  Many central neurons, and in particular certain brainstem aminergic neurons
exhibit spontaneous and fairly regular spiking with frequencies of order a few
Hz. A large number of ion channel types contribute to such spiking so that
accurate modeling of spike generation leads to the requirement of solving very
large systems of differential equations, ordinary in the first instance. Since
analysis of spiking behavior when many synaptic inputs are active adds further
to the number of components, it is useful to have simplified mathematical
models of spiking in such neurons so that, for example, stochastic features of
inputs and output spike trains can be incorporated. In this article we
investigate two simple two-component models which mimic features of spiking in
serotonergic neurons of the dorsal raphe nucleus and noradrenergic neurons of
the locus coeruleus. The first model is of the Fitzhugh-Nagumo type and the
second is a reduced Hodgkin-Huxley model. For each model solutions are computed
with two representative sets of parameters. Frequency versus input currents are
found and reveal Hodgkin type 2 behavior. For the first model a bifurcation and
phase plane analysis supports these findings. The spike trajectories in the
second model are very similar to those in DRN SE pacemaker activity but there
are more parameters than in the Fitzhugh-Nagumo type model. The article
concludes with a brief review of previous modeling of these types of neurons
and its relevance to studies of serotonergic involvement in spatial working
memory and obsessive-compulsive disorder.
