We describe a simple conductance-based model neuron that includes intra- and
extra-cellular ion concentration dynamics and show that this model exhibits
periodic bursting. The bursting arises as the fast spiking behavior of the
neuron is modulated by the slow oscillatory behavior in the ion concentration
variables, and vice versa. By separating these time scales and studying the
bifurcation structure of the neuron, we catalog several qualitatively different
bursting profiles that are strikingly similar to those seen in experimental
preparations. Our work suggests that ion concentration dynamics may play an
important role in modulating neuronal excitability in real biological systems.Comment: The most recent version now contains citation information: Journal of
Biological Physics 37, 361-373 (2011