Ion channel selectivity through ion-modulated changes of selectivity filter pK_a values

Significance

Ion channels that employ carboxylic residues in their selectivity filters (SFs) are found in many realms of life and are important in essential physiological processes. We study bacterial Na_v channels which employ four glutamic acid residues in their SF, and we propose a different view of how ion channel selectivity is achieved in nature, based on the difference in pK_a values of the SF glutamates in the presence of different ion types. Because of the observed sensitivity of pK_a values on the geometry of the SF, this could be important in other channels with carboxylic residues in the SF, e.g., voltage-gated Ca²⁺ channels, and could possibly explain the large variety in observed selectivities of such channels.

Abstract

In bacterial voltage-gated sodium channels, the passage of ions through the pore is controlled by a selectivity filter (SF) composed of four glutamate residues. The mechanism of selectivity has been the subject of intense research, with suggested mechanisms based on steric effects, and ion-triggered conformational change. Here, we propose an alternative mechanism based on ion-triggered shifts in pK_a values of SF glutamates. We study the Na_vMs channel for which the open channel structure is available. Our free-energy calculations based on molecular dynamics simulations suggest that pK_a values of the four glutamates are higher in solution of K⁺ ions than in solution of Na⁺ ions. Higher pK_a in the presence of K⁺ stems primarily from the higher population of dunked conformations of the protonated Glu sidechain, which exhibit a higher pK_a shift. Since pK_a values are close to the physiological pH, this results in predominant population of the fully deprotonated state of glutamates in Na⁺ solution, while protonated states are predominantly populated in K⁺ solution. Through molecular dynamics simulations we calculate that the deprotonated state is the most conductive, the singly protonated state is less conductive, and the doubly protonated state has significantly reduced conductance. Thus, we propose that a significant component of selectivity is achieved through ion-triggered shifts in the protonation state, which favors more conductive states for Na⁺ ions and less conductive states for K⁺ ions. This mechanism also suggests a strong pH dependence of selectivity, which has been experimentally observed in structurally similar NaChBac channels.

Ion channels and their selectivity are crucial for life. Extensive studies have been performed for understanding the permeation and selectivity mechanisms in K⁺ channels, with multiple kinetic and thermodynamics mechanisms proposed (1–10), however, the mechanism has not been settled yet. Similarly, the mechanism of permeation and selectivity in Na⁺ channels (11–20) is still under debate. In this work, we focus on the selectivity mechanism of bacterial voltage-gated Na⁺ (Na_v) channels. Bacterial Na_v channels are tetramers which employ the EEEE (Glu-Glu-Glu-Glu residues) structural motif in their selectivity filter (SF). Here, EEEE are equivalent residues from each of the four chains, not a sequence in one chain. Many other tetrameric cation channels employ either the EEEE or DDDD (Asp-Asp-Asp-Asp residues) motif in their SF, e.g., voltage-gated Ca²⁺ channels, cyclic nucleotide–gated channels, and many transient receptor potential channels. Because of the similarity of their SF motifs, study of bacterial Na_v channels can offer insight into the selectivity of these channels. Eukaryotic sodium channels are heterotetramers and use a DEKA (Asp-Glu-Lys-Ala residues) motif instead of EEEE. Despite the difference in the SF motifs, bacterial and eukaryotic Na_v channels exhibit similar conductances and relative permeabities for Na⁺ over K⁺ ions (21–23). Furthermore, the mechanism of slow inactivation, which is common to both bacterial and eukaryotic Na_v channels, seems to involve the SF residues among other pore domain (PD) residues and leads to the PD collapse (24–27). The main drug-binding regions are also shared between bacterial and mammalian channels (28, 29). Because of these similarities, molecular dynamics simulations on bacterial channels can offer insight into eukaryotic channels.

Selectivity of bacterial voltage-gated sodium (Na_v) channels has been measured for multiple species and shows large variability in spite of the fact that these channels share the same EEEE motif. NaChBac exhibits relatively large selectivity [33 (30) or 171 (21)], whereas Na_vSp1p shows relatively small selectivity [1.7 (31), 3.7 (32), or 4.5 (31)]. The selectivity values measured in Na_vMs and Na_vAb are in between: For Na_vMs, they were greater than 5 (33) or greater than 24 (13); and for Na_vAb, it was determined to be about 6 (28). Most of these selectivity values are the permeability ratios P_Na/P_K measured through reversal potential, except the value of 1.7 for Na_vSp1p (which is the single channel conductance ratio) and the value of 6 for Na_vAb (which is the whole-cell current ratio). This difference in the measurement method could be important. In fact, as mentioned above, the selectivity of Na_vSp1p measured from reversal potentials, 3.7 (32) or 4.5 (31), was greater than the single channel conductance ratio, 1.7 (31). Furthermore, in some Ca²⁺ channels, the permeability ratios and conductance ratios were inverted (34, 35).

