MD simulations for the KcsA channel were conducted based on the crystal structure determined in a conductive conformation (PDB ID: 1K4C) [5]. Most residues were assigned to their standard protonation state at pH 7. The residue Glu71 was modelled in a protonated state to enable the formation of a key hydrogen bond with Asp80 [23] [24] [25]. The ion channel, with its symmetry axis aligned along the z-axis, was embedded in a POPC lipid bilayer. Water molecules were added to solvate the systems. K⁺ and Cl⁻ ions were added to the bulk solvent to reproduce experimental ionic concentrations (150 mM KCl) and to obtain the electric neutrality of the system. Then two simulation models shown in Figure 1(A) (denoted as “KcsA w/o K⁺” and “KcsA w/K⁺”) were constructed. The final systems contain roughly 86,200 atoms. Moreover, we also constructed molecular models based on the NaK channel (PDB ID: 2AHZ) [6] and NavAb sodium channel (PDB ID: 3RVY) [7], with a similar procedure as described above. For improving the computational efficiency, the voltage-sensing domain of the NavAb channel was removed.

All MD simulations were carried out using NAMD2 [26], and visualized and analyzed with VMD [27]. The CHARMM36 force field was employed for protein [28] [29] [30], lipids [31] and ions [32]. The TIP3P model was used for describing water [33]. The long-range electrostatic interactions were computed using the particle mesh Ewald method [34]. A time step of 2 fs was used. All the simulations were performed in the NPT ensemble, whereby the temperature was maintained at 300 K by the Langevin thermostat, and the pressure was maintained at 1 atm by the Langevin piston pressure control [35].

After a 5000-step energy minimization, each system was simulated for 0.5 ns whereby all components except the lipid tails were fixed to remove the gap between the protein and lipid tails. Subsequently, a 1.6 ns pre-equilibration was carried out where a gradually decreasing harmonic constraint was applied to each protein atom. Finally, the production run was performed for 100 ns without any restraints. To avoid the influence of newly inserted ions into the selectivity filter, a fictive wall was applied to repel ions that approach the average z position of P atoms in lipids from the extracellular side of the membrane. The electrostatic potentials were computed with the PMEPot plugin of VMD [36]. In our simulations, a hydrogen bond is considered as being formed between an atom with a hydrogen bonded to it (donor, D) and another atom (acceptor, A), provided that the distance D-A is less than 3.5 Å and the angle D-H-A is less than 30˚.

Figure 2 shows the root-mean-square deviation (RMSD) for the backbone atoms of the selectivity filters of the KcsA, NaK and NavAb channels as a function of simulation time with respect to the crystal structures. In the presence of coordinated ions, the RMSD values of all the three channels are always lower than 1.0 Å in the whole 100 ns MD simulation (Figure 2(A)), confirming the strong stability of the selectivity filters in these channels. In stark contrast, when ions are absent, the RMSD for the KcsA filter quickly exceeds 1.0 Å within 1 ns even when the whole protein is still constrained (black line in Figure 2(B)), and eventually fluctuates around ~1.8 Å. This result is consistent with previous works [10] [11] [12] [13] [14] and shows the worst stability of the KcsA filter among the three studied channels. The RMSD of the NaK filter quickly reaches and fluctuates around ~1.5 Å (red line in Figure 2(B)). However, the RMSD for the NavAb filter stays at ~0.5 Å (blue line in Figure 2(B)) during the 100 ns simulation even in the absence of Na⁺ ions, indicating its higher intrinsic stability as compared to KcsA and NaK. Considering the fact that there are four, two and zero stable ion bindings sites that can coordinate fully dehydrated ions in KcsA, NaK and NavAb filters [4] [5] [6] [7], respectively, it is interesting to note that the filter stability is inversely correlated with the number of stable binding sites in these three cation channels.

By inspecting the MD trajectory, we found that the conformational change (i.e., the origin of the RMSD increase) of the KcsA channel in the absence of K⁺ ions is mainly embodied in the flipping of the carbonyl oxygen of Val76, and the narrowing of the selectivity filter pore around Gly77 (Figure 3). The Val76 carbonyl oxygen, originally pointing toward the lumen to coordinate K⁺ ion, undergoes a ~180˚ reorientation, namely, flipping away from the conduction pathway (marked with blue curved arrows). The narrowing of conduction pathway of the selectivity filter is caused by the inward movement of the α-carbon atom (Cα) of Gly77, which occludes the pore and makes it become a distinct “hourglass” shape (red arrows). In addition, we note that the flipping of Val76 occurs for all four subunits even in the initial pre-equilibration period (see the t = 1.6 ns snapshots) and lasts for the rest of time (Figure 5(B)). On the contrary, the narrowing of the filter around Gly77 occurs for only some of the four subunits (Figure 5(E)). For instance, at t = 1.6 ns, such narrowing only occurs in chain A and C, but not in chain B and D; it occurs in chain B at t = 20 ns, but does not appear in chain D during the whole 100 ns simulation. It is also striking that the narrowing in chain C disappears at t = 94 ns.

