Transient responses of a modeled bursting neuron: analysis with equilibrium and averaged nullclines

Abstract.

We utilized a state-space approach to study the dynamics of a modeled bursting neuron consisting of 11 state variables. Such an approach may be used on a high-order system when a small number of variables are rate-limiting and dominate the dynamics of the model. Calculation of equilibrium and averaged nullclines and saddle-node bifurcations of the full and reduced models provided measures that indicated the transition between silence and spiking and the dynamics of the system during both the silent and spiking phases of the burst cycle. The relative stability of tonic beating solutions in the presence and absence of 5-HT was calculated in the state-space of the slow variables and related to specific biophysical mechanisms. The results were compared with similar simulations performed in Butera et al. (1995) which utilized a current-voltage (I-V)-based method for analysis. While the state-space method is sometimes more difficult to link to specific biophysical mechanisms, it offers a wider portrait of the dynamics of the system. In contrast, the use of I-V plots offers a direct relationship to biophysical processes, but provides no information on the dynamics of non-voltage-dependent processes such as Ca$^{2+}$.