The KCNA2 gene encodes the K _v 1.2 channel, a mammalian voltage-gated K⁺ channel featuring up to 80% homology with the Drosophila Shaker channel (Suárez-Delgado et al., 2020). It is widely expressed in mammals by visceral smooth muscle cells (Wang et al., 1994) and neurons of the central and peripheral nervous system (Niday and Tzingounis, 2018). Its defections/malfunction are linked to neuronal deficiency inducing encephalopathies, ataxia, cerebellar atrophy (Morrison-Levy et al., 2020), and especially childhood epilepsy (Masnada et al., 2017).

Initially, this channel was studied using the structure solved by MacKinnon and colleagues of a modified rat K _v 1.2 channel where the voltage sensor paddle, encompassing the S3 and S4 helices, was replaced by the voltage sensor paddle from the rat K _v 2.1 channel, the so-called “paddle-chimera channel” (Long et al., 2007). Then, the structure of the K _v 1.2 channel was experimentally solved (Chen et al., 2010), revealing that it is characterized by four identical subunits made of six trans-membrane alpha helices each. There are three functional domains: the T1 domain at the amino-terminus, the Voltage Sensor Domain (VSD) that encompasses helices S1 to helix L45 and is sensitive to the membrane potential variation triggering the channel to open, and the Pore Domain (PD) delimited by the S5 and S6 alpha helices with the P-Loop and the Selectivity Filter (SF) (Figure 1A).

Based on the protein architecture, the Kv1.2 channel is classified as a domain-swapped channel where the peripheral VSDs interact with the PDs of the neighboring subunit (dashed circles in Figure 1B). These channels are characterized by a long helical S4–S5 linker (also referred to as L45) that acts as a mechanical lever pushing onto helix S6 of the neighboring subunit and straightening it to close the pore. These are the main features of the domain-swapped channels canonical activation/deactivation mechanism. On the other hand, in non-domain-swapped channels, the linker L45 is non helical and so short that it is unlikely to exert a force on S6 (Barros et al., 2019).

In most K⁺ channels, the ion permeation is regulated by conformational changes occurring at least at opposite sites of the PD: the bending of the S6 alpha helices (at the bottom of S6) causes the inner gate to close, determining the transition from the Open (O) to the Closed (C) state of the channel (Liu et al., 1997; Doyle et al., 1998; del Camino and Yellen, 2001; Long et al., 2005; Jensen et al., 2012). On the other hand, structural rearrangement of the SF that forms the outer gate is the cause of the transition from the O to the Inactivated (I) state, a slow process defined as C-type inactivation (Hoshi et al., 1991; Baukrowitz and Yellen, 1995; Ader et al., 2009). The I state plays a key role in the kinetic behavior of the channels because it is reached immediately after the inner gate opening and, likewise, it allows the channel to close leading the conformation of the inner gate towards the closed state (Monod et al., 1965; Cuello et al., 2010). Despite its central role in channel function, the molecular determinants of the inactivation remained quite elusive.

The transitions O → I and I → C and vice versa are regulated by the membrane potential variation, implying a functional connectivity between the VSD and the SF (Olcese et al., 1997; Loots and Isacoff, 1998). Previous computational studies on Shaker activation/deactivation revealed the existence of an alternative pathway that connected the VSD to the PD excluding the long loop L45 (Fernandez-Marino et al., 2018). Successively, experimental evidences supported the idea of a non-canonical activation/deactivation mechanism in the VSD-PD coupling that involved the S4\S5 and S5\P-Loop interfaces (Carvalho-de Souza and Bezanilla, 2019). Moreover, a very similar non-canonical pathway involving the S1 and S5 helices was identified in hERG, a non-domain-swapped channel, where it contributed to the pore opening (Costa et al., 2021). Finally, Bezanilla and coworkers showed that this alternative pathway operates independent of the canonical coupling endowing the voltage dependence to the SF, suggesting a key role in the inactivation mechanism (Bassetto et al., 2021). In order to characterize the dynamic coupling between VSD and SF in K _v 1.2 inactivation, in this work, we studied the motion propagation between these two regions analyzing equilibrium fluctuations of the open state. The rationale of this strategy is that the open state immediately precedes the inactivated state in the functional cycle of K _v 1.2 with small conformational differences between the two states (Panyi and Deutsch, 2006); in particular, we used the SF as the final endpoint of our search, which is responsible for C-type inactivation (see below).

