Mapping the dynamics of a bursting neuron.

The anterior burster (AB) neuron of the lobster stomatogastric ganglion displays varied rhythmic behavior when treated with neuromodulators and channel-blocking toxins. We introduce a channel-based model for this neuron and show how bifurcation analysis can be used to investigate the response of this model to changes of its parameters. Two dimensional maps of the parameter space of the model were constructed using computational tools based on the theory of nonlinear dynamical systems. Changes in the intrinsic firing and oscillatory properties of the model AB neuron were correlated with the boundaries of Hopf and saddle-node bifurcations on these maps. Complex rhythmic patterns were observed, with a bounded region of the parameter plane producing bursting behavior of the model neuron. Experiments were performed by treating an isolated AB cell with 4-aminopyridine which selectively reduces gA, the conductance of the transient potassium channel. The model accurately predicts the qualitative changes in the neuronal voltage oscillations that are observed over a range of reduction of gA in the neuron. These results demonstrate the efficacy of dynamical systems theory as a means of determining the varied oscillatory behaviors inherent in a channel-based neural model. Further, the maps of bifurcations provide a useful tool for determining how these behaviors depend upon model parameters and comparing the model to a real neuron.