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The Variety of Channels

  • G. Bard Ermentrout
  • David H. Terman
Chapter
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 35)

Abstract

We have discussed several types of active (voltage-gated) channels for specific neuron models. The Hodgkin–Huxley model for the squid axon consisted of three different ion channels: a passive leak, a transient sodium channel, and the delayed rectifier potassium channel. Similarly, the Morris–Lecar model has a delayed rectifier and a simple calcium channel (with no dynamics). Hodgkin and Huxley were smart and supremely lucky that they used the squid axon as a model to analyze the action potential, as it turns out that most neurons have dozens of different ion channels. In this chapter, we briefly describe a number of them, provide some instances of their formulas, and describe how they influence a cell’s firing properties. The reader who is interested in finding out about other channels and other models for the channels described here should consult http://senselab.med.yale.edu/modeldb/default.asp, which is a database for neural models.

Keywords

Firing Rate Hopf Bifurcation Sodium Current Fold Point Squid Axon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. MathematicsUniversity of PittsburghPittsburghUSA
  2. 2.Dept. MathematicsOhio State UniversityColumbusUSA

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