Inner pore hydration free energy controls the activation of big potassium channels

Abstract

Hydrophobic gating is an emerging mechanism in regulation of protein ion channels where the pore remains physically open but becomes dewetted to block ion permeation. Atomistic molecular dynamics simulations have played a crucial role in understanding hydrophobic gating by providing the molecular details to complement mutagenesis and structural studies. However, existing studies rely on direct simulations and do not quantitatively describe how the sequence and structural changes may control the delicate liquid-vapor equilibrium of confined water in the pore of the channel protein. To address this limitation, we explore two enhanced sampling methods, namely metadynamics and umbrella sampling, to derive free-energy profiles of pore hydration in both the closed and open states of big potassium (BK) channels, which are important in cardiovascular and neural systems. It was found that metadynamics required substantially longer sampling times and struggled to generate stably converged free-energy profiles due to the slow dynamics of cooperative pore water diffusion even in the barrierless limit. Using umbrella sampling, well-converged free-energy profiles can be readily generated for the wild-type BK channels as well as three mutants with pore-lining mutations experimentally known to dramatically perturb the channel gating voltage. The results show that the free energy of pore hydration faithfully reports the gating voltage of the channel, providing further support for hydrophobic gating in BK channels. Free-energy analysis of pore hydration should provide a powerful approach for quantitative studies of how protein sequence, structure, solution conditions, and/or drug binding may modulate hydrophobic gating in ion channels.

Graphical abstract

Significance

Voltage-dependent gating of ion channels mediates numerous physiological processes by regulating ion flows in response to membrane potential changes. Many ion channels have been suggested to gate by dehydrating their inner pores without physically occluding the ion permeation pathway. Rigorous free-energy analysis allows quantitative studies of how various structural and physical properties control the pore dewetting in channel gating. This study focuses on BK channels crucial in cardiovascular and nervous systems. The results provide further evidence on how pore-lining residues modulate the stability of liquid water in the inner pore to affect voltage gating. This new mechanistic insight has important implications in how new therapeutics may be developed to target BK channels as well as other hydrophobic gating channels.

Introduction

Hydrophobic dewetting has been proposed to be involved in gating of an increasing number of transmembrane protein ion channels that may be activated by voltage, mechanical force, and/or ligand binding (1,2). This phenomenon arises because water is a surprisingly complex liquid that exists near the liquid-vapor equilibrium under physiological conditions (3). Confinement within a hydrophobic cavity, such as the inner pore of some channel proteins, can readily drive the equilibrium toward the vapor phase, resulting a dewetted state that is unfavorable to the penetration of ions without rehydration first. Members from many classes of ion channels have been suggested to utilize such a hydrophobic gating mechanism (1,2), including mechanosensitive channels (4,5), potassium channels (6), calcium channels (7), transient receptor potential channels (8), and magnesium channels (9). The conformational changes, which induce dewetting, are also diverse. To drive hydrophobic dewetting during gating, some channels require relatively small side-chain rearrangements (5,10), whereas others involve larger motions such as helix twisting (11) and $\alpha$-$\pi$ helix transition (12).

One particular ion channel of great physiological importance is the large conductance potassium (big potassium [BK]) channel, which is also known as slo1, MaxiK, or KCa1.1 (13). BK can be activated by both membrane voltage and intracellular Ca2+ to regulate neural excitability (14,15,16), neurotransmitter release (17), and muscle contraction (18,19). These channels are implicated in an array of human diseases including epilepsy, asthma, stoke, and hypertension (20). The BK channel protein consists of three major domains (Fig. 1 A): the voltage-sensing domain, which senses membrane polarization (15,21,22); the pore-gate domain (PGD), which is responsible for potassium selectivity, permeation, and channel gating; and the cytosolic-tail domain, which senses calcium binding and allosterically modulates channel opening independently of the voltage-sensing domain (23,24,25). The cryoelectron microscopy structures of both the human and Aplysia californica BK channels in the calcium-free, closed conformation revealed that the inner pore under the selectivity filter undergoes only a small contraction and remains physically wide open (Fig. 1 B) (26,27,28). This observation was not necessarily surprising because the BK inner pore was known to remain accessible to quaternary ammonium blockers and methanethiosulfonate reagents even in the deactivated state (29,30,31). It has thus been suggested that the selectivity filter of BK channels may also function as the gate (30,32,33). A study of the negatively charged activators (NCAs) of the two-pore potassium channel found that these NCAs bound in the pore beneath the filter and increased the single-channel conductance (32). Molecular dynamics (MD) simulations further suggested that the negative charge on these NCAs could increase K⁺ occupancy below the filter as a general activation mechanism applicable to BK and other potassium channels (32). Structural studies suggest that NCA binding is dynamic, and experimental support of the mechanism remains ambiguous. Furthermore, one of the NCAs of the BK channels has recently been shown to dramatically effect open and close dwell times but not the single-channel conductance (34).

