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Low-frequency oscillations as internal state integrators of a biosystem model with voltage-gated ion channels

Sergio Portillo1,*, Javier Cervera1, Patricio Ramirez2, and Salvador Mafe1,3,†

  • *Contact author: sergio.portillo@uv.es
  • †Contact author: smafe@uv.es

Phys. Rev. E 114, 044407 – Published 14 October, 2026

DOI: https://doi.org/10.1103/x78y-924k

Abstract

The protein ion channels inserted in cell membranes can act as bioelectrical diodes that control ionic transport. The nonlinear dynamics inherent to voltage-gated channels is useful to process temporal patterns and we explore the response of these channels to low-frequency voltage oscillations, which are observed in most organisms as internal state integrators. To this end, we employ experimentally motivated current-voltage curves in parallel networks of voltage-gated ion channels performing the time-series analysis of a low-frequency oscillatory rhythm. The simulations suggest how channel diversity can contribute to the system-wide internal control, which should be of interest to biophysics and neuromorphic computing.

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References (70)

  1. S. Bartlett and M. L. Wong, Lyfe: Learning to learn better, Interface Focus 15, 20250019 (2025).
  2. A. S. Reber, F. Baluska, and W. Miller, The Sentient Cell: The Cellular Foundations of Consciousness (Oxford University Press, Oxford, UK, 2023).
  3. A. S. Reber, W. B. Miller, Jr., P. Slijepcevic, and F. Baluška, The CBC theory and its entailments, EMBO Rep. 25, 8 (2024).
  4. M. Levin, The computational boundary of a “Self”: Developmental bioelectricity drives multicellularity and scale-free cognition, Front. Psychol. 10, 2688 (2019).
  5. M. Levin and R. Watson, Machines all the way up and cognition all the way down: Updating the machine metaphor in biology, Semin. Cell Dev. Biol. 177–178, 103668 (2026).
  6. B. Hille, Ion Channels of Excitable Membranes (Sinauer Associates, Sunderland, 1992).
  7. J. Cervera, M. Levin, and S. Mafe, Bioelectricity of non-excitable cells and multicellular pattern memories: Biophysical modeling, Phys. Rep. 1004, 1 (2023).
  8. N. Z. Monteiro and R. W. D. Santos, Revisiting the modeling of cell electrophysiology using a delay-based equation, Nonlinear Dyn. 114, 521 (2026).
  9. H. Jaeger and H. Haas, Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication, Science 304, 78 (2004) .
  10. H. Sun, X. Zhou, R. Cao, J. Hou, C. Guan, and S. Leng, Reservoir computing as digital twins for controlling nonlinear dynamical systems, Nonlinear Dyn. 114, 227 (2026).
  11. J. Liu, X. Xu, and E. Li, Sample-weighted reservoir computing for chaotic dynamics prediction with a high proportion of missing data, Nonlinear Dyn. 114, 526 (2026).
  12. X. Wu, Z. Lin, J. Deng, J. Li, and Y. Feng, Nonmasking-based reservoir computing with a single dynamic memristor for image recognition, Nonlinear Dyn. 112, 6663 (2024).
  13. L. Appeltant, M. C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, Information processing using a single dynamical node as complex system, Nat. Commun. 2, 468 (2011).
  14. M. Yan, C. Huang, P. Bienstman, P. Tino, W. Lin, and J. Sun, Emerging opportunities and challenges for the future of reservoir computing, Nat. Commun. 15, 2056 (2024).
