A single Markov-type kinetic model accounting for the macroscopic currents of all human voltage-gated sodium channel isoforms

Modelling ionic channels represents a fundamental step towards developing biologically detailed neuron models. Until recently, the voltage-gated ion channels have been mainly modelled according to the formalism introduced by the seminal works of Hodgkin and Huxley (HH). However, following the continuing achievements in the biophysical and molecular comprehension of these pore-forming transmembrane proteins, the HH formalism turned out to carry limitations and inconsistencies in reproducing the ion-channels electrophysiological behaviour. At the same time, Markov-type kinetic models have been increasingly proven to successfully replicate both the electrophysiological and biophysical features of different ion channels. However, in order to model even the finest non-conducting molecular conformational change, they are often equipped with a considerable number of states and related transitions, which make them computationally heavy and less suitable for implementation in conductance-based neurons and large networks of those. In this purely modelling study we develop a Markov-type kinetic model for all human voltage-gated sodium channels (VGSCs). The model framework is detailed, unifying (i.e., it accounts for all ion-channel isoforms) and computationally efficient (i.e. with a minimal set of states and transitions). The electrophysiological data to be modelled are gathered from previously published studies on whole-cell patch-clamp experiments in mammalian cell lines heterologously expressing the human VGSC subtypes (from NaV1.1 to NaV1.9). By adopting a minimum sequence of states, and using the same state diagram for all the distinct isoforms, the model ensures the lightest computational load when used in neuron models and neural networks of increasing complexity. The transitions between the states are described by original ordinary differential equations, which represent the rate of the state transitions as a function of voltage (i.e., membrane potential). The kinetic model, developed in the NEURON simulation environment, appears to be the simplest and most parsimonious way for a detailed phenomenological description of the human VGSCs electrophysiological behaviour.Author summary: A unifying novel kinetic model of human voltage-gated sodium channels is proposed, which is able to reproduce in detail the macroscopic currents of all the ion-channel isomers, from NaV1.1 to NaV1.9. Its topology consists of six states (two closed, two open, two inactivated) and twelve transitions, and it is particularly well suited to be implemented in biologically inspired multi-compartmental neural cells and neural network models. It represents the most parsimonious kinetic model able to account for the most recently described electrophysiological features, and it has been developed by taking into account the experimental data gathered by published work reporting on each different isomer heterologously expressed in mammalian cell lines. Equipped with original differential equations, the model reproduces in detail the ion-channel macroscopic electrophysiological features with the minimal computational load.