Selectivity filter ion binding affinity determines inactivation in a potassium channel

Significance

The role of the selectivity filter in controlling potassium channel activity is different for different channels, despite identical sequences and structures. While KcsA and voltage-gated channels experience C-type inactivation by collapsing their selectivity filters under reduced potassium concentration, the mechanism by which the MthK channel regulates gating at the filter is unclear. Unlike the KcsA selectivity filter that experiences a uniform titration of its ion binding sites, leading to collapse, high-resolution X-ray structures of the pore-only MthK channel reveal that only the central S2 site loses its ion at low concentrations, insufficient for a conformational change. The selectivity filters of MthK and KcsA differ in their ion affinities due to interactions behind the filter, determining their inactivation phenotypes.

Abstract

Potassium channels can become nonconducting via inactivation at a gate inside the highly conserved selectivity filter (SF) region near the extracellular side of the membrane. In certain ligand-gated channels, such as BK channels and MthK, a Ca²⁺-activated K⁺ channel from Methanobacterium thermoautotrophicum, the SF has been proposed to play a role in opening and closing rather than inactivation, although the underlying conformational changes are unknown. Using X-ray crystallography, identical conductive MthK structures were obtained in wide-ranging K⁺ concentrations (6 to 150 mM), unlike KcsA, whose SF collapses at low permeant ion concentrations. Surprisingly, three of the SF’s four binding sites remained almost fully occupied throughout this range, indicating high affinities (likely submillimolar), while only the central S2 site titrated, losing its ion at 6 mM, indicating low K⁺ affinity (∼50 mM). Molecular simulations showed that the MthK SF can also collapse in the absence of K⁺, similar to KcsA, but that even a single K⁺ binding at any of the SF sites, except S4, can rescue the conductive state. The uneven titration across binding sites differs from KcsA, where SF sites display a uniform decrease in occupancy with K⁺ concentration, in the low millimolar range, leading to SF collapse. We found that ions were disfavored in MthK’s S2 site due to weaker coordination by carbonyl groups, arising from different interactions with the pore helix and water behind the SF. We conclude that these differences in interactions endow the seemingly identical SFs of KcsA and MthK with strikingly different inactivating phenotypes.

Ion permeation gating within the selectivity filter (SF) of potassium (K⁺) channels has been proposed to control channel activity in different ways for different family members. In voltage-dependent K⁺ (K_V) channels, the SF has been proposed to underlie C-type inactivation (1–3), resulting in the progressive loss of current following the activation of a channel gate located near the intracellular side of the pore (4). C-type inactivation in K_V channels has been shown to be strongly dependent on the affinity of a particular binding site for permeant ions in the pore, and the affinity of these pore sites has been proposed to depend not only on the SF chemical composition, but also on regions outside of the SF (5–8). A structure-function model for this mechanism has been provided most specifically by studies of the proton-gated KcsA channel (9–11) where opening of the activation gate is correlated with a conformational constriction and a decrease in ion occupancy within the four K⁺ binding sites of the SF (named S1 to S4) (9, 12–15). Experimental and structural studies of KcsA in low K⁺ showed that the SF constriction consists of an outward flip of the carbonyl groups of the Gly77, in the middle of the signature sequence (TVGYG) of K⁺ channels, associated with a loss of K⁺ binding at site S2 of the SF (9, 14, 16–20). These conformational changes were accompanied by the binding of several water molecules behind the SF, stabilizing this constricted (also called flipped) state by sterically preventing the SF from switching back into its conductive state (16, 18–20). While some reports challenge this view (21, 22), this activation gate-coupled collapse of the SF is now generally accepted as the mechanism underlying C-type inactivation in K⁺ channels.

Several types of ligand-dependent K⁺ channels, including those opened by binding Ca²⁺, such as the BK and MthK channels (23–27), do not exhibit traditional C-type inactivation, despite possessing an identical SF with K_V and KcsA channels. Furthermore, these channels have been proposed to actually gate at the SF (28–32) although a recent cryogenic electron microscopy (cryo-EM) structure of MthK in the absence of calcium (33) revealed a steric closure at the bundle crossing inner gate region, suggesting that there may be two gates involved in calcium gating. Nevertheless, at this time, the structural correlates of SF gating and the difference from inactivation are unknown.

In the present study, we set out to first investigate whether we can capture different gating states of MthK by obtaining X-ray structures of its pore (Fig. 1A) in wide-ranging concentrations of K⁺. MthK channels have been previously shown to display a decrease in activity with depolarization, which is further augmented when external K⁺ concentration is lowered, a signature of SF gating and a hallmark of C-type inactivation (34). We reasoned that K⁺ titration of MthK pore structures may provide insights into the molecular causes for K⁺-dependent SF gating and will indicate whether it shares features with the C-type inactivation observed in KcsA (such as a collapsed SF). Unlike KcsA, MthK SF did not collapse in similarly low K⁺ concentrations, suggesting that the clue to why MthK does not display traditional C-type inactivation may lie in understanding the molecular underpinnings that contribute to SF conformational change. Thus, we next investigated the dependence of SF conformation on ion occupancy and used molecular dynamics (MD) simulations to reveal a uniquely low affinity central S2 site in MthK, which may play a lead role in the SF-based channel closure. Overall, our results illustrate how the exact same sequence and structure of the SF in a K⁺ channel can lead to slight variations in K⁺ binding site chemistry, which in turn can lead to distinct functional phenotypes.

Fig. 1.

Structure of the MthK pore in different K⁺ concentrations. (A) Overall architecture of wild-type MthK pore structure (three subunits of the tetrameric pore shown for clarity) crystallized with 150 mM K⁺. The SF is highlighted by dashed lines. Alignment of this structure with that crystallized in 6 mM K⁺ yields an all-atom root-mean-square deviation (RMSD) value of 0.25 Å. (B) K⁺-omit electron density maps (2F_o – F_c contoured at 2.0 σ) for SF atoms from two opposing subunits. Structures were solved in 150, 50, 11, and 6 mM [K⁺], as indicated. Crystallographic statistics are in SI Appendix, Table S1. (C) MD system with the MthK (ribbons) embedded in a lipid bilayer (gray sticks) bathed in 200 mM KCl (K⁺ as green spheres, Cl⁻ as blue spheres, and water as red and white sticks).

Results

Titration of K⁺ in the MthK Pore Crystal Structure.

