Multiscale simulation reveals a multifaceted mechanism of proton permeation through the influenza A M2 proton channel

Significance

The M2 channel in the influenza A virus is one of three commonly targeted proteins in the viral membrane. Proton permeation across the M2 channel acidifies the virion, releasing the viral RNA and core proteins. This work constitutes, to our knowledge, the first complete characterization of this process by multiscale computer simulation, and the results are in quantitative agreement with prior experimental measurements. The simulations confirm that the mechanism involves a “shuttling” of protons through the His37 tetrad and that the rate-limiting step is histidine deprotonation. The results also reveal several important features, including a large barrier for protons to reach the His37 tetrad and increased conductance for lower pH values due to channel broadening and increased solvent dynamics despite larger charge repulsion.

Abstract

The influenza A virus M2 channel (AM2) is crucial in the viral life cycle. Despite many previous experimental and computational studies, the mechanism of the activating process in which proton permeation acidifies the virion to release the viral RNA and core proteins is not well understood. Herein the AM2 proton permeation process has been systematically characterized using multiscale computer simulations, including quantum, classical, and reactive molecular dynamics methods. We report, to our knowledge, the first complete free-energy profiles for proton transport through the entire AM2 transmembrane domain at various pH values, including explicit treatment of excess proton charge delocalization and shuttling through the His37 tetrad. The free-energy profiles reveal that the excess proton must overcome a large free-energy barrier to diffuse to the His37 tetrad, where it is stabilized in a deep minimum reflecting the delocalization of the excess charge among the histidines and the cost of shuttling the proton past them. At lower pH values the His37 tetrad has a larger total charge that increases the channel width, hydration, and solvent dynamics, in agreement with recent 2D-IR spectroscopic studies. The proton transport barrier becomes smaller, despite the increased charge repulsion, due to backbone expansion and the more dynamic pore water molecules. The calculated conductances are in quantitative agreement with recent experimental measurements. In addition, the free-energy profiles and conductances for proton transport in several mutants provide insights for explaining our findings and those of previous experimental mutagenesis studies.

The influenza type A virus is a highly pathogenic RNA virus that causes flu in birds and mammals (1). The influenza A M2 (AM2) protein (2) contains a homotetramer channel that transports protons across the viral membrane and acidifies the virion interior, enabling the dissociation of the viral matrix proteins, which is a crucial step in viral replication (3). The protein has been the target of antiviral drugs amantadine and rimantadine (4, 5). Much effort has been devoted to discovering the structure and proton transport (PT) mechanism of the AM2 channel, resulting in many crystal structures available in the protein data bank (6–14). Based on the crystal structures and electrophysiology experiments, several PT models have been suggested. These mechanisms can be divided into two main categories, delineated by the role of the four histidine residues (a.k.a. the His37 tetrad) that reside in the middle of the AM2 transmembrane domain (AM2/TM) (Fig. 1A), which has been experimentally shown (15) to account for the proton permeation behavior of the full AM2 protein. The “shutter” mechanism (16, 17) suggests that the His37 tetrad works as a gate. At low pH the gate opens due to the electrostatic repulsion between the biprotonated, positively charged histidine residues. The excess proton is then transferred through continuous water wire via the Grotthuss mechanism, without changing the protonation state of His37. In contrast, the “shuttle” mechanism (14, 18–22) suggests that at acidic pH values the His37 tetrad changes protonation states (Fig. 1B) as it shuttles the proton through the His37–Trp41 quartet region (Trp41 lies just below His37 and is also thought to play an important role in the PT mechanism).

Fig. 1.

(A) Equilibrated structures of the AM2 channel transmembrane domain (definition in main text). The backbones of three helices are shown in gray, and the side chains of pore-lining residues are shown as sticks. From N terminus to C terminus, Val27, Ser31, His37, and Trp41 are shown in blue, yellow, orange, and purple, respectively. The water oxygen densities from the simulations are shown as red shading. One helix is removed for the purpose of clarity. (B) The QM/MM simulations reveal that the excess proton (purple) is delocalized around the entry water cluster and histidine residues as it shuttles although the His37 tetrad. His37 is explicitly protonated in agreement with the shuttle mechanism.