Figure 1.

BK channel structure and key features. (A) Overall conformation in the Ca²⁺-free and presumably deactivated state. The structure was derived from PDB: 6V3G and further refined by MD simulations (see materials and methods). Voltage-sensing domain is drawn in red, the PGD in silver, and the cytosolic-tail domain in blue. (B) Two opposing PGD S6 helices and the selectivity filter (residues 273–330) in both the closed (silver) and open (periwinkle) conformations. A key pore-lining residue A316 is highlighted in red spheres. Potassium ions in the selectivity filter are drawn as gold spheres. To see this figure in color, go online.

Atomistic MD simulations have revealed that the inner pore of BK channels can readily undergo spontaneous dewetting in the calcium-free and presumably closed state, while the pore remains stably hydrated in the calcium-bound and open state (11). The dewetting transition is apparently driven by relatively modest conformational transitions in the PGD that lead to an elongated, narrower, and more hydrophobic inner pore. This illustrates how the liquid-vapor equilibrium of confined water can respond sensitively to changes in pore geometry and surface properties (2). The dry pore produces a “vapor barrier” to ion permeation but remains physically open and accessible to channel blockers and methanethiosulfonate reagents, which readily explains the aforementioned pore accessibility experiments in the closed state (29,30,31). The hydrophobic gating mechanism is also highly consistent with the previous systematic scanning mutagenesis studies showing that modulation of pore hydrophobicity is strongly correlated with the gating voltage of BK channels (35).

Existing studies of hydrophobic dewetting in ion channels have relied on direct MD simulations and are therefore limited by the slow water dynamics and conformational changes of protein channels (4,5,6,36,37,38,39,40). Such studies require extensive sampling on the order of μs for protein channels. They are generally incapable of generating reversible transitions to determine the pore hydration thermodynamics, which is necessary for quantitative analysis of how various structural and physical properties of the pore control hydrophobic dewetting in channel gating. Free-energy calculations have been employed to study hydration thermodynamics in carbon nanotubes and protein surfaces (41,42,43,44,45) but not in protein channels. This motivated our previous work to develop a well-tempered metadynamics (MetaD) protocol to sample reversible dewetting transitions in protein-like nanopores (46), where we showed that the free-energy cost of dewetting is mainly determined by two key thermodynamic parameters, namely the surface tension coefficients of the pore-water and pore-air interfaces (46). In this work, we apply the MetaD protocol to quantify the free-energy cost of inner pore hydration in BK channels. The results reveal a likely fundamental challenge in generating well-converged free-energy profiles within reasonable MetaD simulation times due to slow inherent diffusion along the desired collective variable (CV), namely the pore hydration number. Instead, we find umbrella sampling (US) to be highly effective for calculating the pore hydration free-energy profiles for BK channels in both open and closed states. Comparing the results for the wild-type BK channels and three pore-lining mutants shows that the free-energy costs of pore hydrating is strongly correlated with the experimentally measured gating voltages. We expect that efficient approaches for quantitative free-energy analysis of pore hydration will facilitate the exploration of the properties that ion channels use to control hydrophobic dewetting in gating.

