To establish a baseline for this investigation, we first examined the rate and mechanism of K⁺ permeation through activated Kv2.1 in the absence of any inhibitors. To do so, we carried out an all-atom molecular dynamics (MD) simulation of the channel embedded in a model phospholipid bilayer, under the influence of a transmembrane electric field (Figure 1). The channel structure employed in this calculation was that recently determined by Swartz and coworkers using cryo-EM (Fernández-Mariño et al., 2023); this structure comprises the pore domain and four voltage sensors (Figure 1), solubilized in a lipid nanodisc. To maximize the statistical significance of our results, the simulation was calculated using an Anton 2 supercomputer, which enabled us to generate a continuous 25 μs trajectory. The simulation was initialized with two K⁺ ions inside the narrowest portion of the pore, known as the selectivity filter, and no voltage difference across the membrane; after 500 ns, a voltage difference of 100 mV was introduced, positive on the inside. As shown in Figure 2A, at this point K⁺ ions begin to steadily flow across the channel in a single file and in an outward direction. In the observed mechanism, three K⁺ ions concurrently reside in the filter, fluctuating in a concerted fashion among five transient binding sites therein, termed S₀, S₁, S₂, S₃, and S₄ (Figure 2A and B). Arrival of an additional K⁺ ion through the cytoplasmic gate at a site termed S_cav, near the center of a water-filled cavity adjacent to S₄, leads to a metastable four-ion configuration. This configuration is short-lived, on account of the increased electrostatic repulsion between the K⁺ ions, and the incoming K⁺ ion often returns to the interior (not shown). An alternative outcome, fostered by the applied electric field, is the ejection of the outermost K⁺ ion from the filter into the extracellular space. This event is immediately followed by the outward movement of the two other ions within the filter, and that in S_cav, thereby restoring the initial three-ion configuration (Figure 2B). Four iterations of this molecular cycle thus result in a complete ion permeation event. As has been noted elsewhere, water molecules can co-permeate with K⁺ but do so rarely; in most of the observed permeation events, the ions become completely dehydrated near the center of the selectivity filter (Köpfer et al., 2014; Stix et al., 2023).

In total, we observed 45 complete permeation events, i.e., approximately one K⁺ ion traverses the channel from side to side every 0.5 μs. This high-throughput rate appears to be explained by the fact that K⁺ remains at near bulk density throughout the pore domain (Figure 2C); as K⁺ ions cross the channel, they encounter both free-energy wells and free-energy barriers, but it appears that the balance of intermolecular interactions therein is such that these features are relatively shallow and therefore do not cause large density variations, e.g., 100-fold or greater (Figure 2C). Experimental estimates of the single-channel conductance of Kv2.1 range from 8 to 10 pS depending on the precise condition and type of measurement (Pascual et al., 1997; Chapman et al., 2001; Trapani et al., 2006); by comparison, the permeation rate observed in our simulation translates into 3 pS. Given the myriad approximations and simplifications inherent to MD simulations, this result is very encouraging and suggests our methodology results in an adequate description of the mechanism of ion conduction of this channel. We therefore posit, by extension, that the same simulation design should be appropriate to examine how this mechanism might be modulated by an inhibitor, as described below.

TEA is a well-characterized nonspecific K⁺ channel blocker; it can inhibit K⁺ currents completely, whether applied externally or internally, albeit with modest potency. For Kv2.1 in particular, the IC values are around 5 and 0.2 mM, respectively (Taglialatela et al., 1991; Kirsch et al., 1995). Structural and computational studies carried out two decades ago using the bacterial homolog KcsA as a model system revealed that the binding site for internal TEA (and related quaternary-ammonium blockers) is adjacent to S_cav (Lenaeus et al., 2005; Faraldo-Gómez et al., 2007); from this finding, it is logical to infer that internal TEA enters the pore through the cytoplasmic gate and that it precludes K⁺ ions from reaching the selectivity filter.

To verify this putative inhibitory mechanism, which to our knowledge had not been directly demonstrated before, we carried out a simulation identical to that reported in the previous section, except that TEA was added in solution on the cytoplasmic side of the lipid membrane. The inhibitor was confined to explore a wide cylindrical volume co-axial with the pore but was otherwise permitted to diffuse freely. Under an applied voltage of 100 mV, however, TEA rapidly entered the channel interior through the cytoplasmic gate and did not return to the solution in a 5 μs trajectory (Figure 3A and B). Once in the water-filled cavity under the selectivity filter, the inhibitor continues to be highly dynamic, but tends to reside in a site about 1.5 Å away from S_cav (Figure 3C), and the nitrogen atom that carries the positive charge of the ammonium ion rarely deviates more than 2 Å from the pore axis (Figure 4A and B). Importantly, this simulation did not reveal a single K⁺ permeation event following TEA binding, in spite of the sustained transmembrane voltage driving K⁺ outward (Figure 3B); the inhibitor prevents cytoplasmic K⁺ ions from reaching S_cav (Figure 4B), and in doing so, it precludes the onset of the knock-on mechanism of permeation through the selectivity filter described in the previous section (Figure 2B).

