Whole—Cell Models

  • Arthur S. Sherman
  • Yue-Xian Li
  • Joel E. Keizer
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 20)


In modeling whole cells we try to understand complex properties of cells by combining interlocking transport and regulatory mechanisms. We use a modular approach and develop models of each individual process separately using available experimental data. We then construct progressively more complete models by combining components to understand how they work together. Sometimes, we proceed in the opposite order, beginning with a comprehensive model, which we simplify in order to determine the minimal essential elements. One particularly useful simplification technique is to exploit separation of time scales to set fast processes to equilibrium as described in Chapter 4.


Endoplasmic Reticulum Hopf Bifurcation Bifurcation Diagram Homoclinic Orbit Endoplasmic Reticulum Membrane 
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Suggestions for Further Reading

  1. •.
    Ryanodine receptor adaptation and Ca2+-induced Ca2+ release-dependent Ca2+ oscillations, Joel Keizer and Leslie Levine. This paper is the original source for the Keizer-Levine model (Keizer and Levine 1996).Google Scholar
  2. •.
    Ca2+ excitability of the ER membrane: an explanation for IP3-induced Ca2+ oscillations, Yue Xian Li, Joel Keizer, Stanko S. Stojilković, and John Rinzel. A review of how the gonadotroph model described here was developed, with some equations and discussion of scaling and references to the physiolgical literature (Li et al. 1995b).Google Scholar
  3. •.
    InsP3-induced Ca2+ excitability of the endoplasmic reticulum, Joel Keizer, Yue Xian Li, Stanko Stojilković, and John Rinzel. Another review of the gonadotroph, but in words and pictures. This review contains many references to the physiological literature (Keizer et al. 1995).Google Scholar
  4. •.
    Contributions of modeling to understanding stimulus-secretion coupling in pancreatic β-cells, Arthur Sherman. A review of β-cell modeling oriented toward biologists (Sherman 1996).Google Scholar
  5. •.
    Calcium and membrane potential oscillations in pancreatic β-cells, Arthur Sherman. A mathematical tutorial centered on β-cell models with some connections to general modeling of bursting. Covers phase plane and bifurcation analysis (Sherman 1997).Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Arthur S. Sherman
  • Yue-Xian Li
  • Joel E. Keizer

There are no affiliations available

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