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Mixed mode oscillations in a gonadotropin-releasing hormone (GnRH) neuron model

Authors
Journal
BMC Neuroscience
1471-2202
Publisher
Springer (Biomed Central Ltd.)
Publication Date
Volume
11
Identifiers
DOI: 10.1186/1471-2202-11-s1-p161
Keywords
  • Poster Presentation
Disciplines
  • Biology
  • Mathematics

Abstract

Mixed mode oscillations in a gonadotropin-releasing hormone (GnRH) neuron model POSTER PRESENTATION Open Access Mixed mode oscillations in a gonadotropin- releasing hormone (GnRH) neuron model Sayanti Banerjee1*, Janet Best1, Kelly Suter2 From Nineteenth Annual Computational Neuroscience Meeting: CNS*2010 San Antonio, TX, USA. 24-30 July 2010 Mixed mode oscillations (MMOs) are complex patterns resulting from an inter-mixing of large- and small- amplitude oscillations. Such patterns have been widely observed in experiments as well as mathematical models [1] and are currently an active area of mathematical research. In neurons MMOs often consist of a mixture of spikes and subthreshold oscillations. Our GnRH work leads to a seven-dimensional soma model aimed at investigating the firing properties of GnRH neurons across puberty. The results of our model are supported by published electrophysiological data of Liu and Herbi- son [2]. The model exhibits robust subthreshold oscilla- tions in addition to action potentials, an observation validated by experimental evidence. Previously identified mechanisms giving rise to MMOs in mathematical mod- els include canard-based mechanisms such as folded node singularities and singular Hopf bifurcations [3,4]. MMOs arising out of these mechanisms have character- istic patterns of variation in oscillation amplitudes; in the case of folded nodes there are also bounds for the maximum number of subthreshold oscillations per cycle. The MMOs in our system do not follow these patterns but are instead “exotic” MMOs. In this work we use geometric singular perturbation theory to analyze the source of these MMOs in the model and compare to known mechanisms; we also explore the possible physio- logical function of MMOs in GnRH cells. Bifurcation analysis of our system was performed with the help of the simulation and continuation tool XPPAUT. Our analysis suggests that MMOs in our model persist near a saddle-node of periodic orbits and the geometry further poi

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