Based on the KcsA studies about the influence of the inner pore gate on the conformation of the outer pore gate (Cuello et al., 2010), it has been demonstrated that, in Shaker, the residue I470 at the bottom of S6 helix plays a critical role in the C-type inactivation: when the pore opens, this residue modifies its side-chain orientation and physically makes contact with the SF, inducing a constriction capable of stopping the ion flow (Peters et al., 2013). These experimental evidences support the idea of a different coupling mechanism implicated in the C-type inactivation driven by the modifications of the S6 helices after the channel opening and not by a direct coupling with the VSD. Then, it has been shown that the C-type inactivation in hERG, a non-domain-swapped channel, depends on residue F627 of the SF that blocks rapidly the ion flux (Li et al., 2015); similarly, Shaker-like K ⁺ domain-swapped channels are characterized by this type of inactivation (Hoshi et al., 1991; Baukrowitz and Yellen, 1995; Ader et al., 2009). It is notable that this inactivation mechanism completely occurs within the PD so that a mechanism occurring in a non-domain-swapped channel like hERG may also apply to domain-swapped channels of the Shaker family. After the sequence alignment between hERG and Kv1.2 (shown in Supplementary Figure S2), it is evident that in the SF of Kv1.2, only Y377 has a side-chain characterized by a steric hindrance similar to that of the phenylalanine on hERG, which suggests that Y377 may have a similar role to F627 in hERG. For this reason, in addition to VSD-SF couplings, we studied in detail the pathways connecting the PD to the side-chain re-orientation of Y377 that was chosen to be the key residue of the sink region on the SF for the network analysis (for more details, see Methods).

The C-type inactivation in the K _v 1.2 channel seemingly originates in VSD-SF and PD-SF couplings. Thus, characterizing microscopically this transition amounts to study how conformational changes of the S4 sensor helix and the pore-delimiting S6 helix propagate to the SF. Considering the long-range conformational re-arrangements of the channels occurring during the transitions from one functional state to another, ion channels can be classified as allosteric molecules (Changeux et al., 1984). A promising approach to study allosteric proteins examines how the fluctuations of residue pairs correlate over the course of an equilibrium simulation to reconstruct the propagation of motion across the protein network (Elbahnsi and Delemotte, 2021). This approach was successfully employed to study the long-range communication path in the E2 enzymes (Papaleo et al., 2012) and in the tRNA synthetase (Ghosh and Vishveshwara, 2007). It has recently been applied also to ion channels, in particular to the Kv1.2–2.1 chimera (Fernandez-Marino et al., 2018) and hERG (Costa et al., 2021) to clarify how motion propagation determines their activation and deactivation. Here, we applied this network theoretical approach to clarify the molecular determinants of inactivation in the K _v 1.2 channel.

The initial configuration of K _v 1.2 was taken from the experimentally solved open structure (PDB ID 3LUT) (Chen et al., 2010). Using the CHARMM membrane builder (Jo et al., 2008, 2009), it was embedded in bilayers of 880 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine lipids with 65,408 TIP3P water molecules and 0.15 M of KCl to form a simulation box of ca. 150 × 150 × 175 Å totaling 259,933 atoms. The APBS server (Baker et al., 2001) was used to analyze the protonation states of residues: all aspartates and glutamates were ionized; H271, H378, and H486 were predicted to be in the δ protonation state; H264 was assigned to the ϵ protonation state. Then, the channel was equilibrated in the NPT ensemble for 100 ns. Mutants were produced from the pre-equilibrated wild-type system. At first, they were equilibrated for 6.5 ns in the NPT ensemble applying a time-varying harmonic restraint on each mutated residue and on its neighbors within a cutoff distance of 5.0 Å. The force constant, initially set to 10 kcal/mol/Å, was decreased by 2 units every 0.5 ns of this simulation and then they were equilibrated for 50 ns in the NPT ensemble. All simulations were run with NAMD (Phillips et al., 2005) using the ff14SB force field for the protein (Maier et al., 2015) and the Lipid17 force field for the lipids (Dickson et al., 2014). Pressure was kept at 1.01325 Bar by the Nosé-Hoover Langevin piston method (Martyna et al., 1994; Feller et al., 1995) and the temperature was maintained at 303.15 K by a Langevin thermostat with damping coefficient of 1 ps⁻¹. Long-range electrostatic interactions were evaluated with the smooth Particle Mesh Ewald algorithm with a grid space of 1 Å. For short-range non-bonded interactions, a cutoff of 12 Å with a switching function at 10.0 Å was used. The integration time step was 2 fs.

