TRANSIENT RESPONSES OF A MODELED BURSTING NEURON - ANALYSIS WITH EQUILIBRIUM AND AVERAGED NULLCLINES

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 r ate-limiting and dominate the dynamics of the model, Calculation of eq uilibrium and averaged nullclines and saddle-node bifurcations of the full and reduced models provided measures that indicated the transitio n between silence and spiking and the dynamics of the system during bo th the silent and spiking phases of the burst cycle. The relative stab ility of tonic beating solutions in the presence and absence of 5-HT w as calculated in the state-space of the slow variables and related to specific biophysical mechanisms. The results were compared with simila r simulations performed in Butera et al, (1995) which utilized a curre nt-voltage (I-V)-based method for analysis. While the state-space meth od is sometimes more difficult to link to specific biophysical mechani sms, it offers a wider portrait of the dynamics of the system. In cont rast, 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 Ca2+.