Recently, several high-resolution structures of bacterial Na_v channels have opened the door to detailed mechanistic understanding of the factors governing the selectivity of Na_v channels. These include structures of closed and open channels, pore-domain, or full-length channels for various species of, e.g., Na_vAb, Na_vRh, Na_vMs, and Na_vAe1p (28, 33, 36–42). Full-length structures comprise voltage-sensing domain, PD, and C-terminal domain, as shown in Fig. 1. The PD forms an ion permeation pathway, containing a SF, a central cavity (CC), and an activation gate (AG). The SF is a region where a Na_v channel selects Na⁺ ions over other ions. Structures of open and closed channels differ in several ways; the main difference being that the gate is closed in closed channel structures and open in open channel structures. The structures also have different SF radii, and only open structures exhibit electron density in the SF that is highly likely attributed to sodium ions.

Fig. 1.

Structure of Na_vMs channel, shown in A side view and B top view. In panel (A): “CC” stands for central cavity and “AG” for activation gate; for clarity, pore domains and C-terminal domains of only two opposite chains are shown (colored red and blue, respectively), while voltage-sensing domains of the other two opposite chains are shown (colored gray and yellow, respectively). Side chains of the Glu residues in SF are plotted as spheres, and carbon atoms are colored cyan and oxygen atoms are colored red.

Selectivity has also been studied computationally, and several mechanisms were proposed. The steric model was proposed based on simulations with closed Na_vAb channels; two earliest works calculated the potential of mean force (PMF) by umbrella sampling and showed that a free-energy minimum for Na⁺ in the SF is a barrier for K⁺ (11, 12). The difference between Na⁺ and K⁺ was believed to be due to the larger size of K⁺ ions. This steric model of selectivity was questioned by two later works in closed Na_vAb channels (14, 15) which performed unbiased MD simulations for a total of tens of microseconds and observed a highly flexible SF, where the EEEE side chains were found to have two conformational states, i.e., out-facing and “dunked” (pointing inward). Another PMF calculation in Na_vAb showed little evidence for selectivity of Na⁺ over K⁺ (15). In open Na_vMs channels, conductance values were measured through extensive MD simulations with external electric fields (13, 16), and selectivity was determined as the ratio of conductance values for simulations with different ion species. Ulmschneider et al. (13) observed voltage-dependent conductance ratio for inward conduction in Na_vMs, with a ratio of 11 at 100 mV. They did not propose a particular selectivity mechanism. Furini and Domene (16) showed a much lower conductance ratio of about 1.9 for Na_vMs inward conduction at 100 mV. For outward conduction, Furini and Domene proposed a nonsteric ion-triggered selectivity mechanism in which K⁺ ions trigger a conformational transition of the SF toward a nonconductive state (16). Another work, utilizing a truncated SF-only Na_vAb construct, reported a lack of sodium selectivity with a calculated selectivity ratio of 0.15 to 0.81 (17).

One of the reasons for differences in calculated selectivity values could be the force fields and structures used. The older work on Na_vMs by Ulmschneider et. al., reporting better agreement with experiments (13), used an older force field (CHARMM27) for protein and ion parameters (43, 44) and symmetrized structural model derived from the PDB structure 4F4L, where effectively one of the four chains of a nonsymmetric tetramer was used for symmetrization. A more recent work (16) on Na_vMs, showing poorer agreement with experiments, used the more recent CHARMM36 force field for protein and ions (45) and a more recent PDB structure 3ZJZ. For Na_vAb, with the same SF as Na_vMs, calculated conductance ratios range from 0.15 to 0.81 under different ion concentration conditions (17), in disagreement with experimental selectivity of 6. There could be multiple reasons for disagreement with experiments. In experiments, selectivities are derived from reversal potentials, while in MD works, selectivities were determined by the conductance ratio. As mentioned before, for a similar channel Na_vSp1p, selectivity values from reversal potentials were greater than the conductance ratio (31, 32), suggesting that the selectivity through conductance ratio could be smaller. Unlike selectivity, Na⁺ conductance generally agrees between experiments and computation. For Na_vMs, the experimental conductance of ~33 pS (13), agrees with MD results ranging from 24 pS to 34 pS for inward conduction (13, 16, 46–48). Mismatch of ion concentration between experiment and simulation could also be the reason—most of the computational works used concentration values larger than those in experiments (13, 16).