As mentioned, RY785 is a specific, potent inhibitor of Kv2.1 (IC₅₀=50 nM) (Herrington et al., 2011), but the structural basis for this inhibitory activity has been unknown. Unlike TEA, RY785 is electroneutral and significantly larger, and thus it might have a very different mode of interaction with the channel. To examine this interaction and its mechanistic implications, we carried out an MD simulation identical in every way to that described above for TEA. (Note this simulation required development and optimization of a set of force field parameters for RY785, as described in Methods and in Appendix 1.) This simulation also showed that RY785 can readily penetrate the cytoplasmic gate, though more slowly than TEA (Figure 3D). While RY785 is not cationic, it features an electric dipole, and the 100 mV voltage difference applied across the simulation system (positive inside) orients the inhibitor as it enters the channel. Specifically, the m-methoxybenzene moiety passes through the gate first and is ultimately closer to the selectivity filter, while the benzimidazole and thiazole moieties, which are more electronegative, cross the gate last and thus end up being closer to the cytoplasmic space (Figure 3D and F). Like TEA, RY785 continued to be very dynamic inside the pore, though it primarily sampled a unique binding mode, in four different configurations reflecting the symmetry of the channel; displacements parallel to the pore axis were far less common than for TEA, and RY785 did not escape from the protein interior in a 5.5 μs trajectory (Figure 3E and F). Nevertheless, we observed that RY785 did not prevent the flow of K⁺ ions through the channel, nor did it significantly alter the knock-on mechanism within the filter (Figure 3E). Unlike TEA, RY785 does not prevent cytoplasmic K⁺ ions from reaching the S_cav site, though they clearly do so more rarely; thus, the permeation rate we observe is approximately four times slower than for the uninhibited channel (Figure 3E).

Further inspection of the simulation data reveals why RY785 does not block the outward flow of K⁺ ions. As shown in Figure 4, this inhibitor binds to the wall of the cavity through the benzimidazole and thiazole moieties; the m-methoxybenzene ring projects toward the center of the pore, but the high flexibility of this segment leaves an open pathway for K⁺ throughout the length of the cavity. Logically, this pathway is narrower than for the apo protein, explaining the slower permeation rate, but it is sufficient to permit K⁺ to access the S_cav site and ultimately enter the selectivity filter. This particular mode of interaction stems from persistent hydrophobic interactions with residues in the S6 helices (Figure 5). In particular, the most important contacts are Val409, Pro406, Ile405, Ile401, and Val398 in one or more subunits of the tetramer; among these, Pro406, Ile401, and Val398 appear to be key, as the inhibitor often contacts these residues simultaneously in two protein subunits (Figure 5A). As will be discussed below, this observation is important because several of these residues form the hydrophobic seal that closes the cytoplasmic entrance to the pore in the deactivated, closed state of the channel.

To corroborate the results described above, we used an alternative simulation design wherein no voltage difference was applied across the membrane to drive K⁺ outward. Instead, we induced a knock-on event within the selectivity by forcibly driving the central K⁺ ion (in either S₂ or S₃) to the S₁ site, reasoning this perturbation would result in the immediate ejection of the outermost K⁺, the movement of the innermost K⁺ into S₂ or S₃, and the creation of an artificial vacancy in the S₄ site. With either TEA or RY785 occupying the water-filled cavity, just as in the simulations described above, we asked which inhibitor would permit or preclude reloading of site S₄ by a K⁺ ion entering the pore through the cytoplasmic gate.

As shown in Figure 6, the ion dynamics within the selectivity filter were as anticipated, reproducibly and irrespective of which inhibitor is bound to the channel. The simulations with TEA and RY785 clearly differ otherwise. While TEA is bound, the S₄ site remains vacant after the induced knock-on event; only when TEA spontaneously diffuses back into the cytoplasm prior to the induced knock-on event (note that no electric field is applied) do we observe a K⁺ ion quickly binding to S₄, thereby restoring the preferred three-ion configuration (Figure 6A). Reloading of a K⁺ is also what we observed in all the simulations we carried out with bound RY785, consistent with the observation this inhibitor does not physically occlude the pathway for K⁺ into the selectivity filter in the open state of the channel (Figure 6B). These results are completely coherent with those obtained when voltage was used as a driving force for K⁺ flow in demonstrating that TEA is an open-channel blocker, but RY785 is not.

