Small molecule NS11021 promotes BK channel activation by increasing inner pore hydration

Abstract

The Ca²⁺ and voltage-gated big potassium (BK) channels are implicated in various diseases including heart disease, asthma, epilepsy and cancer, but remains an elusive drug target. A class of negatively charged activators (NCAs) have been demonstrated to promote the activation of several potassium channels including BK channels by binding to the hydrophobic inner pore; yet the underlying molecular mechanism of action remains poorly understood. In this work, we analyze the binding mode and potential activation mechanism of a specific NCA named NS11021 using atomistic simulations. The results show that NS11021 binding to the pore in deactivated BK channels is nonspecific and dynamic. The computed binding free energy of −8.3±0.7 kcal/mol ($K_D=0.3-3.1\mathrm{\mu }\mathrm{M}$) calculated using umbrella sampling agrees well with the experimental EC50 range of 0.4–2.1 μM. The bound NS11021 remains dynamic and is distal from the filter to significantly impact its conformation. Instead, NS11021 binding significantly enhances the pore hydration due to the charged tetrazol-phenyl group, thereby promoting the opening of the hydrophobic gate. We further show that the free energy barrier to K⁺ permeation is reduced by ~3 kcal/mol regardless of the binding pose, which could explain the ~62-fold increase in the intrinsic opening of BK channels measured experimentally. Taken together, these results support that the molecular mechanism of NS11021 derives from increasing the hydration level of the conformationally closed pore, which does not depend on specific binding and likely explains the ability of NCAs to activate multiple K⁺ channels.

Graphical Abastract

Introduction

Ion channels are an important class of drug targets and are the targets for ~20% of drugs with FDA approval.¹ The Ca²⁺ and voltage-gated K⁺ channel (Figure 1A), also referred to as K_Ca1.1, MaxiK, or big potassium (BK) channel,^2–4 has been extensively studied for its role in the nervous system,⁵ smooth muscle contraction,^6,7 and hearing.⁸ It has been implicated in numerous diseases, including stroke,^9–11 ischemia-reperfusion injury,^12,13 asthma,^14–16 epilepsy,^17–20 urinary bladder disorder,^21–23 rheumatoid arthritis^24,25 and cancers of numerous types.^26–28 Several BK channel activators are on the market for treating breast cancer,²⁹ epilepsy,^30,31 and blood flow,³² and Andolast has been approved in Italy as asthma medication.³³ Despite these advances, the BK channel remains a challenging drug target and there are no compounds with FDA approval that directly target the BK channel. This deficit is not for a lack of tool compounds with known activity for the BK channel.^34–36 Rather, it is due to challenges such as designing molecules specific for a tissue-localizing β or γ subunit and achieving sufficient potency yet minimal off-target effects.^37,38 Another important challenge lies in limited understanding of the molecular mechanisms of action of known compounds.

Figure 1: Structures of the BK channel and activator NS11021.

A) Human BK channel α subunit in the Ca²⁺-free, presumably deactivated state (PDB: 6v3g³⁹). For clarity, only two of the four VSD (red) and PGD (silver) are rendered. The CTD is blue and the K⁺ in the selectivity filter are gold. B) Chemical structure of NS11021, with tetrazol-phenyl (AZ) and trifluoromethyl-phenyl (FB) groups labelled. Partial charges of the AZ group are shown in Figure S1 and in the Gromacs parameter file accessible from the Data and Software Availability section.

