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Molecular mechanism of lytic polysaccharide monooxygenases

The lytic polysaccharide monooxygenases (LPMOs) are copper metalloenzymes that can enhance polysaccharide depolymerization through an oxidative mechanism and hence boost generation of biofuel from e.g. cellulose. By employing density functional theory in a combination of quantum mechanics and molecular mechanics (QM/MM), we report a complete description of the molecular mechanism of LPMOs. The QM/MM scheme allows us to describe all reaction steps with a detailed protein environment and we show that this is necessary. Several active species capable of abstracting a hydrogen from the substrate have been proposed previously. We investigate previously suggested paths as well as new ones. We describe the generation of the reactive intermediates, the abstraction of a hydrogen atom from the polysaccharide substrate, as well as the final recombination step in which OH is transferred back to the substrate. We show that a superoxo [CuO2]+ complex can be protonated by a nearby histidine residue (suggested by recent mutagenesis studies and crystallographic work) and, provided an electron source is available, leads to formation of an oxyl-complex after cleavage of the O-O bond and dissociation of water. The oxyl complex either reacts with the substrate or is further protonated to a hydroxyl complex. Both the oxyl and hydroxyl complexes are also readily generated from a reaction with H2O2. The C-H abstraction by the oxyl and hydroxy complexes is overall favorable with activation barriers of 69 and 94 kJ/mol, compared to the much higher barrier (156 kJ/mol) obtained for the copper-superoxo species. We obtain good structural agreement for intermediates for which structural data are available and the estimated reaction energies agree with experimental rate constants. Thus, our suggested mechanism is the most complete to date and concur with available experimental evidence.


Introduction
Widespread and abundant polysaccharide bio-polymers constitute a major resource whose utilization in production of biofuel or commercial chemicals would constitute a large step towards a more sustainable exploitation of resources. Unfortunately, this requires degradation of the polysaccharide into smaller sugars, which has shown to be a major obstacle and requires both hydrolytic enzymes and thermal work due to the remarkable stability of many naturally occuring polysaccharides. 1,2 A class of copper-dependent enzymes, called lytic polysaccharide monooxygenases (LP-MOs), have been shown to enhance polysaccharide depolymerization, thereby providing a route to efficient conversion of polysaccharides into smaller carbohydrates. [3][4][5][6] The key to this enhancement is the ability of LPMOs to oxidise the C−H bond of the glycoside linkage connecting the sugar units in polysaccharides, which ultimately leads to cleavage of the glycoside link. A number of different LPMOs have been categorized, belonging to four distinct classes, AA9, 4 AA10, 8 A11 9 and AA13. 10,11 Speculations on the underlying molecular mechanism have begun, [12][13][14][15][16] but the picture is still far from complete. Mechanistic studies are complicated by the fact that the different LPMOs have remarkably varying amino-acid sequences and target a wide range of different polysacharride substrates, 17-20 many of which are insoluble. Moreover, they have varying regioselectivity: some LPMOs oxidise only the C1 atom of the glycoside linkage, whereas others oxidise only the C4 atom, and still others can oxidise both C1 and C4. 16,[21][22][23][24] However, a common feature of all LPMOs is the active site, in which a copper ion 8,[25][26][27][28][29][30][31][32] is ligated by three nitrogen donor atoms in a so-called histidine brace moiety, in which one histidine residue coordinates with the N 2 atom, whereas the other one (which is the amino-terminal residue) coordinates with both the side-chain N δ1 and the backbone N atoms. 8 A similar coordination environment is also seen in the particulate methane monooxygenases (but with an additional monodentate histidine ligand). 33,34 The net oxidation of a substrate RH by O 2 by the LPMOs proceeds under consumption of two electrons and two protons, as shown in Scheme 1. The active site and some putative RH + O 2 + 2 H + + 2 e -→ROH + H 2 O Scheme 1: Reaction catalyzed by LPMOs. mechanisms for the reaction are shown in Figure 1. In the resting state, the metal ion is in the Cu(II) state (1). We focus on AA9 LPMOs, for which the resting state without the substrate typically displays an octahedral coordination with an axial tyrosine ligand and two water molecules, one axial (trans to tyrosine) and the other equatorial (trans to the Nterminal amino group). When the polysaccharide substrate binds, the axial water molecule is probably displaced, as shown in a recent crystal structure of an LPMO-substrate complex, 7 although this does not seem to be universal for all substrates. 35 Presumably, 1 is reduced to Cu(I) (2), which leads to dissociation of the second, equatorial water molecule 7,36 as is indicated for reaction 1→2 in Figure 1. It is not known if this reduction takes place before or after the binding of the saccharide. The following steps are even more unclear. From 2, most studies have suggested a mechanism employing O 2 as co-substrate, leading to the oxygen species [CuO 2 ] + (3) and (after reduction, protonation and dissociation of water) [CuO] + (6b) in Figure 1. Both 3 12,21,25,26 and 6b 12,14,[37][38][39] have been suggested as the reactive species that abstracts a hydrogen atom from the substrate.
