Binding and Movement of Individual Cel7A Cellobiohydrolases on Crystalline Cellulose Surfaces Revealed by Single-molecule Fluorescence Imaging*

Background: Molecular level mechanisms underlying cellulose hydrolysis by cellulases remain poorly understood. Results: The majority of cellobiohydrolase molecules on cellulose surfaces were stationary. Conclusion: There is a need for improved understanding of cellulose properties resulting in large fractions of stalled cellulases. Significance: Dynamic single-molecule imaging of cellulases provides insights on productive/nonproductive binding and surface diffusion on cellulose. The efficient catalytic conversion of biomass to bioenergy would meet a large portion of energy requirements in the near future. A crucial step in this process is the enzyme-catalyzed hydrolysis of cellulose to glucose that is then converted into fuel such as ethanol by fermentation. Here we use single-molecule fluorescence imaging to directly monitor the movement of individual Cel7A cellobiohydrolases from Trichoderma reesei (TrCel7A) on the surface of insoluble cellulose fibrils to elucidate molecular level details of cellulase activity. The motion of multiple, individual TrCel7A cellobiohydrolases was simultaneously recorded with ∼15-nm spatial resolution. Time-resolved localization microscopy provides insights on the activity of TrCel7A on cellulose and informs on nonproductive binding and diffusion. We measured single-molecule residency time distributions of TrCel7A bound to cellulose both in the presence of and absence of cellobiose the major product and a potent inhibitor of Cel7A activity. Combining these results with a kinetic model of TrCel7A binding provides microscopic insight into interactions between TrCel7A and the cellulose substrate.

The efficient catalytic conversion of biomass to bioenergy would meet a large portion of energy requirements in the near future. A crucial step in this process is the enzyme-catalyzed hydrolysis of cellulose to glucose that is then converted into fuel such as ethanol by fermentation. Here we use single-molecule fluorescence imaging to directly monitor the movement of individual Cel7A cellobiohydrolases from Trichoderma reesei (TrCel7A) on the surface of insoluble cellulose fibrils to elucidate molecular level details of cellulase activity. The motion of multiple, individual TrCel7A cellobiohydrolases was simultaneously recorded with ϳ15-nm spatial resolution. Timeresolved localization microscopy provides insights on the activity of TrCel7A on cellulose and informs on nonproductive binding and diffusion. We measured single-molecule residency time distributions of TrCel7A bound to cellulose both in the presence of and absence of cellobiose the major product and a potent inhibitor of Cel7A activity. Combining these results with a kinetic model of TrCel7A binding provides microscopic insight into interactions between TrCel7A and the cellulose substrate.
Lignocellulosic biomass is the most abundant biological material on earth. It has been projected that the available land resources of the United States are sufficient for producing the biomass needed for cellulosic biofuels to meet 30% of the nation's transportation fuel requirements by the middle of this century (1). However, at present, the high cost of producing such cellulosic biofuels prevents their widespread use. Processes for the biochemical conversion of lignocellulosic biomass to biofuels are typically comprised of three steps (2): (i) pretreatment: cellulose is separated from the plant cell wall matrix and rendered into a form more susceptible to enzyme degradation; (ii) enzyme degradation: a mixture of cellulases and other enzymes catalyzes the hydrolysis of cellulose fibrils, a chemically stable assembly of cellulose molecules having a degree of polymerization of 100 -20,000 to its monomer component, glucose, a simple sugar (3); and (iii) fermentation: microbial conversion of glucose to biofuels such as ethanol and other useful hydrocarbon products. Currently, the high cost of the second step is a roadblock to the economical, large scale conversion of lignocellulosic biomass to fuel. The enzyme-catalyzed hydrolysis of cellulose is complex; it entails the synergistic action of enzymes known collectively as cellulases consisting of endoglucanases and exoglucanases on the insoluble substrate. According to the consensus model of synergistic cellulose catalysis, endoglucanases randomly break accessible cellulose chains; cellobiohydrolases engage free ends of cellulose chains and processively move along the chains releasing primarily cellobiose, a glucose dimer, and to a lesser extent monomeric glucose and longer glucose polymers (up to 6-mers) into solution. Other enzymes, ␤-glucosidases, catalyze the cleavage of these soluble products to monomeric glucose.
