An analysis of neuronal networks with recurrent excitation
Takeuchi, Ryusei Melody.
2017
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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, and/... read moreor 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 - ID:
- br86bf69v
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