Crystal structures of oxygen-bound LPMOs (without substrate) have been reported 40,41 and it is known that substrate-free LPMO can activate O 2 and produce H 2 O 2 . 36,42 Meanwhile, studies on model systems have suggested both hydroxyl 14,43 and hydroperoxyl complexes as reactive intermediates. 44 Quantum mechanical (QM) calculations on small cluster models of the enzyme have suggested that O 2 is not reactive enough to abstract a hydrogen atom from the substrate, and that either oxyl 38,39,45 or hydroxyl complexes 38 are more likely.
By comparing calculated hydrogen bond-dissociation energies for small cluster models, we could recently show 38 that complexes with Cu−O or Cu−OH moieties (6a-6c in Figure 1) are sufficiently reactive to abstract C−H, whereas complexes with Cu−OO or Cu−OOH moieties (3 and 4a-4b) had too low bond-dissociation energies to abstract hydrogen. Yet, we did not consider the associated activation energies, how complexes 6a-6c may form or the effect of the surrounding protein, although we for complexes 1-3 have demonstrated that the protein imposes large strucutral changes on the active site. 46 A recent study with larger QMcluster models supported this and further confirmed that the hydrogen-abstraction by the oxyl-complex is favored over intermediates with intact O−O bonds. 39 Different pathways for the formation of an oxyl-complex have been considered. Importantly, Bissaro et al. 47 recently showed that H 2 O 2 rather than O 2 could be the co-substrate.
In this paper we have performed a full investigation of the reaction mechanism of the LPMOs. The investigation is based on a recent crystal structure of a LPMO-oligosaccharide complex. 7 We investigate formation of both Cu-oxyl (6b) and hydroxyl (6c) complexes along several suggested pathways, starting from the Cu(II)-superoxide complex (3 in Figure   1). Moreover, we investigate reaction paths where the Cu-oxyl and hydroxyl complexes are formed from hydrogen peroxide (5→6b and 5→6c). Several of the pathways discussed in this paper have not previously been considered, neither theoretically nor experimentally. However, the QM-cluster study in Ref. 39 did consider coordination of H 2 O 2 to Cu(I), while a very recent a QM/MM study 48 have also considered generation of 6b from peroxide.
Unfortunately, the two studies obtain contradictory results regarding the H 2 O 2 coordination to the Cu metal. We compare our results to these recent studies whenever possible. In all calculations we include the oligosaccharide substrate to investigate the reactivity of the reactive oxygen species in C−H abstraction from the substrate. The calculations employ the combined QM and molecular mechancis approach (QM/MM) to include possible effects of the surrounding protein.

General computational setups
Calculations in this paper were performed with the QM/MM approach, using the QM software Turbomole 7.1 49 and the MM software AMBER 14. 50 The QM/MM calculations were performed with the ComQum interface, 51,52 which combines these two programs. In ComQum, the total studied system is divided into three subsystems, denoted systems 1, 2 and 3. System 1 is described with a QM method, while systems 2 and 3 both are described with an MM force field. The structure of system 2 can optionally be optimised at the MM level, whereas system 3 is always kept fixed at the starting structure. When there is a bond between systems 1 and 2 (a junction), the hydrogen link-atom approach is employed: the QM region is capped with hydrogen atoms (hydrogen link atoms), the positions of which are linearly related to those of the corresponding carbon atoms (carbon link atoms) in the full system. 51,53 The total QM/MM energy is calculated as E QM+ptch is the QM energy of system 1, including hydrogen link atoms and a point-charge model of systems 2 and 3 (taken from the Amber force field and excluding only the carbon link atoms). 54 E MM123 is the total MM energy of the full system (but with the charges of the QM system zeroed) and E MM1 is the MM energy of system 1 (still with zeroed charges; it is included to avoid double-counting of the energy of system 1). We will for some reactions discuss the electrostatic effect of the protein, which is calculated as where E QM is taken from a calculation in vacuum with the QM/MM optimised structure.
All QM calculations employed density functional theory and reported energies were obtained with the dispersion-corrected TPSS-D3 functional, 55,56 employing a def2-TZVPP basis set 57 (unless otherwise specified). The energies were also checked (using the same structures and basis set) with the B3LYP-D3 58-60 functional. All energies were obtained as single-point calculations on structures optimised with TPSS-D3 and the def2-SV(P) basis set. 57,61 In general, we only report QM/MM energies, but a more detailed breakdown of E QM/MM in the QM and MM energy components (and E ptch from Eq. 2) is provided in the supporting information (SI). The SI also contains a more detailed account of the computational and protein setup (including the alternate configurations and protonation states of individual amino acids).
The QM system (system 1) consisted of the copper ion and its first coordination sphere.
For all intermediates this is the imidazole ring of His78 and the phenol ring of Tyr164, both capped with a hydrogen atom replacing C α . The entire His1 residue, which coordinates to Cu through the terminal amino group, as well as the imidazole side chain, was alsoincluded.
The neighboring Thr2 residue was included up to the C α atom, which was replaced by a hydrogen atom. The last ligand in the first coordination sphere varies between the different intermediates in Figure 1. In 1 and 2, the ligand is H 2 O. In the next steps the water ligand is replaced in accordance with the various steps shown in Figure 1. In addition, the two first glucose rings of the substrate were also included in system 1, whereas the third glucose unit was always described by MM. Apart from a few initial calculations, the His147 residue was generally also included (both in HID, HIE and HIP forms). Representative examples of the QM systems employed are shown in Figure S1 in the SI.

Results
In the first part of this section, we compare the obtained QM/MM structures with structures from earlier QM-cluster 45,62 and QM/MM studies. 46 Here we focus on intermediates 1-3, for which we briefly discuss differences in our structures compared to previous theoretical work. Next, we discuss the formation of the reactive oxygen species, i.e. 6a-6c in Figure 1, before we finally investigate the C 4 −H abstraction by 6b and 6c (reactions 6→7), as well as the recombination to form a Cu + species and ROH (reactions 7→8).

The resting state and the initial reduction
We start by qualitative discussion of the structural changes accompanying the first reduction Figure 1). A comparison between our previous QM/MM results, QM-cluster calculations and experimental results were given in Ref. 46, and we here focus on a comparison of differences for the 1 and 2 states to our previous QM/MM structures without substrate. 46 We note that this comparison cannot directly be carried out with available experimental data, since the LPMO-substrate crystal structure has Clcoordinating to Cu in the equatorial position and an empty axial coordination site. (2), to emphasize that the water molecule always is included in the QM system for 1 and 2, although it might not bind directly to Cu(I). For the AA9 enzymes, the reduction is also associated with an elongation of the Cu−O bond to the axial tyrosine. 36,45,46,62,63 This Tyr ligand is typically not present in the AA10 LPMOs, which results in a different (trigonal bipyramidal) geometry in the AA10 LPMOs. 29,63 The active sites in our QM/MM optimised structures are shown in Figure 2. The Cu-O distance to the water ligand in 1 is 2.17Å and when one electron is added to this structure, the water molecule dissociates to form 2 (the Cu-O distance is 3.07Å, as can be seen in Figure 2).
In contrast to our previous QM/MM calculations without substrate, 46 the Cu−O bond length to tyrosine is remarkably constant (2.29 and 2.31Å, respectively). It has been argued that this bond shortens upon substrate binding. 7 Our results suggest the bond may remain short also in the 2 state due to the lack of the axially coordinated water in the substrate-LPMO complex. 7 We note that an elongation of this bond was suggested in the QM-cluster results of Ref. 39. We have previously discussed this bond, 46 which has shown to be flexible and rather sensitive to the computational setup. We investigated wheather the different starting structures in Ref. 39 and our study could be the underlying reason. However, the overlay of the structures employed here (5ACF 7 ) and by Bertini et al. 39 (4EIS 21 ) in Figure   S2 shows that they are fairly similar. It seems therefore more likely that slight differences in basis set and functional choice, or possibly the lack of dispersion corrections in Ref. 39, is the underlying reason for this discrepancy.
To ensure that the employed QM/MM model is sufficiently accurate, we also carried out optimisations with system 2 optimised with MM. As can be seen in Figure S3 in the SI, nearly identical conclusions were obtained and the distances within the first ligand-sphere change little when system 2 is relaxed. However, some changes in the second coordination sphere are observed, shifting the position of the active site (cf. Figure S4). This indicates that an energetically accurate description may require a larger QM region for reaction 1→2, underlining that our discussion of this step is qualitative. It is nevertheless reassuring that our model can reproduce the experimentally observed water dissociation upon reduction. As will be discussed in the next subsection, the structure of the [CuO 2 ] + (3) state changes much less when system 2 is relaxed. Before discussing this state, we note that we also optimised the The optimisations were carried out with TPSS-D3/def2-SV(P) and system 2 fixed.
intermediates 1 and 2 with the larger def2-TZVPD basis, which lead to only minor changes.

The superoxide state
We next consider the [CuO 2 ] + state (3 in Figure 1), i.e. the state formed by binding of O 2 to the reduced active site. As for 1 and 2, we have previously investigated 3, 46 but for a different LPMO and without any substrate. It should be noted that it is not known wheather this state is formed before or after binding of the substrate, since all available crystal structures of oxygen-bound states are substrate-free and their reduction level is unknown. 40,41 The optimised structure for 3 are shown in Figure 3 (upper part); selected structural parameters are compared to earlier results in Table S1 in the SI. The optimised structure has a relative short Cu−O Tyr bond (2.28Å), compared to previous QM/MM 46  In our optimized structures of 3 with and without substrate (cf . Table S1), we obtain a decrease around 0.1Å, which fits well to the experiment.
Allowing system 2 to relax for 3 has a much smaller effect than for intermediates 1 and 2. The optimised structures are compared in Figure S5 in the SI. Both the Cu-ligand distances and the overall placement of the active site are almost identical for the structures with and without system 2 relaxed. The same is true when employing a larger basis set (def2-TZVPD), as was also seen for the substrate-free QM/MM results 46 (cf. entries 3, 6 and 7 in Table S1).  46. We therefore focus on the triplet state in the following.
Next, we included the second-sphere residue His147 in the QM system in various pro- it is also a putative proton donor. 40 The latter implies that it is in the doubly protonated state (denoted HIP in the following), which is also the most probable form at the pH value of maximum activity for many cellulases (5.0). It has also been shown that the activity of some LPMOs is reduced 64 by mutations of His147, suggesting a role of His147 in the mechanism.
The role could be that His147 facilitates the formation of 4a and 4b, and perhaps ultimately the Cu-oxyl (6a-6b) or hydroxy (6c) species. We investigate the first step in this section, 3→4a, and several possibilities for the fate of 4a below.
