Prediction of the Glucose-Induced Changes in Membrane Ionic Permeability and Cytosolic Ca2+ by Mathematical Modeling

  • J. Rinzel
  • T. R. Chay
  • D. Himmel
  • I. Atwater
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 211)


Probably the most interesting property of pancreatic β-cells is their ability to detect and respond to the concentration of glucose in the plasma. Most experiments performed on islets are done in search of understanding this enigmatic process. For example, electrophysiological studies on the β-cell have indicated that the oscillations in membrane potential, which involve repetitive bursts of action potentials, are a necessary part of the glucose recognition process.4,10,28,29,33 This “burst pattern” is generated by the interplay between ionic channels in the β-cell membrane.1,2,3,4,5,7,19,20,22 One proposal is that the glucose sensitivity is due to changes in the efflux rate of ionic Ca from the cytosol.7 Recently, Chay and Keizer,14,15 and Chay12 developed a mathematical model which reproduces the β-cell’s unique glucose-sensitive bursting pattern of electrical activity. The model is based upon experimentally determined membrane ionic permeabilities: voltage-gated Ca-channels,2 voltage-gated K-channels,5 Ca-activated K-channels.3,7,22 In the model, glucose recognition is equated to the rate of Ca2+ uptake, kCa in the β-cell.


Membrane Potential Silent Phase Glucose Sensitivity Steady State Potential Phase Plane Analysis 


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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • J. Rinzel
    • 1
    • 2
  • T. R. Chay
    • 1
    • 2
  • D. Himmel
    • 1
    • 2
  • I. Atwater
    • 1
    • 2
  1. 1.LCBG and MRB, NIDDKNational Institutes of HealthBethesdaUSA
  2. 2.Dept. of Biological SciencesUniversity of PittsburghPittsburghUSA

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