  15. G. Milano, G. Pedretti, K. Montano, et al., In materia reservoir computing with a fully memristive architecture based on self-organizing nanowire networks, Nat. Mater. 21, 195 (2022).
  16. Y. Chen, Y. Qian, and X. Cui, Time series reconstructing using calibrated reservoir computing, Sci. Rep. 12, 16318 (2022).
  17. N. Ghenzi, T. W. Park, S. S. Kim, H. J. Kim, Y. H. Jang, K. S. Woo, and C. S. Hwang, Heterogeneous reservoir computing in second-order Ta2O5/HfO2 memristors, Nanoscale Horiz. 9, 427 (2024).
  18. S.-B. Hua, L. Zhang, R.-H. Zheng, and X. Guo, Dynamically nonlinear NbOx memristors for multifunctional reservoir and neuromorphic computing, J. Mater. Chem. C 14, 3146 (2026).
  19. T. M. Kamsma, J. J. Teijema, R. van Roij, and C. Spitoni, Echo state and band-pass networks with aqueous memristors: Leaky reservoir computing with a leaky substrate, Chaos 35, 093133 (2025).
  20. S. Park, H. Kim, and H. W. Jang, Device‐level implementation of reservoir computing with memristors, Adv. Intell. Syst. 8, e202500843 (2026).
  21. A. S. Mohamed, N. X. Armendarez, M. S. Hasan, and J. S. Najem, Memimpedance‐based biomolecular device for adaptive physical reservoir computing, Adv. Intell. Syst. 7, 2500281 (2025).
  22. G. Xu, M. Zhang, T. Mei, W. Liu, L. Wang, and K. Xiao, Nanofluidic ionic memristors, ACS Nano 18, 19423 (2024).
  23. A. Ismail, G.-H. Nam, A. Lokhandwala, S. V. Pandey, K. V. Saurav, Y. You, H. Jyothilal, S. Goutham, R. Sajja, A. Keerthi, and B. Radha, Programmable memristors with two-dimensional nanofluidic channels, Nat. Comm. 16, 7008 (2025).
  24. D. Manikandan and S. Chakraborty, Reversible charge inversion enables field-programmable nanofluidic memristor and synapse for neuromorphic applications, Nano Lett. 26, 2405 (2026) .
  25. T. M. Kamsma, M. S. Klop, W. Q. Boon, C. Spitoni, B. Rueckauer, and R. van Roij, Chemically regulated conical channel synapse for neuromorphic and sensing applications, Phys. Rev. Res. 7, 013328 (2025).
  26. J. Cervera, S. Portillo, P. Ramirez, and S. Mafe, Modeling of memory effects in nanofluidic diodes, Phys. Fluids 36, 047129 (2024).
  27. P. Robin, T. Emmerich, A. Ismail, A. Niguès, Y. You, G.-H. Nam, A. Keerthi, A. Siria, A. K. Geim, B. Radha, and L. Bocquet, Long-term memory and synapse-like dynamics in two-dimensional nanofluidic channels, Science 379, 161 (2023).
  28. T. M. Kamsma, J. Kim, K. Kim, W. Q. Boon, C. Spitoni, J. Park, and R. van Roij, Brain-inspired computing with fluidic iontronic nanochannels, Proc. Natl. Acad. Sci. USA 121, e2320242121 (2024).
  29. Q. Fan, J. Shang, X. Yuan, Z. Zhang, and J. Sha, Emerging liquid‐based memristive devices for neuromorphic computation, Small Methods 9, 2402218 (2025).
  30. C. S. Law, J. Wang, K. Nielsch, A. D. Abell, J. Bisquert, and A. Santos, Recent advances in fluidic neuromorphic computing, Appl. Phys. Rev. 12, 021309 (2025).
  31. Y. Ling, L. Yu, Z. Guo, F. Bian, Y. Wang, X. Wang, Y. Hou, and X. Hou, Single-pore nanofluidic logic memristor with reconfigurable synaptic functions and designable combinations, J. Am. Chem. Soc. 146, 14558 (2024) .
  32. K. Liu, Y. Wang, M. Sun, J. Lu, D. Shi, and Y. Xie, Resistance-restorable nanofluidic memristor and neuromorphic chip, Nano Lett. 25, 6530 (2025).
  33. Y. Niu, Y. Ma, and Y. Xie, Soft memristor at a microbubble interface, Nano Lett. 24, 10475 (2024).
