific activity of the enzyme for this substrate than for cellulose I b , but is not due to a larger surface area. As hydrothermal treatment does not cause any change of shape of cellu- lose microfibrils [33], differences of specific activity should reflect differences in the arrangements of cellu- lose chains in the two crystalline polymorphs. Quite recently, the detailed structures of celluloses I a and I b were solved by synchrotron X-ray and neutron fiber diffraction analyses [4,5]. The top views of the hydro- phobic surfaces of celluloses I a and I b are compared in Fig. 8. If cellulose chains of the first layer (colored cyan) are superimposed in the two crystalline poly- morphs, the cellobiose units in the second layer of cel- luloses I a (colored yellow) are completely opposed to those of cellulose I b (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]. The enzyme concentration dependence of absorp- tion ([F]–A plot; Fig. 3A) fitted well to the two-bind- ing site equation reported by Sta ˚ hlberg 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 A B C Fig. 7. Surface density dependence of high- (solid line) and low- affinity (dashed line) adsorption of Cel7A with plot of cellobiose pro- duction. 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 I a from Cladophora;B,cel- lulose I b from Halocynthia; C, cellulose I b from hydrothermally trea- ted Cladophora. Surface density of GH family 7 cellobiohydrolase K. Igarashi et al. 2874 FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS may involve only CBD (nonproductive binding). In Table 1, moreover, a higher K ad1 -value was observed for cellulose I a than cellulose I b , although K ad2 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 I a more tightly than cellulose I b , resulting in higher cellobiose production from cellu- lose I a than cellulose I b at same q-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 q,as shown in Fig. 7. To elucidate the relationship between adsorption and hydrolysis, further experi- ments 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 kin- etics at a solid–liquid interface. This approach not only provides novel insights into cellulose–cellulase interac- tion, 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% NaClO 2 solutions [35], then broken into small frag- ments 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 cellu- lose microcrystals dispersed in water were prepared as reported previously [36]. Cel7A from Trichoderma viride (formerly known as cello- biohydrolase I) was purified from a commercial cellulase mixture, Meicelase (Meiji Seika Kaisha Co., Ltd, Tokyo, Japan) as described previously [25,37]. Recombinant cello- biose 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 b-glu- cosidase 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. Fig. 8. Views of the hydrophobic surfaces of cellulose I a (left) and cellulose I b (right). The cellulose chains in the first layer are su- perimposed and colored cyan. The chains in the second layer are colored yellow (cellu- lose I a ) and green (cellulose I b ). The struc- tures are based on the results reported by Nishiyama et al. [4,5]. K. Igarashi et al. Surface density of GH family 7 cellobiohydrolase FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS 2875 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, Abs 280 $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 lL) was collected. The absorbance at 280 nm of the supernatant was measured after the termination of the enzymatic reaction, and the con- centration of free enzyme [F](lm) was determined based on an absorption coefficient at 280 nm of 88 250 m )1 Æcm )1 for T. viride Cel7A, estimated from the amino acid sequence of the enzyme [41]. The amount of adsorbed enzyme (A, nmolÆmg 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: A ¼ A 1 =ð1=K ad1 þ½FÞ þ A 2 =ð1=K ad2 þ½FÞ ð1Þ where A 1 and A 2 are the adsorption maxima of high- and low- affinity binding (nmol ⁄ mg-cellulose); K ad1 and K ad2 are the adsorption constants of the high- and low-affinity binding sites (lm )1 ). The maximum amount of adsorbed enzyme (A max ,nmolÆmg cellulose )1 ) and the surface density (q)of Cel7A were defined according to the following equations: A max ¼ A 1 þ A 2 ð2Þ q ¼ A=A max ¼ A=ðA 1 þ A 2 Þð3Þ 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 lL) was then incubated for 3 min with 200 nm recombinant CDH and 50 lm 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 (Abs 525.6 : isosbestic point of oxidized and reduced cytochrome c) and 550.0 nm (Abs 550.0 ) were measured. The reduced cytochrome c concentrations were calculated using the following equations Abs 550:0 ¼ e ox 550:0 ½C ox þe red 550:0 ½C red ð4Þ Abs 525:6 ¼ e 525:6 ð½C ox þ½C red Þ ð5Þ ½C red ¼ðe 525:6 Abs 550:0 À e ox 550:0 e red 550:0 Abs 525:6 Þ= e 525:6 ðe red 550:0 À e ox 550:0 Þð6Þ where e ox 550:0 (¼ 7.80 mm )1 Æcm )1 ) and e red 550:0 (¼ 25.8 mm )1 Æcm )1 ) are the absorption coefficients at 550.0 nm for oxidized and reduced cytochrome c, respectively; e 525.6 (¼ 10.2 mm )1 Æcm )1 ) is the absorption coefficient of cytochrome c at 525.6 nm; [C ox ] and [C red ] are the concentrations of oxid- ized and reduced cytochrome c, respectively. The proportion of b-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 b-anomeric cellobiose. Examination of the cellobiose concentration after 18 h incubation at 4 ° C indicated that further hydrolysis was minimal (< 2 l m), and this was con- firmed by comparison of the cellobiose concentrations in reaction mixtures containing supernatant with and without ultrafiltration. Since precipitation prevented the measure- ment of cellobiose concentration at the highest enzyme con- centration (Abs 280 $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 Va ¨ ljama ¨ e et al. [22]: PðtÞ¼að1 À e Àbt Þþcð1 À e Àdt Þð7Þ where P(t) is the cellobiose concentration (lm); t is time (min); and a, b, c, and d are empirical constants. The rate of cellobiose production (v) was calculated by the differenti- ation of Eqn 7 as follows: v ¼ dPðtÞ=dt ¼ abe Àbt þ cde Àdt ð8Þ Thus, the specific activity of adsorbed enzyme k (min )1 ) was defined as follows: k ¼ v=A ð9Þ 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 phys- ical interpretation to the equations or the constants since they are empirical. Surface density of GH family 7 cellobiohydrolase K. Igarashi et al. 2876 FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS Acknowledgements The authors are grateful to Professor Gunnar Johans- son (Department of Biochemistry, University of Upp- sala) 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. References 1 Atalla RH & Vanderhart DL (1984) Native cellulose. A composite of two distinct crystalline forms. 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Surface density of GH family 7 cellobiohydrolase K. Igarashi et al. 2878 FEBS Journal 273 (2006) 2869–2878 ª 2006 The Authors Journal compilation ª 2006 FEBS . Surface density of cellobiohydrolase on crystalline celluloses A critical parameter to evaluate enzymatic kinetics at a solid–liquid interface Kiyohiko. cellulose. This approach has several advantages: (1) A max pro- vides a measure of the surface area of crystalline cellu- lose available as a substrate of cellulase.