The BK channel α subunit is a homotetramer, composed of a transmembrane (TM) region which houses two domains, and a cytosolic tail domain (CTD) primarily responsible for sensing Ca²⁺ (Figure 1A). The TM region includes a voltage sensing domain (VSD), which consists of five TM helices S0-S4, and pore gating domain (PGD), which consists of the two innermost TM helices S5-S6 and the K⁺ selectivity filter (Figure 1A). The smooth muscle relaxant NS11021 (Figure 1B),^21,40,41 is a BK channel activator known to act on the pore.⁴² It belongs to a class of negatively-charged activators (NCA) of K_2P, hERG and BK channels.⁴³ These NCAs share a common pharmacophore that contains a negatively charged group attached to aromatic and hydrophobic moieties. X-ray crystallography together with cysteine-scanning mutagenesis and molecular docking revealed that the NCA BL-1249 binds to the TREK-2 K_2P channel in the pore with the negatively-charged group pointed towards the selectivity filter.⁴³ The binding location of BL-1249 was inferred from peaks in anomalous difference maps interpreted as the location of a bromine atom in brominated BL-1249, as no other electron density corresponding to BL-1249 was observed.⁴³ Patch-clamp electrophysiology experiments revealed that BL-1249 increases the single-channel conductance of TREK-2,⁴³ putatively by inducing a change in selectivity filter conformation.⁴⁴ Atomistic simulations further suggested that the increase in conductance results from the stabilization of K⁺ binding beneath the filter (in the “S6” site).⁴³ Similar positioning of K⁺ ions was previously shown via atomistic simulation to alter the conformation of the selectivity filter, thereby opening the filter gate of K_2P channels.⁴⁴ It was proposed that the NCA NS11021 acts on the BK channel via a similar mechanism.⁴³

There are several key experimental observations which inform how NS11021 acts on the BK channel. Rockman, et al. showed that NS11021 activity had little Ca²⁺-dependence and that truncation of the CTD did not significantly alter its activity, suggesting that NS11021 does not interact with the CTD.⁴⁵ Furthermore, NS11021 activity has minimal voltage-dependence, suggesting that it has minimal impact on VSD activation or VSD-PGD coupling.⁴⁵ By fitting many voltage-dependent dose-response curves with the Hill equation, they showed that the molecule binds in a 1:1 molar ratio with the channel. Together, these electrophysiological analyses strongly support the notion that the molecule binds in the central pore and acts on the PGD itself, consistent with the observation from X-ray crystallography.⁴³ The authors further performed limiting slope experiments, where the voltage-dependence of the channel’s intrinsic open probability $P_O$ was measured down to −200 mV in 0 Ca²⁺, a regime in which the VSD is resting. The results reveal that NS11021 increases the $P_O$ by 62-fold at 30 μM, the molecule’s aqueous solubility limit. Therefore, the primary effect of NS11021 is to shift the pore open-close equilibrium towards the open state, by increasing the average open state dwell time while substantially decreasing the average dwell time of closed states.⁴⁵ However, NS11021 does not significantly the increase single-channel conductance,⁴⁵ which suggests that the activity of NS11021 in BK is not likely through the putative filter-gate previously proposed.⁴³

In this study we use atomistic molecular dynamics (MD) simulations to examine the molecular detail and free energy of NS11021 binding to the inner pore of the BK channel in the deactivated state. The results show that the NS11021 binds nonspecifically to the hydrophobic surface of the pore and remains highly dynamic inside the pore, which could explain a lack of resolvable density for NCA BL-1249 in TREK2 discussed above.⁴³ The calculated free energy of binding of ~ −8 kcal/mol is consistent with published experimental EC50 measurements.^42,45 Importantly, the presence of NS11021 in the pore significantly increase the level of hydration. This effect is significant because it has been proposed that BK channels likely followed the hydrophobic gating mechanism, where the pore undergoes a spontaneous dewetting transition to deactivate the channel.^46–48 Increasing the pore hydration will stabilize the hydrated open state, as suggested by electrophysiological analysis.⁴⁵ Furthermore, analysis of K⁺ permeation free energy profiles with NS11021 in three representative binding conformations show that the free energy barrier is reduced by 3–5 kcal/mol compared to the empty pore. This is in good agreement with the experimentally derived 62-fold shift in the intrinsic $P_O$ induced by NS11021,⁴⁵ which corresponds to a 2.5 kcal/mol decrease in the K⁺ permeation barrier. Taken together, these results strongly support that NS11021 promotes BK activation by lowering the barrier to pore hydration instead of direct modulation of the putative filter gate.