Cellulases secreted by the filamentous fungus Trichoderma reesei have received the most scientific and commercial attention to date. This organism is known to produce two cellobiohydrolases, Cel7A (CBH I) and Cel6A (CBH II). Here we use the newer CAZy classification system to denote these enzymes (4); their older names are given in parentheses. These cellulases have similar structures consisting of a large (ϳ450 amino acids) catalytic domain connected by a ϳ30-amino acid peptide linker to a small (ϳ35 amino acids) cellulose-binding module. T. reesei Cel7A (TrCel7A), a processive cellobiohydrolase (ϳ50 -60% of total protein secreted by T. reesei), is known to degrade cellulose from the reducing ends of the chains, whereas the somewhat less processive Cel6A (ϳ15-20% of total protein secreted by T. reesei) shows activity toward nonreducing chain ends. The different catalytic functions of these cellulases have been attributed to differences in the structures of their catalytic domains.
In contrast to homogeneous solution phase catalysis, it is well known that the overall efficiency of this heterogeneous catalysis process depends on factors in addition to the catalytic rates of the cellulases, including: cellulase adsorption, desorption, and diffusion rates on the insoluble cellulose substrate and the processivity of exoglucanase-catalyzed hydrolysis of individual cellulose molecules. To date, in large part because of limitations of the bulk analysis methods used for its study, this heterogeneous reaction is poorly understood. Here we have used time-resolved, single-molecule fluorescence imaging to monitor the binding and movement of individual TrCel7A molecules on highly crystalline cellulose isolated from Cladophora sp. algae. We compare the binding behaviors of TrCel7A cellobiohydrolase from Trichoderma under various conditions that are either conducive to or inhibitory to cellulase catalysis. Additionally we have measured the distribution of residence times of individual TrCel7A molecules bound to the cellulose substrate both in the presence of and in the absence of cellobiose.

EXPERIMENTAL SECTION
Enzyme Purification and Labeling-For the present study, TrCel7A was purified from a commercially available source, Celluclast (Novozymes), following a variation of previously described methods (5,6). An affinity purification step using a p-aminophenylcellobioside matrix (7) was included to ensure complete removal of endoglucanases in the purified TrCel7A preparation. The purified cellulase was labeled with a cyanine fluorophore (Cy5; GE Healthcare) according to procedures specified by the manufacturer, with some modification. The labels are functionalized with N-hydroxysuccinimidyl ester that reacts with the primary amines of lysine residues on the enzyme. To control the dye to protein ratio of the fluorescently labeled cellulase, the labeling reaction was done under less than favorable conditions, i.e., lower pH (pH 7.5-8.0) and reduced dye to protein ratio (1:2). SDS-PAGE confirmed the purity of both the unlabeled and Cy5-labeled TrCel7A (Fig. 1A). Singlemolecule photobleaching step measurements of the labeled protein showed that the labeling scheme successfully limited the number of dyes attached to the individual enzyme to one or two (Fig. 1, B and C). Similarly labeled cellulases have previously been shown to retain their original activity on cellulose (8,9). This was confirmed for our labeled enzymes with activity assays.
Enzyme Activity Assay-The activities of both labeled and unlabeled TrCel7A on insoluble Cladophora sp. cellulose were compared using the 2,2Ј-bicinchoninic acid assay to measure the reducing sugars produced by cellulase catalyzed hydrolysis of the substrates. 40 mol of TrCel7A and Cy5-TrCel7A cellulase per gram of cellulose were incubated with 1.5 and 0.75 mg/ml of Cladophora sp. cellulose at room temperature for 18 and 114 h. The solutions were spun down to remove the insoluble fibers, and the supernatant was used to perform the colorimetric 2,2Ј-bicinchoninic acid assay (10). The results ( Fig. 2A) were base line-corrected for background absorptions caused by the presence of the enzyme and substrate. Cellulase activities were also measured using the fluorogenic substrate 4-methylumbelliferyl-␤-D-cellobioside (Sigma-Aldrich) as described previously (11). Briefly, 0.1 mM of substrate was incubated at room temperature with either TrCel7A or Cy5-TrCel7A at concentrations of 125 and 500 nM in 50 mM sodium acetate (pH 5). Cleavage of the substrate produces a fluorescence signal to indicate the cellulase activity. 1 M sodium carbonate (pH 10) was used to quench the hydrolysis reaction. The fluorogenic assay was used to measure the activities of all the enzymes used in this study, both unlabeled and labeled. This assay was also used to measure verify inhibition of cellulase activities by cellobiose as well as to verify the retention of cellulase activity in the presence of glucose, a major component of the oxygen-scavenging system used to reduce photobleaching of the Cy5 fluorophore in the single-molecule imaging experiments (Fig. 2C).
