Applied Mathematics, University of Waterloo
Persistent Oscillations in the Aplysia bag cell network
The Aplysia bag cell neuron serves as an ideal model for dynamical switching in persistent neural systems. Persistent neural systems can exhibit long-term responses to stimulus,
often switching from the traditional excitable, steady-state dynamics to a period of repeated spiking or bursting. In Aplysia, such behavior, known as the afterdischarge, is exhibited by the bag cell neuron and regulated by second messenger calcium dynamics.
A model is constructed based on experimental data that includes many qualitative features of the Aplysia bag cell electrophysiology, including use-dependence, non-selective cation channels, calcium persistence, all of which contribute to afterdischarge dynamics. Several methods are used to fit experimental data and construct the model, including hand tuning, parameter forcing, genetic algorithms, and continuation analysis in an effort to overcome degeneracy, sensitivity, and other barriers to complex model construction. Once the neuron model is established, a diffusively-coupled network model is constructed to simulate the electrical coupling observed in bag cell clusters in nature. A simple two-neuron network reproduces some experimental results and larger networks are considered. Little is known about the topology of Aplysia bag cell neurons. The final chapter of this thesis explores different topologies in a 100-neuron network, exploring how the coupling constant, topology, and size of the network affects the network’s ability to synchronize.