The structure and dynamics of water in the AM2 protein have also gained attention, because it is the essential medium for proton permeation. The high-resolution crystal structure [Protein Data Bank (PDB) code 3LBW] crystallized at pH 6.5 revealed layers of well-ordered water clusters above the His37 tetrad (12). However, the water dynamics in the AM2 protein probed using 2D infrared (2D-IR) spectroscopy revealed that the well-ordered “ice-like” pore water dynamics at pH 8.0 change to more mobile and “liquid-like” dynamics (on the timescale of a few picoseconds) at pH 3.2 (23). This result suggests an interesting pH-dependent behavior of the AM2 protein that is highly relevant for understanding its PT mechanism.

Although many computational studies have investigated the features of AM2 that may influence its PT in recent years (12, 24–40), only a few have explicitly simulated any aspect of the explicit PT process (24, 25, 29, 37, 38). This is because it is challenging to accurately model the charge delocalization and Grotthuss shuttling of the hydrated excess proton in a computationally tractable way. Among these studies, only one so far has provided a free-energy profile [potential of mean force (PMF)] for PT across the entire AM2/TM channel (25), which is the essential property for understanding the full proton permeation mechanism. However, this particular free-energy study was limited by the approximation that the His37 tetrad remains in a fixed protonation state during the proton conduction; therefore, it could not capture the more plausible shuttle mechanism (14, 18–22). More recently, Carnevale et al. (29) used a quantum mechanics/molecular mechanics (QM/MM) approach to investigate PT in the specific region of the His37 tetrad of AM2. Although they could not achieve sufficient sampling to calculate a free-energy profile, this work did allow the His37 tetrad to change protonation states as necessitated by the shuttle mechanism. Their work in fact helped to lay the foundation for the study of PT in the His37 tetrad, using a QM/MM approach in that region of the channel.

In the present study, a powerful multiscale combination of classical, reactive, and ab initio (QM/MM) molecular dynamics (MD) simulations is used to systematically investigate the proton solvation and transport mechanism through the full AM2 protein. By using a classical force field, the conformational ensemble of AM2/TM is characterized starting from two recent high-resolution structures in low- and intermediate-pH conditions [PDB codes 3C9J (9) and 3LBW (12), respectively]. The influence of pH on the protein and water dynamics is then investigated. It is found that as the pH is lowered, the channel adopts a more open conformation, the channel pore is more hydrated, and the pore water molecules are more mobile. Following this we use a synthesis of the reactive multistate empirical valence bond (MS-EVB) (41) and QM/MM approaches to calculate complete proton permeation free-energy profiles (PMFs) through the AM2/TM channel. Because the MS-EVB potential can be derived by force matching of ab initio MD simulation data (42), and because the force-matching algorithm provides a PMF for the reference potential, this unique combination of approaches yields a consistent multiscale computational framework for obtaining an ab initio-level quality PT free-energy profile. This multiscale combination of methods is thus used to calculate the PMFs for excess protons permeating through the entire AM2/TM channel, accounting for the charge delocalization and shuttling of hydrated excess protons through both water and the His37 tetrad explicitly. By virtue of this methodology, it is found that at lower pH values the free-energy barrier for a proton to diffuse to His37 is decreased and the proton conductance increased, explaining the unique pH-dependent activation mechanism of AM2. We also report the PMFs of several AM2 mutants, including the amantadine-resistant and transmissible mutants V27A and S31N. The calculated conductances of both the wild-type AM2 and its mutants are in close agreement with experimental results and provide microscopic explanations for their trends.

Results and Discussion

pH-Dependent Conformational Ensemble and Water Dynamics.

