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Cryo-EM structures reveal ubiquinone-10 binding to mitochondrial complex I and conformational transitions associated with Q-site occupancy

Mitochondrial complex I is a central metabolic enzyme that uses the reducing potential of NADH to reduce ubiquinone-10 (Q10) and drive four protons across the inner mitochondrial membrane, powering oxidative phosphorylation. Although many complex I structures are now available, structures of Q10-bound states have remained elusive. Here, we reconstitute mammalian complex I into phospholipid nanodiscs with exogenous Q10. Using cryo-EM, we reveal a Q10 molecule occupying the full length of the Q-binding site in the ‘active’ (ready-to-go) resting state (plus a matching substrate-free structure) and apply molecular dynamics simulations to propose how the charge states of key residues influence the Q10 binding pose. By comparing ligand-bound and ligand-free forms of the ‘deactive’ resting state (that require reactivating to catalyse), we begin to define how substrate binding restructures the deactive Q-binding site, providing insights into its physiological and mechanistic relevance.


Introduction
Mitochondrial complex I (NADH:ubiquinone oxidoreductase) is an intricate ~1 MDa multimeric membrane-bound complex that is essential for mitochondrial metabolism 1,2 . It comprises 14 catalytic core subunits that are conserved across all kingdoms of life, and up to 31 supernumerary subunits that contribute to its stability, regulation, and/or biogenesis [3][4][5] . As an entry point into the electron transport chain (ETC), complex I is a key contributor to oxidative phosphorylation, mitochondrial homeostasis, and redox balance. Specifically, it couples electron transfer from NADH to ubiquinone (Q) to proton translocation across the inner mitochondrial membrane, building the proton motive force (∆p) to drive ATP synthesis. Due to its central roles in metabolism, complex I is implicated in ischaemia-reperfusion (IR) injury 6 and its dysfunctions lead to neuromuscular and metabolic diseases 7,8 .
Two biochemically characterised, physiologically relevant states, the 'active' and 'deactive' resting states, have previously been identified by electron cryomicroscopy (cryo-EM) on mammalian complex I. They are distinguished by subtle domain movements and conformational changes at the Q-binding site and in adjacent membrane-domain subunits 5,[9][10][11][12][13] . In the absence of substrates and at physiological temperatures, mammalian complex I relaxes gradually from the ready-tocatalyse active resting state into the profound deactive resting state, with a partially unstructured Q-binding site 5,9,10,[14][15][16][17] . The deactive state forms spontaneously during ischaemia (when lack of O2 prevents ETC turnover). Then, when NADH and ubiquinone are added/replenished (for example, upon reperfusion), it slowly reactivates and returns to catalysis. During reperfusion the deactive state protects against IR injury by minimising complex I-mediated production of reactive oxygen species by reverse electron transfer 13,18,19 . Cryo-EM studies of mammalian complex I have also identified a third state of particles that lack key regions of density, which we suggested previously to arise from complex I in the first stages of dissociation 5,11 .
The Q-binding site in complex I is an unusually long and heterogeneous channel. Advances in cryo-EM have allowed identification of several inhibitors 12,20-24 , adventitious detergents 25 , and substrate analogues 21,22,26,27 bound in the site, but native Q species (Q9 and Q10, with nine and ten isoprenoid units) have so far only been observed with their Q-headgroups close to the channel entrance 28-30 ). For catalysis, the headgroup must enter much further in and approach its proposed ligating partners (His59 NDUFS2 and Tyr108 NDUFS2 ) at the tip of the channel 31,32 -as observed for the short-chain substrate analogues decylubiquinone (dQ) 21,22,27 and piericidin A 12,21 , and predicted by molecular dynamics simulations [33][34][35][36] . In order to position its headgroup in this reactive centre, the native substrate must span the entirety of the channel.
Here, we describe the structure of bovine complex I reconstituted into phospholipid nanodiscs with exogenous Q10. The nanodiscs provide a native membrane-like environment and eliminate potential artefacts from the detergent micelle typically used in cryo-EM analyses. Using cryo-EM, we resolve five distinct structures at global resolutions up to 2.3 Å, including, for the first time, a Q10 molecule occupying the full length of the Q-binding channel. By comparing the structures of substrate/ligand-bound and -apo (substrate/ligand-free) forms of both the active and deactive states, as well as a structure of the poorly characterised third state, we probe substrate/liganddriven conformational changes in the Q-binding site and the physiological and catalytic relevance of each state.

Results
All the established hallmarks for the active state 5,10,12 are present in the active maps/models, including well-defined densities for the loops in NDUFS2, ND3 and ND1 (residues 52-62, 24-55 and 194-217, respectively) that constitute the Q-binding site, an extended NDUFA5/NDUFA10 interface, and a fully α-helical ND6-transmembrane helix (TMH) 3. [Note we use the human subunit nomenclature throughout for simplicity]. The same is true for the deactive maps/models, where the hallmarks include disordered/alternate conformations of the above loops, a restricted NDUFA5/NDUFA10 interface, and a π-bulge in ND6-TMH3 5,9,10,13 . Furthermore, NDUFS7 residues 47-51 form a loop in the active state and a β-strand in the deactive state, and the adjacent loop (residues [74][75][76][77][78][79][80][81][82][83] is 'flipped over' between the two states, reorientating the hydroxylated conserved Arg77 NDUFS7 . As reported previously 5 , the state 3 map (see Supplementary Fig. 5) lacks clear density for the C-terminal half of the ND5 transverse helix and its TMH16 anchor; subunit NDUFA11 (barring a short fragment facing the intermembrane space); and the 40-residue N-terminus of NDUFS2. These densities remain unclear at the current (much higher) resolution, confirming these elements are disordered or in multiple unresolved conformations. Here, we focus on the occupancy of the Q-binding channel in each state and present a Supplementary Discussion to evaluate the biochemical relevance of the state 3 structure.

Characterisation of nanodisc-bound complex I
In all three states, two belt-like densities representing two MSP2N2 monomers are visible, enveloping the membrane domain in place of the usual detergent:phospholipid micelle (Fig. 1). Two 391 residue-long polyalanine models fit into them well, overlapping as four parallel helices below NDUFA9 (Fig. 1b), a subunit just above the expected membrane surface that has been observed to bind phospholipids 10 . The overlapping contrasts with the 'dangling' termini observed for shorter MSPs 42 . Quantitative biochemical analyses showed the CxI-NDs contain an average of 295 phospholipids, sufficient for a layer only one or two deep around the enzyme, and 2.66 Q10.
Although this equates to 12 mM Q10 in the phospholipid phase, substantially above the KM value in proteoliposomes 37 , there is no 'bulk' bilayer to support quinone diffusion, consistent with the low dQ/Q10 reductase activity ( Supplementary Fig. 1b). Furthermore, the MSP2N2s wrap tightly around the enzyme like stretched rubber bands, creating direct enzyme-MSP2N2 contacts in some regions and phospholipid-filled crevices and cavities where there are protein voids in others ( Fig.  1 and Supplementary Fig. 6a).
Comparison of the CxI-ND active-state structure with a DDM-solubilised active-state bovine structure [Protein Data Bank (PDB) ID: 7QSD; Electron Microscopy Data Bank (EMDB) ID: 14127] 43 revealed no material differences, with convincing map-to-map correlation (0.97) and RMSD values (0.26-0.31 Å for the membrane-bound core subunits, 0.32-0.35 Å overall). As expected, none of the three DDMs observed in the reference structure 43 were observed in CxI-NDs, while the phospholipids increased from 22 to 42 ( Supplementary Fig. 6b). There is no evidence that 'lateral pressure' tightens the subunit interfaces in the CxI-ND membrane domain, and further comparisons with detergent-solubilised mammalian complex I structures 9,10,12,13,22,23,43 revealed only three very minor structural differences (see Supplementary Discussion).

