• James Keener
  • James Sneyd
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 8/1)

We have seen in previous chapters that the control of cell volume results in a potential difference across the cell membrane, and that this potential difference causes ionic currents to flow through channels in the cell membrane. Regulation of this membranepotential by control of the ionic channels is one of the most important cellular functions. Many cells, such as neurons and muscle cells, use the membrane potential as a signal, and thus the operation of the nervous system and muscle contraction (to name but two examples) are both dependent on the generation and propagation of electrical signals.

To understand electrical signaling in cells, it is helpful (and not too inaccurate) to divide all cells into two groups: excitable cells and nonexcitable cells. Many cells maintain a stable equilibrium potential. For some, if currents are applied to the cell for a short period of time, the potential returns directly to its equilibrium value after the applied current is removed. Such cells are nonexcitable, typical examples of which are the epithelial cells that line the walls of the gut. Photoreceptors (Chapter 19) are also nonexcitable, although in their case, membrane potential plays an extremely important signaling role nonetheless.


Hopf Bifurcation Phase Portrait Bifurcation Diagram Phase Plane Applied Current 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • James Keener
    • 1
  • James Sneyd
    • 2
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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