Methods

Parameterization of small molecule NS11021

Molecular model parameters for the NS11021 ligand were assigned by identifying similar atom, bond, angle, dihedral types as well as charges from similar small molecules within the CHARMM General Force Field (CGenFF).^49,50 Parameter assignment using CGenFF was carried out in this fashion because the automated assignment with CGenFF web application gave large charge and parameter penalties for bromo-tetrazol-phenyl group and the thiourea dihedrals, likely because similar molecules were not in the CGenFF training set. The structure of this group was optimized at the MP2/6–31G* level using the program GAMESS,^51–53 and the atomic charges were then calculated using the Merz-Singh-Kollman scheme⁵⁴ as implemented in the Multiwfn program⁵⁵ (Figure S1). The CGenFF parameters released in July 2022 included a methylthiourea torsional profile with barriers of 5 kcal/mol. We simulated a single NS11021 molecule in CHARMM TIP3P water for 100 ns using the July 2022 thiourea dihedral parameters and observed many reversible transitions. All four syn- and anti- combinations (Figure S2) were accessible with stabilities differing by ~1–3 kcal/mol (Figure S3), in qualitative agreement with solution NMR data of diaryl-thiourea compounds.⁵⁶ See Data and Software Availability section for the GitHub repository for the model topology and parameter files.

Atomistic simulations of BK channels

The BK channel structure was derived from the apo-structure 6v3g.³⁹ We used the same system setup as previously described, including initial minimization, seven steps of NVT equilibration while iteratively lowering restraints on the system’s components, and additional relaxation simulations to allow a spurious π-helix bulge on the pore-lining S6 helix to spontaneously refold back to a continuous α-helix.⁴⁸ We performed all simulations using only the TM region and C-linkers to mimic the Core-MT construct,^57,58 which retains voltage gating but has no Ca²⁺ dependence. All C_α atoms of the protein were harmonically restrained with a force constant of 0.2 kcal/mol/Ų during free energy calculations. The simulations were performed using the MPI-enabled GROMACS version 2019^59,60 and PLUMED version 2.7.^61,62 The initial simulation box with a POPC lipid bilayer, TIP3P water and 150 mM KCl plus neutralizing ions was generated using the CHARMM-GUI webserver.^63,64 The final simulation boxes were approximately of dimension 160 × 160 × 100 Å, and contained ~270,000 atoms. We observed frequent reversible lipid entry through the fenestration window between S6 helices, as observed consistently in previous simulations and multiple cryo-EM maps.^{39,46–48,65} Occasionally, some lipid tails may remain in the pore for tens of ns. To avoid sampling these infrequent events during umbrella sampling free energy calculations (see below), a linear restraint of the form $k{N}_{lipid}$ with $k=40\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$ was imposed to prevent the lipids from fully entering the pore using the PLUMED collective variable (CV) COORDINATION, as previously described.⁴⁸

The systems were described using the CHARMM36m protein^66,67 and CHARMM36 lipid⁶⁸ force fields, and CHARMM TIP3P water with rigid internal geometry.⁶⁹ Lengths of all hydrogen-containing bonds were constrained with the LINCS algorithm,^70,71 the MD timestep was 2 fs, Electrostatics were treated with the particle mesh Ewald algorithm⁷² using a 12 Å distance cutoff, and Van der Waals forces were smoothly switched off from 10 to 12 Å. The Nosé-Hoover thermostat^73,74 was used with reference temperature of 303.15 K and coupling constant ${\tau }_T$ of 1 ps⁻¹. Constant pressure was imposed using the Parrinello-Rahman^75,76 semi-isotropic barostat in $x$ and $y$ directions using reference pressure of 1 bar, compressibility of 4.5 × 10⁻⁵ bar⁻¹, and pressure coupling constant ${\tau }_P$ of 5 ps⁻¹.

Umbrella sampling of NS11021 binding to the pore

Four independent unbiased simulations were run with NS11021 in different bound configurations generated using steered MD simulations and each one lasted 250 ns. The results showed that NS11021 had sufficient space in the pore to sample a wide range of orientations and binding configurations, even though the exchange appeared relatively slow compared to umbrella sampling timescales (up to 100 ns per window). Accordingly, we performed umbrella sampling simulations in two parallel sets, initiating each set of windows with either the (3,5)- FB or AZ group facing up (towards the pore and filter) (Figure 1B). Sampling from both sets of windows will be combined to derive the overall free energy surface. In each umbrella sampling window, harmonic distance restraint potential was imposed on the z-distance between the centers-of-mass (CoM) of NS11021 and the selectivity filter with a force constant of 0.5 kcal/mol/Ų. The CoM of the selectivity filter is determined using the backbone heavy atoms of residues 286, 287 and 288, which effectively corresponds to the S4 K⁺ binding site.⁷⁷ In all windows flat-bottom harmonic restraints were applied to the x- and y-distance of the COM of the molecule from the axis of the pore with a width of 16 Å with a force constant 5 kcal/mol/Ų to improve convergence. To generate the initial binding configurations of all windows, two 8-ns steered MD simulations were performed with either the FB or AZ group pointing up towards the filter. Both sets of umbrella sampling simulations consist of five windows centered at z-distance to filter of 12, 14, 16, 18, and 22 Å, respectively.

