Kinetic insights into the role of the reductant in H2O2-driven degradation of chitin by a bacterial lytic polysaccharide monooxygenase

Lytic polysaccharide monooxygenases (LPMOs) are monocopper enzymes that catalyze oxidative cleavage of glycosidic bonds in polysaccharides in the presence of an external electron donor (reductant). In the classical O2-driven monooxygenase reaction, the reductant is needed in stoichiometric amounts. In a recently discovered, more efficient H2O2-driven reaction, the reductant would be needed only for the initial reduction (priming) of the LPMO to its catalytically active Cu(I) form. However, the influence of the reductant on reducing the LPMO or on H2O2 production in the reaction remains undefined. Here, we conducted a detailed kinetic characterization to investigate how the reductant affects H2O2-driven degradation of 14C-labeled chitin by a bacterial LPMO, SmLPMO10A (formerly CBP21). Sensitive detection of 14C-labeled products and careful experimental set-ups enabled discrimination between the effects of the reductant on LPMO priming and other effects, in particular enzyme-independent production of H2O2 through reactions with O2. When supplied with H2O2, SmLPMO10A catalyzed 18 oxidative cleavages per molecule of ascorbic acid, suggesting a “priming reduction” reaction. The dependence of initial rates of chitin degradation on reductant concentration followed hyperbolic saturation kinetics, and differences between the reductants were manifested in large variations in their half-saturating concentrations (KmRapp). Theoretical analyses revealed that KmRapp decreases with a decreasing rate of polysaccharide-independent LPMO reoxidation (by either O2 or H2O2). We conclude that the efficiency of LPMO priming depends on the relative contributions of reductant reactivity, on the LPMO's polysaccharide monooxygenase/peroxygenase and reductant oxidase/peroxidase activities, and on reaction conditions, such as O2, H2O2, and polysaccharide concentrations.

Recent studies have shown that LPMOs can use H 2 O 2 as co-substrate (22,23). For a review of the (potential) involvement of H 2 O 2 and LPMOs in degradation of lignocellulose, see Bissaro et al. (24). Although the possibility of a (O 2 -using) monooxygenase reaction is still being debated, the fact is that the (H 2 O 2 -using) peroxygenase reaction is several orders of magnitude more efficient (23,25,26). Computational studies also support the plausibility of H 2 O 2 as co-substrate for LPMOs (27)(28)(29). The peroxygenase-like reaction also depends on an external electron donor; however, in principle, the reductant is only needed for initial activation (priming) of the Cu(II) resting state to the catalytically active Cu(I) state (23). Once activated, the LPMO would in principle be capable of catalyzing multiple cleavage reactions, if fueled with H 2 O 2 . Of note, LPMO priming by a one-electron reduction is part of some of the currently proposed monooxygenase mechanisms (30), but these mechanisms do not alleviate the need for two electrons being delivered per catalytic cycle.
Provided with H 2 O 2 as cosubstrate and a low amount (0.1 mM) of AscA, SmLPMO10A shows high efficiency in chitin oxidation with the k cat /K m for H 2 O 2 being on the order of 10 6 M Ϫ1 s Ϫ1 (k cat ϭ 6.7 s Ϫ1 and K m for H 2 O 2 ϭ 2.8 M) (25). Recent work on a fungal LPMO also indicated high k cat values for the peroxygenase activity on cello-oligosaccharides (26). Such a high catalytic efficiency and the low K m for H 2 O 2 call for revisiting existing kinetic data for LPMO reactions with different reductants. Next to priming the LPMO, reductants will be involved in the generation of H 2 O 2 , by enzyme-independent reduction of O 2 and/or by fueling LPMO-catalyzed production of H 2 O 2 (16,31). The futile reaction of reduced mediators with O 2 is a well-known challenge in the application of monooxygenases and is referred to as the oxygen dilemma (32). H 2 O 2 is a product of these oxidations, as it can be formed directly by two-electron reduction of O 2 or indirectly from a superoxide radical intermediate generated by one-electron reduction of O 2 , as shown, for example, for the oxidation of AscA (33). Notably, the incorporation of the 18 O label into the oxidized chitooligosaccharide products generated by SmLPMO10A in reactions with 18 O 2 , seemingly supporting a monooxygenase mechanism (3), could also result from a reaction with H 2 18 O 2 , originating from in situ reduction of 18 O 2 either by the reductant or by the LPMO (23). The interpretation of data are further complicated by irreversible inactivation of the LPMO by a surplus of H 2 O 2 in the presence of reductant (5,23,25,34). Consequently, it is difficult to judge whether and to what extent the differences between different reductants reported so far reflect the efficiency of the reductant in reducing the LPMO or the effect of the reductant on the production of H 2 O 2 in the reaction mixtures.
Here, we set out to obtain insights into the effects of the reductant on LPMO activity using the chitin-active SmLPMO10A as a model enzyme. Sensitive detection of 14 C-labeled degradation products of chitin enabled accurate initial rate measurements and allowed discrimination between the effects of the reductant on priming of the LPMO and side effects involving the production of H 2 O 2 . We show that the different tested reductants, namely AscA, GA, and methylhydroquinone (MHQ), differ in their ability to support SmLPMO10A activity, and we provide a kinetic and theoretical framework for understanding reductant function.