Q10 bound in the active state
Following focussed 3D classification to resolve heterogeneous density features in the Q-binding site (see Methods and Supplementary Fig. 3), the active class was split into a ligand-bound subclass with a continuous density matching a Q10 molecule spanning the Q-binding channel (henceforth active-Q10; 23,449 particles, 2.84 Å resolution), and a substrate-free sub-class with a presumably water-filled cavity (henceforth active-apo; 38,209 particles, 2.76 Å) ( Table 1 and Supplementary Fig. 4). The Q-binding site is fully structured in both cases.
In active-Q10, the Q10 density occupies the entirety of the channel, starting between subunits NDUFS2 and NDUFS7 (with the Q-headgroup adjacent to Tyr108 NDUFS2 and His59 NDUFS2 ) then extending, as the isoprenoid chain, along the NDUFS2-NDUFS7 then ND1-NDUFS7 interfaces to exit from ND1. The His sidechain forms a hydrogen bond (H-bond) with the 3-methoxy of the Qheadgroup, rather than with either of the reactive carbonyls, which are in geometrically unfavourable positions (Fig. 2a). The Tyr sidechain is too distant (>4.3 Å) from the headgroup for a H-bond, but interacts via two mediating water molecules and a water is also H-bonded between the 4-carbonyl and Asp160 NDUFS2 . In an alternative lower-occupancy orientation of the Q10, represented by weaker density, the headgroup is flipped by 180° and the first isoprenoid is in a different position (Fig. 2a inset). While the His now interacts with the 2-methoxy the H-bonding pattern is similar. In both cases, attempts to reposition the headgroup to create reactive H-bonds to the Tyr and His without moving the isoprenoid chain out of its density were unsuccessful. A number of waters were also observed adjacent to the isoprenoid chain, stabilised by H-bonding to nearby sidechains, clustered particularly in the more charged protein section around the middle of the isoprenoid chain 37 (Fig. 2b).
To probe further why the Q10 appears to have 'paused' in this pre-reactive conformation, we applied molecular dynamics simulations with enhanced sampling to explore the charge state and flexibility of reactive groups in the Q-binding site (see Methods for details). A collective variable (CV) was used to describe the Q-headgroup position along the binding channel, with lower values denoting the headgroup closer to Tyr108 NDUFS2 (Fig. 3a-d). Three charge-states were tested, all with cluster N2 oxidised but different protonation states for His59 NDUFS2 and Asp160 NDUFS2 (Figs. 2a and 3a). The free energy profile obtained for the [AspH + His] charge-state exhibits a well-defined single minimum, indicating stable binding at CV = 23.8 Å (Fig. 3a) with the Q-headgroup position matching that observed in the active-Q10 cryo-EM model at CV = 23.6 Å (Fig. 3a). The other two charge-states ([Asp -+ His] and [AspH + HisH + ]) show multiple minima, with the lowest at CV ~25 Å having the Qheadgroup distant from the reactive site. Additional structural properties ( Supplementary Fig. 7) also showed significantly better agreement with the active-Q 10 cryo-EM model for the [AspH + His] charge-state. The [Asp -+ HisH + ] charge-state was excluded because the cryo-EM model did not suggest an ionic-pair interaction. Thus, our simulations strongly suggest the experimental structure is in the [AspH + His] charge-state and that the Q-headgroup binding pose at the top of the Qchannel is modulated by the charge-states of nearby groups.
Our active-Q10 model was built with the His59 NDUFS2 dihedral angle 2 = -95.5 o (Fig. 2a), but the conformer with a 'flipped' sidechain also fits well. Interestingly, simulations for the [AspH + His] charge-state (Fig. 3e) revealed a flexible His59 sidechain with a barrier for the ring to flip of <15 kJ mol -1 at the stable binding position (CV = 23.8 Å), consistent with Cβ-Cγ bond rotamers with 2 = -100 o or +80 o being equally populated at the physiological temperature simulated. When the Qheadgroup approaches Tyr108 NDUFS2 (CV = 22.5 Å, Fig. 3b), the flexibility of His59 NDUFS2 2 is slightly decreased (Fig. 3e) and a H-bond, which is absent at the stable binding position (Fig. 3c), forms between His59 NDUFS2 -Nε2 and the protonated Asp160 NDUFS2 sidechain (Fig. 3f). It may also re-form when the Q-headgroup dissociates (Fig. 3d), in line with previous simulations on complex I from T. thermophilus 34,35 . The H-bond between His59 NDUFS2 -Nδ1 and the Q-headgroup 3-methoxy is easily broken (Fig. 3g). In fact, when the Q-headgroup occupies its stable binding position it has sufficient conformational freedom to twist and flip during the physiological-temperature simulations, also visiting configurations compatible with the flipped subpopulation observed in the cryo-EM data (Fig. 2a inset).
In the absence of contiguous density attributable to bound Q10 (active-apo structure), we suggest that the discrete densities scattered throughout the Q-binding channel, including in isoprenoidbinding regions, are dynamic water molecules in H-bonding networks (Fig. 2c). Intriguingly, there is also a clear but unidentified density observed at the channel entrance (it may be a Q10 or phospholipid inserted tail-first, but is also consistent with a molecule of MOPS buffer) that appears to separate the water-filled cavity from the hydrophobic membrane (Fig. 2c). In the reactive site, the His59 NDUFS2 side chain is rotated by 90˚ relative to in the active-Q10 structure (Fig. 2c) and stabilised by H-bonding to the carbonyl backbone of Ile423 NDUFS2 ; the water molecule between the Q-headgroup and Asp160 NDUFS2 shifts by ~1 Å in response (Fig. 2c). The two waters between Tyr108 NDUFS2 and the Q-headgroup are not resolved in the active-apo sub-state, but we suggest a poorly-resolved density extending from Tyr108 NDUFS2 represents a network of dynamic water molecules, in place of the headgroup. Apart from His59 NDUFS2 , the only difference in residue conformation between the Q-binding sites in the active-Q10 and active-apo structures is at Glu202 ND1 . Although, as may be expected for carboxylates 44 , the sidechain densities are not wellresolved, the models suggest that in active-Q10 Glu202 ND1 forms a water-mediated H-bond to Glu227 ND1 whereas in active-apo, Glu202 ND1 has undergone a rotameric shift that reconfigures the H-bonding interactions between the two glutamates. These observations hint that Glu202 ND1 responds to the channel occupancy, and may function as a 'control point' for proton transfer.
Ligand binding to the deactive state Q-binding site loops in subunits NDUFS2, ND1 and NDUFS7 are characteristically disordered in the deactive state 9,10,13 and so further classification of the deactive particles focussed on the whole Qbinding region ( Supplementary Fig. 3). Two sub-classes were resolved: an occupied, ligand-bound sub-class (deactive-ligand; 235,957 particles, 2.30 Å resolution) and an apparently unoccupied 'apo' sub-class (deactive-apo; 23,583 particles, 2.81 Å resolution) ( Table 1, and Supplementary Fig. 4). In the deactive-apo structure, the Q-binding site loops in NDUFS2, ND3 and ND1 are largely disordered, whereas in the deactive-ligand structure the NDUFS2 and ND1 loops are in ordered conformations different from those in the active state (Fig. 4). The overall structure remains deactive (with a restricted NDUFA5/NDUFA10 interface, disordered ND3 loop, π-bulge in ND6-TMH3, and deactive NDUFS7 conformation). The restructured NDUFS2-β1-β2 loop (which carries His59) has moved into the space occupied by the Q-headgroup in the active-Q10 structure (Figs. 4b and f), and together with the restructured ND1-TMH5-6 loop, it constricts the Q-binding channel (Fig. 4b). In contrast, in the deactive-apo structure, the disordered loops fail to enclose the channel, which appears as a gaping crevice open to the matrix (Fig. 4e).
The ligand density observed in the deactive-ligand structure displays features consistent with both Q10 and DDM, suggesting a mixed population that could not be separated by focussed classification. The DDM used for complex I preparation may have been retained in the channel when the external DDM molecules were removed during reconstitution. The shape of the headgroup density suggests Q10 at low map thresholds but matches two six-membered maltoside rings at higher thresholds, while a long, zigzagged protrusion resembles an isoprenoid chain ( Supplementary Fig. 8). Fitting a Q10 molecule into the density reveals just one polar interaction, a H-bond from Arg274 ND1 to the Q-headgroup, while the fitted DDM molecule additionally interacts with His55 NDUFS2 and Glu202 ND1 , and an intervening water molecule bridges it to Glu24 ND1 (Fig. 5a). DDM may thus stabilise the deactive state, but whether it also promotes deactivation 25,45 remains unclear. His55 NDUFS2 and Glu202 ND1 are on the displaced NDUFS2-β1-β2 and ND1-TMH5-6 loops, respectively, consistent with their restructuring in the deactive-ligand structure and with continued disorder in the ND3-TMH1-2 loop, which is stabilised in the active state 25 by interaction between His55 NDUFS2 and Cys39 ND3 . Notably, the DDM molecule modelled here differs from the one observed in Y. lipolytica complex I 25 , which is slightly further into the Q-binding channel with its maltoside rings in different positions ( Supplementary Fig. 9g-i). Similarly, the modelled positions of Q10 in plant complex I 29 , Q9 in Y. lipolytica complex I 28 , and dQ in closed and open ovine complex I 22 (Supplementary Fig. 9mp) overlap with the Q10/DDM modelled here, but do not align well. Clearly, the lower section of the Q-binding channel can accommodate a variety of extended hydrophobic and amphipathic molecules, including substrates, inhibitors and detergents, and their binding may modify surrounding protein structures.