We note that a metastable state occurs in several unbiased trajectories where the CoM of NS11021 reaches to the filter and blocks it substantially. This state is a kinetic trap which complicates our analysis of the interaction of NS11021 in the pore with water and at most one K⁺ during the K⁺ permeation PMF calculations. We proceeded with our analysis and subsequent umbrella sampling focusing on states where only part of the molecule interacts directly with the filter, but the CoM reaches only to ~10 Å.

During umbrella sampling simulations, NS11201 could rarely exchange between “AZ-up” and “FB-up” orientations (Figure S4, Figure S5, and Figure S6). This adds to the sampling challenge, and thus requires long sampling time of 100 ns per window to achieve sufficient convergence in the final free energy surfaces. In addition, four windows centered at 24, 26, 29 and 32 Å were added to improve sampling in the bulk region outside the pore (Figure 2B). Finally, to improve convergence around the narrowest region of the pore where sampling of NS11021 binding configurations is slow, four more windows were added to the 12–16 Å region as follows: two windows centered at 14 and 16 Å, respectively with initial FB-up orientations, one window centered at 16 Å with the AZ and FB groups at the same level, and one window centered at 12 Å in an AZ-up orientation with N_water harmonically restrained at 15 with a force constant of 0.2 kcal/mol/N_water². All windows lasted 100 ns and snapshots were saved every 5 ps for subsequent analysis. We discarded the initial 5 ns of each window and used the remaining samples to construct potentials of mean force (PMFs) using the weighted histogram analysis method (WHAM).⁷⁸ See Data and Software Availability section for the GitHub repository for the configuration files and initial structures for umbrella sampling.

Figure 2: Umbrella sampling of NS11021 binding to the BK pore.

Representative snapshots and z-distance to the filter histograms for the set of windows with NS11021 in the A) FB-up and B) AZ-up orientations. Panel B) also shows histograms and a representative snapshot from the four bulk sampling windows (see Methods). Representative snapshots depict two opposing pore-lining S6 helices and the selectivity filter (residues 273–330) in silver. Potassium ions are drawn as gold spheres, and NS11021 and water molecules are drawn as bonds, where oxygen atoms are drawn in red, hydrogen in white, carbon in cyan, nitrogen in blue, fluorine in purple, and bromine in pink. Note that the pore is largely dehydrated without NS11021.

Calculation of K⁺ permeation free energy

To compute the K⁺ permeation PMF without NS11021, we used eight umbrella sampling windows along the K⁺ z-distance to the filter CoM as defined above from 22 Å to 8 Å spaced in 2 Å increments. The initial binding configurations were generated using a 2-ns steered MD simulation. In each window, the selected K⁺ was harmonically restrained using a force constant of 1.0 kcal/mol/Ų. All windows were run for 20 ns, and the first 1 ns was discarded in WHAM analysis. To calculate the K⁺ permeation PMF with NS11021 bound in the pore, we selected representative conformations of three distinct bindings states and harmonically restrained the CoM of NS11021 along the pore’s z-axis to the initial position with a force constant of 0.5 kcal/mol/Ų. This restraint allows the molecule to respond to K⁺ but prevents NS11021 from moving too far from the initial pose. The same distribution of eight umbrella sampling windows was used as described above. For most windows, 20 ns was sufficient since there was minimal interaction between K⁺ and NS11021. However, in the windows centered at 8, 10, 12 and 14 Å, NS11021’s z-distance and orientation with respect to the filter, as well as the K⁺ z-distance to the filter, required extended equilibration over the first ~15 ns (Figure S7). Consequently, these windows were extended to 100 ns, and the initial 15% of sampling with NS11021 present were discarded prior to analysis.

