Measuring PETase enzyme kinetics by single-molecule microscopy

Polyethylene terephthalate (PET) is one of the most widely produced man-made polymers and is a significant contributor to microplastics pollution. The environmental and human health impacts of microplastics pollution have motivated a concerted effort to develop microbe- and enzyme-based strategies to degrade PET and similar plastics. A PETase derived from the bacteria Ideonella sakaiensis was previously shown to enzymatically degrade PET, triggering multidisciplinary efforts to improve the robustness and activity of this and other PETases. However, because these enzymes only erode the surface of the insoluble PET substrate, it is difficult to measure standard kinetic parameters, such as kon, koff and kcat, complicating interpretation of the activity of mutants using traditional enzyme kinetics frameworks. To address this challenge, we developed a single-molecule microscopy assay that quantifies the landing rate and binding duration of quantum dot-labeled PETase enzymes interacting with a surface-immobilized PET film. Wild-type PETase binding durations were well fit by a biexponential with a fast population having a 2.7 s time constant, interpreted as active binding events, and a slow population interpreted as non-specific binding interactions that last tens of seconds. A previously described hyperactive mutant, S238F/W159H had both a faster on-rate and a slower off-rate than wild-type PETase, potentially explaining its enhanced activity. Because this single-molecule approach provides a more detailed mechanistic picture of PETase enzymatic activity than standard bulk assays, it should aid future efforts to engineer more robust and active PETases to combat global microplastics pollution.


Introduc'on
Polyethylene terephthalate (PET) is one of the most widely produced man-made polymers, and is derived from petroleum by the esterificaNon of terephthalic acid and ethylene glycol.
AccumulaNon of PET and other microplasNcs in the environment is a pressing global problem that has moNvated efforts to develop microbe-and enzyme-based strategies to degrade PET (1,2).In 2016, Yoshida et al. reported a newly discovered bacterium, Ideonella sakaiensis 201-F6, that was able to use PET as its major carbon and energy source for growth.The PETase enzyme derived from this microbe, IsPETase, was shown to convert PET to mono(2-hydroxyethyl) terephthalic acid (MHET), with trace amounts of terephthalic acid (TPA) and bis(2-hydroxyethyl)-TPA (BHET) as secondary products (3).This discovery set off a global interdisciplinary effort to idenNfy, characterize and opNmize PET degrading enzymes, with the hope that these biodegradaNon approaches can be scaled up to reduce microplasNcs polluNon in the environment (4,5).
Current methods to evaluate the specific acNvity of PETases have included analysis of PET surface erosion by scanning electron microscope (SEM), quanNfying decreases in PET crystallinity using differenNal scanning calorimetry, and measuring product released by HPLC (6)(7)(8).These bulk assays provide quanNtaNve informaNon on enzyme acNvity, but relaNng these measurements to the specific enzyme kineNc parameters of the PETase enzymes is complicated by the insolubility of PET and the fact that enzymes only act on exposed surfaces.AlternaNvely, there are turbidimetric or colorimetric methods for PETase enzyme acNvity, such as the soluble substrates p-nitrophenyl acetate (pNPA) and p-nitrophenyl butyrate (pNPB), but these soluble substrates are poor analogs for crystalline PET (7,9).Like PETases, cellulases and cuNnases are enzymes that react only with the surface of their insoluble subtrates (10).Because the effecNve surface: volume relaNonship is generally not known, it is difficult to directly apply the Michaelis-Menten formalism to these reacNons.Specifically, the resulNng KM values are not in typical molar concentraNons, making it difficult to extract the bimolecular on-and off-rates, kon and koff, as well as the enzyme turnover rate, kcat.One approach that has been used extensively on enzymes like cellulases or cuNnases is to vary the enzyme concentraNon rather than the substrate concentraNon in the soluNon, such that enzymes parNNon to bound and soluble fracNons (11)(12)(13).However, even here the available area,  !, is a key parameter that must be esNmated rather than precisely measured.In contrast, singlemolecule approaches directly measure binding rates and duraNons, and thus they offer more direct access to true biochemical parameters of enzymes.Further, because the acNvity of the enzyme (rather than the substrate) is monitored, they sidestep the requirement of relaNng exposed surface area to substrate mass or volume, which bulk assays typically require.To this end, by imaging the cellulase Cel7A binding to and moving along its insoluble substrate, cellulose, we were able to extract enzyme kineNc parameters from the single-molecule tracking dynamics (14).
Previous work that used bulk enzymaNc assays and molecular dynamics simulaNons to invesNgate key residues in the substrate binding clei of Ideonella sakaiensis PETase idenNfied two mutants with altered acNviNes (6).A hyperacNve mutant, S238F/W159H, was created that narrowed the substrate binding clei towards that of naNve cuNnase, and an impaired mutant, W185A was created by mutaNng a highly mobile tryptophan thought to play a role in substrate binding.The altered enzyme acNviNes were measured by imaging the surface erosion of PET using electron microscopy and by monitoring changes in the crystallinity of the PET substrate.These experimental approaches clearly showed changes in enzyme acNvity, parNcularly the enhanced acNvity of the hyperacNve mutant, but because the methodology did not quanNfy kon, koff and kcat, it is difficult to define in enzymaNc terms which transiNon rates are altered by the mutaNons.
In the present work, we measured the single-molecule binding dynamics of Ideonella sakaiensis PETase wild-type and both the hyperacNve and impaired mutants characterized previously.We used total internal reflecNon fluorescence microscope (TIRFM) of quantum dot (Qdot) labeled PETase reversibly binding to glass coverslips funcNonalized with a thin film of PET.By measuring the residence Nme of the enzymes on the substrate, we calculate an apparent off-rate that provides informaNon about both the turnover rate of the enzyme and its binding affinity to the PET substrate.This work provides new insights into PETase funcNon and introduces a new approach for invesNgaNng the enzymology of other enzymes that react with insoluble substrates.
Frozen cell pellets were resuspended in a lysis buffer (300 mM NaCl, 10 mM imidazole, 20 mM Tris HCl, pH 7.4,) and lysed by sonicaNon.Lysate was clarified by centrifugaNon at 45,000 rpm for 35 minutes.The supernatant was then applied to a 2 mL Ni Sepharose 6 Fast Flow (CyNva) column and eluted by eluNon buffer containing 300 mM NaCl, 300 mM imidazole, 20 mM Tris HCl, pH 7.5.