Experimental set-up
The kinetics of H 2 O 2 -driven oxidation of chitin ( 14 C-labeled crystalline ␣-chitin nanowhiskers (CNWs)) by SmLPMO10A with 0.1 mM AscA as reductant has been characterized in detail before (25). The k cat value for oxidative cleavage of CNWs was 6.7 s Ϫ1 , and K m values were 2.8 M and 0.58 mg ml Ϫ1 for H 2 O 2 and CNWs, respectively (25). The quantification of the radioactivity in the supernatants of SmLPMO10A reactions enables sensitive detection of soluble products, the concentration of which is expressed in GlcNAc equivalents (NAG eq ). Under the conditions used in previous studies, the turnover of one molecule of H 2 O 2 results in one oxidative cleavage, which is manifested in the release of four soluble NAG eq (25). Because about 50% of the oxidized groups remain associated with the insoluble substrate, the average degree of polymerization of soluble products is 8 NAG eq (25). Importantly, under these conditions (typ-ically 1 mg ml Ϫ1 CNWs, 42 nM SmLPMO10A, and reaction time Ͻ 10 min), and as long as enzyme inactivation and H 2 O 2 depletion are avoided, release of NAG eq is linear over time up to levels of 190 M released soluble NAG eq (25). Therefore, in the present study, we used 1 mg ml Ϫ1 CNWs as initial substrate concentration, and the maximum levels of released NAG eq remained well below the 190 M threshold. If not stated otherwise, the concentration of SmLPMO10A was 42 nM. Time courses of the release of NAG eq were measured at two initial H 2 O 2 concentrations, 20 and 100 M, and the nature and the concentration of the reductant were varied.
Kinetic studies of LPMOs with H 2 O 2 as cosubstrate in an aerobic environment are complicated by the simultaneous presence of O 2 and a reducing agent. Because of the low K m value of SmLPMO10A for H 2 O 2 (25), low H 2 O 2 concentrations must be used in kinetic studies, and care must be taken to account for the formation/depletion of the H 2 O 2 in enzymeindependent and enzyme-dependent background reactions. For example, the formation of H 2 O 2 in the reaction between AscA and molecular oxygen is well-known (35). Furthermore, the oxidation of AscA by O 2 is catalyzed by metal ions, like Cu(II) (36,37), so that their presence even in trace amounts can significantly affect the formation of H 2 O 2 and interpretation of the results of LPMO kinetics. The problem is further amplified by the occurrence of metal ions in polymeric substrates of LPMOs, such as cellulose and chitin (38 -40).
When setting up our experimental conditions, we first assessed the activity of SmLPMO10A in experiments without added H 2 O 2 , hereinafter referred to as "background activity." Considerable variation in background activity was observed between different CNW batches in reactions containing AscA (0.1 mM) as reductant (Fig. 1A). This indicates that the quality of the water and/or buffer components used in the preparation of CNW batches (see "Experimental procedures") affects background activity. The addition of peroxidase completely removed the background activity, indicating that the formation of H 2 O 2 drives catalysis under these conditions (Fig. 1B). The addition of EDTA (5 mM) also completely removed the background activity, suggesting that divalent metal ions are involved (41). The addition of catalase caused more than 10-fold reduction of the background activity (Fig. 1B). Collectively, these results suggest that, under the conditions used here, the background activity is related to the formation of H 2 O 2 by divalent metal ion-catalyzed oxidation of AscA by O 2 .
It is worth noting that, whereas EDTA removed the background activity, the LPMO remained active when supplied with H 2 O 2 . The ability of LPMOs to withstand EDTA has been reported before (8) and coincides with very high reported copper affinities (8,42). Apparently, the strong binding of copper and slow off rates (43) ensure that there is no significant transfer of copper from the LPMO to EDTA, provided that the contact time is kept short, as is the case here. Accordingly, in experiments with 0.1 mM AscA as reductant and 20 M load of H 2 O 2 , EDTA had no effect on the kinetics of SmLPMO10A. However, at lower AscA concentration (10 M), EDTA became inhibitory for the LPMO reaction (Fig. 1A). One may speculate that EDTA can sequester only the Cu(II) from LPMO and becomes inhibitory when the reduction of LPMO becomes less efficient. Con-

Effects of the reductant on the kinetics of LPMO catalysis
sidering these complications, the use of EDTA was judged not applicable in further studies of reductant efficiency.
To minimize complexity, in further work, we only used "lowbackground" CNW in the experiments with AscA as reductant. Unlike reactions with AscA, within the time scales used, there was no significant background signal when GA and methyl hydroquinone (MHQ) were used as reductants (Fig. S1), regardless of the CNW batch used. This is corroborated by a reported much higher stability of the latter reductants against oxidation (i.e. H 2 O 2 production) compared with AscA (10). We also attempted to use 1,4-dihydroxy-2,6-dimethoxybenzene, an efficient reductant in supporting AA9's activity (10), but the high background activities (data not shown) did not permit accurate measurement of SmLPMO10A kinetics, and this reductant was omitted from further studies. As found for AscA before (25), the order of the addition of reductant and H 2 O 2 had no effect on the outcome of the experiment (Fig. S1). The experimental set-up where the reductant was added to premixed CNW/SmLPMO10A 30 s before the reaction was started by the addition of H 2 O 2 (zero time point) was used throughout this study.
Importantly, considering the above, and as a result of precisely tailoring the reaction conditions, in all of the experiments described below, the rates of SmLPMO10A without added H 2 O 2 were always insignificant compared with reactions containing a 20 or 100 M initial load of H 2 O 2 . Thus, in the experiments described below, the effects of various possible O 2 -, reductant-, and/or SmLPMO10A-dependent H 2 O 2 producing pathways are negligible.

Time curves with different reductants
We studied the effect of reductants on chitin oxidation using either 20 or 100 M H 2 O 2 as initial load. We have previously shown (25) Fig. 2 show that the rate of NAG eq formation depends on the nature and concentration of the reductant. Although there is some uncertainty associated with the precise measurement of the plateau values for reactions with largely different rates, all time curves tend to reach a plateau value of NAG eq ([NAG eq ] max ) close to 80 M (Fig. 2). Of note, the consistency between the measured and expected [NAG eq ] max values shows that side reactions leading to production or consumption of H 2 O 2 are not significant under our experimental conditions.
As a clear exception, the experiments with AscA at low concentrations (0.2 and 0.5 M) yielded lower values of [NAG eq ] max ( Fig. 2A). The addition of a fresh portion of AscA (up to 100 M) at the point in the time curve where the formation of NAG eq had decayed caused a new burst in activity and subsequent leveling off at a [NAG eq ] max around 80 M ( Fig. 2A). This indicates that at low AscA concentrations, depletion of the reductant limits the reaction. [NAG eq ] values from experiments with low [AscA] were fitted to Equation 1 (25) using nonlinear regression analysis ( Fig. 2A).
Plotting the [NAG eq ] max values obtained for the three lowest AscA concentrations against the concentration of AscA results in a linear correlation, showing that 73 Ϯ 20 NAG eq are released per molecule of AscA (Fig. 3). Considering that 4.0 Ϯ 0.3 NAG eq are released per H 2 O 2 consumed and that one H 2 O 2 supports one oxidative cleavage (23,25), we can thus estimate that an average of 18 Ϯ 5 oxidative cleavages are performed by SmLPMO10A per reduction (priming) event under our experimental conditions.