The optimised structure of 3 including His147 in the HIE form (i.e. protonated only on the N 2 atom) is shown in Figure 3 (lower part), whereas we show the corresponidng complex with His147 in the HIP form in Figure 4 (left Another significant change between the HIE and HIP variants is that the distance between the H 2 proton and O -2 changes from 2.26 to 1.87Å, reflecting the positive charge in the latter structure. This change most likely facilitates proton transfer. The structures along the reaction path for such a transfer are shown in Figure 4, along with the calculated QM/MM energies (see further Table S3 and Figure S6; the latter shows energies for individual O−H distances). It can be seen that the reaction is nearly thermoneutral with a small barrier (15-18 kJ/mol, depending on the functional), showing that protonation is facile. As can be seen from the structures in Figure 4, the reaction proceeds with small changes in the structures, even for distances within the first ligand sphere. Inter- Figure 4: Reactant 3 (left), transition state (middle) and product 4a (right) for the reaction 3→4a. All structures were optimised with TPSS/def2-SV(P) and system 2 fixed. estingly, the electrostatic contributions from the environment increase steady as the proton moves from His147 to O 2 . This is shown in Figure S6 and it can be seen that in vacuum the reaction is uphill by more than 50 kJ/mol (cf. ∆E QM in Table S3).
The net reaction (Scheme 1) involves addition of two electrons and two protons, but the order of these additions is unknown. Although the reaction might proceed with reduction first or with simultaneous reduction and protonation, the results in this sections shows that it is reasonable to assume that the first step in the reaction chain is the protonation of 3 to 4a, as this reaction was found to be facile. The further reactions from 4a to form oxyl or hydroxyl intermediates (6 in Figure 1) will be investigated below.

Formation of Cu-oxyl and hydroxyl species from O 2
We now proceed to consider formation of Cu-oxyl or hydroxyl species with O 2 as substrate, i.e., by subsequent protonation and reductions as laid out in the route 3→4→6 in Figure 1.
We Additionally, we also investigated a pathway in which O−O is cleaved after reduction of 4b, which would mean O−O cleavage occurs after two-electron reduction. However, this also turned out to be unfavorable, since it was found the reduction of 4b did not lead to reduction of the [CuOOH] + unit, but rather reduced histidine (His147). A similar conclusion for this state was obtained in our previous QM-cluster study. 38 Therefore, we focus on the one-electron reduced state and the 4b→6a reaction.  Table S4. Interestingly, they show that the reaction energy strongly depend on the employed functional: With B3LYP, the reaction is uphill with 54 kJ/mol. The activation energy is less functional dependent, with a B3LYP value of 66 kJ/mol. Still, the reaction is predicted to be feasible both with TPSS and B3LYP, although in the latter case the product, 6a, is expected to have a shorter life time.
Further analysis of the reaction shows that the electrostatic contributions increase steadily Figure   S8). The effect is significant already for the transition states: depending on the functional, the effect is 50-100 kJ/mol for the activation energy and around 100 kJ/mol for the reaction energy (cf. In light of the recent proposal that H 2 O 2 is the co-substrate, we have also investigated coordination of H 2 O 2 to the Cu(I) ion, i.e. species 5 in Figure 1. Initially, we investigated all three forms of His147, namely HIP, HIE and HID (i.e. protonated only on the N δ1 atom) in the singlet spin state. However, the HID form was found to be less stable than HIE and we therefore focus on the HIE and HIP forms (we also investigated the corresponding triplet spin-states which, as expected, always was higher in energy than the singlet).
For all three protonation states of His147, coordination of H 2 O 2 turned out to be unstable, which is not unexpected, considering that Cu(I) typically prefers low coordination numbers.
For the HIE variant, we have optimised a second-sphere singlet state (5) Figure   S7 in the SI). These intermediates are similar to the "caged OH • " structures obtained in Ref.
48. However, they were appreciably less stable than a structure in which H 2 O 2 is cleaved to the triplet state. The resulting structure is shown in Figure 6 (lower ). It is about 70 kJ/mol more stable than 5 (in the singlet state). Interestingly, the C 4 −H distance is 2.2Å, so it is appearently set up for hydrogen abstraction.  Table S5 and Figure S9), making this reaction highly unlikely.
