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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 2006 Oct 5;103(42):15398–15403. doi: 10.1073/pnas.0601451103

Mapping protein dynamics in catalytic intermediates of the redox-driven proton pump cytochrome c oxidase

Laura S Busenlehner *, Lina Salomonsson , Peter Brzezinski , Richard N Armstrong *,‡,§
PMCID: PMC1622835  PMID: 17023543

Abstract

Redox-driven proton pumps such as cytochrome c oxidase (CcO) are fundamental elements of the energy transduction machinery in biological systems. CcO is an integral membrane protein that acts as the terminal electron acceptor in respiratory chains of aerobic organisms, catalyzing the four-electron reduction of O2 to H2O. This reduction also requires four protons taken from the cytosolic or negative side of the membrane, with an additional uptake of four protons that are pumped across the membrane. Therefore, the proton pump must embody a “gate,” which provides alternating access of protons to one or the other side of the membrane but never both sides simultaneously. However, the exact mechanism of proton translocation through CcO remains unknown at the molecular level. Understanding pump function requires knowledge of the nature and location of these structural changes that is often difficult to access with crystallography or NMR spectroscopy. In this paper, we demonstrate, with amide hydrogen/deuterium exchange MS, that transitions between catalytic intermediates in CcO are orchestrated with opening and closing of specific proton pathways, providing an alternating access for protons to the two sides of the membrane. An analysis of these results in the framework of the 3D structure of CcO indicate the spatial location of a gate, which controls the unidirectional proton flux through the enzyme and points to a mechanism by which CcO energetically couples electron transfer to proton translocation.

Keywords: conformational change, mass spectrometry, hydrogen/deuterium exchange


Two proton-conducting pathways, composed of polar residues and bound water molecules leading from the cytosol to the catalytic site of cytochrome c oxidase (CcO) from Rhodobacter sphaeroides, have been identified through biochemical and structural analysis (refs. 14; Fig. 1A). One pathway, the K pathway, provides 1–2 protons to reduce the catalytic site. The second pathway, the D pathway, supplies the remaining substrate protons plus four protons to be pumped across the membrane. Therefore, the D pathway must contain a branching point from which protons are distributed either to the catalytic site or to an outlet for the pumped protons. This branching point is thought to be at or near E286, which resides at the end of the D pathway (1, 8). After E286, the pathway for proton transfer to the catalytic site or to the exit channel is unclear but may involve transient hydrogen-bonded water chains that translocate substrate protons to the catalytic site (912). The exit channel for pumped protons is proposed to begin in the area around the D ring propionates of hemes a and a3 (1, 1215). It is anticipated that control of proton distribution involves local structural changes near these propionates that are linked to conformational changes involving E286 and surrounding residues (1, 12, 16, 17). The location of residues involved in accepting protons and the organization of water molecules are crucial for determining the mechanism of redox-coupled proton translocation.

Fig. 1.

Fig. 1.

Proton transfer pathways and the catalytic reaction cycle for O2 reduction. (A) The D and K pathways are indicated with black and blue solid lines, respectively, where CuA (green), heme a (yellow), CuB (light green), heme a3 (cyan), Mg2+ (magenta), and H2O (red spheres) are shown. D pathway protons are directed to the catalytic site for O2 reduction (dashed black line) or to be pumped (dashed red line). (B) The oxidized catalytic site (O) is reduced with two electrons and two protons from the K pathway to form (R). Dioxygen binds to heme a3 (A), then the O-O bond is broken forming the peroxy intermediate (Pm). Transfer of an electron and a D pathway proton results in formation of the ferryl intermediate (F). An additional electron is transferred, along with net proton uptake through the D pathway, which re-forms O. Proton pumping (HP+) via the D pathway occurs from Pm→F, F→O (5), and possibly from O→R (6, 7). Tyr-288 is represented by YOH.