In order to better understand how the SF gates ion conduction in Ca²⁺-dependent K⁺ channels, we explored whether the MthK SF can change its conformation, as seen in high-resolution crystal structures of the isolated transmembrane pore (23, 25). We crystallized the wild-type MthK pore (31) in the presence of various concentrations of K⁺ to investigate if the conductive MthK structure collapses to a “constricted” structure in low-mM K⁺ concentration ([K⁺]), similar to what was observed in low [K⁺] and low [Tl⁺] structures of KcsA (20, 35). Initially, the purified MthK pore was dialyzed into a crystallization buffer containing 1 mM [K⁺] (and 150 mM [Na⁺]). This sample failed to crystallize in conditions that readily yielded crystals in 150 mM [K⁺] buffer. The same 1 mM [K⁺] protein sample formed crystals when an additional 5, 10, or 50 mM [K⁺] was supplemented to the crystallization reagent. Crystals in lower [K⁺] were very small (typically ∼10 to 15 μm in the smallest dimension); however, high-resolution diffraction (<2 Å) could be obtained for each condition (SI Appendix, Table S1).

Crystallization of the MthK pore in all [K⁺] between 6 and 150 mM resulted in nearly identical structures (Fig. 1A), including the SF, where a “conductive” conformation was maintained (Fig. 1B) even for [K⁺] as low as 6 mM, unlike what was previously found for KcsA (20, 35). The lack of filter collapse at 6 mM (the lowest concentration at which crystal structures could be solved) may appear consistent with the high MthK activity observed when external [K⁺] is lowered to this concentration, with the caveat that the electrophysiology experiments were performed in asymmetric conditions where internal [K⁺] was much higher, 200 mM (34). The lowering of K⁺ concentration had an intriguing effect: K⁺ binding to the S2 site dropped markedly when [K⁺] was lowered from 150 to 6 mM, visible as a decrease in electron density within the site (Fig. 1B). The titration of K⁺ in S2 and the relatively strong K⁺ binding to the S1, S3, and S4 sites can be visualized with one-dimensional profiles of K⁺-omit electron density maps along the channel fourfold axis (Fig. 2A and SI Appendix, Fig. S1). Interestingly, the residual density within S2 at the lowest [K⁺] tested appeared weaker than that of water molecules elsewhere in the structure, suggesting that S2 is mostly vacant. In previous studies, where [K⁺] was decreased by soaking high-K⁺ preformed crystals in 1 mM K⁺-containing buffer (the MthK pore crystals in this study were grown directly in the desired K⁺ concentration), such a vacancy was not observed, although decreased K⁺ binding within S2 was detected (25).

Fig. 2.

Analysis of K⁺ occupancy within the SF. (A) K⁺-omit electron density maps (2F_o – F_c) (Fig. 1B) were sampled along the MthK channel axis, indicating the relative amount of K⁺ (K1 to K4) bound to the canonical S1 to S4 binding sites for the four crystallization conditions ([K⁺], mM: 6 blue, 11 orange, 50 green, 150 black). (B) Mean K⁺ occupancies (K1 to K4) from 16 independent MthK pore crystal structures (SI Appendix, Tables S1 and S3) refined in SF sites (S1 to S4). Error bars represent the SD (SI Appendix, Tables S3–S6). K⁺ occupancies for the S2 site were approximated by a single-site binding model with apparent dissociation constant (K_D^ap) = 50 mM (dotted gray line). Electron density consistent with water (10 electrons, equivalent to K⁺ occupancy of 0.55) is indicated (dashed cyan line), suggesting S2 is significantly vacant below 50 mM [K⁺].

We next evaluated the number of K⁺ ions bound inside the SF for each of our crystallization conditions. K⁺ occupancies were estimated directly as additional parameters during crystallographic refinement (36). Multiple refinement tests indicated that our final ion occupancies and atomic displacement parameters (ADPs) were converged, reproducible, and independent of the initial ion occupancy and B-factor parameters (SI Appendix, Figs. S2 and S3). Furthermore, the K⁺ occupancy values were highly reproducible across many datasets (SI Appendix, Tables S3–S5). These refinements explicitly assumed that the SF sites were either occupied by K⁺ or were vacant as simultaneous refinement of overlapping K⁺ and water occupancies was not feasible. In the case of high [K⁺] conditions (150 mM), our estimated occupancy values are ∼10 to 15% lower than the previously reported values for the MthK pore (36).

The occupancy analysis shows that K⁺ binding to S2, but not S1, S3, or S4, changes significantly between 6 and 150 mM [K⁺]. An approximate single-site binding model indicates that the S2 site binds K⁺ with an apparent affinity of ∼50 mM (a precise value is not possible because the [K⁺]-dependence is not described well by the model) (Fig. 2B and Eq. 1). The other three binding sites bind K⁺ with much higher apparent affinities, of the order 1 mM or lower (Fig. 2B). K⁺ occupancy is also reduced slightly in S1, S3, and S4 by ∼5 to 8% at each site as [K⁺] is reduced from 150 to 6 mM (Fig. 2 and SI Appendix, Table S2).

The crystallography titration experiments indicated that reduction in [K⁺] from 150 to 6 mM led to emptying of the S2 site of ions with no associated conformational change while near-maximal K⁺ occupancy was maintained at the other sites. It is possible that further decreases in [K⁺] might also empty other sites and lead to a change in channel structure or dynamics that are incompatible with the known crystal form or difficult to trap with crystallography. To explore this possibility, we examined the effect of K⁺ occupancy on MthK gating with computational methods.

MD Simulations of MthK in the Absence of K⁺ Reveal SF Collapse.

In order to determine how K⁺ occupancies influence the conformational stability of the conducting MthK SF, we simulated the membrane-bound MthK (Fig. 1C) with different ion configurations (SI Appendix, Table S7). During the reference simulation (Sref), including K⁺ ions in S0, S2, and S4, and water molecules in S1 and S3, representing a canonical multi-ion configuration in a K⁺ channel SF (20, 37, 38), the conductive MthK SF remained in a stable conformation, with backbone dihedral angles of the central V60 and G61 residues showing a strong preference for the values seen in the crystal structure (Fig. 3A, crystal structure values as black and white diamonds). In contrast, when simulating a channel where all K⁺ ions in the SF were replaced with water molecules for different external K⁺ concentrations (“empty” simulation SE1, Fig. 3B; control SE2 and SE3 simulations, SI Appendix, Fig. S4), water binding at the central S2 site was lost within 6 ns, accompanied by SF conformational constriction similar to that observed in the low [K⁺] KcsA crystal structure (20), as well as in simulations of K⁺-free KcsA (16). Interestingly, although a K⁺ replaced the water molecule in the S4 site during SE1 and SE2 simulations, this did not change the constricted conformation of the SF, indicating that a K⁺ ion in S4 is unable to enforce a conductive state of the SF. Despite the stability of the constricted SF conformation, the peptide linkage of V60-G61 (TVGYG; second and third (bolded) residues in the signature sequencecoordinating the S2 site) underwent dynamic reorientations by ∼180°, flipping both V60 and G61 carbonyls away from the conduction pathway (Fig. 3B). Such backbone dynamics have been previously observed in simulations of both KcsA and MthK and may be a key feature of SF gating (39, 40).