None of the previous computational works on selectivity considered pH dependence and calculated pK_a values for the SF through the more detailed microscopic methods. However, pH dependence of selectivity of Na_v channels has been experimentally demonstrated. In a bacterial Na_v channel, NaChBac selectivity was reduced from 33 to 7 when pH was lowered from 7.4 to 5.8 (30). Conductance of this channel was also pH dependent: It was reduced by lowering pH, with an estimated pK_a of about 7.6 [calculated by Chen et al. (48) based on data reported by DeCaen et al. (49)]. In eukaryotic Na_v channels, which exhibit the DEKA SF motif, conductance was observed to decrease with lowering of pH, exhibiting a pK_a of about 5 to 6 (50–54). Eukaryotic voltage-gated calcium (Ca_v) channels, which have the EEEE motif in the SF (55), also exhibited an elevated pK_a estimated to be greater than 7 (56). These three pK_a values are macroscopic values reflecting the pH dependence of channel conduction. Furthermore, in Ca_v channels, the fully deprotonated state was believed to associate with a high-conductance state, and singly protonated state with a low-conductance state (57). A single Glu-to-Gln mutation in the EEEE motif, mimicking a single protonation, abolished the high-conductance state (57).

The pH dependence of conductance of Na_v channels has been explored computationally by simulating different protonation states of the EEEE motif. In closed Na_vAb channels, Boiteux et al. showed that both fully deprotonated state and singly protonated state could be conductive as they observed continuous ion densities, suggesting ions’ exchanging movements between the SF and extracellular side (15). In contrast, in the same channel, Furini et al. observed that higher barriers in the SF precluded sodium ions’ permeation when one of the EEEE was protonated (58). Free-energy profiles of the closed Na_vAb channels indicated that SF with two, three, or four protonated Glu residues were nonconducting (12, 15, 58). A recent work by Damjanovic et al. reported the first pK_a calculations of the EEEE motif by MD-based methodologies, i.e., through constant pH methods (59, 60) and free-energy calculations in fully explicit solvent (61). The pK_a values were shown to decrease with each ion bound to the SF, suggesting that the number of ions bound to the channel can influence the protonation state of the SF (61). Inferring from the pK_a values, fully deprotonated, singly and doubly protonated states are accessible at physiological pH. In a more recent work on fully open Na_vMs channel, via longer free-energy calculations, Chen et al. (48) determined EEEE’s pK_a values to be 6.4 and 6.7 for two types of lipid compositions. Through extensive molecular dynamics simulations for the deprotonated, singly and doubly protonated states, they demonstrated that channel conductance decreased with each additional proton bound to the EEEE motif. This trend agrees with experiments of the structurally similar channel NaChBac (49).

Here, we simulate conduction in Na⁺ and in K⁺ solutions, in multiple protonation states and extend the free-energy methodology from Chen et al. to calculate the pK_a values of the SF Glu residues. From there, we discuss how selectivity arises. We employ the latest crystal structure of the full-length Na_vMs channel and embed it into a membrane bilayer including negatively charged lipids. We use a concentration of 150 mM for the salt solution to match the experimental condition. The most recent CHARMM force field is used, together with NBFIX parameters for both Na⁺ and K⁺. The sampling is enhanced by performing ten independent simulations for each condition.

Results

Conductance at Different Protonation States.

In an earlier work (61), we determined that fully deprotonated state (S0), singly protonated state (S1), and doubly protonated state (S2) are all accessible at physiological pH. Thus, here we calculate the channel conductance for all three protonation states for both Na⁺ and K⁺ ions under −100 mV (Table 1). To reduce statistical errors in calculated conductance, we performed 10 simulations for each condition (SI Appendix, Table S1) and reported the associated SE for the averaged conductance values. As shown in Table 1, K⁺ conductance is higher than Na⁺ conductance for all three protonation states. Specifically, the conductance ratio is 0.7 ± 0.1 for the S0 state, 0.8 ± 0.2 for the S1 state, and 0.2 ± 0.3 for the S2 state. These ratios are not consistent with the Na_v channel's preference for Na⁺ ions over K⁺ ions. Furthermore, under different simulation conditions, i.e., two lipid compositions and with or without K⁺-carboxylate O NBFIX parameters, most of the conductance ratios at a given protonation state are smaller than 1 (SI Appendix, Table S2). We also simulated outward conduction under +100 mV and observed very similar conductance values (SI Appendix, Table S3).

Table 1.

Calculated conductance of three protonation states

	Na+	K+	Na+/K+
S0	29 ± 4	39 ± 4	0.7 ± 0.1
S1	12 ± 2	14 ± 3	0.8 ± 0.2
S2	0.5 ± 0.7	2.3 ± 1.3	0.2 ± 0.3

The unit of conductance is pS. Numbers are averaged over ten independent simulations. Uncertainties are the corresponding SEs.

pK_a Values of SF Glu Residues.

To obtain the conductance weighted by population of each protonation states, we need to determine the population of each state. For this purpose, we carried out free-energy perturbation (FEP) simulations to calculate the pK_a values of sidechains of the Glu residues in SF. For each ion type, we report two pK_a values, pK_a1, corresponding to the S0 to S1 transition, and pK_a2, corresponding to the S1 to S2 transition. We started FEP simulations from both protonation states involved in those transitions. We ran four independent simulations at each condition to reduce random errors, resulting in a total of eight independent simulations for each ion type and each pK_a value.