As described in recent measurements of the four pK_a values for the His37 tetrad (20, 43), lowering the pH corresponds to increasing the number of protonated His37 residues from one to four. To illustrate the dependence of AM2/TM conformation on pH value, eight equilibrated AM2/TM structures, representing each possible protonation state and initially aligned with either PDB code 3LBW or 3C9J, are shown in Fig. 2. The notations Q1, Q2, Q3, and Q4 are used to denote the His37 tetrad in its +1, +2, +3, and +4 protonation states, respectively. The two starting crystal structures 3C9J and 3LBW (denoted by prefixes S and D, respectively) were crystalized at different pH values and thought to potentially represent different protonation states of the His37 tetrad. After extensive simulation in the high-pH environment (namely the Q1 and Q2 states), the Trp41 residues at the C terminus are tightly packed in the C4 symmetry, similar to the 3LBW structure and regardless of the starting structure. See SI Text for more details. As shown in Fig. 2, lowering the pH value (i.e., increasing the number of positively charged His37 residues to the Q3 and Q4 states) resulted in a more open packing of the α-helices at the C terminus, allowing more water molecules to enter the channel (27). To probe the change of pore water dynamics upon lowering the pH value in an experimentally verifiable way, we calculated the lifetimes of the Gly34 amide-I group hydrogen bonds (HBs) for various protonation states (Table 1). The HB donor was defined as water oxygen atoms, and the HB acceptor was the Gly34 carbonyl oxygen atoms. The HB autocorrelation function $C\left(\tau \right)=\langle s_i\left(t\right)s_i(t+\tau )\rangle$ was calculated for the HB between Gly34 and water (44), where $s_i\left(t\right)$ is unity if the HB exists at time $t$ and 0 otherwise. The autocorrelation function was then integrated to obtain the average HB lifetime. The high-pH simulations (Q1, Q2) feature long HB relaxation times (6.1–9.4 ps), suggesting the water molecules around each Gly34 carbonyl group remain immobilized. In contrast, the low-pH simulations indicate faster water reorientation, with the Q4-state HB lifetime being 0.9–2.4 ps and that of the Q3 state being 2.7–3.2 ps. In a recent study, Ghosh et al. probed the hydration of the Gly34 carbonyl group by 2D-IR spectroscopy and reported pH-dependent water dynamics in the AM2/TM (23). At pH 6.2, the spectral dynamics have a relaxation time of ∼1.3 ps, whereas at pH = 8.0 the relaxation time is ∼10 ps (23). Our simulations quantitatively capture the experimentally reported acceleration of channel water HB dynamics upon lowering the pH value. An important consequence of this is that PT in the water cluster would be hindered by the slow water dynamics at high pH values, whereas it would be facilitated at low pH values. This is discussed further in the next section.

Fig. 2.

(A and B) Equilibrated AM2 channel transmembrane domain structures at various protonation states and aligned with either starting crystal structure 3LBW (A) or 3C9J (B). The notations Q1, Q2, Q3, and Q4 are used to denote the His37 tetrad in its +1, +2, +3, and +4 protonation states, respectively. His37 is shown with the licorice model, and Trp41 is illustrated with the ball–stick model. Helices B, C, and D in the equilibrated structures are removed, for the purpose of clarity.

Table 1.

Calculated dominant H-bond lifetime (picoseconds), between pore-lining residue Gly34 amide-I groups and their nearest water molecules

Helix	Q2	Q3	Q4
A	9.4	2.7	1.4
B	6.0	2.9	1.0
C	9.1	2.7	1.4
D	6.1	2.8	2.2
Experimental	∼10	∼1.3

The simulations are started from the 3LBW crystal structure. The Q2, Q3, and Q4 notations denote +2, +3, and +4 protonation states of the His37 tetrad in the classical MD simulation, respectively. Experimental values are taken from ref. 23.

Proton Permeation in Wild-Type AM2.

