Multistability in a neuron model with extracellular potassium dynamics

Experiments show a primary role of extracellular potassium concentrations in neuronal hyperexcitability and in the generation of epileptiform bursting and depolarization blocks without synaptic mechanisms. We adopt a physiologically relevant hippocampal CA1 neuron model in a zero-calcium condition to better understand the function of extracellular potassium in neuronal seizurelike activities. The model neuron is surrounded by interstitial space in which potassium ions are able to accumulate. Potassium currents, Na{+}-K{+} pumps, glial buffering, and ion diffusion are regulatory mechanisms of extracellular potassium. We also consider a reduced model with a fixed potassium concentration. The bifurcation structure and spiking frequency of the two models are studied. We show that, besides hyperexcitability and bursting pattern modulation, the potassium dynamics can induce not only bistability but also tristability of different firing patterns. Our results reveal the emergence of the complex behavior of multistability due to the dynamical [K{+}]{o} modulation on neuronal activities.