Skip to main content
SpringerLink
Log in

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

  • Chapter
Biophysics of the Pancreatic β-Cell

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 211))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. M. Ashcroft, D. E. Harrison, and S. J. H. Ashcroft, Glucose induces closure of single postassium channels in isolated rat pancreatic β-cells, Nature 312:446 (1984).

    Article  PubMed  CAS  Google Scholar 

  2. I. Atwater, C. M. Dawson, G. T. Eddlestone, and E. Rojas, Voltage noise measurements across the pancreatic β-cell membrane: calcium channel characteristics, J. Physiol. 314:195 (1981).

    PubMed  CAS  Google Scholar 

  3. I. Atwater, C. M. Dawson, B. Ribalet, and E. Rojas, Potassium permeability activated by intracellular calcium ion concentration in the pancreatic β-cell, J. Physiol. (London) 288:575 (1979).

    CAS  Google Scholar 

  4. I. Atwater, C. M. Dawson, A. Scott, G. Eddlestone, and E. Rojas, The nature of the oscillatory behavior in electrical activity for pancreatic β-cells, J.Horm. Metabolic Res. Suppl. 10:101 (1980).

    Google Scholar 

  5. I. Atwater, B. Ribalet, and E. Rojas, Mouse pancreatic β-cells: tetraethylammonium blockage of the postassium permeability increase induced by depolarization, J. Physiol. (London) 288:561 (1979).

    CAS  Google Scholar 

  6. I. Atwater, A. Goncalves, and E. Rojas, Electrophysiological measurement of an oscillating potassium permeability during the glucose-stimulated burst activity in mouse pancreatic β-cell, Biomedical Research 3:645 (1982).

    CAS  Google Scholar 

  7. I. Atwater, L. Rosario, and E. Rojas, Properties of the Ca-activated K-channel in pancreatic β-cells, Cell Calcium 4:451 (1983).

    Article  PubMed  CAS  Google Scholar 

  8. I. Atwater and J. Rinzel, The β-cell bursting pattern and intra-cellular calcium, in: “Ionic Channels in Cells and Model Systems,” R. Latorre, R., Ed., Plenum, New York (1986).

    Google Scholar 

  9. J. A. Bangham, P. A. Smith, and P. C. Groghan, Modelling the β-cell electrical activity, this book.

    Google Scholar 

  10. P. M. Beigelman, B. Ribalet, and I. Atwater, Electrical activity of mouse pancreatic β-cells. II. Effects of glucose and arginine, J. Physiol. (Paris) 73:201 (1977).

    CAS  Google Scholar 

  11. A. E. Boyd, III, R. S. Hill, T. Y. Nelson, J. M. Oberwetter, and M. Berg, The role of cytosolic calcium in insulin secretion from a hamster β-cell line, this book.

    Google Scholar 

  12. T. R. Chay, Chaos in a three-variable model of an excitable cell, Physica. D. 16:223 (1985).

    Article  Google Scholar 

  13. T. R. Chay, Glucose response to bursting-spiking pancreatic β-cells by a barrier kinetic model, Biol. Cybern. 52:339 (1985).

    Article  PubMed  CAS  Google Scholar 

  14. T. R. Chay and J. Keizer, Minimal model for membrane oscillations in the pancreatic β-cell, Biophys. J. 42:181 (1983).

    Article  PubMed  CAS  Google Scholar 

  15. T. R. Chay and J. Keizer, Theory of the effect of extracellular potassium on oscillations in the pancreatic β-cell, Biophysical J. 48:815 (1985).

    Article  CAS  Google Scholar 

  16. T. R. Chay and J. Rinzel, Bursting, beating, and chaos in an excitable membrane model, Biophysical J. 47:357 (1985).

    Article  CAS  Google Scholar 

  17. T. R. Chay, Oscillations and chaos in the pancreatic β-cell, in: “Biomathematics, Non Linear Oscillations in Biology and Chemistry,” Lecture Notes in Biomathematics, Springer Verlag, NY (1986).

    Google Scholar 

  18. T. R. Chay, The role of intracellular calcium on the Ca2+ sensitive K+-sensitive K+-channel on the bursting pancreatic β-cell, Biophys. J., in press (1986).

    Google Scholar 

  19. D. L. Cook and C. N. Hales, Intracellular ATP directly blocks K+ channels in pancreatic β-cells, Nature 311:271 (1984).

    Article  PubMed  CAS  Google Scholar 

  20. D. L. Cook, M. Ikeuchi, and W. Y. Fujimoto, Lowering of pHi inhibits Ca2+-activated K+ channels in pancreatic β-cells, Nature 311:269 (1984).

