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Resetting behavior in a model of bursting in secretory pituitary cells: distinguishing plateaus from pseudo-plateaus

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  • V Stern, Juli
  • Hinke M Osinga
  • Andrew LeBeau
  • Arthur Sherman
Original languageEnglish
Publication date2007
StateIn press

Abstract

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 timecourses 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.

Additional information

Additional information: To appear in Bulletin of Mathematical Biology

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