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Active quantum memory: Exploring the quantum dynamical process of voltage-gated ion channel

Yu-Juan Sun* and Wei-Min Zhang†

  • *Contact author: sunyj28@phys.ncku.edu.tw
  • †Contact author: wzhang@mail.ncku.edu.tw
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Phys. Rev. Research 8, 033134 – Published 4 August, 2026

DOI: https://doi.org/10.1103/ll5d-t22x

Abstract

It is known that the opening or closing mechanism of a voltage-gated ion channel is triggered by the potential difference across the cell membrane in the nervous system. Based on this picture, we model the ion channel as a nanoscale two-terminal ionic tunneling junction. We apply an external time-varying voltage on the junction to mimic the membrane potential difference in the stimulation of neurons. We derive the non-Markovian quantum Langevin equation from the first principle of quantum mechanics for the ion transport in ion channels, and obtain the ion transport current in terms of quantum tunnelings of ions controlled by the time-varying voltage. We find that the time-varying voltage induces an effective magnetic flux, which causes quantum coherence in ion tunnelings. This effective magnetic flux induces further an oscillatory component to the spectral structure of the ion system, forming a time-dependent quantum memory. Such voltage-induced memory is defined as the active quantum memory, which manifests in the system with a regular oscillatory sideband structure in the ion transport current. The sideband structure demonstrates a multicrossing hysteresis in the current-voltage (I−V) curve, responding to the variation of the time-varying voltage (membrane potential difference). We also find that the strength of active quantum memory can be described by the ratio of amplitude and frequency of the time-varying voltage, and can be quantitatively measured through the number of nonzero cross points in the I−V hysteresis and conductance-voltage diagram. Additionally, we explore the temperature dependence of the active quantum memory in such a system. Further, we apply this model to the ion channel system on the biological energy scale. The description of these active quantum memory characteristics provides a quantum mechanical understanding to the underlying mechanism of ion channel dynamics.

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References (68)