As shown in SI Appendix, Fig. S1, simulations started from different protonation states exhibited very different pK_a values at the beginning, but the convergence increased over time. Thus, we report here the pK_a values averaged over the second half (a more converged region) in Table 2. With K⁺ ions, the average pK_a1 value is 0.6 units higher than that with Na⁺ ions. In addition, this difference is larger than the sum of associated errors, with a P value of 0.048 (see calculation details in SI Appendix), which means that this pK_a difference is statistically significant. The pK_a2 values are the same with both ion types.

Table 2.

Average pK_a values, protonation state populations at pH 7.4, and average conductance values

	pKa1	pKa2	%S0	%S1	%S2	Conductance [pS]
Na+	6.9 ± 0.3	6.7 ± 0.4	72	23	5	23.8
K+	7.5 ± 0.2	6.7 ± 0.3	40	50	10	22.8

The pK_a values are averaged over the last 100 ns and eight independent simulations.

Calculated pK_a values are relatively high and close to the physiological pH of 7.4. Glu residues having higher pK_a values with K⁺ ions leads to greater population of protonated states (S1 and S2) and consequently results in a lower conductance of K⁺ ions. In fact, the populations of S0, S1, and S2 states are 40%, 50%, and 10%, respectively, when in K⁺ solution, while with Na⁺ ions, these populations are 72%, 23%, and 5% (Table 2, equations for population calculation are in SI Appendix). Clearly, with K⁺ ions, channel conducts more through protonated states, which are also low-conductance states. Considering multiple protonation states results in a decrease in K⁺ conductance from 39 pS (its S0 conductance) to 23 pS (protonation-state-averaged). This increases the Na⁺/K⁺ conductance ratio to 1.0, which is larger than previous ratios evaluated at single protonation state (0.7, 0.8, or 0.2). This demonstrates that the ion-induced pK_a difference contributes to the channel selectivity. The Na⁺/K⁺ protonation-state-averaged conductance ratio can vary depending on the simulation condition. For example, in the POPC system without K⁺-carboxylate O NBFIX parameters, the conductance ratio is 1.6 (SI Appendix, Table S2), higher than the ratio present here (1.0).

Dependence of Selectivity on Ion-Related pK_a Difference.

We note that our calculated ΔpK_a1 value of 0.6 (between Na⁺ and K⁺, for S0 to S1 transition, as shown in pK_a1 entries in Table 2) is close to the experimental value observed in a Ca²⁺ channel (0.8) (62). Because this value was observed for a Ca²⁺ channel (which also has EEEE motif in SF), and is not available for Na_vMs, direct comparison to experiment is precluded. Even though we use state-of-the-art methodology, which accounts for both effects of explicit water molecules, ions and conformational relaxation, our calculated pK_a values could have errors, for example, due to the lack of polarizability in the force field used. For this reason, but also for the sake of understanding the dependence of selectivity on pK_a value differences and exploring the upper limit of selectivity under this mechanism, we discuss the selectivity for hypothetical pK_a value differences. Fig. 2A is showing the Na⁺/K⁺ conductance ratio vs. ΔpK_a1 and ΔpK_a2, where ΔpK_a1 is pK_a1(K⁺) − pK_a1(Na⁺) and ΔpK_a2 is pK_a2(K⁺) − pK_a2(Na⁺). The red circle symbol represents the calculated ΔpK_a values (ΔpK_a1 = 0.6 and ΔpK_a2 = 0). Fig. 2A shows that if ΔpK_a1 and ΔpK_a2 are both increased by 1 pK_a unit (red triangle symbol), the conductance ratio will increase from 1.0 to 3.4. If the shifts are 2 pK_a units (red square symbol), the ratio will further increase to 8.3. This indicates that a pK_a difference of about 2 units could explain the selectivity of up to about 8. The shifts of ΔpK_a1 and ΔpK_a2 do not need to be the same. The values we use here (1 or 2 pK_a units) are arbitrarily chosen for demonstration purposes. The highest possible selectivity is the ratio of Na⁺ ion's S0 conductance to K⁺ ion's S2 conductance, which is about 13. This selectivity will be realized when pK_a values with Na⁺ ions are very low and pK_a values with K⁺ ions are very high, so that populations of the S0 state in Na⁺ solution and S2 state in K⁺ solution are both close to 100%. Additionally, the K⁺ ion's S2 conductance of 2.3 ± 1.3 pS has a large error. Using the lower boundary (1 pS) of it, the conductance ratio could be further pushed up to as large as 29. Fig. 2B shows the pH dependence of Na⁺/K⁺ conductance ratio with the three sets of ΔpK_a values. As ΔpK_a values increase, the ratio peak increases and shifts toward the right.

Fig. 2.