Similar to KcsA, the selectivity filter of the NaK channel also shows significant conformational change, as shown in Figure 4. The residue Val64 in the NaK channel, equivalent to Val76 in the KcsA channel, also undergoes flipping during

the MD simulation (blue curved arrows). However, different from KcsA, such flipping does not occur in all four subunits, but instead, only in chain B. In addition, chain B also undergoes narrowing around Gly65, a residue equivalent to Gly77 in KcsA (red arrows). Such flipping and narrowing both occur within the initial pre-equilibration period and lasts for the rest of time (Figure 5(C) and Figure 5(F)). These results suggest that the NaK channel shares a similar conformational change process with that of the KcsA channel, but at a lower degree.

About four decades ago, Almers and Armstrong suggested that the repulsive electrostatic forces between negative charges or dipoles lining in the pore will destroy the pore structure of potassium channels [37]. Based on the available crystal structure, we now know that there exists four backbone carbonyl oxygen atoms and threonine side chain oxygen with electro-negativity in each subunit exposing toward the pore lumen in KcsA. It is natural to speculate that the presence of K⁺ ions contributes to the overall stability of the selectivity filter by counterbalancing the repulsive electrostatic forces between the negatively charged oxygen atoms. Below we validate this hypothesis by measuring the electrostatic potential distribution in the KcsA channel and show that this mechanism is extendable to the NaK and NavAb channels (Figure 6).

The average electrostatic potential maps along the x-z plane (y = 0 Å) inside the channel pores for KcsA in different three states are shown in Figure 6(A) to Figure 6(C): in the absence of K⁺ before flipping (“w/o K⁺, before flipping”), in the absence of K⁺ after flipping (“w/o K⁺, after flipping”), and in the presence of K⁺ (“w/K⁺”). The electrostatic potential changes along the channel axis in these systems are show in Figure 6(D). The electrostatic potentials in all three maps are uniform in bulk water regions away from the lipid membrane and the protein. However, difference arises between these maps particularly in the selectivity filter region. For instance, prior to the flipping of the Val76 carbonyl oxygen, there is a large and deep electrostatic potential valley in selectivity filter region (Figure 6(A) and Figure 6(D)). This electrostatic potential valley is caused by

the dense, negatively charged oxygen atoms of the backbone carbonyls. As a consequence, these negatively charged carbonyl oxygen atoms tend to escape from this region (e.g., via flipping), due to a strong repulsive electrostatic force imposed by the electrostatic potential valley. When the flipping occurs, the electrostatic potential valley becomes insignificant, indicating that the repulsive electrostatic forces become much weaker, and the structure of selectivity filters should be more stable (Figure 6(B) and Figure 6(D)). It is noteworthy that, if K⁺ ions are present in the selectivity filter, a slightly positive electrostatic potential can be observed, indicating that the carbonyl oxygen atoms are not subject to strong repulsive electrostatic forces (Figure 6(C) and Figure 6(D)). Therefore, the huge difference in electrostatic potential leads to the distinct stability of the selectivity filter, between systems with and without the presence of K⁺. Indeed, not restricted to Val76, other residues in the selectivity filter such as Tyr78 also experience reorientation due to the electrostatic repulsion, but however, at a lower extent.

We also calculated the electrostatic potential distributions in the NaK and NavAb channels, as shown in Figure 6(E) and Figure 6(F). Prior to the flipping of the Val64 carbonyl oxygen, there is a large and deep electrostatic potential valley in the selectivity filter region of NaK channel (black solid line in Figure 6(E)). Just like the situation in KcsA, the induced repulsive electrostatic force on the negatively charged carbonyl oxygen atom results in its flipping. Compared with the KcsA channel, the electrostatic potential valley in NaK channel is less significant (Figure 6(E)), and therefore in good agreement with the smaller conformational change of the NaK selectivity filter. In sharp contrast to the KcsA and NaK channels, the electrostatic potential in the NavAb channel does not display significant valleys (Figure 6(F)), and as a result, the electrostatic interaction in the selectivity filter region is relatively weak and the structure is stable. In addition, in the presence of coordinated ions, the smooth electrostatic potential profiles for all the three channels (red solid curves in Figure 6(D) to Figure 6(F)) are consistent with the observation of very high stability in this situation (see Figure 2(A)).