    Article  PubMed  CAS  Google Scholar 

  21. G. T. Eddlestone, A. Goncalves, J. A. Bangham, and E. Rojas, Electrical coupling between cells in islets of Langerhans from mouse, J. Membrane Biol. 77:1 (1984).

    Article  CAS  Google Scholar 

  22. I. Findlay, M. J. Dunne, and O. H. Petersen, High-conductance K+ channel in pancreatic islet cells can be activated and inactivated by internal calcium, J. Membrane Biol. 83:169 (1985).

    Article  CAS  Google Scholar 

  23. B. Hellman, E. R. Gylfe, and P. Bergsten, Mobilization of different pools of glucose-incorporated calcium in pancreatic β-cells after muscarinic receptor activation, this book.

    Google Scholar 

  24. D. M. Himmel, T. R. Chay, Computer simulations of the electrical activity of pancreatic β-cells as a function of glucose, Biophys. J. (submitted).

    Google Scholar 

  25. A. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (London) 117:500 (1952).

    CAS  Google Scholar 

  26. P. Lebrun and I. Atwater, Chaotic and irregular bursting electrical activity in mouse pancreatic β-cells, Biophys. J. 48:529 (1985).

    Article  PubMed  CAS  Google Scholar 

  27. P. Meda, I. Atwater, A. Goncalves, A. Bangham, L. Orci, and E. Rojas, The topography of electrical synchrony among β-cells in the mouse islet of Langerhans, Quart. J. Exp. Physiol. 69:719 (1984).

    CAS  Google Scholar 

  28. H. P. Meissner and M. Preissler, Glucose-induced changes of the membrane potential of pancreatic β-cells: their significance for the regulation of insulin release, in “Treatment of Early Diabetes,” R. A. Camerini-Davalos and B. Hanover, eds., Plenum Press, New York (1979).

    Google Scholar 

  29. H. P. Meissner and H. Schmelz, Membrane potential of beta-cells in pancreatic islets, Pflugers Arch. 351:195 (1974).

    Article  PubMed  CAS  Google Scholar 

  30. O. H. Petersen and Y. Maruyama, Calcium-activated potassium channels and their role in secretion, Nature 307:693 (1984).

    Article  PubMed  CAS  Google Scholar 

  31. M. Prentki and C. B. Wollheim, Cytosolic free Ca2+ in insulin secreting cells and its regulation by isolated organelles, Experientia 40:1052 (1984).

    Article  PubMed  CAS  Google Scholar 

  32. P. Rorsman, H. Abrahamsson, E. Gylfe, and B. O. Hellman, Dual effects of glucose on the cytosolic Ca2+ activity of mouse pancreatic β-cells, FEBS Lett. 170(1): 196 (1984).

    Article  PubMed  CAS  Google Scholar 

  33. A. M. Scott, I. Atwater, and E. Rojas, A method for the simultaneous measurement of insulin release and β-cell membrane potential in single mouse islets of Langerhans, Diabetologia 21:470 (1981).

    Article  PubMed  CAS  Google Scholar 

  34. Trube and P. Rorsman, Calcium and potassium currents recorded from pancreatic β-cells under voltage clamp control, this book.

    Google Scholar 

  35. C. B. Wollheim and T. Pozzan, Correlation between cytosolic free Ca2+ and insulin release in an insulin-secreting cell line, J. Biol. Chem. 259:2262 (1984).

    PubMed  CAS  Google Scholar 

  36. G. H. J. Wolters, M. Vank, and A. Pajma, Relationship between extracellular Na+ and the total ionized Ca2+ content of rat pancreatic islets, this book.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LCBG and MRB, NIDDK, National Institutes of Health, Bethesda, MD, USA

    J. Rinzel, T. R. Chay, D. Himmel & I. Atwater

  2. Dept. of Biological Sciences, University of Pittsburgh, Pittsburgh, PA, USA

    J. Rinzel, T. R. Chay, D. Himmel & I. Atwater

Authors
  1. J. Rinzel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. R. Chay
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Himmel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. I. Atwater
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. National Institutes of Health, Bethesda, Maryland, USA

    Illani Atwater  & Eduardo Rojas  & 

  2. University of Alicante, Alicante, Spain

    Bernat Soria

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Plenum Press, New York

About this chapter

Cite this chapter

Rinzel, J., Chay, T.R., Himmel, D., Atwater, I. (1986). Prediction of the Glucose-Induced Changes in Membrane Ionic Permeability and Cytosolic Ca2+ by Mathematical Modeling. In: Atwater, I., Rojas, E., Soria, B. (eds) Biophysics of the Pancreatic β-Cell. Advances in Experimental Medicine and Biology, vol 211. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5314-0_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-5314-0_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-5316-4

  • Online ISBN: 978-1-4684-5314-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation