Voltage Gated Ionic Currents

  • Christopher P. Fall
  • Joel E. Keizer
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 20)


In Chapter 1 we introduced models of simple channel behavior but ignored the idea that something might flow through such a channel. In this chapter we will learn how to model current flowing through ion channels and how to include the feedback regulation of the channel behavior by voltage. But let us be very clear about what we are modeling in this chapter. Only in the most idealized sense are we modeling the behavior of excitable cells like neurons. In fact, we will be creating point models of patches of membrane, with only implicit consideration through the use of ion concentrations of the idea that the membrane encloses a compartment. We do not consider at all that a neuron is a highly complicated cell that integrates signals within dendrites and a soma before producing action potentials in an excitable axon. Some of the diverse neuronal shapes are shown in Figure 2.1.


Ionic Battery Stable Limit Cycle Stable Steady State Squid Giant Axon Unstable Limit Cycle 
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© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Christopher P. Fall
  • Joel E. Keizer

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