(A) pK_a dependence of Na⁺/K⁺ conductance ratio at physiological pH 7.4. The red circle symbol represents calculated ΔpK_a values (ΔpK_a1 = 0.6 and ΔpK_a2 = 0). The red triangle symbol represents ΔpK_a1 = 1.6 and ΔpK_a2 = 1. The red square symbol represents ΔpK_a1 = 2.6 and ΔpK_a2 = 2. (B) pH dependence of Na⁺/K⁺ conductance ratio. The vertical dotted lines indicate the physiological pH 7.4. In both panels, pK_a1(Na⁺) and pK_a2(Na⁺) are set to 6.9 and 6.7 (the calculated values), respectively. The conductance values of each protonation state are set to calculated values shown in Table 1. Equations for calculations in this figure are shown in SI Appendix.

Ion-Triggered Relocation of SF Glu Sidechains.

To understand the origin of the pK_a difference between Na⁺ and K⁺ ions, we show in Fig. 3 the distribution of Cδ atoms of the SF Glu residues in z-radius plane, where “z” is the channel pore axis and “radius” is the lateral distance from the pore center. Fig. 3 demonstrates that, in the K⁺ solution, charged (deprotonated) Glu sidechains prefer to occupy more inner positions (with a smaller radius), which means that the sidechains are closer to each other. Then, a follow-up question would be as follows: Why do charged Glu sidechains prefer to stay closer? A possible explanation comes from the different dehydration extent of the two ion types. SI Appendix, Fig. S2 shows that K⁺ ions have to lose more water when passing through the SF, and more protein oxygen atoms show up in the first solvation shell of K⁺ ions, which indicates a stronger interaction between K⁺ ions and these protein oxygen atoms (including the carboxylate groups in SF Glu residues). As a result, when K⁺ ions are present, charged Glu sidechains could get attracted more and end up with a more compact configuration. It is not obvious if these conformational differences are the reason for the pK_a shift. However, Fig. 3 also shows that in K⁺ solution, the protonated Glu sidechain (blue) stays further away from the deprotonated sidechains (red), while in Na⁺ solution, a blue density cloud is found inside the red density cloud and two blue clouds are found nearby. This demonstrates that K⁺ ions trigger larger conformational change upon deprotonation than Na⁺ ions. That structural change could have an energetic cost that significantly contributes to the higher pK_a value for K⁺.

Fig. 3.

Spatial distribution of Cδ atoms of SF Glu residues in z–r plane. Z is plotted on the vertical axis, and radius r is calculated as $\sqrt{x^2+y^2}$ and plotted on the horizontal axis. The first row shows distributions in Na⁺ solution, and the second row shows those in K⁺ solution. The first column is for the S0 state, and the second column is for the S1 state. Deprotonated sidechains are represented in red and protonated in blue. Darker color means higher frequency. The system was centered to the center of mass of N, C, O, and Cα atoms of residues 176 to 179 (Thr, Leu, Glu, and Ser in the SF) from all four chains. The z = 0 position roughly corresponds to the carbonyl oxygen atoms of L177 residues. All data shown are averaged over ten 600-ns simulations. For clarity, pixels with probability density less than 0.008 are not shown. 1D distributions in z and r are shown in SI Appendix, Fig. S4.

To discriminate whether the origin of the pK_a shift is in the closer location of the charged Glu sidechains or the shift in the conformation of the protonated Glu sidechain, we performed additional free-energy calculations where every Glu sidechain in the SF was restrained in an assigned conformation, “up” state or “dunked” state (see the caption of SI Appendix, Fig. S3 for more details). Results from these restrained simulations (SI Appendix, Fig. S3) show that the pK_a difference between Na⁺ and K⁺ was eliminated when Glu sidechain rearrangements were prohibited (as each sidechain was restrained in one conformational state), which suggests that the origin of the pK_a difference is the different population of the protonated Glu sidechain conformations.

Discussion

The selectivity mechanism in Na_v channels is still under debate. While some MD works observed a rigid SF (11–13, 16) and proposed the steric mechanism, others observed a highly flexible SF (14, 15, 48). Such highly flexible SF is also seen in our present simulations. For example, we observed the “dunked” state of SF Glu sidechains (Fig. 3, roughly corresponding to clouds with z < 1 Å), in line with earlier studies (15, 16). Additionally, SF conformational transitions toward a nonconductive state triggered by K⁺ ions were reported for outward conduction (16). In our present simulations, outward conduction behaves similarly to inward conduction in terms of conduction rates.