The quantity of interest and of most value in understanding proton permeation through AM2 is the free-energy profile (PMF) for the PT. Although finding the reaction path of proton permeation through a simple channel is not a significant challenge, combining a simulation methodology that captures the essential physics with a sampling protocol that enables statistical convergence is. These features are especially challenging for a system like AM2 where multiple reactive sites (e.g., four protonatable His37 residues) are in close proximity such that the reactive pathway through them is not clear and their coupled participation in the reaction is likely. To capture PT through the His37 tetrad with the MS-EVB method alone would require developing titratable MS-EVB models for the four His37 moieties that simultaneously allowed for proton transfer between each other and with the surrounding solvent (45). This approach would further require the treatment of multiple-shuttling excess protons in the His37 tetrad region. Although possible, these MS-EVB models can be hard to develop and benchmark in highly complex environments. In contrast, QM analysis of the His37 tetrad is more likely to accurately treat the requisite charge delocalization and multiple-proton shuttling events between the histidine residues. Given the size of the full system, QM/MM simulation is necessary to capture the surrounding environment. On the other hand, the cost of QM/MM analysis on a system this large also limits the sampling to tens to hundreds of picoseconds and is not feasible for simulating PT over the entire channel length. This limitation is especially true when slower conformational restructuring of the protein is important. Indeed, as described below, both solvation and protein structural changes are coupled to PT in the regions above and below the His37 tetrad. Hence much longer sampling times are required to converge the full-channel PT free-energy profile than can be obtained with QM/MM MD simulations alone.

In the present work, the challenges described above are overcome by combining the advantages of the MS-EVB and QM/MM methods to calculate the full free-energy profile for PT across the entire AM2/TM channel. The PT through the regions above and below the His37–Trp41 quartet is described with the MS-EVB method, which has been extensively validated for water-mediated PT in many systems (41, 46–49), whereas the PT through the His37–Trp41 quartet is described with the QM/MM MD method to allow for the explicit protonation and deprotonation of the His37 tetrad. Two complete PMFs corresponding to the proton permeation process at different pH conditions are then investigated by bridging the MS-EVB and QM/MM PMFs in a multiscale fashion (as explained in Materials and Methods and SI Text). The first PMF (denoted the +2 PMF) describes the PT process at an intermediate-pH value, wherein the channel begins in the Q2 state (two biprotonated His37 residues) and a third excess proton passes through the channel. The second PMF (denoted the +3 PMF) describes the process at lower pH value with the channel in the Q3 state and a fourth proton passing through. The charge states for the two processes are chosen based on the experimental finding that AM2 conduction occurs when three or more His37 residues are protonated (20, 43) (which includes in our case the translocating proton).

The +2 PMF (Fig. 3) reveals several important events along the proton conduction pathway. First, there is a small free-energy minimum as the excess proton reaches the interface between bulk water and the hydrophobic Val27 residues (z ∼ −14 Å). This minimum is caused by the anisotropic solvation structure of the hydrated excess proton, which makes it somewhat amphiphilic in nature. Such interfacial enrichment of the hydrated excess proton has been predicted by MS-EVB simulations (50) and subsequently confirmed in experiments (51, 52). Second, the free energy around Val27 (−13 Å < z < −10 Å) increases due to proton desolvation and hydrophobic interactions with the Val27 tetrad. Unlike previous classical MD simulations (26) that were lacking a shuttling explicit excess proton in the system, our results can now confirm an important role of Val27 for the PT through AM2. Third, and possibly most important, there is a large free-energy barrier for the proton to diffuse from Val27 to the His37 tetrad. Several factors contribute to this free-energy barrier. As discussed above and in ref. 23, the water is more ice-like inside the channel in the Q2 state and exhibits slower orientational dynamics. Because a successful proton transfer event from one water molecule to the next requires collective rearrangement of the surrounding HB network (53, 54), the slow dynamics of channel water inhibit PT. Furthermore, the positively charged His37 tetrad (+2 in the Q2 state) both repels the excess proton and creates an electric field that orients the water dipoles in a way that further increases this free-energy barrier.