Analysis of simulations

The WHAM⁷⁸ was used to calculate the PMFs of K⁺ permeation with the first and second halves of sampling after discarding the initial equilibration region of each window. Each PMF is the mean of these two blocks and the error bars are the difference between the two blocks divided by $\sqrt{2}$. The bulk PMF was obtained from 200 ns unbiased simulation, with the average of the region > 30 Å set to 0 kcal/mol, and the other PMFs were aligned to the bulk region by a single shift of 0.1 kcal/mol. 2D WHAM was used to reweight and combine all windows and to generate combined PMFs along the biased CV as well as an additional unbiased CV such as pore water count ($N_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$) and the orientation of NS11021. The orientation of NS11021 in the pore was characterized using the difference in z-distances from the filter of the CoMs of the FB and AZ groups, ΔZ_FB-AZ. ΔZ_FB-AZ < 0 indicates that the FB group is closer to the filter (FB-up), and ΔZ_FB-AZ > 0 indicates that the AZ group is closer to the filter (AZ-up). When ΔZ_FB-AZ ≈ 0, NS11021’s long axis is perpendicular to the pore Z axis, and the internal dihedral conformation is mainly syn-syn (Figure S2). The level of convergence was examined by comparing 2D PMFs derived from the first and second halves of umbrella sampling trajectories (after discarding the initial 5 ns). As shown in Figure S8. even though sampling of some of the deep pore orientational states are not fully converged (due to the slow exchange timescale as noted above), the overall PMF is well converged, particularly along the z-distance to the filter dimension (e.g., see the two 1D marginal plots along z-distance). Combining windows generated from two distinct binding configurations using WHAM can be potentially misleading, since the relative weight of the two “pathways” will be assumed to be equal. Figure S9 shows 2D PMFs that result from combining the windows outside the pore, centered at Z = 24–32, with windows spanning Z = 12–22 with either AZ-up or FB-up initial binding configurations, which shows that the $\Delta G_{bind}$ remains ~8 kcal/mol in both cases, which provides reasonable evidence that the windows can be safely combined.

To estimate the overall $K_D$ and free energy of NS11021 binding to the pore, we first derived the bound and unbound populations and then calculated $K_D=P_{unbound}/P_{bound}$ and $\Delta G_{bind}=RTln{K}_D$. There is no need to account for the Jacobian entropy correction necessary in normal radial PMFs since we applied flat-bottom harmonic restraints to keep the molecule within an approximately-constant volume as inside the pore. Since $K_D$ is a dimensionless quantity, we implicitly multiply by the standard concentration $C^0=1\mathrm{M}$ to compare it to experimental EC50 values. Often in the literature this factor is implicit, since $K_D$ is widely referred to as $\frac{\left[P\right]\left[L\right]}{\left[PL\right]}$ with units M, rather than the dimensionless $\frac{\left[P\right]\left[L\right]}{C^0\left[PL\right]}$.⁷⁹ The z-distance cutoff of 30 Å was used to identify the bound versus unbound state. The errors in $K_D$ and ${\Delta G}_{bind}$, were estimated as the standard error of results calculated from the first and second halves of the umbrella sampling trajectories. To obtain the EC50 of NS11021 at 0 mM Ca²⁺, NS11021 ${\mathrm{V}}_{1/2}$ data from Rockman, et al. were fit to the log-dose response curve using the Hill equation (Figure S10),

$${\mathrm{V}}_{\frac{1}{2}}\left(\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{C}\right)=\mathrm{m}\mathrm{a}\mathrm{x}+\frac{\mathrm{m}\mathrm{i}\mathrm{n}-\mathrm{m}\mathrm{a}\mathrm{x}}{1+10^\left({\mathrm{n}}_{\mathrm{h}\mathrm{i}\mathrm{l}\mathrm{l}}\mathrm{*}\left(\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{E}\mathrm{C}50-\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{C}\right)\right)},$$

where $logC$ is the log-dose concentration (in μM), $min$ and $max$ are the minimum and maximum $logC$, and the $n_{hill}$ and $logEC50$ are fitted parameters. The fit yielded EC50 = 2.1 μM. We are assuming in our analysis of both the computed ${\mathrm{K}}_{\mathrm{D}}$ and experimental EC50 that the dominant reference state is the aqueous solution, based in part on the relatively small volume of bilayer available in a patch-clamp electrophysiology experiment. All molecular renderings were created with VMD version 1.9.3,⁸⁰ and all data plots were created with matplotlib.⁸¹