Fig. 3.

SF conformation, dynamics, and water binding depend on K⁺ occupancy. (A) Simulation Sref, with K⁺ bound in S2 and S4, remaining in a “conductive” state. Free energy maps for V60 and G61 dihedral angles (Phi and Psi) to the Left. Carbonyl groups that form S2 prefer to point toward the ion but occasionally rotate by ∼90°. To the Right is the free energy map for water binding, indicating two to three molecules behind the SF. Angles and water positions in the crystal structure are indicated as black and white diamonds. A representative snapshot of two opposing MthK SF subunits is shown on the Right. (B) Results from simulation with waters instead of K⁺ ions in S1 to S4 (SE1). Loss of water in S2 and increased water behind the SF correlates with SF “pinching.” S2-forming carbonyls underwent rotations by ∼180°, with three to six waters behind the SF. (C–F) Cases of single ions bound to the SF, as described in K+ Occupancy at Specific Sites Prevents SF Collapse.

MthK displays two well-localized water molecules behind the SF in X-ray structures (SI Appendix, Fig. S5A). These water molecules are mobile within the P-loops but remain stable during MD simulations where the SF stays in its conductive conformation (Fig. 3 A, Right, C, Right, and D, Right). During the conformational constriction, we identify an average of 3.5 prominent, though delocalized, water molecules penetrating the space behind the SF (Fig. 3 B, Right). These waters interact directly with the perturbed backbone of the SF. This is similar to KcsA, which presents one water molecule behind the SF in its conductive state (20), contributing to the E71/D80 bridge stability (SI Appendix, Fig. S5B), and three water molecules in its constricted state (20), forming a stable water wire that has been previously hypothesized to contribute to the stability of that conformation (16, 18, 19). The number of water molecules in the MthK P-loop is well correlated with the extent of SF constriction (Fig. 4A), and, while less tightly constrained than in KcsA, they also form a stabilizing network of interactions with flipped V60 and G61 (Fig. 4B). Therefore, without K⁺ inside the SF, MthK undergoes structural changes similar to those observed in simulations of KcsA: constriction of the K⁺-conduction pathway, free rotation of V60 and G61 carbonyl groups, and stabilization by water molecules behind the SF.

Fig. 4.

Water binding behind the SF correlates with SF pinching. (A) Number of water molecules in P-loops as a function of the SF constriction (relative to X-ray structure) at G61 (trend indicated with a dashed line). MD simulations (Sref, SS0, SS1, SS2, SS3, SS4, SV2, SW2, SE1, SE2, and SE3) are described in SI Appendix, Table S7. Conformational dynamics, constriction of the SF and water binding behind the SF were hindered by K⁺ in S1, S2, or S3. (B) Molecular representation of the collapsed SF (SE1) with P-loop water displaying a ring of hydrogen bonds with carbonyl oxygen of V60 and G61, and amide of G61, stabilizing a flipped, nonconductive state.

K⁺ Occupancy at Specific Sites Prevents SF Collapse.

Next, we characterized the relative importance of each site in regard to the MthK SF stability by restraining a single K⁺ in S1, S2, S3, or S4 (single occupancy simulations, SS1 to SS4) (Fig. 3 C–F), with all other sites occupied by water molecules. Although these situations may not represent dominant ion configurations during permeation and may not correspond to a dominant ion configuration at a given physiological ion concentration, the purpose of these controlled simulations is to isolate the effects of anion within each site, within the low ion occupancy regime. Simulations with a K⁺ in either the S1 or S2 site (Fig. 3 C and D) resulted in a stable conductive conformation, similar to that seen in Fig. 3A for the three-ion conductive configuration (Sref). With a K⁺ located in S4 (Fig. 3F), dramatic changes in structure and water penetration behind the SF were seen, similar to the ion-free case (Fig. 3B), although with reduced dynamics due to the presence of the ion. Similar results are obtained with a single K⁺ ion held in site S0 (simulation SS0, SI Appendix, Fig. S4). In the case of a single K⁺ located in S3, increased dynamics of the SF is seen, but with dominant free energy minima corresponding to the conductive conformation (indicated with diamonds; Fig. 3E), and water penetration that is increased, but resembling the situation with two tightly bound waters in the upper P-loop (Fig. 3E).

These results suggest that ions from S1, S2, and S3 sites need to evacuate in order for the SF to collapse while our MthK crystal structures in 6 mM K⁺ show that S1 and S3 are almost fully occupied with K⁺, even at the lowest [K⁺] tested, explaining the still conductive MthK SF conformation. In fact, the K⁺ concentration would likely need to drop below 1 mM (not encountered physiologically) in order for most of those sites to empty and allow the MthK filter to collapse. Furthermore, although these sites appear the same structurally, with S1 to S3 being chemically identical, binding to individual sites has different impact on the SF conformation. The S4 site is chemically different from the other three (S4 is made of four carbonyls and four hydroxyls while S1 to S3 are composed of eight carbonyls) while site S1 is exposed to the extracellular milieu, thus making S1 and S4 objectively different. A particular conundrum is why central sites S2 and S3, which appear identical at first sight, interact differently with K⁺.

Carbonyl Interactions at Specific SF Sites Control Ion Affinities.

To understand what drives reduced affinity for K⁺ in the S2 site of MthK, we used free energy perturbation (FEP) calculations to obtain the relative free energy of K⁺ binding between the chemically equivalent central sites S2 and S3, within a constant three-ion SF occupancy (consistent with our experimental estimates at high concentration) (SI Appendix, Table S2). Calculations with two K⁺ ions held in both S1 and S4 and one K⁺ in either S2 or S3 showed a net preference for the K⁺ to be in S3 rather than S2 when the neighboring site was vacant (ΔG_KKVK→KVKK = −2.5 ± 0.2 kcal/mol) (Fig. 5 and SI Appendix, Fig. S6) as well as, but to a lesser extent, when the neighboring site contained a water molecule (ΔG_KKWK→KWKK = −0.5 ± 0.1 kcal/mol) (SI Appendix, Fig. S6). The greater free energy difference for vacancy-mediated compared to water-mediated transformation implies that the water molecule is more stable in S3 than S2 by ∼2 kcal/mol (via a thermodynamic cycle) (SI Appendix), which is consistent with X-ray analysis implicating a vacancy at site S2 in MthK. Moreover, the computed free energy differences between K⁺ in S3 and S2 sites correspond to relative dissociation constants (K_S2/K_S3) of 64 ± 21 (vacancy-mediated) and 2.3 ± 0.4 (water-mediated) at 303 K, with the vacancy-mediated estimate more consistent with the apparent affinity estimates from experimental occupancies of S2 and S3 sites in Fig. 2B (on the order of 50 mM/1 mM).