Fig. 3.

Proton transport +3 free-energy profiles (PMFs) (blue) compared with +2 (black). The origin is the center of mass of 4 Cα of Gly34. The positions of Val27, His37, and Trp41 are labeled with text boxes. The regions sampled by MS-EVB and QM/MM are labeled and separated by black dashed vertical lines for +2 PMF and blue dashed vertical lines for +3 PMF.

When the excess proton reaches the so-called “entry” water cluster (12) (two solvation shells above the His37 tetrad, −4 Å < z < 0 Å), there is a plateau in the free energy. The flat free-energy profile for PT in the entry cluster agrees well with the more limited QM/MM sampling result of Carnevale et al. (29), which suggested that the excess proton diffuses across this region in a nearly barrierless fashion. The plateau is likely caused by a balancing of the excess proton’s charge interactions—repulsive from the positively charged His37 residues but attractive to the unprotonated Nδ of the neutral histidines to which it forms water-mediated hydrogen bonds. As the excess proton then protonates the third histidine, the system transitions from the Q2 to the Q3 state and there is a free-energy decrease in the PMF culminating in a deep minimum (z ∼ 6 Å). This result verifies that the shuttle mechanism, involving the explicit protonation of His37, dominates and that the excess proton is substantially stabilized by charge delocalization among the His37 tetrad and nearby water molecules. The stability of the triply charged His37 tetrad is also in line with the result of Carnevale et al. (29), who did not calculate a PMF but did observe in their QM/MM simulations that an unrestrained excess proton starting from the entry cluster prefers to protonate the uncharged His37 residue, whereas no proton in the charged His37 residue was transferred to the entry cluster. Following this, the deprotonation of histidine gives rise to a large free-energy barrier of ∼10 kcal/mol. Such a large deprotonation barrier would make histidine deprotonation the rate-limiting step in the overall proton permeation process, as suggested in previous experimental work (14, 55). Finally, after the proton passes the Trp41 tetrad there is large free-energy decrease, consistent with the fact that it is energetically unfavorable for the excess proton to reach the His37 tetrad from the virus interior. The energetic cost of this reverse process may be ascribed to proton desolvation, steric hindrance from the Trp41 tetrad, and repulsion from the positively charged histidines.

Unlike other studies to date, the simulations reported herein were not limited to the protonation/deprotonation of one presumed histidine residue. Because our collective variable, which defines the location of the excess proton, can be fully delocalized among the entire histidine tetrad and surrounding water molecules (SI Text), all possible protonation/deprotonation processes were accounted for. It was found that more than one histidine residue participates in proton shuttling. In fact, once the Q3 state is reached, the three positively charged histidines are nearly indistinguishable due to charge delocalization. It is actually the solvation structure below the histidines that determines which residue gets deprotonated. The most likely candidate is the residue that has the most accessible water molecule below it, not the His37 that was protonated by the entering excess proton as one might assume. As shown in Table 2, it is encouraging that the calculated conductance (details in SI Text) agrees well with recent experimental values (56).

Table 2.

Conductance comparison between simulation and experiments calculated from the +2 process (defined in main text)

Source	Conductance, fS
Experimental (56)	1–4
Simulation	1.2

For the experimental value, the conductance is measured at T = 291 K, pH_out = 6, and extrapolated to T = 310 K (56).