The contact map analysis was carried out computing for each couple of residues the probability to be in contact during the equilibrium simulations. Precisely, two residues were considered to be in contact when a pair of heavy atoms of the side chains was closer than 5.0 Å for at least 75% of the trajectory.

For the network analysis, the protein was represented as a graph (Bondy and Murty, 1976) where nodes correspond to residues and edges to interactions between pairs. Edge weights were calculated using: d ij = − log C o r r ij where Corr_ij is the correlation coefficient, that is, the normalized covariance of C _α positions: C o r r ij = ⟨ r ⃗ i − ⟨ r ⃗ i ⟩ r ⃗ j − ⟨ r ⃗ j ⟩ ⟩ ⟨ r ⃗ i − ⟨ r ⃗ i ⟩ 2 ⟩ ⟨ r ⃗ j − ⟨ r ⃗ j ⟩ 2 ⟩ (1) where r ⃗ i and r ⃗ j are the position vectors of the i and j residues and Corr_ij assumes values in the interval [−1, 1]. Spheres of radius 6 Å were centered on two key residues on S4 and S6 helices and on SF of the neighboring subunit to identify all residues inside them for at least 75% of the trajectory defining the source and sink regions. Shortest pathways were computed using Dijkstra’s algorithm (Dijkstra et al., 1959). The betweenness of each residue was computed with Brandes algorithm (Brandes, 2001) as implemented in the NetworkX library (Hagberg et al., 2008). For more details, see Supporting Methods.

In this study, a combined simulations/network theoretical approach was applied to identify dynamical pathways as the possible molecular basis of C-type inactivation in the K _v 1.2 channel. This dynamic analysis allowed us to identify two routes of motion propagation that occur during this transition. In particular, our results revealed that the constriction of the SF is coupled to the VSD displacement (i) through helix S5 and the P-Loop and (ii) through a direct connection with the PD.

In the first path, the inactivation starts from helix S4, which is the only part of the channel that responds to changes in the membrane potential. From here, the motion propagates to helix S5 of the neighboring subunit using two bridges in the middle helix, corresponding to residues V301 and I304, respectively. By mutating residues on the top of the helix, we noticed an impairment of inactivation, in agreement with the experimental results obtained in Shaker channels (Yang et al., 2007; Bassetto et al., 2021). It is noteworthy that this pathway encompasses residues L293 and F302, whose mutations into histidine and leucine, respectively, are known to modify the inactivation of K _v 1.2 leading to epileptic encephalopathy (Masnada et al., 2017; Pantazis et al., 2020).

Moreover, a second communication pathway was identified coupling the SF to the PD excluding the VSD. In this case, the starting point of the motion propagation is represented by the bending region on helix S6 whose movements, after the channel opening, are transferred to Y377 on the SF through the contact between I402 and T373. Interestingly, residue P405 lays on this path, and it is correlated to slight changes in the inactivation if mutated into a leucine: similar to L293H and F302L, mutation P405L has been shown to induce epilepsy (Syrbe et al., 2015).

Finally, in order to support our computational results, we mutated some residues implicated in the paths whose effects have been demonstrated to modify the inactivation in Shaker channels. The computed changes in the path lengths account for a delayed inactivation in the majority of cases while an acceleration occurs for W366F (see Table 2); these results yield microscopic insights into experimental results (Perozo et al., 1993; Yang et al., 2007; Cuello et al., 2010; Cordero-Morales et al., 2011; Bassetto et al., 2021), in particular on the allosteric mechanism of inactivation.

In summary, our work has unveiled the molecular determinants of C-type inactivation in the K _v 1.2 channel through a novel approach combining molecular dynamics simulations and network theoretical techniques. Two pathways were found coupling the VSD and the inner pore gate with the SF providing a tentative explanation of the inactivation mechanism. Interestingly, some pathological mutants shown to impair the inactivation lay on the pathways that we identified, strengthening our computational results.