The number and strength of hydrogen bonding networks between residues in the selectivity filter and its adjacent pore helix (especially Glu71) are thought to play an important role in the structural stability of the KcsA selectivity filter [4] [5] [38]. Herein, careful examination of the present simulation trajectories identifies a few key hydrogen bonds closely related to the conformational change process. The backbone amide group of Tyr78 forms a hydrogen bond with the side chain of Glu71 (Figure 7(A); denoted as i), and the backbone amide group of Gly77 forms a hydrogen bond with the carbonyl oxygen in the backbone of Glu71 (denoted as ii). We first calculated the surviving probability of these two hydrogen bonds, before the flipping of Val76. Note that, the simulation trajectory with K⁺ in the selectivity filter was used for these calculations, because the trajectory without K⁺ in the filter involves very few frames before flipping, and thus cannot offer reliable statistics. We find that the surviving probability of the hydrogen bond ii is 31.85%, significantly lower than the hydrogen bond i at 60.47% (Figure 7(B)). Thus, the hydrogen bond ii may first be broken if no ions were present in the selectivity filter, facilitating the flipping of Val76. Meanwhile, the relatively robust hydrogen bond i, the breaking of which is relevant to the narrowing around Gly77, is in agreement with the observation that not all four subunits of the KcsA channel undergo narrowing.

In addition to the hydrogen bonds i and ii, we also identified a previously unnoticed hydrogen bond, formed between the carbonyl group of Val76, in its flipped conformation, and the backbone amide group of Tyr78 (Figure 7(C); denoted as iii). To explore the relevance of this hydrogen bond to the narrowing

of selectivity filter, we calculated the probability distribution of local radius R of the selectivity filter and distance d between the backbone amide nitrogen of Tyr78 (possible donor for the hydrogen bond iii) and carbonyl oxygen of Val76 (possible acceptor). The probability distribution map shows two visible spots. The upper right spot is centered at R = ~5.2 Å and d = ~5 Å; the large d value impedes the formation of the hydrogen bond iii, and the large R value means the absence of narrowing. In contrast, the lower left spot is centered at R = ~2.7 Å and d = ~3 Å; the small d value facilitates the formation of the hydrogen bond iii, and meanwhile, the small R value indicates the occurrence of narrowing.

Because the selectivity filter in the NaK channel shows similar conformational change process with the KcsA channel filter, we discuss below the hydrogen bonds in the NaK channel equivalent to those in the KcsA channel. The backbone amide group of Gly65 forms a hydrogen bond with the backbone carbonyl oxygen of Val59 (Figure 8(A); denoted as i), and the carbonyl group of Val64, in its flipped conformation, forms a hydrogen bond with the backbone amide group of Asp66 (Figure 8(C); denoted as ii). As shown in Figure 7(B), the hydrogen bond i that helps stabilize the Val64 carbonyl oxygen has a higher surviving probability in all four subunits than that in the KcsA channel. This observation is in line with the fact that the NaK channel filter is more stable than the KcsA channel filter. In addition, the hydrogen bond ii is seen to be formed only in chain B which is the sole subunit that undergoes narrowing (Figure 8(D)). This result confirms the above observation in the KcsA channel that the formation of this hydrogen bond is crucial for the narrowing of selectivity filter.

We also inspected the hydrogen bonding networks in NavAb and identified four hydrogen bonds supporting the structure of selectivity filter (Figure 9). Note that, different from KcsA and NaK, the simulation trajectory without ions in the NavAb selectivity filter is used for subsequent analysis. The Glu177 side chain of NavAb is supported by an elaborate architecture. The Glu177 side chain

forms a hydrogen bond (denoted as i) with the Ser178 side chain, and a hydrogen bond (denoted as ii) with the backbone amide group of Met181 from the neighboring subunit. These two hydrogen bonds stabilize the Glu177 side chain directly. The carbonyl group of Glu177 forms a hydrogen bond (denoted as iii) with the Gln172 side chain, which further stabilizes the selectivity filter. Moreover, the hydrogen bond (denoted as iv) formed by Thr175 and Trp179 in the adjacent subunit forces the Thr175 and Leu176 carbonyls to point toward the pore lumen. Except for the hydrogen bond iii, the surviving probabilities of these key hydrogen bonds are very high (>75%), such that the selectivity filter of NavAb is quite stable even in the absence of Na⁺ ions.