Microscopy and image analysis
PET film (Goodfellow, UK) was cleaned in purified water by sonicaNon, wiped with 100% ethanol, cut into pieces, and dissolved in trifluoroaceNc acid (TFA) (Sigma Aldrich; Cas: 76-05-1) to a concentraNon of 1 wt%.5-7 μL of PET soluNon was dripped onto a plasma cleaned coverslip, covered with a second cleaned coverslip, and the two coverslips were then separated and dried in air at room temperature for 30 min.Next, the coverslips were transferred to a 120°C oven for 20 min to achieve a smooth PET coaNng, followed by cooling at room temperature.Flow cells were assembled with the PET-coated coverslips using double-sided tape.The PET surface was blocked to minimize nonspecific protein adsorpNon by flowing 0.33 mg/mL casein into the flow cell for 3 min, followed by an enzyme soluNon consisNng of 8 nM wild-type PETase or its mutant labeled with 0.8 nM Qdot655 (Thermo ScienNfic), 2 mM 2-Mercaptoethanol (Sigma-Aldrich; Cas: 60-24-2), and 4 mM 4-Nitrophenyl acetate (Sigma-Aldrich; Cas: 830-03-5) in a buffer containing 100 mM NaCl and 50 mM sodium phosphate, pH 7.4.The Qdot655-labeled PETase was imaged by total internal reflecNon fluorescence microscopy (TIRFM) using a 488 nm laser (70 mW or 150 mW) on a custom-built microscope (15).Movies began immediately before the enzyme soluNon was added to the flow cells.All experiments were performed at 22°C.The 10:1 enzyme:Qdot raNo was chosen because binding events were quite rare and lower raNos resulted in insufficient parNcle counts to accurately calculate landing rate and duraNon parameters.
PETase landing events and binding duraNons on the surface-immobilized PET film were measured by Kymograph analysis in ImageJ, as follows.Image stacks consist of a cube of x-y images at sequenNal Nmes, t.First, the "Reslice" command was used to generate mulNple x-t (horizontal) slices at varying y (verNcal).The "Output spacing" was set to 5 pixels, which corresponds to the ~300 nm full width at half maximum of the point spread funcNon of our microscope (15).Next, the "Grouped z projecNon" command was used to compress the mulNple slices along the y axis into a single x-t image (see Fig. 1).From this kymograph, the binding duraNons are measured by the length of the verNcal lines, where one pixel equals one frame, and the landing rate is measured by counNng the total number of events throughout the enNre movie.This approach of generaNng an x-t Kymograph is similar in principle to the approach of Peyersson et al (16).