  1. A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117, 500 (1952).
  2. E. Neher and B. Sakmann, Single-channel currents recorded from membrane of denervated frog muscle fibres, Nature (London) 260, 799 (1976).
  3. O. P. Hamill, A. Marty, E. Neher, B. Sakmann, and F. J. Sigworth, Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches, Pflugers Arch. 391, 85 (1981).
  4. D. A. Doyle, J. M. Cabral, R. A. Pfuetzner, A. Kuo, J. M. Gulbis, S. L. Cohen, B. T. Chait, and R. MacKinnon, The structure of the potassium channel: Molecular basis of K+ conduction and selectivity, Science 280, 69 (1998).
  5. R. MacKinnon, Potassium channels, FEBS Lett. 555, 62 (2003).
  6. W. A. Catterall, Ion channel voltage sensors: Structure, function, and pathophysiology, Neuron 67, 915 (2010).
  7. A. K. Singh, L. L. McGoldrick, K. Saotome, and A. I. Sobolevsky, X-ray crystallography of TRP channels, Channels 12, 137 (2018).
  8. J. García-Nafría and C. G. Tate, Cryo-electron microscopy: Moving beyond X-ray crystal structures for drug receptors and drug development, Annu. Rev. Pharmacol. Toxicol. 60, 51 (2020).
  9. A. Mironenko, U. Zachariae, B. L. de Groot, and W. Kopec, The persistent question of potassium channel permeation mechanisms, J. Mol. Biol. 433, 167002 (2021).
  10. Y. Wu, Y. Yan, Y. Yang, S. Bian, A. Rivetta, K. Allen, and F. J. Sigworth, CryoEM structures of Kv1.2 potassium channels, conducting and non-conducting, eLife 12, RP89459 (2025).
  11. C. M. Armstrong and B. Hille, Voltage-gated ion channels and electrical excitability, Neuron 20, 371 (1998).
  12. D. Naranjo, H. Moldenhauer, M. Pincuntureo, and I. Díaz-Franulic, Pore size matters for potassium channel conductance, J. Gen. Physiol. 148, 277 (2016).
  13. G. Klesse, S. Rao, M. S. P. Sansom, and S. J. Tucker, CHAP: A versatile tool for the structural and functional annotation of ion channel pores, J. Mol. Biol. 431, 3353 (2019).
  14. C. C. Cruickshank, R. F. Minchin, A. C. Le Dain, and B. Martinac, Estimation of the pore size of the large-conductance mechanosensitive ion channel of Escherichia coli, Biophys. J. 73, 1925 (1997).
  15. S. Bernèche and B. Roux, Energetics of ion conduction through the K+ channel, Nature (London) 414, 73 (2001).
  16. J. H. Morais-Cabral, Y. Zhou, and R. MacKinnon, Energetic optimization of ion conduction rate by the K+ selectivity filter, Nature (London) 414, 37 (2001).
  17. Y. Zhou, J. H. Morais-Cabral, A. Kaufman, and R. MacKinnon, Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0Å resolution, Nature (London) 414, 43 (2001).
  18. A. Vaziri and M. B. Plenio, Quantum coherence in ion channels: Resonances, transport and verification, New J. Phys. 12, 085001 (2010).
  19. L. T. Hall, C. D. Hill, J. H. Cole, B. Städler, F. Caruso, P. Mulvaney, J. Wrachtrup, and L. C. L. Hollenberg, Monitoring ion-channel function in real time through quantum decoherence, Proc. Natl. Acad. Sci. USA 107, 18777 (2010).
  20. J. Summhammer, V. Salari, and G. Bernroider, A quantum-mechanical description of ion motion within the confining potentials of voltage-gated ion channels, J. Integr. Neurosci. 11, 123 (2012).
  21. V. Salari, H. Naeij, and A. Shafiee, Quantum interference and selectivity through biological ion channels, Sci. Rep. 7, 41625 (2017).
  22. B. Roux, T. Allen, S. Bernèche, and W. Im, Theoretical and computational models of biological ion channels, Q. Rev. Biophys. 37, 15 (2004).
  23. C. Maffeo, S. Bhattacharya, J. Yoo, D. Wells, and A. Aksimentiev, Modeling and simulation of ion channels, Chem. Rev. 112, 6250 (2012).
  24. N. Modi, M. Winterhalter, and U. Kleinekathöfer, Computational modeling of ion transport through nanopores, Nanoscale 4, 6166 (2012).
  25. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 1996).
  26. S. B. Long, E. B. Campbell, and R. MacKinnon, Crystal structure of a mammalian voltage-dependent Shaker family K+ channel, Science 309, 897 (2005).