The MD simulations of activated wild-type Kv2.1 are based on the cryo-EM structure of the activated, open state (PDB entry 8SD3) (Tan et al., 2022). In all cases, the simulations examined a construct encompassing residues 174–426 (S1-S6), with neutral N- and C-termini and all ionizable side chains in their default protonation state at pH 7, which in this construct results in a net charge of zero. Two K⁺ ions were initially positioned in the selectivity filter, one coordinated by residues 373 and 374 (site S₃) and another by residues 375 and 376 (site S₁) (Figure 1C); a third ion was positioned below the side chain of 373, outside the filter, and two water molecules were modeled between the three ions. (This configuration was very short-lived and replaced by others in which three K⁺ ions concurrently occupy the filter, typically without water molecules in between – see Results.) For all systems, we used Dowser (Zhang and Hermans, 1996) to model structural water molecules within the protein that were not resolved in the experimental density maps. To complete the initial simulation setup of the experimental cryo-EM structure, the construct including ions and water molecules was energy-minimized using CHARMM (Brooks et al., 2009) and the CHARMM36m force field (Huang et al., 2017; Best et al., 2012; Klauda et al., 2010); specifically, the minimization used the steepest-descent algorithm for 250 steps, and then conjugate-gradient algorithm for another 250 steps.

The channel was simulated in a POPC lipid bilayer and a 300 mM KCl solution. (Note that while this concentration is atypical in the intracellular environment, it is often used in electrophysiological studies. In the simulation context, this choice is sensible in that it leads to a greater number of permeation events, and therefore, greater statistical confidence in the calculated ion conductance, or its inhibition.) To generate a molecular model of this membrane/solvent environment, we created a coarse-grained (CG) POPC-lipid bilayer in 300 mM KCl in an orthorhombic box of ~150×150×100 Å using insane.py (Wassenaar et al., 2015). To equilibrate this CG system, we carried out a 20 μs MD simulation using GROMACS 2018.8 (Pronk et al., 2013) and the MARTINI 2.2 force field (de Jong et al., 2013; Marrink et al., 2007) at constant temperature (303 K) and constant semi-isotropic pressure (1 atm) and with periodic boundary conditions. The integration time-step was 20 fs. We then embedded the structure of the Kv2.1 channel in this environment; to do so, the atomic structure of the channel was first coarse-grained with martinize.py (de Jong et al., 2013) and overlaid onto the equilibrated membrane/solvent system, removing all overlapping lipid and water molecules. Then, to optimize the resulting protein/lipid/solvent interfaces, we carried out a 10 μs MD simulation of the complete system using GROMACS 2018.8 (Pronk et al., 2013) and MARTINI 2.2 (de Jong et al., 2013; Marrink et al., 2007) at constant temperature (303 K) and constant semi-isotropic pressure (1 atm), with periodic boundary conditions and an integration time-step of 20 fs. Having ascertained the equilibration of the membrane structure and of the position and orientation of the protein in the lipid bilayer, the final snapshot of the CG trajectory was transformed into an all-atom representation compatible with the all-atom CHARMM36m force field (Huang et al., 2017; Best et al., 2012; Klauda et al., 2010). To do so, lipid and solvent molecules were back-mapped onto all-atom models (Wassenaar et al., 2014), while the CG version of Kv2.1 was replaced (not back-mapped) with the energy-minimized all-atom construct described above, after optimally superposing the Cα trace of the latter onto that of the former. The resulting all-atom molecular system includes 526 POPC lipids, 38,629 water molecules, and 208 K⁺ and 239 Cl⁻ (300 mM KCl) in an orthorhombic box of ca. 150×150×100 Å. To further optimize this all-atom model, the simulation system was first energy-minimized for 5000 steps with NAMD 2.13 (Phillips et al., 2020; Fiorin et al., 2013) and CHARMM36m (Huang et al., 2017; Best et al., 2012; Klauda et al., 2010), using the conjugate-gradient algorithm. We then carried out a series of MD simulations wherein structural restraints applied to the protein and ions/water within the selectivity filter are progressively weakened over the course of ~150 ns, as previously described (Stix et al., 2023; Tan et al., 2022). These simulations were carried out using NAMD 2.13 (Phillips et al., 2020; Fiorin et al., 2013) and CHARMM36m (Huang et al., 2017; Best et al., 2012; Klauda et al., 2010) at constant temperature (298 K) and constant semi-isotropic pressure (1 atm) with periodic boundary conditions and an integration time-step of 2 fs. Electrostatic interactions were calculated using the Particle-Mesh Ewald method (Darden et al., 1993), with a real-space cutoff value of 12 Å; van der Waals interactions were also cut off at 12 Å, with a smooth switching function taking effect at 10 Å.