All previous computational works assumed that Na⁺ and K⁺ ions were conducted through the same protonation state (13, 15, 16, 63). In the two works for Na_vMs, Furini and Domene only considered the S0 state (16), while Ulmschneider et al. considered S0 and S2 states and observed ion fluxes only in the S0 state (13). Boiteux et al. studied free-energy profiles of ions in Na_vAb in Na⁺/K⁺ mixtures for S0 and S1 states and found “little evidence for discrimination against K⁺” (15). We also started with the same-state assumption, but we simulated three states (S0, S1, and S2), as they were all shown to be conductive in our previous work (48). Calculated conductance values of Na_vMs in Na⁺ and K⁺ solutions for each of the three protonation states (S0, S1, and S2) are shown in Table 1. The conductance ratio of Na⁺ to K⁺ is 0.7 for state S0, 0.8 for state S1, and 0.2 for state S2, suggesting that K⁺ ions travel faster than Na⁺ ions, and clearly, selectivity for Na⁺ over K⁺ ions cannot be achieved. This finding agrees with the work by Callahan and Roux in 2018, which reported less-than-one Na⁺/K⁺ conductance ratios within a SF of the Na_vAb sodium channel (17). However, two other works contradict our results and show higher conductance for Na⁺ ions in the Na_vMs channel: Ulmschneider et al. reported conductance ratios ranging from 2.5 to 18, depending on the transmembrane voltage (13), while Furini and Domene reported a conductance ratio of 1.9 for inward conduction and 1.5 for outward conduction (16). As mentioned in the introduction, one possible reason for the discrepancy between their results and ours might be their usage of a high concentration (500 mM) for NaCl and KCl. Under this high concentration of 500 mM, Cl^- ions have been observed [by us and in another publication (47)] to move into the CC via the AG, which may alter the conduction kinetics and affect the Na⁺/K⁺ conductance ratio. Furthermore, both of the works used pore-domain-only protein structures, while a full-length model is used in this work. Force fields employed are also different: Ulmschneider et al. used an older CHARMM27 force field for protein, and even though Furini and Domene used the newer CHARMM36, they did not include the K⁺-carboxylate O NBFIX. Another reason could be the difference in lipid compositions. While we use a mixture of charged and neutral lipids, mimicking the cell membrane ratios, those two works both used POPC bilayer, which seems to enhance the Na⁺/K⁺ conductance ratios compared to those using the mixed lipids, according to SI Appendix, Table S2. Also, due to the observed large fluctuation among different simulations under the same condition (SI Appendix, Table S1), it is crucial to perform sufficient independent simulations for one condition, so that statistical uncertainty can be reduced. However, Ulmschneider et al. only performed a single run for each condition, and Furini and Domene had three runs for inward conduction and four and eight for Na⁺ and K⁺, respectively, for outward conduction. These are potentially less reliable than our ten-simulation results.

Here, we propose an alternative mechanism based on ion-modulated change in the pK_a values of the SF glutamates. We calculated that the pK_a values of SF Glu residues for S0 to S1 and S1 to S2 transitions are 6.9 and 6.7, respectively, in the Na⁺ solution, and 7.5 and 6.7, respectively, in K⁺ solution. Thus, the observed pK_a differences shift the population of protonation states such that at physiological pH, the S0 state is dominant in the Na⁺ solution, and the partially protonated states are dominant in the K⁺ solution. Our calculated conductance values of the three protonation states show that the S0 state is the most conductive state and each bound proton decreased the channel conductance. Thus, this pK_a difference results in K⁺ ions traveling predominantly through the low-conducting states. Note that, proton on/off rates for a similar channel (Ca²⁺ channel also containing EEEE motif) are much lower than conduction rates (56). Thus, the protonation state of one channel is mostly fixed during one conduction event. Therefore, the preference of a protonation state is reflected in an ensemble of channels, not a single channel. While it has been shown in other proteins that being in a particular protonation state is crucial to ion selectivity [e.g., in a sodium-potassium pump (64)], we show here that ion-triggered difference in the population of states gives rise to selectivity.

The perspective provided here is a thermodynamic, rather than a kinetic perspective. Considering the thermodynamic cycle in SI Appendix, Fig. S5, since free energy is a state function, the ΔΔG of the two horizontal events (i.e., protonation of the SF in the presence of Na⁺ or K⁺) must exactly match the ΔΔG of the two vertical events (i.e., the substitution of K⁺ for Na⁺ in a deprotonated or protonated SF). As we have obtained the pK_a values for the protonation events, we can calculate that the ΔΔG equals 0.8 kcal/mol, so that ΔG_S0(Na⁺→K⁺) − ΔG_S1(Na⁺→K⁺) equals 0.8 kcal/mol. This free-energy difference means that the recruitment of K⁺ ions vs. Na⁺ ions in S1 state is easier by 0.8 kcal/mol compared to that in S0 state, which leads to an increase in selectivity. This statement is true regardless of the relative frequency of vertical events vs. horizontal events. Other kinetic mechanisms may exist as an alternative explanation of Na_v selectivity. For example, K⁺ ions have been observed to block the entrance to the SF in both NaChBac (30) and Na_vAb (65). However, such a phenomenon was not observed in our simulations for Na_vMs.