Materials and methods

BK channel structures and atomistic simulation setup

The initial protein conformations for the closed and open human BK channels were taken from PDB: 6V3G and 6V38, respectively (28). Several short loops absent only in one structure were rebuilt using the other structure as template using the Swiss-PDB server (47) as described previously (48). Missing N- and C-terminal segments as well as several long loops (e.g., V53-G92, A614-V683, and D834-I870) are presumably dynamic and thus not included in equilibration simulations of the full-length channel. The protein constructs were solvated in POPC lipids, TIP3P water, and 0.15 M KCl plus neutralizing ions using the CHARMM-GUI server (49,50,51). The systems were described using the CHARMM36m protein (52) and CHARMM36 lipid force fields (53) and simulated using the GPU-enabled Gromacs 2019 (54,55). All hydrogen-containing bonds were constrained with the LINCS algorithm (56,57), and the MD timestep was 2 fs. Electrostatics were treated with the particle mesh Ewald algorithm (58) with a cutoff of 12 Å. van der Waals forces were smoothly switched off from 10 to 12 Å. The Nosé-Hoover thermostat (59,60) was used with T = 303.15 K and ${\tau }_T$ = 1 ps⁻¹. In constant number of particles, pressure, and temperature (NPT) simulations, the Parrinello-Rahman semiisotropic barostat was applied in x and y directions with p = 1 bar, compressibility = 4.5 × 10⁻⁵ bar⁻¹, and ${\tau }_p$ = 5 ps⁻¹.

Initially, each solvent box was minimized for 5000 steps with the steepest descent algorithm. Then, the system was equilibrated in several steps where the positions of heavy atoms of the protein and lipids were harmonically restrained (61,50). In each step, the force constants gradually decreased from 4000 to 0.1 kcal/(mol Ų). The final NPT equilibration was run for 10 ns with only protein heavy atoms restrained to ensure the box size remained stable. As described below, an additional simulation step was taken to relax a spurious and unstable $\pi$-helix turn (residues 317–320) in the S6 helices of the closed channel structure (Fig. S1). For all subsequent simulations and free-energy calculations, the cytosolic-tail domain was removed to mimic the Core-MT construct (62,63), which only includes the transmembrane domains and C-linker of mSlo1 and an 11-residue tail from the mouse K_V 1.4. These final simulation boxes are approximately 160 × 160 × 100 Å and contain ∼270,000 atoms. After generating each A316 mutation, the mutants were minimized by 50,000 steps of steepest descent followed by 1 ns NPT equilibration of the new side chain.

Structural relaxation of a spurious S6 π-helix turn in PDB: 6V3G

The Ca²⁺-free, closed structure of human BK channels (PDB: 6V3G) contains a π-helix turn in residues 317–320, which is not present in either the Ca²⁺-bound structure (PDB: 6V38) or the previous A. californica BK structures (26,28). Curiously, this π-helix turn does not appear to be consistent with the raw electron density map (28) (Fig. S1 A). In MD simulations, the $\pi$-helix turns spontaneously relax to α-helices (Fig. S1 B) and could give rise to substantial instability in the pore structure (e.g., Fig. S1 C). To more carefully relax and refine the S6 helices, we performed 100 ns of an equilibration simulation with position restraints applied to the P-loop, selectivity filter (T273 to D292), and RCK2 (A614 to C-terminus) and two additional sets of distance restraints designed to enforce the fourfold symmetry of the S6 helices. The first set of restraints ensure that the distance between S6 residues 312–325 in opposing pairs (chains A C versus chains B D) remain the same. They take the form $V_i=\frac{1}{2}k{\left(r_{ACi}-r_{BDi}\right)}^2$, where $k$ = 2 kcal/(mol Ų) and $r_{ACi}$ and $r_{BDi}$ are the distances between the Cα atoms of residue $i$ in opposing chains. The second set of restraints ensures that residues in neighboring chain pairs (e.g., chains A B versus chains B C versus chains C D versus chains D A) have the same distance apart, imposed using the same form as above. The S6 conformation stabilized within ∼50 ns during the 100 ns restrained simulation after modest changes relative to PDB: 6V3G. Independent 100 ns unrestrained simulations confirm that the relaxed conformation is more stable than the initial structure with the π-helical turns (see Fig. S1 C). Note that while the relaxed S6 helix no longer contains the spurious π-helix turns, the final backbone root-mean-square deviation of residues 312–325 is only ∼2 Å with respect to the initial structure PDB: 6V3G. Note that the initially hydrated pore spontaneously dewetted during the equilibration simulation (Fig. S1 D), consistent with our previous simulations of based on homology models derived from A. californica BK channel structures (11).

MetaD for enhanced sampling of reversible pore hydration

Sampling many reversible dewetting transitions requires an enhanced sampling technique, which biases the water count in the pore. MetaD is an appealing technique for its power, the simplicity of analysis, and the fact that it generates continuous trajectories (64,65,66,67,68,69,70,71). In particular, for the well-tempered MetaD, biasing potentials or “hills” are deposited at a fixed deposition rate along a selected CV, and the height of the hills decreases as a function of the total bias potential accumulated at each CV position (65). The sampling efficiency can be tuned by judicious selection of the key parameters such as the hill size, deposition rate, and so-called bias factor that controls how quickly the hill height is reduced as bias potential accumulates. Rationale for the selection of these parameters have been thoroughly discussed in the literature (46,65,71).