Results and Discussion

NS11021 remains dynamic in the pore of BK channels

NS11201 is highly dynamic in solution, with both the AZ and FB groups freely rotatable around the central thiourea group (Figure 1B). A recent solution NMR study of the dihedral conformational propensity of diaryl-thiourea compounds demonstrated that several conformations involving syn-anti isomerization are accessible in solution (Figure S2).⁵⁶ Using the dihedral parameters for methylthiourea CHARMM36 force field released in July 2022, we found that indeed NS11021 is dynamic in solution (Figure S3). The least stable state is the most extended anti-anti state, which agrees with the NMR data on phenylthiourea compounds⁵⁶ and is consistent with the limited solubility of NS11021.⁴⁵ Equilibrium simulations with NS11021 in various bound conformations generated using steered MD simulations confirms that the drug remained highly dynamic inside the deactivated BK pore. As illustrated in Figure 2, not only the internal thiourea dihedrals are quite dynamic in the pore, but also the overall position (z-distance to the filter) and orientation (ΔZ_FB-AZ) can exchange between various states on the 50 – 100 ns timescale. Figure S10 shows three additional 250-ns equilibrium simulations initiated from different initial binding configurations, which display similar dynamics in both the internal conformation and the overall binding position and orientation. Such a heterogenous and dynamic bound state of NS11021 in the deactivated BK pore is not surprising considering that the pore is relatively large and hydrophobic and there is a lack of any significant pockets to support specific binding. Note that NS11021 is more dynamic than BL-1249 in previous simulations in the pore of TREK-2,⁴³ which is a secondary diarylamine with two relatively bulky groups (Figure S12).⁸² Nonetheless, the lack of resolvable density for the bound BL-1249 in the pore suggests that its binding to TREK-2 may be dynamic as well.⁴³

NS11021 binds the pore via nonspecific hydrophobic interactions

To better characterize the interaction of NS11021, we employed umbrella sampling to sample its conformations and orientations within the confinement of the BK pore. As detailed in Methods, we employed two parallel sets of windows, where the initial binding configuration of each window was either ΔZ_FB-AZ > 0 or ΔZ_FB-AZ < 0. The sampling of all these windows, as well as several windows to sample the bulk solvent region, were combined to produce a single 2D PMF of NS11021 interaction with the BK pore (Figure 4). The PMF highlights a broad conformational landscape with multiple minima of similar free energy levels within the pore, consistent with the observations from the equilibrium MD runs with NS11021 in the pore (Figure 3 and Figure S11). Initial binding is driven primarily by hydrophobic interaction between the hydrophobic FB group and the pore walls, while the charged AZ group remains solvated. As a result, there is a strong preference of the molecule entering the pore in the FB-up orientation. Once NS11021 fully enters the pore (e.g., z-distance < 18 Å), it can sample all three major orientations (FB-up, AZ-up and flat) with similar probabilities. There is only a ‘forbidden region’ in the middle of the pore (z-distance ~13–14 Å) where ΔZ_FB-AZ cannot be near 0, due to steric constraints.

Figure 4: Free energy surface of NS11021 binding to the deactivated BK pore.

The 2D PMF was calculated as a function of the orientation of NS11021 (x-axis), described using ΔZ_FB-AZ (see Figure 3 caption), and the z-distance between the CoMs of NS11021 and the selectivity filter (y-axis). The color bar tick marks and black contours are each distributed in 2 kcal/mol intervals. The marginal plot is the 1D PMF of NS11021 as a function of z-distance from the filter, with error bars showing standard error calculated from block analysis as described in Methods. Representative conformations are shown for representative orientations (FB-up, Az-up and flat) drawn from three minima marked by green, pink and orange circles. The rendering style is the same as in Figure 2.

Figure 3: Dynamics of NS11021 in the deactivated BK pore.

