Resetting Behavior in a Model of Bursting in Secretory Pituitary Cells: Distinguishing Plateaus from Pseudo-Plateaus
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We study a recently discovered class of models for plateau bursting, inspired by models for endocrine pituitary cells. In contrast to classical models for fold-homoclinic (square-wave) bursting, the spikes of the active phase are not supported by limit cycles of the frozen fast subsystem, but are transient oscillations generated by unstable limit cycles emanating from a subcritical Hopf bifurcation around a stable steady state. Experimental time courses are suggestive of such fold-subHopf models because the spikes tend to be small and variable in amplitude; we call this pseudo-plateau bursting. We show here that distinct properties of the response to attempted resets from the silent phase to the active phase provide a clearer, qualitative criterion for choosing between the two classes of models. The fold-homoclinic class is characterized by induced active phases that increase towards the duration of the unperturbed active phase as resets are delivered later in the silent phase. For the fold-subHopf class of pseudo-plateau bursting, resetting is difficult and succeeds only in limited windows of the silent phase but, paradoxically, can dramatically exceed the native active phase duration.
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- Resetting Behavior in a Model of Bursting in Secretory Pituitary Cells: Distinguishing Plateaus from Pseudo-Plateaus
Bulletin of Mathematical Biology
Volume 70, Issue 1 , pp 68-88
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- Calcium oscillations
- Stable and unstable manifolds
- Fast-slow systems
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- 1. Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD, USA
- 2. Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering Mathematics, University of Bristol, Queen’s Building, University Walk, BS8 1TR, Bristol, UK