Another interesting selectivity mechanism proposed by previous works is based on the “multi-ion multi-Glu complexes”(15, 19, 20), where Na⁺ ions can stably form these complexes which are observed to facilitate ion conduction, but K⁺ ions cannot. This was observed in both bacterial (15) and eukaryotic sodium channels (20). In this mechanism, the “multi-K⁺ multi-Glu complexes” are energetically disfavored, thus K⁺ ions have a smaller occupancy in the SF. However, we observed that Na⁺ and K⁺ ions have similar z-distributions in the channel (SI Appendix, Fig. S6). The SF Glu sidechains also exhibit similar z-distributions with either ion type (SI Appendix, Figs. S4A and S7), though there are small differences: in the S0 state, the peak around z = 3 Å is higher when with Na⁺ ions (SI Appendix, Fig. S4 A, Left), and in the S1 state the peak around z = −2 Å is higher when with K⁺ ions (SI Appendix, Fig. S4 A, Right). These differences indicate that, with different ion species, Glu sidechains would reside in slightly different locations and the multi-ion multi-Glu complexes are formed in different configurations. However, the above differences do not lead to a reduction in K⁺ conduction efficiency. In fact, the conduction rates of K⁺ are higher. Furthermore, we checked the transitions between ion occupancy states (SI Appendix, Fig. S8), which should essentially demonstrate the pattern of conduction process. Na⁺ and K⁺ ions again show similar patterns, only with small differences in populations of states and transition rates. Considering these data as a whole, this leads us to expect that the observed multi-ion multi-Glu complexes will not be a strong determining factor for Na⁺/K⁺ selectivity, though we do not rule it out as an additional factor that could support higher conductivity for Na⁺. Also, note that reference 20 used a eukaryotic Na_v channel model with DEKA SF motif, which may contribute to observed differences with this study.

It is unexpected that the pK_a values of SF Glu residues are different in Na⁺ and K⁺ solutions. However, differences in the pH behavior between Na⁺ and K⁺ were observed in other proteins: For example, three G protein–coupled receptors exhibited different pH titrations in the presence of Na⁺ and K⁺ (66). Furthermore, an older experiment shows a similar pK_a difference in Ca²⁺ channels: A pK_a value of 8.2 was measured in K⁺ solution and 7.4 in Na⁺ solution, with a pK_a difference of 0.8 (62). In that work, conformational changes induced by ions were speculated to be the reason for the pK_a difference. We believe that this is indeed the case, as we observe that protonated Glu sidechains experience larger conformational change upon deprotonation with K⁺ ions than with Na⁺ ions (Fig. 3). Previous MD simulations of protonation/deprotonation-triggered conformational rearrangements in staphylococcal nuclease have shown that the shift in pK_a values positively correlates with the magnitude of the conformational change of the sidechain between charged and neutral forms (67).

Ulmschneider et al. experimentally measured that the single channel conductance for Na⁺ ions is 33 pS in a Na_vMs channel at pH 7.4 (13). This agrees well with the Na⁺ conductance we obtained here for the S0 state (29 ± 4 pS) and in other MD papers (16, 46, 47), suggesting that it was predominantly the S0 state which was captured by Ulmschneider et al. in the single channel measurements. This again agrees with our findings from pK_a calculations that about 72% of channels would be in the S0 state when in the Na⁺ solution. Though the Na⁺ conductance values match, our Na⁺/K⁺ conductance ratio (=1.0, considering all three protonation states) is much smaller than the Na⁺/K⁺ permeability ratio (>24) Ulmschneider et al. calculated from the measured reversal potential. However, work by Naylor et al. showed a much lower permeability ratio of >5 (33). More importantly, the conductance ratios should not be directly compared to the permeability ratios calculated from reversal potential, as the two types of ratios could be different or even inverted (see Introduction).

While the pH dependence of the Na_vMs channel was not studied experimentally, qualitative comparison to other similar channels supports our mechanism. In Ca²⁺ channels, which also contain the EEEE motif in the SF, transitions between two protonation states were observed with either ion (Na⁺ or K⁺) as the charge carrier, when pH is close to the physiological pH (62). This is consistent with our calculation that multiple protonation states are involved in the conduction process. Second, in NaChBac channels, lowering pH from 7.4 to 5.8 decreases Na⁺/K⁺ permeability ratio significantly from 33 to 7 (30). The drop in selectivity is also seen in our calculation for the pH dependence of conductance ratio, as shown in Fig. 2B.

As shown in Fig. 2A, the Na⁺/K⁺ selectivity is very sensitive to pK_a values of the SF Glu residues. Specifically, a change of two pH units in ΔpK_a increases the conductance ratio by a factor of about eight. This pK_a sensitivity may help explain why similar sodium channels could have very different Na⁺/K⁺ selectivity. While the bacterial sodium channels have similar structures, their Na⁺/K⁺ permeability ratios were measured to be as high as 171 in NaChBac channels (21) and as low as 3.7 in Na_vSp1p channels (32). This big selectivity difference may come from a small structural difference in SFs. For example, the SF sequence for NaChBac is LESWA, while it is LESWS for Na_vMs, Na_vAb, and Na_vSp1p. Other small sequence differences also exist near the SF. Because the pK_a value is sensitive to local environment (68, 69), these small structural differences near the SF Glu residues could shift the Glu's pK_a values more or less and thus lead to a possibly big change in the channel selectivity, which is pK_a sensitive.