  27. Q. Kuang, P. Purhonen, and H. Hebert, Structure of potassium channels, Cell. Mol. Life Sci. 72, 3677 (2015).
  28. I. Kaufman, P. V. E. McClintock, and R. S. Eisenberg, Coulomb blockade model of permeation and selectivity in biological ion channels, New J. Phys. 17, 083021 (2015).
  29. M. W. Y. Tu and W.-M. Zhang, Non-Markovian decoherence theory for a double-dot charge qubit, Phys. Rev. B 78, 235311 (2008).
  30. J. Jin, M. W.-Y. Tu, W.-M. Zhang, and Y. Yan, Non-equilibrium quantum theory for nanodevices based on the Feynman-Vernon influence functional, New J. Phys. 12, 083013 (2010).
  31. C. U. Lei and W.-M. Zhang, A quantum photonic dissipative transport theory, Ann. Phys. 327, 1408 (2012).
  32. P.-Y. Yang, C.-Y. Lin, and W.-M. Zhang, Master equation approach to transient quantum transport in nanostructures incorporating initial correlations, Phys. Rev. B 92, 165403 (2015).
  33. P.-Y. Yang and W.-M. Zhang, Master equation approach to transient quantum transport in nanostructures, Front. Phys. 12, 127204 (2017).
  34. C.-Z. Yao, H.-L. Lai, and W.-M. Zhang, Quantum transport theory of hybrid superconducting systems, Phys. Rev. B 108, 195402 (2023).
  35. W.-M. Zhang, P. Y. Lo, H.-N. Xiong, M. W.-Y. Tu, and F. Nori, General non-Markovian dynamics of open quantum systems, Phys. Rev. Lett. 109, 170402 (2012).
  36. W.-M. Zhang, Exact master equation and general non-Markovian dynamics in open quantum systems, Eur. Phys. J. Spec. Top. 227, 1849 (2019).
  37. N. S. Wingreen, A.-P. Jauho, and Y. Meir, Time-dependent transport through a mesoscopic structure, Phys. Rev. B 48, 8487(R) (1993).
  38. A.-P. Jauho, N. S. Wingreen, and Y. Meir, Time-dependent transport in interacting and noninteracting resonant-tunneling systems, Phys. Rev. B 50, 5528 (1994).
  39. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics: Basic Concepts, Tools, and Applications (Wiley-VCH, Weinheim, 2020), Vol. 1.
  40. A. Marais, B. Adams, A. K. Ringsmuth, M. Ferretti, J. M. Gruber, R. Hendrikx, M. Schuld, S. L. Smith, I. Sinayskiy, T. P. J. Krüger, F. Petruccione, and R. van Grondelle, The future of quantum biology, J. R. Soc. Interface. 15, 20180640 (2018).
  41. I. G. Ishida, G. E. Rangel-Yescas, J. Carrasco-Zanini, and L. D. Islas, Voltage-dependent gating and gating charge measurements in the Kv1.2 potassium channel, J. Gen. Physiol. 145, 345 (2015).
  42. B. Sakmann and E. Neher, Single-Channel Recording (Plenum, New York, 1983).
  43. J. Shuai and I. Parker, Optical single-channel recording by imaging Ca2+ flux through individual ion channels: Theoretical considerations and limits to resolution, Cell Calcium 37, 283 (2005).
  44. M. Mortensen and T. G. Smart, Single-channel recording of ligand-gated ion channels, Nat. Protoc. 2, 2826 (2007).
  45. N. Fertig, M. Klau, M. George, R. H. Blick, and J. C. Behrends, Activity of single ion channel proteins detected with a planar microstructure, Appl. Phys. Lett. 81, 4865 (2002).
  46. J. K. Rosenstein, S. Ramakrishnan, J. Roseman, and K. L. Shepard, Single ion channel recordings with CMOS-anchored lipid membranes, Nano Lett. 13, 2682 (2013).
  47. A. J. W. Hartel, P. Ong, I. Schroeder, M. H. Giese, S. Shekar, O. B. Clarke, R. Zalk, A. R. Marks, W. A. Hendrickson, and K. L. Shepard, Single-channel recordings of RyR1 at microsecond resolution in CMOS-suspended membranes, Proc. Natl. Acad. Sci. USA 115, E1789 (2018).
  48. S. Shekar, C.-C. Chien, A. Hartel, P. Ong, O. B. Clarke, A. Marks, M. Drndic, and K. L. Shepard, Wavelet denoising of high-bandwidth nanopore and ion-channel signals, Nano Lett. 19, 1090 (2019).
  49. D. R. Hochbaum, Y. Zhao, S. L. Farhi, N. Klapoetke, C. A. Werley, V. Kapoor, P. Zou, J. M. Kralj, D. Maclaurin, and N. Smedemark-Margulies, All-optical electrophysiology in mammalian neurons using engineered microbial rhodopsins, Nat. Methods 11, 825 (2014).
