Cavity hydration dynamics in cytochrome c oxidase and functional implications

Significance

Cytochrome c oxidase (CcO) reduces molecular oxygen to generate the proton motive force across the membrane that drives ATP synthesis. Internal water molecules in and near a central cavity play important roles in mediating the proton transfers. Molecular simulations of CcO reveal reversible transitions between wet and dry configurations of this internal cavity in response to the charge state of key cofactors and residues. Quantitative analysis of the free energy change and timescale of the transition suggests that hydration-level change of the central cavity is an essential feature that contributes to the vectorial efficiency of proton pumping in CcO. Thus, wetting transition of protein internal cavities can be functionally significant, especially for the transport of charged species.

Abstract

Cytochrome c oxidase (CcO) is a transmembrane protein that uses the free energy of O₂ reduction to generate the proton concentration gradient across the membrane. The regulation of competitive proton transfer pathways has been established to be essential to the vectorial transport efficiency of CcO, yet the underlying mechanism at the molecular level remains lacking. Recent studies have highlighted the potential importance of hydration-level change in an internal cavity that connects the proton entrance channel, the site of O₂ reduction, and the putative proton exit route. In this work, we use atomistic molecular dynamics simulations to investigate the energetics and timescales associated with the volume fluctuation and hydration-level change in this central cavity. Extensive unrestrained molecular dynamics simulations (accumulatively $\sim$4 $\mathrm{\mu }$s) and free energy computations for different chemical states of CcO support a model in which the volume and hydration level of the cavity are regulated by the protonation state of a propionate group of heme a₃ and, to a lesser degree, the redox state of heme a and protonation state of Glu286. Markov-state model analysis of $\sim$2-$\mathrm{\mu }$s trajectories suggests that hydration-level change occurs on the timescale of 100–200 ns before the proton-loading site is protonated. The computed energetic and kinetic features for the cavity wetting transition suggest that reversible hydration-level change of the cavity can indeed be a key factor that regulates the branching of proton transfer events and therefore contributes to the vectorial efficiency of proton transport.

Cytochrome c oxidase (CcO) is a biomolecular pump that uses the free energy of O₂ reduction to pump protons across the membrane (1–3) (Fig. 1); the generated proton concentration gradient is then used in ATP synthesis by the F₀F₁-ATP synthase. The stoichiometry of the pumping process (i.e., the number of protons pumped relative to the number of electrons consumed) differs among the various isoforms (4); the specific type of interest here pumps four protons during the reduction of each molecular oxygen (i.e., with the consumption of four electrons).

Fig. 1.

Schematic representation of CcO with key residues and cofactors highlighted near the central cavity surrounded by the two heme groups and Glu286, which are magnified for illustration.

Through decades of experimental studies (2, 3, 5, 6), augmented by computational analyses (7–27), the working mechanism of CcO is known in an outline form. Four electrons are transferred sequentially through heme a to oxygen to make two water molecules at the binuclear center (BNC) (Fig. 1); protons are pumped in each of the four distinct BNC redox states, and the general mechanism for how electron transfers and proton transfers are coupled is believed to be qualitatively the same for the four pumping steps (summary of sequence of events in Fig. 2 A and B). As to the identity of the transient “proton-loading site” (PLS), the current consensus is that one or more propionates of heme a₃ or heme a are involved; among them, the propionates of heme a₃ (PRDa₃/PRAa₃) are the most discussed candidates and both are likely to contribute (28).

Fig. 2.

A schematic representation of electron/proton transfer events in a pumping substep in CcO. The parallelograms represent heme a and the BNC, and the circles indicate Glu286 and the PLS. A solid red circle indicates reduction, while a solid blue circle indicates protonation. (A and B) Commonly accepted sequence of electron and proton transfer events. The dotted arrow in A highlights one example of kinetic gating (i.e., competition between proton transfers to different sites) that has been proposed to be essential to the proton-pumping efficiency in CcO (see SI Appendix for additional discussions).

