Surface diffusion of cellulases and their isolated binding domains on cellulose.

The surface diffusion rate of bacterial cellulases from Cellulomonas fimi on cellulose was quantified using fluorescence recovery after photobleaching analysis. Studies were performed on an exo-beta-1-4-glycanase (Cex), an endo-beta-1-4-glucanase (CenA), and their respective isolated cellulose-binding domains (CBDs). Although these cellulose-binding domains bind irreversibly to microcrystalline cellulose, greater than 70% of bound molecules are mobile on the cellulose surface. Surface diffusion rates are dependent on surface coverage and range from a low of 2 x 10(-11) to a maximum of 1.2 x 10(-10) cm2/s. The fraction of mobile molecules increases only slightly with increasing fractional surface coverage density. Results demonstrate that the packing of C. fimi cellulases and their isolated binding domains onto the cellulose surface is a dynamic process. This suggests that the exclusion of potential CBD binding sites on the cellulose due to steric effects of neighboring bound CBDs may not fully explain the apparent negative cooperativity exhibited in CBD adsorption isotherms. Comparison with the kinetics of cellulase hydrolysis of crystalline substrate suggests that surface diffusion rates do not limit cellulase activity.

the enzymes must freely diffuse across the substrate surface to gain access to susceptible bonds, since enzyme activity is enhanced by the presence of a CBD. To test this hypothesis, we have determined the mobility of Cex, CenA, and their isolated CBDs on a cellulose surface using fluorescence recovery after photobleaching (FRAP). Enzymes or CBDs, labeled with a fluorescent tag, were adsorbed to sheets of crystalline cellulose microfibrils prepared from the cell walls of Valonia ventricosa, a large unicellular marine algae. A small, well defined region of the surface-bound fluorescent molecules was then irreversibly photobleached using a high intensity laser pulse. Recovery of fluorescence in the bleached region was subsequently monitored by confocal laser scanning microscopy to determine the diffusive mobility of the bound molecules. The results of this study provide unequivocal evidence for surface diffusion of C. fimi cellulases on crystalline cellulose and give new insights into the process of cellulase adsorption and the mechanism of cellulose hydrolysis.
FRAP has been used previously to measure the diffusion of ␣-D-glucan maltohydrolase on insoluble starch (6) and of collagenase adsorbed to a peptide substrate covalently coupled to an insoluble support (7). In each of these systems, surface mobility of the adsorbed enzyme was thought to arise because the proteins made multiple binding contacts with the sorbent surface. Individual bonds at contact points were presumed to be weak enough to permit diffusion across the surface, but the ensemble of bonds maintained the protein at the surface. Indeed, it was suggested that the combined effect of multiple weak interaction sites on a single molecule and the dynamics of protein structure and folding oscillations could result in a molecular motion similar to that observed for a centipede (8).

EXPERIMENTAL PROCEDURES
Protein Production and Purification-The genes encoding the exoglycanase Cex or the isolated CBD Cex were subcloned into the pTZEO7 vector and expressed in Escherichia coli JM101 (9). The gene fragments encoding the catalytically inactive mutant of the endoglucanase CenA (D252A) and the isolated CBD CenA were subcloned into the vector pUC18 and expressed in E. coli JM101 (10). Fermentations were carried out in a 20-liter Chemap fermenter at 37°C. Cellulases and their isolated CBDs were purified by affinity chromatography on Avicel PH101 (FMC; County Cork, Ireland), a microcrystalline form of cellulose (11). Contaminating oligosaccharides from the Avicel affinity column were removed by size exclusion chromatography on a Superose-12 column (Pharmacia; Uppsula, Sweden) (5).
Protein Labeling with Fluorescein-CBD Cex has only two amino groups that can react with fluorescein isothiocyanate (FITC): the N terminus and a single, surface-exposed lysine residue. Neither is on or near the putative binding face of the CBD (12). CBD CenA also has two potential reaction sites that are sufficiently removed from the binding face so that FITC labeling does not influence adsorption characteristics. Proteins were labeled by standard procedures (13). Briefly, 0.15 mg of FITC was added per mg of protein at 1 mg of protein/ml. The pH was adjusted to approximately 9 to initiate the reaction, and the solution was gently mixed in the dark at 4°C for 5 h. The labeled protein was passed twice through a 5-ml Sephadex G50 column (Pharmacia) in a 50 mM phosphate buffer mobile phase to separate unbound FITC from labeled protein. Fractions containing significant amounts of protein were pooled, and the absorbance at 280 and 495 nm was used to determine the number of FITC molecules bound per protein. On average, 1.5 mol of FITC bound per mol of CBD protein. A slightly higher conjugate ratio of ϳ2.2 was found for whole enzymes. Protein solutions were stored in the dark at 4°C until use.
