Bursting regimes in a reaction-diffusion system with action potential-dependent equilibrium.

Area of Science:

• Computational neuroscience
• Mathematical biology
• Biophysics

Background:

• Neural cell dynamics rely on the Nernst potential.
• Current models often assume constant intracellular and extracellular ion concentrations during neural excitation.
• This assumption may limit understanding of brain function and dysfunction.

Purpose of the Study:

• To investigate the impact of time-dependent ionic concentrations on neural electrical dynamics.
• To explore how varying Nernst potentials influence transmembrane potential.
• To model complex neural behaviors, including oscillations and pattern formation.

Main Methods:

• Incorporated potential-dependent Nernst shifts into a one-dimensional Morris-Lecar reaction-diffusion model.
• Analyzed a parameter space exhibiting self-sustaining oscillations without external forcing.
• Studied system behavior near the bifurcation boundary under external stimulation.
• Extended the model to a one-dimensional cable of excitable tissue.

Main Results:

• Identified a parameter regime supporting self-sustaining oscillations.
• Demonstrated system vulnerability to external stimuli, leading to stable equilibria.
• Observed complex spatiotemporal pattern formation in stimulated excitable tissue.
• Showcased the emergence of neuronal bursting and seizure-like activity.

Conclusions:

• Varying ionic concentrations are crucial for understanding neural excitability.
• The model provides a framework for exploring normal and pathophysiological brain activity.
• Findings have implications for understanding neuronal bursting and seizure dynamics.