Molecular Dynamics Simulations of Ion Permeation in Human Voltage-Gated Sodium Channels

The recent determination of cryo-EM structures of voltage-gated sodium (Nav) channels has revealed many details of these proteins. However, knowledge of ionic permeation through the Nav pore remains limited. In this work, we performed atomistic molecular dynamics (MD) simulations to study the structural features of various neuronal Nav channels based on homology modeling of the cryo-EM structure of the human Nav1.4 channel and, in addition, on the recently resolved configuration for Nav1.2. In particular, single Na+ permeation events during standard MD runs suggest that the ion resides in the inner part of the Nav selectivity filter (SF). On-the-fly free energy parametrization (OTFP) temperature-accelerated molecular dynamics (TAMD) was also used to calculate two-dimensional free energy surfaces (FESs) related to single/double Na+ translocation through the SF of the homology-based Nav1.2 model and the cryo-EM Nav1.2 structure, with different realizations of the DEKA filter domain. These additional simulations revealed distinct mechanisms for single and double Na+ permeation through the wild-type SF, which has a charged lysine in the DEKA ring. Moreover, the configurations of the ions in the SF corresponding to the metastable states of the FESs are specific for each SF motif. Overall, the description of these mechanisms gives us new insights into ion conduction in human Nav cryo-EM-based and cryo-EM configurations that could advance understanding of these systems and how they differ from potassium and bacterial Nav channels.


Definition of the Cross Distances
In this section, we report the list of the cross distances (CDISTs) mapped during the standard MD simulations. The average for each CDIST is reported in Table S3.
Here, atoms are defined in the CHARMM notation, with the following assumptions: • CA defines the C α atoms of the backbone for each residue; • all the others are the most external carbon atoms in the side-chain of each selected residue.

Homology-based Nav1.2 model (2 fs)
Homology-based Nav1.2 model (4 fs) 1.48 ± 0.14 Å ! ± " 1.71 ± 0.28 Å Homology-based Nav1.1 model (4 fs) ! ± " 1.83 ± 0.18 Å Homology-based Nav1.6 model (4 fs) ! ± " 1.95 ± 0.49 Å Cryo-EM Nav1.2 structure (4 fs) Cryo-EM Nav1.2 structure (4 fs) 1.73 ± 0.22 Å Figure S5: Backbone RMSD of the P-loops for each system during standard MD simulations. We also report the average (µ) and the standard deviation (σ) of the RMSD for each simulation.   Figure S7: Additional MD of the WT Cryo-EM Na v 1.2 structure with two Na + confined in the C/SF (HMR set-up). Results from configuration 1. For each simulation, we report the z-coordinate of the two Na + ions in the C/SF, of the COM of the two cations and of the nitrogen atom of the K1422 side-chain.  Figure S8: Additional MD of the WT Cryo-EM Na v 1.2 structure with two Na + confined in the C/SF (HMR set-up). Results from configuration 2. For each simulation, we report the z-coordinate of the two Na + ions in the C/SF, of the COM of the two cations and of the nitrogen atom of the K1422 side-chain.  Figure S9: Additional MD of the WT Cryo-EM Na v 1.2 structure with two Na + confined in the C/SF (HMR set-up). Results from configuration 3. For each simulation, we report the z-coordinate of the two Na + ions in the C/SF, of the COM of the two cations and of the nitrogen atom of the K1422 side-chain. 0.98 ± 0.13 Å 1.08 ± 0.12 Å 1.07 ± 0.13 Å

S13
1.08 ± 0.11 Å 1.07 ± 0.12 Å 1.08 ± 0.12 Å Figure S11: RMSD of the backbone P-loops (DEKA SF) for each system during the OTFP 1 simulations. We also report the average (µ) and the standard deviation (σ) of the RMSD. For each calculation, we report the average (µ and the standard deviation σ).

REPLICA5
! ± " 1.07 ± 0.12 Å Figure S22: RMSD of the backbone P-loops (DEK +1 A SF) for each replica during the OTFP  Figure S23: Total energy during OTFP 1 simulations for the Cryo-EM Na v 1.2 structure (DEK +1 A SF) for the set-up with standard atomic masses with ∆t = 2 fs (Replica1-3, on the left) and for HMR with ∆t = 4 fs (Replica1-5, on the right). We also report the average µ and the standard deviation σ for each MD run.

List of Movies
Single ion permeation events observed for the various WT systems. In all the movies we represent the first three repeats, following the legend of Figure 1: domain DI, gray; domain DII, yellow; domain DIII, green. The fourth domain is excluded for clarity. The side-chains of the most external residues belonging to the EEDD motif are represented as red sticks.
The charged residues of the three represented repeats belonging to the DEKA motif are also included (D and E are represented again with red side chains. The side-chain of the lysine is shown in blue sticks, with the NZ atom shown as a sphere). The internal carbonyl oxygen atoms of the two proceeding residues in each repeat are also included as red points. The permeating Na + ion is represented as an orange VdW sphere. Movies are available free of charge at https://github.com/BeatriceCorradi/Nav_Channels_movies.git • Movie S1. Permeation of a single Na + ion in the MD simulation of the homologybased Na v 1.2 model (time-step ∆t = 2 fs). Unrestrained production.
• Movie S2. Single Na + ion residing in the region of the internal carbonyls during the MD simulation of the homology-based Na v 1.1 model (time-step ∆t = 4 fs). Restrained equilibration.
• Movie S3. Permeation of a single Na + ion in the MD simulation of the homologybased Na v 1.2 model (time-step ∆t = 4 fs). Restrained equilibration.
• Movie S4. Permeation of a single Na + ion in the MD simulation of the homologybased Na v 1.6 model (time-step ∆t = 4 fs). Restrained equilibration.
• Movie S5. Permeation of a single Na + ion in the MD simulation of the Cryo-EM Na v 1.2 structure (time-step ∆t = 4 fs -run 1). Unrestrained production.
• Movie S6. Permeation of a single Na + ion in the MD simulation of the Cryo-EM Na v 1.2 structure (time-step ∆t = 4 fs -run 2). Restrained equilibration + unrestrained production.