  34. W. Wang, Y. Liang, Y. Ma, D. Shi, and Y. Xie, Memristive characteristics in an asymmetrically charged nanochannel, J. Phys. Chem. Lett. 26, 6848 (2024).
  35. Z. Li, S. K. Myers, J. Xiao, Y. Li, N. Noy, A. Leuski, and A. Noy, Neuromorphic ionic computing in droplet interface synapses, Sci. Adv. 11, eadv6603 (2025).
  36. M. Zhang, R. Lan, Z. Si, J. Dai, W. Liu, W. Chang, J. Liu, G. Xu, and K. Xiao, Ionic species programmable synaptic plasticity in multimodal nanofluidic devices, Natl. Sci. Rev. 13, nwag036 (2026).
  37. Z. Guo, Y. Ling, Y. Ouyang, Y. Hou, J. Tong, and X. Hou, Artificial intelligence for bioinspired nanofluidic iontronics, Nano Lett. 26, 6735 (2026).
  38. M. Ali, P. Ramirez, S. Nasir, J. Cervera, S. Mafe, and W. Ensinger, Ionic circuitry with nanofluidic diodes, Soft Matter 15, 9682 (2019).
  39. N. E. Fraiman, B. Sabbagh, G. Yossifon, and A. Fish, Toward an ion-based large-scale integrated circuit: Design, simulation, and integration, Commun. Eng. 4, 180 (2025).
  40. P. Ramirez, V. Garcia-Morales, V. Gomez, M. Ali, S. Nasir, W. Ensinger, and S. Mafe, Hybrid circuits with nanofluidic diodes and load capacitors, Phys. Rev. Appl. 7, 064035 (2017).
  41. J. Cervera, P. Ramirez, S. Portillo, S. Nasir, M. Ali, W. Ensinger, and S. Mafe, Multiple negative differential resistances in nanofluidic conical pores: A phenomenological model, J. Phys. Chem. Lett. 16, 12321 (2025).
  42. J. R. M. Harvey, A. E. Plante, and A. L. Meredith, Ion channels controlling circadian rhythms in suprachiasmatic nucleus excitability, Physiol. Rev. 100, 1415 (2020).
  43. O. Jensen and L. L. Colgin, Cross-frequency coupling between neuronal oscillations, Trends Cognit. Sci. 11, 267 (2007).
  44. A. Murugan, K. Husain, M. J. Rust, C. Hepler, J. Bass, J. M. J. Pietsch, P. S. Swain, S. G. Jena, J. E. Toettcher, A. K. Chakraborty, K. G. Sprenger, T. Mora, A. M. Walczak, O. Rivoire, S. Wang, K. B. Wood, A. Skanata, E. Kussell, R. Ranganathan, H.-Y. Shih, N. Goldenfeld, et al., Roadmap on biology in time varying environments, Phys. Biol. 18, 041502 (2021).
  45. J. Cervera, J. M. Claver, and S. Mafe, Individual variability and average reliability in parallel networks of heterogeneous biological and artificial nanostructures, IEEE Trans. Nanotech. 12, 1198 (2013).
  46. O. V. Aslanidi, O. A. Mornev, O. Skyggebjerg, P. Arkhammar, O. Thastrup, M. P. Sørensen, P. L. Christiansen, K. Conradsen, and A. Scott, Excitation wave propagation as a possible mechanism for signal transmission in pancreatic islets of Langerhans, Biophys. J. 80, 1195 (2001).
  47. H. X. Nguyen, R. D. Kirkton, and N. Bursac, Engineering prokaryotic channels for control of mammalian tissue excitability, Nat. Commun. 7, 13132 (2016).
  48. H. M. McNamara, R. Salegame, Z. A. Tanoury, H. Xu, S. Begum, G. Ortiz, O. Pourquie, and A. E. Cohen, Bioelectrical domain walls in homogeneous tissues, Nat. Phys. 16, 357 (2020).
  49. J. Cervera, A. Alcaraz, and S. Mafe, Membrane potential bistability in nonexcitable cells as described by inward and outward voltage-gated ion channels, J. Phys. Chem. B 118, 12444 (2014).
  50. S. Shabala, L. Shabala, D. Gradmann, Z. Chen, I. Newman, and S. Mancuso, Oscillations in plant membrane transport: Model predictions, experimental validation, and physiological implications, J. Expt. Bot. 57, 171 (2006).