Cellulose Sample and Labeling-Purified cellulose from the green algae Cladophora sp. was prepared as previously described (12). Because the cellulose was isolated from the organism using a sulfuric acid treatment, we soaked it in a mild solution of hydrochloric acid (0.1 M HCl) with 5 min of incubation in a sonicator bath to remove sulfur groups left by the treatment. Dispersed suspensions of the cellulose fibrils were obtained using a series of ultrasonication steps totaling 30 min in 50 mM sodium acetate buffer (pH 5). For fluorescence imagingofthecellulosefibrils,thecellulosewaslabeledwithdichloro- triazinyl aminofluorescein (DTAF; Sigma-Aldrich) 2 according to the protocol described previously (13,14). Differential interference contrast and fluorescence images of the DTAF-labeled cellulose verified the specificity of the DTAF labeling for the cellulose (Fig. 3, B and C). Cellobiose (Sigma-Aldrich) was purchased and used without further purification.
Single-molecule Imaging and Analysis-A suspension of cellulose fibrils was introduced into the imaging chamber, which was fabricated from a quartz slide coupled with a coverslip (inner volume, ϳ10 l), and incubated overnight. The fibrils were deposited onto the imaging surface by gravity and adhered to the surface by nonspecific interactions. After washing to remove unbound fibrils, the imaging surface was blocked with BSA by treatment with 1 mg/ml of BSA solution for 15 min. The BSA blocking was required to reduce nonspecific interactions between the cellulase and the glass surface. Without BSA blocking, significant nonspecific binding of enzyme to the glass surface was observed. It has been reported that BSA only weakly interacts with various celluloses including delignified celluloses similar to one used in this study (15,16). Therefore, we expect BSA to have a negligible effect on the interactions between cellulases and cellulose. Enzyme samples were preincubated under the various conditions used (pH 5, pH 5 ϩ 20 mM cellobiose, or pH 10) for 30-300 s prior to their introduction into the imaging chamber. We refer to reactions conducted at pH 5 as the "standard condition," indicating conditions conducive to enzyme hydrolysis. Picomolar concentrations of labeled enzyme were introduced into the imaging chamber for the fluorescence imaging experiments. Single-molecule imaging was performed using prism type total internal reflection fluorescence microscopy (supplemental Fig. S1). Laser excitation at 633 and 488 nm was used to excite the Cy5-labeled cellulases and DTAF-labeled cellulose fibrils, respectively. A ϫ60 1.2 NA water immersion objective (UPlanS Apo; Olympus) was used to image the emission from the sample surface (ϳ54 ϫ 27 m area) onto an electron multiplying charge coupled device camera (Photon Max; Princeton Instruments). Laboratory-constructed dual view optics and appropriate emission filters (Semrock) were used to form a pair of images centered on the emissions of the fluorescein, and Cy5 fluorophores used to label the cellulose and cellulase, respectively. The overall magnification resulted in a pixel size of 106 nm. Image sequences were collected at integration times of 0.1 s (10 frames/s) and 1 s (1 frames/s) over intervals of up  to 1200 s. The excitation lasers were blocked except during image acquisition to avoid photobleaching the samples. Image data were collected from previously unilluminated regions of the sample surface (supplemental Fig. S3). Buffer solutions consisting of 50 mM sodium acetate or 50 mM glycine were used to fix the pH at 5 and 10.4, respectively. Oxygen scavenging components consisting of glucose, glucose oxidase, catalase, and Trolox TM (6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid) were added to the imaging buffers to improve the photostability of the Cy5 fluorophore used to label TrCel7A. The activity assay using 4-methylumbelliferyl-␤-D-cellobioside showed that these additional components had no effect on cellulase activity. All of the imaging experiments were performed at room temperature.
The image data were initially visualized and analyzed using ImageJ software (National Institutes of Health) and a program written in IDL (ITT Visual Information Solutions) and then further analyzed using the Igor Pro (Wave Metrics) and Matlab (Mathworks) programs. Trajectories of individual fluorescently labeled TrCel7A molecules were generated by a frame by frame analysis of the image data. In each frame, spatially isolated fluorescence spots with intensities above a preset threshold were identified. The centroid positions of these spots were determined from fits to two-dimensional Gaussians over pixels within a ϳ700-nm radius of the peak intensity pixel. The spatial registration between the two image channels was done by twodimensional polynomial mapping to subpixel accuracy (17). Mapping coefficients were generated from calibration images of 0.1-m diameter fluorescent beads (TetraSpeck TM ; Invitrogen) with emission spectra covering both channels. Using the centroid positions of spots identified during an initial analysis, time trajectories of the spot fluorescence intensities were calculated by summing the signal intensity in 5 ϫ 5-pixel regions around the spot centroid positions. These time histories were used to compile the binding time distributions shown in Fig. 7.