To quantify the ion-conducting properties of activated Kv2.1, a 25 μs MD trajectory was calculated under an applied voltage (positive inside) using an Anton 2 supercomputer (Shaw et al., 2014) and the all-atom CHARMM36m force field (Huang et al., 2017; Best et al., 2012; Klauda et al., 2010). The starting configuration for this simulation was the final configuration of the abovementioned equilibration process. The simulation was again carried out at constant temperature (298 K) and semi-isotropic pressure (1 atm), using the Nosé-Hoover thermostat (Nosé, 1984; Hoover, 1985) and the Martyna-Tobias-Klein barostat (Martyna et al., 1994), respectively, with periodic boundary conditions and an integration time-step of 2.5 fs. Electrostatic interactions were calculated using the Gaussian-split Ewald method (Shan et al., 2005); van der Waals interactions were cut off at 10 Å. To preclude large-scale changes in the secondary or tertiary structure of the channel that might develop in the 25 μs timescale, due to cumulative force field inaccuracies, the energy function of the simulation was supplemented with a weak biasing potential that favors the known experimental geometry, while permitting the structure to locally fluctuate as required for ligand recognition and ion permeation (Stix et al., 2023; Tan et al., 2022). This potential acts on all ϕ\begin{document}$\phi $\end{document}, ψ\begin{document}$\psi $\end{document}, and χ1\begin{document}$\chi _{1}$\end{document} dihedral angles in the protein and is defined by:U(θt)=k∑m=1m=6(−1)m[1+cos⁡(mθt−m(θexpt−180))]/m!\begin{document}$$\displaystyle U\left (\theta _{t}\right)=k\sum _{m=1}^{m=6}\left (- 1\right)^{m}[1+\cos(m\theta_t-m(\theta_{expt}-180))]/m!$$\end{document}

where θt\begin{document}$\theta _{t}$\end{document} is the value of each dihedral angle at time t\begin{document}$t$\end{document} in the simulation, θexpt\begin{document}$\theta _{expt}$\end{document} denotes the corresponding value in the experimental structure, and k=1kBT\begin{document}$k=1k_{B}T$\end{document}. Note this potential is identical to that used in previous studies based on multi-microsecond Anton 2 simulations (Pan et al., 2019; Jensen et al., 2012; Park et al., 2023), except the magnitude of the bias in this study is considerably weaker (i.e. smaller k). To drive K⁺ ions outward, a transmembrane voltage difference was applied across the membrane, positive inside. This voltage difference was applied as a jump from 0 to 100 mV at timepoint 0.5 μs and sustained thereafter. The desired voltage resulted from the application of an outwardly directed, constant electric field perpendicularly to the membrane plane (Gumbart et al., 2012). For a simulation box of approximately 92 Å in that direction, a voltage difference of 100 mV corresponds to an electric field of 0.024 kcal mol⁻¹ Å⁻¹ e⁻¹ (note that 1 kcal mol⁻¹ Å⁻¹ e⁻¹ = 43.4 mV/Å).

Additional MD simulations were carried out to examine the mode of TEA and RY785 binding and inhibition. These simulations used, as a starting point, the final configuration of the 25 μs MD trajectory described above; a molecule of TEA or RY785 was added about 10 Å below the cytoplasmic gate, and overlapping water molecules were removed. These constructs were then energy-minimized using CHARMM (Brooks et al., 2009) and the CHARMM36m force field (Huang et al., 2017; Best et al., 2012; Klauda et al., 2010); specifically, the minimization consisted of 100 steps using the steepest-descent algorithm with the protein and K⁺ ions within fixed. To further optimize these all-atom models, the simulation systems were then energy-minimized for 5000 steps with NAMD 2.13 (Phillips et al., 2020; Fiorin et al., 2013) and the CHARMM36m force field (Huang et al., 2017; Best et al., 2012; Klauda et al., 2010), using the conjugate-gradient algorithm. Again using NAMD 2.13, we then carried out a 20 ns MD simulation of each channel-inhibitor system wherein weak structural restraints identical to those used in the 25 μs MD trajectory were applied to the protein. In addition, a flat-bottom confining potential was applied to TEA or RY785 to keep the inhibitor inside a cylindrical volume co-axial with the channel pore, 20 Å in diameter. Specifically, we used atoms Y376:C_β and V409:C_β in the four protein subunits to define this axis, and the inhibitor was confined by a potential of the form:U(dt)=0.5k(dt−do)2ifdt>do\begin{document}$$\displaystyle U\left (d_{t}\right)=0.5k\left (d_{t}- d_{o}\right)^{2}\,if\,d_{t}\gt d_{o}$$\end{document}U(dt)=0ifdt≤do\begin{document}$$\displaystyle U\left (d_{t}\right)=0\,if \,d_{t}\leq d_{o}$$\end{document}

