Michael Leone

Date of Award

2014

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Keywords

Mathematics, Neurons, Mathematical Model, Simulation, Beta Rhythm

Area of Concentration

Mathematics

Abstract

A network of neurons is, in many aspects, a coupled system of nonlinear oscillators. We adopt this interpretation for the purpose of mathematically modeling a beta-rhythmic, Layer 5 cortical microcircuit which supports selective attention through interlaminar interaction (28). We assume that the foundation of the beta rhythm is the interaction between the intrinsic bursting pyramidal neuron and the low-threshold spike interneuron, where the period of the rhythm is determined by the period of the M-current inherent to both neuron types. We test the robustness of oscillations and circuit response to periodic forcing in the (5-20 Hz) range. Differences between synaptic and gap junction coupling are explored in the context of the synchrony state. Simulations demonstrate that intrinsic bursting neurons respond to coupling with inhibition-boosted ring. The effects of excitatory forcing depend on the relative frequencies of the forcing current and the network: oscillation coherence may either be weakened, preserved, or strengthened, and in a variety of cases, neuron clustering is induced. We also find that for larger networks with sparse connectivity, gap junction coupling between intrinsic bursting neurons is necessary for a coherent rhythm.

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