The free-energy profile for PT at low pH (the +3 PMF in Fig. 3) is similar in shape to the +2 PMF, but with lower barriers. In this process, the channel is more solvated such that continuous water wires form around the histidine residues. Because our collective variable definition does not impose an a priori bias toward either the shutter mechanism or the shuttle mechanism (SI Text), at lower pH one might expect to see the proton diffuse more along the water wire via the Grotthuss mechanism (i.e., the shutter mechanism) rather than protonation of a His37 residue. However, this is not the case. The histidine protonation/deprotonation (i.e., the shuttle mechanism) process still occurs. The calculated conductance from the low-pH PMF is higher (14 fs), which is in reasonable agreement with the experimental conductance (20) and supports the unique acid-activation feature of this channel. The increased conductance can be ascribed to several factors. First, the histidine deprotonation barrier is lower due to the opening of the Trp gate and more water molecules accessible to His37 residues. Second, the water molecules between Val27 and His37 are more dynamic as described earlier, facilitating hydrogen bond network rearrangement and thus PT. Finally, the pore radius is larger and the presence of more water molecules increases the screening of the electrostatic repulsion between the His37 tetrad and the incoming proton, which further lowers the free-energy barrier for PT from Val27 to His37.

As the proton passes through the histidine tetrad, it is again observed that more than one histidine is involved in protonation/deprotonation. In the Q4 state with four identical positively charged histidine residues, the deprotonation process is controlled by the availability of water molecules.

Proton Permeation in AM2 Mutants.

In addition to wild-type (WT) AM2, the PT PMFs for several important mutants (30) were studied. The PMFs are plotted in Fig. 4 and the conductances relative to WT AM2 are listed in Table 3. For S31N, the overall free-energy profile along the proton conduction pathway is similar to WT; thus, the conductance is similar to wild type. This is in line with the fact that a virus with the S31N mutation is just as transmissible as those with a WT AM2 channel (30). For V27A, the channel entrance radius is larger; thus, the entrance barrier height is reduced, resulting in increased conductance. This behavior once again confirms the role of Val27 for secondary modulation of the proton permeation. In addition, the WT free-energy minimum in this region disappears in this mutant, because the Ala27 residues are not bulky enough to form a hydrophobic interface with the bulk water. For V27R, there exists a free-energy barrier before the proton enters the channel due to Arg27 at the channel entrance electrostatically repelling the proton. The overall conductance is thus lowered compared with WT. Finally, it is encouraging that our simulation results reproduce the experimental conductance trends (30) (in nearly quantitative agreement), which further supports the reliability of the multiscale simulation approach taken herein. One approximation in the mutant PMF calculations is the use of WT QM/MM PMF for the His37–Trp41 region. This approximation was necessary due to the great computational cost of the QM/MM simulations and was considered to be reasonable because the positions of the mutated residues are far from the His37–Trp41 region. It was further supported by calculating the pore radius and water density in the His37–Trp41 region, which remains nearly identical to WT.

Fig. 4.

Proton transport free-energy profiles (PMFs) for mutants compared with the WT AM2 channel. The origin is the center of mass of 4 Cα of Gly34. The positions of Val27, His37, and Trp41 are labeled by the text boxes. The regions sampled by MS-EVB and QM/MM are labeled and separated by black dashed vertical lines.

Table 3.

Relative experimental (30) and calculated (present work) conductances for AM2 mutants normalized to the conductance of wild type (WT)