V. ventricosa Microcrystalline Cellulose-V. ventricosa is a marine algae that grows in many temperate marine environments. Its cell wall has a multilamellar structure organized with each lamella positioned orthogonal to its neighbor. Each lamella contains several parallel layers of cellulose microfibrils (14). The individual microfibrils are highly crystalline with a square cross-section of approximately 18 nm corresponding to the 220 and the 220 crystallographic planes. Electron diffraction measurements show that the 220 face of the microfibrils is preferentially oriented parallel to the cell wall. Both orientations of the microfibril longitudinal axis occur within each lamella.
Preparation of Cellulose Surfaces for Analysis-Preparation and cleaning of V. ventricosa cell walls were based on the method of Gardner and Blackwell (15). Wall layers were carefully peeled apart under a dissecting microscope, typically into about six distinct sheets. The outermost and innermost sheets were discarded. Each of the remaining sheets were then floated and spread evenly onto a normal number 1 glass coverslip (Baxter Canlab; Montreal, Canada). After drying, the sheet was trimmed to a 3.5-mm square and permanently fixed to the coverslip using a narrow border of Quickmount mountant (Fisher). Microscopic examination showed that the mountant did not permeate past the perimeter of the cellulose sheet. Mounted cellulose samples were stored at room temperature.
Binding of Proteins to V. Ventricosa Cellulose Sheets-A short length of tubing was fixed over the dried cellulose sheet on the coverslip to form a well. Prior to binding CBDs, the well was filled with 50 mM phosphate buffer, incubated for 10 min, and then inverted and gently shaken to remove excess liquid. 400-l aliquots of labeled protein diluted in 50 mM phosphate buffer were then added to the wells. Equilibrium between the bound and free protein fractions was reached within 3 h (data not shown), after which the supernatant was removed and set aside for subsequent determination of the unbound protein concentration. The sheet was rinsed thoroughly with 50 mM phosphate buffer and then soaked for 30 min with a buffer change after 15 min. The tube that formed the well over the cellulose sheet was removed, and the cellulose sheet was mounted over a small well drilled into a normal microscope slide (Baxter) (approximate volume, 8 mm 3 ) containing 50 mM phosphate buffer. The coverslip was sealed around the well with silicon grease to prevent evaporation during imaging.
For comparison with previous results, CBD Cex binding isotherms were determined using V. ventricosa cellulose from sheets disrupted by sonication. A new approach to CBD binding analysis was developed to permit analysis of protein concentrations at pmol levels. Disrupted cellulose and FITC-labeled CBDs were added to an Eppendorf tube that had been "preblocked" with bovine serum albumin to minimize nonspecific adsorption to the container walls. The filled tubes were placed on rotating mixers for 3 h at 25°C in the dark to allow binding to come to equilibrium. Following binding, the tubes were centrifuged at 10,000 rpm for 10 min to pellet the cellulose adsorbent. The supernatant was collected and added to preblocked Eppendorf tubes containing a 25-fold excess of Avicel (based on saturation capacity) to concentrate the unbound CBD-FITC. Samples containing a known amount of CBD-FITC (standards) were prepared in a similar fashion. Tubes were then placed on a rotating mixer for 24 h at 25°C in the dark. Following binding, the tubes were spun at 10,000 rpm for 10 min to pellet the cellulose adsorbent. The Avicel pellet was resuspended in 100 l of 50 mM phosphate buffer and transferred to wells in a 96-well plate. Sample fluorescence was determined using a 96-well plate fluorimeter (IDEXX; Portland, ME) at an excitation wavelength of 488 nm and emission wavelength of 535 nm.
FRAP Analysis Using a Confocal Microscope-The Bio-Rad MRC 600 confocal microscope (Bio-Rad) used for imaging and FRAP experiments consists of laser scanning mirrors, filters for excitation and emission, and photomultiplier tube(s) (PMT) mounted onto a conventional Nikon Optiphot-II microscope. ϫ 10 (N.A. 0.8) and ϫ 60 (N.A. 1.4) objective lenses were used for imaging. A 100-milliwatt krypton/argon laser was used for excitation at 488 nm. Excited fluorescence intensity was measured using a 535-nm band pass filter and PMT. The PMT gain was adjusted to maximize the dynamic range in all images. The PMT black level was set at 4.7 for all imaging. The confocal aperture is noted for each image in the figure legends.