The natural choice of CV for MetaD simulations of hydrophobic dewetting is the number of water molecules within the pore region (N_water). We used the open-source, community-developed PLUMED library (72), v.2.7 (73), to define our CVs. The large size of a fully solvated transmembrane protein simulation box motivated the use of the PLUMED COORDINATIONNUMBER CV (74), which uses a neighbor list to speed up the N_water calculation. For example, a cutoff distance of 20 Å coupled with an update frequency of every 10 MD steps leads to ∼threefold acceleration for the current systems with ∼270,000 atoms. Specifically, N_water is defined as the total occupancy of all water oxygen atoms within a predefined sphere (Fig. 2). The center of the sphere was chosen to be the center of mass of Cα atoms of all four M314 residues to optimally position the sphere based on water counts in the original unbiased simulations (11) such that the maximally dewetted region was encompassed by the sphere. The occupancy is one within the sphere and smoothly switches to zero beyond the sphere. Specifically, the Gaussian switching function, $S\left(r\right)={\mathrm{e}}^{{\left(-\frac{r-D_0}{2R_0}\right)}^2}$, was used when ${r>D}_0$ with the sphere radius $D_0$ = 8 Å and Gaussian width $R_0$ = 1.5 Å. Here, $r$ is the distance between each water oxygen and the center of mass of the Cα atoms of all four M314 residues. The switching function was truncated at $D_{\mathit{MAX}}$ = 13 Å such that $S\left(r\right)$ = 0 for all distances $r>D_{\mathit{MAX}}$ and normalized with $S_{norm}\left(r\right)=\frac{S\left(r\right)-S\left(D_{\mathit{MAX}}\right)}{S\left(D_0\right)-S\left(D_{\mathit{MAX}}\right)}$. During MetaD simulations, N_water was restrained with a flat-bottom wall potential between 2 and 90 and with a force constant of 50 kcal/mol to prevent the system from hitting the hard wall at 0 or over-sampling unneeded space in the CV, respectively. We observed occasional penetration of lipid tails into the pore region through fenestrations between the S6 helices in the closed state, and the dynamics of lipid tail diffusion is slow (e.g., see Figs. S2 and S3). To prevent these rare events and achieve better convergence of the pore hydration sampling, we use a similar “coordination” CV to impose a restraint for preventing a lipid tail group from entering the pore. A linear penalty was applied to the lipid count with the form: $E\left(N_{lipid}\right)=k{N}_{lipid}$, with $k$ = 40 kcal/mol to prevent lipids from penetrating deep into the pore region. Specifically, the Gaussian switching function was used with cutoff distance $D_0$ = 5 Å, switching length $R_0$ = 1 Å, and $D_{\mathit{max}}$ = 9 Å. The neighbor list for pore lipid occupancy has a cutoff of 20 Å and an update frequency of every 10,000 MD steps. Note that the slow diffusion of lipids permits infrequent updates.

Figure 2.

Definition of pore water for BK channels. Two facing PGDs are drawn in silver cartoon from residues 230 to 330. The spherical counting region centered on the center of mass of M314 is drawn as a transparent blue sphere with a radius of 9.2 Å, which corresponds to the distance within the switching region where the occupancy is 0.5. Pore-lining residues I312, A316, P320, and E324 are drawn with the licorice style, together with water molecules within 10 Å of the central axis. Potassium ions within the filter are shown as gold spheres. To see this figure in color, go online.

