Table Info

Table 1.

The numbers of transmembrane-electrostatically localized protons/cations charges (TELC) per μm² of membrane surface area or per cell computed from the resting membrane potential, stimulation threshold, and action potential peak level in a typical ellipsoidal Neuro2A (N2A) cell with a cell volume of 2,700 μm³ and extracellular membrane surface area of about 1,000 μm², using specific membrane capacitance C/S of 9.2 mf/m² based on measured experimental data [37]

	Neural membrane potential	TELC per μm² on extracellular membrane surface	TELC per μm² on cytoplasmic membrane surface	TELC per cell on extracellular membrane surface	TELC per cell on cytoplasmic membrane surface
Resting potential level	–70 mV	3,900 excess protons + cations	3,900 excess anions	3,900,000 excess protons + cations	3,900,000 excess anions
Stimulation threshold level	–55 mV	3,100 excess protons + cations	3,100 excess anions	3,100,000 excess protons + cations	3,100,000 excess anions
Action potential peak level	+30 mV	1,700 excess anions	1,700 excess protons + cations	1,700,000 excess anions	1,700,000 excess protons + cations

Supplementary materials

The supplementary material for this article is available at: https://www.explorationpub.com/uploads/Article/file/100685_sup_1.xlsx.

Declarations

Acknowledgments

Special thanks to Dr. Bertrand Coste (CNRS, France) for his highly insightful review and suggestion feedbacks on this manuscript.

Author contributions

JWL: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Software, Resources, Supervision, Validation, Visualization, Writing—original draft, Writing—review & editing.

Conflicts of interest

The author declares no conflicts of interest.

Ethical approval

Not applicable.

Consent to participate

Not applicable.

Consent to publication

Not applicable.

Availability of data and materials

All datasets generated for this study are included in the manuscript and the supplementary files.

Funding

This research was supported in part by a Multidisciplinary Biomedical Research Seed Funding Grant from the Graduate School, the College of Sciences, and the Center for Bioelectrics at Old Dominion University, Norfolk, Virginia, USA. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright

Publisher’s note

Open Exploration maintains a neutral stance on jurisdictional claims in published institutional affiliations and maps. All opinions expressed in this article are the personal views of the author(s) and do not represent the stance of the editorial team or the publisher.

References

Martinac B. 2021 Nobel Prize for mechanosensory transduction. Biophys Rev. 2022;14:15–20. [DOI] [PubMed] [PMC]

Zheng W, Holt JR. The Mechanosensory Transduction Machinery in Inner Ear Hair Cells. Annu Rev Biophys. 2021;50:31–51. [DOI] [PubMed] [PMC]

Cox CD, Bavi N, Martinac B. Biophysical Principles of Ion-Channel-Mediated Mechanosensory Transduction. Cell Rep. 2019;29:1–12. [DOI] [PubMed]

Martinac B, Nikolaev YA, Silvani G, Bavi N, Romanov V, Nakayama Y, et al. Cell membrane mechanics and mechanosensory transduction. Curr Top Membr. 2020;86:83–141. [DOI] [PubMed]

Guichard M, Thomine S, Frachisse JM. Mechanotransduction in the spotlight of mechano-sensitive channels. Curr Opin Plant Biol. 2022;68:102252. [DOI] [PubMed]

Goodman MB, Haswell ES, Vásquez V. Mechanosensitive membrane proteins: Usual and unusual suspects in mediating mechanotransduction. J Gen Physiol. 2023;155:e202213248. [DOI] [PubMed] [PMC]

Tortorella I, Argentati C, Emiliani C, Morena F, Martino S. Biochemical Pathways of Cellular Mechanosensing/Mechanotransduction and Their Role in Neurodegenerative Diseases Pathogenesis. Cells. 2022;11:3093. [DOI] [PubMed] [PMC]

Di X, Gao X, Peng L, Ai J, Jin X, Qi S, et al. Cellular mechanotransduction in health and diseases: from molecular mechanism to therapeutic targets. Signal Transduct Target Ther. 2023;8:282. [DOI] [PubMed] [PMC]

Coste B, Mathur J, Schmidt M, Earley TJ, Ranade S, Petrus MJ, et al. Piezo1 and Piezo2 are essential components of distinct mechanically activated cation channels. Science. 2010;330:55–60. [DOI] [PubMed] [PMC]

10.