Three-dimensional structures of various oxidases provide a framework for functional analysis but do not define how these enzymes coordinate proton distribution during turnover. In this paper, we report the detection of distinct redox-linked conformational transitions in the catalytic cycle of CcO by monitoring amide hydrogen/deuterium (H/D) exchange kinetics along the protein backbone by MS (18). Briefly, catalytic intermediate states of CcO were pulsed with deuterium oxide (D2O) at pH 7.0 for varying times (15 s to 6 h), quenched with acid to stop in-exchange, and digested with either pepsin or Rhizopus newlase proteases. The resulting peptides were separated by HPLC, and deuterium incorporation was determined as a function of time by MS. The kinetics of H/D exchange monitors differences in structure and dynamics among discrete intermediate states and not the actual transitions between them. The four redox states of CcO that are sufficiently stable for analysis include the oxidized state (O), the four-electron reduced state (R), the “peroxy” intermediate (Pm), and the “ferryl” intermediate (F) (Fig. 1B). The rates at which amide H/D exchange occurs depends on many factors (19, 20). Despite this observation, the fast phase of H/D exchange occurring in the first 15 s (k > 4 min−1) generally reports on the relative solvent accessibility of amide protons, whereas the intermediate and slow phases reflect changes in protein dynamics (19, 20).

Results and Discussion

Proton-Uptake Pathways.

The K pathway, formed, in part, by residues K362, T359, S365, and Y288 (1), provides one to two protons during the O→R transition (2, 2123). In the O state, a peptide containing residues 354–366 (Fig. 2), which embodies most of the K pathway (Fig. 1A), is in a solvent-inaccessible conformation as shown by the low percentage of amide hydrogens that exchange in the fast phase (18% deuterium incorporation within 15 s) (Fig. 3A). However, after full reduction (R state), the K pathway opens to solvent, exposing the amide hydrogens to base-catalyzed exchange that results in increased incorporation of deuterium along the backbone (63% within 15 s). Although only two water molecules within the channel are observed in the structure of oxidized CcO (Fig. 1A), it is clear that to form R, the K pathway must create a hydrogen-bonded chain for efficient proton transfer (1). These data indicate that proton uptake through the K pathway for reduction of the catalytic site involves a specific conformational transition that allows water from the bulk solution to participate in the translocation. Upon formation of the Pm state and further to the F state, the peptide containing the K pathway residues has restricted access to solvent (Fig. 3A), consistent with its role exclusively in the reductive half of the cycle (O→R) (2, 22, 23). These results are also in agreement with data from small molecule inhibitors of proton uptake that indicate differences in water access with changes in the redox state of CcO (24).

Fig. 2.

Fig. 2.

Peptides that undergo redox-dependent conformational changes. Peptides that display alterations in H/D exchange kinetics of backbone amides are indicated on the structure of oxidized CcO subunits I (gray) and II (light pink). The peptides are colored as follows: 354–366, green; 282–292, blue; 123–135, yellow-green; 136–145, reddish-orange; 193–203, hot pink; 540–551, purple; 169–175, red; 320–340, orange; and II225–229, gold. The general location of the D and K proton uptake channels are indicated by the black and blue arrows, respectively. E286 (blue) is shown in stick format. The kinetic profiles of deuterium incorporation for each peptide are shown in Figs. 3 and 4.

Fig. 3.

Fig. 3.

Amide H/D exchange kinetic profiles of selected K and D pathway peptides for the four intermediate states of CcO. Deuterium incorporation into selected peptides for each intermediate state (O; red), (R; black), (Pm; blue), and (F; green) are shown. The total number (left axis) or percentage (right axis) of deuterium incorporated into the peptide backbone as a function of time are fit to exponential equations (Table 1, which is published as supporting information on the PNAS web site). (A) Peptide 354–366 of subunit I contains K pathway residues. (B) Peptide 282–292 contains the D pathway residue E286 and the Y288-H284 covalent cross-link. Y288 is in the K pathway and H284 is a CuB ligand. (C) Peptide 123–135 contains D132 at the entrance of the D pathway. (D) Peptide136–145 contains the D pathway residue N139. (E) Peptide 193–203 contains the D pathway residue S201. (F) Peptide 540–551 of subunit I resides in a loop at the cytosolic entrance to the D pathway.