As done previously (46), we carefully evaluated the effect that the well-tempered MetaD parameters have on the efficient sampling of pore hydration. The choice of bias factor sensitively impacts both the convergence and the space that can be sampled efficiently (Fig. S4). An aggressive bias factor of 20, with a hill height of 0.2 kcal/mol and deposition rate of 0.1 ps–1, led to excellent sampling of reversible pore hydration transitions (Fig. S4 A) but poor convergence in the free-energy profile (Fig. S4 B). A mild bias factor of three with a larger hill height of 0.6 kcal/mol and faster deposition rate of 1 ps⁻¹ resulted in fewer reversible hydration transitions (Fig. S4 C) but a curious appearance of better converged free-energy profiles (Fig. S4 D). In the results, we will further analyze the challenges of MetaD simulations for generating reliable free-energy profiles using a representative protocol with moderate choices of various parameters. Specifically, the protocol includes a deposition rate of 0.1 ps⁻¹, hill height of 0.2 kcal/mol, hill width of 1 unit, and a bias factor of 5. The hills were accumulated on a grid with minimum at 0 and maximum at 92 and with default grid spacing of 0.2 units for better efficiency in long MetaD runs. All protein Cα atoms were harmonically restrained with a force constant of 0.1 kcal/(mol Ų) during MetaD simulations. The potential mean forces (PMFs) are calculated as the cumulative sum of all the bias potentials from the start to the specified time point, negating that result and shifting the minimum to zero.

US and analysis of pore hydration and ion permeation

US (75) is a well-established free-energy simulation protocol frequently used to study proteins (76). US simulations were performed using the same N_water CV as described above, with sampling windows spaced every 5 units of N_water. The initial configuration for each window was chosen from representative snapshots from MetaD simulation trajectories that do not contain potassium ions in the pore. Similar restraints were applied to the protein and lipid tails as in the MetaD protocol (see above). For each window, the N_water CV is harmonically restrained with a force constant of 0.2 kcal/mol. The total sampling time in each window was 10 ns, with snapshots saved every 10 ps. Upon inspection of the biased histograms, the windows centered at N_water = 15 and 20 for both the closed wild-type (WT) and closed A316I mutant channels were extended for an additional 10 ns to allow for improved convergence, for a total of 20 ns in those windows only. We only covered the regions of the N_water space with free energy no greater than ∼10 kcal/mol. We estimated the extent of this space based on the volume available in the WT and the size of each mutant side chain. Additional windows were added later as needed. The total sampling time of US calculations for each PMF ranges from 90 ns for A316D in the opened state (nine windows) to 140 ns for A316 and A316I in the closed state (12 windows, two windows for 20 ns total). The weighted histogram analysis method (WHAM) (77,78) was used to construct the PMF along the CV with a bin width of 1 water unit. For WHAM analysis, the first 1 ns of each window were discarded, and the remaining frames were analyzed as two separate blocks to estimate the errors. For windows extended to 20 ns, the initial 5 ns prior to full equilibration was discarded. The final PMFs are the average PMF from the two blocks, and the error bars are the difference between the two blocks divided by $\sqrt{2}$. Analysis of the dependence of convergence on sampling time per window in a representative case is given in Fig. S5, showing that the overall PMF started to converge with 5 ns sampling in most regions of N_water CV. We chose 10 ns sampling time unless otherwise noted to ensure a high level of convergence for subsequent analysis of inner pore mutants.

US was also used to calculate the free energy of ion permeation through the inner pore of BK channels. For this, we used the z-distance to the selectivity filter as the CV, and eight windows were evenly spaced by 2 Å from 22 to 8 Å. The location of the filter was chosen to be the center of mass of the backbone heavy atoms of residues 286, 287, and 288, which is within the so-called S4 potassium binding site of the filter (79). Harmonic restraints were used along the z-distance to the filter of the ion with a force constant of 200 kJ/(mol nm²) or 0.48 kcal/(mol Ų). Each window was run for 20 ns, except that the window at 16 Å was extended for an additional 20 ns (Fig. S6). 1D PMF was calculated for the full trajectories using WHAM as described above. WHAM was also applied to calculate the 2D PMF as a function of ion z-distance to the filter and N_water. Note that there is no bias on N_water during US of ion permeation, so each 2D histogram was effectively reweighted using its single 1D (K⁺ z-distance to filter) weight. The convergence in the N_water can be expected to be limited without bias in that dimension. The convergence was analyzed using separate 2D PMFs of the first and last halves of the sampling (Fig. S7). All plots were generated with matplotlib (80), and all molecular representations were rendered with VMD (81). Example plumed run files for the final MetaD and US protocols are stored on GitHub at https://github.com/enordquist/BKDewet_SI.

