Bulletin of Mathematical Biology

, Volume 70, Issue 1, pp 68–88

Resetting Behavior in a Model of Bursting in Secretory Pituitary Cells: Distinguishing Plateaus from Pseudo-Plateaus

  • Julie V. Stern
  • Hinke M. Osinga
  • Andrew LeBeau
  • Arthur Sherman
Original Article

DOI: 10.1007/s11538-007-9241-x

Cite this article as:
Stern, J.V., Osinga, H.M., LeBeau, A. et al. Bull. Math. Biol. (2008) 70: 68. doi:10.1007/s11538-007-9241-x

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 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.

Keywords

Bursting Calcium oscillations Pituitary Stable and unstable manifolds Fast-slow systems 

Copyright information

© Society for Mathematical Biology 2007

Authors and Affiliations

  • Julie V. Stern
    • 1
  • Hinke M. Osinga
    • 2
  • Andrew LeBeau
    • 1
  • Arthur Sherman
    • 1
  1. 1.Laboratory of Biological ModelingNational Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of HealthBethesdaUSA
  2. 2.Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering MathematicsUniversity of BristolBristolUK