Ligand binding to state 3
Following focussed classification procedures, all the state 3 particles were retained in a single homogenous class that contains densities for two bound ligands. First, a clear density at the entrance to the Q-binding channel ( Fig. 4c and f) is consistent with a cholate molecule (added for the reconstitution) in two orientations (Fig. 5b), in close proximity to either Arg25 ND1 , Asp51 ND1 , and Trp46 NDUFS7 , or Arg274 ND1 , Thr21 ND1 , and Tyr228 ND1 for polar interactions. As in the deactiveligand structure, the NDUFS2-β1-β2 and ND1-TMH5-6 (but not ND3-TMH1-2) loops are ordered, but in different conformations to in the deactive-ligand or active states, so the shape of the Qbinding channel also differs ( Fig. 4c and f). The NDUFS2-β1-β2 loop is translated up the channel relative to both its active and deactive-ligand conformations, bringing the backbone carbonyls of Ala58 NDUFS2 and His59 NDUFS2 to within H-bonding distance (2.6-2.8 Å) of the Tyr108 NDUFS2 hydroxyl and restricting the cavity. The ND1-TMH5-6 loop does not run across the Q-binding channel as in the deactive-ligand state, but is retracted downwards, beyond its conformation in the active state, so the Q-binding site again appears open to the matrix. It is not possible to tell if these changes result from cholate binding or are intrinsic to state 3. Regardless of the physiological and mechanistic relevance of state 3, our structure affirms the flexible nature of the Q-binding site and its ability to accommodate ligands. Second, a clear density for an ordered Q10 molecule is observed at the extended interface between subunits ND2 and ND4 (see Supplementary Discussion and Supplementary Figs. 5a and 5b) resulting from their opposing rotation and retraction 5,46 , and is accommodated by a π-bulge in ND4-TMH6 not present in the active or deactive states. However, the Q10 headgroup is 100 Å away from cluster N2 and the Q-binding channel, which is clearly too far for catalytic electron transfer.

State-dependent structural features in the ND1 cavity and E-channel
To probe whether the different Q-site structures propagate changes to the membrane domain, we investigated the structures of the E-channel, which leads from the Q-binding site and the solventaccessible cavity in ND1 to the first antiporter-like subunit, ND2.
The shapes of the ND1 cavities, surrounded by subunits ND1, ND3, and ND6, were visualised using the CASTp software with a 1.4 Å diameter probe 47 (Figs. 2b-c, 4a-e and 6). In both active-Q10 and active-apo, the cavity extends past Glu227 ND1 and Glu192 ND1 (Fig. 2b-c) but is blocked from the next E-channel residue (Glu143 ND1 ) by Tyr142 ND1 , which may thus act as a 'proton gate' (Fig. 6a and d). Two water molecules, on each side of Tyr142 ND1 , connect the hydrated ND1 cavity to Glu143 ND1 and Asp66 ND3 . In both deactive-ligand and deactive-apo, the ND1 cavity extends past Glu227 ND1 , Glu192 ND1 , Glu143 ND1 , and up to Asp66 ND3 . The cavity is extended by the straightening of ND1-TMH4, which forces Tyr142 ND1 to rotate out of the way, shifting the Glu192 ND1 sidechain towards Glu143 ND1 into an electrostatic interaction as described previously 22,25,36 , and bringing additional hydration ( Fig. 6b and e). In this state, Glu143 ND1 and Asp66 ND3 are stabilised by two intermediary water molecules H-bonded to the backbone carbonyl of Gly62 ND6 . As in other structures in the deactive 13,25,27 or open 22 state, as well as in simulations 36 , the ND6-TMH3 π-bulge wedges Met64 ND6 into the ~12.5 Å-long Asp66 ND3 -to-Glu34 ND4L H-bond network that is continuous in the active state, disrupting it and releasing Glu34 ND4L to flip away towards ND2 ( Fig. 6b and e). In this region, state 3 matches the deactive state (Fig. 6c). Beyond this region, we did not observe any substantial changes in the membrane domain between the active-Q10/-apo and deactive-ligand/apo states.