FRAP is typically performed using a laser spot focused through a microscope on the surface to be investigated. The laser is equipped with a shutter that permits the rapid attenuation of beam intensity so that recovery can be monitored following bleaching. Confocal laser scanning microscopes (CLSMs) have recently been used for FRAP analysis (e.g. Refs. 16 and 17). Confocal laser scanning microscopy has the significant advantage of permitting recovery monitoring at a defined image plane of the specimen. For relatively slow transport processes, a CLSM without a rapid laser attenuation shutter can be used for FRAP analysis. Slower recovery processes also permit the acquisition of entire image planes, which may include several bleached regions on the sample. In principle, this permits the determination of diffusive anisotropy across the surface under investigation.
For FRAP analysis, a 0.06% transmission filter was placed in the laser path in front of the instrument's standard filter set to attenuate the laser for recovery monitoring. The neutral density filter wheel on the Bio-Rad instrument was set to 3 (3% transmission) during all imaging scans. An image collected prior to bleaching was used to normalize fluorescence intensities to prebleach levels. The CLSM was then electronically zoomed (zoom ϭ 8) so that only a small region of the surface was illuminated during laser scanning. One scan was performed at this high zoom to produced a large, bleached reference region. The CLSM zoom was then returned to its normal setting (zoom ϭ 2), and the neutral density filter wheel on the Bio-Rad instrument set to 0 (100% transmission). Using six successive laser parking and shutter opening (ϳ100 ms each) sequences, six bleached spots were produced for FRAP analysis (Fig. 3). The neutral density filter was then returned to the 3 position, and recovery monitoring was initiated. Fluorescence intensity was monitored until greater than 95% of fluorescence recovery had occurred.
Data Analysis-The center of each bleach spot was determined by averaging several successive bleach spot images and selecting the pixel with the minimum intensity as the bleach spot center. The bleach spot intensity profile was then radially averaged to obtain an intensity cross-section with spatial heterogeneity of the crystalline cellulose microfibrils averaged out. A Gaussian curve was fit by nonlinear least squares regression to the averaged radial profile of fluorescence intensity within the bleach spot. In all cases, the averaged spot profile was well fit by a Gaussian function. The parameters from the Gaussian fit (width, depth, and offset) were used to calculate the fluorescence intensity at the spot center. The offset value (fluorescence intensity three spot diameters from the spot center) was used to estimate the "background" fluorescence bleaching occurring during recovery monitoring. Laser intensity was attenuated to minimize bleaching during recovery monitoring (less than 5%). Smoothed recovery time profiles were normalized against the initial prebleach fluorescence. The surface diffusion coefficient and mobile fraction were determined from the normalized recovery curves by nonlinear regression of the parameters in the series solution for spot FRAP diffusion analysis developed by Axelrod et al. (18). Fig. 1A shows images of a mounted cellulose sheet stained with the fluorescein-labeled binding domain of the exoglycanase Cex (CBD Cex -FITC). The parallel array microfibril structure and uniformity of the surface is evident. V. ventricosa cellulose has a very high degree of crystallinity (Ͼ95%; Ref. 15) and a high binding capacity for CBDs. Uniform, flat regions on the cellulose surface were selected for photobleaching experiments. Fig. 1B shows a cross-section perpendicular to the surface at the axis indicated in Fig. 1A. The sheets of V. ventricosa cell wall prepared for our studies are approximately 1 m thick. The axial resolution of the confocal microscope under our imaging conditions is on the order of 1 m. All fluorescence signals collected during recovery monitoring thus arise within or very near the cellulose sheet.

RESULTS
To ensure that binding of labeled and unlabeled CBDs was equivalent, binding isotherms were measured for mixtures containing 10, 20, and 50% labeled CBD Cex . The affinity constants and saturation capacities of the CBD on cellulose for the mixtures were in quantitative agreement, indicating that FITC labeling of the CBD did not affect its binding properties. Quantitative fluorescence microscopy and isotherm analysis showed that CBD-FITC fluorescence intensity/mol of bound protein was independent of surface concentration, indicating that FITC self-quenching at these surface concentrations is not significant. Fig. 2 shows the binding isotherm for FITC-labeled CBD Cex on disrupted cellulose fibers. The use of fluorescently labeled protein permitted data to be collected at much lower concentrations than have been reported previously. The adsorption isotherm data was analyzed by nonlinear regression using a model that includes two classes of binding sites (5). Table I reports regressed binding constants and capacities. The saturation capacity of V. ventricosa cellulose was determined independently using a mixture of labeled and unlabeled protein.