Wu J, Young M, Lewis AH, Martfeld AN, Kalmeta B, Grandl J. Inactivation of Mechanically Activated Piezo1 Ion Channels Is Determined by the C-Terminal Extracellular Domain and the Inner Pore Helix. Cell Rep. 2017;21:2357–66. [DOI] [PubMed] [PMC]

11.

Coste B, Xiao B, Santos JS, Syeda R, Grandl J, Spencer KS, et al. Piezo proteins are pore-forming subunits of mechanically activated channels. Nature. 2012;483:176–81. [DOI] [PubMed] [PMC]

12.

Handler A, Ginty DD. The mechanosensory neurons of touch and their mechanisms of activation. Nat Rev Neurosci. 2021;22:521–37. [DOI] [PubMed] [PMC]

13.

Wang J, Hamill OP. Piezo2—peripheral baroreceptor channel expressed in select neurons of the mouse brain: a putative mechanism for synchronizing neural networks by transducing intracranial pressure pulses. J Integr Neurosci. 2021;20:825–37. [DOI] [PubMed]

14.

Brohawn SG, Su Z, MacKinnon R. Mechanosensitivity is mediated directly by the lipid membrane in TRAAK and TREK1 K⁺ channels. Proc Natl Acad Sci U S A. 2014;111:3614–9. [DOI] [PubMed] [PMC]

15.

Young M, Lewis AH, Grandl J. Physics of mechanotransduction by Piezo ion channels. J Gen Physiol. 2022;154:e202113044. [DOI] [PubMed] [PMC]

16.

Zhou Z, Martinac B. Mechanisms of PIEZO Channel Inactivation. Int J Mol Sci. 2023;24:14113. [DOI] [PubMed] [PMC]

17.

Delmas P, Parpaite T, Coste B. PIEZO channels and newcomers in the mammalian mechanosensitive ion channel family. Neuron. 2022;110:2713–27. [DOI] [PubMed]

18.

Lee JW. Protonic conductor: better understanding neural resting and action potential. J Neurophysiol. 2020;124:1029–44. [DOI] [PubMed]

19.

Lee JW. Application of TELC model to neurology: Review and commentary responding to Silverstein’s critique. Curr Trends Neurol. 2023;17:83–98.

20.

Lee JW. Protonic Capacitor: Elucidating the biological significance of mitochondrial cristae formation. Sci Rep. 2020;10:10304. [DOI] [PubMed] [PMC]

21.

Lee JW. Mitochondrial energetics with transmembrane electrostatically localized protons: do we have a thermotrophic feature? Sci Rep. 2021;11:14575. [DOI] [PubMed] [PMC]

22.

Lee JW. Electrostatically localized proton bioenergetics: better understanding membrane potential. Heliyon. 2019;5:e01961. [DOI] [PubMed] [PMC]

23.

Lee JW. Proton-Electrostatics Hypothesis for Localized Proton Coupling Bioenergetics. Bioenerg. 2012;1:104. [DOI]

24.

Lee JW. A possible electrostatic interpretation for proton localization and delocalization in chloroplast bioenergetics system. Biophys J. 2005;88:324a–5a.

25.

Lee JW. Isothermal Environmental Heat Energy Utilization by Transmembrane Electrostatically Localized Protons at the Liquid-Membrane Interface. ACS Omega. 2020;5:17385–95. [DOI] [PubMed] [PMC]

26.

Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952;117:500–44. [DOI] [PubMed] [PMC]

27.

Silverstein TP. Lee’s “Transmembrane Electrostatically-Localized Proton” model does NOT offer a better understanding of neuronal transmembrane potentials. J Neurophysiol. 2023;130:123–7. [DOI] [PubMed]

28.

Silverstein TP. Explaining neuronal membrane potentials: The Goldman equation vs. Lee’s TELC hypothesis. Neuroscience. 2025;567:1–8. [DOI] [PubMed]

29.

Lee JW. Experimental Demonstration and Study of Transmembrane-Electrostatically Localized Protons Prevail. Water. 2025;14:35–58. [DOI]

30.

de Grotthuss CJT. Sur la décomposition de l’eau et des corps qu’elle tient en dissolution à l’aide de l’électricité galvanique. Ann Chim. 1806;58:54–73. French.

31.

Marx D, Tuckerman ME, Hutter J, Parrinello M. The nature of the hydrated excess proton in water. Nature. 1999;397:601–4. [DOI]

32.

