Chapter in “Case Studies in Mathematical Modeling—Ecology, Physiology, and Cell Biology,” H. G. Othmer, F. R. Adler, M. A. Lewis, and J. C. Dallon, eds. Prentice Hall,1997.
The chapter, Calcium and Membrane Potential Oscillations in Pancreatic beta-Cells: Unofficial PDF Version with Exercises (314K).
The figures in the chapter can be reproduced using the files below, which are inputs for the ODE solver xpp.
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Basic Model (Figs. 1 - 7, 11)
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Two variable (fast subsystem) vn.ode (Figs. 2 - 3, 7).
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Two variable (for IV curves only) ivcurves.ode (Fig. 1).
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Three variable bursting model (Figs. 5, 6).
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v-s pseudo-phase plane for Z-curves and slow nullclines zeecurves.ode (Figs. 5, 7).
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Bursting Model with Electrical Coupling of Two Cells (Fig. 11).
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Extended Model with Endoplasmic Reticulum for muscarinic bursting (Fig. 9).
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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]
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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]
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Example of a bursting model with a Non-Planar Fast Subsystem from A. Sherman, J. Keizer, and J. Rinzel. 1990. Domain model for Ca2+ inactivation of Ca2+ channels at low channel density. Biophys. J. 58:985-995. [PubMed] (Ex. 10).