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Another interpretation of the Goldman–Hodgkin–Katz equation based on Ling’s adsorption theory

  • Hirohisa Tamagawa
  • Kota Ikeda
Original Article
  • 33 Downloads

Abstract

According to standard membrane theory, the generation of membrane potential is attributed to transmembrane ion transport. However, there have been a number of reports of membrane behavior in conflict with the membrane theory of cellular potential. Putting aside the membrane theory, we scrutinized the generation mechanism of membrane potential from the view of the long-dismissed adsorption theory of Ling. Ling’s adsorption theory attributes the membrane potential generation to mobile ion adsorption. Although Ling’s adsorption theory conflicts with the broadly accepted membrane theory, we found that it well reproduces experimentally observed membrane potential behavior. Our theoretical analysis finds that the potential formula based on the GHK eq., which is a fundamental concept of membrane theory, coincides with the potential formula based on Ling’s adsorption theory. Reinterpreting the permeability coefficient in the GHK eq. as the association constant between the mobile ion and adsorption site, the GHK eq. turns into the potential formula from Ling’s adsorption theory. We conclude that the membrane potential is generated by ion adsorption as Ling’s adsorption theory states and that the membrane theory of cellular potential should be amended even if not discarded.

Keywords

Membrane theory Goldman–Hodgkin–Katz Permeability coefficient Ling’s adsorption theory Association constant 

Notes

Acknowledgements

This work was carried out under the financial support by Koshiyama Science and Technology Foundation.

References

  1. Boström M, Lima ERA, Biscaia EC Jr, Tavares FW, Nostro PL, Parsons DF, Deniz V, Ninham BW (2009) Anion-specific partitioning in two-phase finite volume systems: possible implications for mechanisms of ion pumps. J Phys Chem B 113:8124CrossRefPubMedGoogle Scholar
  2. Chang D (1977) A physical model of nerve axon—I. Ionic distribution, potential profile, and resting potential. Bull Math Biol 39:1PubMedGoogle Scholar
  3. Chang D (1983) Dependence of cellular potential on ionic concentrations. Data supporting a modification of the constant field equation. Biophys J 43:149CrossRefPubMedPubMedCentralGoogle Scholar
  4. Clay JR (2009) Determining K+ channel activation curves from K+ channel currents often requires the Goldman–Hodgkin–Katz equation. Front Cell Neurosci 3:1Google Scholar
  5. Clay JR, Shrier A (2001) Action potentials occur spontaneously in squid giant axons with moderately alkaline intracellular pH. Biol Bull 201:186CrossRefPubMedGoogle Scholar
  6. Clay JR, Paydarfar D, Forger DB (2008) A simple modification of the Hodgkin and Huxley equations explains type 3 excitability in squid giant axons. J R Soc Interface 5:1421CrossRefPubMedPubMedCentralGoogle Scholar
  7. Colacicco G (1965a) Electrical potential at an oil/water interface. Nature 207:936CrossRefGoogle Scholar
  8. Colacicco G (1965b) Reversal of potential across a liquid non-aqueous membrane with regard to membrane excitability. Nature 207:1045CrossRefPubMedGoogle Scholar
  9. Cronin J (1987) Mathematical aspects of Hodgkin–Huxley neural theory. Cambridge University Press, New YorkCrossRefGoogle Scholar
  10. Einstein A (1902) On the thermodinamic theory of the difference in potentials between metals and fully dissociated solutions of their salts and on an electrical method for investigating molecular forces. Annalen der Physik 8:798CrossRefGoogle Scholar
  11. Ermentrout GB, Terman DH (2010) Mathematical foundations of neuroscience. Springer, New YorkCrossRefGoogle Scholar
  12. Lagi M, Nostro PL, Fratini E, Ninham BW, Baglioni P (2007) Insights into Hofmeister mechanisms: anion and degassing effects on the cloud point of dioctanoylphosphatidylcholine/water systems. J Phys Chem B 111:589CrossRefPubMedGoogle Scholar
  13. Ling GN (1992) A revolution in the physiology of the living cell. Krieger, Malabar, FLGoogle Scholar
  14. Ling GN (2011) Truth in basic biomedical science will set future mankind free. Physiol Chem Phys Med NMR 41:19PubMedGoogle Scholar
  15. Mentré P (2006) Saibou no naka no mizu (Japanese translation) (Water in the cell). University of Tokyo Press, TokyoGoogle Scholar
  16. Ninham BW, Duignan TT, Parsons DF (2011) Approaches to hydration, old and new: insights through Hofmeister effects. Curr Opin Colloid Interface Sci 16:612CrossRefGoogle Scholar
  17. Ninham BW, Larsson K, Nostro PL (2017) Two sides of the coin. Part 1. Lipid and surfactant self-assembly revisited. Colloids Surf B Biointerface 152:326CrossRefGoogle Scholar
  18. Nostro PL, Peruzzi N, Severi M, Ninham BW, Baglioni P (2010) Asymmetric partitioning of anions in lysozyme dispersions. J Am Chem Soc 132:6571CrossRefPubMedGoogle Scholar
  19. Olschewski A, Olschewski H, Bräu ME, Hempelmann G, Vogel W, Safronov BV, Respir J (2001) Basic electrical properties of in situ endothelial cells of small pulmonary arteries during postnatal development. Cell Mol Biol 25:285Google Scholar
  20. Pollack GH (2001) Cells, gels and the engines of life. Ebner & Sons, SeattleGoogle Scholar
  21. Pollack GH (2013) The fourth phase of water: beyond solid, liquid, and vapor. Ebner & Sons, SeattleGoogle Scholar
  22. Pollack GH (2015) Cell electrical properties: reconsidering the origin of the electrical potential. Cell Biol Int 39:237CrossRefPubMedGoogle Scholar
  23. Tamagawa H, Morita S (2014) Membrane potential generated by ion adsorption. Membranes 4:257CrossRefPubMedPubMedCentralGoogle Scholar
  24. Tamagawa H, Ikeda K (2017) Generation of membrane potential beyond the conceptual range of Donnan theory and Goldman–Hodgkin–Katz equation. J Biol Phys 43:319CrossRefPubMedPubMedCentralGoogle Scholar
  25. Tamagawa H, Funatani M, Ikeda K (2016) Ling’s adsorption theory as a mechanism of membrane potential generation observed in both living and nonliving systems. Membranes 6:11CrossRefPubMedCentralGoogle Scholar
  26. Temsamani KR, Cheng KL (2001) Studies of chloride adsorption on the Ag/AgCl electrode. Sens Actuators B Chem 76:551CrossRefGoogle Scholar
  27. Uteshev VV (2010) Evaluation of Ca2+ permeability of nicotinic acetylcholine receptors in hypothalamic histaminergic neurons. Acta Biochim Biophys Sin 42:8CrossRefPubMedGoogle Scholar
  28. Wnek GE (2016) Perspective: Do macromolecules play a role in the mechanisms of nerve stimulation and nervous transmission? J Poly Sci 54:7CrossRefGoogle Scholar
  29. Wright EM, Diamond JM (1968) Effects of pH and polyvalent cations on the selective permeability of gall-bladder epithelium to monovalent ions. Biochim Biophys Acta 1635:57CrossRefGoogle Scholar

Copyright information

© European Biophysical Societies' Association 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringGifu UniversityGifuJapan
  2. 2.Graduate School of Advanced Mathematical SciencesMeiji UniversityNakano-kuJapan

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