Event Abstract

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

  • 1 'Salvatore Maugeri' Foundation, IRCCS, Department of Neurorehabilitation, Scientific Institute of Pavia via Boezio, Italy
  • 2 University of Genova, Department of Informatics, Bioengineering, Robotics and System Engineering - DIBRIS, Italy
  • 3 Karolinska Institute, Department of Neuroscience, Sweden
  • 4 KTH The Royal Institute of Technology, Department of Computational Science and Technology, Sweden

Modelling ionic channels represents a fundamental step to develop realistic neural 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. On the contrary, 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 transition, such Markov models are often equipped with a considerable number of states and related transitions, which make them computationally heavy and not suitable to be implemented in multi-compartmental conductance-based biologically realistic neuron models and large networks of those. In addition, when developing Markov-type kinetic models, the researchers' focus is often on single ion-channels subtypes, so that models independently derived from different subtypes of the same ionic channel can vary considerably, despite the structural similarity between the two isomers. In this study, assuming that a molecular analogy can bear functional similarity, we developed a Markov-type kinetic model for all human voltage-gated sodium channels (VGSCs), which is detailed, global (i.e., it accounts for all ion-channel isoforms) and computationally efficient (i.e. with a minimal set of states and transitions). The study was aimed at bridging the gap between the available studies of individual ion channels and what is needed to develop reliable models for computing neural activity in detailed cell and network models. The proposed model does not take into account the gating currents, in the sense that it does not replicate states and transitions with no effect on macroscopic currents. However, at variance with the HH formalism, it tries to not contradict the known biophysical features of the voltage-gated ionic channels. The real electrophysiological data to be modelled were 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). As a result, the developed model faithfully replicates the following electrophysiological macroscopic features of every human VGSC subtype: intensity-voltage curves and intensity-voltage relationship, normalized peak conductance-voltage relationship, steady-state current-voltage relationship during fast inactivation (also known as availability after steady-state fast inactivation), recovery from fast inactivation. In addition, the model consistently reproduces the first and second time constants of the decay from activation, as well as the deactivation kinetics, whenever these experimental data are available. By adopting a minimum sequence of states (closed, open, inactivated), and a unique state diagram for all the distinct isoforms, the model ensures the lightest computational load, and the most efficient use in neuron models and neural networks of increasing complexity. The transitions between the states are described by single original ordinary differential equations, which govern the rate of the transitions in function of time and voltage. By simply changing the ‘constant’ parameters of the differential equations the model is able to consistently approximate the functional properties of the distinct channel isoforms. In summary, 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. Finally, a comparison with a modified version of a HH model, as well as some examples of the use of the same kinetic model with other voltage-gated ion-channels are provided.

Keywords: Markov models, voltage-gated sodium channels, isoforms, macroscopic currents, electrophysiological behaviour

Conference: Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016.

Presentation Type: Poster

Topic: Computational neuroscience

Citation: Balbi P, Massobrio P and Hellgren-Kotaleski J (2016). A single Markov-type kinetic model reliably accounts for the macroscopic currents of all human voltage-gated sodium channel isoforms. Front. Neuroinform. Conference Abstract: Neuroinformatics 2016. doi: 10.3389/conf.fninf.2016.20.00024

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Received: 26 Apr 2016; Published Online: 18 Jul 2016.

* Correspondence: Dr. Pietro Balbi, 'Salvatore Maugeri' Foundation, IRCCS, Department of Neurorehabilitation, Scientific Institute of Pavia via Boezio, Pavia, PV, 27100, Italy, piero.balbi@icsmaugeri.it

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