Results

Challenges in achieving convergence with MetaD: Slow inherent dynamics of cooperative pore hydration

MetaD was highly effective in our previous study of hydration free energy of model nanopores with smooth wall surfaces (46). Real protein pores have several important differences, including roughness of the surrounding pore surface and the presence of a mixture of hydrophobic and hydrophilic chemical groups. Nonetheless, MetaD is able to drive many reversible pore hydration transitions within 500 ns for the WT BK channel in the closed state (Figs. 3 A and S4), providing one to two orders of magnitude acceleration compared with direct MD simulations (11). Curiously, the resulting PMF profiles remain oscillatory even with 500 ns simulation time (Figs. 3, B and C). This is somewhat surprising and in strong contrast to the case of model nanopores, where 50 ns MetaD simulations were sufficient to generate well-converged pore hydration free-energy profiles even for a case with >10 kcal/mol free-energy differences between the dry and hydrated states (46). We have carefully reexamined the choice of MetaD parameters, particularly the hill deposition pace and bias factor (e.g., see Fig. S4), which together control how quickly the biasing potential accumulates (46,65). The results suggest that the apparent challenge of achieving stable convergence of hydration free-energy profile of the BK channel pore is likely not due to overly aggressive MetaD protocol (e.g., with fast pace and/or large bias factor). In fact, the MetaD protocol used in Fig. 3 is much less aggressive than those used in the previous study of model nanopores, with 10-fold reduction in the hill deposition rate and twofold reduction in the bias factor.

Figure 3.

MetaD simulation of pore hydration the wild-type BK channel in the closed state. (A) N_water as a function of simulation time during a 500 ns MetaD simulation. (B) PMFs from successive 50 ns blocks drawn as an accumulation of bias (see materials and methods). See materials and methods for details of the MetaD protocol. (C) Fluctuation of the relative free energy at N_water = 40 with respect to the minimum (near N_water = 10) as a function of the simulation length. To see this figure in color, go online.

The poor convergence of BK pore hydration free energy even with 500 ns sampling time makes MetaD ineffective for quantitative analysis of how various factors control hydrophobic gating. This challenge may be attributed to the inherent dynamics of diffusion along the CV. A fundamental premise of MetaD is that, given a properly chosen CV that captures the rate-limiting degrees of freedom, if a bias potential can be accumulated to cancel out all free-energy barriers, the system would be able to readily diffuse along the CV well within an acceptable time frame (e.g., ∼ns for model nanopores). This premise does not seem to hold even for the relatively simple N_water CV here. Due to the rugged protein surface and presence of hydrophilic patches, the cooperative dewetting and rehydration transitions of the BK pore are relatively slow even in the barrierless limit. For example, as illustrated in Fig. 3 A, the major barrier (N_water ∼ 20) can be readily crossed (due to the bias potential), yet the crossing processes remain slow, with an average length of ∼50 ns. As a result of the slow diffusion along N_water, biasing hills keep accumulating to drive the diffusion along the CV, analogous to tidal waves behind a surfer, leading to oscillatory PMFs as shown in Figs. 3, B and C. Therefore, even though MetaD is a powerful method for driving many realistic barrier-crossing transitions, it can be ineffective for generating well-converged PMFs. This drawback appears to be a fundamental one for any situation where the diffusion along the selected CV is slow such that the time required for the system to spontaneously fluctuate between the desired range along the CV is long even in the barrierless limit. Importantly, many nontrivial CVs, such as those describing protein conformational transitions, likely share slow inherent diffusion dynamics, and great caution should be taken when deploying MetaD to derive free-energy quantities.

US yields well-converged PMFs of BK pore hydration

To address the convergence problem encountered using MetaD, we turned to US (75), where harmonic biasing potentials are imposed along the CV and the system is restrained to fluctuate within small subspaces instead of the whole range of interest. This feature is highly effective for overcoming the slow inherent dynamics of diffusion along the CV. For example, a total of 12 simulation windows, each lasting 10 ns, was sufficient to cover the space between N_water = 0 and 65 for the WT BK channel in the closed state (Figs. 4, A and B). The two windows neighboring the barrier around N_water = 18 were run for an additional 10 ns. Together, well-converged free-energy profiles of pore hydration were readily generated (Fig. 4 C), even though the total sampling time of 140 ns was only about ∼1/4 of MetaD runs. The converged PMF reveals a dehydrated pore state (N_water ∼ 6) and a metastable partially hydrated state (N_water ∼ 36) (Fig. 4 C). The relatively small apparent barrier of ∼1.8 kcal/mol further supports the notion that the key challenge of generating converged PMFs of pore hydration is the slow diffusion kinetics along N_water due to hidden barriers in the orthogonal degrees of freedom. Due to the hydrophobic nature of the BK pore in the closed state, there is no local minimum for the fully hydrated state, which should locate at N_water ∼60, estimated based on high-temperature simulations (see Fig. S8).