Since oxygen reduction also requires protons, a mechanism has to determine when a proton goes to the BNC for chemistry and when it is stored at the PLS and subsequently gets pumped to the P side of the membrane. For example, as shown in Fig. 2A, it is essential that proton transfer from the conserved Glu286 to PLS occurs before the transfer to the BNC; otherwise recombination of the proton and electron at the BNC would abolish the driving force for the loading of the PLS, leading to the so-called “decoupling” phenotype (i.e., oxygen reduction without proton pumping), which was observed in mutations that sometimes are far away from the BNC (29–35). The molecular mechanism that governs the specific sequence (or timing) of proton transfers in CcO is not well understood. In general, both thermodynamic (1, 26, 28) and kinetic (7, 9, 17, 20, 21, 27) factors may contribute; the former concerns the $p{K}_a$s of proton acceptor groups, while the latter depends on the barriers of proton transfer to different sites. The underlying challenge is to identify, at an atomic level, how these factors are controlled by the structural, energetic, and dynamical features of the protein and internal water molecules.

An issue of interest in this context concerns the role of the hydration level in the central cavity that bridges Glu286 to both the BNC and the propionates of heme a/a₃. The cavity contains zero or one water molecule in the available crystal structures, an observation consistent with the fact that the free volume of the cavity in the crystal structures is small. The cavity was seen to expand, however, in molecular dynamics simulations (26) when PRDa₃ was protonated, leading to a substantially higher level of cavity hydration. Hybrid quantum mechanical/molecular mechanical (QM/MM) and continuum electrostatic $p{K}_a$ calculations consistently showed that wetting of the cavity and neutralization of PRDa₃ together lower the $p{K}_a$ of Glu286, allowing it to deliver its proton to the BNC (26). Although the study clearly highlighted the importance of cavity hydration to the thermodynamic driving force of key proton transfers, it did not observe closure of the cavity upon deprotonation of PRDa₃; for the cavity transformation to be an essential component of the proton-pumping mechanism, it needs to be reversible. Moreover, to establish whether the wetting transition of the cavity controls competitive proton transfer pathways requires understanding the free energy change and, more importantly, the kinetics of such transition, in response to the driving redox reactions in CcO; the transition does not constitute a valid control element if it is too fast compared with all relevant proton transfers (Discussion). These are the central topics for the present analysis using unrestrained molecular dynamics (MD), free energy simulations, and Markov-state models.

Results

We focus on the P$\to$F transition because it has been extensively analyzed in previous experimental (3) and computational studies; the redox and protonation states of key cofactors in the enzymatic states studied (P_R, P′_R, P″_R, and ${\mathrm{P}}_{M,R}$ etc.) are summarized in SI Appendix, Table S1.

Specific Charge States of Heme Groups Induce Cavity Transformation.

We first conduct unrestrained MD simulations in the range of 50–500 ns for different enzymatic states to probe how specific charge states of cofactors and/or nearby residues impact the cavity configuration; compared with ref. 26, the present simulations are at a lower temperature (303 K vs. 323 K) due to the use of different lipids (POPC/DSPE vs. DPPC/POPE), are longer in timescale, and probe additional enzymatic states and starting structures (SI Appendix, Table S1). Overall, the qualitative trends are consistent with ref. 26; the cavity prefers a compact and dry configuration when PRDa₃ is ionized (Fig. 3A), while a protonated PRDa₃ is correlated with an expanded and hydrated cavity (Fig. 3B). In Fig. 4, we illustrate the time dependence of several key collective variables (CVs): the distance between the center of mass of the aromatic ring of Trp172 and the C$\alpha$ of Gly283 [$d_{WG}$, which measures displacement of the loop that contains Trp172 (26) relative to the transmembrane helix containing Glu286], the number of water molecules in the cavity ($n_{H_{2}O}$), and the side-chain dihedral angle of Glu286 (${\varphi }_E$; SI Appendix). When starting with the crystal structure [1M56 (36)] and water molecules inserted into the cavity by grand canonical Monte Carlo (37) (SI Appendix), all simulations with an ionized PRDa₃ feature a closed cavity (e.g., Fig. 4A) with tight packing ($d_{WG}\le 6\text{Å}$), very little water ($n_{H_{2}O}\le 2$), and Glu286 adopting the “down” orientation (${\varphi }_E\in (-0.6,-0.8)\pi$). By contrast, independent of the protonation state of Glu286 and the redox state of Tyr288, a protonated PRDa₃ leads to an expanded cavity (Fig. 4B), which is featured with loop displacement ($d_{WG}\ge 8\text{Å}$), rotation of Glu286 toward the “up” orientation (${\varphi }_E\approx 0$), and a significant increase in the number of water molecules ($n_{H_{2}O}=6\sim 12$). The only exception is for the ${\mathrm{P}″}_{\mathit{M},\mathrm{R}}$ state, which features a reduced heme a, oxidized Tyr288, and protonated Glu286; the cavity remains closed during 50 ns of MD simulation despite having a protonated PRDa₃.

Fig. 3.

(A and B) Comparison of structure and water H-bond network in a closed (A) and an open (B) cavity configuration. A closed cavity typically contains 0$\sim$2 water molecules, with Glu286 in the down orientation, pointing to the D channel. An open cavity has 5$\sim$10 water molecules with Glu286 adopting an up orientation. In the shown open state, H-bonding networks are formed between Glu286 and both the PLS and the BNC.

Fig. 4.

Representative time dependence of key collective variables in unrestrained MD simulations. W172–G283 distance ($d_{WG}$) indicates the loop displacement correlated with cavity volume, and a large distance indicates an expanded cavity; ${\varphi }_E$ indicates Glu286 side-chain orientation, up (around 0 rad) vs. down (around −0.5 $\pi$ rad); and $n(H_{2}O)$ is the amount of water in the cavity. (A and C) P_R; (B) P″_R; (D) ${\mathrm{P}}_{M,R}$. PRDa₃ is ionized in all cases shown except for P″_R; heme a is oxidized in P_R and ${\mathrm{P}}_{\mathit{R}}^{″}$ and reduced in $P_{M,R}$; see SI Appendix, Table S1 for further details for the protonation/redox states of key cofactors. A and B start with the crystal structure and several water molecules added to the compact cavity using grand canonical Monte Carlo; C and D start with a snapshot from a P″_R trajectory that features an expanded cavity.

The EQ-C/O sets of simulations start from the final snapshots of MD trajectories that were initiated with the crystal structure (1M56) for the P_R state (which features a compact and dry cavity) and the P″_R state (which features an expanded and hydrated cavity), respectively; they lead to a range of behaviors that further hint at the impact of heme a reduction on the cavity behavior. For example, while P_R (Fig. 4C) and P_M simulations starting with an open cavity do not lead to cavity closure in 200 ns despite featuring an ionized PRDa₃, the cavity is observed to close spontaneously in the ${\mathrm{P}}_{M,R}$ state, which features an ionized PRDa₃ and a reduced heme a (Fig. 4D). The latter observation suggests that heme a reduction is likely to stabilize a dry cavity; this is consistent with the observation that ${\mathrm{P}″}_{M,R}$ and ${\mathrm{P}\prime }_{M,R}$ simulations starting with a compact and dry cavity do not lead to cavity opening in 50 ns despite featuring a protonated PRDa₃. The protonation state of Glu286 is also seen to make a minor contribution; for example, the EQ-C set of P″_R simulations (in which both PRDa₃ and Glu286 are protonated) at the 100- to 150-ns timescale leads to a cavity that is intermediate between the fully closed and open configurations (SI Appendix, Fig. S2), in contrast to P′_R, which features a protonated PRDa₃ but a deprotonated Glu286 and readily leads to cavity expansion.

Free Energy Surface for Cavity Expansion and Wetting Transition.

To better understand how cavity transformation is determined by the charge states of key cofactors and nearby residues, metadynamics simulations are conducted to compute the relevant free energy surfaces (Fig. 5 and SI Appendix, Fig. S9); the collective variables are $d_{WG}$ and $n(H_{2}O)$ since the free energy surface appears less sensitive to the orientation of Glu286 (discussed below). For all enzyme states considered, the free energy surface has two basins although their relative stability varies significantly in response to the redox state of heme a and protonation state of PRDa₃. In ${\mathrm{P}}_{M,R}$ and P_R, PRDa₃ is ionized and the free energy surfaces (Fig. 5 A and B) indicate that the cavity clearly prefers the compact ($d_{WG}\sim 6$ Å) and dry ($n(H_{2}O)\sim$1–3) configuration, with the expanded ($d_{WG}\sim 8-10$ Å) and hydrated ($n(H_{2}O)\sim$6–10) basin being at least 5 kcal/mol higher; compared with P_R, reduction of heme a in ${\mathrm{P}}_{M,R}$ further stabilizes the compact and dry configuration relative to the expanded configuration by a few kcal/mol. In P′_R and P″_R, the protonated PRDa₃ clearly stabilizes the expanded and wet basin (Fig. 5 C and D); the protonation state of Glu286 also contributes: the ionized Glu286 makes the wet basin much more stable in P′_R, while the two free energy basins are similar in stability in P″_R, in which Glu286 is charge neutral. Reduction of heme a is again observed to stabilize the compact and dry state; in ${\mathrm{P}\prime }_{M,R}$ (SI Appendix, Fig. S9), the free energy bias toward the expanded and wet cavity is substantially reduced compared with P′_R.