  51. C. Verdia-Baguena, V. Gomez, J. Cervera, P. Ramirez, and S. Mafe, Energy transduction and signal averaging of fluctuating electric fields by a single protein ion channel, Phys. Chem. Chem. Phys. 19, 292 (2017).
  52. M. Queralt-Martín, M. L. López, M. Aguilella-Arzo, V. M. Aguilella, and A. Alcaraz, Scaling behavior of ionic transport in membrane nanochannels, Nano Lett. 18, 6604 (2018).
  53. J. Cervera, J. A. Manzanares, and S. Mafe, The interplay between cooperativity and diversity in model threshold ensembles, J. R. Soc. Interface 11, 20140099 (2014).
  54. A. Hanson, Spontaneous electrical low-frequency oscillations: A possible role in Hydra and all living systems, Phil. Trans. R. Soc. B 376, 20190763 (2021).
  55. P. Mougkogiannis, A. Nikolaidou, and A. Adamatzky, On emergence of spontaneous oscillations in kombucha and proteinoids, BioNanoScience 15, 65 (2025).
  56. J. Lisman and G. Buzsaki, A neural coding scheme formed by the combined function of gamma and theta oscillations, Schizophr. Bull. 34, 974 (2008).
  57. MathWorks, Statistics and Machine Learning Toolbox, Classification Trees, https://www.mathworks.com/help/stats/classificationtree.htmlutm_source=chatgpt.com.
  58. M. Levin, Bioelectric signaling: Reprogrammable circuits underlying embryogenesis, regeneration, and cancer, Cell 184, 1971 (2021).
  59. A. Goldbeter, D. Gonze, G. Houart, J.-C. Leloup, J. Halloy, and G. Dupont, From simple to complex oscillatory behavior in metabolic and genetic control networks, Chaos 11, 247 (2001).
  60. A. Prindle, J. Liu, M. Asally, S. Ly, J. Garcia-Ojalvo, and G. M. Süel, Ion channels enable electrical communication in bacterial communities, Nature (London) 527, 59 (2015).
  61. J. Canales, C. Henriquez-Valencia, and S. Brauchi, The integration of electrical signals originating in the root of vascular plants, Front. Plant Sci. 8, 2173 (2018).
  62. R. Yuste, From the neuron doctrine to neural networks, Nat. Rev. Neurosci. 16, 487 (2015).
  63. J. Cervera, J. A. Manzanares, M. Levin, and S. Mafe, Oscillatory phenomena in electrophysiological networks: The coupling between cell bioelectricity and transcription, Comp. Biol. Med. 180, 108964 (2024).
  64. G. Lanzavecchia, A. Sapunova, A. M. Szalai, S. Weng, A. Douaki, M. Tsutsui, R. Krahne, G. Acuna, and D. Garoli, Three-dimensional plasmonic nanopores for DNA-PAINT and dual-material Au/Si architectures, J. Nanobiotechnol. 24, 605 (2026).
  65. A. J. Savage, S. S. Wilder, and R. Y. Adhikari, Mimicking neural habituation behavior with pristine leaf-based memristors, APL Electron. Devices 2, 026122 (2026).
  66. S. V. Pandey, K. V. Saurav, A. Ismail, S. Rahaman, and B. Radha, Nanofluidic ionic memory for next-generation computing, Nat. Rev. Mater. (2026).
  67. N. R. Aluru, S. B. Darling, J. W. Elam, O. Gang, A. Salleo, Z. Siwy, A. A. Talin, and A. Noy, Knowledge gaps for neuromorphic ionic computing, Science 392, 592 (2026).
  68. S. Bezrukov and I. Vodyanoy, Noise-induced enhancement of signal transduction across voltage-dependent ion channels, Nature (London) 378, 362 (1995).
  69. D. Noble, A theory of biological relativity: No privileged level of causation, Interface Focus 2, 55 (2012).
  70. F. Baluška and A. S. Reber, CBC-Clock Theory of Life–Integration of cellular circadian clocks and cellular sentience is essential for cognitive basis of life, Bioessays 43, 2100121 (2021).

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