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The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title: Roles of gap junctions in neuronal networks
Author: Ha, Joon
View Online: njit-etd2008-062
(xiii, 79 pages ~ 5.8 MB pdf)
Department: Department of Mathematical Sciences
Degree: Doctor of Philosophy
Program: Mathematical Sciences
Document Type: Dissertation
Advisory Committee: Bose, Amitabha Koshal (Committee chair)
Nadim, Farzan (Committee member)
Golowasch, Jorge P. (Committee member)
Rotstein, Horacio G. (Committee member)
Medvedev, Georgi (Committee member)
Date: 2008-05
Keywords: Gap junction
Neuronal networks
Graph theory
Theta neuron model
Cable theory
Availability: Unrestricted

This dissertation studies the roles of gap junctions in the dynamics of neuronal networks in three distinct problems. First, we study the circumstances under which a network of excitable cells coupled by gap junctions exhibits sustained activity. We investigate how network connectivity and refractory length affect the sustainment of activity in an abstract network. Second, we build a mathematical model for gap junctionally coupled cables to understand the voltage response along the cables as a function of cable diameter. For the coupled cables, as cable diameter increases, the electrotonic distance decreases, which cause the voltage to attenuate less, but the input of the second cable decreases, which allows the voltage of the second cable to attenuate more. Thus we show that there exists an optimal diameter for which the voltage amplitude in the second cable is maximized. Third, we investigate the dynamics of two gap-junctionally coupled theta neurons. A single theta neuron model is a canonical form of Type I neural oscillator that yields a very low frequency oscillation. The coupled system also yields a very low frequency oscillation in the sense that the ratio of two cells' spiking frequencies obtains the values from a very small number. Thus the network exhibits several types of solutions including stable suppressed and 1 N spiking solutions. Using phase plane analysis and Denjoy's Theorem, we show the existence of these solutions and investigate some of their properties.

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