Effects of the reductant on the kinetics of LPMO catalysis
Previous studies using 0.1 mM AscA as reductant showed that, under otherwise identical conditions, the initial addition of 100 M H 2 O 2 yields reaction kinetics that are dominated by enzyme inactivation. Under these conditions, a maximum of only 25 M NAG eq was reached (i.e. 6.25% of the theoretical maximum) (25). Dose-response experiments with GA as reductant (Fig. 4) show that increasing the GA concentration leads to faster product formation and faster enzyme inactivation. For instance, fitting of the data to Equation 1 shows halflives of 220 and 90 s for the reactions with 50 and 500 M GA, respectively. At GA concentrations above 100 M, the maximum levels of NAG eq reach 25 M (Fig. 4)

Dependence of initial rates on the nature and concentration of the reductant
The linear regions of the time curves of NAG eq formation were used to calculate the initial rates of reactions carried out with AscA, GA, and MHQ and an initial H 2 O 2 load of 20 M. Fig. 5A shows the results obtained for GA, and Fig. S2 shows the results obtained for the other reductants. Fig. 5B shows the dependences of the initial rates of NAG eq formation on the concentration of reductants. The initial rates versus [reductant] curves were in general accordance with hyperbolic saturation kinetics (Equation 2).
In Equation 2, the v i is the initial rate of the formation of NAG eq , [R] is the concentration of the reductant, and K mR app and V max app represent the apparent half-saturating concentration of the reductant and apparent V max of the formation of NAG eq . The V max app is related to the apparent catalytic constant for oxidative cleavage of CNWs (k cat app ) according to V max app ϭ nk cat app E tot where n is an average number of NAG eq released per oxidative cleavage (n ϭ 4) and E tot is the total concentration of enzyme. The parameters of Equation 2 are referred to as apparent parameters because the reaction was studied at one set of substrate concentrations only (20 M H 2 O 2 and 1 mg ml Ϫ1 CNWs). Table 1 lists the values of K mR app and V max app and shows that differences between the reductants are primarily manifested by largely different K mR app values amounting to 2, 86, and 700 M, for AscA, GA, and MHQ, respectively. The differences between V max app values obtained with different reductants were less prominent (Table 1), which is as expected because close to full reduction of the LPMO should be reached in all cases, regardless of the reductant.
With GA as reductant, the K mR app and V max app were determined for two different initial H 2 O 2 loads, 20 and 100 M. At the higher H 2 O 2 load, the V max app decreased (indicating inhibition by H 2 O 2 ), whereas the K mR app increased ( Table 1). The reasons for

Effects of the reductant on the kinetics of LPMO catalysis
this apparent decrease in reductant efficiency (k cat app /K mR app in Table 1) with increasing H 2 O 2 concentration are addressed in the theoretical analysis, described below.

Theoretical analysis of the reduction/oxidation of the LPMO in the absence of chitin
The reduced LPMO will be subject to nonproductive reoxidation primarily when it is not bound to substrate, because that exposes the reduced copper site to both O 2 and H 2 O 2 . To gain further insight into the dependence of K mR app and V max app on the nature of the reductant and on the concentration of H 2 O 2 , we thus first considered oxidation/reduction of the LPMO in the absence of chitin, as outlined in Fig. 6A (the effects of including chitin into the reaction scheme are discussed below). In Fig. 6A, the chemically inert complexes ECu(I)-R, ECu(II)-O 2 , and ECu(II)-H 2 O 2 are omitted for clarity. The scheme of Fig. 6A assumes that both reduction and oxidation of the LPMO are irreversible. This assumption is plausible when analyzing initial rates, as product concentrations and, thus, rates of possible reverse reactions are negligible.
The catalytically active form of SmLPMO10A is the ECu(I) form, which has been proposed to bind to chitin followed by the binding of H 2 O 2 and oxidative cleavage of the glycosidic bond (25,44). The equation for steady-state [ECu(I)] is given in Fig. 6 (Fig. 6). Note that in doing so, we assume that concentration of CNWs has no effect on the steady-state [ECu(I)]. Using these equations, one can predict how the apparent catalytic properties of the LPMO depend on the efficiency of the reductant, k red /K R , as shown in Fig. 6 (B-E). Fig. 6B shows that in the presence of O 2 and H 2 O 2 , the concentration of the catalytically active ECu(I) form is always lower than E tot . The equation for k cat app shows that this parameter is always reduced compared with its maximum value, when all enzyme is expected to be in its Cu(I) form (k cat(max) app ), at least by a factor of 1 ϩ [O 2 ]/K O2 ϩ [H 2 O 2 ]/K H2O2 . This is evident by inspection of the expression of k cat app in Fig. 6, assuming conditions of very efficient reduction (i.e. when the value of the rate constant for the reduction (k red ) is much higher than the rate constants for oxidation of LPMO by O 2 (k oxO2 ) and H 2 O 2 (k oxH2O2 )). The similar V max app values for different reductants ( (regardless of k red ), whereas the value of K mR app approaches zero (Fig. 6). Fig. 6C shows that, as expected, the k cat app increases with an increasing k red value of the reductant (Fig. 6C), whereas the K mR app decreases (Fig. 6D). The dependence of k cat app /K mR app on the efficiency of the reductant (k red /K R ) was found to be linear (Fig. 6E).