Figure 1. PETase binds reversibly to PET film. (A)
Experimental design for single-molecule TIRF analysis of Qdotlabeled PETase interac@ng with surface-immobilized PET film.Image is not to scale.(B) Kymograph analysis.A movie, consis@ng of a stack of x-y images at various t is captured and resliced into x-t frames for each y, and then compressed into a single x-t image.The image is then rotated by 90° to generate a single x-t kymograph (shown at right), where ver@cal streaks are single-molecule binding events of varying dura@ons.(C) Binding dura@ons of wild-type PETase, ploOed as 1 -cumula@ve distribu@on func@on (1-cdf).FiRng to a biexponen@al func@on reveals a fast phase, represen@ng reversible binding interac@ons, as well as a slow phase.Inset: first 15 s to show details of fast phase.

Qdot655-labeled PETase binds reversibly to PET substrate
To observe the behavior of PETase enzymes on an immobilized PET surface, PET was dissolved in trifluoroaceNc acid and dripped onto the surface of a coverslip, which was then covered by another plasma cleaned coverslip to make thin PET film on the surface of both coverslips.The PET-funcNonalized coverslip was incorporated into a flow cell, and 0.33 mg/ml casein was flowed through to reduce nonspecific protein adsorpNon.Ideonella sakaiensis PETase (Addgene Number: #112202) (6) was bacterially expressed and bioNnylated (see Methods), and combined with streptavidin-coated Qdot parNcles at a 10:1 enzyme:Qdot raNo.The PETase-Qdot complexes were then introduced into the flow cell and allowed to interact with the PET surface.Landing events were imaged by total internal reflecNon fluorescence microscopy (TIRFM) on a custom-built mulNmodal microscope (15), and movies were obtained of the enzymes reversibly binding to the surface-immobilized PET.
To quanNfy the reversible binding interacNons, we developed a kymograph-based approach (Fig. 1B; described in Methods) to measure the frequency and duraNon of PETase binding events.The 5 frames/s video consists of a stack of x-y images through Nme.The binding events in our assay are focal-limited spots of diameter ~300 nm, corresponding to the point-spread funcNon of the microscope (15).Because the events are relaNvely rare, we can collapse a given image in ywithout superimposing different events.When this image is rotated by 90°, the resulNng image corresponds to the posiNons in x along the horizontal axis and Nme along the verNcal axis (Fig. 1B).From this kymograph, the binding duraNons are measured by the length of the verNcal lines, where one pixel equals one frame, and the landing rate is measured by counNng the total number of events throughout the enNre movie.
We found that the distribuNon of binding duraNons of wild-type PETase was well fit by a double exponenNal funcNon consisNng of a fast phase with a Nme constant of 2.7 ± 0.12 s (fit ± SE of the fit for all Nme constants) and a slow phase with a Nme constant of 38.6 s (Fig. 1C).mW illumina@on with biexponen@al fit.Inset: early @mes to show fast phase.(B) Binding dura@ons of PETase-free Qdots at 150 mW illumina@on with biexponen@al fit.(C) Photobleaching rates of immobilized Qdots at varying illumina@on intensi@es.Par@cles were nonspecifically bound to the surface and the average image intensity over @me ploOed at 70 mW and 150 mW illumina@on intensi@es.Fit to exponen@al fall gives @me constants for Qdot photobleaching of 117.9 s and 76.3 s at 70 mW and 150 mW illumina@on, respec@vely.