Fig. 5.

Free energy perturbation for KKVK→KVKK in MthK (A and B) and KcsA (C and D). Calculations with K⁺ ions held in S1 and S4 and in either S2 (left in A and C) or S3 (right in B and D) showed a net preference for K⁺ to be in S3 over S2 with a vacant neighboring site in MthK (Top, ΔG_KKVK→KVKK = −2.5 ± 0.2 kcal/mol) and KcsA (Bottom, ΔG_KKVK→KVKK = −1.2 ± 0.2 kcal/mol). This difference in relative stability can be attributed to changes in carbonyl orientations and adjacent K⁺ to K⁺ distances (gray dotted lines) (see SI Appendix, Fig. S7 for mean angle and distance values). These variations are linked to different interactions between SF amine hydrogens, P-loop residues (V55, D64, and Y51 in MthK; and E71, D80, and W67 in KcsA), and P-loop water molecules (1 in KcsA, 2 in MthK) behind the SF (dashed lines). In KcsA, E71 stabilizes G77 carbonyls via their interaction with Y78 amides. In MthK, Y62 amides are bound weakly to mobile water molecules.

In SI Appendix, Table S8, we show additional FEP calculations for configurations where up to four K⁺ ions are included in the SF. In these high-occupancy cases, there exists an even stronger preference for K⁺ binding to S3 over S2 (by ∼−10 kcal/mol). However, because these configurations are so unstable (e.g., by 16 to 26 kcal/mol for a KKKK configuration) (SI Appendix, Table S8, bottom row), relative free energies may depend on how they are maintained with constraints. Moreover, the highly unfavorable situation with three to four ions in close contact leads to the favoring of a water-mediated configuration, with ΔΔG_KKWK→KKKK − ΔΔG_KKVK→KKKK and ΔΔG_KWKK→KKKK − ΔΔG_KVKK→KKKK ≈ 2 kcal/mol, which we consider to be an artifact of the unstable high ion occupancy configurations.

To gain insight into what leads to the free energy difference between sites S2 and S3, we dissected the energetic contributions to binding from the ion’s immediate environment, for the FEP calculations of Fig. 5. When the neighboring position to the ion was vacant (SI Appendix, Table S9), the interactions between K⁺ and the surrounding carbonyls from G61 and V60 (which form S2) were less attractive by ∼23 kcal/mol than those between K⁺ and the surrounding carbonyls from T59 and V60 (which form S3). This is caused by a difference in the orientation of carbonyls that line each site, with respect to the bound K⁺. The S3-forming carbonyl of T59 is better directed to stabilize its bound K⁺ than the S2-forming carbonyl of G61 (149 ± 1° in S3 compared to 110 ± 1° in S2). The V60 carbonyls, shared by both S2 and S3 sites, favor S2, but not enough to compensate for the poor coordination of S2 by G61 carbonyls (angles are 130 ± 1° and 120 ± 4° from V60 carbonyl to the ion, in S2 and S3, respectively) (SI Appendix, Fig. S7). Additionally, repulsive interactions from neighboring K⁺ ions in S1 (adjacent to the ion in S2) and S4 (adjacent to the ion in S3) favor K⁺ in S3 over S2 by almost 7.5 kcal/mol (SI Appendix, Table S9). This can be explained by the nature of the S4 site, which is formed by one ring of carbonyls and another of more flexible hydroxyl side chains. This allows the ion in S4 to move easily away from an adjacent ion in S3 to reduce repulsion energy (S1 to S2 ion distance is 4.2 ± 0.1 Å, compared to 4.7 ± 0.2 Å for S3 to S4) (SI Appendix, Fig. S7). Overall, the less well-directed carbonyls forming S2, combined with the asymmetric distribution of adjacent S1 and S4 ions within the SF, conspire to reduce binding affinity in S2, relative to its neighboring site S3.

In the presence of a water molecule rather than a vacancy in the adjacent site, the differences between S2 and S3 are diminished. Steric repulsion from the intercalating water molecule spaces out the ions within the SF, leading to better interactions with G61 and T59 carbonyls in S2 and S3, by ∼14 and 5 kcal/mol, respectively (SI Appendix, Table S10). In addition, the V60 carbonyl, while maintaining similar interaction with the S2 ion, has weakened its interaction with the ion in S3, by ∼10 kcal/mol, largely due to competing carbonyl interactions with that water molecule (SI Appendix, Table S10). As a result, the large energetic contribution from carbonyl groups in S2 and S3 almost disappears when a water is present. Interactions with neighboring ions and water in total (+7.8 kcal/mol in SI Appendix, Table S10) are similar to those seen for the ion–ion contributions when the adjacent site is vacant (+7.4 kcal/mol in SI Appendix, Table S9). Overall, S3 is thus only marginally favored over S2 when the ions are separated by a water molecule, in contrast to the crystallographic data, again implying a vacancy between ions is the energetically preferred configuration.

Differences between KcsA and MthK SFs.

Despite an identical SF to MthK, KcsA has been crystallized in a collapsed conformation at low permeant ion concentrations (20). Furthermore, the occupancy of the KcsA SF binding sites titrates quasi-uniformly across S1 to S4 before the SF collapses (20, 35, 41). Since MthK and KcsA have different SF gating phenotypes as well, we sought to understand the causes for the different stabilities of SFs with different ion configurations in these channels, and in particular the reduced affinity in the central S2 site in MthK. FEP calculations performed on KscA also reveal a small preference for K⁺ to bind in S3 rather than S2, when the neighboring site is vacant (ΔG_KKVK→KVKK ≈ −1.2 ± 0.2 kcal/mol), but to a lesser extent than MthK (Fig. 5). Similar to MthK, the difference between S2 and S3 in KcsA is reduced or eliminated when a water molecule is present in the adjacent site (ΔG_KKWK→KWKK = 0.0 ± 0.2 kcal/mol).

Decomposition of energetic contributions shows that interaction with T75 in S3 is ∼3 kcal/mol less favorable while interaction with G77 in S2 is ∼3 kcal/mol more favorable, compared to MthK, when a vacancy is in the adjacent site (SI Appendix, Table S9). This comes from a slight difference (∼4° between the channels) in orientations of T75 and G77 carbonyls in S2 and S3 (SI Appendix, Fig. S7). Another contributing factor is that the interactions with neighboring ions are less destabilizing in S2 relative to S3 in KcsA, by over 4 kcal/mol (SI Appendix, Table S9), which arises from decreased ion–ion distance when the K⁺ resides in S3 in KcsA (SI Appendix, Fig. S7, right structures). To understand these differences, we first note the role of glutamate E71 behind the KcsA SF that shares a proton with D80. Direct interactions with E71 have little effect on the relative stabilities of a K⁺ ion in S2 and S3. Instead, KcsA’s E71 side chain stabilizes the orientation of the G77 carbonyls via an H-bond with the amide of the G77-Y78 linkage (SI Appendix, Fig. S5). MthK lacks a residue with a similar role (V55 at the E71 position), and its Y62 amide is bound more weakly to a mobile water molecule (SI Appendix, Fig. S5). These different interactions behind the SF result in a small change in the direction of carbonyl groups, more effectively stabilizing the ion in S2 in KcsA.