Unlike the K pathway, the D pathway contains a number of crystallographically resolved water molecules that connect the cytoplasm of subunit I to E286 (1), suggesting the existence of a preorganized proton conducting “wire” (Fig. 1A). Despite the presence of these bound waters, amide H/D exchange kinetics of several peptides spanning the D pathway reveal that water molecules in the channel either do not exchange rapidly with bulk solvent or that base-catalyzed H/D exchange is unfavorable in all intermediate states (Fig. 3 BE). In the O state, one peptide that displays moderate deuterium incorporation at longer incubation times is 282–292 (Fig. 2), which contains the gating residue E286 and the H284-Y288 covalent cross-link. In the R state, this peptide incorporates less deuterium over 6 h compared with O (Fig. 3B). This result indicates that when the K pathway is open to reduce the catalytic site, the terminal region of the D pathway near the catalytic site becomes less dynamic and more restrictive to water access. This change may reflect formation of a barrier limiting protonic contact between the two pathways. Further, upon formation of the Pm and F intermediates, deuterium exchange into peptide 282–292 is reversed and displays kinetic profiles similar to the O state. Although no specific data on the proposed E286 proton gate can be obtained, it is clear that the backbone between residues 282–292 is able to undergo redox-dependent conformational changes.

Interestingly, a cytosolic loop (peptide 540–551) at the entrance to the D pathway (Fig. 2) shows decreased deuterium incorporation from O→R in the fast phase and subsequent intermediate phase (Fig. 3F). An additional overlapping peptide, 540–550, also displays the same kinetic behavior and indicates reproducibility of this change in deuterium incorporation (data not shown). This region is proposed to act as a proton “antenna” involving residues E548 and H549 (2527). These results suggest that structural organization of the loop, located outside the membrane at a distance of >40 Å from the catalytic site (1), may create a barrier to proton uptake through the preformed D pathway wire when the K pathway is open. For all other intermediate states, the kinetic profiles for 540–551 (Fig. 3F) resemble that of the O intermediate, an observation that indicates the conformation is specific for the R state. Although the structure of bovine CcO has been solved in both the O and R states, no significant changes in conformation were observed in the regions discussed here (28). Crystallography typically provides static views of structures that do not accurately reflect changes in protein dynamics. Clearly, more structural and biochemical analysis is required to understand the specific role of the cytosolic loop in reduction of CcO.

Proton Exit Path and the Subunit I-II Interface.

Indirect evidence has implicated the interface between subunits I and II in the proton exit route (1, 1215). This region is highly solvated, where several water molecules observed in the crystal structure form a hydrogen-bonded network that connects hemes a/a3 and Mg2+ to the outside of the protein (1). Based on H/D exchange, one of the most solvent-accessible peptides in this region (160–175) resides in a loop directly above E286 (Fig. 2) and harbors W172, a residue hydrogen-bonded to a heme a3 propionate thought to be a proton acceptor in the exit route (Fig. 1A; refs. 1, 13, 15, and 17). Peptide 160–175 is extensively exchanged with deuterium within 2 min in the O, R, and Pm intermediates (Fig. 4A). However, the most dramatic alteration in H/D exchange occurs in the F intermediate, which displays a significant decrease in deuterium content over 30 min, indicating a kinetic restriction to solvent. Overlapping peptides indicate that the changes in H/D exchange are located primarily between residues 169–175 (data not shown). These results are in agreement with rapid-quench experiments that reported fast H2O/D2O exchange (kex ≥ 3,000 s−1) at the Mn2+ site in oxidized CcO (29). The Mn2+ (or Mg2+) is part of a hydrogen-bonded network; therefore, these results suggest that a kinetically relevant channel in this region allows water or protons to exchange with bulk water molecules in those intermediate states not involved in proton pumping.

Fig. 4.

Fig. 4.

Amide H/D exchange kinetic profiles of selected peptides for intermediate states of CcO. The total number (left axis) or percentage (right axis) of deuterium incorporated into the peptide backbone as a function of time are fit to single- or double-exponential equations as necessary (Table 2, which is published as supporting information on the PNAS web site). (A) Peptide 160–175 of subunit I is located in a loop above E286. (B) Peptide 320–340 is located at the subunit I-II interface and contains two ligands to CuB, H333, and H334. (C) Peptide II225–229 of subunit II is located in a β-strand at the subunit I-II interface. This peptide is a subtraction of II229–235 from II225–235.

In contrast to 160–175, exchange into peptide 320–340 at the subunit I-II interface (Fig. 2) is specifically enhanced in the F state and is 90% deuterated within 4 min (Fig. 4B). This peptide contains two CuB ligands, H333 and H334. Several lines of evidence suggest that one or more of these His residues may be involved in the proton exit pathway through redox-coupled changes in CuB coordination (10, 30). The alteration in H/D exchange into 320–340 indicates that structural changes involving these residues may control solvent access to CuB at specific times during catalysis. The crystal structure of CcO reveals that residues 320–340 also line a channel from the catalytic site toward bulk solvent outside of the membrane (1).