Slow binding phase is consistent with non-specific binding
To beyer understand the origin of the fast and slow binding populaNons, we carried out a control experiment using Qdots with no PETase bound.Using 70 mW laser power, Qdots were observed to reversibly bind to the surface, and the binding duraNons followed a biexponenNal with a fast phase of 1.5 ± 0.08 s (faster than the PETase fast phase of 2.7 s) and a slow phase of 51.1 ± 2.0 s (Fig. 2A).We hypothesized that the slow Nme constant may be due to nonspecific and/or irreversible binding of Qdots to the surface, with the apparent unbinding rate being due to photobleaching or blinking of the Qdots.If this were the case, then increasing laser power to accelerate bleaching should shorten the Nme constant of the slow phase.To test this, we repeated the control Qdot experiment using a 150 mW laser illuminaNon and found that the slow Nme constant shortened from 51.1 s to 23.3 s, as expected, while the fast Nme constant remained at 1.5 s (Fig. 2B).This result is consistent with the slow phase being due to irreversible binding events whose duraNons are truncated by photobleaching or blinking, rather than dissociaNon.
To further validate our photobleaching hypothesis, we immobilized Qdots on the surface and quanNfied their populaNon-level photobleaching rate.To do this, we flowed 50 pM Qdots (lacking PETase) into the flow cell without first blocking the PET surface to prevent nonspecific adsorpNon, washed away any free Qdots that did not bind, and imaged these nonspecifically-bound Qdots under conNnuous laser illuminaNon.The average fluorescence intensity of the image fell exponenNally over Nme due to photobleaching of the immobilized Qdots (Fig. 2C).At 70 mW laser power, the Nme constant was 118 s, and at 150 mW laser power, the Nme constant fell to 76.3 s, consistent with faster Qdot photobleaching at higher laser powers.This populaNon-level result reinforced our single-molecule result in Fig. 2AB, supporNng our conclusion that the slow Nme constant in the PETase experiments (Fig. 1) is due to slow photobleaching of Qdots that are nonspecifically bound to the surface.1C), and impaired and hyperac@ve mutant PETase (From Fig. 3A and B, respec@vely).Dashed line is @me constant fast phase from Qdot control (see Fig. S1 for Qdot binding dura@on distribu@on).Error bars are standard error of the fit.(D) Single-molecule PETase landing rates, including all events independent of dura@on.Dashed line indicates PETase-free Qdot control landing rate.Error bars are SEM with N = 7 to 11 screens.Asterisks denote data are significantly different from one another with p <0.05 by a two-sample t-test.Addi@onally, all landing rates were significantly different from the Qdot control (red dashed line), with p<0.05 by two sample t-test.