Kinetics at low levels of O 2
Because the steady-state concentration of catalytically active Cu(I) form of LPMO is expected to depend in part on [O 2 ] (Fig.  6), we also measured the kinetics of the degradation of CNWs by SmLPMO10A under reduced [O 2 ] (i.e. under N 2 atmosphere). AscA, GA, and MHQ were used as reductants. The concentration of added H 2 O 2 was 20 and 100 M. In general, the kinetics (time curves and initial rates) measured in N 2 atmosphere were similar to those measured in normal air conditions ( Fig. 7 and Fig. S3). This result is in line with earlier observations that, when provided with H 2 O 2 , the presence of O 2 has no effect on the activity of an LPMO (23). Of note, the binding of LPMO to cellulose has also been shown to be independent of the presence of O 2 (45). Collectively, these results suggest that in the experimental set-ups with initial H 2 O 2 supply, the O 2 -involving pathways in Fig. 6 are not significant.

Binding to CNWs in the absence of reductant
The binding of SmLPMO10A to CNWs in the presence of 0.1 mM AscA has been measured before (25) and resulted in the half-saturating concentration for CNWs of 0.68 Ϯ 0.01 mg ml Ϫ1 . In the absence of reductant, the binding of LPMO to CNWs results in the formation of a nonproductive ECu(II)-CNW complex. In the case of nonefficient priming, this nonproductive complex can exist also in the presence of reductant but may be converted to a productive complex if reduction of LPMO within the complex with CNW is possible (e.g. through long-range electron transfer). To assess possible nonproductive binding, we measured the binding of SmLPMO10A to CNWs in the absence of reductant. SmLPMO10A was incubated with nonlabeled CNWs, and after separation of bound enzyme by centrifugation,theconcentrationofchitin-freeenzymewasmeasured by measuring its activity in the supernatant using 14 Clabeled CNWs (1.0 mg ml Ϫ1 ) and H 2 O 2 (20 M) as substrates

Effects of the reductant on the kinetics of LPMO catalysis
and 0.1 mM AscA as reductant. As a control experiment, we measured the time curves of the degradation of CNWs at different concentrations of SmLPMO10A (Fig. 8A).
The time curves for reactions with lower concentration of SmLPMO10A (below 25 nM) leveled off below the theoretical [NAG eq ] max value (80 Ϯ 6 M) that can be released in experiments with 20 M H 2 O 2 . As pointed out before, the [NAG eq ] max value is a product of two competing processes, catalysis and inactivation. The inactivation is first-order with enzyme, and changing the concentration of SmLPMO10A has no influence on its half-life. At the same time, the rate of chitin oxidation is linear with the concentration of SmLPMO10A. Therefore, it is likely that at low concentration of SmLPMO10A, the enzyme is inactivated before it can perform enough oxidative cleavages to reach the theoretical [NAG eq ] max value. Fig. 8B shows a linear correlation between the initial rate of the LPMO reaction and the total concentration of SmLPMO10A. Of note, such a linear relationship has never been reported for O 2 -driven reactions, in line with the notion that in such reactions, other factors, such as H 2 O 2 generation, are rate-deter-  In calculations for C-E, the K R was kept at 1 mM, and k red was varied between 0.01 and 10 s Ϫ1 . k cat(max) app represents the maximum value of k cat app (i.e. it represents the hypothetical situation when all enzyme is in its active form, [ECu(I)] ϭ E tot ). For the calculations in C and E, the value of k cat(max) app was set to 10 s Ϫ1 .

Effects of the reductant on the kinetics of LPMO catalysis
mining. Besides providing the control for the linearity between the initial rate and the enzyme concentration, this result indicates that the binding sites on CNWs were in excess at all enzyme concentrations used (up to 84 nM). The latter condition is a prerequisite for the applicability of steady-state kinetic models, but it is not often easy to achieve in the case of heterogeneous interfacial catalysis (46).
The time curves for the formation of NAG eq by nonbound SmLPMO10A present in the supernatants of binding experiments are shown in Fig. S4. Analysis of the dependence of the ratio of initial rates measured in the presence (v CNW ) and absence (v CNW ϭ 0 ) of chitin in the binding experiment on the concentration of CNWs in binding experiments (Fig. 8C) according to Equation 4 results in a half-saturating concentration for CNWs of 3.0 Ϯ 0.7 mg ml Ϫ1 . This concentration is 4.5-fold higher than the corresponding concentration measured in the presence of 0.1 mM AscA (25), which is well in line with the recent results by Kracher et al. (45), who demonstrated that the binding of the Cu(I) form of Neurospora crassa LPMO9C to cellulose is stronger compared with binding of the Cu(II) form. This latter study showed that reduction of N. crassa LPMO9C increased both the binding strength and binding capacity but that the effect was strongest (4.7-fold increase) at the level of the partition coefficient (initial slope of the Langmuir binding isotherm) (45). Because here we measured LPMO binding in conditions satisfying an excess of binding sites, the effects of reductant on binding (4.5-fold increase) reflect mainly effects on the partition coefficient of the Langmuir binding isotherm. The fact that similar results were obtained with Neurospora crassa LPMO9C and SmLPMO10A may be taken to suggest that the effects of the redox state of active site copper on binding of LMPOs to their polysaccharide substrate may be similar for LPMOs belonging to different families, but may also be coincidental because the two LPMOs have different substrates.  (4,23,25).