Discussion
The active-Q10 structure described here is the first structure with a native ubiquinone substrate inserted fully into the complex I Q-binding channel. However, the Q-headgroup is not bound in the expected reactive state with its 1,4-carbonyls H-bonding to Tyr108 NDUFS2 and His59 NDUFS2 , ready to receive their protons following electron transfer from cluster N2. Simulations of the reactive state in T. thermophilus complex I 33,36 proposed that the 4-carbonyl always H-bonds to Tyr108 NDUFS2 , but the 1-carbonyl may either H-bond or π-stack with His59 NDUFS2 . Our active-Q10 structure shows none of these interactions. Furthermore, previous structures with the Q 10 analogue dQ and the inhibitor piercidin A1 bound are also not modelled in the expected reactive state (Supplementary Fig. 9a-f).
In the ovine 'closed' state supplemented with dQ and NADH 22 the dQ-headgroup is rotated ~35 (in-plane) relative to our primary binding pose so that His59 NDUFS2 H-bonds to the 4-carbonyl instead of the 3-methoxy, but the 1-carbonyl is ~4.5 Å from Tyr108 NDUFS2 . The dQ-headgroup is 5-6 Å away from Tyr108 NDUFS2 (Tyr144 NDUFS2 ) in Y. lipolytica complex I also 27 . In contrast, the dQheadgroup in a crystal structure of T. thermophilus complex I 21 is flipped and rotated out-of-plane, with Tyr108 NDUFS2 (Tyr87 Nqo4 ) H-bonding with both the 4-carbonyl and 3-methoxy but His59 NDUFS2 (His38 Nqo4 ) not interacting. A similarly flipped binding pose was captured in another set of simulations on T. thermophilus complex I 34 , where the Q10-headgroup was stabilized by a H-bond to (protonated) His59 NDUFS2 but did not engage Tyr108 NDUFS2 . The binding poses observed in two piericidin-bound structures 12,21 match the pose for dQ in the T. thermophilus structure 21 , although neither recapitulates the currently unique NDUFS2-β1-β2 loop conformation that increases the separation of Tyr108 NDUFS7 and His59 NDUFS2 in this structure.
Here, we showed excellent agreement between our experimentally determined Q10 binding pose and predictions from simulations with cluster N2 oxidised and a defined [AspH + His] charge-state for Asp160 NDUFS2 and His59 NDUFS2 . Our results imply that the protonation and charge states of key active-site residues are intimately connected to the binding pose. Furthermore, in both our structure and simulations, cluster N2 is oxidised, so the state we observe is non-reactive for this reason also. Reduction of cluster N2 is likely a key driver for the changes required to bring the Qheadgroup into the reactive state, including 'flipping' the Q-headgroup to orientate the 4-carbonyl toward Tyr108 NDUFS2 , shifting local protonation equilibria to protonate His59 NDUFS2 , and changing the conformation of the NDUFS2-β1-β2 loop to bring it into a coordinating position. We suggest that our observed state is structurally equivalent to a 'pre-reactive' state that occurs naturally on the catalytic cycle, similar to that proposed previously by Teixeira and Arantes 35 , in which the Q 10 pauses before dehydration and ligation of the 1,4-carbonyls finally brings it into the reactive conformation.
On the surface of it, our results may alternatively be taken to suggest the possibility of ubiquinone reduction in improperly ligated states, consistent with the considerable (inhibitor-sensitive) NADH:Q1/Q2 activities of the Tyr108 NDUFS2 -equivalent Y144F/W/H mutants in Y. lipolytica 32 . However, ubiquinone reduction potentials depend on the ligation environment and binding mode 48 , and engaging water molecules around the headgroup as non-specific proton donors appears unlikely in the context of an efficient energy-conserving mechanism. Bound Q1/Q2 have much greater conformational freedom without the long isoprenoid tail to constrain them 37,49 , so they may exhibit alternative hydration patterns and conformational distribution 35 , and become artefactually activated for reduction.
Here, reconstituting complex I into phospholipid nanodiscs with Q10 allowed us to resolve substrate/ligand-bound and substrate/ligand-free forms of both the active and deactive states of mammalian complex I, plus a ligand-bound form of state 3. Whether deactive-like states (in which the NDUFS2-β1-β2, ND3-TMH1-2, ND1-TMH5-6 loops and a loop in subunit NDUFS7 are altered/disordered 10,25 ) are intermediates in catalysis 22 or pronounced off-cycle resting states [14][15][16][17] is currently a major controversy. First, we note the high similarity of our bovine/murine active and deactive states with the closed and open conformations, respectively, of ovine complex I, supported by high map-map correlations, small overall RMSD values (Supplementary Table 1b) and matching structural hallmarks 9,10,22 . Whereas we attribute the deactive state to an off-cycle pronounced resting state, Kampjut and Sazanov 22 proposed that 'open' deactive-like states must form during catalysis for Q10 to enter the Q-binding channel, which would then 'close' as it moves to the reactive site. Their model excludes unoccupied active-like/closed states as catalytic intermediates. However, the simplest explanation for our observation of both the active-Q10 and active-apo states, with near-identically structured Q-binding sites (as also observed in several inhibitor-bound structures 12,22-24 ), is that Q-binding may occur within active-like/closed conformations. In this case, individual structural elements involved in the deactive transition may move during catalysis, but would not be coordinated to produce the extensive domain-level conformational changes required to generate a full deactive-like state. Simulations of Qbinding/dissociation differ in the extent to which they predict conformational changes are required 34,35,50-52 , and the controversy will probably only be resolved when the intermediates generated by turnover of a sample in which deactive-like states are not already present are observed. The presence of deactive-like/open states in both the pre-turnover and turnover samples characterised by Kampjut and Sazanov 22 is consistent with both models, as they may represent off-cycle resting states that are not actively catalysing.
Common to both interpretations of deactive/open states is the concept that substrate binding triggers restructuring of the Q-binding channel, either during catalysis or reactivation. Here, comparison of our deactive-ligand and deactive-apo structures shows how Q10/DDM-binding in the lower section of the channel restructures the NDUFS2-β1-β2 and ND1-TMH5-6 loops in the oxidised deactive state. These restructured loop conformations match the conformations observed in the NADH-reduced open states of ovine complex I, with ubiquinone/ubiquinol modelled in a position overlapping with that occupied here by Q10/DDM 22 . Furthermore, in the partially restructured deactive-ligand state the NDUFS2-β1-β2 loop blocks substrate access to the reactive centre, suggesting that the deactive state is resistant to reactivation under the conditions for reverse electron transport (ubiquinol and NAD + ) because ubiquinol is unable to react with the oxidised enzyme. As a result, the deactive resting state of complex I protects against the damage caused by reverse electron transfer and the coupled generation of reactive oxygen species in ischaemia-reperfusion injury 13,18,19 .
Further modifications of our CxI-ND reconstitution strategy now provide new opportunities to capture and characterise hitherto-unknown catalytic intermediates that are formed as the native Q10 substrate binds and is reduced, triggering energy transfer to the proton-pumping membrane domain.    and His59 NDUFS2 neutral (His, Nδ1-protonated π tautomer) or di-protonated (HisH + , both Nδ1-and Nε2-protonated). The collective variable (CV) describes the Q-headgroup position along the binding channel, as illustrated with His59 NDUFS2 , Tyr108 NDUFS2 and Asp160 NDUFS2 sidechains in (b) for CV = 22.5 Å, (c) for CV = 23.8 Å, and (d) for CV = 25.5 Å. The dashed line in (a) shows CV = 23.6 Å measured from the active-Q10 cryo-EM model. Two-dimensional profiles for the [AspH + His] charge-state along the CV coordinate and coloured by free energy are shown in (e) for the His59 NDUFS2 χ2 dihedral (Cβ-Cγ bond torsion), (f) for the distance between the His59 NDUFS2 -Nε2 and Asp160 NDUFS2 -Cγ atoms, and (g) for the distance between the Q-headgroup 3-methoxy O and His59 NDUFS2 -N δ1 atoms. Symbols correspond to the structural properties observed in cryo-EM models active-Q10 with the primary (star) and flipped (bullet) Q-headgroups. showing varying extents of disorder indicated as the (green) cavities detected by CASTp 47 . Where visible, His59 NDUFS2 , Tyr108 NDUFS2 and Asp160 NDUFS2 are shown as sticks. f) Superimposed structures of the active-Q10 (purple), deactive-ligand (green) and state 3 (turquoise) states, showing the NDUFS2-β1-β2 and ND1-TMH5-6 loops in cartoon, and His59 NDUFS2 and Tyr108 NDUFS2 in sticks.

Transformation and recombinant expression of membrane scaffold protein, MSP2N2
Bacterial strain Escherichia coli NiCo21(DE3) was kindly provided by Dr Ali Ryan, Northumbria University, UK. Chemically competent E. coli NiCo21(DE3) cells were prepared and transformed with pMSP2N2 (Addgene) using a standard New England BioLabs (NEB) heat shock protocol. For heterologous overexpression of MSP2N2, a starter culture of E. coli NiCo21(DE3) containing pMSP2N2 was grown overnight at 37 °C in LB broth with 50 µg mL -1 kanamycin. 4 x 2 L Fernbach flasks containing 500 mL of fresh LB media supplemented with antibiotic were inoculated with 1% v/v starter culture and grown at 37 °C, 250 rpm until the culture reached an OD600 of 0.6. Protein expression was induced using 0.1 mM IPTG and the cells were cultured for a further 4 h at 37 °C with 250 rpm shaking. Cells were harvested by centrifugation at 6,000 x g for 20 min at 4 °C, resuspended in 40 mL lysis buffer (50 mM Tris-HCl pH 8, 500 mM NaCl, 5% glycerol, 1% v/v Triton X-100, 0.002% v/v PMSF, and 1 EDTA-free protease inhibitor tablet (Roche)) and stored at -80 °C.

Purification of MSP2N2
The method for purification of MSP2N2 was adapted from a published protocol 38 . Cell suspensions were thawed and lysed by sonication on ice using a Q700 sonicator (Qsonica) (50% output amplitude, 30 cycles of 10 s on, 20 s off). The cell lysate was clarified by centrifugation using a SS34 rotor at 30,000 x g for 1 h at 4 °C. The supernatant was collected, syringe filtered through a 0.22 µm membrane (Merck Millipore Ltd.) and applied to a 1 mL Ni-NTA column (His-Trap TM HP, Cytiva) equilibrated with 50 mM Tris-HCl (pH 8), 500 mM NaCl (= buffer A) + 1% v/v Triton X-100. The column was washed with 10 column volumes of buffer A + 1% v/v Triton X-100 followed by 10 column volumes of buffer A + 50 mM sodium cholate. Non-specifically bound proteins were washed with 10 column volumes of buffer A + 80 mM imidazole and finally MSP2N2 was eluted with buffer A + 400 mM imidazole. To obtain highly pure MSP2N2, the eluate from 1 mL Ni-NTA column was reapplied to a 5 mL Ni-NTA column (His-Trap TM HP, Cytiva) and the same procedure was repeated. Pure MSP2N2 fractions were pooled and dialysed against 2 L of 10 mM MOPS (pH 7.5 at 4 °C), 50 mM KCl at 4 °C. Sample homogeneity was confirmed by SDS-PAGE, and the protein flash frozen and stored at -80 °C.

Preparation of bovine mitochondria, membranes, and complex I
Bovine heart mitochondria were prepared as described previously 54 , and mitochondrial membranes prepared using a method modified from that used previously for Mus musculus 10 . Briefly, mitochondria were thawed and diluted to 5 mg mL -1 with 20 mM Tris-HCl (pH 7.55 at 20 °C), 1 mM EDTA, 10% glycerol, then ruptured by three 5 s bursts of sonication with 30 s intervals on ice using a Q700 micro-tip Sonicator (Qsonica) at 65% output amplitude setting. The membranes were pelleted at 75,000 x g using an MLA80 rotor (Beckman Coulter) for 1 h, then resuspended in the same buffer. Bovine complex I was prepared as described previously 37 with a minor modification to match the mouse complex I preparation 10 (solubilised membranes were centrifuged at 48,000 x g for 30 mins instead of 8,500 x g for 12 mins) and kept on ice until reconstitution into nanodiscs.