Fig. 5.

Two-dimensional free energy surfaces for cavity expansion and hydration-level change in different enzymatic states from metadynamics. (A) ${\text{P}}_{M,R}$; (B) P_R; (C) P′_R; (D) P″_R. An ionized PRDa₃ favors a compact and dry cavity (A and B), while a protonated PRDa₃ stabilizes an expanded and wet cavity (C and D). To a lesser degree, heme a reduction in ${\text{P}}_{M,R}$ stabilizes the compact-dry cavity compared with P_R (A vs. B), while an ionized Glu286 in P′_R further stabilizes the expanded-wet cavity compared with P″_R (C vs. D).

Effect of Heme a Reduction on Cavity Properties.

The unrestrained MD simulations (Fig. 4D) and free energy results (Fig. 5) have revealed that, in addition to the protonation state of PRDa₃, the redox state of heme a also has an impact on the cavity properties. Reduction of heme a favors a compact and dry cavity. To understand this new observation, we plot the difference of electric field on the cavity water between ${\mathrm{P}}_{M,R}$ and P_R states (represented as red arrows on water oxygen in Fig. 6). The electron transfer from heme a to Tyr288 following the ${\mathrm{P}}_{M,R}$ → P_R transition leads to significant changes in the electric field in the cavity, which in turn lead to strong directional force toward heme a, represented by the green arrows in Fig. 6. Evidently, the change in the electric field upon heme a reduction provides a driving force for the water molecules to leave the cavity.

Fig. 6.

Difference of electrostatic field and force between ${\text{P}}_{M,R}$ and P_R on water molecules in the cavity calculated from the trajectory of ${\text{P}}_{M,R}$ starting from an open cavity configuration. (A) At 12.5 ns; (B) at 25 ns. The electric field difference vector (arrows colored in red) shows strong directionality toward heme a from heme a₃, which results in an evacuation force on water molecules (arrows colored in green), driving a drying transition of the cavity observed in Fig. 4D.

Orientation of Glu286 Does Not Strongly Impact the Free Energy Surface.

The preferred orientation of Glu286 has been much discussed in the literature in the context of gating proton transfers (13, 16, 18, 22), and thus we investigate whether the isomerization of Glu286 has any major impact on cavity hydration. First, we conduct a metadynamics simulation using ${\varphi }_E$ and $n(H_{2}O)$ as the two CVs for P_R. As shown in Fig. 7A, although $d_{WG}$ is not explicitly biased in this metadynamics simulation, it is strongly correlated with $n(H_{2}O)$, which again highlights the role of loop displacement in the cavity expansion and wetting transition (26). By contrast, ${\varphi }_E$ undergoes rapid oscillations and shows little correlation with the hydration level. Indeed, the free energy surface in Fig. 7B indicates that the isomerization of Glu286 has a small barrier of 5 kcal/mol and is essentially decoupled from hydration level of the cavity. Moreover, we repeat the free energy simulations shown in Fig. 4 for P_R and ${\mathrm{P}\prime }_{M,R}$ with Glu286 constrained to specific (up or down) orientations. As shown in SI Appendix, Fig. S9, the orientation of Glu286, regardless of protonation state, has limited impact on the free energy surface, especially concerning the relative stability of the compact-dry and expanded-wet basins. For additional discussion of Glu286 orientation in the context of gating proton transfers, see SI Appendix.

Fig. 7.

