Extracellular Potassium Dynamics and Epileptogenesis

Extracellular ion concentrations change as a function of neuronal activity and also represent important factors influencing the dynamic state of a population of neurons. In particular, relatively small changes in extracellular potassium concentration ( K+ o) mediate substantial changes in neuronal excitability and intrinsic firing patterns. While experimental approaches are limited in their ability to shed light on the dynamic feedback interaction between ion concentration and neural activity, computational models and dynamic system theory provide powerful tools to study activity-dependent modulation of intrinsic excitability mediated by extracellular ion concentration dynamics. In this chapter, we discuss the potential role of extracellular potassium concentration dynamics in the generation of epileptiform activity in neocortical networks. Detailed bifurcation analysis of a model pyramidal cell revealed a bistability with hysteresis between two distinct firing modes (tonic firing and slow bursting) for mildly elevated K+ o. In neocortical network models, this bistability gives rise to previously unexplained slow alternating epochs of fast runs and slow bursting as recorded in vivo during neocortical electrographic seizures in cats and in human patients with the Lennox-Gastaut syndrome. We conclude that extracellular potassium concentration dynamics may play an important role in the generation of seizures. INTRODUCTION Epilepsy is one of the most common neurological disorders. Close to 5% of people in the world may have at least one seizure in their lifetime. At any time, 50 million people have epilepsy, especially in childhood, adolescence and old age. In developed countries, the annual incidence of epilepsy is estimated at 50 per 100 000 of the general population. Studies in developing countries, however, suggest that this figure is nearly double at 100 per 100 000 people. Up to 30% of people with epilepsy may not respond to pharmacological treatment (http://www.who.int/mediacentre/factsheets/fs165/en). These data illustrate that little is known about the mechanisms of epileptogenesis to treat it effectively. For the development of more effective antiepileptic drugs, it is therefore essential to understand better the underlying causes of the different forms of epileptic brain activity. Due to the complexity of neural dynamics, computational models with biological plausibility have become an important tool to understand better the epileptic brain. While changes in the ionic composition of the extracellular milieu clearly modulate cortical network dynamics, experiments have only had limited success in providing a mechanistic understanding of ion concentration dynamics and epileptogenesis. In this chapter, we show how recent computational models of cortical circuits with extracellular potassium concentration ( K+ o) dynamics help to overcome these previous limitations and contribute towards a more refined and experimentally testable theory of K+ o dynamics and epilepsy. We first set the grounds by discussing the cortical origin of neocortical paroxysmal oscillations, in vivo and in vitro experiments concerning K+ o dynamics, and the cortical network model with K+ o dynamics. Then, we describe single cell dynamics including detailed bifurcation analysis of a novel bistability with hysteresis between tonic spiking and slow bursting mediated by K+ o. Next, we extend the model to the network level and describe mechanisms underlying slow state transitions between two distinct oscillatory firing modes (slow bursting and fast run). The transitions between episodes of slow bursting and fast run observed in the model exhibit the same qualitative features as those recorded in vivo during neocortical electrographic seizures in cat and in human patients with the Lennox-Gastaut syndrome. Then, we show mechanisms of seizure cessation. We conclude by discussing the novel insights derived from computational models and the potential implications for clinical research.