We recently found the same employing a QM-cluster approach, although no activation barriers were calculated. 38 Another recent QM-cluster study also came to the same conclusion. 39 Therefore, we focus on the [CuO] + (6b) and [CuOH] 2+ (6c) intermediates in the following.
However, before investigating the reactions 6b→7a and 6c→7b, we investigated the protonation state of His147 for the reactants and products. For intermediates 6b and 7a, the HIE state is 120 and 122 kJ/mol more stable than the HID state, respectively. The corresponding energy differences for 6c and 7b are 116 kJ/mol and 187 kJ/mol, also in favor of the HIE state. On the one-hand, this large energy-difference in favor of the HIE tautomer suggest that the abstraction reaction occurs from the HIE form, unless the barrier is significantly higher in this form. On the other hand, the HID form is more natural to employ for the C 4 −H abstraction, as this form is obtained directly from reactions 5→6c and 4→6 (in which HIP donates a proton and thereby becomes HID). With these considerations in mind, we decided to investigate the C 4 −H abstraction with both the HIE and HID forms of His147. It turned out, that for 6b and to a lesser degree 6c, the protonation state of the nearby His147 residue strongly influences the activation energies.
We We next turn to the Cu-hydroxyl complex (6c→7b). The reactant, transition state and product structures and corresponding energies are shown in Figures 10 and 11 (additional details are given in Figure S11 and Table S7). In contrast to the 6b→7a reaction, we obtain a large change in the Cu−O distance, from 1.9Å to 2.2-2.3Å, reflecting a change from  hydroxyl to water.
The ground state of 6c was found to be a singlet, but as is evident from Figure S11, we find that the singlet-triplet energy splitting gradually decreases during the C−H abstraction (as expected): For the TPSS functional, the triplet becomes energetically lower than the singlet for a C 4 −H distance of 1.45Å (1.40Å with B3LYP) and for the product, the triplet is significantly more stable. In the following, we estimate the activation energy from the energy at the singlet-triplet crossing.   the reaction energies of 6b and 6c are similar. We note also that the electrostatic environment contributions are uniformly small (2-10 kJ/mol, see Figures S10 and S11), which is in marked contrast to the much more sensitive proton-transfer reactions discussed above.
To investigate the relative stability of 6b and 6c, we finally studied the protonation of 6b to 6c. Here, His147 acted as the proton donor and hence was in the HIP form. Protonation of 6b turned out to be facile with a low energy barrier (below 20 kJ/mol) and with a overall reaction energy of around −150 kJ/mol. Therefore, 6b should be rapidly converted to 6c in acidic media. Considering the fact that 6c is very easy to generate, this intermediate should be considered the favored one, despite its slightly higher activation energy.

Recombination step and product formation
The final reaction is the recombination of the saccharide radical and the Cu ligand, i.e.
the 7a→8a or 7b→8b reactions in Figure 1. We first studied the reaction from [CuOH] +  Tables S8-S9 and Figure S12 for further details). The reaction involves a transition from  shorter bond distance (2.2Å) and the activation energy is slightly higher (53 kJ/mol, see Table S8). Independent of the employed functional, the reaction is strongly downhill by 182-193 kJ/mol. Both activation and reaction energies are similar for the HID state (albeit generally 10 kJ/mol lower, cf. Figure 14). The corresponding activation energy for the HIP state is either slightly higher (62 kJ/mol with TPSS) or similar to that with the HIE form (B3LYP), while the reaction is still significantly downhill (158-165 kJ/mol), independent of the employed functional.
As expected, attempts to obtain a protonated ROH + 2 product state directly from 7b were unsuccessful. They were carried out with His147 in the HID state to allow the possibility for the product to protonate this residue, but this did not occur. However, the reaction (7b→8a under protonation of HID to HIP) is downhill by between 43 and 47 kJ/mol, depending on the functional. Therefore, it may occur with a concerted protonation of HID to HIP under the transfer of OH • . Since the active site is close to the surface, the deprotonation may also occur through connections to the bulk solvent. Another possible reaction path for 7b could be protonation of His147 in the HID form to form 7a + HIP. We are currently investigating these different possibilities.