(A and B) Time dependence of (A) key CVs and (B) the 2D free energy map of Glu286 side-chain isomerization and hydration-level change from metadynamics simulation of P_R. Note that Glu286 isomerization (${\varphi }_E$) is much faster than the hydration-level change and loop displacement, and the corresponding free energy profile is almost decoupled from the hydration level of the cavity. The two basins of ${\varphi }_E$ in up (around 0 rad) vs. down (around −0.5 $\pi$ rad) configurations are isoenergetic with a barrier $\sim$5 kcal/mol.

Cavity Transition Kinetics Revealed by Markov-State Model.

Although the free energy simulations clearly reveal the coupling between cavity properties and charge state of specific cofactors, the computed free energy barriers are not sufficient for an evaluation of kinetics for the cavity transition. Since both loop displacement and hydration changes are involved, it is difficult to establish the proper prefactor in a rate expression. Therefore, we have conducted a large number of independent trajectories (150 $\times$ 10 ns) starting from different structures sampled in the metadynamics simulations; along with five multihundred-nanosecond trajectories, a total of 2.1 $\mu$s of simulation are used to construct a Markov-state model and to extract the relevant kinetic information (for more details, see SI Appendix). We focus on the P_R state as an example. Fig. 8 shows the distribution of 300 microstates constructed based on the three CVs of interest ($d_{WG},n(H_{2}O),{\varphi }_E$); these are then further coarse grained into five kinetic macrostates, using the PCCA + clustering algorithm (38), and color mapped in Fig. 8.

Fig. 8.

Markov-state model constructed for the cavity dynamics in P_R, using a total of 2.1 $\mu$s unrestrained MD simulations. Three hundred structurally clustered microstates are drawn as solid circles, and the size of the circle represents the relative population. The microstates are further kinetically coarse grained into five macrostates, which are represented with five different colors (dark red, orange, white, light blue, and dark blue). (A–C) Projection of the microstates and macrostates onto different combinations of the three key CVs [$d_{WG}$, $n(H_{2}O)$, and ${\varphi }_E$] used for clustering in the Markov-state model. In A, the mean first passage times computed between the compact-dry ($n(H_{2}O)\sim 1$, colored in orange) and the expanded-wet (colored in dark blue) macrostates are shown. Note that a completely dry ($n(H_{2}O)=0$) macrostate is also sampled (shown as dark red), although its population is small. (D) Transition-path theory analysis (with a 25-mesostate model that bridges the 300-microstate and 5-macrostate models) highlights that dominant pathways involve coupled hydration change and cavity expansion (discussion of SI Appendix, Fig. S5 in SI Appendix).

As shown in Fig. 8A, the loop motion clearly separates the compact-dry and the expanded-wet cavity basins, and all of the open microstates are kinetically well connected while the compact microstates are further separated into four kinetically distinct macrostates, which differ in the level of hydration (nH2O∼0 colored in red, $\sim$1 in orange, $\sim$ 2–4 in white, and $\sim$ 3–6 in light blue). As noted above, Glu286 rotation is fast—both up and down conformations are observed in the same set of kinetic macrostates in Fig. 8B; note that the protonated Glu286 strongly prefers the downward conformation when the cavity contains no water molecule (i.e., similar to the crystal structure) while it prefers the up conformation in a wet cavity (Fig. 8C). Further analysis of transition pathways indicates that the cavity becomes gradually hydrated without the loop motion initially, and then the moderately hydrated yet compact cavity ($d_{WG}\sim$6.5 Å and nH2O∼2–5) transitions to the open configuration through loop displacement (Fig. 8D and SI Appendix, Fig. S5). The implied relaxation timescale shown in SI Appendix, Fig. S3 shows four slow relaxation times that approach a plateau after about a 1-ns lag time, and the slowest relaxation time is 47 ns; the eigenvector associated with this mode (SI Appendix, Fig. S4) indicates that the process corresponds to population depletion of the compact-dry cavity macrostate. The mean first passage time computed between the most populated compact-dry and expanded-wet macrostates is in the range of 100–200 ns (Fig. 8A); for first passage times among different macrostates, see SI Appendix, Table S2. Considering the stabilization of the dry cavity by heme a reduction as shown in Fig. 5, the timescale for the same transition in the ${\mathrm{P}}_{M,R}$ state is estimated to be in the range of 3.5 $\mu$s (assuming the same prefactor in a rate expression).

Water Exchange Pathways to Protein Surface.

