Stability analysis of action potential generation using Markov models of voltage-gated sodium channel isoforms

TL;DR

This study uses Markov models to analyze how different sodium channel isoforms affect neuron excitability and action potential generation, revealing isoform-specific stability and oscillation properties.

Contribution

It introduces a combined Markov and conductance-based model to compare nine sodium channel isoforms and maps their influence on neuronal excitability using bifurcation analysis.

Findings

NaV1.3, NaV1.4, NaV1.6 support broad excitable regimes

NaV1.7 and NaV1.9 show minimal oscillatory behavior

The model helps guide synthetic neuron design by identifying stable parameter regions

Abstract

We investigate a conductance-based neuron model to explore how voltage-gated ion channel isoforms influence action-potential generation. The model combines a six-state Markov representation of NaV channels with a first-order KV3.1 model, allowing us to vary maximal sodium and potassium conductances and compare nine NaV isoforms. Using bifurcation theory and local stability analysis, we map regions of stable limit cycles and visualize excitability landscapes via heatmap-based diagrams. These analyses show that isoforms NaV1.3, NaV1.4 and NaV1.6 support broad excitable regimes, while isoforms NaV1.7 and NaV1.9 exhibit minimal oscillatory behavior. Our findings provide insights into the role of channel heterogeneity in neuronal dynamics and may help to guide the design of synthetic excitable systems by narrowing the parameter space needed for robust action-potential trains.