Secondly, we observe that carbonyl–ion interactions in the lower SF of KcsA (T75) are weaker than in MthK (T59). The KcsA lower SF is wider than that of MthK by ∼0.2 Å on average, with the T75 C_α further from the channel axis (SI Appendix, Fig. S5 C and D). This is a result of different interactions between the SF bottom and the inner helix, where T75 is further from F103 in KcsA than in MthK (equivalent residues T59 and F87) (SI Appendix, Fig. S8 A and B), arising from the different rotamers of F103/F87 (SI Appendix, Fig. S8C). The corresponding increase in carbonyl displacement required to coordinate an ion, due to the widening of the lower SF (with similar stiffness, according to the variance in SI Appendix, Fig. S5C, Bottom), would lead to reduced stabilization in KcsA’s S3 site. Finally, the repulsive interaction from neighboring K⁺ ions in the KcsA SF doesn’t favor S3 as much as it does for MthK, with a difference of only 2.9 kcal/mol (compared to 7.6 kcal/mol in MthK) (SI Appendix, Table S9), which we attribute to a closer packing of S3 and S4 ions in the KcsA lower pore (∼4.4 compared to 4.7 Å in MthK) (SI Appendix, Fig. S7). This can be appreciated by noting that the relatively splayed lower KcsA SF means that the K⁺ ion in S4 moves slightly upwards (toward S3) to be coordinated more by the upper carbonyls than the lower hydroxyl groups of S4 (compare Lower and Upper of Fig. 5 and SI Appendix, Fig. S7). Overall, these observations suggest that small structural differences between MthK and KcsA that maintain the shape and orientations of the SF lead to slightly stronger K⁺ binding in S2 relative to S3 in KcsA.

MthK SF Collapse Is Coupled with Conformational Changes at the Intracellular Gate.

A previous investigation into MthK gating suggested that closure of the SF gate is coupled with a narrowing at the intracellular gate (31, 32), with similar findings in eukaryotic BK channels (42, 43). We investigated whether the MthK pore SF collapse we see with MD simulations is accompanied by motions at the intracellular side of the TM2 helices. We found that SF-TM2 interfacial residues T59 and I57 (SF) and I84 and F87 (TM2) are more closely packed with a conductive compared to a nonconductive SF, and that the transition to a nonconductive SF was well correlated to TM2 straightening (Fig. 6A). The root-mean-square fluctuation (RMSF) of the backbone of the protein also reveals a correlation between the SF and the inner gate, with particularly large fluctuations in simulations with collapsed SF (Fig. 6B), consistent with previous experimental observations (12, 32, 44), providing strong evidence of coupling between movements of the SF and the intracellular gate.

Fig. 6.

Coupling of SF and TM2 helices. (A) SF-TM2 packing (mean repulsive component of the Lennard Jones potential) via the I57/T59–I84/F87 interface correlates with TM2 straightening (dashed line indicates trend). TM2 angle is calculated between vectors formed by residues 80 to 70 and 85 to 95 (180° being straight). Simulations with reduced packing (SS0, SS4, SE1, SE2, and SE3) are accompanied by TM2 straightening. Insets show loss of I57 (dark green)–T59 (beige) contact at the P-loop and I84 (light blue)–F87 (dark blue) on TM2, as the SF collapses, with a straightened TM2 (arrows indicate motions of residues). (B) Correlation of inner gate (residues 90 to 98) and SF (residues 59\63) RMSF (dashed line indicates trend). (Insets) Dynamical network analysis reveals dominant paths between SF and inner gate (G61 and V91): G61-T59-I57-F87-V91 (red; 63%); and G61-T59-I84-F87-V91 (green; 23% of all paths).

Using correlation network analysis, we identify a dominant path, G61-T59-I57-F87-V91 (63% of all paths) (Fig. 6 B, Inset, red), and two alternative paths, G61-T59-I84-F87-V91 (23%, green) and G61-V55-I57-F87-V91 (9%) (SI Appendix, Fig. S9, orange), going through the P-loop (V55) rather than the bottom of the SF (T59). The shortest paths between residues G61 (SF) and V91 (TM2) include the same residues responsible for SF-TM2 packing above (T59, I57, I84, and F87) (Fig. 6). Changes in packing of T59, I57, I84, and F87 between conducting and collapsed SF states lead to the lengthening (reduction in correlation) for these paths and the emergence of an alternative path, involving G61-T59-I57-I84-F87-V91 (9%) (SI Appendix, Fig. S9, blue).

Correlation network analysis of KcsA (SI Appendix, Fig. S10) shows that communication between the SF (G77) and TM2 (T107) follows similar paths to MthK, although the most common path, G77-E71-A73-F103-T107 (50%) (SI Appendix, Fig. S10, orange), includes E71 (V55 in MthK), followed by G77-T75-A73-F103-T107 (33%) (SI Appendix, Fig. S10, red) and G77-T75-I100-F103-T107 (17%) (SI Appendix, Fig. S10, green). This change in the dominant communication pathway may relate to the specific role played by E71 in KcsA inactivation in response to the opening of the TM2 gate, with mutation E71A leading to a noninactivating channel (17), a role unmatched by the equivalent V55 in MthK. In MthK, communication from TM2 to SF occurs primarily via the base of the SF (T59) as a consequence of stronger packing to TM2 (SI Appendix, Fig. S8). The width of the SF at the level of T59 impacts the relative affinity of S3 and S2 for K⁺ and has recently been shown to affect both conductance and occupancy in the SF (45), suggesting a potential role for T59 for the onset of TM2-induced slow inactivation in MthK. Despite this difference, the hinge of communication in both channels is a cluster of common residues (T59/I84/F87 in MthK and T75/I100/F103 in KcsA), consistent with recent simulations suggesting a role in TM2-SF communication for I84 in MthK (46) and for I100/F103 during inactivation in KcsA (9).

Discussion

K⁺ channels are currently believed to gate at two different locations: a cytoplasmic bundle-crossing gate and an SF gate. In some voltage-dependent K⁺ channels, and KcsA, stimulus leads to opening of a bundle-crossing gate, followed by closure (inactivation) of the SF (17, 47). Ca²⁺-gated channels, such as eukaryotic BK and prokaryotic MthK, do not exhibit a stimulus-induced C-type inactivation although, for MthK, a voltage-driven closure/inactivation gate has been described (31, 34, 40). Our aim here was to gain insight into the mechanisms by which identical SFs confer different inactivation phenotypes.