While the cavity transition takes place in a submicroseconds to microseconds timescale, the individual water molecules in the cavity exchange frequently with other water molecules both inside and outside of the protein (Movies S1 and S2. Analysis of MD trajectories that feature the cavity drying and wetting transitions (see SI Appendix for details) identifies three major pathways for such exchange (Fig. 9 A–C), which branches out from the cavity and directs toward heme a (I), toward heme a₃ (II), or between Trp172 and Glu286 (III). Pathway I involves two conserved polar residues Asn96 and Thr100 around which the pathway branches out into two subpathways, extending to His93/Glu182 and His260B/Tyr262B, respectively (Fig. 9A). Pathway II is highly hydrophilic in nature and involves conserved polar residues Tyr175, Gln276, and Asp229B as well as the Mg site, terminating at a surface residue Arg234B (Fig. 9B); this path features the largest amount of water exchange with the cavity. By contrast, pathway III (Fig. 9C) is mostly hydrophobic and overlaps with the oxygen pathway identified in the crystal structure (36). The three pathways are consistently observed in the enzyme states analyzed, although the amounts of water exchange along them vary in different redox states (SI Appendix, Figs. S12 and S13). Although whether all three water exchange pathways are involved in proton transfers requires further analysis, identification of residues along these pathways points to new opportunities for future mutagenesis studies to reveal the proton exit pathway(s).

Fig. 9.

Pathways (I, II, and III) for water exchange between the central cavity and protein surface identified in the drying transition MD trajectory of the ${\text{P}}_{M,R}$ state (SI Appendix). The pathways are represented by the centerlines that connect different water locations following a clustering analysis, and the size of the centerline spheres is proportional to the population of each cluster; the colors label the 6 dominant clusters (among a total of 30) of water positions. (A–C) Key residues along the dominant pathways I (A), II (B), and III (C). Note that pathway III is consistent with the oxygen pathway identified in the crystal structure 1M56 (36). For comparison, path I is also shown in transparent mode in C.

Discussion

Hydration Dynamics of the Cavity.

The combination of unrestrained MD simulations, free energy computations, and Markov-state model analysis provides a thorough characterization of the hydration dynamics of the central cavity in CcO. Overall, the results bolster the previous finding (26) that the cavity hydration level is strongly coupled with the protonation state of PRDa₃; an ionized PRDa₃ favors a compact and dry cavity, while protonation of PRDa₃ stabilizes an expanded and hydrated cavity due largely to the displacement of a nearby loop that contains Trp172. Simulations of additional enzyme states in this work further elucidate that the cavity hydration level, to a lesser degree, is also influenced by the redox state of heme a and the protonation state of Glu286. In particular, reduction of heme a is observed to stabilize a compact-dry cavity while an ionized Glu286 stabilizes an expanded-wet cavity. Thus, ${\mathrm{P}}_{M,R}$, which features reduced heme a, protonated Glu286, and ionized PRDa₃, strongly favors the compact-dry cavity configuration (Fig. 5A), while P′_R, which features oxidized heme a, ionized Glu286, and protonated PRDa₃, strongly favors an expanded-wet cavity (Fig. 5C). In these limiting cases, the free energy difference between the two cavity configurations is about $7$ kcal/mol, which corresponds to a population ratio of 10⁵. In other cases, the free energy difference is smaller; for example, in P″_R, in which both PRDa₃ and Glu286 are protonated, the two configurations are iso-energetic (Fig. 5D). The kinetics of the hydration change estimated from Markov-state model analysis are fast relative to the proton-pumping timescale; for P_R (${\mathrm{P}}_{M,R}$), the mean first passage time for the cavity to transition from a compact-dry to an expanded-wet configuration is estimated to be 120 ns (3.5 $\mu$s), compared with the timescale of 150 $\mu$s for the P_R → F transition measured experimentally. Thus, the cavity transformation is not rate limiting during the pumping cycle, although it may gate specific proton transfer steps (below).