Figure 4.

US for calculating the pore hydration free-energy profile of the wild-type BK channel in the closed state. (A) N_water as a function of time during 10 ns US for all windows. The additional 10 ns of sampling in windows 15 and 20 are not shown. (B) Raw (biased) histograms of N_water for all windows. (C) 1D PMF as a function of N_water calculated using WHAM. Representative snapshots are shown for three selected hydration states. The S6 helix and filter region of two opposing subunits are drawn in silver. Potassium ions in the filter are drawn in gold, and pore waters are drawn as bonds with oxygen in red and hydrogen in white. Residue A316 are highlighted in cyan. Error bars shown are difference between results derived from the first and second halves of the production sampling divided by squared root of 2. To see this figure in color, go online.

Pore hydration explains effects of pore-lining mutations on channel gating

It was previously shown that mutations to deep-pore residues L312, A313, and A316 sensitively perturb the gating voltage of BK channels (35) and that the effect of these mutations correlated strongly with the side-chain hydrophobicity (11). It was speculated that changes in side-chain solvation as a result of rearrangement in the open-closed transition were involved (35), which was not supported by recent cryoelectron microscopy structures (26,27,28). The discovery of hydrophobic gating in BK suggests that these mutants may control channel gating by modulating inner pore hydration (11). To more rigorously test this, we performed US simulations to calculate the free-energy cost of pore hydration for three selected mutations of pore-lining A316, located at the center of the BK inner pore. Fig. 5 compares the PMFs of pore hydration of the WT BK channel and three A316 mutants in both the open and closed states. The open state is clearly well hydrated in the WT channel and all three mutants (Fig. 5 A) as expected; each of the constructs is conductive with sufficient membrane depolarization and/or intracellular Ca²⁺ binding (35). The differences in preferred number of waters in the pore is likely due to the volume occupied by the additional side-chain heavy atoms as well as changes in the pore surface hydrophobicity. For example, A316I introduces 12 additional heavy atoms and significantly increases the hydrophobicity of the pore surface, leading to ∼20 fewer waters in the optimally hydrated state compared with the WT channel (Fig. 5 A, blue versus gray curves).

Figure 5.

Pore hydration PMF for wild-type and three mutant BK channels in both open (A) and closed (B) states. Representative snapshots are shown for the state of free energy minimum for each of the mutant channel. The S6 helix and filter region of two opposing subunits are shown in silver cartoon, potassium ions in the filter in gold spheres, and pore waters as bonds with oxygen in red and hydrogen in white. Side chains of residues at position 316 are drawn in blue, red, and green for A316I, A316S, and A316D, respectively. Error bars shown are difference between results derived from the first and second halves of the production sampling divided by squared root of 2. To see this figure in color, go online.

On the other hand, the closed WT channel is preferentially dehydrated but contains a metastable partially hydrated state that was also observed in unbiased simulations (11). The hydrophobic mutation A316I, which stabilizes the closed state and increases the gating voltage, increases the free-energy cost of this partially hydrated state (Fig. 5 B, blue versus gray curves). In fact, the metastability of that state is greatly affected such that the barrier around N_water = 18 is removed, leading to a smooth downhill slope from the hydrated state to dewetted state. As a result, the mutant A316I pore dewets much faster than the WT channel without lingering in a partially hydrated state, as was observed in previous simulations of the analogous A316V mutant (11). Conversely, polar and charged mutations (A316S and A316D), which destabilize the closed state and reduce the gating voltage, increase the stability of the partially hydrated state. In the case of A316D, the dry state becomes extremely unstable (>>10 kcal/mol), and the channel can be expected to remain conductive even in the absence of membrane depolarization or Ca²⁺ binding, as also shown experimentally (35). Note that the barrier for crossing between the partially hydrated and dewetted states in the WT, A316S, and 316I is near N_water = 20. Here, water wires starting to evaporate into the pore tend to either form stable water bubbles or collapse back to the mouth of the pore (Fig. S9). Notably, the fully hydrated state corresponding to N_water = 60 is significantly stabilized in the A316S and A316D mutations by about 4 and 5 kcal/mol, respectively.