Complex I reconstitution into nanodiscs
Complex I was reconstituted into nanodiscs using a protocol based on the reconstitution of complex I into proteoliposomes 23 . Each sample was transferred into a 1.5 mL Eppendorf tube, centrifuged at 7,000 x g for 10 min in a bench-top centrifuge, then each supernatant was transferred to a new tube and incubated on ice for 10 mins. MSP2N2 and bovine complex I (prepared as described above) were pooled gently with the lipid-Q10 mixture at a molar ratio of 400:10:1 (lipid:MSP2N2:complex I). Each sample was then diluted 2-fold with 0.5 mL 10 mM MOPS (pH 7.5 at 4 °C), 50 mM KCl to a total volume of 1 mL, and incubated on ice for 20 min. Then each sample was run over a separate PD10 desalting column (Cytiva) at 4 °C to remove the peripheral detergents. The eluates were pooled together, concentrated using a 100 kDa MWCO Amicon® Ultra concentrator (Merck Milipore Ltd.) to ~100 µL, and filtered using a 0.22 µm Corning® Costar® Spin-X® plastic centrifuge tube filter (Merck Milipore Ltd.). The concentrated sample was applied to a Superose 6 increase 5/150 column (Cytiva) equilibrated with 10 mM MOPS (pH 7.5 at 4 °C), 50 mM KCl, and the most concentrated fractions from the monodisperse CxI-ND peak were used for grid preparation.

Characterisation of complex I-reconstituted nanodiscs
The complex I concentration in the nanodisc preparation was quantified relative to a detergent solubilised sample of known concentration using the NADH:APAD + activity assay with 500 µM APAD + , 1 µM piericidin and 100 µM NADH, as described previously 23,37,39 , except that 0.15% soy bean asolectin (Avanti Polar Lipids) and 0.15% CHAPS (Merck Chemicals Ltd.) were present. CxI-ND concentrations (i.e. combined protein concentrations of complex I and MSP2N2) were determined using the Pierce™ bicinchoninic acid (BCA) protein assay kit (Thermo Fisher Scientific). For the sample subjected to cryo-EM analyses, the complex I and CxI-ND concentrations were 3.7 and 4.8 mg mL -1 , respectively, and the same ratio was observed consistently in several independent preparations. Phospholipid contents were determined as described previously 23,37,39 . The average phospholipid molecular weight was taken to be 771.6 g mol -1 , and the volume of the phospholipid phase was estimated by assuming that 1 mg of phospholipid occupies ~1 µL 55 . Q10 contents were quantified by HPLC, by reference to a set of standard samples, using a Nucleosil 100-5C18 column and a Dionex Ultimate 3000 RS electrochemical detector as described previously 23,37,39 . Q10 concentrations were defined relative to the phospholipid phase volume.
All catalytic activity assays were conducted at 32 °C in 96-well plates using a Molecular Devices Spectramax 384 plus plate reader. Catalysis was initiated by addition of 200 µM NADH and monitored at 340 and 380 nm (340-380 = 4.81 mM -1 cm -1 ). Linear rates were used for activity calculations, and inhibitor-insensitive rates (determined by the addition of 1 µM piericidin A) subtracted from each measured rate where noted. Isolated complex I used for reconstitution and CxI-ND samples used for cryo-EM analyses were diluted to 0.5 µg mL -1 in 20 mM Tris-HCl (pH 7.5 at 32 °C), and activity assays performed with 200 µM decylubiquinone (dQ), 0.15% asolectin/CHAPS, and/or 10 µg mL -1 alternative oxidase (AOX), prepared as described previously 37 .

Cryo-EM grid preparation and image acquisition
UltrAuFoil gold grids (0.6/1, Quantifoil Micro Tools GmbH) 56 were prepared as described previously 9 . Briefly, grids were glow discharged (20 mA, 90 s), incubated in a solution of 5 mM 11mercaptoundecyl hexaethyleneglycol (TH 001-m11.n6-0.01, ProChimia Surfaces) in ethanol for two days in an anaerobic glovebox (Belle), then washed with ethanol and dried just before use. Using a Vitrobot Mark IV (FEI), 2.5 µL of 4.8 mg mL -1 CxI-ND solution (from the same preparation) were applied to the grids before blotting for 10 s at force setting -10, at 100% relative humidity and 4 °C, and then plunge-frozen into liquid ethane. Twelve grids were screened for particle number and distribution and two grids were selected for two 2-day data collections. They were imaged using a Gatan K3 detector and a post-column imaging energy filter (Gatan BioContinuum) operating in zero-energy mode with a slit width of 20 eV mounted on an FEI 300 keV Titan Krios microscope (Thermo Fisher Scientific) with a 100 µm and 70 µm objective and C2 apertures, respectively, and EPU v. 2.7.0.5806REL at the Department of Biochemistry, University of Cambridge. Data were collected in super-resolution electron counting mode at a pixel size of 0.535 Å pixel -1 (81,000x nominal magnification) with a defocus range -1.0 to -2.4 in 0.2 µm intervals, and the autofocus routine run every 10 µm. Aberration-free image shift (AFIS) was used for data acquisition on day 1 of the 2-day data collection for the first grid but was abandoned due to frequent occurrences of erratic image beam shifts observed in collected movies. The dose rates for the two datasets were 16.9 electrons Å -2 s -1 , with 2.4 sec exposures captured in 40 frames. The total dose was thus 40.5 electrons Å -2 in both cases. Data were retrieved as non-gain-corrected LZWcompressed tiff movie stacks.

