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. 1963 Sep;3(5):399–431. doi: 10.1016/s0006-3495(63)86829-0

The Squid Giant Axon

Mathematical Models

Rosalie C Hoyt
PMCID: PMC1366457  PMID: 14062458

Abstract

The voltage clamp results of Hodgkin and Huxley have been reanalyzed in terms of alternative mathematical models. The model used for the potassium conductance changes is similar to that of the HH model except that an empirical functional relationship replaces the fourth power Law used by HH and the twenty-fifth power law used by Cole and Moore. The model used for the sodium conductance changes involves the explicit use of one variable only rather than the two variables m and h of HH. The rise and fall of the sodium conductance during a depolarizing voltage clamp is obtained by specifying that this one variable satisfies a second order differential equation which results from the coupling of two first order equations. Not only can the adjustable parameters of these models be made to give good fit to the clamp conductance data but the models can also then be used to compute action potential curves. Theoretical interpretations can also be given to these mathematical models.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

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