Subunit II residues II225–229 form the top of the water channel (Fig. 2) and are more accessible to deuterium in both the Pm and F intermediates (100% incorporation by 30 min) compared with the O and R states (Fig. 4C). Peptide 320–340 also exhibits increased deuterium incorporation from R→Pm (Fig. 4B). Given the proximity of II225–229 to residues 320–340 and the observed changes in H/D exchange, it is likely that these residues participate in the proton exit channel. Computational analysis suggests that residues IIK227 and IID229 may be involved in the proton exit pathway (31). The Pm state may play a role in organizing the proton exit channel before pumping. The signal for this event still is unclear, but may be related to tyrosyl radical formation (Y288O·) at the active site.

Amide H/D exchange kinetics have led to the identification of a specific conformational transition related to the F intermediate involving two regions of the protein that are connected to the same water channel. In one region, peptide 160–175, deuterium access is restricted, whereas H/D exchange in the second region, peptide 320–340, is enhanced (Fig. 5). The kinetic profiles are reversed in the other states. One explanation of these data is that a gate lies between the two regions. The F specific conformation of CcO, which leads to decreased deuterium incorporation localized to residues 169–175, may be functionally important for proton distribution. Molecular dynamics simulations support a role of W172 in organizing water molecules in the hydrophobic cavity between E286 and heme a3 (12, 17). Moreover, results from studies with the W164F mutant in Paracoccus denitrificans (corresponding to W172 in R. sphaeroides) implicate involvement of the equivalent residue in proton pumping (17). Taken together with the results from the H/D exchange studies, it appears that the loop surrounding W172 changes its conformation during turnover to act possibly as a gate controlling the proton/water access through CcO. Although a small population of Pm is present in the F preparation, it is clear that the H/D exchange profiles for 160–175 and 320–340 are distinct from Pm, indicating a different conformation exists in the F state around the proposed gate and proton exit pathway.

Fig. 5.

Fig. 5.

Summary of redox-dependent changes in deuterium incorporation. Hemes a and a3 are represented with boxes, and the D and K pathways are represented with large arrows. The gate region corresponds to 169–175, where the solid circle indicates the gate. The proposed exit channel refers to 320–340 (bottom arrow) and II225–229 (top arrow). The loop at the D pathway entrance corresponds to 540–551. Increases and decreases in deuterium incorporation with respect to the previous state are indicated in red and blue, respectively. In the R state (O→R), the K pathway experiences increased solvent access, whereas the D pathway loop and the gate region exhibit small decreases in dynamics, leading to less deuterium incorporation. In addition, part of the exit channel shows a decrease in solvent accessibility. In the Pm intermediate (R→Pm), the K pathway closes to solvent, whereas the D pathway entrance loop exhibits an increase in dynamics. The exit channel peptides show increases in solvent accessibility, but the pathway is considered “closed” for proton pumping. Formation of the F state (Pm→F) further reduces exchange in the K pathway, presumably to allow for H+ translocation through the D pathway via a preformed proton wire. The exit channel (320–340) opens to solvent, whereas the gate region shows a considerable decrease in deuterium incorporation and dynamics over 30 min of exchange. From F→O, the exit channel becomes more restrictive to solvent and less dynamic, resulting in decreased exchange, whereas the gate relaxes to its starting, solvent-accessible conformation.

Mechanistic Implications for CcO Proton Pumps.

Structural changes are expected for a proton pump in which the accessibility for proton transfer to the two sides of the membrane must change during catalysis. One example where such changes have been observed for catalytic intermediate states is bacteriorhodopsin (32). However, crystal structures of oxidized and fully reduced bovine CcO do not reveal significant conformational differences between the two states (28). Here, we show that there are redox-dependent structural and dynamic perturbations in Rhodobacter CcO. Amide H/D exchange kinetics reveal conformational transitions from O→R that control proton uptake via the K pathway are connected to structural changes that may block proton access to the D pathway (Fig. 5). Upon oxygen binding (R→Pm) the K pathway closes, an event that may be linked to removal of the proposed barrier at the D pathway entrance. In addition, the exit pathway is prepared for proton pumping. Both subsequent transitions, Pm→F and F→O, are associated with structural changes that regulate proton uptake specifically from one side of the membrane and proton release to the other side (5, 33).