Cryo-EM data processing
The two datasets were processed separately until stated otherwise, using RELION 3.1.0 40 ( Supplementary Figs. 2 and 3). The micrographs were motion-corrected using RELION's implementation of MotionCorr with 5 x 5 patches and amplitude contrast of 0.1, and contrast transfer function (CTF) estimated using CTFFIND-4.1 57 with ResMax set to 5 Å. Micrographs were filtered to remove those with a negative rlnCtfFigureOfMerit value, an rlnMaxResolution value worse than 6 Å, or an rlnCtfAstigmatism value lower than 20 or greater than 1000. Icecontaminated micrographs were further removed manually to give 2,639 and 1,797 micrographs for datasets 1 and 2, respectively, from which 804,367 and 382,037 particles were selected using RELION's AutoPicking tool with a 3D map input 43 . Particles were extracted with an initial 4.5x downscaling to 2.4075 Å pixel -1 , and filtered to select those with an rlnAutopickFigureOfMerit value between 0 and 4. Following one round of 2D (with alignment) and 3D (without alignment) classification to remove junk particles, the remaining particles were re-extracted at the nominal pixel size (1.07 Å pixel -1 ; 2x bin) for another round of 3D classification with local angular search to remove aberrant classes of particles. 251,045 (dataset 1) and 140,731 (dataset 2) particles were brought forward for iterative rounds of CTF refinement 40,58 , to estimate anisotropic magnification, beam tilt, trefoil, 4 th order aberration, and per-particle defocus, astigmatism and B-factor parameters. Particles with an rlnNrOfSignificantSamples value greater than 2,999 were removed, and the two datasets combined to give 367,615 particles. These particles were then re-extracted with re-centring, subjected to Bayesian polishing, CTF refined and 3D classified (local angular search) to remove any remaining junk. At this early stage, 358,326 particles were 3D refined with solvent flattening to give a global resolution of 2.28 Å (according to a gold-standard Fourier shell correlation (FSC) of 0.143). Signal subtraction was performed to remove most of the non-complex I contribution: a tight complex I mask was first generated from a working model using RELION MaskCreate, and subtracted from the consensus map to obtain densities for the nanodisc; leftover complex I densities from subtraction were removed using a volume eraser in UCSF Chimera 59 , and the complex I-subtracted map then used to make a mask for the nanodisc in RELION. 3D classification (number of classes, K = 6, local angular search to 0.2° sampling) was then performed, which separated the particles into active, deactive and state 3 complex I classes. Two classes arising from atypically shaped nanodisc complexes (C1) and junk (C2) were excluded from subsequent rounds of processing. Active (C4), deactive (C5 and C6) and state 3 (C3) classes retained 61,654, 259,547, and 22,019 particles, respectively, which were then signal reverted to include the nanodisc densities, and repolished at 0.7523 Å pixel -1 . The three classes refined to 2.65, 2.28, and 3.02 Å resolution, respectively, at the calibrated pixel size of 0.7496 Å pixel -1 (Supplementary Fig.  2) determined by comparison with existing mammalian complex I structures 12 . Focussed 3D classification without alignment (regularisation parameter, T = 100) was performed on the active, deactive, and state 3 classes (Table 1 and Supplementary Fig. 3). All individual classes were first subject to signal subtraction to retain roughly only the peripheral arm of complex I, and then focussed classified using a mask generated from a tentatively modelled Q10 (active), a mask generated from a provisional partial protein model (ND1, NDUFS2, and NDUFS7) encapsulating the Q-binding site (deactive), or a mask generated from a tentatively modelled DDM (state 3) (Supplementary Fig. 3); 7 junk particles were discarded in this step for the deactive class. Masks for focussed classification were generated using RELION MaskCreate with up to 10 pixels of extensions and soft cosine edges. The identified sub-states outlined in the main text were then signal reverted to give the global map, and the global resolution estimated from the FSC between two independent, unfiltered half-maps (FSC = 0.143) ( Table 1 and Supplementary Fig. 3 and 4). As no obvious differences were identified between the state 3 sub-states, which were evenly balanced, they were kept as a single class. The model-generated mask used for 3D refinement with solvent flattening and resolution estimation was generated in UCSF Chimera 59 using the 'molmap' function, before being low-pass filtered to 15 Å and having a 6-pixel soft cosine edge added using RELION MaskCreate. Mollweide projections were plotted using Python and Matplotlib.
All consensus maps were locally sharpened from the unsharpened, unfiltered half-maps generated from RELION post-process (user-provided B-factor and ad-hoc low-pass filter set to 0 and Nyquist, respectively; the output pixel size was altered to match the calibrated pixel size) using phenix.autosharpen in Phenix 1.18.2-3874 60 , setting the resolution limit to the highest local resolution determined from RELION LocalRes ( Supplementary Fig. 4), and with a local sharpening box size of 15 3 pixels and a targeted overlap of 5 pixels. The deactive-ligand map was split into three sections (distal and proximal membrane domains, and peripheral domain) for manual multibody refinement (i.e. signal subtraction, followed by focussed refinements) following nanodisc subtraction (Supplementary Fig. 3). The focus-refined maps were then globally sharpened in RELION post-process, and using the globally sharpened consensus deactive-ligand map as a reference, combined to make a composite map using phenix.combine_focused_maps in Phenix 1.19-4092 60 ( Supplementary Fig. 3). The composite map was carefully compared to the consensus map to ensure that there were no map distortions or anomalies. The locally sharpened global maps (active-Q10, active-apo, deactive-apo, and state 3) and globally sharpened composite map (deactive-ligand) were used for model building and refinement (Table 1). Nanodisc maps were generated by complex I subtraction and focussed refinement (i.e. subtract-refinement) using a nanodisc mask, either with alignment (all particles combined) or without alignment (individual substates).

Model building, refinement and validation
Working models derived from a model for bovine complex I in the active state (PDB ID: 7QSD) 43 were rigid-body fitted into maps using the Fit in Map tool in UCSF Chimera 59 , rigid-body real space refinement in Phenix 1.18.2-3874 60 , and Curlew all-atom-refined using Coot 0.9.4-pre 61 . The models were checked, and new resolvable regions built manually in Coot 0.9.4.2-pre. Local bovine populations are known to have a polymorphism at residue position 255 of subunit NDUFA10 -cDNA sequencing has shown evidence for both asparagine 62 and lysine 3 , while electrospray ionisation mass spectrometry supports the latter 63 . On the basis of these reports and the Coulomb potential densities in the CxI-ND maps, we modelled it as Lys255 NDUFA10 . Similarly, residue position 129 (glutamine) of subunit NDUFS2 was modelled as Arg129 NDUFS2 . Densities for existing and additional phospholipid molecules were identified with the Unmodelled blobs tool in Coot. All DDM molecules in the starting model were removed or replaced with phospholipid molecules where the CxI-ND map features indicated, and lipid tails were clipped where necessary using the delete tools in Coot and PyMOL. The manually inspected models were then real-space refined against the respective locally sharpened consensus (active-Q10, active-apo, deactive-apo, and state 3) or composite (deactive-ligand) maps in Phenix 1.18.2-3874 60 with Ramachandran restraints set to Oldfield (favoured) and Emsley8k (allowed and outlier) to remove genuine forced twists. This realspace refinement step was performed iteratively with manual adjustments in Coot. Water molecules were placed into distinct density peaks as identified with the Find Waters function in Coot, with the minimum and maximum distance to protein atoms set to 2.4 and 3.4 Å, respectively. The identified waters were manually edited to remove falsely placed waters (based on H-bonding geometries, strength and shape of densities, and steric clashes) and bulk solvent waters, and to add waters missed due to uncertain positions of surrounding side chains or waters. Atom resolvabilities (Q-scores) in the respective cryo-EM maps were calculated using MapQ 64 , and any outliers identified and corrected. The models were then real-space refined in Phenix as outlined above. The model statistics for the five sub-states in active, deactive and state 3 classes (Table 1) were produced by Phenix, MolProbity, and EMRinger. Model-to-map FSC curves were generated using phenix.validation_cryoem. Model-map CCmask values for various substrate/ligand poses were calculated by first extracting the ligand coordinates from the protein models and then running phenix.validation_cryoem against their respective final maps.
A provisional poly-alanine model for the two MSP2N2 nanodisc belts was built and refined into a 7.4 Å subtract-refined nanodisc map made from all three major species of complex I-reconstituted nanodiscs using interactive molecular dynamic simulations in ISOLDE 1.2.2 65 with α-helical secondary structure restraints.

Comparisons of cryo-EM maps and models
Map-to-map real-space correlations were performed using the Fit in Map function in UCSF ChimeraX 53 (Supplementary Table 1) following low-pass filtering of the relevant maps to the resolution of the lowest resolution map in the set in RELION 66 . RMSD calculations were performed using the Align command in PyMOL 67 .

Identification of hydrogen bonds
H-bonding contacts within individual CxI-ND models (with hydrogens added using phenix.ready_set and/or phenix.reduce 60 ) were identified using the hbonds command in UCSF ChimeraX 53 , for which the geometric criteria are based on a survey of small-molecule crystal structures 68 , and atom types adapted and extended from the program IDATM 69 .