RESULTS
Single-molecule fluorescence imaging was used to monitor the binding and movement of individual, fluorescently labeled TrCel7A cellobiohydrolases on crystalline cellulose substrates.
Fluorescence microscopy permits precise measurement of the positions of fluorescent molecules by localization, in the image plane, of the centroids of the point spread functions of optically resolved molecules (18 -20). In the limit of zero background noise, the localization precision scales as ϳ/ͱN, where is the standard deviation of the point spread function, and N is the number of detected fluorescence photons comprising the point spread function. In our imaging setup, ϭ ϳ180 nm, and we detect several thousand photons per fluorescent molecule per second. In the absence of background, detection of 1000 photons from a single fluorescent molecule would permit its localization to well under 10 nm. However, in practice, localization precision is substantially degraded by the presence of noise (background emission from the sample and CCD camera readout noise) in the image (19,20). Under our imaging conditions, background noise limits the localization precision to ϳ15 nm. This "super-resolution" optical method provides resolution approaching that of scanning electron microscopy, while enabling time-resolved imaging under physiological conditions.

Specific Binding of Cellulase Enzyme on Cellulose Substrates-
To render cellulases fluorescent, TrCel7A was labeled with one or more cyanine fluorophores via surface-exposed lysine residues on its catalytic domain. Our cellulose substrate was highly crystalline cellulose fibrils isolated from Cladophora sp. algae. Atomic force microscopy imaging (Fig. 3A) showed that the smaller cellulose fibrils were ϳ1-3 m in length, ϳ100 -400 nm wide, and ϳ10 -40 nm high. The larger fibril structures were visible using conventional light microscopy; however, the smaller cellulose fibrils were not. Therefore, it was necessary to verify that observed cellulases were actually bound to the cellulose substrate (and not the glass substrate) and moved along the fibrils. We tested the binding specificity of the cellulases to the cellulose in our imaging setup. Because the total internal reflection fluorescence microscopy imaging setup provides laser excitation ϳ100 nm beyond the glass-water interface, it can be used to monitor the binding of fluorescently labeled enzymes to the ϳ10 -40 nm high cellulose substrates immobilized to the glass substrate (supplemental Fig. S1). For colocalization experiments, cellulose was fluorescently labeled with DTAF as described under "Experimental Procedures." Fig. 4 and supplemental Video S1 show that Cy5-TrCel7A binds specifically to cellulose and that super-resolution localization images of the positions of individual molecules bound to the cellulose can be reconstructed (Fig. 4C). The colocalization of the DTAFlabeled cellulose emission and Cy5-TrCel7A spot positions (Fig. 4, A and B) verifies the specific binding of enzyme to the cellulose substrate (also see supplemental Fig. S2).
Fluorescently labeled cellulases were observed to bind to and desorb from the immobilized cellulose substrate during data collection. This behavior is shown in supplemental Video S1. Fig. 4B shows the composite image formed by the summation of 1200 1-s frames to show the extent of enzyme binding on the cellulose substrate. The super-resolution image of the same area (Fig. 4C) reconstructed from the accumulated centroid positions of single Cy5-labeled TrCel7A cellobiohydrolases bound to the cellulose fibrils shows the distribution of cellulase binding to the cellulose. We observed that the cellulases bind over the entire lengths of the fibrils with no preference for either the ends or middle of the fibrils. However, some areas showed extensive binding, whereas others showed little or no binding. For example, comparing the locations of the cellulose fibrils and the distribution of cellulase binding in Fig. 4, there are areas of fibrils where there were very few cellulase binding events over the course of 1200 s.
We observed that TrCel7A bound rapidly to the cellulose and remained bound to the cellulose fibrils even after extensive washing with buffer solution. Our results are consistent with electron microscopy imaging studies of Cel7A binding to microcrystalline cellulose from Valonia macrophysa (21,22). In addition, there were occasional observations of movement of TrCel7A on the cellulose, as demonstrated in supplemental Fig.  S4 and the supplemental videos.