In the present work, proton transfer reactions are not explicitly considered. Therefore, our results do not exclude the scenario that hydration change in the cavity is strongly coupled to the proton transfer such that the two processes occur concurrently. In the recent study by Liang et al. (17), 2D free energy simulations are conducted using multistate empirical valence bond (MS-EVB) models to explicitly probe the coupling between hydration-state change and proton transfer between Glu286 and PRDa₃; the starting enzyme states correspond to ${\mathrm{P}}_{M,R}$ and P_R, while the corresponding product states are ${\mathrm{P}\prime }_{M,R}$ and P′_R, respectively. Qualitatively, the MS-EVB free energy surfaces are consistent with the classical simulation results shown in Fig. 5 regarding the coupling between cavity hydration level and protonation state of PRDa₃, despite differences in the CVs and length of sampling. Although approximate minimum free energy paths shown in ref. 17 correspond to concurrent hydration change and proton transfers, the free energy surfaces therein indicate that the alternative pathway in which hydration change occurs before any proton transfer has comparable energetics. Therefore, it remains mechanistically relevant to consider hydration change and proton transfers as separate kinetic events.

Functional Implications of the Cavity Hydration Dynamics.

In previous work, QM/MM simulations with density functional tight binding of third order (DFTB3) as the QM method were applied to study proton transfers in CcO with different levels of cavity hydration (27). It was found that even in a hydrated cavity, proton transfer from Glu286 to PRDa₃ is unfavorable; this is qualitatively supported by the MS-EVB simulations of Liang et al. (17), who also found an uphill proton transfer to PRDa₃ in both ${\mathrm{P}}_{M,R}$ and P_R states (additional discussions in SI Appendix). Therefore, we supported a “concerted” mechanism (9) for the loading of PRDa₃ (i.e., steps 2 and 3 in Fig. 2A are tightly coupled), in which a protonated Glu286 relays the proton transfer from a hydronium in the D channel to the ionized PRDa₃; since Glu286 is not explicitly deprotonated in this process, the reaction proceeds with a low barrier even in a cavity with only two water molecules. Moreover, since the concerted mechanism involves the transfer of a net charge, the loading of PRDa₃ is energetically favored by the reduction of heme a. The strongly preferred low level of hydration observed for the ${\mathrm{P}}_{M,R}$ state in this study (with a population ratio of 10⁵, Fig. 5A) lends further support to the concerted mechanism, since a low level of cavity hydration was found to drive the ionized PRDa₃ to rotate downward to accept the excess proton (27), minimizing the chance of premature proton transfer to the BNC (i.e., the competition illustrated in Fig. 2A). Following the concerted proton transfer and subsequent electron transfer from heme a to the BNC, the enzyme reaches P″_R, in which the expanded-wet configuration is stabilized (Fig. 5D); this in turn lowers the $p{K}_a$ of Glu286 and therefore facilitates its proton transfer to the BNC. Following reprotonation of Glu286 and proton release from the PLS, heme a undergoes reduction, which stabilizes a compact and dry cavity and the pumping cycle repeats.

To consider whether the wetting transition acts as a control element, we need to consider the kinetics of three processes: loading of the PLS in a dry or a wet cavity ($k_{PLS}^{d/w}$), wetting transition of the cavity ($k_{cav}$), and proton transfer to the BNC in a dry or wet cavity ($k_{BNC}^{d/w}$). The concerted mechanism just described would require $k_{PLS}^d>k_{cav}>k_{BNC}^w>k_{BNC}^d$; this is indeed supported by our previous DFTB3/MM simulations (27), which found a modest barrier ($\sim$2–4 kcal/mol) for the concerted pathway with heme a reduced, and our present estimate of the cavity wetting transition kinetics, which occur on the timescale of 100 ns to 3.5 $\mu$s in P_R and ${\mathrm{P}}_{M,R}$ states; although we have not explicitly computed $k_{BNC}^{w/d}$, the timescales were estimated by MS-EVB simulations (17) to be in the required range of 10²$\mu$s or longer. In this description, protonation of the BNC is gated by PLS loading and subsequent wetting transition. An alternative scenario implicates a fast wetting transition compared with all relevant proton transfers: $k_{cav}>k_{PLS}^w>k_{BNC}^w$. In the MS-EVB study of Liang et al. (17), the stepwise proton transfers in the P_R state from Glu286 to the PLS and BNC were computed to occur on the timescale of 2 $\mu$s and 200 $\mu$s, respectively; these data, coupled with the estimate of $k_{cav}$ in the present work, point to a scenario where the wetting transition is a necessary step but does not act as a control element in the sense that it does not directly influence the order of proton transfers. While further studies are needed to firmly establish which mechanism is operative (SI Appendix), the discussion here indicates that the reversible hydration dynamics of the central cavity are an essential component of the proton-pumping mechanism.