We crystallized the MthK pore in low [K⁺] with the goal of investigating whether a different SF conformation appears, as seen in KcsA, previously crystallized with a collapsed SF conformation in low K⁺ (20). We required at least 6 mM [K⁺] for MthK pore crystallization but found that the SF remained firmly in the previously reported conductive conformation (Fig. 7) (25). In addition to the SF not changing conformation, this experiment resulted in several mechanistic insights. First, site S2 is a low apparent affinity K⁺ binding site as it is the only one titrating in the mM [K⁺] range employed here. The other three sites have higher apparent affinity, which likely titrate in the submillimolar range. Our free energy simulations suggested that this reduced affinity in S2 in MthK is primarily a result of glycine carbonyl groups being less well-directed toward the ion, due to the absence of a direct H-bond to the pore helix behind the SF, compared to KcsA, which maintains strong interactions with residue E71 (we note, however, that other interactions can also be important for conferring C-type inactivation, as seen in K_V channels that rely on a pore-helix Trp side chain) (3, 48). Second, in 6 mM [K⁺], the S2 SF site was to a significant degree vacant, with arguably no water replacing the K⁺ in this position, also consistent with our free energy calculations. Overall, the distribution of ions and water within the SF can be seen to be sensitive to interactions within the P-loop, as well as packing of the lower SF to the TM2 pore-lining helix that differs between MthK and KcsA channels.

Fig. 7.

MthK and KcsA SFs exhibit the same sequence and structure and the same ability to collapse, but have different K⁺ affinities for S1 to S4 sites. Schematics of SF for MthK (Left) and KcsA (Right), with two subunits shown in different [K⁺] regimes. The SFs are the same in high [K⁺] (Top), with carbonyl oxygens (red sticks) pointing inward to form 4 K⁺ (green) sites. In low [K⁺] (Middle), MthK loses the K⁺ in S2, but not in S1, S3, and S4, and maintains a conductive filter. In contrast, KcsA experiences reduced K⁺ occupancy in both S2 and S3, leading to a collapsed, inactivated state. In the absence of ions in the SF (Bottom), both SFs are collapsed.

Functional Importance for a Low Binding Affinity for K⁺ in S2.

While three of the SF sites bind K⁺ strongly (likely with submillimolar affinity), in agreement with studies of K⁺ binding to KcsA and MthK using isothermal titration calorimetry (ITC) (49, 50) or NMR (51), S2 binds K⁺ with an ∼50 mM apparent affinity; a very low affinity for an SF binding site, never directly measured before. The existence of a low affinity K⁺ binding site (called the “enhancement” site) was previously proposed in BK channels based on electrophysiological studies of the interaction of K⁺ ions with a Ba²⁺ blocker (52). It is tempting to assign this “enhancement” site to the SF S2 site (53). Additionally, low affinity SF binding of K⁺ can be an important ingredient for rapid conduction of K⁺ (54). During a transport cycle under the influence of a driving force, the low affinity for K⁺ in S2 would be exploited to allow for fast release of K⁺ and consequently high ionic throughput.

The loss of K⁺ binding at site S2 was previously interpreted to be an initial step in the inactivation process, whereby vacant S2 increases the dynamic behavior of the SF backbone (39, 40), which may in turn decrease K⁺ affinity at other SF sites. This idea was inspired by several KcsA structural studies, including [K⁺] and [Tl⁺] titrations (35, 41) and open-inactivated mutant KcsA structures (9), which show that the progressive loss of K⁺ at S2 correlates with physical constriction of the SF (but also see refs. 21 and 22). Our simulations indeed suggest that MthK possesses the same ability to collapse its SF as KcsA but likely lacks stabilizing configurations of protein and water behind the SF to lock in an inactivated state.

We showed here that, in MthK, there is a selective loss of K⁺ binding at site S2 as the other S1, S3, and S4 sites still hang on to their ions, even in low millimolar [K⁺]. This is different from the more uniform change in ion occupancy in KcsA channels with [K⁺], where all sites lose ions at similar rates. Loss of ions uniformly from all K⁺ binding sites can explain why the KcsA SF collapses in low [K⁺], while similar decrease in [K⁺] for MthK only leads to site S2 being emptied, and thus no collapse, because the other sites are quasi-fully occupied, indicating higher affinity for K⁺(Fig. 7). In agreement, previous studies on K_V channels have also showed that high affinity for K⁺ at binding sites within the pore is associated with lower rates of C-type inactivation (5–8).

Under a driving force, such as a membrane potential (or a physiological K⁺ concentration gradient), ions may exit the SF at a faster rate than the SF can be refilled by ions diffusing into the pore, thus transiently emptying the SF and leading to collapse. The transient SF collapse will halt ion permeation and can lead to the appearance of closed intervals whose length and/or frequency depend on the voltage applied across the SF. This offers a possible explanation for the decrease in open probability with depolarization, also known as voltage-gating in MthK (31, 34). This could be examined in the future with large-scale simulations of MthK and KcsA under the action of varying membrane potentials to examine ion escape and subsequent collapse events.

K⁺ Occupancy and Vacancy-Containing Ion Configurations in MthK.

Potassium channels are famous for their selectivity for K⁺ over Na⁺. Recently and controversially, selectivity for K⁺ over water has been proposed based on MD simulations of K⁺ transport (36, 55), as well as a reanalysis of ion occupancy in published structures of several K⁺ channels (36). In this model, the SF is occupied by an average of three ions, and vacancies are preferred over intervening water permeation events. This recent model is against the more accepted view that K⁺ and water are relatively equal in their passage (35, 38, 41, 56) but is reminiscent of older proposals that suggested three or more ions are required in order to decrease the overall ion affinity and increase throughput (52, 57).

In light of this controversy, we judiciously analyzed the K⁺ occupancies in our MthK pore structures. We estimated that ∼3.2 K⁺ ions may simultaneously occupy the MthK SF in 150 mM [K⁺] (SI Appendix, Table S2), 14% less than a recently reported estimation (∼3.7 K⁺) where a different refinement program was used (36). It is interesting to note that our overall apparent occupancy is nearly identical to the number of Tl⁺ found in KcsA using yet another refinement strategy (35).