Dynamics of TrCel7A on Cellulose Substrates-We used single-molecule trajectories obtained from fluorescence imaging data to characterize the movement (e.g., diffusive versus linear motion) of individual TrCel7A molecules on the cellulose substrate. Because we collected image sequences at frame rates as high as 10 per second, we were able to monitor the binding (see supplemental Video S2) and movement (see supplemental Video S3) of individual cellulases on the cellulose substrate. We observed that, under standard conditions (conducive to hydrolysis at pH 5), the majority (Ͼ90%) of the TrCel7A molecules bound to the cellulose were stationary within our ϳ15-nm localization precision. In addition, we observed that a similar fraction (ϳ5%) of enzymes show a "stop and go" type of motion, undergoing a rapid, sliding movement between the slow/stationary periods. Fig. 5 shows an example of this type of motion for an individual TrCel7A molecule moving on a cellulose fibril (see supplemental Video S3). The time history of the motion of this cellobiohydrolase molecule can be interpreted as follows. In seconds 0 -4, the enzyme in the solution approached the cellulose surface and bound weakly as evidenced by its relatively large velocity (25-30 nm/s) and concomitantly high position variance during this time. In seconds 5 and 6, the enzyme moved rapidly (ϳ350 nm/s) along the cellulose fibril. Given the high speed of movement, we interpret this as a rapid diffusional motion rather than processive movement associated with hydrolysis of the cellulose substrate. In seconds 7-59, the enzyme stopped its rapid movement and bound tightly to the cellulose substrate as evidenced by its small position variance. During this stationary phase, the enzyme's position variance was due to the ϳ15-nm localization precision of our measurement. A possible interpretation of this behavior is that the enzyme bound to an active hydrolysis site and began slow, processive hydrolysis of the cellulose substrate. Given the range of turnover rates (ϳ1-4 per second) expected for TrCel7A, this enzyme likely did not processively hydrolyze the substrate over the entire time, ϳ50 s, it was tightly bound to the substrate because it would have moved ϳ50 -200 nm over this time. Its position change during this time was within our localization precision (ϳ15 nm) so its processivity in this instance was ϳ15 turnovers or less. During seconds 60 -72, the enzyme molecule again began to move rapidly along the cellulose fibril, stopping briefly at several sites before finally desorbing from the surface. The movement of the enzyme is summarized in Fig. 5. Fig. 5A is a plot of the enzyme's trajectory on the cellulose substrate. Fig.  5B shows the displacement of the enzyme from its initial binding position versus time. The "stop and go" movements are evidenced by the abrupt changes in displacement. Fig. 5C is a plot of the enzyme's velocity versus time. The enzyme moved at a speed of ϳ350 nm/s during its first large displacement and at an average speed of ϳ84 nm/s during its subsequent stop and go movements. We again emphasize that only a small fraction (ϳ5%) of bound spots show rapid movements between stationary periods, whereas majority of the spots remained stationary within our 15-nm localization precision. More of these events are shown in supplemental Fig. S5 and supplemental Videos S4 and S5.
Occasionally we observed an interesting phenomenon where a second enzyme would bind in close proximity to a previously bound enzyme (see supplemental Videos S6 and S7). This was evidenced by the appearance of elongated, oval spot shapes caused by the binding of two or more enzymes in close proximity that evolved into a single, brighter round spot as one enzyme moved even closer to the other (see supplemental Video S8). This binding mode is often accompanied by a rapid (ϳ100 nm/s) codirectional, sliding movement of the spots that may indicate the concerted movement of two or more enzymes to the next stopping point.
TrCel7A Binding Behavior in the Presence of Inhibitor-To test the effect of a catalysis inhibitor on cellulase binding, TrCel7A was preincubated with cellobiose in the buffer before flowing into the imaging chamber containing the cellulose. Cellobiose, the major product of TrCel7A activity, is known to be an effective inhibitor of Cel7A activity (23). Our bulk assay using the fluorogenic substrate (4-methylumbelliferyl-␤-D-cellobioside) also confirmed that the activities of unlabeled and labeled TrCel7A decreased by more than 10-fold in the presence of 20 mM cellobiose (Fig. 2C). In the imaging experiments at pH 5 in the presence of 20 mM cellobiose, we observed a slight reduction in the number of TrCel7A molecules bound to the cellulose substrate compared with that observed under standard conditions (pH 5). Moreover, in the presence of cellobiose, we observed an increase in the number of TrCel7A molecules that moved substantial distances (Ͼ100 nm) along the cellulose fibrils. In one example, Fig. 6 shows TrCel7A enzyme moving ϳ700 nm along the fibril in the presence of cellobiose. This movement is shown in supplemental Video S9, composed of three separate image sequences that show similar motions by three enzyme molecules at different times (at ϳ5, ϳ350, ϳ440, and ϳ760 s) of observation. This movement was similar to the stop and go motion we occasionally observed (Fig. 5) for TrCel7A under standard conditions without cellobiose, the main differences being that in the presence of cellobiose, the distance moved during rapid diffusional steps increased (ϳ160 nm) and the time spent between steps decreased (supplemental Fig. S5).