A) Dihedral angles ${\varphi }_{FB}$ and ${\varphi }_{AZ}$ (see Figure 1B) and B) z-distance between the CoMs of NS11021 and the filter, and the orientational CV ΔZ_FB-AZ, defined by the relative z-distance between the CoMs of the FB and AZ groups to that of the filter. ΔZ_FB-AZ > 0 indicates AZ-up and ΔZ_FB-AZ < 0 indicates FB-up.

It is important to note that the nonspecific and dynamic nature of NS11021 interaction with the pore does not suggest that the binding is weak. The free energy as a function of z-distance to the filter reveals a broad and stable minimum of ~ −8 kcal/mol from z-distance ~ 10 – 20 Å (Figure 4). It can be estimated that the total binding free energy ${\Delta G}_{bind}=-8.3\pm 0.7\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$, which is equivalent to $K_D\left(K_D{C}^0\right)=0.3-3.1\mathrm{\mu }\mathrm{M}$ (see Methods). This is in good agreement with an EC50 of 0.4 μM reported by Bentzen, et al.⁴² Using data in Rockman, et al.⁴⁵ we estimated the EC50 to be 2.1 μM (Figure S10), which again agrees well with the umbrella sampling free energy calculation. We note that directly comparing experimental EC50 range to the calculated $K_{\mathrm{D}}$ range assumes that the relationship between NS11021 binding and binding-driven activation is approximately linear, which may not be the case. NS11021 may bind to other parts of the BK channel and in more than just the inactivated state. The distribution of open-state dwell times calculated by Rockman, et al.⁴⁵ demonstrates that NS11021 could indeed affect both states. However, most of the orthogonal experimental evidence, namely the dramatic change in closed-state dwell times and the increase in the intrinsic $P_O$, suggests that NS11021 binds in the closed state. The agreement between our calculated $K_D$ and experimental EC50 suggests that interaction with the closed pore may dominate the measured effects. Furthermore, the agreement rests on the assumption that the kinetic trap state near the filter involving interactions with the filter K⁺ ions, as the presence or absence of a K⁺ in the pore affects many things including pore hydration and drug configuration in a non-trivial and slowly-converging fashion.

NS11021 promotes the pore hydrating in the closed state

The pore of BK channels remains physically open with a diameter of ~ 10 Å in the deactivated state.^{39,65,83–86} It has been proposed that these channels follow the hydrophobic gating mechanism, where the hydrophobic pore undergoes spontaneous dewetting to create a (water) vapor region to block the ion flow.^46–48 We have previously shown that the free energy cost of hydrating the pore correlates well with the measured gating voltage of mutant BK channels.⁴⁸ We observed that NS11021 binding significantly increase the pore water number from both equilibrium and umbrella sampling simulations (e.g., see Figures 2 and 3), apparently due to the charged AZ group (Figure 1). Using the umbrella sampling simulations of NS11021 binding, we calculated the 2D PMF of NS11021 binding and pore hydration ($N_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$) (Figure 5). When NS11021 is outside of the pore, the pore remains stably dehydrated and experienced rare partial hydration events (z-distance > 25). Once NS11021 enters the pore, the hydration free energy of the pore is significantly reduced. There is a new free energy minimum around $N_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}~20–30$ (and z-distance ~14 Å), which corresponds to a partially hydrated pore state with NS11021 bound in the inner pore. The increased pore hydration can be expected to shift the pore conformational equilibrium and stabilize the open hydrated pore state as previously suggested by Rockman et al.’s electrophysiological experiment and analysis⁴⁵ (also see Introduction).

Figure 5: Free energy surface of NS11021 binding and pore hydration.

The 2D PMF was calculated as a function of the number of waters in the pore (${\mathrm{N}}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$) (x-axis) and the z-distance between the CoMs of NS11021 and the selectivity filter (y-axis). The color bar tick marks and black contours are each distributed in 2 kcal/mol intervals.