In the present study, we have been able to illustrate that the structure of the F intermediate in the CcO reaction cycle is different from that of the Pm and O states, specifically between the proposed gate (residues 169–175) and proton exit channel (residues 320–340). The differences between the Pm, F, and O states expose conformational changes in these pathways that are involved in CcO turnover. The Pm state prepares CcO for pumping by organizing the proton exit route. Inasmuch as proton uptake and pumping occurs before formation of F (Pm→F) and also occurs in the following transition (F→O), the “trapped” F intermediate represents a specific CcO conformation that is poised for subsequent proton uptake/pumping. Our observations also indicate that the gate controlling this proton access may be formed, in part, by loop residues within 169–175. This gate appears to switch access upon formation and decay of the F state (Fig. 5), an event that may be controlled by the orientation and hydrogen bonding of W172 or other loop residues. Such a gate is a central part of a proton pump, and the results of this study provide a previously undescribed experimental indication of its location within CcO.

Concluding Remarks.

Amide H/D exchange monitored by MS has proven to be a valuable technique in probing the structural and dynamic features of proteins, now including that of the complex membrane protein CcO. A complete understanding of enzyme catalysis requires that the conformational changes that occur during catalysis be mapped to the structure. In this report, we demonstrate that backbone amide H/D exchange kinetics can yield molecular insight into catalysis by exposing structural differences between specific catalytic intermediates that occur during enzymatic turnover. This application of H/D exchange MS should open new avenues for investigation into the complex enzymatic functions of many proteins, including large, integral membrane proteins.

Materials and Methods

Growth of Bacteria and CcO Purification.

His-tagged CcO (subunits I–III only) was prepared from R. sphaeroides grown aerobically with shaking and was purified as described in ref. 34. CcO was demonstrated to be fully active, with turnover numbers consistent with those reported in ref. 34. The enzyme final concentration used for subsequent H/D exchange studies was 110 μM in 0.1 M Hepes, pH 7.4 supplemented with 0.1% n-dodecyl-β-d-maltoside.

Identification of Proteolytic Fragments.

Pepsin or newlase protease digests of CcO (5:1 pepsin/CcO or 10:1 newlase/CcO wt/wt) were performed under optimized conditions (0.1 M potassium phosphate/0.02% n-dodecyl-β-d-maltoside, pH 2.4 in H2O; 8-min digestion). Peptides were separated by reversed-phase HPLC on a microbore 1 × 50 mm C18 column with a 2–80% acetonitrile/H2O gradient (0.1 ml/min). Both mobile phases contained 0.4% formic acid. Peptides were sequenced by using a ThermoFinnigan (San Jose, CA) TSQ Quantum triple-quadrupole mass spectrometer in positive-ion mode by data-dependent MS/MS collision-induced dissociation. Possible identities of the peptides were determined by using massXpert (35) and were confirmed by comparison of the MS/MS spectra to fragmentation patterns generated by MS-Product (36). Protease digests were found to be highly reproducible under the optimized conditions. The peptide maps of subunits I, II, and III are shown in Fig. 7, which is published as supporting information on the PNAS web site.

Amide H/D Exchange Mass Spectrometry.

H/D exchange was performed on the O, R, Pm, and F states of CcO. The O state refers to the oxidized enzyme as purified. The R state is the four-electron reduced state obtained by incubating oxidized CcO (110 μM) with excess sodium dithionite (0.2 M) under nitrogen before the addition of D2O to initiate exchange. The Pm state was obtained by purging oxidized CcO (110 μM) under nitrogen before purging with CO gas (>99.5%) for 2 min. Each sample for H/D exchange was allowed to incubate for 2 h, then was exposed to air before D2O addition. The F state was prepared by adding 10 mM hydrogen peroxide to CcO (110 μM) for 2 min before the addition of D2O. This preparation results in 75% F intermediate and 25% Pm intermediate. The UV-visible spectra for each intermediate state as a function of time are shown in Fig. 8, which is published as supporting information on the PNAS web site. The R, Pm, and F states are stable (<20% loss) for 6 h, 2 h, and 30 min, respectively. The H/D exchange kinetics were measured within these limits.

