Abstract

Many central neurons, particularly certain brainstem aminergic neurons, exhibit spontaneous and fairly regular spiking with frequencies of order a few Hz. Many ion channel types contribute to such spiking, so accurate modeling of spike generation requires solving very large systems of differential equations, ordinary in the first instance. Since the 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, inputs and output spike features trains can be incorporated, including stochastic effects. In this article, we consider a simple two-component model whose solutions can mimic features of spiking in serotonergic neurons of the dorsal raphe nucleus and noradrenergic neurons of the locus coeruleus. The model is of the Fitzhugh-Nagumo type, and solutions are computed with two representative sets of parameters. Frequency versus input currents reveals Hodgkin type 2 behavior, which is supported by bifurcation and phase plane analysis. The article concludes with a brief review of the previous modeling of these types of neurons and their relevance to serotonergic and noradrenergic involvement studies in certain cognitive processes and pathologies.