Thus, three parameters were regressed from the adsorption isotherm: high and low affinity constants and fraction of high affinity sites. The binding parameters for CBD Cex agree well with earlier values determined using unlabeled CBD and bacterial microcrystalline cellulose derived from Acetobacter xylinum (5).
Previous studies indicate that the binding of CBD Cex to bacterial microcrystalline cellulose (BMCC) is effectively irreversible (5). The binding characteristics of CBD Cex to BMCC and V. ventricosa cellulose are very similar (Table I), consistent with the highly crystalline nature of these two substrates. However, it was not certain that the binding of CBD Cex to V. ventricosa cellulose is also irreversible. Because irreversible association is a critical condition in our interpretation of the FRAP measurements, this question was examined in detail. First, FITC-labeled CBD was adsorbed to cellulose sheets according to the protocol for FRAP analysis. Following washing, the proteinloaded cellulose was equilibrated with 50 mM phosphate buffer. No fluorescence could be detected in the equilibrated buffer solution after 8 h of incubation, indicating that no CBD had been released from the surface. To demonstrate that CBD was not released from the cellulose surface during FRAP, the bottom side of the microscope slide well was sealed with a coverslip bearing a second unlabeled sheet of V. ventricosa cellulose. This surface acted as the capture surface for any CBD that might desorb from the target cellulose surface during FRAP. After a series of FRAP measurements, the top sheet with bound protein and the bottom sheet, which initially had no protein adsorbed to it, were imaged using the confocal microscope. The confocal aperture was adjusted for a depth of field of approximately 1 m so that fluorescence from opposing walls was excluded. The fluorescence intensity of the unlabeled cellulose sheets did not increase during FRAP experiments, confirming that the adsorption of these CBDs to crystalline cellulose is effectively irreversible under these conditions.
Photobleaching Analysis of CBD-FITC on Crystalline Cellulose- Fig. 3 shows typical images recorded for FRAP analysis of FITC-labeled CBD Cex on V. ventricosa cellulose. Fluorescence intensity measurements of the surface just prior to bleaching (Fig. 3A) were used to normalize subsequent measurements to prebleach intensities. Gaussian profile spots were bleached with a series of high intensity laser pulses in the pattern shown (Fig. 3B), and the fluorescence intensity was recorded over time by successive imaging of the bleached spots and surrounding area. Approximately 7 min after bleaching, substantial fluorescence recovery is evident in the bleached spots and at the

TABLE I Adsorption isotherm analysis for CBD Cex on crystalline cellulose
Results from adsorption isotherm analysis of this CBD are summarized. A two-site model was assumed (5). Nonlinear regression was used to determine the high and low affinity constants and the relative fraction of each. Saturation capacities were determined independently using mixtures of labeled and unlabeled proteins. Binding parameters are in good agreement with studies using unlabeled CBD and BMCC (5).

Surface Diffusion of Cellulases on Cellulose
interface between the bleached reference region and the surrounding unbleached area (Fig. 3C). Fig. 4A shows the time profiles for fluorescence intensity at the center of the bleach spot, the unbleached region of the cellulose sheet, and the center of the bleached reference region. Under the monitoring conditions selected, background bleaching was less than 5% during recovery. The bleach spot recovery profiles were therefore analyzed directly without compensating for bleaching as a result of monitoring. Fluorescence did not recover in the large bleached reference region, indicating that no highly diffusive species were present on the surface or in solution and that chemical recovery of the bleached FITC was not occurring (19).
Surface diffusion coefficients and mobile fractions were determined by nonlinear regression of FRAP data of the analytical solution developed by Axelrod (18) for the one-dimensional radial diffusion equation applied to a bleach spot with a Gaussian intensity profile, where f (t) is the normalized fluorescence intensity at the bleach spot center, t is time, d is the characteristic diffusion time for the molecular species, and , the bleach rate constant, is related to the sensitivity of the system to bleaching. The measured fluorescence intensities were normalized by the fluorescence intensity recorded just prior to bleaching. The first 20 terms in the series given in Equation 1 were used to regress d and to normalized FRAP recovery curves such as that shown in Fig. 4B. Several initial guesses were used for each fitting to ensure unique convergence of parameters during fitting.
The diffusion coefficient is related to the estimated characteristic diffusion time d by the equation, where , the half-width of the Gaussian profile (at e Ϫ2 times the spot profiles depth), was obtained by regression of the initial bleach spot profile. The mobile fraction R was determined from the long time recovery intensity by the equation, where F(ϱ) is the effective infinite time recovery, F(0) the fluorescence just after bleaching, F(i) the fluorescence intensity prior to bleaching, and F k (i) the fluorescence intensity just after bleaching. Fig. 4B shows normalized FRAP results for CBD Cex at 60% maximal surface coverage. Under these conditions, the two-FIG. 3. Image sequence collected during FRAP analysis. Prior to bleaching, an image is collected of the region to be bleached (zoom ϭ 2) (A). This image is analyzed to obtain the initial fluorescence intensities. The CLSM is then electronically zoomed (zoom ϭ 8) so that only a small region of the surface is illuminated during laser scanning. One scan is performed at this high zoom to produced a large, bleached reference region (Fig. 3B). The CLSM zoom is then returned to 2, and six bleached spots are rapidly produced with six successive 100-ms laser exposures (Fig. 3B). Fluorescence intensity is monitored for several minutes until recovery is greater than 95% complete (see Fig. 3C). Note the lack of recovery of the central area of the bleached reference region.

FIG. 4. Photobleaching analysis of CBD-FITC on Valonia.
Time profiles of the fluorescence signal for the bleach spot center (ϫ), the unbleached region of the cellulose surface (E), and the center of the bleached reference region (q) are shown in Fig. 4A. Less than 5% background bleaching occurred during recovery monitoring. Also, the reference region has less than 5% fluorescence recovery during monitoring. Fig. 4B presents a typical recovery profile used for the estimation of the diffusion coefficient and the mobile fraction of CBD Cex at a surface coverage density of ϳ60%. Fluorescence intensity is normalized by the prebleach fluorescence signal. Under these conditions, the diffusion rate for CBD Cex on crystalline cellulose is 6.0 Ϯ .5 (10 Ϫ11 ) cm 2 /s. The mobile fraction of CBD Cex is 70 Ϯ 5%. dimensional diffusion coefficient for CBD Cex on crystalline cellulose is 6.0 (Ϯ 0.9) ϫ 10 Ϫ11 cm 2 /s. This diffusion coefficient is more than 4 orders of magnitude slower than the free solution diffusion rate of 10 Ϫ6 cm 2 /s estimated from the Einstein equation for a globular protein with a mean diameter of 3 nm. If diffusion is strictly stochastic (i.e. no preferred direction or orientation), this diffusion rate corresponds to a cellobiose unitcell transit time of approximately 0.18 ms.
Based on the maximum recovery of fluorescence, the mobile fraction of CBD Cex on the crystalline cellulose surface is 65 Ϯ 5%. Therefore, on the time scale of these experiments, the majority of the CBD adsorbed to the lattice surface is mobile. FRAP analysis repeated on cellulose sheets stored in buffer at 4°C for 48 h yielded similar diffusion parameter estimates. There were no obvious changes in the morphology of the cellulose surface or microfibril packing with incubation time, indicating that the CBD had not significantly altered the cellulose structure.
Control experiments were performed to examine the effect of void spaces and the resulting potential for hindered diffusion due to molecular sieving within the cellulose fibril network of the V. ventricosa cellulose sheets. FITC-labeled myoglobin was prepared as described above. Myoglobin was selected because it is similar to CBD Cex in size (17.5 kDa) and has no measurable affinity for crystalline cellulose. Mounted cellulose sheets were incubated for 4 h with FITC-labeled myoglobin at a molar concentration 5 times the saturation level for CBD Cex and then washed in 50 mM phosphate buffer. No increase in cellulose surface fluorescence was observed, indicating that no FITCmyoglobin was bound to, or trapped within, the microcrystalline cellulose fibril network. Identical results were obtained when the cellulose sheet was preincubated with unlabeled CBD Cex , indicating that the CBDs did not modify the cellulose microfibril structure. FRAP experiments performed with unwashed cellulose sheets containing free FITC-myoglobin gave fluorescence recovery rates at least 3 orders of magnitude faster than those observed for CBDs bound to the cellulose surface. This indicates that the fibril network of the V. ventricosa cellulose sheet imposes little hindrance to solution diffusion of the labeled protein molecule, presumably because the void space is made up of pores much larger than individual protein molecules.
