"Pancreatic Beta-Cell Models"

Chapter in "Case Studies in Mathematical Modeling"

The chapter: Unofficial gzipped PostScript Version with Exercises (177K); (PDF version) (314K).

The figures in the chapter can be reproduced using the files below, which are inputs for Bard Ermentrout's xpp interactive program for solving ODEs. They are also human-readable and easily translated into formats usable by other differential equation solvers. For a list of other solvers, click here.

• Basic Model (Figs. 1 - 7, 11)
  • Two variable (fast subsystem) (Figs. 2 - 3, 7).

  • Two variable (for IV curves only) (Fig. 1).

  • Three variable bursting model (Figs. 5, 6).

  • v-s pseudo-phase plane for Z-curves and slow nullclines (Figs. 5, 7).

  • Bursting Model with Electrical Coupling (Two Cells) (Fig. 11).

• Extended Model with Endoplasmic Reticulum for muscarinic bursting (Fig. 9).

• Bi-phasic Transient (Fig. 10) with model from R. Bertram, P. Smolen, A. Sherman, D. Mears, I. Atwater, F. Martin, and B. Soria. 1995. A role for calcium-release activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells. Biophys. J. 68:2323-2332.  [PubMed]
  [Lab reprint list].

• Two Parameter Diagram (Fig. 8) and phase plane sketches (Fig. 4) are taken from R. Bertram, M. Butte, T. Kiemel, and A. Sherman. 1995. Topological and phenomenological classification of bursting mechanisms. Bull. Math. Biol. 57:413-439.  [PubMed]
  [Lab Reprint List]).

• Example of a bursting model with a Non-Planar Fast Subsystem (Ex. 10).

(Note: The U. S. government is not responsible for content of any links to sites outside the NIH.)

Please send your comments/suggestions about this page to:

asherman@nih.gov

To go back to Sherman's Home Page click here

Last Updated 07/07/05