Past REU Participants & Project Pages

2006 REU Porjects
2006 REU Projects
2006 Participant: Josilaida Lawrence
Project Title: Modeling mammalian SCN neuron behavior as circadian oscillators

Advisors:John L. Hudson Ph. D, Istvan Z. Kiss Ph. D., Joseph J. Maurer M.Sc.
Introduction:
Circadian rhythms are important in determining daily patterns of all animals and humans. There are clear patterns of several biological activities linked to these rhythms. In mammals, a clock in the suprachiasmatic nucleus (SCN) comprises multiple autonomous single-cell oscillators, but it is unclear how SCN cells interact to form a tissue with coherent metabolic and electrical rhythms that might account for circadian animal behaviors. The objectives of this research are the modeling of two and three oscillators in a linear pattern and the determination of the value of the minimum coupling strength needed to reach synchrony. This model was made using the Goodwin equations. This system of equations presents the model of circadian oscillations in mammalian cells. To obtain a model of different oscillators, parameter v1 was varied. The system was modeled using different initial conditions for the system of equations and varying the value of the parameter K. Parameter K represents the coupling strength in the system. For each value of K, the period of the oscillator was measured. This leads to a plot of Period vs. Coupling Strength that shows the behavior of the oscillators as they interact with each other. For two oscillators, the obtained data showed the value of K at which both oscillators synchronize is 0.1. For a system of three oscillators, the data showed that the synchronization is reached when K is 0.09. The modeling of these systems proved that adding a third cell to a system of two cells, reduces the coupling strength needed to reach synchronization.

Conclusion:
Based on the obtained data, all of the objectives were accomplished. We could analyze the behavior of a system of two and three oscillators and determine the minimum value of parameter K to reach synchronization. Desynchronization of neurons can result in sleeping disorders, unbalanced hormones, epilepsy and different biological activities. The research of this field can lead to a better understanding of why these cells can be desynchronized and how they can be made to synchronize again. Expansion of this research can include the analysis of the behavior of three oscillators when alternating the values of parameter v1.
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