A series of FRAP experiments were performed with three different objective lenses (ϫ 60, 40, and 20) to create a range of initial bleach spot diameters to determine whether the observed fluorescence recovery for bound CBD Cex in FRAP experiments was due to surface diffusion or exchange between bound and unbound CBDs. For a diffusion-limited process, the characteristic fluorescence recovery time varies with the square of the half-width of the initial bleach spot diameter (see Equation  2). For a recovery process dominated by exchange from solution, two possible rate-limiting cases must be considered. If the desorption step is rate-limiting, d will be independent of . If the desorption step is not rate-limiting, d will be scaled linearly with 2 , and the slope will yield a diffusion coefficient on the order of 10 Ϫ6 to 10 Ϫ7 cm 2 /s. As expected for a diffusionlimited process, d scales linearly with 2 (Fig. 5). From Equation 2, the slope of the line in Fig. 5 yields a diffusion coefficient of 3.0 ϫ 10 Ϫ11 cm 2 /s. This value is in good agreement with the diffusion coefficients calculated from the observed recovery curves and is at least 4 orders of magnitude slower than the estimated diffusion rate of a small globular protein in solution.
The dependence of the mobile fraction estimate on the initial bleach spot radius was also examined. Over a range of characteristic recovery times, the contribution to fluorescence recovery of a relatively slow process would become more significant at shorter recovery times. As a consequence, the estimated mobile fraction of molecules would increase as decreases. However, in our experiments the mobile fraction of adsorbed CBDs was independent of the initial bleach spot size (data not shown). Therefore, a single characteristic time constant adequately characterizes the observed fluorescence recovery. The second-order dependence of recovery time on bleach spot size and the independence of the mobile fraction on characteristic recovery time strongly support our contention that fluorescence recovery results from surface diffusion of CBDs adsorbed onto microcrystalline cellulose.
Surface Diffusion Rate as a Function of Bound CBD Surface Coverage Density- Fig. 6 shows diffusion coefficients and mobile fractions regressed from FRAP measurements of CBD Cex on V. ventricosa cellulose at various fractions of the maximal surface coverage (⌫/⌫ max ). Measured binding isotherms for CBDs on the prepared sheets were used to estimate fractional surface coverage densities. The maximal protein loading was 0.4 nmol of CBD Cex /cm 2 of cellulose. The average sheet thickness was approximately 1.0 m as determined by imaging several cross-sections using a confocal microscope. Each sheet therefore represents a total cellulose volume of approximately 1.2 ϫ 10 Ϫ5 cm 3 of cellulose, or approximately 147 g of cellulose/cm 2 of cellulose sheet based on a crystalline cellulose density of 1.5 g/cm 3 . These results give a binding capacity of 5.5 mol of CBD/g of Valonia cellulose. This capacity agrees well with values from isotherms prepared using disrupted cellulose sheets, indicating that most of the surface of the undisrupted sheet is available for binding.
The diffusion rate of CBD Cex increases with surface coverage up to a ⌫/⌫ max of ϳ0.9, after which the estimated diffusion rate decreases as the surface becomes saturated (Fig. 6A). At low surface coverages, the diffusion rate is about 3.0 ϫ 10 Ϫ11 cm 2 /s, increasing to a maximum of about 1.2 ϫ 10 Ϫ10 cm 2 /s at ⌫/⌫ max Results are shown for a series of FRAP experiments performed with three different objective lens magnifications (ϫ 60 (f), 40 (ࡗ), and 20 (q)) to create a range of initial bleach spot diameters. The estimated characteristic recovery time is plotted against the initial bleach spot radius squared. A linear relationship is observed as expected for a diffusive process. The slope of the fitted line yields a diffusion coefficient estimate of ϳ 3.0 ϫ 10 Ϫ11 cm 2 /s. This value is in good agreement with the diffusion coefficient for CBD Cex on crystalline cellulose determined using nonlinear regression fitting of Axelrod's series solution to the measured recovery curve. of ϳ0.9. The mobile fraction of CBD Cex also increases slightly as a function of ⌫/⌫ max (Fig. 6B). At low surface coverages, the mobile fraction is approximately 60%. At high surface coverage density, the mobile fraction reaches a maximum of about 85%.
