Abstract
The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed.
Highlights
Understanding neural activity is an endeavor spanning several decades of research
An external stimulation current can be applied to raise the membrane potential V above the model’s threshold at which a rapid rise in potential occurs, causing an increase in the potassium current. This rising potassium current brings the membrane potential back down, overshooting equilibrium and resulting in a recovery time (“refractory period”) during which no further stimulation generates an action potential. This basic picture of an action potential event is characteristic of virtually all common models used to study electrical activity in cardiac and muscular cells, and we wish to explore how this picture changes when the Nernst potential is allowed to vary due to the charge depletion expected to occur within smaller neurons
The addition of a variable Nernst potential creates a region in parameter space in which self-sustaining oscillations, or stable limit cycles, exist without requiring external driving or leakage currents
Summary
Understanding neural activity is an endeavor spanning several decades of research. Promising advances have been made in modeling both individual neurons as well as the combination of neurons making up a network. The goal of such work is to understand how our brains store and access information through identifying the internal and external factors which play important roles in these processes. Synchronization of the electrical disturbances in neurons, or action potentials, is believed to play a crucial role in memory formation [1]. By introducing additional nonlinearities to the governing equations, a strong tendency toward synchronization in one-dimensional cables was previously observed within the “soliton-like.
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