where dt\begin{document}$d_{t}$\end{document} is the distance between the center-of-mass of the inhibitor and the channel axis, perpendicularly to that axis, do\begin{document}$d_{o}$\end{document} is 10 Å and k=100\begin{document}$k=100$\end{document} kcal/mol/Ų. To preclude the inhibitor from diffusing across the periodic boundary of the system (i.e. preserving it in the cytoplasmic side of the channel), a confining potential of the same functional form was also applied relative to the center of the four V409:C_β atoms; in this case, dt\begin{document}$d_{t}$\end{document} is the projection of the distance onto the channel axis, while do\begin{document}$d_{o}$\end{document} is 15 Å. Following these 20 ns equilibrations, trajectories of 5 and 5.5 μs were calculated on Anton 2 for the TEA and RY785 systems, respectively, using exactly the same settings as those reported above for the channel-only simulation.

The simulations described in Figure 6 used, as starting point, the final configurations of the trajectories calculated with Anton 2 for the channel-inhibitor systems (Figure 3). In these starting configurations, three K⁺ ions occupy the selectivity filter, and TEA or RY785 resides within the cavity. To create a vacancy in the S₄ site, without a voltage difference across the membrane, the central K⁺ ion (which fluctuates between S₂ and S₃) was driven outward at t=100 ns, by activating a set of restraints that bring the ion within coordination distance of the carbonyl O atoms of Y376 and G375 in all four subunits (ca. 3 Å, k=3 kcal/mol/Ų). As a result, the outermost K⁺ ion (which fluctuates between S₀ and S₁) was ejected, and the innermost K⁺ ion moved to the center of the filter, creating the desired vacancy in S₄. The simulations were then continued for 100 ns to examine whether or not K⁺ ions would reload this vacancy. These simulations were carried out using NAMD 3.0b6 (Phillips et al., 2020; Fiorin et al., 2013) and the CHARMM36m force field (Huang et al., 2017; Best et al., 2012; Klauda et al., 2010). All other settings, including confining potentials, were as described above.

To our knowledge, no molecular-mechanics (MM) force field for RY785 was publicly available prior to this work. Thus, a new force field had to be developed and optimized to be able to introduce this molecule in our simulations of Kv2.1 – specifically one compatible with the CHARMM General Force Field, or CGenFF (Vanommeslaeghe and MacKerell, 2012). Following recommended procedures (Vanommeslaeghe and MacKerell, 2012; Vanommeslaeghe et al., 2010; Vanommeslaeghe et al., 2012), we carried out a series of quantum chemical calculations to generate ab initio benchmarking data, including atomic charges, optimized molecular geometries, and multiple potential energy surfaces (PESs) generated by relaxed scan of selected bond and dihedral angles; these calculations were performed in the gas phase using Gaussian 16 (Gaussian, Inc, Wallingford, CT, 2016), using the MP2/6-31G(d) method. Structural properties and calculated PESs were then used to adjust atomic-charge, bond-angle, and dihedral-angle parameters lacking adequate entries in CGenFF. These MM parameters were refined targeting the benchmark QM data, including interaction energies and H-bond distances for multiple RY785-H₂O binary complexes. Each of these RY785-H₂O conformers probes the interaction of a H₂O molecule with a different H-bond donor (C-H or N-H) or acceptor (N or S) in RY785. The complexes were set up with an ideal H-bond interaction between RY785, in its MP2/6-31G(d) optimized geometry, and a water molecule, in its idealized TIP3P geometry (Jorgensen et al., 1983). The interaction distances in these complexes were optimized at the HF/6-31G(d) level while keeping all other degrees of freedom fixed; the interaction energy was then calculated without correction for basis set superposition error and multiplied by a factor of 1.16, as suggested elsewhere (Vanommeslaeghe et al., 2012). Further details can be found in Appendix 1.