Analysis of pacemaker activity in a two-component model of some brainstem neurons Henry C. Tuckwell1,2∗, Ying Zhou3,, Nicholas J. Penington 4,5 1 School of Electrical and Electronic Engineering, University of Adelaide, Adelaide, South Australia 5005, Australia 2 School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia 3 Department of Mathematics, Lafayette College, 1 Pardee Drive, Easton, PA 18042, USA 4 Department of Physiology and Pharmacology, 5 Program in Neural and Behavioral Science and Robert F. Furchgott Center for Neural and Behavioral Science State University of New York, Downstate Medical Center, Box 29, 450 Clarkson Avenue, Brooklyn, NY 11203-2098, USA ∗ Corresponding author: Henry C. Tuckwell, School of Electrical and Electronic Engineering, University of Adelaide, North Terrace, Adelaide, SA 5005, Australia; Tel: 61-481192816; Fax: 61-8-83134360: email:
[email protected] September 11, 2018 arXiv:1704.03941v2 [q-bio.NC] 15 Apr 2017 1 Abstract Serotonergic, noradrenergic and dopaminergic brainstem (including midbrain) neu- rons, often exhibit spontaneous and fairly regular spiking with frequencies of order a few Hz, though dopaminergic and noradrenergic neurons only exhibit such pacemaker- type activity in vitro or in vivo under special conditions. A large number of ion channel types contribute to such spiking so that detailed modeling of spike generation leads to the requirement of solving very large systems of differential equations. It is use- ful to have simplified mathematical models of spiking in such neurons so that, for example, features of inputs and output spike trains can be incorporated including stochastic effects for possible use in network models.