Surface Diffusion Rates for Different Cellulose-binding Proteins-Table II presents recovery results for two different C. fimi cellulases and their respective CBDs at 60% surface coverage. The exoglycanase Cex has little activity on crystalline cellulose (11); hence, enzymatic modification of the cellulose surface during the course of diffusion experiments was not a concern. The endoglucanase CenA is moderately active on crys-talline cellulose. A catalytically inactive mutant of CenA was therefore used to prevent surface degradation (10). This mutant binds substrate with wild-type affinity but is unable to cleave substrate because the acid catalyst Asp-252 is mutated to alanine. Diffusion coefficients and mobile fractions are presented for equivalent molar concentrations of protein. In both cases, the whole enzyme has a significantly higher diffusion rate than the isolated binding domain, with Cex having a higher diffusion rate than CenA. The mobile fraction of CenA is about 85% compared with 65% for Cex. The mobile fractions appear to be a function of the CBD domain and do not depend upon whether the domain is isolated or part of the enzyme. DISCUSSION Both CBD Cex and CBD CenA are family II cellulose-binding domains (2). CBD Cex binds irreversibly to crystalline cellulose; dilution of the free CBD at otherwise constant conditions does not result in desorption over time (5). How then does the bound enzyme find available substrate when it is distributed across the cellulose surface? Our FRAP results indicate that the irreversibly adsorbed enzyme finds reactive ␤-1,4-glucopyranoside linkages by diffusing in two dimensions across the cellulose surface. Surface diffusivities of Cex and the inactive mutant of CenA are similar; both diffuse about 30% faster than their respective isolated binding domain.
The three-dimensional solution structure of CBD Cex has recently been solved by NMR (12). The molecule has a compact ␤-barrel motif with no helix content. These results and others (20) implicate three Trp residues (Trp-54, -72, and -17) exposed on a planar face of the molecule in binding interactions with cellulose. This putative binding face presents a cluster of hydrophobic residues flanked by hydrogen bond donors and acceptors to the cellulose surface. This motif is preserved across the CBD type II family. Using titration microcalorimetry, we recently demonstrated that dehydration effects dominate the driving force for binding of CBD Cex to crystalline cellulose (5). We proposed that a CBD-cellulose complex is formed when a number of the hydrophobic residues along the CBD binding face make sufficient contact to dehydrate both the binding face and the underlying sorbent. Dehydration of the interface facilitates the formation of hydrogen-bonding pairs between the protein and the cellulose surface. Each hydrogen bond interaction has a modest affinity and dissociation rate, but the sum of interactions results in irreversible association.
The observed surface mobility of adsorbed CBD brings into question the validity of our previous model, based on a twodimensional extension of the steric exclusion theory of McGhee and von Hippel (21), for CBD Cex adsorption to crystalline cellulose (11). Steric exclusion theory assumes that adsorbed protein molecules are static, which is not supported by our FRAP results. A large fraction of bound CBD molecules are mobile  and can therefore redistribute on the surface so that binding site exclusion does not occur and close packing of adsorbed CBDs is possible. Therefore, we conclude that a two-site adsorption model is more appropriate to explain CBD-cellulose adsorption data. Several groups have noted a concentration dependence of diffusion coefficients for proteins in bilipid membranes (e.g. Refs. 22 and 23) or bound nonspecifically at surfaces (24). In each of these studies, the rate of surface diffusion decreased with increasing concentration of protein. For single sorbate diffusion on a homogeneous surface containing a single class of adsorption sites, these results are supported by theory, which predicts near 0 order dependence at low surface coverage with a strong decrease in surface diffusivity as the sorbate surface concentration approaches the jamming limit (i.e. surface saturation) (25). In accordance with this simple theory, measured surface diffusivities for CBD Cex on crystalline cellulose (Fig. 5) are insensitive to surface concentration at ⌫/⌫ max Ͻ 0.4. A marked drop in the diffusion coefficient is also observed with increasing surface coverage near surface saturation. However, in contrast to theory, we observe an increase in the diffusion coefficient with increasing surface coverage over the range 0.4 Ͻ ⌫/⌫ max Ͻ 0.9. Clearly, this system is not well described by the simple model of a single self-diffusing species on a homogeneous crystalline lattice.
