Intrinsic mechanisms in the gating of resurgent Na+ currents

The resurgent component of the voltage-gated sodium current (INaR) is a depolarizing conductance, revealed on membrane hyperpolarizations following brief depolarizing voltage steps, which has been shown to contribute to regulating the firing properties of numerous neuronal cell types throughout the central and peripheral nervous systems. Although mediated by the same voltage-gated sodium (Nav) channels that underlie the transient and persistent Nav current components, the gating mechanisms that contribute to the generation of INaR remain unclear. Here, we characterized Nav currents in mouse cerebellar Purkinje neurons, and used tailored voltage-clamp protocols to define how the voltage and the duration of the initial membrane depolarization affect the amplitudes and kinetics of INaR. Using the acquired voltage-clamp data, we developed a novel Markov kinetic state model with parallel (fast and slow) inactivation pathways and, we show that this model reproduces the properties of the resurgent, as well as the transient and persistent, Nav currents recorded in (mouse) cerebellar Purkinje neurons. Based on the acquired experimental data and the simulations, we propose that resurgent Na+ influx occurs as a result of fast inactivating Nav channels transitioning into an open/conducting state on membrane hyperpolarization, and that the decay of INaR reflects the slow accumulation of recovered/opened Nav channels into a second, alternative and more slowly populated, inactivated state. Additional simulations reveal that extrinsic factors that affect the kinetics of fast or slow Nav channel inactivation and/or impact the relative distribution of Nav channels in the fast- and slow-inactivated states, such as the accessory Navβ4 channel subunit, can modulate the amplitude of INaR.


Sample-size estimation
• You should state whether an appropriate sample size was computed when the study was being designed • You should state the statistical method of sample size computation and any required assumptions • If no explicit power analysis was used, you should describe how you decided what sample (replicate) size (number) to use Please outline where this information can be found within the submission (e.g., sections or figure legends), or explain why this information doesn't apply to your submission:

Replicates
• You should report how often each experiment was performed • You should include a definition of biological versus technical replication • The data obtained should be provided and sufficient information should be provided to indicate the number of independent biological and/or technical replicates • If you encountered any outliers, you should describe how these were handled • Criteria for exclusion/inclusion of data should be clearly stated • High-throughput sequence data should be uploaded before submission, with a private link for reviewers provided (these are available from both GEO and ArrayExpress) Please outline where this information can be found within the submission (e.g., sections or figure legends), or explain why this information doesn't apply to your submission: The experiments here were designed to quantify the detailed time-and voltagedependent properties of the Nav currents in cerebellar Purkinje neurons to facilitate the development of a computational model to recapitulate the gating of the underlying Nav channels. Sample sizes were determined based on mean data (and associated standard deviations) obtained from analyses of voltage-clamp recordings of Nav currents in mouse cerebellar Purkinje neurons acquired and described previously (Ransdell et al., 2017). This information is provided in the Methods section under 'Electrophysiological recordings and analysis ' (lines 197-199).
The numbers of cells used to obtain each referenced experimental result are reported in the Results section and in the Figure legends. All of the experimental data presented in this manuscript reflect biological replicates. Technical replicates (repeating voltage-clamp paradigms on the same cell) were occasionally acquired to ensure that the properties of the Nav currents did not change during prolonged whole-cell recordings. Technical replicates are not included in the data presented. This information is provided in the Methods section under 'Electrophysiological recordings and analysis ' (lines 199-204).
The criteria for the inclusion (or exclusion) of acquired voltage-clamp data are described in the Methods section (lines 206-207). No outliers were encountered.

Statistical reporting
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Please outline where this information can be found within the submission (e.g., sections or figure legends), or explain why this information doesn't apply to your submission: (For large datasets, or papers with a very large number of statistical tests, you may upload a single table file with tests, Ns, etc., with reference to sections in the manuscript.)

Group allocation
• Indicate how samples were allocated into experimental groups (in the case of clinical studies, please specify allocation to treatment method); if randomization was used, please also state if restricted randomization was applied • Indicate if masking was used during group allocation, data collection and/or data analysis Please outline where this information can be found within the submission (e.g., sections or figure legends), or explain why this information doesn't apply to your submission: Additional data files ("source data") • We encourage you to upload relevant additional data files, such as numerical data that are represented as a graph in a figure, or as a summary table • Where provided, these should be in the most useful format, and they can be uploaded as "Source data" files linked to a main figure or table • Include model definition files including the full list of parameters used • Include code used for data analysis (e.g., R, MatLab) • Avoid stating that data files are "available upon request" Please indicate the figures or tables for which source data files have been provided: Means and standard error of the means are reported in the Results section and in the Figure legends. The statistical test used in the analyses of the data presented in Figure  5 is indicated in the Figure legend; the exact p-value obtained is provided in the legend to Figure 5. The approach used for the numerical optimization of the computational model is described in the Methods section (lines 228-236).
In this manuscript, we have compared acquired experimental data with results obtained in computational simulations; experimental group allocation was not necessary.
Model definition files and Matlab scripts used for experimental simulations have been uploaded to https://github.com/morenomdphd/Resurgent_INa. This link is provided in the Methods section (lines 219-220).