Quinone cavity determination
The interior surface of the Q-binding channel was predicted using CASTp 47 , which computes a protein surface topology from a PDB model. The default 1.4 Å radius probe was used and the results were visualised in PyMOL 67 using the CASTpyMOL 3.1 plugin and by UCSF ChimeraX 53 .
The modelled protein complex was embedded 72 in a solvated bilayer with a composition mimicking that of the inner mitochondrial membrane 73 . The final solvated and inserted system contains 368 DNPC (179 in the matrix leaflet), 294 DNPE (143 in the matrix leaflet), 96 CDL (half in each leaflet) and 22 oxidised Q10 molecules, all initially in the membrane phase. The asymmetry in DLPC and DLPE composition between the two leaflets is due to chain NDUFA9 occupying an area of the matrix leaflet only. The water phase contains 205,387 molecules plus 553 Na + and 348 Cl − ions to neutralize the total system charge and maintain ~0.1 M salt concentration. The resulting simulation model contains a total of 861,975 atoms. Water solvation of the apo Q-binding channel and regions near the oxidised N2 FeS centre was compared to the active-Q 10 and previous cryo-EM models (PDB ID: 6YJ4) 25 and adjusted accordingly.
The simulation model was relaxed and equilibrated during molecular dynamics (MD) simulations of 740 ns in total. Initially all protein heavy atoms were tethered to their initial position by harmonic restraints, then the force constants were decreased progressively from 1,000 to 10 kJ mol -1 nm -1 , and all atoms were free to move in the last 210 ns. Membrane packing (area per lipid) and hydration of several groups in the Q-binding channel were monitored and checked for stability after 400 ns. Then, the final configuration of this simulation had one Q10 molecule inserted into the binding channel. The Q10 coordinates, as well as those of the sidechains of His59 NDUFS2 , Tyr108 NDUFS2 , Thr156 NDUFS2 , Met70 NDUFS7 and Ser205 ND1 , were adjusted to the superimposed active-Q10 cryo-EM model (Fig. 2a). Clashing water molecules in the channel were removed and the protonation states of His59 NDUFS2 and Asp160 NDUFS2 were changed to the three charge-states studied ([Asp -+ His]; [AspH + His]; [AspH + HisH + ]). If necessary, charge neutrality was maintained by removing a counter-ion. Each charge-state was further relaxed and equilibrated during 235 ns of MD simulation, with initial harmonic restraints in heavy protein atoms, the distances between atoms His59 NDUFS2 -Nδ1-Q10O3 and His59 NDUFS2 -Nε2-Asp160 NDUFS2 -Cγ, and the collective variable (CV) described below. Restraint forces were progressively reduced to zero and removed fully in the last 50 ns. Hydration of the Q-binding channel was again monitored and checked for stability. This procedure was designed and implemented to generate equilibrated and unbiased simulation models in the three charge-states studied. A canonical MD trajectory of 300 ns without any restraints was obtained for each charge-state. The root-mean squared deviation (RMSD) for the positions of the Cα atoms of chains NDUFS7, NDUFS2 and ND1 remained stable during these trajectories at ~1.4 Å in relation to both the initial model (PDB 6ZR2) and the current active-Q10 cryo-EM model.
A pathway collective variable (CV) 74 , as used previously for Q-binding simulations 35 , was applied to describe the position of the Q-headgroup along the channel. This CV (see Fig. 3b-d) is a combination of distances between the heavy atoms in the Q-headgroup and the Cα atoms of residues in subunits NDUFS7, NDUFS2 and ND1 exposed to the Q-binding channel. Distances are evaluated with respect to four milestone configurations that represent progressive binding of Q10.
Finally, well-tempered metadynamics 75 simulations were performed for each charge-state, starting from a configuration taken at 75 ns of each canonical MD trajectory described above. Metadynamics were activated in the CV coordinate (position on the path, p1.sss, and distance from the path, p1.zzz) and in the His59 NDUFS2 χ2 dihedral (Cβ-Cγ bond torsion) with Gaussians deposited every 500 time steps (1 ps), at initial height of 0.6 kJ mol -1 , widths of 0.4 and 0.02 units for the CV and dihedral, respectively, and a bias factor of 15.0. Walls were included to restrict sampling for the CV at 21 < p1.sss < 26 Å and -2.45 < p1.zzz < -2.20 Å, with force constant of 1000 kJ mol -1 nm -1 . Productive metadynamics simulations lasted 140 ns for each charge-state. Due to the enhanced sampling nature of this method, simulation times significantly shorter than for canonical MD are sufficient for an appropriate conformational sampling of restricted regions, such as the reactive position of the complex I Q-binding site. Convergence within ±1 kJ mol -1 of free energy differences in the CV profile (Fig. 3a) was reached after 70 ns. The effects of metadynamics and of restraints were removed by re-weighting the distribution of structural properties (distances, dihedral, CV) and the resulting free energies are shown in Fig. 3a, e-g and Supplementary Fig. 7.
In all MD simulations the interactions of protein, lipids and ions were described with the all-atom CHARMM36m force-field [76][77][78] . Water was represented by the standard TIP3P model 79 81 . Q10 interactions were represented by our calibrated force-field 73,82 . The remaining cofactors were described by available CHARMM and CGenFF parameters (charmm36-mar2019.ff) 78 . All simulations were conducted with GROMACS (version 2020.3) 71 at constant temperature of 310 K, pressure of 1 atm and a time step of 2 fs. Long-range electrostatics were treated with the Particle Mesh Ewald method 83 . Metadynamics simulations were performed with the PLUMED plugin (version 2.6.1) 84 .

Data availability statement
Data supporting the findings of this manuscript, and simulation workflow scripts, are available upon reasonable request.

Contents:
Supplementary Table 1 Map-to-map correlations and RMSD values between the complex I maps and models determined here and those available in the protein and electron microscopy data banks.
Supplementary Supplementary Fig. 9 Comparisons between the available cryo-EM and X-ray crystal structures of ligands bound in the Q-binding site of complex I.  The CxI-NDs elute at 1.6 mL, the same as the DDM-bound enzyme. b) Specific NADH:dQ activity data on CxI-DDM and CxI-NDs show that the complex I in CxI-NDs is highly catalytically competant, but catalysis is limited by substrate access. The reference activity (DDM-CxI, before reconstitution) is conserved in CxI-NDs following addition of CHAPS (to dissociate them) and asolectin (to create a lipidic phase). Without CHAPS/asolectin the activity was much lower, so either dQ does not exchange effectively in and out of the nanodisc, its mobility is restricted, or the MSPs prevent it from entering the active site. The low observed rate of NADH oxidation, which is further decreased in the absence of dQ, may either result from dQ reduction by complex I, or dQ-mediated reoxidation of the Q10H2 generated by complex I. Note that inhibitor-insensitive background rates have not been subtracted. 200 µM NADH was added in all cases (see Methods for experimental details).

Supplementary
Supplementary Fig. 2: Cryo-EM data processing -global classification. a) A flow chart of cryo-EM data processing up to the final global 3D classification leading to the three major classes -active, deactive and state 3. D1 and D2 denote Datasets 1 and 2, respectively. Where applicable, the red box denotes that this is the final map for the class. b) A representative raw micrograph from the data collections. c) A representative 2D classification from the data processing. Supplementary Fig. 3: Cryo-EM data processing -local classification. A flow chart of cryo-EM data processing leading from the active and deactive major classes to their local substates (active-Q10, active-apo, deactive-ligand, and deactive-apo) by local classification. As substantial heterogeneity (apparent as weaker and/or discontinuous densities) was observed in the Q-binding sites of the active and deactive CxI-ND maps, the major classes were first signal subtracted to retain the hydrophilic arm, focus-refined, and then 3D focus-classified without alignment using classspecific local masks. A tight mask generated from a tentative Q10 model was used for local classification for the active class, and a more generous mask made from a provisional partial protein model (ND1, NDUFS2, and NDUFS7) encapsulating the Q-binding site region proved more successful for the deactive class. The consensus map for the deactive-ligand class showed poor densities at the distal region of the membrane arm due to movement in this region (subtle differences in the 'openness' of the hydrophilic and membrane arms and stronger alignment to the former mean that flexibility is exaggerated in the distal membrane domain). For this reason, a composite map was made for the deactive-ligand class. The consensus map was split into three regions by signal subtraction and focus-refinement using the three overlaid masks shown in transparent colours. Local resolution maps are shown for the distal (left) and proximal (middle) membrane domains, and the peripheral domain (right). Local resolutions were estimated using the Local Resolution function in RELION and plotted using UCSF ChimeraX 53 with contour levels set to 0.015. The coloured key on the right indicates the resolution in Å, and the map resolution ranges are indicated in brackets for the respective maps, in blue. RELION half-map (sky blue) FSC curves are shown for each domain. The RELION map sharpening B-factors (Å 2 ) for the consensus map, the distal and proximal membrane domains, and the peripheral domain were -58, -53, -49, and -51, respectively. The resulting composite map is shown in gray at contour level of 6.0. Composite maps were not made for the other classes either because there was little flexibility in the distal membrane domain (active-Q10 and active-apo) or because it did not lead to a marked improvement in map densities (deactive-apo and state 3). Where applicable, the red boxes denote the final maps for the classes.
Supplementary Fig. 4: Local resolution maps, Mollweide projections, and Fourier shell correlation curves for the five CxI-ND states. Local resolution consensus maps (left), Mollweide projections (middle), and Fourier shell correlation (FSC) curves (right) are shown for the (a) active-Q10, (b) active-apo, (c) deactive-ligand, (d) deactive-apo, and (e) state 3 structures. The deactiveligand map is the composite map described in Supplementary Fig. 3. Local resolutions were estimated using the Local Resolution function in RELION and plotted using UCSF ChimeraX with contour levels 6.5, 6.0, 4.0, 6.5, and 6.5, respectively. Coloured keys indicate resolution in Å. Mollweide projections were plotted using Python and Matplotlib. RELION half-map (sky blue) and model-map (black -locally-sharpened consensus maps; purple -focus-refined composite map) FSC curves are shown.

Contents:
Supplementary Discussion 1 Biochemical relevance of the state 3 structure.
Supplementary Discussion 2 Minor differences between the structures of nanodiscreconstituted and DDM-solubilised complex I.