Discussion
Here, we occasionally encountered significant activity of SmLPMO10A in experiments without added H 2 O 2 . This background activity depended on the nature of the reductant and showed strong variation between different working batches of chitin (Fig. 1A). Numerous control experiments (Fig. 1B) suggested that the background activity is related to generation of H 2 O 2 in the divalent metal ion-catalyzed oxidation of the reductant. Therefore, the addition of copper salts to reaction mixtures likely has effects beyond supplementing the LPMO with catalytically essential copper, and great care must be taken when doing so (47).
Regarding our studies on background activities, the effect of catalase is worth a short discussion. In some studies, it has been noticed that the addition of catalase improves the efficiency of LPMO-containing enzyme mixtures, which was ascribed to the potentially damaging effect of radical formation when H 2 O 2 reacts with transition metals in the reaction mixture (48). For a similar reason, catalase is added in experimental set-ups where LPMO reactions are supplied with excess copper (49 (52,53), special care must be taken in dosing catalase and interpreting potential effects. The K m for H 2 O 2 of the bovine liver catalase used in this study is around 100 mM (52). Based on the rate of NAG eq formation in the background reaction (0.36 M NAG eq min Ϫ1 ; Fig. 1B) and the values of

Effects of the reductant on the kinetics of LPMO catalysis
kinetic parameters of SmLPMO10A published before (25), one can estimate a steady-state concentration of 0.025 M for H 2 O 2 in the experiment with 0.1 mM AscA. As defined by the commercial suppliers, the unit of catalase activity (mol of H 2 O 2 min Ϫ1 ) is measured at an H 2 O 2 concentration around 10 mM. Therefore, the activity of catalase in our experiment is expected to be 10,000 M/0.025 M ϭ 4 ϫ 10 5 -fold lower than the activity that could be estimated from the information provided by the supplier. This may be the reason why an apparently huge dose of catalase (200 units ml Ϫ1 ) did not completely inhibit the background activity of SmLPMO10A (Fig. 1B).
As pointed out before, the optimal harnessing of the catalytic potential of LPMO takes an experimental set-up with controlled in situ production (e.g. using oxidases) or continuous external supply of H 2 O 2 (23,25,54). Provided that enzyme inactivation is avoided, the effect of reductant in these set-ups is expected to be similar to the effects of reductant on initial rates measured here (Fig. 5 and Table 1). Note that whereas the necessary reductants under some conditions may contribute to H 2 O 2 generation, in the present study, conditions were such that the observed efficiency of reductants reflects the efficiency in priming of the LPMO. The stoichiometry of 18 Ϯ 5 oxidative cleavages made per molecule of reductant, as measured in reactions with low concentrations of AscA (Fig. 3), supports the use of reductant in priming reduction and not as substrate in our experiments. This result is in accordance with conclusions drawn from reactions in which cellulose was degraded by an LPMO-containing commercial cellulase mixture, which showed that, when controlling the supply of H 2 O 2 , ϳ200 M AscA was needed to produce ϳ3000 M oxidized products, leading to an approximate stoichiometry of 15 (23).
In accordance with previous studies (10,12), the present data show that different reductants have very different efficiencies (k cat app /K mR app ) in supporting SmLPMO10A catalysis. Although different reductants have somewhat different k cat app values, we show that the differences in efficiency primarily relate to largely different apparent half-saturating concentration (K mR app ) ( Table 1), which again is strongly correlated with the rate constant for LPMO reduction (k red ) ( Fig. 6D; K mR app decreases sharply as k red increases). Of note, measuring the true electron transfer efficiency of the reductant (i.e. the values of k red and K mR ) implies measurements of electron transfer in the pre-steady state regime. Stopped-flow experiments with cellobiose dehydrogenase indicate a second-order rate constant (cf. k red /K mR ) of 6.4 10 5 M Ϫ1 s Ϫ1 for electron transfer between SmLPMO10A and the cellobiose dehydrogenase of Myriococcum thermophilum (4).
The different efficiencies of the reductants are likely related to their varying midpoint potentials, as demonstrated in an earlier study by Kracher et al. (10). Kracher et al. (10) showed that MHQ is a moderately effective reductant, which coincides with its high K mR app (and, thus, low k red ) value reported here. MHQ undergoes two successive one-electron and one-proton transfers, leading to the semiquinone and quinone form, with redox potentials of 23 and 460 mV versus NHE, respectively. The standard potential for the direct transfer of two electrons and two protons to reduce the quinone to MHQ is 230 mV versus NHE (55). SmLPMO10A has a midpoint potential of 275 mV versus NHE (42). Ascorbic acid and gallic acid, two of the most commonly used reductants in LPMO research, are oxidized irreversibly (56,57), which prevents the determination of standard midpoint potentials, and which, as such, may affect their efficiency. Comparative studies of oxygen reduction by Kracher et al. (10) indicated that ascorbic acid is a much better reductant than gallic acid and MHQ, which is compatible with the differences observed here.
From the analysis of the reaction scheme in Fig. 6, it follows that there is a linear relationship between the value of k cat app /K mR app for chitin degradation and the value of the efficiency constant for LPMO priming by the reductant (k red /K mR ) according to Equation 3.
The rate constants and binding constants of Equation 3 are defined in the legend to Fig. 6. To what extent the value of k cat app /K mR app (Table 1) reflects the value of (k red /K mR ) depends on the rates of LPMO reoxidation (i.e. the terms in the denominator of Equation 3; note that these are all terms referring to a situation without bound substrate, which is the most common, if not the only, situation in which reduction occurs). To decide which route, O 2 -or H 2 O 2 -driven, governs LPMO reoxidation,