  50. H. Zhang, E. Reichert, and A. E. Cohen, Optical electrophysiology for probing function and pharmacology of voltage-gated ion channels, eLife 5, e15202 (2016).
  51. L. Filipis and M. Canepari, Optical measurement of physiological sodium currents in the axon initial segment, J. Physiol. 599, 49 (2021).
  52. H. T. Kratochvil, J. K. Carr, K. Matulef, A. W. Annen, H. Li, M. Maj, J. Ostmeyer, A. L. Serrano, H. Raghuraman, S. D. Moran et al., Instantaneous ion configurations in the K+ ion channel selectivity filter revealed by 2D IR spectroscopy, Science 353, 1040 (2016).
  53. H. Tsukamoto and Y. Furutani, Optogenetic modulation of ion channels by photoreceptive proteins, in Optogenetics, edited by H. Yawo, H. Kandori, A. Koizumi, and R. Kageyama, Advances in Experimental Medicine and Biology, Vol. 1293 (Springer, Singapore, 2021), pp. 73–88.
  54. E. G. Govorunova, Y. Gou, O. A. Sineshchekov, H. Li, X. Lu, Y. Wang, L. S. Brown, F. St-Pierre, M. Xue, and J. L. Spudich, Kalium channelrhodopsins are natural light-gated potassium channels that mediate optogenetic inhibition, Nat. Neurosci. 25, 967 (2022).
  55. S. M. Sternson and B. L. Roth, Chemogenetic tools to interrogate brain functions, Annu. Rev. Neurosci. 37, 387 (2014).
  56. B. L. Roth, DREADDs for neuroscientists, Neuron 89, 683 (2016).
  57. E. J. Campbell and N. J. Marchant, The use of chemogenetics in behavioural neuroscience: Receptor variants, Br. J. Pharmacol. 175, 994 (2018).
  58. Y. Li, C. Chang, Z. Zhu, L. Sun, and C. Fan, Terahertz wave enhances permeability of the voltage-gated calcium channel, J. Am. Chem. Soc. 143, 4311 (2021).
  59. Z.-H. Hu, W.-P. Lv, D.-X. Hui, X.-J. Wang, and Y.-N. Wang, Permeability enhancement of the KcsA channel under radiation of a terahertz wave, Phys. Rev. E 105, 024104 (2022).
  60. Y. Liu, X. Liu, Y. Shu, and Y. Yu, Progress of the impact of terahertz radiation on ion channel kinetics in neuronal cells, Neurosci. Bull. 40, 1960 (2024).
  61. Z. Song, L. Xue, Q. Ouyang, and C. Song, Impact of a terahertz electromagnetic field on the ion permeation of potassium and sodium channels, Commun. Chem. 8, 101 (2025).
  62. X. Liu, Z. Qiao, Y. Chai, Z. Zhu, K. Wu, W. Ji, D. Li, Y. Xiao, L. Mao, C. Chang, et al., Nonthermal and reversible control of neuronal signaling and behavior by midinfrared stimulation, Proc. Natl. Acad. Sci. USA 118, e2015685118 (2021).
  63. G. A. Miller, E. Galanter, and K. H. Pribram, Plans and the Structure of Behaviour (Henry Holt and Co., New York, 1960).
  64. R. C. Atkinson and R. M. Shiffrin, Human memory: A proposed system and its control processes, in The Psychology of Learning and Motivation: Advances in Research and Theory, edited by K. W. Spence and J. T. Spence (Academic Press, New York, 1968), Vol. 2, pp. 89–195.
  65. A. D. Baddeley and G. Hitch, Working memory, in The Psychology of Learning and Motivation: Advances in Research and Theory, edited by G. H. Bower (Academic Press, New York, 1974), Vol. 8, pp. 47–89.
  66. N. Cowan, Evolving conceptions of memory storage, selective attention, and their mutual constraints within the human information-processing system, Psychol. Bull. 104, 163 (1988).
  67. N. Cowan, An embedded-processes model of working memory, in Models of Working Memory: Mechanisms of Active Maintenance and Executive Control, edited by A. Miyake and P. Shah (Cambridge University Press, Cambridge, 1999), pp. 62–101.
  68. A. Baddeley, The episodic buffer: A new component of working memory? Trends Cogn. Sci. 4, 417 (2000).

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Phys. Rev. Research 8, 033134– Published 4 August, 2026
  • Received 23 November 2024
  • Accepted 10 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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