Princeton University Library Catalog

Coarse-­‐Graining the Dynamics of Coupled Oscillators to Model Neurons in the Suprachiasmatic Nucleus

Anand, Angad [Browse]
Senior thesis
Kevrekidis, Yannis G. [Browse]
Princeton University. Department of Chemical and Biological Engineering [Browse]
Class year:
52 pages
Summary note:
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.