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

Research output: Contribution to journalArticle

21 Citations (Scopus)

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
StatePublished - Jan 1999

Fingerprint

Period Doubling
Glucose
Spike
Cascade
oscillation
Oscillation
glucose
Cell
cells
Unimodal Map
Membrane Potential
Insulin
Rate of change
insulin secretion
Secretion
Asymptotic Theory
Singular Perturbation
Calcium
membrane potential
Membrane Potentials

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

Cite this

Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells. / Deng, Bo.

In: Journal of Mathematical Biology, Vol. 38, No. 1, 01.1999, p. 21-78.

Research output: Contribution to journalArticle

@article{b0333c63e3ab4778887ed60e3c50b7c8,
title = "Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells",
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.",
keywords = "Asymptotic expansion, Bursting-spiking oscillations, Continuous spiking oscillations, Junction point, Junction-fold point, Kneading sequence, Period-doubling cascade, Poincar{\'e} map, Slow manifold, Stable and unstable foliations, Turning point",
author = "Bo Deng",
year = "1999",
month = "1",
doi = "10.1007/s002850050141",
language = "English (US)",
volume = "38",
pages = "21--78",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
number = "1",

}

TY - JOUR

T1 - Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells

AU - Deng, Bo

PY - 1999/1

Y1 - 1999/1

N2 - 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.

AB - 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.

KW - Asymptotic expansion

KW - Bursting-spiking oscillations

KW - Continuous spiking oscillations

KW - Junction point

KW - Junction-fold point

KW - Kneading sequence

KW - Period-doubling cascade

KW - Poincaré map

KW - Slow manifold

KW - Stable and unstable foliations

KW - Turning point

UR - http://www.scopus.com/inward/record.url?scp=0032603032&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032603032&partnerID=8YFLogxK

U2 - 10.1007/s002850050141

DO - 10.1007/s002850050141

M3 - Article

C2 - 10065539

AN - SCOPUS:0032603032

VL - 38

SP - 21

EP - 78

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 1

ER -