Discussion
We have calculated reaction and activation energies for the full putative mechanism of the LPMOs in Figure 1. In this section, we relate our findings to known experimental data and previous theoretical results. Our suggested mechanism is shown in Figure 14 along with the calculated reaction and activation energies.
It is known that the investigated LPMO is C4-specific. Focusing on the structural parameters, we note that for our optimised structure of the [CuO 2 ] + (3) complex, the distances  Table S1). These distances are slightly longer with the larger def2-TZVPD basis set (2.35Å and 2.41Å, Table S1). The similarity of these distances suggests that a regiospeci- With the present results, it is naturally interesting to compare the two investigated mech-anisms for generation such species. Starting with the O 2 pathway in Figure 1, the initial protonation of the superoxide 3→4a is certainly feasible with an activation energy below 20 kJ/mol. The cleavage of the O-O bond in 4a requires further reduction to 4b and our calculations suggest that the second reduction (of 4b in Figure 1 Finally, we note that it has recently been suggested that deprotonation of the terminal NH 2 unit may be part of the mechanism, 14,43 but no conclusive evidence for this deprotonation has yet been published. A recent neutron and X-ray diffraction study has been claimed show such a state, 41 but the crystallographic data are ambiguous: In a separate study we have re-investigated this crystal structure using quantum refinement. We see no evidence of a terminal NH 2 deprotonation and this path is therefore not considered here. Moreover, our QM-cluster studies showed that deprotonation did not lead to any enhanced reactivity. 38

Conclusions
In this paper, we have investigated the substrate-LPMO complex with QM/MM methods, starting from a recently published crystal structure. 7 The full mechanism has been mapped out and the results are shown (together with activation and reaction energies) in Figure 14.
The calculations show that protonation of a superoxo [CuO 2 ] + complex is feasible and can lead to formation of an oxyl complex after reduction and dissociation of water. This oxyl complex is readily protonated to a Cu-hydroxyl complex. Both Cu-oxyl and Cu-hydroxyl (6b and 6c) are sufficiently reactive to abstract a hydrogen from the polysaccharide substrate. In addition, we have shown that the protonation state of the second-sphere histidine (His147) can shift the balance between two intermediates by enhancing the reactivity of the The individual residues were visually inspected and their solvent exposure and hydrogenbond network were assessed. Based on this, we concluded that all arginines and lysines are protonated (+1) and the aspartic and glutamine acids are in their carboxylate form (−1). Three of these charged residues are buried inside the protein, Glu103, Arg140 and Glu142. Glu103 forms an ionic pair with the ammonium group of Lys100, whereas Arg140 and Glu140 from another ionic pair. Therefore, they were considered in the charged forms.
The protein contains two cysteine residues (Cys41 and Cys167) that are cross-linked by a disulfide bridge.
Histidine residues have two possible protonation sites and in the following, we denote histidines as HIE (N 2 protonated), HID (N δ1 protonated) or HIP (both nitrogens protonated).
The N-terminal histidine is a special case, because the imidazole is methylated on the N 2 atom, whereas N δ1 coordinates to the Cu ion. For the remaining histidine residues, we employed the protonation states HIP66, HID78, HIP79, HIP122, HID125, HIP131 and HIE147.
