Mixed mode oscillations as a mechanism for pseudo-plateau bursting |
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Authors: | Theodore Vo Richard Bertram Joel Tabak Martin Wechselberger |
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Institution: | (1) School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia;(2) Department of Mathematics and Programs in Neuroscience and Molecular Biophysics, Florida State University, Tallahassee, FL, USA;(3) Department of Biological Science, Florida State University, Tallahassee, FL, USA; |
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Abstract: | We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a
novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell,
is characterized by small impulses or spikes riding on top of an elevated voltage plateau. Oscillations with these characteristics
have been called “pseudo-plateau bursting”. Unlike standard bursting, the subsystem of fast variables does not possess a stable
branch of periodic spiking solutions, and in the case studied here the standard fast/slow analysis provides little information
about the underlying dynamics. We demonstrate that the bursting is actually a canard-induced mixed mode oscillation, and use
canard theory to characterize the dynamics of the oscillation. We also use bifurcation analysis of the full system of equations
to extend the results of the singular analysis to the physiological regime. This demonstrates that the combination of these
two analysis techniques can be a powerful tool for understanding the pseudo-plateau bursting oscillations that arise in electrically
excitable pituitary cells and isolated pancreatic β-cells. |
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