Experimentally measuring the gating voltage reports the free-energy cost of channel opening at some given Ca²⁺ concentration, which includes contributions from both the protein conformational transition and changes in the pore hydration state (35). The former may be assumed to be similar for all constructs because the A316 position is pore lining and not involved in structural contacts. As such, we examine if the measured shift in gating voltage may be directly correlated with the free-energy cost of hydrating the closed pore. For this, we first determine the required hydration level for ion conductance by calculating the 2D free-energy surface as a function of ion permeation and pore hydration (see materials and methods). As shown in Fig. 6, N_water increases to about 40–50 as the ion enters the pore (z-distance ∼18 Å). There appear to be two key barriers for the ion to reach the filter (and permeate through the channel). The major one is the initial hydration of the pore, at N_water ∼20 and z-distance ∼17 Å, where the pore flickers between water wires and bubbles (e.g., see Fig. S9). The second barrier is a mild one, where the pore remains partially hydrated with N_water ∼40 to 50 as the ion approaches the filter. Based on the free-energy analysis, we identified N_water = 45 is a representative partially hydrated and potentially conductive state and extracted the hydration free energy (ΔG_hydr) from the PMF profiles shown in Fig. 5 B. Note that ΔG_hydr for A316D is only approximate due to an extremely unfavorable dry state. The experimental $\Delta$V_1/2 (shift in voltage where the channel open probability is 50%) is also undefined, as the channel remains fully conductive even at extreme depolarization (<−200 mV) (35). The ΔG_hydr and ΔV_1/2 for A316D were estimated to ∼20 kcal/mol and ∼400 mV, respectively, and are denoted with an empty circle and dashed error bars, respectively, to reflect the approximate nature of these values. The results, summarized in Fig. 7, show that the ΔG_hydr of the closed state correlates very well with the experimentally derived ΔV_1/2 shifts. The strong correlation reveals that the pore hydration property is a key determinant of changes in the voltage-gating properties of the BK channels. This is an important observation and provides further support to the hydrophobic gating mechanism in BK channels.

Figure 6.

2D free-energy surface of pore hydration and potassium permeation. The surface was derived from US simulations as a function of N_water and the z-position of K⁺ relative to the selectivity filter. Black contour lines and color bar ticks are drawn at the same energy levels and are drawn every 2 kcal/mol. 1D PMFs along N_water and K⁺ positions are shown along the top and left sides, respectively. Convergence analysis is provided in Figure S7. To see this figure in color, go online.

Figure 7.

Correlation of BK pore hydration free energy and shift in gating voltage. The experimental ΔV_1/2 values were taken from Chen et al. (35). The dry and wet states are taken at N_water = 8 and 45, respectively. The markers for A316D are an empty circle and dashed error bars to denote its approximate nature (see text). The dashed line indicates a linear fit. To see this figure in color, go online.

Conclusions

We explore two enhanced sampling approaches for determining the hydration free energy of nanoscale inner pores of transmembrane protein ion channels, which have been suggested to be involved in the gating of many channels. It was found that even though MetaD could readily drive many reversible pore hydration and dewetting transitions using the pore hydration number as the CV, the resulting free-energy surface of hydration of the inner pore of BK channels would converge surprisingly slowly. This is due to the slow dynamics of cooperative pore water diffusion even in the barrierless limit. Instead, we showed that the conventional US was much more effective in calculating well-converged PMFs with less sampling time compared with MetaD. We applied US to calculate the hydration PMFs of the human BK channel in both the open and closed states, as well as for three pore-lining mutants of the BK channel, namely A316S, A316I, and A316D, which are experimentally known to strongly modulate the channel gating voltage. The results show that the pore hydration in the closed conformation has a finite free-energy cost roughly commensurate with the barrier of ion permeation and further reveal that the free-energy cost of hydrating the pore to a conductive state correlates with the experimentally determined shift in the gating voltage of these channels. Therefore, the pore-lining mutations mainly tune pore hydration in the closed state to modulate voltage activation, strongly supporting the hydrophobic gating mechanism in BK channels. Quantitative analysis of pore hydration free energy will likely play a key role in elucidating the molecular mechanism of drug molecules including channel activating compounds (82), which have been shown to modulate pore opening solely via interactions with the PGD (32, 34).

Author contributions

E.B.N., Z.J., and J.C., conception of the study; E.B.N. and Z.J., performing the simulations and analyses; E.B.N., Z.J., and J.C., analysis of results and writing and revision of the manuscript.

Editor: Alan Grossfield.