The failure to capture this effect with existing simple diffusion models based on a single diffusing species on a homogeneous binding surface suggests that the crystalline cellulose surface presents a heterogeneous array of binding sites. Adsorption isotherms for CBD Cex on crystalline cellulose are well fit by a model that recognizes two distinct classes of binding sites on the cellulose surface (5). Model predictions are in quantitative agreement with isothermal titration calorimetry data for the binding event and in qualitative agreement with fluorescence microscopy images of CBD Cex -FITC bound to crystalline cellulose at low and high surface coverages. At monolayer coverage, about 20% of the adsorbed protein is bound to lower affinity sites. FRAP analysis measures the mean self-diffusion rate. The increase in CBD diffusion rate observed with increasing ⌫/⌫ max could therefore be the result of averaging between a self-diffusion rate of CBDs on high affinity sites, diffusing at ϳ3 ϫ 10 Ϫ11 cm 2 s Ϫ1 , and an increasing fraction of CBDs bound at lower affinity sites and thus diffusing at a much higher rates. This interpretation is consistent with the two-site model for adsorption. The observed results are reproduced in simulations with 20% of binding interactions of a lower affinity type such that the second diffusion coefficient is 2 orders of magnitude greater than that for proteins bound to the high affinity sites. This higher rate is in the same range as that reported for bovine serum albumin adsorbed nonspecifically to a polymethylmethacrylate film (24).
Geometric considerations of the lamella structure of the V. ventricosa cell wall indicate that some fraction of bound CBDs may move axially with respect to the scanning laser probe. Electron microscopy of CBDs absorbed at low surface coverage suggests that CBDs have a preference for crystal edges or for one of the crystalline faces of the cellulose microfibril (26). Thus, if the CBD has a preference for the 220 crystal plane, preferentially oriented parallel to the laser scanning axis, the increase in diffusion coefficient with ⌫/⌫ max may be a result of the unequal partitioning of CBDs between the two crystal faces at lower ⌫/⌫ max . Molecules that diffuse on surfaces parallel to the laser scanning axis will appear to diffuse more slowly because translation along the laser axis is not observable in our experiments (although fluorescence intensity is). Our experi-ments do not allow one to determine whether there is diffusion direction anisotropy resulting, for instance, from the migration of CBDs along the cellulose fiber axis.
Relatively little can be said about the nature of the immobile fraction of CBD molecules. The mobile fraction of bound CBD molecules was ϳ70% and increased only slightly with increasing ⌫/⌫ max . The immobile species may be due to the existence of sites that promote a very slow diffusion rate or to the trapping of adsorbed CBDs on chain ends or discontinuities in the cellulose crystal.
The role of the CBD in the activity of cellulases is not completely clear. Removal of the CBD by proteolysis or genetic manipulation reduces cellulase activity on insoluble substrates but not on soluble analogues. We have shown previously that the family II CBDs of Cex and CenA disrupt the structure of Ramie cotton fibers and release small particles from Avicel and cotton (26). Since the CBDs have no hydrolytic activity, we attribute these effects to the disruption of noncovalent binding between fibers or particles. In the present study, we saw no evidence that the CBDs or enzymes disrupted the regular structure of the V. ventricosa cellulose sheets. It seems unlikely that the CBDs can penetrate this matrix. Thus, the disruptive effects of CBDs on fibers and Avicel particles presumably relates more to macroscopic structures with weaker interactions.
CBDs can target the catalytic domain of a cellulase to its substrate, thereby increasing the local enzyme concentration. Surface diffusion of the CBD-bound enzyme would then allow the enzyme to search the cellulose surface for accessible glucosidic linkages. Little is known about substrate accessibility on the surface of crystalline cellulose. Presumably, the marked differences in the activity of endoglucanases on crystalline substrates relate in a large part to their ability to disengage microfibrils from the crystalline array and thus access new sites; however, the processivity of the enzyme may also be important. For example, the C. fimi endoglucanases CenA, CenB, and CenD display almost equal activity on Avicel, but their activities on highly crystalline BMCC vary by 2 orders of magnitude (28). Each of these enzymes has a family II CBD, so the differences in activity cannot be attributed to the CBD.
Since the spacing of accessible cleavage sites on the cellulose surface is not known, we cannot determine unequivocally whether or not the rate of surface diffusion limits cellulase activity. However, based on our measurements, this seems unlikely. At the diffusion rates reported here, the CBD will traverse several hundred lattice units on the cellulose crystal in 1 min. CenA has only moderate activity on crystalline cellulose with 0.23 mol of reducing sugar being released per mol of enzyme per min for BMCC degradation (28). Other C. fimi cellulases are more active on crystalline cellulose substrate, with turnover rates up to ϳ10.0 mol of reducing sugar/mol of enzyme/min. These low rates suggest that surface diffusion of CBDs does not limit substrate catalysis.