Effects of the reductant on the kinetics of LPMO catalysis
one needs numerical estimates for the corresponding terms in the denominator of Equation 3. The K H2O2 in this denominator reflects the binding of H 2 O 2 to free reduced LPMO (Fig. 6A). This binding mode has been proposed to be responsible for the inactivation of SmLPMO10A and has low affinity (K H2O2 Ͼ 100 M as estimated from the data in Ref. 25). The k oxH2O2 is the catalytic constant for the oxidation of ECu(I) by H 2 O 2 . This H 2 O 2 -dependent oxidative route can lead to irreversible inactivation of LPMO but also to reoxidation of LPMO to its ECu(II) form without inactivation (as in Fig. 6A). The secondorder rate constant for inactivation of SmLPMO10A is on the order of 10 3 M Ϫ1 s Ϫ1 (25). Using this number, one can estimate the rate of reoxidation (k obs(oxH2O2) ) of SmLPMO10A to be around 0.02 s Ϫ1 (H 2 O 2 at 20 M). Note that the true reoxidation rate by H 2 O 2 is expected to be 1/p i -fold higher, where p i is the probability that enzyme is inactivated upon reacting with H 2 O 2 in the absence of chitin (Fig. 6A). The rate of O 2 -mediated reoxidation of SmLPMO10A is not known, but similar initial rates measured under normal air and anaerobic conditions (Fig.  7) suggest that under the conditions used in our study, reoxidation is governed by H 2 O 2 . Regarding other LPMOs, the data for the rate of O 2 -mediated reoxidation of nonsubstrate-bound LPMOs vary a lot. Some studies support rate constants below 1 min Ϫ1 (10,31,34,58), whereas others support values above 10 min Ϫ1 (59,60). Recently, Breslmayr et al. (61) showed that the oxidation of 2,6-dimethoxy phenol by N. crassa NcLPMO9C is driven by H 2 O 2 and does not depend on the presence of O 2 , suggesting that in the absence of a polysaccharide substrate, O 2 -driven reoxidation of the LPMO is much slower than H 2 O 2driven reoxidation, although this of course would depend on the concentrations of the two co-substrates. More studies are needed to make general conclusions about the contribution of possible oxidase/peroxidase reactions in reoxidation of substrate-free LPMOs.
The simplest mechanism of H 2 O 2 -driven degradation of CNWs by SmLPMO10A that can account for the observations and considerations described here is depicted in Fig. 9A. For simplicity, binding of the Cu(II) form of the LPMO to chitin was omitted. This simplification is, at least to some extent, justified by the experimentally observed weaker binding of the Cu(II) form of SmLPMO10A compared with the Cu(I) form ( Fig. 8C and data in Ref. 25). Weaker binding of the Cu(II) form is also supported by computational studies of SmLPMO10A (44). It has been proposed that H 2 O 2 -driven catalysis by SmLPMO10A follows a compulsory order ternary complex mechanism, with chitin being the first substrate to bind to the reduced enzyme (25,44). Simulations suggest that when SmLPMO10A is bound to chitin, a channel connecting the bulk solvent to the active site would regulate access of reagents to the latter (44). These considerations imply that the binding modes of H 2 O 2 to free SmLPMO10A and to the complex of SmLPMO10A with CNWs are different. Therefore, binding of the LPMOCu(I)-H 2 O 2 complex to CNWs is omitted in the scheme of Fig. 9A. Because the O 2 -driven mechanism has been shown to follow a random-order mechanism (60) we do not make a similar assumption for binding of O 2 (Fig. 9A). Because in the experimental conditions used to determine the initial rates, the oxidation of chitin without external H 2 O 2 supply was not signifi-cant, the possible O 2 -driven route of chitin oxidation is omitted in the scheme of Fig. 9A.
The steady-state solution for the mechanism in Fig. 9A was found using the King-Altman procedure (62) and analyzed numerically. In general, the numerical solutions for the dependence of chitin degradation on the efficiency of reductant ( Fig.  9) are in qualitative accordance with the analytical solutions found using the scheme that does not consider chitin (Fig. 6).
The dependence of initial rates on the concentration of reductant followed Michaelis-Menten saturation kinetics regardless of the k red (Fig. 9B), similar to the dependence of the concentration of the ECu(I) form of LPMO on the concentration of reductant found by analytical solutions to the scheme without CNWs (Fig. 6B). The k cat app increased and the K mR app decreased with increasing efficiency of reduction (data not shown), similarly to predictions derived from the model without explicit inclusion of chitin (Fig. 6, C and D). Both reaction schemes yielded a linear dependence of k cat app /K mR app on the true efficiency of reductant (k red /K mR ), but the slope found in the scheme with the explicit presence of chitin (Fig. 9A) was higher than that predicted in the absence of chitin (Fig. 9C). This can be accounted for by the reduced rate of LPMO reoxidation in the presence of chitin, as only the reoxidation of chitin-free enzyme is considered in Fig. 9A. Numerical solutions to the scheme in Fig. 9A also predicted inhibition by H 2 O 2 (Fig. 9D), as indeed observed when using GA as reductant (Fig. 5B). Of note, this hitherto nonobserved phenomenon refers to true inhibition, reflected in reduced initial rates, and should not be confused with irreversible inactivation caused by H 2 O 2 .
Regarding the application of LPMOs, it is important to note that the requirements for the reductant (e.g. its halfsaturating concentration) in supporting polysaccharide degradation depend not only on the catalytic efficiency of the reductant (k red /K mR ) (Figs. 6 (C-E) and 9C) but also on the rate of LPMO reoxidation (Fig. 9, E-G). The increase of K mR app (Fig. 9F) and decrease of k cat app (Fig. 9E) with increasing rate of LPMO reoxidation is caused by the competition between the possible polysaccharide monooxygenase/peroxygenase and reductant oxidase/peroxidase activities of the LPMO. Increasing the polysaccharide concentration favors the monooxygenase/peroxygenase reactions, at the expense of the oxidase/peroxidase reactions that take place with free LPMOs, and this is reflected in decreasing K mR app (Fig. 9F) and increasing k cat app (Fig. 9E). Because the irreversible inactivation of LPMO is also related to the reoxidation of free LPMO by H 2 O 2 (23,25,26), the high dry matter conditions used in industrial scale degradation of lignocellulosic biomass (63) should reduce the needed amounts of the reductant for the priming of LPMO as well as reduce the inactivation of LPMO. Obviously, careful control of the amount of available H 2 O 2 is also of importance, because this will avoid unproductive oxidation of the reductant as well as LPMO inactivation (54).
Regarding the natural environment of LPMOs and potential sources of H 2 O 2 , a plethora of H 2 O 2 suppliers as potential candidate partner enzymes have been identified for fungal LPMOs involved in lignocellulose conversion, although most connections remain to be clearly established (24). In the case of bacte-

Effects of the reductant on the kinetics of LPMO catalysis
rial LPMOs, even less is known because no obvious, conserved redox partner, like cellobiose dehydrogenase in fungi, has been identified yet. As to the matter of the availability of H 2 O 2 , reported concentrations in natural ecosystems span several orders of magnitude, but existing data need to be interpreted with caution because H 2 O 2 concentrations measured in vivo may reflect the result of multiple, and sometimes unknown, production and consumption fluxes (24) In summary, the optimal concentration and the performance of the reductant depend on the relative activities of the different reactions catalyzed by a particular LPMO, but also on process conditions like the concentrations of O 2 , H 2 O 2 , and the polysaccharide substrate.