An important effect of NS11021 on BK channels is the 62-fold increase in intrinsic opening of BK channels.⁴⁵ It has been previously suggested that intrinsic opening is due to the leakage of the vapor barrier in hydrophobic gating,⁸⁷ which can be directly estimated from the free energy barrier of K⁺ permeation through the vapor barrier. For this, we selected three representative free energy basins from the 2D PMF (Figure 4), which represents FB-up, AZ-up and flat orientations, and calculated the PMFs of K⁺ permeation in presence of NS11021 in the deactivated BK pore (see Methods). The results, summarized in Figure 6, show that the barrier is reduced from ~7.5 kcal/mol to ~ 3–5 kcal/mol with NS11021 bound. This compares well to the 62-fold reduction in intrinsic opening, which suggests a reduction of ~ RT ln 62 = 2.5 kcal/mol in the free energy barrier of K⁺ leakage. The modest apparent over-estimation of K⁺ permeation free energy barrier reduction may be attributed to a few factors. The most important is that we did not consider the conformational response of the pore to NS11021 binding, due to the need to restrain the pore structure to achieve good convergence in free energy. It is possible that the pore may contract upon NS11021 binding, making it more difficult for a hydrated K⁺ to leak through. Furthermore, we did not explicitly consider the effect of slowly-exchanging orientations of NS11021 within the pore, which can have nontrivial effects on the K⁺ permeation through the deactivated pore.

Figure 6: Free energy of K+ permeation with NS11021 bound in the pore in three representative binding configurations.

NS11021 restrained to the representative states shown in Figure 4 (FB-up, AZ-up and flat). The black curve is the PMF without NS11021 in the pore as a reference, and the dashed curve is the PMF extending away from the protein into the bulk solute derived from unbiased simulations.

An article was recently published arguing that accounting for electronic polarization effects⁸⁸ in the confined environment of the BK pore may be important to derive quantitative properties such as hydration free energy,⁸⁹ which likely applies to interactions involving NS11021. Nevertheless, comparing experimental results to trends observed in the free energy calculations presented here is a robust way to meaningfully interpret said experiments.

Conclusions

Atomistic simulations and free energy analysis were performed to examine the molecular detail of binding and possible activation mechanism of a small molecule activator NS11021 on the BK channel. The results show that the molecules initially contacts the pore with the hydrophobic FB end facing into the dewetted, hydrophobic pore in the deactivated state. Once inside the inner pore, NS11021 remains dynamic and sample a wide range of conformational and orientational states. The dynamic binding mode is consistent with a lack of resolvable electron density in the X-ray crystallography despite mutational data supporting the pore binding. Despite the dynamic nature, the drug molecule makes extensive hydrophobic contacts with the inner pore. The effective $K_D$ of 0.3–3.1 μM derived from the free energy analysis agrees well with the experimental EC50 range of 0.4–2.1 μM.^42,45 The most prominent effect of NS11021 binding seems to be a substantial increase in the pore hydration. BK channels have been suggested to follow the hydrophobic gating mechanism, where the pore does not physically close but rely on hydrophobic dewetting to create a vapor barrier to block ion permeation.^46–48 As such, increased pore hydration by NS11021 likely drives the open-close equilibrium of the channel towards the open state suggested by electrophysiological analysis. It has been previously shown that intrinsic opening of BK channels likely derive from leakage of vapor barrier in hydrophobic gating.⁸⁷ Therefore, increased pore hydration level in the presence of NS11021 binding likely also explains the large 62-fold increase in intrinsic opening of the BK channel. Indeed, K⁺ permeation PMFs calculated with NS11021 restrained in three distinct and representative orientations reveal significant decrease of K⁺ leakage barrier, by 3–5 kcal/mol. Taken together, the current study provides new insights on the molecular basis of the activation effect of NS11021 on BK channels. The proposed mechanism of promoting hydration is largely insensitive to the NS11021 binding pose within the pore. Instead, it only requires nonspecific hydrophobic interactions mediated by the nonpolar moieties the drug molecule to bring the negative charged group into the pore and increase hydration propensity. Such a general mechanism could explain why the class of NCAs is able to activate many different K⁺ channels. This knowledge will inform the use of NCAs in studies of K⁺ channel function and may also prove useful in future efforts to directly target the hydrophobic gate via therapeutic agents.

Data and software availability:

The topology and parameters used for the whole system, including the NS11021 ligand, as well as all initial snapshots and representative GROMACS MD parameter (mdp) and PLUMED run files for the umbrella sampling simulations, are available at https://github.com/enordquist/BK_NS11021_SI/.