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Title: Coarse-­‐Graining the Dynamics of Coupled Oscillators to Model Neurons in the Suprachiasmatic Nucleus
Authors: Anand, Angad
Advisors: Kevrekidis, Yannis G.
Department: Chemical and Biological Engineering
Class Year: 2016
Abstract: The circadian rhythm is the oscillation of certain genes and proteins with approximate periods of 24 hours in many organisms, including humans. In mammals, the circadian rhythm is controlled by a part of the hypothalamus called the suprachiasmatic nucleus (SCN). Our model of the SCN, described by twenty-­‐one ordinary differential equations, makes two parameters heterogeneous, an intrinsic one and a structural one. The intrinsic heterogeneity is included by selecting the value of one of the parameters in the ODEs from a Gaussian distribution for each neuron; therefore, each neuron would have a different value for the parameter. We constructed small-­‐world networks to model the connectivity of neurons, and the structural heterogeneity we considered was “degree,” the number of other neurons in the network a neuron was connected to. We looked for regimes in which the variation is explained by both the structural and intrinsic heterogeneity, not just the intrinsic one. We also propose a way to simulate the SCN using coarse projective integration, which would allow for the simulation of more neurons over a longer period of time.
Extent: 52 pages
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Chemical and Biological Engineering, 1931-2017

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