SF gating, long associated with C-type inactivation in voltage-dependent K⁺ channels, is known to depend on the external concentration of permeant ions (2). The voltage-dependent inactivation of MthK is also dependent on the external K⁺ concentration ([K⁺]_ext) and is characterized by an electronic valence of ∼1.4e₀ (31, 34). Assuming the membrane voltage drops mostly across the SF for an open channel (31, 58), the MthK voltage dependence is roughly consistent with three ions, positioned for example in sites S1 to S3, being driven out of the SF in order to close the gate. This suggests a transition from a high occupancy SF (with more than two K⁺) to a state similar to our “0-K⁺” simulation that shows a constricted (closed) SF and a single bound K⁺ ion at S4 (Fig. 3B). Therefore, it seems at least plausible from functional experiments that high K⁺ occupancy within the MthK SF can occur during permeation. However, the crowding of ions within the S1 to S4 sites (one ion in each of the four canonical binding sites), as suggested by Köpfer et al.’s reinterpretation of X-ray crystallographic data (36), leads to very large free energy values in our MD simulations (SI Appendix, Table S8), caused by unstable configurations that must be maintained by strong constraints. Instead, we observed, in simulations at ambient temperature, that, if four K⁺ ions are allowed to move freely in the SF, the ions prefer to space out, with the ion in S1 moving to S0 and the ion in S4 moving toward the cavity site (SI Appendix, Table S8, upper row), as also witnessed by Köpfer et al. (36). While the precise locations of ions in a high occupancy SF may depend on the chosen force field and ion–carbonyl interaction parameters (59), the elevated energies of a tightly organized S1-S2-S3-S4 configuration of K⁺ ions indicates an unlikely situation at ambient temperatures. Such a high concentration of ions in a small volume, away from the aqueous phase, also calls for the use of polarizable force fields (59) in future.

Furthermore, our titration of the S2 site in MthK suggests that a vacancy is preferred over water between ions, apparently in agreement with a previous proposal of an ion permeation mechanism that is not reliant on intervening waters, leading to a low affinity state that supports high conduction (36). Both vacancy- and water-mediated equilibrium ion configurations appear consistent with two-dimensional (2D) infrared spectroscopy with specific isotope labels within the SF (55, 60). Moreover, while solid state NMR has suggested lack of water involvement in the permeation pathway (61), this remains inconsistent with studies implying cotransport of ions and water (56, 62). These studies suggest that the relationship between X-ray crystallographic, equilibrium spectroscopic, and nonequilibrium permeation mechanisms has yet to be fully reconciled (59).

MthK SF Collapse in the Absence of Central K⁺ Ions and Communication with Gate.

Simulations performed in the absence of K⁺ bound inside the S1, S2, or S3 SF sites resulted in rapid, dynamic distortion of the SF structure and constriction of the pathway upon clearance of the S2 site, stabilized by water interactions behind the SF. These structural features are remarkably similar to what is observed in the constricted KcsA structure, either by crystallography (20) or by simulation (16). First, the constricted MthK SF is highly dynamic at the V60–G61 peptide bond, and, second, the space behind the SF supports two waters in the conductive state and approximately four waters in the constricted state. Therefore, in both channels, SF constriction accommodates the addition of two stabilizing water molecules (16, 19, 20). However, unlike KcsA, in the absence of an equivalent to E71 in MthK to confine them, P-loop water molecules occupy less well-defined locations, forming a less restricting network of interactions with the flipped backbone of the SF.

Collapse of the SF due to ion depletion has been shown here to be coupled to movements of the intracellular gate, in a state-dependent manner. While this coupling exists in both MthK and KcsA, differences in pore helix sequences and the packing of the SF to TM2 helices lead to distinct pathways of allosteric communication that may relate to differing functional roles for SF-driven gating in these channels. This is in agreement with previous findings in K_V channels where affinities for K⁺ binding sites in the pore have been suggested to be determined not only by the specific coordination provided by the signature sequence, but also by nearby regions (8). It seems reasonable to conclude that there are essential features that control SF gating mechanisms in all K⁺ channels, but that ion occupancy-dependent gating depends on the precise chemical structure of the channel pore loop, potentially explaining mechanistic variation across the superfamily (Fig. 7) and allosteric control of the SF by distant ligand-binding domains.

Conclusions

To understand the molecular mechanism responsible for the differences between KcsA and MthK inactivation phenotypes, we first performed a structural titration of the MthK pore using a large K⁺ concentration range. We found that going to as low as 6 mM K⁺ did not affect the conductive conformation of the MthK SF, while, under similarly low K⁺, the KcsA SF is collapsed. Using MD simulations we found that, while the MthK filter has a similar ability to collapse/gate, it is not observed in the same concentration range as KcsA. Surprisingly, we found that the MthK central S2 site alone becomes depleted of ions (not seen before for KcsA), with the neighboring sites not depleting in that range, preventing SF collapse. We carried out detailed analysis that explained the differences in ion and water affinities in terms of minor differences in the channel structures and also revealed a common filter-intracellular gate communication mechanism, which is a hallmark of C-type inactivation in KcsA. We conclude that, although KcsA and MthK share similar abilities to change conformation (Fig. 7), the functional phenotypes are governed by their affinity for ions, which are affected by small changes in the structure around the filter.

Materials and Methods

MthK Purification, Pore Isolation, and Crystallization.

Wild-type MthK channels were expressed and purified using protocols described previously (26, 31). Reagents were purchased from Sigma unless indicated otherwise. Hexahistidine-tagged MthK was extracted from Escherichia coli using N-decyl-β-d-maltopyranoside (DM) (Anatrace), purified using HiTrap Co²⁺-charged metal-affinity and Superdex 200 gel filtration columns (GE Healthcare) using 100 mM KCl, 20 mM 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (Hepes), 5 mM DM (pH 8.0).

MthK pore domain was isolated and purified following digestion of the intracellular Ca²⁺-binding domains and crystallized (23, 25, 31). Trypsin type I (T8003; Sigma) was used at 1:50 trypsin:MthK (mass) for 2 h. Trypsin inhibitor type II-O (T9253; Sigma) was added at twice the mass of the trypsin enzyme, and the transmembrane domain was purified on a Superdex 200 column using protein buffer with 5 mM DM. A second gel filtration pass used 100 mM KCl, 10 mM 3-(N-morpholino)propanesulfonic acid (Mops), pH 8.0 (KOH), 10 mM Anagrade n-dodecyl-N,N-dimethylamine-N-Oxide (LDAO) (Anatrace). Purified protein was either used in high (∼150 mM total) [K⁺] crystallization experiments or dialyzed into a low [K⁺] buffer consisting of 100 mM NaCl, 1 mM KCl, 10 mM Mops, pH 8.0 (NaOH), 10 mM LDAO.