Binding Time Distributions of TrCel7A Bound to Cellulose- Fig. 7 shows measured distributions of residence times of single TrCel7A cellobiohydrolases bound to the cellulose substrate. For each individual TrCel7A, the residence time was assessed as the time during which the enzyme remained at a given location before desorbing or diffusing on the cellulose. Under standard conditions (pH 5), 1025 TrCel7A molecules were observed (Fig.  7A), whereas 1035 TrCel7A molecules were measured in the presence of cellobiose (Fig. 7B). At pH 5, the TrCel7A binding time distribution (Fig. 7A) shows a biexponential decay. The time constants and relative amplitudes of the two decay components are a ϭ 30 s (84%) and b ϭ 173 s (16%), giving an amplitude-weighted average lifetime of 53 s. At pH 5 in the presence of 20 mM cellobiose (Fig. 7B), the TrCel7A binding time distribution is also biexponential with time constants and relative amplitudes of a ϭ 9.5 s (97%) and b ϭ 145 s (3%) and an average lifetime of 14 s. The average residence time of TrCel7A molecules bound to the cellulose in the presence of cellobiose was lower than that without cellobiose.
TrCel7A Binding Behavior at Higher pH-At high pH (glycine/NaOH, pH 10), a condition known to reduce the structural stability and lower the melting temperature of the catalytic domain (CD), thereby reducing TrCel7A activity (24), we observed weaker binding of TrCel7A to the cellulose substrate, similar to that observed for TrCel7A at pH 5 in the presence of 20 mM cellobiose. The surface coverage of bound enzyme decreased as compared with that observed for TrCel7A under standard conditions (pH 5). We also found that the residence time of the bound enzyme decreased compared with that observed under standard conditions. At pH 10, bound TrCel7A exhibited increased mobility similar to that we observed for TrCel7A at pH 5 in the presence of cellobiose (see supplemental Video S10).

DISCUSSION
Super-resolution imaging of fluorescently labeled TrCel7A bound to cellulose fibrils from Cladaphora sp. (Fig. 4) showed spatial heterogeneity in the degree of binding of the enzyme to the substrate. The origin of this binding heterogeneity is unknown. Given that TrCel7A is known to hydrolyze cellulose from the reducing end of the cellulose polymer, one possible explanation is that the observed binding heterogeneity reflects the distribution of productive binding sites (free reducing ends) on the cellulose fibrils. Another possibility is that where little to no TrCel7A was observed, the hydrophobic faces of the fibrils where the family 1 CBMs of TrCel7A have been shown to localize (25) are not exposed. However, we cannot discount the possibility that areas that show no binding are physically inaccessible to the enzyme. Further experimentation, for example comparison of TrCel7A binding behaviors on cellulose substrates having different crystalline morphologies (e.g., Cellulose II and Cellulose III) and controlling the orientation of the fibrils, is needed to answer this question.
Under conditions conducive for enzyme-catalyzed hydrolysis (pH 5), we observed that the majority (Ͼ90%) of the TrCel7A molecules were stationary to within ϳ15 nm, the lateral resolution in our images. Presumably these cellobiohydrolases were either nonproductively bound to the substrate or had stalled after completing a limited number of catalytic turnovers. Given the ϳ15-nm lateral resolution in our images and the expected ϳ1-nm displacement of the enzyme along the substrate per turnover, only the movement of an enzyme executing more than ϳ15 turnovers can be tracked in our images. As a result, we cannot differentiate between low processivity (Ͻ15 turn-  over) catalysis events and stationary, nonproductive binding events in our images. Igarashi et al. (26,27) observed the movement of individual TrCel7A cellobiohydrolases on the surface of Cellulose I with high speed atomic force microscopy and showed that the enzyme moves up to ϳ50 nm with an average speed of ϳ3.5 nm/s. A significant difference between our work and that of Igarashi et al. is that our experiments were performed at Ͼ1000-fold lower (subnanomolar) enzyme concentration than the micromolar enzyme concentration used by Igarashi et al. This may account for our different results; at the low enzyme concentrations we used, the highly processive events observed by Igarashi et al. may be exceedingly rare.