HIP66 forms hydrogen bonds from N δ1 to the O δ1 carboxyl group of Asp72 and from N 2 to a hydroxy group of the substrate. HID78 coordinates to Cu through N 2 , whereas HIP79 forms a salt-bridge from H δ1 to the carboxylate group of Asp116 and a hydrogen bond to a crystal water molecule through H 2 . HIP122 forms a hydrogen bond to the carboxyl group of Asp70 through H δ1 and is exposed on the surface of the protein and was therefore chosen to be doubly protonated. HID125 forms a hydrogen bond to a crystal water molecule from H δ1 and N 2 accepts a hydrogen bond from the NH group of the Trp64 side chain. HIP131 is solvent exposed on the surface and was chosen to be doubly protonated (in the crystal structure one of the hydrogen interacts with a Clion). HIE147 is close to the active site and may participate in the reaction mechanism as the proton donor. The preperation tool in Maestro originally flipped this residue, but we decided instead to employ the HIE form in the conformation obtained in the crystal structure. This form is in agreement with a recent Equilibration and QM/MM setup The system described above was equilibrated by simulated annealing. Both the equilibration and the QM/MM calculations followed closely our previous investigations S8 and here we only highlight differences. The previous calculations were carried out on a system without substrate, but in this study, we included a trisaccharide substrate (cf. Figure 1 in the paper). The substrate was described by the glycam.v06 force field, S9 which is tailored for oligosaccharides. The protein was described with the Amber FF14SB force field S10 and water molecules with the TIP3P model. S11 The equilibration was performed on state 1, which was obtained by replacing the coordinating Clion in the crystal structure with H 2 O. For the equilibration, restrained electrostatic potential (RESP) charges were employed for the metal center and its first coordination sphere (cf. Figure S1) The employed structure was taken from the crystal structure and only the hydrogen atoms were optimized, employing the S3 TPSS functional S12 together with the def2-SV(P) basis set. S13,S14 The electrostatic potential was calculated in points that were sampled with the Merz-Kollman scheme S15,S16 using default radii for the light atoms and 2 Å for Cu. S17 They were employed by the RESP program (a part of the AMBER software package) to calculate the charges.
The QM system (system 1) consisted of the copper ion and its first coordination sphere i.e. the imidazole ring of His78 and the phenol ring of Tyr164, both capped with a hydrogen atom replacing C α . The entire His1 residue, which coordinates to Cu through the terminal amino group as well as the imidazole side chain, was included. The neighboring Thr2 residue was included up to the C α atom, which was replaced by a hydrogen atom. In addition, the two first glucose rings of the substrate were also included in system 1, whereas the third glucose unit was described by MM. Thus, for the 1 state, the QM region comprised 111 atoms (see Figure S1, middle).
Since the reduction of 1 without substrate has been discussed in several previous computational QM-cluster S4,S18,S19 and QM/MM studies, S8 we have also considered the reduced The QM/MM structure optimizations employed the dispersion-corrected TPSS-D3 functional S12,S20 with Becke-Johnson damping S21 and the def2-SV(P) basis set. S13,S14 The [CuO 2 ] + and [CuO] + intermediates have low-lying singlet states, which are best calculated as an open-shell singlet with the broken-symmetry approach. S22 All species with an even number of electrons have been calculated both as triplet and singlet species. The most stable state was employed, but small singlet-triplet splittings are commented. All reported energies were obtained from TPSS-D3 single-point calculations (with the full protein represented by S4 point-charges) with the def2-TZVPP basis set S13 on structures obtained with TPSS-D3/def2-SV(P). In addition, we also report energies for similar calculations with TPSS-D3 replaced with B3LYP-D3. S23-S25 For selected states (1-3), we have probed the quality of the structures obtained with the TPSS-D3 functional and def2-SV(P) basis set by increasing the basis set to def2-TZVPD.
In addition, test calculations were also performed with system 2 optimised. System 2 was defined as all atoms within 6 Å of any atom in system 1. We use the labels "free" and "fixed" for calculations in which the coordinates of atoms in system 2 were or were not optimized, respectively.
Overlay of active sites in 5ACF and 4EIS crystal structures Figure S2: Overlay of active site structures from 5CAF and 4EIS (yellow). Hydrogen atoms are not shown. Residues numbering is accoriding to 5CAF. Table S1: Cu-ligand bond lengths (Å) in the present and in previous studies for 3 with substrate (entries 1-3 and 9-11) and without substate (entries 4-8 and 12,13). All QM/MM results were obtained with the TPSS-D3 functional and def2-SV(P) basis set (unless otherwise noted).    Singlet-triplet splittings of intermediate 3 Reaction profiles and energetics for intermediates 3-7