Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells

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Abstract

In the presence of stimulatory concentrations of glucose, the membrane potential of pancreatic β-cells may experience a transition from periods of rapid spike-like oscillations alternating with a pseudo-steady state to spike-only oscillations. Insulin secretion from β-cells closely correlates the periods of spike-like oscillations. The purpose of this paper is to study the mathematical structure which underlines this transitional stage in a pancreatic β-cell model. It is demonstrated that the transition can be chaotic but becomes more and more regular with increase in glucose. In particular, the system undergoes a reversed period-doubling cascade leading to the spike-only oscillations as the glucose concentration crosses a threshold. The transition interval in glucose concentration is estimated to be extremely small in terms of the rate of change for the calcium dynamics in the β-cells. The methods are based on the theory of unimodal maps and the geometric and asymptotic theories of singular perturbations.

Original languageEnglish (US)
Pages (from-to)21-78
Number of pages58
JournalJournal of Mathematical Biology
Volume38
Issue number1
DOIs
Publication statusPublished - Jan 1999

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Keywords

  • Asymptotic expansion
  • Bursting-spiking oscillations
  • Continuous spiking oscillations
  • Junction point
  • Junction-fold point
  • Kneading sequence
  • Period-doubling cascade
  • Poincaré map
  • Slow manifold
  • Stable and unstable foliations
  • Turning point

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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