Other recent studies measured TrCel7A processivities that were much lower (ϳ1-100 (28) and ϳ10 (29,30)) than the degree of polymerization in native celluloses (ϳ1000 -100000) or the intrinsic processivity (ϳ500 -4000) estimated for this enzyme. This low processivity was attributed to limitations (obstacles) imposed by the substrate morphology on enzyme catalysis (28). The lower processivity also explains the predominance of stationary enzymes in our images under standard conditions. Kinetic measurements by Westh and co-workers (29) showed that the majority of TrCel7A molecules (Ͼ70% of the total enzyme pool) are stalled on the insoluble substrate after only ϳ30 s following the addition of the enzyme. Our results are also consistent with recent work by Sugimoto et al. (31), who analyzed and compared the adsorption of a fusion protein analog of TrCel7A and that of intact TrCel7A on crystalline cellulose from Cladophora sp. Their results suggest that only a small fraction of the cellobiohydrolases bound to the cellulose may be truly active. Fluorescence imaging by Moran-Mirabal et al. (9) also observed no sustained surface diffusion of fluorescently labeled bacterial cellulases (Cel5A, Cel6B, and Cel9A from Thermobifida fusca) on bacterial microcrystalline cellulose.
A small population of the isolated TrCel7A molecules (ϳ5%) exhibited rapid, sliding movements between slow/stationary periods on the cellulose ( Fig. 5 and supplemental Fig. S5). We attribute this stop and go sliding movement to a population of weakly bound TrCel7A not engaged in processive hydrolysis. Although we cannot discount the possibility that the observed "sliding" movement is due to rapid dissociation and rebinding of the TrCel7A molecule along the substrate, the molecule cannot be moving very far above the substrate because it would become invisible because of the small (ϳ100 nm) penetration depth the excitation intensity into the aqueous phase imposed by the total internal reflection excitation geometry used in our imaging setup. Such incidences of stop and go sliding motion increased under conditions inhibiting TrCel7A activity (in the presence of cellobiose or at pH 10). Moreover, the mobility of bound TrCel7A increased (see Fig. 6, supplemental Fig. S5, and supplemental Videos S9 and S10), and average binding lifetime was reduced (Fig. 7B). We note here that the stop and go motion observed in our experiments is distinct from that observed by Igarashi et al. (27), who previously attributed the stop and go motion observed on a smaller length scale (Ͻ50 nm) in their experiments to the formation and resolution of enzyme "traffic jams" caused by obstacles encountered on the cellulose substrate during enzyme-catalyzed hydrolysis. For hydrolysis to occur, the reducing end of the cellulose chain must be threaded into the catalytic tunnel of the CD and bound to the catalytic site. We hypothesize that this conformation corresponds to the "tight binding" (stationary) mode we observed for the majority of the TrCel7A under standard conditions (pH 5) and is represented by the population of TrCel7A with the longer binding time (173 s) observed in these experiments (Fig. 7A). In contrast, we hypothesize that the population with the shorter residence time of 30 s (Fig. 7A) corresponds to TrCel7A bound only by the cellulose binding module (CBM). When binding through the CD is inhibited either by the cellobiose inhibitor or by alkaline conditions, the enzyme remains bound to the substrate through its CBM. This binding mode is weaker, as evidenced by our observations of increased diffusive motion (Fig. 6 and supplemental Video S9) and reduced binding lifetimes from 30 to 9.5 s (Fig. 7B). Moreover, an increase in the fraction of the overall bound TrCel7A population with the shorter residence time (84 -97%) was observed, indicating that more of the TrCel7A enzymes were weakly bound in the presence of cellobiose. Our observation that TrCel7A binds to cellulose either in the presence of the cellobiose inhibitor or under alkaline conditions is consistent with previous studies that showed that the binding affinity of the TrCel7A CBM to the cellulose substrate is relatively insensitive to the presence of cellobiose (32,33) or to pH change in the range of 3-10 (24).