Experimental procedures
Substrates and enzymes 14 C-Labeled CNWs were prepared from ␣-chitin of crab shells (Sigma C7170) using N-acetylation of free amino groups with 1-14 C acetic anhydride, as described by Kuusk et al. (64). The specific radioactivity of the CNW preparation was 4.18 ϫ 10 6 dpm mg Ϫ1 . A mother stock suspension of CNWs (8.5 mg ml Ϫ1 ) was kept at 4°C in 50 mM NaAc buffer pH 6.1 (0.01% NaN 3 ). The batches of CNWs were prepared from the mother stock by washing out the NaN 3 through repetitive centrifuga-  Fig. 6A. The routes shown with gray are not included in the analyses. Numerical solutions for the steady-state are shown in B-G. If not stated otherwise, the values of k 1 , k 3 , k 5 , k 9 , and k 10 were set to 10 3 mM Ϫ1 s Ϫ1 . The values of k Ϫ3 , k Ϫ5 , and k Ϫ9 were set to 100 s Ϫ1 , whereas the value of k Ϫ1 was 10 3 s Ϫ1 . Therefore, the K R , K O2 , and K H2O2 (for definitions, see the legend to Fig. 6) had values of 1, 0.1, and 0.1 mM, respectively. The binding constants for CNWs were adjusted to 0.5 mg ml Ϫ1 by setting k 7 ϭ k 8 ϭ 100 ml mg Ϫ1 s Ϫ1 and k Ϫ7 ϭ k Ϫ8 ϭ 50 s Ϫ1 .  Fig. 6B. C, dependence of k cat app /K mR app for chitin oxidation on the efficiency of reductant (k red /K R ) based on reaction schemes with (CNWϩ; Fig. 9A) or without (CNWϪ; Fig. 6A and Equation 3) the inclusion of chitin. Obviously, there is no LPMO activity without chitin, but the calculations without chitin were included as they represent a prediction of what will happen in the situation where chitin does not influence the steady-state [ECu(I)]. In the calculations, the K R was kept at 1 mM, and k red was varied between 0.01 and 10 s Ϫ1 . As in B, the rates of LPMO reoxidation by O 2 and H 2 O 2 were both set to 0.02 s Ϫ1 . D, dependence of initial rates of NAG eq formation (v i ) on the concentration of reductant at different concentrations of H 2 O 2 (as shown in the plot). The concentration of enzyme was set to 0.05 M, and four NAG eq are released per molecule of H 2 O 2 . The values of k red and k oxH2O2 were set to 0.01 and 0.1 s Ϫ1 , respectively. The binding strength of O 2 (K O2 ) was set to 1.0 or 10 mM as indicated in the plot. E-G, dependence of k cat app (E), K mR app (F), and k cat app /K mR app (G) on the rate of LPMO reoxidation (k obs(ox) ). k obs(ox) is the sum of the rate constants of oxidation by O 2 (k obs(oxO2) ) and H 2 O 2 (k obs(oxH2O2) ), which were calculated according to k obs(oxO2) ϭ k oxO2 [O 2 ]/ K O2 and k obs(oxH2O2) ϭ k oxH2O2 [H 2 O 2 ]/K H2O2 . The value of k red was set to 1.0 s Ϫ1 . The values of k obs(oxO2) and k obs(oxH2O2) were varied by varying the values of k oxO2 (between 0.0025 and 5.0 s Ϫ1 ) and k oxH2O2 (between 0.025 and 50 s Ϫ1 ). The effect of k obs(ox) on apparent parameters of the reductant was assessed using three different scenarios: (i) k obs(oxO2) ϭ k obs(oxH2O2) , (ii) k obs(oxH2O2) ϭ 0 (mimicked by setting k 5 ϭ 0), and (iii) k obs(oxO2) ϭ 0 (mimicked by setting [O 2 ] ϭ 0). All scenarios were analyzed at two concentrations of CNWs, 1.0 mg ml Ϫ1 (solid lines) and 10 mg ml Ϫ1 (dashed lines). Note that the results of the first two scenarios (blue and green lines) overlap. Note also that the scale for k cat app /K mR app is logarithmic.

Effects of the reductant on the kinetics of LPMO catalysis
tion (5 min, 2,900 ϫ g) and resuspension (in 50 mM NaAc buffer, pH 6.1) steps. Although the water was Milli-Q ultrapure water (Ͼ18.2 megaohms cm Ϫ1 ), we encountered variation in the background activity between working batches of CNWs when AscA was used as reductant, as described under "Results." Apart from the experiments shown in Fig. 1, only the working batches of CNWs with low background activity were used in the experiments with AscA as reductant. There were no differences in background activities between working batches of CNWs when GA or MHQ were used as reductants, and the results with these reductants represent results obtained using different working batches of CNWs. Nonlabeled CNWs used in the binding experiment were prepared from ␣-chitin of crab shells (Sigma C7170) exactly as described by Kuusk et al. (64). Ascorbic acid (Sigma, A7506), gallic acid (Sigma, G7384), methylhydroquinone (Sigma-Aldrich, 89600), and 1,4-dihydroxy-2,6-dimethoxybenzene (Aldrich, 565032) stock solutions were prepared in water less than 10 min before use. EDTA and AmplexRed were from Sigma. Dilutions of a commercial H 2 O 2 stock solution (Honeywell, lot SZBG2070) with known concentration (30 weight %, 9.8 M) were prepared in water less than 10 min before use. The water was Milli-Q ultrapure water (Ͼ18.2 megaohms cm Ϫ1 ) throughout.
SmLPMO10A was produced and purified as described previously (65). Purified SmLPMO10A was saturated with copper by incubating with CuSO 4 and following removal of unbound copper by ultracentrifugation exactly as described by Kuusk et al. (25). The concentration of SmLPMO10A was determined by absorbance at 280 nm using a theoretical molar extinction coefficient of 35,200 M Ϫ1 cm Ϫ1 . Catalase from bovine liver (Sigma, C9322) and peroxidase from horseradish (Sigma, P8375) were used as purchased.