On-and off-rates of hyperac0ve and impaired PETases differ from wild-type
We next used our single-molecule PETase assay to invesNgate the reversible binding dynamics of two previously described PETase mutants.AusNn et al. generated a hyperacNve double mutant, S238F/W159H, which was designed to narrow the acNve site of the enzyme and was found to degrade crystalline PET more effecNvely than wild-type (6).They also generated an inacNve mutant W185A, which was found to have impaired acNvity compared to wild-type PETase (6).
RepeaNng our wild-type approach, we bacterially expressed, purified, and bioNnylated the two mutants, adsorbed them to Qdots, and quanNfied their binding duraNons.Comparing the fast phases, which correspond to reversible binding, the hyperacNve mutant had a Nme constant of 4.0 ± 0.07 s (fit ± SE of the fit), longer than the wild-type (2.7 ± 0.12 s), whereas the impaired variant had a Nme constant of 1.7 ± 0.18 s, shorter than wild-type (Fig. 3A-C).These binding duraNons are consistent with the hyperacNve mutant having a higher PET binding affinity, and the impaired mutant having a lower binding affinity than wild-type.
To quanNfy the relaNve on-rates for PET binding, we quanNfied the binding frequency of the three PETase enzymes along with the Qdot control (Fig. 3D).Binding rates were normalized to the enzyme concentraNon and to the area of the microscope image.The binding rate of the impaired mutant, 1014 ± 282 μm -2 • s -1 • M -1 (mean ± SEM for N=7 movies) was similar to the wild-type rate of 1070 ± 310 μm -2 • s -1 • M -1 (N = 9).Notably, the hyperacNve mutant landed more frequently, at 2141 ± 254 μm -2 • s -1 • M -1 (N = 7) than wild-type.Taken together, the results suggest that the hyperacNve mutant achieves a higher PET binding affinity through both a faster on-rate and a slower off-rate.Finally, the landing rate for the Qdot control lacking PETase was 394 ± 113 / μm 2 • s • M (N = 11), roughly 1/3 of wild-type PETase (Fig. 3D, dashed line).This nonspecific Qdot-PET interacNon in the absence of enzyme means that the observed landing rates of the three enzymes are somewhat overesNmated; it follows that the measured enhancement of the landing rate of the hyperacNve mutant is a lower limit of the effect.A rough correcNon for this nonspecific binding fracNon is to consider the dashed red line in Fig 3D as the baseline.(C) Rela@ve amplitude in biexponen@al fit of the fast phase for Qdot control, impaired mutant, wild-type PETase and hyperac@ve mutant in the absence (blue bar) and presence of 4mM pNPA (green bar).(D) Corrected landing rate (defined as the overall landing rate mul@plied by the rela@ve amplitude of the fast phase) for Qdot control, impaired mutant, wild-type PETase and hyperac@ve mutant in the presence (green bar) and absence of 4 mM pNPA (blue bar).
Error bars are SE of the fit.

pNPA acts as a compe00ve inhibitor for PET binding
To more thoroughly confirm that the observed binding interacNons truly reflect the enzymaNc acNvity of the wild-type and mutant PETases, we used a PETase inhibitor to more clearly separate out specific binding from the various non-specific interacNons that may be occurring.4-Nitrophenyl acetate (pNPA) is a model soluble substrate that is used for measuring the acNvity of esterases including PETases (7).We reasoned that when used at high concentraNons, pNPA should serve as a compeNNve inhibitor of the PETases, occupying the acNve site and blocking enzyme binding to the immobilized PET film.Thus, we repeated the single-molecule binding experiments in the presence of 4 mM pNPA.
pNPA reduced the binding duraNon of wild-type PETase and the hyperacNve variant, but had negligible effect on the binding duraNons of the impaired mutant and the control Qdots lacking bound PETase (Fig. 4A).The clear effects of pNPA on the wild-type and hyperacNve PETase provide further validaNon that the fast binding duraNons are reporNng producNve interacNons of the enzymes with the immobilized PET.In contrast, the finding that the binding duraNon of the impaired mutant did not change in the presence of pNPA calls into quesNon whether this mutant is specifically binding to the immobilized PET at all under our condiNons.
The impacts of pNPA on the landing rate mirrors the effects on the binding duraNon.Specifically, pNPA strongly diminished the landing rate of the wild-type and hyperacNve mutant, whereas it had a negligible effect on the landing rate of the impaired mutant and the Qdot control (Fig. 4B).
To beyer separate out contribuNons to the landing rate from specific binding versus nonspecific binding, we first quanNfied the relaNve amplitudes of the fast and slow phases from the biexponNal fits (Fig. 4C).For wild-type and the hyperacNve mutant, the amplitudes of the fast duraNons were diminished by pNPA, consistent with the inhibitor blocking the specific (fast) interacNons.As expected, the relaNve amplitudes of the impaired mutant and the Qdot control were unaffected by pNPA.In the final analysis in Fig. 4D, we mulNplied the overall landing rate from Fig. 4B by the relaNve amplitude of the fast phase from Fig. 4C.This corrected landing rate corresponds to the degree to which the pNPA inhibitor blocks funcNonal binding of the PETases to the immobilized PET.In summary, the pNPA results argue that both wild-type and hyperacNve mutant PETase bind specifically and reversibly to the PET, with hyperacNve mutant having a faster relaNve on-rate.

