An analysis of neuronal networks with recurrent excitation
Takeuchi, Ryusei Melody.
Abstract: The mutual synaptic excitation of neurons belonging to the same
local network is termed recurrent excitation. Understanding the effects of recurrent
excitation on the network's system and their dependence on network parameters is complex.
In this thesis, we study models of neuronal networks with recurrent excitation and ask what
conditions lead to persistent, reverberating activity, ... read moreand/or high-frequency runaway
activity. We examine those questions by analyzing the parameters in several neuronal
models, creating surfaces that depict the dependence of firing frequency (f) on external
drive (I) and the strength of recurrent excitation (ge). The simplest model generates our
first f − I − ge surface, the cusp catastrophe. From here, we increase the complexity of
the models, drawing connections between each subsequent surface. The single-cell models we
use are the self-exciting LIF neuron, the self-exciting theta neuron, the self-exciting,
self-inhibiting LIF neuron, and the self-exciting, self-inhibiting theta neuron. Sudden
transitions from low to high firing frequency are depicted in our surfaces. These abrupt
jumps correspond to runaway transitions. Following this, we look at medium-sized networks
composed of excitatory reduced Traub-Miles pyramidal neurons and inhibitory Wang-Buzsáki
interneurons with NMDA and AMPA receptor-mediated synapses. We numerically analyze the
strong PING rhythms these networks create, as well as weak PING rhythms, both
deterministically and stochastically driven. For the networks, we add recurrent excitation
and relate the simulations to what was seen for the single-cell models. The goal of these
analyses is to put a quantitative measure on real biological phenomena. Firing fueled by
recurrent excitation is thought to be the neuronal basis of working memory. Changes in the
frequencies of this firing may be associated with schizophrenia. Runaway activity may also
be related to the onset of seizures. Throughout this dissertation, the possible biological
significance of our mathematical findings will be discussed.
Thesis (Ph.D.)--Tufts University, 2017.
Submitted to the Dept. of Mathematics.
Advisor: Christoph Borgers.
Committee: Christoph Borgers, James Adler, Xiaozhe Hu, and Horacio Rotstein.
Keywords: Mathematics, and Neurosciences.read less