Protein was concentrated to 15 mg⋅mL⁻¹ (assuming 1 optical density at 280 nm [OD₂₈₀] = 1 mg⋅mL⁻¹) for crystallization in 20 °C sitting-drops. Crystallization conditions were 3.5 to 4.0 M 1,6-hexanediol (Hampton), 100 mM 2-(N-morpholino)ethanesulfonic acid (MES) (pH 6.75). For crystallization in ∼150 mM [K⁺], the MES buffer was pH-adjusted with KOH (raising the total [K⁺] to ∼150 mM). Crystallization in lower K⁺ used NaOH titrated MES, and an additional 5, 10, or 50 mM KCl was included in the crystallization reagents. Crystallization with 6 mM [K⁺] also included 5 mM tetrabutylantimony. Crystallization with 11 mM [K⁺] also included 10 mM tetrapentylammonium or 5 mM bromo-benzyltributylammonium. Crystallization with 50 mM [K⁺] also included 10 mM tetrahexylammonium. Addition of quaternary ammonium blockers did not visibly alter the electron density maps due to very low occupancy inside the MthK crystals (31).

Crystal Diffraction Data Collection and Analysis.

MthK pore crystals were frozen in liquid N₂, and diffraction datasets were collected at the X25 beamline (National Synchrotron Light Source at Brookhaven National Laboratory) or the 14-1 beamline (Stanford Synchrotron Radiation Lightsource). Datasets were integrated and scaled relative to one another in P42₁2 using XDS and XSCALE (63). Molecular-replacement (Protein Data Bank [PDB] ID code 3LDC) (25) and model refinement were done using Phenix (64) with model building in Coot (65). σ-scaled electron density maps were calculated using Phenix. One-dimensional sampling of electron density maps (Fig. 2A and SI Appendix, Fig. S1) was performed using MAPMAN (66). Graphical representation of models and electron density were generated using PyMOL 1.7.4 (Schrödinger, LLC).

Refinement of K⁺ occupancies inside the SF was performed near the end of model refinement. Parameter convergence was tested using 50 macrocycles of refinement from several initial values for K⁺ B-factor and occupancy values (SI Appendix, Figs. S2 and S3). ADPs for the MthK protein chain contained either three or four translation/libration/screw (TLS) groups (67). The K⁺ ions were initially modeled with an isotropic B-factor and were refined using individual anisotropic ADPs during final occupancy refinement. Four wild-type MthK models, crystallized in different [K⁺], were deposited in the PDB (SI Appendix, Table S1). Between one and five additional crystal datasets from each of these crystallization conditions were collected and analyzed in order to assess the reproducibility of K⁺ occupancy determinations (SI Appendix, Tables S3–S6).

Occupancy titration of the K⁺ (K2) in site S2 (Fig. 2B) was compared to a single-site binding curve,

$$O_{K2}=\frac{1}{1+\frac{K_D^{ap}}{\left[K^{+}\right]}}$$ [1]

O_K2 is the occupancy of K⁺ in site S2, K_D^ap is the apparent dissociation constant, and [K⁺] is the K⁺ concentration. Since the titration of K⁺ binding occurs simultaneously over multiple sites (Fig. 2B), we calculated the summed K⁺ occupancy within the SF, O_total (SI Appendix, Tables S2–S5)

MD Simulations and Analysis.

Simulation systems.

The pore-only MthK X-ray crystal structure (PDB ID code 3LDC) (25) was embedded in bilayers of palmitoyl-oleoyl-phosphatidylcholine (POPC), with explicit transferable intermolecular potential with three points (TIP3P) water and 20 to 200 mM KCl solution to create 11 independent all-atom systems. Systems were built and preequilibrated with the CHARMM program (68). Simulations were performed using NAMD 2.9 (69) using the CHARMM36 force field (70), at constant pressure (1 atm) and temperature (303 K). Varying [KCl] and constraints were used to maintain distinct occupancy states (SI Appendix, Table S7), including the following: a reference simulation (Sref) with ions in sites S0, S2, and S4; single ions in S0 to S4 restrained with flat-bottom potentials (SS0-4); ions in S1, S3, and S4, including either water (SW2) or vacancy (SV2) in S2 (trapped with flat-bottom constraint); and an ion-free SF with high (200 mM; SE1) or low (20 mM; SE2) external [K⁺], or with bound K⁺ ions in the sites above and below the SF to prevent binding of other K⁺ ions (20 mM; SE3). Each system was run until convergence (40 to 300 ns) (SI Appendix, Table S7). Lennard–Jones parameters, to describe interactions between K⁺ and carbonyl oxygens, were chosen to reproduce free energies of solvation in the backbone mimic, N-methyl-acetamide (71). Similar systems were built and equilibrated using KcsA (PDB ID code1K4C) (41), to create four independent simulations with different occupancy states, each running for 30 to 100 ns (SI Appendix, Table S7).

Analysis of MD simulations.

Positions of K⁺ and water molecules were measured relative to the SF backbone (residues T59 to G63) center of mass (COM). SF constriction is defined as the ratio of average radius at G61 and of the SF (residues 59, 60, 62, and 63). Free energy maps for SF dihedral angles φ_i and ψ_i for residue i were calculated as $W\left({\phi }_i,{\psi }_i\right)=-k_{B}T\ln \left[\rho \left({\phi }_i,{\psi }_i\right)\right]+C$, where $\rho$ is the probability. The RMSF of the SF is reported for residues 59 to 63 while that for the TM2 gate includes residues 90 to 98. Correlation network analysis was performed to examine communication between the SF and intracellular gate using the Dynamical Network Analysis plugin (72) of VMD and Carma (73) to calculate pairwise correlations (see SI Appendix for details).

Free energy calculations.

To examine the relative stability of ions and water molecules in different SF sites, FEP (74) was performed, transforming between K⁺, water, or vacancy within specific ion configurations. We considered K⁺→Vacancy in S2 with Vacancy→K⁺ in S3 (KKVK→KVKK), corresponding to the relative free energy of K⁺ in S2 and S3, with adjacent vacancy; and K⁺→Water in S2 together with Water→K⁺ in S3 (KKWK→KWKK, with adjacent water). Initial forward and backward transformations were performed sequentially in 20 steps, followed by 4 ns per window of production in parallel. Mean and SEs were determined using the ParseFEP plugin of VMD (75). FEP calculations were performed simultaneously in S2 and S3 while S1 and S4 were occupied by K⁺ ions, maintaining a total of three ions in the SF (as suggested by X-ray fitting) (SI Appendix, Table S2). To understand the different ion affinities for binding sites, we calculated energy contributions for ions in S2 or S3 with carbonyl groups and neighboring K⁺ ions and waters, as well as long-range contributions from P-loop residues in MthK and KcsA (SI Appendix, Tables S9 and S10). FEP calculations were also performed in S2 and S3 in the presence of three other K⁺ ions (SI Appendix, Table S8).

Data Availability.

Models and structure factors for the wild-type MthK pore structures have been deposited in the Protein Data Bank under accession codes 6U9P, 6U9T, 6U9Y and 6U9Z, for 150, 50, 11, and 6 mM [K⁺], respectively.