Discussion
Despite a number of studies that have used bulk assays and computaNonal simulaNons to invesNgate the enzymaNc acNviNes of PETases, there has been liyle work at the single-molecule level aimed at uncovering their enzymology.Because the single-molecule approaches developed here enable us to measure and quanNfy binding events directly, they provide new informaNon that can be integrated into more comprehensive studies of the enzymology of PETases and similar enzymes.These molecular insights can point to new direcNons for opNmizing PETases to the point that they can be scaled up to tackle the significant problem of microplasNcs polluNon in the environment.
The most challenging aspect of these single-molecule invesNgaNons was separaNng specific binding of the enzymes from nonspecific binding by the Qdot probes.Due to autofluorescence of the PET sample, labeling the PETases with standard fluorophores such as rhodamine resulted in an insufficient signal-to-noise for reliable detecNon.Instead, we turned to Qdots, which gave a very good signal-to-noise, but suffered from non-specific binding to the PET.We explored using surfactants to reduce nonspecific binding but were unable to find condiNons that eliminated nonspecific binding while retaining specific binding.Thus, we carried out a series of control experiments to determine source of the fast and slow Nme constants we idenNfied in our biexponenNal dwell Nmes fits.
By characterizing Qdots lacking bound PETase and varying laser intensity to characterize photobleaching, we concluded that the slow Nme constant (~tens of seconds) of our biexponenNal fit to the dwell Nme distribuNons was due to nonspecific binding.The Qdot control lacking any bound enzymes had a residual binding interacNon with a dwell Nme of 1.9 ± 0.12 s, but the landing frequency was substanNally lower than Qdots containing a bound PETase (Fig. 3C     and D).This lower landing rate and the elevated binding duraNons of the wild-type PETase and the hyperacNve mutant were the first indicaNon that the assays were detecNng specific PET-PETase interacNons.The strongest evidence that the fast binding populaNon was indeed specific binding of the PETase to the immobilized PET was the fact that in the presence of the inhibitor pNPA, both the dwell Nmes and the landing rates of the wild-type PETase and the hyperacNve mutant fell to near the Qdot control (Fig. 4).The most important experimental result was that the mean dwell Nme of wild-type PETase was 2.7 s, the dwell Nme of the hyperacNve S238F/W159H mutant was 4.0 s, and the dwell Nme of the impaired W185A mutant was 1.7 s, which was similar to control Qdots.
What can single-molecule imaging of enzymes tell us about their kineNc parameters?The Michaelis-Menten framework consists of a reversible binding step, with rates kon and koff, and a catalyNc step, kcat.
The standard assumpNon is that product unbinding is fast relaNve to the catalyNc step and is thus lumped into kcat.For single-molecule visualizaNon of enzymes binding to an insoluble substrate, we are visualizing the ES complex (meaning the clock starts when the fluorescent enzyme binds to the surface).What we measure is dissociaNon from the surface, which is described by the apparent dissociaNon rate,  "## $%%.=  "## +  '$( .If we assume that the fast binding duraNons we measure are reflecNng the residence Nme of the enzyme on the PET substrate, then this apparent off-rate can be calculated from our binding duraNons as  "## $%%.= ) * !"#$ . From the fast Nme constants in Fig. 3C,  "## $%%.are 0.37 s -1 for the wild-type, 0.25 s -1 for the hyperacNve mutant, and 0.6 s -1 for the impaired mutant.
The first result that comes out of this analysis is that the upper limit for kcat for wild-type PETase is 0.37 s -1 .This conclusion comes from the fact that dissociaNon of the enzyme from the substrate is either through unbinding before catalysis (koff) or via a catalyNc event followed by dissociaNon from the "product" (cleaved PET in our case), with rate kcat.It should be noted that the catalyNc event may be considerably faster than this, meaning that the lumped kcat parameter is ratelimited by product release.However, the funcNonal turnover rate would be the same in this case, as would the apparent kcat that we observed.This relaNvely slow turnover rate presumably is related to the crystallinity of PET film and the fact that experiments were performed at room temperature.Previous work showed that higher degrees of crystallinity lead to greater resistance of PET to enzymaNc hydrolysis (17,18).It is proposed that as temperatures approach the glass transiNon temperature of PET, the mobility of the PET chain increases and results in more rapid enzymaNc hydrolysis (11,19).Using bulk assays with the same wild-type PETase as used here, Erickson et al measured a kcat of 1.5 s -1 on amorphous PET and 0.8 s -1 on crystalline PET at 30 °C (20), somewhat faster, but within the range of our kcat of 0.37 s -1 at 22 °C.
The enzyme dissociaNon rates that we measure also provide insights into how mutaNons alter the kineNc parameters of the enzymes.We interpret our data in the context of the simple Michaelis-Menten model showin in Fig. 5.The hyperacNve mutant, S238F/W159H was chosen by AusNn et al. because the mutaNons narrowed the acNve clei of the enzyme to match that of other cuNnases (6).Induced fit docking simulaNons predicted that this double mutant would have much higher affinity for PET, though no predicNons were made on how the mutaNons may alter kcat.We find that  "## $%%.drops from 0.37 s -1 for the wild-type to 0.25 s -1 for the hyperacNve mutant.First, because a faster kcat predicts a faster  "## $%%.(Fig. 5), our data argue that the greater surface erosion and decrease in crystallinity seen with this mutant in a previous study (6) do not result from an elevated kcat.Consistent with this, Erickson et al. measured a kcat of 0.5 s -1 for this hyperacNve mutant at 30 °C, slower than their wild-type kcat of 0.8 -1.5 s -1 in the same study (20).This value at 30 °C is twice our inferred kcat at 22 °C, which is reasonable agreement.However, this lower kcat measured by Erickson et al. seems at odds with the elevated PET surface erosion of this mutant (6).One possible explanaNon of our slower apparent off-rate is that the rate of reversible binding from the substrate, koff, is slowed in the hyperacNve mutant.The first effect of slowing koff is a lower KM, which will improve performance at sub-saturaNng substrate concentraNons.The second effect is that for every enzyme-substrate encounter, there is a higher probability that the enzyme will hydrolyze the substrate (with ; Fig. 5) rather than simply unbinding without acNng on the substrate (with probability  123.24 = ).
We can also use this analysis to interpret the impaired mutant.Previous work suggested that residue W185 reorients upon producNve binding to PET and may contribute p-stacking interacNons with aromaNc groups in the PET substrate (6).The W185A mutaNon was found to have reduced surface erosion acNvity on PET and a smaller reducNon in PET crystallinity, compared to wild-type (6).First, it should be noted that, because we found that  #$-( for the impaired mutant was indisNnguishable from that for Qdots alone (Fig. 3C), the  "## $%%. of 0.6 s -1 for the impaired mutant should be considered a lower limit.Importantly, the landing rate of the impaired mutant was considerably faster than Qdots alone (Fig. 3D), which argues that the impaired mutant is not totally inacNve.The simplest interpretaNon of the faster apparent off-rate is that the off-rate of the impaired mutant from the PET substrate is considerably faster than wildtype.This effect makes sense based on the proposed role of W185 in PET binding, and in bulk assays would lead to a larger KM.Another way to describe the mutaNon is that for every binding encounter, the probability of a catalyNc event,  '$($+,-.-= , is smaller, making the enzyme less producNve.