Conclusion

By characterizing both thermodynamic and kinetic features of the cavity wetting transition, we further bolster the previous model (26) that the hydration-level change of the central cavity is an essential feature that contributes to the vectorial efficiency of proton pumping in CcO. The hydration level in the cavity is observed to be coupled most strongly with the protonation state of PRDa₃, although the redox state of heme a and protonation state of Glu286 are also seen to contribute to a lesser degree. The combination of a reduced heme a and an ionized PRDa₃ leads to the largest stabilization of a compact and dry cavity, which facilitates a strong electrostatic coupling between PRDa₃ and Glu286 for an efficient loading of the PLS through a concerted proton transfer mechanism (27). By contrast, an oxidized heme a and protonated PRDa₃ stabilize the expanded and wet cavity state that is required for the proton transfer from Glu286 to the BNC. The tight coupling of cavity dynamics to the oxidation/protonation states of key cofactors ensures that the cavity transformations are in sync with the driving proton/electron transfer events during the proton-pumping cycle. Although proton transfer and hydration change in the cavity may occur simultaneously (17), kinetic analysis conducted here indicates that cavity hydration change occurs at a timescale well separated from both fast (concerted proton transfer to PRDa₃) and slow (stepwise proton transfer to PRDa₃/BNC) proton transfer events. Therefore, the present results further warn against limiting the analysis of proton transfer pathways based solely on hydration pattern in static (crystal) structures while highlighting hydration change of internal cavities as an integral part of gated proton (ion) transports in biomolecules (17, 26, 39–41).

To further understand the cavity transition experimentally, nonlinear spectroscopy (42) coupled with mutants that implicate residues identified here to control the cavity hydration and water exchange will be informative; mutations of particular interest include rigidification of the loop that contains Trp172 and changing several polar residues along water exchange pathways (e.g., Asn96, Thr100, and Gln276) to be nonpolar. As illustrated in ref. 43, interpretation of nonlinear spectroscopy data in structural and dynamic terms presents another opportunity for quantitative computational analysis.

Finally, we note that while it is important to study water penetration in CcO and its functional implication, a key challenge for understanding the vectorial nature of proton pumping remains to be the identification of the gating element that prevents the backflow of protons in the presence of a membrane potential (see SI Appendix, Fig. S11).

Materials and Methods

The four subunits of CcO from Rhodobacter sphaeroides in the fully oxidized state (PDB 1M56) (36) are embedded in a POPC lipid bilayer and solvated with TIP3P water and 0.15 M KCl. All atom molecular dynamics simulations are performed without any restraints after equilibration. To probe the coupling between charge state of residues/cofactors in the cavity and the hydration level, different redox/protonation enzymatic states relevant to the P$\to$F transition have been studied; see SI Appendix, Table S1 for a detailed summary. Three CVs—$d_{WG}$, ${\varphi }_E$, and $n(H_{2}O)$—are monitored to characterize the loop motion, Glu286 orientation, and hydration level of the cavity, respectively, during 50$\sim$200 ns of unrestrained simulation for each state. Two-dimensional free energy surfaces, mainly focusing on $d_{WG}$ and $n(H_{2}O)$, are calculated using multiwalker well-tempered (MWWT) metadynamics (44) simulations. In MWWT simulations, eight walkers are initiated starting from eight different configurations selected from unrestrained MD simulations to represent different regions in the CV space; they are simulated for 20 ns each while sharing the history of biasing potential with each other. The cavity hydration kinetics are analyzed by constructing Markov-state models (MSMs), using a large number of unrestrained MD simulations of length 10$\sim$200 ns; the accumulated trajectories span $2.1\mu$s. The trajectories are projected into the space spanned by the three CVs of interest, and the conformations are clustered into 300 microstates, which are further coarse grained into five kinetic macrostates based on the constructed MSM. The mean first passage times (MFPTs) of the opening and closing transitions of the cavity are calculated from the transition matrix of the MSM. More detailed description of the simulation protocols (force-field parameters, definition of CVs, MWWT metadynamics simulations, the construction and validation of the MSM, and the water pathway analysis) and additional discussions are summarized in SI Appendix.