Kinetic Model of TrCel7A Binding-The biphasic distribution of the binding lifetimes of TrCel7A on cellulose (Fig. 7) supports our hypothesis of two binding modes (tight binding and weaker binding) of TrCel7A on cellulose. We modeled these two binding modes as two kinds of complexes formed by TrCel7A on cellulose: the CBM binding to hydrophobic regions on the cellulose surface to produce nonproductive (NP) complexes and the CD binding to the reducing ends of the cellulose chains leading to the formation of multivalent productive (P) complexes with chain ends (Fig. 8). The lifetime of the NP complex bound to regions of cellulose fibrils other than the reducing ends is related to the rate of desorption of the CBM from the cellulose surface (k off ). We further modeled TrCel7A binding to reducing ends by either the CBM or CD as singly bound enzymes (E 1 ) with a rate of 2k on or doubly bound (P) complex (by both CBM and CD) with intramolecular binding rate constant, k on . A detailed model that allows for different k on and k off values for the CD and CBM domains is provided in the supplemental materials. Here, we make the simplification that adsorption and desorption rates are similar for both the CD and CBM domains to reduce the number of free parameters used to fit the experimental data shown in Fig. 7 (two binding lifetimes). Considering the model depicted in Fig. 8, under steady state conditions, the lifetimes for E 1 ( 1 ) and P ( P ) are related as shown in Equations 2 and 3.
Solving the above equations for lifetimes led to Equations 4 and 5.
This shows that the lifetimes for productive doubly bound ( p ) or singly bound complexes ( 1 ) should be longer than that of the nonproductive complex ( NP ). The lifetimes 1 of E 1 and P of P are similar (within 5-15 s) and cannot be distinguished within the resolution of our measurements. Therefore, we assign the short and long time components in the experimental residence time distributions (Fig. 7) to lifetimes of the nonproductive (NP) and productive (P) complexes, respectively. Solving the above equations for NP and P using the assigned experimental residence times, we obtain k off ϭ 0.03 s Ϫ1 and k on ϭ 0.28 s Ϫ1 for binding of TrCel7A on the Cladophora sp. cellulose surface ( Table 1). The desorption rate obtained using this model is consistent with the typical values that have been reported in the literature (29,34). We applied the same model to the TrCel7A binding time distributions measured in the presence of a catalytic inhibitor (cellobiose) (Fig. 7B) to obtain k on ϭ 2.9 s Ϫ1 and k off ϭ 0.11 s Ϫ1 (Table 1). These results suggest that the rate of desorption of the CBM from the cellulose surface is faster in the presence of the cellobiose (k off ϭ 0.11 and 0.03 s Ϫ1 , with and without cellobiose, respectively), suggesting that the CBM can desorb faster from the cellulose surface when cellobiose is bound to its CD. One possibility is that cellobiose may be blocking or clogging the tunnel of CD domain, thereby leading to faster desorption of CBM through an allosteric mechanism. Additional experiments are needed to explain the molecular underpinnings of this observation. The results further suggest that the intramolecular binding rate of the enzyme to the end of the cellulose chain was an order of magnitude faster in the presence of cellobiose (k on ϭ 2.9 and 0.28 s Ϫ1 , with and without cellobiose, respectively). Surprisingly, these results imply that the affinity of TrCel7A to cellulose is higher in the presence of cellobiose. This is consistent with molecular dynamics simulations of TrCel7A showing that the affinity of the enzyme for cellobiose is higher in the substrate bound complex as compared with when the substrate was not present (35). The greater affinity of cellobiose to cellulose bound TrCel7A was due to the exclusion of water molecules in the catalytic tunnel of the enzyme. The higher affinity for the substrate in the presence of the inhibitor seems to be an evolutionary cost associated with the closed active site architecture associated with processive enzymes.
Conclusion-Time-resolved, super-resolution single-molecule fluorescence imaging revealed the complex nature of cellulase activity on crystalline cellulose substrates. Our imaging results showed that under conditions conducive to hydrolysis (pH 5), the majority (Ͼ90%) of the TrCel7A cellobiohydrolase molecules were stationary to within the ϳ15-nm resolution of our measurement, whereas ϳ5% of the population translated with rapid, linear, sliding motion. We interpret these populations as a majority of enzymes that were nonproductively bound or stalled after completing less than ϳ10 catalytic turnovers and a small fraction that were weakly bound, thus diffusing rapidly along the cellulose surface. Moreover, we found that competitive inhibition by cellobiose promoted more rapid desorption of nonproductively bound TrCel7A (bound only by its CBM), while simultaneously increasing the likelihood of "productive engagement" by TrCel7A (binding by both CD and CBM). The results accentuate the need for improved understanding of substrate properties that result in large fractions of nonproductively bound or physically stalled cellulases. Our results demonstrate that single-molecule imaging will be a powerful tool to directly assess the effectiveness of substrate processing strategies to improve the efficiency of cellulases on cellulose.  Fig. 7. b Model depicted in Fig. 8.