Conclusion and future outlook
We show here that single-molecule imaging can be used to deduce kineNc parameters of PETase enzymes.This approach provides a new tool that can be combined with exisNng bulk methods and computaNonal tools to engineer more acNve and robust PETases that address microplasNcs polluNon.Further development of this single-molecule approach will require reducing the nonspecific adsorpNon that complicates interpretaNon of the kineNc data.PotenNal soluNons include using probes other than Qdots to label the enzymes, improved processing of the PET substrate to reduce the autofluorescence, and idenNfying surfactants or other alteraNons in buffer condiNons that minimize nonspecific binding.Notably, more acNve enzymes that have higher kcat values are predicted to bind for shorter duraNons, and nonspecific Qdot binding currently limits the upper limit of apparent koff values that can be measured.One approach that has been explored for improving PETase funcNon is ayaching a Carbohydrate Binding Module (CBM) or another hydrophobic domain to PETases to improve their PET binding affiniNes (21,22).If such a strategy is successful in creaNng a processive enzyme that diffuses along the surface while carrying out mulNple chain cleavage reacNons, this acNvity should be measurable as both a slower apparent off-rate of the enzyme measured by the current approach, as well as diffusive movements that could be detected by single-molecule tracking.In conclusion, the methods developed here  Free PETase in solu@on binds to PET film reversibly with associa@on rate constant kon to form an enzyme-substrate complex.The complex then either disassociates with rate constant koff or proceed to the PET cleavage step with turnover rate kcat, followed by rapid dissocia@on.Qdot-labeled PETase molecules bind in the ES state and dissociate with an apparent rate constant  '(( )**.=  '(( +  ,)-, which is equal to the inverse of the fast phase dwell @me.For each binding interac@on, the probability that catalysis proceeds rather than the enzyme unproduc@vely dissocia@ng is:  ,)-)./010= Figures S1-S2

