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. 1972 Jul;69(7):1723–1726. doi: 10.1073/pnas.69.7.1723

On the Theory of Ion Transport Across the Nerve Membrane, VI. Free Energy and Activation Free Energies of Conformational Change*

Terrell L Hill 1, Yi-Der Chen 1
PMCID: PMC426787  PMID: 4505649

Abstract

Empirical functions, such as n∞(V) and τn(V) (of the Hodgkin-Huxley type), can be recast in terms of more fundamental functions F(V) (related to a conformational free energy change) and θ(V) (related to the corresponding free energies of activation). Examples of F(V) and θ(V) are given, for squid and frog node. F(V) is essentially a quadratic function of V. The possible molecular origin, for protein-like subunits, of the linear (e.g., net charge) and quadratic (e.g., polarizability) terms in F(V) is discussed. The F(V), θ(V) kind of analysis leads rather automatically to a simple explanation of the well-known approximate coincidence in location (V value) of the maximum in τn(V) (time constant) and the steeply rising part of n∞(V) (also m, 1 - h).

Keywords: protein complex, electric field, net charge, polarizability, time constant maximum

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Selected References

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

  1. FRANKENHAEUSER B. INACTIVATION OF THE SODIUM-CARRYING MECHANISM IN MYELINATED NERVE FIBRES OF XENOPUS LAEVIS. J Physiol. 1963 Nov;169:445–451. doi: 10.1113/jphysiol.1963.sp007271. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. FRANKENHAEUSER B. Quantitative description of sodium currents in myelinated nerve fibres of Xenopus laevis. J Physiol. 1960 Jun;151:491–501. doi: 10.1113/jphysiol.1960.sp006455. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. FRANKENHAEUSER B. Steady state inactivation of sodium permeability in myelinated nerve fibres of Xenopus laevis. J Physiol. 1959 Oct;148:671–676. doi: 10.1113/jphysiol.1959.sp006316. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Gilbert D. L., Ehrenstein G. Effect of divalent cations on potassium conductance of squid axons: determination of surface charge. Biophys J. 1969 Mar;9(3):447–463. doi: 10.1016/S0006-3495(69)86396-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Hill T. L., Chen Y. D. Cooperative effects in models of steady-state transport across membranes. II. Oscillating phase transition. Proc Natl Acad Sci U S A. 1970 May;66(1):189–196. doi: 10.1073/pnas.66.1.189. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Hill T. L., Chen Y. D. Cooperative effects in models of steady-state transport across membranes. IV. One-site, two-site, and multisite models. Biophys J. 1971 Sep;11(9):685–710. doi: 10.1016/S0006-3495(71)86248-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Hill T. L., Chen Y. D. On the theory of ion transport across the nerve membrane. 3. Potassium ion kinetics and cooperativity (with x=4,6,9). Proc Natl Acad Sci U S A. 1971 Oct;68(10):2488–2492. doi: 10.1073/pnas.68.10.2488. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Hill T. L., Chen Y. D. On the theory of ion transport across the nerve membrane. II. Potassium ion kinetics and cooperativity (with x = 4). Proc Natl Acad Sci U S A. 1971 Aug;68(8):1711–1715. doi: 10.1073/pnas.68.8.1711. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Hill T. L., Chen Y. Cooperative effects in models of steady-state transport across membranes. 3. Simulation of potassium ion transport in nerve. Proc Natl Acad Sci U S A. 1970 Jul;66(3):607–614. doi: 10.1073/pnas.66.3.607. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Hill T. L. Electric fields and the cooperativity of biological membranes. Proc Natl Acad Sci U S A. 1967 Jul;58(1):111–114. doi: 10.1073/pnas.58.1.111. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Hoyt R. C., Adelman W. J., Jr Sodium inactivation. Experimental test of two models. Biophys J. 1970 Jul;10(7):610–617. doi: 10.1016/S0006-3495(70)86323-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Kirkwood J. G., Shumaker J. B. The Influence of Dipole Moment Fluctuations on the Dielectric Increment of Proteins in Solution. Proc Natl Acad Sci U S A. 1952 Oct;38(10):855–862. doi: 10.1073/pnas.38.10.855. [DOI] [PMC free article] [PubMed] [Google Scholar]

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