Degradation of CNWs by SmLPMO10A
Reactions were prepared essentially as described by Kuusk et al. (25). All reactions were performed in 1.5-ml polypropylene microcentrifuge tubes in NaAc buffer (50 mM, pH 6.1) at 25°C without stirring, although the suspension was mixed by pipetting before withdrawing samples, at each sampling time point. If not stated otherwise, the reaction mixture contained 14 C-labeled CNW (1.0 mg ml Ϫ1 ), SmLPMO10A (42 nM), H 2 O 2 , and reductant. The total volume of the reactions was 0.8 ml.
SmLPMO10A was added to CNWs, and after 5-10 min of incubation, the reductant was added. 30 s after the addition of reductant, the reactions were initiated (zero time point) by the addition of H 2 O 2 to a desired concentration. At selected time points, 0.1-ml aliquots were withdrawn and mixed with 25 l of 1.0 M NaOH to stop the reaction. Nonlabeled CNWs (to 3 mg ml Ϫ1 ) in 0.2 M NaOH were added to improve the sedimentation of the CNWs during centrifugation (25). After centrifugation (5 min, 10 4 ϫ g), 50 l of supernatant was withdrawn, and the radioactivity in the supernatant was measured using a scintillation counter (PerkinElmer Life Sciences). The sample for the zero-time point was withdrawn before the addition of H 2 O 2 and was treated as the other samples. The reading of the zerotime point was subtracted from the readings of all time points. The reactions without the addition of H 2 O 2 were performed exactly as described above with the addition of an equal amount of NaAc buffer (50 mM, pH 6.1) instead of H 2 O 2 . Concentrations of soluble products were expressed in NAG eq , which were calculated from the radioactivity readings exactly as described by Kuusk et al. (25). At least two independent replicates were carried out for each experiment (S.D. values are derived from at least two experiments).
Control reactions for testing the effect of the order of the addition of reductant and H 2 O 2 (Fig. S1) were set up with 1 mM GA or MHQ as reductants. The reaction mixtures contained SmLPMO10A (42 nM), CNWs (1.0 mg ml Ϫ1 ), and H 2 O 2 (20 M) as described above but with an opposite order of addition for the reductant and H 2 O 2 . In one set of experiments, the reaction was started by the addition of H 2 O 2 , but the preincubation time of CNW/SmLPMO10A mixture with reductant was extended from the usual 30 s to 5 min.
For the degradation of CNWs in anaerobic conditions, the reactions were performed in a glovebox under N 2 atmosphere. Before use, the buffer (50 mM NaAc, pH 6.1) was N 2 -saturated by five cycles of 5 min of vacuum degassing and 5 min of bubbling with N 2 gas. The CNW working batch (8 ml in a 15-ml tube) and stock solution of SmLPMO10A (0.5 ml in a 1.5-ml microcentrifuge tube) were treated by repeated flowing of N 2 gas into the headspace of the tube. The stock solutions of H 2 O 2 and reductant were prepared in a glovebox using N 2 -saturated buffer. The N 2 -saturated buffer constituted 85% of the total volume of the SmLPMO10A reactions set up in the glovebox.

Binding of SmLPMO10A to CNWs in the absence of reductant
In the binding experiment, SmLPMO10A (84 nM) was incubated with nonlabeled CNWs (at different concentrations), and after 5 min, the CNWs were pelleted by centrifugation (1 min, 10 4 ϫ g). The concentration of unbound SmLPMO10A was estimated by measuring LPMO activity in the supernatant using 14 C-labeled CNWs as substrate. To do this, labeled CNWs and AscA were added to the supernatant. 30 s after the addition of AscA, the reaction was initiated by the addition of H 2 O 2 , and the release of 14 C-labeled products over time (in NAG eq ) was measured. The final concentrations of 14 C-labeled CNWs, AscA, and H 2 O 2 were 1.0 mg ml Ϫ1 , 0.1 mM, and 20 M, respectively. In this procedure, the supernatant of the binding reaction was diluted 2-fold, meaning that the maximal (i.e. no binding of SmLPMO10A to nonlabeled CNWs) total concentration of SmLPMO10A in the activity measurement was 42 nM. The control experiment ([CNW] ϭ 0 mg ml Ϫ1 ) was undertaken exactly as described above but without the nonlabeled CNWs in the binding experiment. The results of the binding experiments were fitted to Equation 4. In Equation 4, v CNW and v CNW ϭ 0 are the initial rates of CNW degradation by the supernatants from the binding experiment made in the presence and absence of CNWs, respectively.
[CNW] is the concentration of CNWs in the binding experiment, and K i(CNW) is the half-saturating concentration of CNWs at which 50% of the SmLPMO10A molecules are bound to CNWs and 50% are free in the solution.

Effects of the reductant on the kinetics of LPMO catalysis
Author contributions-P. V. conceived and coordinated the study. S. K., R. K., and P. V. designed, performed, and analyzed the experiments, interpreted data, and wrote the paper. A. H. assisted with the experiments. P. K. derived the rate equations. B. B., M. S., and V. G. H. E. interpreted data and wrote the paper. All authors reviewed the results and approved the final version of the manuscript.