The large effect of ΔpK_a on selectivity could be a source of an error in our calculation, and a slightly larger change in ΔpK_a could result in larger selectivity (Fig. 2). The inaccuracy in calculated conductance could also introduce errors. First, we note that independent simulations under the same condition can exhibit very different conductance. For example, in the ten simulations for the S0 state in Na⁺ solution, the highest observed conductance is 48 pS and the lowest is 11 pS, with a very large range of 37 pS. This large fluctuation presents a difficulty in determining the true value of conductance. Furini and Domene also noted a large difference in calculated conductance values. Second, we observed somewhat different conductance values and ratios in simulations with different force fields and lipid compositions (SI Appendix, Table S2). This indicates that the conductance calculations could be influenced by the simulation setup, which adds more uncertainty to the measurements.

In this paper, we propose an alternative selectivity mechanism for bacterial sodium channels, which relies on ion-modulated shift in pK_a-values of the SF residues. Through this mechanism, Na⁺ ions mainly travel through the more conductive, fully deprotonated S0 state, while K⁺ ions travel predominantly through the less conductive, protonated states (S1 and S2). This mechanism may be common in channels with EEEE or DDDD SF motif. To further investigate this mechanism, we hope for measurements of the pH dependence of selectivity, with a wider range of pH values and a small pH spacing. If the results look like Fig. 2B, that would strongly support our proposal.

Methods

Systems.

The protein structure used is a fully open crystal structure of NavMs, Protein Data Bank (PDB) code 5HVX (42), from Magnetococcus marinus MC-1, with four mutations per chain introduced at the AG (L211A, F214A, I215A, and I218A). Surrounding lipids consist of neutral lipids (148 POPC, 80 POPE, and 48 OSM) and negatively charged lipids (8 POPG, 88 POPS, and 32 POPI; full names of these lipids are provided in SI Appendix), which are, together with the protein, solvated in 150 mM NaCl or KCl, using the TIP3P water model. This lipid composition mimics the experimentally measured cell membrane composition (70). Three protonation states are simulated in this work: deprotonated state S0 (all E178s were deprotonated), singly protonated state S1 (only one E178 was protonated), and a doubly protonated state S2 (two opposite E178s were protonated). The protonation state setup is described in SI Appendix.

Molecular Dynamics.

All simulations in the main text were carried out with Amber software (71) using CHARMM36m force field (72) with pair-specific NBFIX corrections for interactions between cations (Na⁺ or K⁺) and Cl⁻ ions or carboxylate oxygen atoms (73–75). Systems were minimized and equilibrated through a 11-step protocol (SI Appendix, Table S4) as described in the SI Appendix. During the equilibration, restraints were gradually released. Only distance restraints on the channel AG remained at the end and were also kept in the production. These distance restraints were applied on alpha carbon atoms of gate residues 214 to 219 to restrict their inward movements with a force constant of 0.5 kcal/mol/Å^2 and with reference to the PDB structure. Production simulations were performed under a voltage of −100 mV, using an NVT ensemble, at a temperature of 310.15 K, and with a time step of 2 fs. Ten independent copies, starting from different initial velocities, were generated for each simulation condition, and all simulations were 600 ns long. Conductance and selectivity are both reasonably converged within 600 ns (SI Appendix, Table S5). The method for calculating channel conductance is described in SI Appendix.

Free-Energy Calculations.

We calculated free-energy differences between protonated and deprotonated states with Bennett’s acceptance ratio method to derive microscopic pKa values for E178 residues, following the procedure described in SI Appendix. Discrete protonation state models (76) are used rather than the continuous lambda dynamics method. Twelve replicas were invoked in the Hamiltonian replica exchange process coupled to FEP. To achieve better convergence, Hamiltonians of the middle nonphysical states were set to change approximately linearly by finely tuning the charges and the Lennard-Jones parameters of E178 residues (see SI Appendix, Table S6 for details). For each transition (S0 to S1 or S1 to S2), four independent 200-ns FEP calculations were performed starting from snapshots of MD simulations of each of the two states in the transition. After obtaining the microscopic pKa values from FEP simulations, the macroscopic pKa values were calculated through Eqs. 1 and 2 to take account of the symmetry correction for proton-binding constants (61).

$${pKa1}_{mac.}={pKa1}_{mic.}+\log \left(4\right),$$ [1]

$${pKa2}_{mac.}={pKa2}_{mic.}+\log \left(\frac{3}{2}\right).$$ [2]

Eq. 2 is derived from the equation (3) of ref. 61 while assuming that the three microscopic binding constants for S1 to S2 transition are the same.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Simulations and scripts data have been deposited in Johns Hopkins Research Data Repository (https://doi.org/10.7281/T1/2DKJB2) (77).