Pomès R, Roux B. Molecular mechanism of H⁺ conduction in the single-file water chain of the gramicidin channel. Biophys J. 2002;82:2304–16. [DOI] [PubMed] [PMC]

33.

Marx D. Proton transfer 200 years after von Grotthuss: insights from ab initio simulations. Chemphyschem. 2006;7:1848–70. [DOI] [PubMed]

34.

Hammond C. Chapter 3 - Ionic gradients, membrane potential and ionic currents. In: Hammond C, editor. Cellular and Molecular Neurophysiology (Fourth Edition). Boston: Academic Press; 2015. pp. 39–54. [DOI]

35.

Azzone G, Benz R, Bertl A, Colombini M, Crofts A, Dilley R, et al. Transmembrane measurements across bioenergetic membranes. Biochim Biophys Acta Bioenerg. 1993;1183:1–3. [DOI]

36.

Bertl A, Blumwald E, Coronado R, Eisenberg R, Findlay G, Gradmann D, et al. Electrical measurements on endomembranes. Science. 1992;258:873–4. [DOI] [PubMed]

37.

Gentet LJ, Stuart GJ, Clements JD. Direct measurement of specific membrane capacitance in neurons. Biophys J. 2000;79:314–20. [DOI] [PubMed] [PMC]

38.

Lulevich V, Zimmer CC, Hong HS, Jin LW, Liu GY. Single-cell mechanics provides a sensitive and quantitative means for probing amyloid-β peptide and neuronal cell interactions. Proc Natl Acad Sci U S A. 2010;107:13872–7. [DOI] [PubMed] [PMC]

39.

Coste B, Murthy SE, Mathur J, Schmidt M, Mechioukhi Y, Delmas P, et al. Piezo1 ion channel pore properties are dictated by C-terminal region. Nat Commun. 2015;6:7223. [DOI] [PubMed] [PMC]

40.

Fang XZ, Zhou T, Xu JQ, Wang YX, Sun MM, He YJ, et al. Structure, kinetic properties and biological function of mechanosensitive Piezo channels. Cell Biosci. 2021;11:13. [DOI] [PubMed] [PMC]

41.

Schrenk-Siemens K, Wende H, Prato V, Song K, Rostock C, Loewer A, et al. PIEZO2 is required for mechanotransduction in human stem cell-derived touch receptors. Nat Neurosci. 2015;18:10–6. [DOI] [PubMed]

42.

Woo SH, Ranade S, Weyer AD, Dubin AE, Baba Y, Qiu Z, et al. Piezo2 is required for Merkel-cell mechanotransduction. Nature. 2014;509:622–6. [DOI] [PubMed] [PMC]

43.

Zeng WZ, Marshall KL, Min S, Daou I, Chapleau MW, Abboud FM, et al. PIEZOs mediate neuronal sensing of blood pressure and the baroreceptor reflex. Science. 2018;362:464–7. [DOI] [PubMed] [PMC]

44.

Song Y, Li D, Farrelly O, Miles L, Li F, Kim SE, et al. The Mechanosensitive Ion Channel Piezo Inhibits Axon Regeneration. Neuron. 2019;102:373–89.e6. [DOI] [PubMed] [PMC]

45.

Kefauver JM, Ward AB, Patapoutian A. Discoveries in structure and physiology of mechanically activated ion channels. Nature. 2020;587:567–76. [DOI] [PubMed] [PMC]

46.

Moroni M, Servin-Vences MR, Fleischer R, Sánchez-Carranza O, Lewin GR. Voltage gating of mechanosensitive PIEZO channels. Nat Commun. 2018;9:1096. [DOI] [PubMed] [PMC]

47.

Lewis AH, Cui AF, McDonald MF, Grandl J. Transduction of Repetitive Mechanical Stimuli by Piezo1 and Piezo2 Ion Channels. Cell Rep. 2017;19:2572–85. [DOI] [PubMed] [PMC]

48.

Meltzer S, Santiago C, Sharma N, Ginty DD. The cellular and molecular basis of somatosensory neuron development. Neuron. 2021;109:3736–57. [DOI] [PubMed] [PMC]

49.

Bourane S, Grossmann KS, Britz O, Dalet A, Del Barrio MG, Stam FJ, et al. Identification of a spinal circuit for light touch and fine motor control. Cell. 2015;160:503–15. [DOI] [PubMed] [PMC]