Mutant	Experiment	Simulation
WT	1.0	1.0
S31N	1.3	1.4
V27A	1.5	2.2
V27R	0.2	0.3

Conclusions

We have presented the complete free-energy profile and conductance calculations for proton permeation through the influenza A M2 channel, as well as several key experimental mutants. The results were obtained via a combination of classical, reactive, and ab initio MD simulations. Classical MD simulations first revealed that as the pH is lowered, the channel is expanded to accommodate more water molecules with increased mobility, in agreement with experimental 2D-IR results. Free-energy profiles (PMFs) were then calculated using a multiscale simulation approach for both the intermediate- and low-pH ranges. These provide explicit confirmation of current proposals for the AM2 conduction mechanism, such as the importance of V27 for proton channel entry, the role of the His37 tetrad in excess proton charge delocalization (i.e., the shuttle mechanism), the barrier for His37 deprotonation, and a role for Trp41 conformation. Importantly, the complete free-energy profiles also provide previously unidentified insights. First, the presence of a large barrier (∼10 kcal/mol) for an excess proton to shuttle to the His37 tetrad has not been previously discussed. This barrier is caused by a combination of proton desolvation, charge repulsion from the positively charged His37 tetrad, and immobile water in this region. Interestingly, this barrier decreases at lower pH value despite the increased charge of the His37 tetrad. The decreased barrier is induced by channel broadening, increased solvation, and more mobile hydrogen bond dynamics. For both pH conditions, the deprotonation of the His37 tetrad is rate limiting and largely influenced by the water structure and dynamics below the histidines and through the Trp41 tetrad. The histidine shuttling can involve more than one residue, and at low-pH conditions the shuttle mechanism is still present. The mutant studies, which are in good agreement with experimental conductance results, not only help to validate our computational methodology for studying the AM2 channel, but also point to various physical explanations for the altered mutant conductance rates. The insights presented in this work, particularly the presence of multiple targetable portions of the channel and their relationship to the proton conductance, may help guide future efforts to alter or block the AM2 channel.

Materials and Methods

Modeling of the pH-Dependent Conformational Ensemble and Water Dynamics.

Two high-resolution structures for the G34A mutant (3BLW and 3C9J—crystallized at pH 6.5 and pH 5.3, respectively) (9, 12) were used as the initial structures for MD simulations. To provide a clear picture of the channel conformation change upon acidification, the His37 tetrad was modeled at each possible protonation state. For the Q1, Q2, and Q3 states the neutral histidine residues are assigned to be in the ε tautomer form (12). Further details for system equilibration using the classical force field and the simulation results for the different starting conformations are provided in SI Text.

Modeling of Proton Permeation.

The solvation and transport of an excess proton requires special treatment due to its delocalized nature and the dynamic rearrangement of covalent and hydrogen bonding via the Grotthuss mechanism. To characterize free-energy profiles of PT in the AM2/TM, umbrella sampling was used. The collective variable was defined by the difference between the z coordinate of the center of mass of C_α atoms of the four Gly34 residues and that of the excess proton center of excess charge. The collective variable was restrained by a harmonic potential in the direction of the channel’s principal axis (z direction). The simulations of the windows centered outside the His37 tetrad (z < −4 Å or z > 12 Å for the intermediate-pH PMF and z < 1 Å or z > 10 Å for the low-pH PMF) were performed with the multistate empirical valence bond version 3 (MS-EVB3) model (57). Details of the MS-EVB methodology are provided in previous studies and reviews (41, 42, 45–49). The MS-EVB simulations were performed using the RAPTOR software (58) interfaced with the LAMMPS MD package (http://lammps.sandia.gov) (59). For the simulations of windows centered near and within the His37 tetrad (−4 Å < z < 12 Å for the intermediate-pH PMF and 1 Å < z < 10 Å for the low-pH PMF), a QM/MM MD approach was used to describe the excess charge delocalized around the ionizable His37 tetrad and nearby water molecules. The QM region, including the His37 tetrad and surrounding water molecules, was treated with density functional theory, using the Becke exchange (60) and Lee−Yang−Parr correlation (61) functionals, corrected by semiempirical dispersion terms (62). The QM/MM simulations were performed with the CP2K software package (63). Further details on the MS-EVB and QM/MM simulations are provided in SI Text.

The final PMFs for PT across the entire channel were generated in multiscale fashion by combining MS-EVB and QM/MM windows obtained using WHAM (64–66). The statistical errors were estimated by a block-average analysis. For the mutants, the trajectories for the wild-type QM/MM windows were used in the WHAM calculations (more details in SI Text).

The single-channel maximum proton conductances were estimated by using the one-dimensional approximation of the Poisson–Nernst–Planck (PNP) theory, as described in SI Text. The PT PMFs through the channel region, and diffusion constants, are used to estimate the proton conductances. This approach to calculate conductance is justified by ref. 67.