Bulletin of Mathematical Biology

, Volume 73, Issue 6, pp 1292–1311 | Cite as

From Plateau to Pseudo-Plateau Bursting: Making the Transition

  • Wondimu Teka
  • Krasimira Tsaneva-Atanasova
  • Richard Bertram
  • Joël Tabak
Original Article

Abstract

Bursting electrical activity is ubiquitous in excitable cells such as neurons and many endocrine cells. The technique of fast/slow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been identified with this technique, plateau and pseudo-plateau bursting, are often observed in neurons and endocrine cells, respectively. These two types of bursting have very different properties and likely serve different functions. This latter point is supported by the divergent expression of the bursting patterns into different cell types, and raises the question of whether it is even possible for a model for one type of cell to produce bursting of the type seen in the other type without large changes to the model. Using fast/slow analysis, we show here that this is possible, and we provide a procedure for achieving this transition. This suggests that the design principles for bursting in endocrine cells are just quantitative variations of those for bursting in neurons.

Keywords

Bursting Pituitary cells Islets Calcium Mathematical model 

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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • Wondimu Teka
    • 1
  • Krasimira Tsaneva-Atanasova
    • 2
  • Richard Bertram
    • 3
  • Joël Tabak
    • 4
  1. 1.Department of MathematicsFlorida State UniversityTallahasseeUSA
  2. 2.Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering MathematicsUniversity of BristolBristolUK
  3. 3.Department of Mathematics, and Programs in Neuroscience and Molecular BiophysicsFlorida State UniversityTallahasseeUSA
  4. 4.Department of Biological ScienceFlorida State UniversityTallahasseeUSA

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