Paper List

Journal: ArXiv Preprint
Published: Unknown
Computational NeuroscienceBiophysics

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

School of Mathematics and Statistics, Rochester Institute of Technology | School of Physics, Rochester Institute of Technology | School of Physics and Astronomy & School of Mathematics and Statistics, Rochester Institute of Technology

Youssof Abdullah, Violet Hart, Moumita Das
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The 30-Second View

IN SHORT: This work addresses the challenge of systematically characterizing how the high-dimensional parameter space of Markov models for different sodium channel isoforms influences the robustness and excitability of neuronal firing.

Innovation (TL;DR)

  • Methodology Integrates a six-state Markov model for nine human NaV isoforms with a simplified KV3.1 model, enabling a unified framework for isoform-specific stability analysis.
  • Methodology Applies bifurcation theory and local stability analysis to map 'excitable landscapes' across the (g_Na, g_K) parameter space, visualizing regions supporting stable oscillatory behavior.
  • Biology Quantitatively ranks NaV isoforms by their supported excitable regimes, identifying NaV1.3, 1.4, and 1.6 as broadly supportive and NaV1.7 and 1.9 as minimally oscillatory.

Key conclusions

  • Isoforms NaV1.3, NaV1.4, and NaV1.6 support the broadest parameter regions for stable limit cycles (oscillatory firing), indicating their robustness in sustaining action potential trains.
  • Isoforms NaV1.7 and NaV1.9 exhibit minimal oscillatory behavior across the tested conductance parameter space, correlating with their specialized roles in peripheral nociception.
  • The hybrid Markov-HH modeling and stability analysis framework successfully narrows the vast parameter search space for designing synthetic excitable systems, moving from trial-and-error to principled design.
Background and Gap： Classical Hodgkin-Huxley models treat sodium channel dynamics as homogeneous, failing to capture the functional diversity of NaV isoforms. Furthermore, the high-dimensional parameter space of mechanistic Markov models makes their global dynamical behavior difficult to characterize and poorly understood.

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.