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Low-frequency oscillations as internal state integrators of a biosystem model with voltage-gated ion channels
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)
- S. Bartlett and M. L. Wong, Lyfe: Learning to learn better, Interface Focus 15, 20250019 (2025).
- A. S. Reber, F. Baluska, and W. Miller, The Sentient Cell: The Cellular Foundations of Consciousness (Oxford University Press, Oxford, UK, 2023).
- A. S. Reber, W. B. Miller, Jr., P. Slijepcevic, and F. Baluška, The CBC theory and its entailments, EMBO Rep. 25, 8 (2024).
- M. Levin, The computational boundary of a “Self”: Developmental bioelectricity drives multicellularity and scale-free cognition, Front. Psychol. 10, 2688 (2019).
- 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).
- B. Hille, Ion Channels of Excitable Membranes (Sinauer Associates, Sunderland, 1992).
- J. Cervera, M. Levin, and S. Mafe, Bioelectricity of non-excitable cells and multicellular pattern memories: Biophysical modeling, Phys. Rep. 1004, 1 (2023).
- N. Z. Monteiro and R. W. D. Santos, Revisiting the modeling of cell electrophysiology using a delay-based equation, Nonlinear Dyn. 114, 521 (2026).
- H. Jaeger and H. Haas, Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication, Science 304, 78 (2004) .
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- Y. Chen, Y. Qian, and X. Cui, Time series reconstructing using calibrated reservoir computing, Sci. Rep. 12, 16318 (2022).
- 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 memristors, Nanoscale Horiz. 9, 427 (2024).
- S.-B. Hua, L. Zhang, R.-H. Zheng, and X. Guo, Dynamically nonlinear memristors for multifunctional reservoir and neuromorphic computing, J. Mater. Chem. C 14, 3146 (2026).
- 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).
- S. Park, H. Kim, and H. W. Jang, Device‐level implementation of reservoir computing with memristors, Adv. Intell. Syst. 8, e202500843 (2026).
- 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).
- G. Xu, M. Zhang, T. Mei, W. Liu, L. Wang, and K. Xiao, Nanofluidic ionic memristors, ACS Nano 18, 19423 (2024).
- 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).
- D. Manikandan and S. Chakraborty, Reversible charge inversion enables field-programmable nanofluidic memristor and synapse for neuromorphic applications, Nano Lett. 26, 2405 (2026) .
- 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).
- J. Cervera, S. Portillo, P. Ramirez, and S. Mafe, Modeling of memory effects in nanofluidic diodes, Phys. Fluids 36, 047129 (2024).
- 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).
- 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).
- Q. Fan, J. Shang, X. Yuan, Z. Zhang, and J. Sha, Emerging liquid‐based memristive devices for neuromorphic computation, Small Methods 9, 2402218 (2025).
- 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).
- 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) .
- 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).
- Y. Niu, Y. Ma, and Y. Xie, Soft memristor at a microbubble interface, Nano Lett. 24, 10475 (2024).
- 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).
- 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).
- 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).
- Z. Guo, Y. Ling, Y. Ouyang, Y. Hou, J. Tong, and X. Hou, Artificial intelligence for bioinspired nanofluidic iontronics, Nano Lett. 26, 6735 (2026).
- M. Ali, P. Ramirez, S. Nasir, J. Cervera, S. Mafe, and W. Ensinger, Ionic circuitry with nanofluidic diodes, Soft Matter 15, 9682 (2019).
- 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).
- 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).
- 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).
- 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).
- O. Jensen and L. L. Colgin, Cross-frequency coupling between neuronal oscillations, Trends Cognit. Sci. 11, 267 (2007).
- 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).
- 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).
- 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).
- H. X. Nguyen, R. D. Kirkton, and N. Bursac, Engineering prokaryotic channels for control of mammalian tissue excitability, Nat. Commun. 7, 13132 (2016).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- A. Hanson, Spontaneous electrical low-frequency oscillations: A possible role in Hydra and all living systems, Phil. Trans. R. Soc. B 376, 20190763 (2021).
- P. Mougkogiannis, A. Nikolaidou, and A. Adamatzky, On emergence of spontaneous oscillations in kombucha and proteinoids, BioNanoScience 15, 65 (2025).
- J. Lisman and G. Buzsaki, A neural coding scheme formed by the combined function of gamma and theta oscillations, Schizophr. Bull. 34, 974 (2008).
- MathWorks, Statistics and Machine Learning Toolbox, Classification Trees, https://www.mathworks.com/help/stats/classificationtree.htmlutm_source=chatgpt.com.
- M. Levin, Bioelectric signaling: Reprogrammable circuits underlying embryogenesis, regeneration, and cancer, Cell 184, 1971 (2021).
- 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).
- 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).
- 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).
- R. Yuste, From the neuron doctrine to neural networks, Nat. Rev. Neurosci. 16, 487 (2015).
- 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).
- 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).
- 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).
- S. V. Pandey, K. V. Saurav, A. Ismail, S. Rahaman, and B. Radha, Nanofluidic ionic memory for next-generation computing, Nat. Rev. Mater. (2026).
- 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).
- S. Bezrukov and I. Vodyanoy, Noise-induced enhancement of signal transduction across voltage-dependent ion channels, Nature (London) 378, 362 (1995).
- D. Noble, A theory of biological relativity: No privileged level of causation, Interface Focus 2, 55 (2012).
- 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).