Supplementary Discussion 1. Biochemical relevance of the state 3 structure.
Improvements in resolution of the third state of complex I, state 3, now enable a more comprehensive consideration of this poorly understood class of particles ( Supplementary Fig. 5). Previously, for state 3 we described a loss of clear density for the C-terminal half of the ND5 transverse helix and its anchor helix (TMH16), much of the adjacent NDUFA11 subunit, and the Nterminal loop of NDUFS2 5,11 . The resolution of our early data was low (5.6 Å), but the same characteristics are conserved in our current higher resolution map (3.0 Å), so it is clear that these structural elements are disordered and/or have dissociated from the structured binding locations that they occupy on the complex in the active and deactive states. Our data now reveals also that ND6-TMH4 has lost its α-helical secondary structure in state 3, instead appearing as a poorly ordered loop, on the same exposed side of the complex as NDUFA11 and ND5-TMH16, extending the region affected by the disorder. Comparison of the nanodisc structures also shows clear differences in this region ( Supplementary Fig. 6). Instead of clear densities stretching around NDUFA11 (as observed in the active and deactive states), the MSP2N2 helices in state 3 are not clearly resolved, consistent with substantial disorder in subunit NDUFA11 and/or with the MSP2N2 helices contracting inwards to occupy the space where NDUFA11 is usually observed. This change in nanodisc structure suggests that state 3 was present in the preparation before the enzyme was reconstituted into the nanodiscs. Therefore, it may result from destabilisation of the detergentsolubilised enzyme during its purification, but is not an artefact from cryo-EM grid preparation due to instability induced at the air-water interface [85][86][87] . Interestingly, NDUFA11 has been reported to be the only subunit in the membrane arm of complex I that undergoes rapid protein turnover in C2C12 myotubes 88 , consistent with a higher propensity to dissociate in vivo. Furthermore, in the mammalian respirasome NDUFA11 is sandwiched in-between complex III and the core subunits of complex I [89][90][91] , and the removal of complex III during solubilisation of the membrane may introduce additional instability to NDUFA11 and adjacent structures.
Comparing the three states of complex I resolved here shows clearly that state 3 has more in common with the deactive state than the active state. Globally, the apparent angle between the hydrophilic and hydrophobic domains of the complex is most acute in the active state, considerably more obtuse in the deactive state and similar, or greater still, in state 3. Key structural features that distinguish the deactive state from the active state are also present in state 3, including the π-bulge in ND6-TMH3, disordered ND3 TMH1-2 loop and structures around NDUFS7-Arg77. In contrast, the NDUFS2-β1-β2 and ND1 TMH5-6 loop conformations differ from those observed in both the active and deactive states. However, as features of the Q-binding site are known to be remodelled by ligands, it is unclear whether their conformations are a feature of state 3 or determined by ligand binding. Finally, the features discussed above that are disordered in state 3 are clearly ordered (and equivalent) in both the active and deactive states, and the ND2-ND4 interface is closed in both those states. Therefore, state 3 shares a substantial number of distinguishing features with the deactive state -but it shares none of them with the active state. Due to the extra-relaxed and disordered characteristics of state 3, we propose to name this state 'slack' complex I in the future.
The three 'open' states described for native ovine complex I 22 exhibit all the key structural features observed in our deactive states, but also features that are specific to our state 3 structure. In particular, the state named open3 displays extensive disorder (evident as weak or absent densities) for NDUFA11, the C-terminal half of the ND5 transverse helix and its anchor helix (TMH16), the ~40 N-terminal residues of NDUFS2, and ND6-TMH4. These comparisons suggest that the open conformations of ovine complex I exist on a structural spectrum between our deactive state and state 3. Similar state 3-like characteristics are also observed in maps for ovine complex I reported to be in the deactive state, which we note was prepared by incubating a concentrated aliquot of the detergent-solubilised complex I at 32 °C for 30 min after anion exchange 22 , rather than by deactivating the enzyme in its stabilising native membrane environment 9,10,13 .
In state 3 the extended interface between subunits ND2 and ND4 contains an ordered Q10 molecule, accommodated by a π-bulge formed in ND4-TMH6. It is possible that the ND4-TMH6 π-bulge forms during catalysis, such that state 3 represents a relaxed state of a hitherto-uncharacterised intermediate, in which the π-bulge causes Tyr148 ND4 to pivot away from its usual hydrogen bond to Glu559 ND5 . By doing so it may destabilise the ND2-ND4 interface, propagating instability to the transverse helix and associated structures, resulting in the observed loss of structural integrity. The interfaces between NDUFA10, ND4, and ND2 have also been observed to accumulate strain in simulation work, and proposed to modulate conformational changes within the membrane domain 46 . Intriguingly, the position of the Q10-headgroup bound at the ND2-ND4 interface in state 3 coincides with the position of a rotenone inhibitor molecule detected previously in ovine complex I open conformations 22 . Although it is difficult to conceive of any functional role for Q10 binding at this site, so distant from any of the enzyme's redox cofactors, it is possible that any molecule binding here could lock the position of Tyr148 ND4 and thereby be inhibitory -if reorganisation of ND4-TMH6 really does occur on the catalytic cycle.
Loosening the structural constraints of the transverse helix in state 3 and opening up of the ND2-ND4 interface may alternatively allow the Q10/rotenone molecule to enter in adventitiously. The propensity of the enzyme to fracture at this interface is highlighted by treatment of bovine complex I with the zwitterionic detergent N,N-dimethyldodecylamine N-oxide (LDAO) to form the ND4-ND5containing subcomplex of the distal membrane domain known as subcomplex Iβ 92 . The same fragmentation occurred during crystallisation trials on the DDM-solubilised enzyme 93 , yielding a structure of subcomplex Iβ 92 in which the C-terminal section of ND5 is highly disordered. The tendency of the ND4-ND5 module to dissociate was also illustrated by Y. lipolytica knock-out strain nb8m∆ (where NB8M is a homologue of subunit NDUFB7, adjacent to the C-terminus of ND5), in which the distal membrane domain was absent 94 . These observations argue that state 3 may represent an enzyme in the initial stages of degradation, not a catalytically relevant state.
To define the catalytic capability of state 3 it will be necessary to produce a homogeneous sample of it and characterise it both functionally and structurally. It is currently unclear how to achieve this for bovine complex I, but we note that a structure we solved previously for complex I from rhesus macaque (Macaca mulatta) 11 was dominated by particles in this state (lacking clear densities for NDUFA11, the C-terminal half of the ND5 transverse helix and its anchor helix (TMH16), the N-terminus of NDUFS2, and parts of ND6-TMH4) -and the preparation exhibited only a very low activity of 0.5 µmol min -1 mg -1 11 . Current evidence to suggest that state 3-like states do exist on the catalytic cycle is limited to their presence in a sample of ovine complex I treated with the substrates for turnover -however, similar states were present in the starting mixture and may simply not have responded to the addition of substrates 22 . Further investigations of complex I samples under established turnover conditions and in defined biochemical states will be necessary to finally establish the relevance of this intriguing enzyme state.

Supplementary Discussion 2: Minor differences between the structures of nanodiscreconstituted and DDM-solubilised complex I
First, in all CxI-ND maps, the tip of the β-hairpin in the ND6 TMH4-5 loop on the intermembrane space face is shifted by 3-3.5 Å towards subunit ND2, so that it makes contact with the ND2-TMH4-5 helix-loop-helix motif and ND4L-TMH1. In the DDM-solubilised reference active-state structure 43 , there is an unmodelled density between the two structural elements that resembles a DDM molecule displacing the ND6-β-hairpin. The β-hairpin motif is not present in M. musculus complex I 10,13 , while in the lauryl maltose neopentyl glycol (LMNG)-solubilised ovine enzyme 22 its conformation matches the CxI-ND conformation.
Second, a density for a steroid molecule (modelled as a cholate, which was added at the reconstitution step) is present in all CxI-ND maps at the interface between subunits ND5 and NDUFB6. The nearby NDUFB6 matrix helix/loop is resolved for the first time here, perhaps as a result of the structure being stabilised by incorporation of the additional cholate molecule and enclosed by the adjacent MSP2N2 helices -although the previously unstructured region makes remarkably few direct contacts with any other subunits.
Third, the C-terminal peptide of mammalian subunit NDUFS1 (ca. 10 residues) is also resolved for the first time here, with the terminal Cys704 NDUFS1 residue lodged between subunits NDUFS1, NDUFS6, and NDUFS8. The absence of DDM in the sample buffer may be responsible for the