Figure 2 .
Figure 2. Time constant of the slow phase varies with laser power.(A) Binding dura@ons of PETase-free Qdots at 70

Figure 3 .
Figure 3. HyperacAve and impaired mutants have different fast-phase Ame constants and overall landing rates.(A) Distribu@on of binding dura@ons of hyperac@ve PETase mutant, fit by a biexponen@al.Inset: first 15 s to show details of fast phase.(B) Distribu@on of binding dura@ons of impaired PETase mutant, fit by biexponen@al.Inset: first 15 s to show details of fast phase.(C) Time constants of fast phase for wild-type (from Fig. 1C), and impaired and

Figure 4 .
Figure 4.The compeAAve inhibitor pNPA blocks PETase binding to PET. (A) Time constant for fast phase of Qdot control, impaired mutant, wild-type PETase, and hyperac@ve mutant in the presence (green bar) or absence of 4 mM pNPA (blue bar).See Fig. S2 for binding dura@on distribu@ons.(B) Overall landing rate of Qdot control, impaired mutant, wild-type PETase, and hyperac@ve mutant in the presence (green bar) and absence of 4 mM pNPA (blue bar).
provide a new tool for screening engineered PETases with enhanced funcNons, which should contribute to mulNdisciplinary efforts to use biocatalysts to reduce microplasNcs polluNon in the environment.

Figure 5 .
Figure 5. KineAc model of PETase binding to PET film.Free PETase in solu@on binds to PET film reversibly with Figures S1-S2.

Figure S1 (related to Fig. 3 )
Figure S1 (related to Fig. 3): Binding durations of PETase-free Qdot control.Distribution of binding durations of Qdot control, fit by a biexponential.Inset: first 15 s to show details of fast phase.

Figure S2 (related to Fig. 4 )
Figure S2 (related to Fig. 4): Binding durations in the presence of 4 mM pNPA.(A) Distribution of binding durations of Qdot control in the presence of 4 mM pNPA, fit by a biexponential.Inset: first 15 s to show details of fast phase.(B) Distribution of binding durations of wild-type PETase in the presence of 4 mM pNPA, fit by a biexponential.Inset: first 15 s to show details of fast phase.(C) Distribution of binding durations of the inactive PETase mutant in the presence of 4 mM pNPA, fit by a biexponential.Inset: first 15 s to show details of fast phase.(D) Distribution of binding durations of the hyperactive PETase mutant in the presence of 4 mM pNPA, fit by a biexponential.Inset: first 15 s to show details of fast phase.