An open system kinetic transport model for the hodgkin-huxley equations

Michael E. Starzak, Daniel A. Tranchina

Research output: Contribution to journalArticle

Abstract

A discrete state "ion-hopping" mechanism is developed for the description of potassium ion flows in voltage clamped squid giant axon membranes. Although the mechanism differs from the "gating" mechanism proposed by Hodgkin & Huxley, it yields an identical mathematical description. The discrete state transport mechanism requires interaction between the ions and the channel and is based on the concept of an "open" system. The bathing solutions on each side of the membrane act as ion sources for states within the membrane. The feasibility of a sequential mechanism is explored and the experimental procedures of Hodgkin & Huxley are re-examined to show their consistency with both the gating and sequential, kinetic mechanisms. The basic sequential kinetic scheme. (i; ⇌; 4 β) (1) (α; ⇌; 3 β) (2) (2 α; ⇌; 2 β) (3) (3 α; ⇌; β) (4) (4α; →;). with the Hodgkin-Huxley rate constants α and β yields the mathematical form of the Hodgkin-Huxley equations. The sequential kinetic model can be differentiated from the gating model by a straightforward experiment which is discussed.

Original languageEnglish (US)
Pages (from-to)283-299
Number of pages17
JournalJournal of Theoretical Biology
Volume56
Issue number2
DOIs
StatePublished - Feb 1976

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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