A Mathematical Model for the Transition in Firing Patterns Across Puberty of a Gonadotropin-Releasing Hormone Neuron

<p>Puberty has remained a longstanding biological puzzle for scientists. Much remains to be understood about mechanisms that trigger this important development. What is however established is that, the activity of a certain network of neurons called Gonadotropin-Releasing Hormone (GnRH) neurons lies at the very heart of this puzzle. For my thesis, I develop and analyze a deterministic mathematical model of a GnRH neuron consisting of a system of differential equations based on experimental observations and published results. Using the results of the model we test hypotheses of possible neurobiological mechanisms mediating the transitions in the activity patterns of GnRH neurons across puberty.</p><p>For a regime of parameter values the model neuron exhibits subthreshold (small-amplitude) membrane oscillations in conjunction with spikes (large-amplitude oscillations). Their intermixing can produce complicated patterns called mixed mode oscillations (MMOs). Mathematically, the occurrence of MMOs raises important questions pertaining to the geometry of invariant manifolds of the underlying dynamical system. Using geometric singular perturbation theory methods and mathematical software packages I analyze the MMOs arising in the GnRH model. This analysis is presented through a sequence of theorems that comprise the core results of my thesis.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

The Ohio State University

Year dc:date

2013

Author dc:creator

• Banerjee, Sayanti P.

Contributors dc:contributor

• Best, Janet

• Biology
• Mathematics
• Neurosciences
• GnRH neurons
• Puberty
• Mathematical Model
• Mixed Mode Oscillations

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=osu1357249691

OAI identifier oai:identifier

oai:etd.ohiolink.edu:osu1357249691