Deuterium exchange was initiated by the addition of 5 μl of CcO (67.5 μg) to 45 μl of D2O. The sample was incubated at 23°C for 15 s to 6 h, after which the exchange reaction was quenched with 50 μl of quench buffer (0.1 M potassium phosphate/0.02% n-dodecyl-β-d-maltoside, pH 2.4 in H2O; 0°C) and a subsequent transfer to ice. After 25 s, pepsin (337 μg) or newlase (675 μg) was added, and the digestion proceeded for 8 min on ice. All protein samples for the H/D exchange were prepared individually and were run on the same day.

The H/D exchange procedure has been described in detail in ref. 37 with the differences noted below. The digested peptides were separated over 15 min (100 μl/min) by a 2–50% acetonitrile gradient. An additional wash step with a 2-propanol-containing solvent (50% acetonitrile/45% 2-propanol/5% H2O/0.4% formic acid) was included after each injection to remove detergent and undigested protein from the column. Mass spectra were recorded on a ThermoFinnigan TSQ Quantum triple-quadrupole mass spectrometer by using positive ion electrospray ionization, essentially as described in ref. 37. Data processing was performed by using Finnigan Xcalibur software and MagTran (38), as outlined in ref. 37.

H/D Exchange Controls.

The extent of artifactual in-exchange of deuterium during the quench and digestion were determined via a zero-time control (m0%) (18). Basically, 5 μl of CcO (67.5 μg) was added to 50 μl of quench buffer at 0°C followed by addition of 45 μl of D2O. Protease was subsequently added, as described. The amount of deuterium back-exchanged for protium during chromatography was determined by using a fully deuterated protein control (m100%) (18). Fully deuterated CcO was obtained by incubating 5 μl of CcO (67.5 μg), 12.5 μl of 8 M d4-urea (2 M final concentration in D2O) and 32.5 μl of D2O at 40°C for 8 h. Then, 50 μl of deuterated quench buffer (0.1 M potassium phosphate/0.02% n-dodecyl-β-d-maltoside, pD 2.4 in D2O) was added and incubated for an additional 2 h at 40°C. After incubation, the sample was digested with protease and analyzed as described. The amount of deuterium lost during HPLC fractionation was between 20–40% after normalizing to 100% deuterium incorporation, consistent with reported values (39, 40). Back-exchange was calculated for each peptide in each intermediate state and did not vary significantly with treatment.

Kinetic Analysis.

All kinetic traces are an average of three independent determinations for each intermediate state with each protease. The procedure for calculating the corrected number of deuterium atoms incorporated has been described in refs. 18 and 37. The corrected amount of deuterium (D) incorporated in each peptide was plotted as a function of time and the resulting progress curve for each peptide fit by using KaleidaGraph (Synergy Software, Reading, PA) to the sum of first-order rate terms according to Eq. 1:

graphic file with name zpq04206-3666-m01.jpg

where N is the number of amide protons that exchange at a given rate constant, ki, during the time allowed for exchange, t (18). The kinetic profiles were fit to single-, double-, or triple-exponential equations as appropriate. Those amides that exchange before the first 15-s time point (fast phase) cannot be fit and are reported as amplitudes only with an estimated ki > 4 min−1.

Supporting Information.

Additional data can be found in Tables 3–5, which are published as supporting information on the PNAS web site.

Supplementary Material

Supporting Information

Acknowledgments

This work was supported by National Institutes of Health Grants R01 GM30910, F32 ES013105, T32 ES07028, and P30 ES00267 and Swedish Research Council grants.

Abbreviations

CcO

cytochrome c oxidase

H/D

hydrogen/deuterium

O

oxidized state

R

reduced state

Pm

peroxy intermediate

F

ferryl intermediate.

Footnotes

The authors declare no conflict of interest.

This article is a PNAS direct submission.

The H284-Y288 cross-linked peptide (282–292) was observed in all intermediate states; however, a small population of a noncross-linked peptide corresponding to residues 283–304 was observed consistently in the O, R, and Pm states, but not the F state. The H/D exchange kinetic profiles for the O and Pm states of peptide 283–293 without the cross-link (generated by subtraction of 293–304) are similar to those of 282–292 with the cross-link, as shown in Fig. 6, which is published as supporting information on the PNAS web site.

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