The Influence of Sodium and Potassium Dynamics on Excitability, Seizures, and the Stability of Persistent States: I. Single Neuron Dynamics

TL;DR

This paper develops a mathematical model of a neuron with ion concentration dynamics to analyze how sodium and potassium influence excitability, seizures, and persistent activity, revealing mechanisms underlying pathological states like epilepsy.

Contribution

It introduces a reduced, bifurcation-analysable model linking ion dynamics to neuronal excitability and seizure-like oscillations, highlighting the importance of ion homeostasis.

Findings

Ion concentration oscillations can resemble seizure activity.

Intrinsic currents, pumps, glia, and diffusion interact to produce slow oscillations.

The model predicts testable phenomena related to neuronal excitability.

Abstract

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra- and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy.