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Cited by 71Biofield Effects and BiophysicsAdvanced Mathematical Theories and ApplicationsNeural dynamics and brain function

Fractal, scale free electromagnetic resonance of a single brain extracted microtubule nanowire, a single tubulin protein and a single neuron

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Saxena, Komal, Singh, Pushpendra, Sahoo, Pathik, Sahu, Satyajit, Ghosh, Subrata, Ray, Kanad, Fujita, Daisuke, Bandyopadhyay, Anirban·2020·Fractal and Fractional
DOI 10.3390/fractalfract4020011
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Abstract

Biomaterials are primarily insulators. For nearly a century, electromagnetic resonance and antenna–receiver properties have been measured and extensively theoretically modeled. The dielectric constituents of biomaterials—if arranged in distinct symmetries, then each vibrational symmetry—would lead to a distinct resonance frequency. While the literature is rich with data on the dielectric resonance of proteins, scale-free relationships of vibrational modes are scarce. Here, we report a self-similar triplet of triplet resonance frequency pattern for the four-4 nm-wide tubulin protein, for the 25-nm-wide microtubule nanowire and 1-μm-wide axon initial segment of a neuron. Thus, preserving the symmetry of vibrations was a fundamental integration feature of the three materials. There was no self-similarity in the physical appearance: the size varied by 106 orders, yet, when they vibrated, the ratios of the frequencies changed in such a way that each of the three resonance frequency bands held three more bands inside (triplet of triplet). This suggests that instead of symmetry, self-similarity lies in the principles of symmetry-breaking. This is why three elements, a protein, it’s complex and neuron resonated in 106 orders of different time domains, yet their vibrational frequencies grouped similarly. Our work supports already-existing hypotheses for the scale-free information integration in the brain from molecular scale to the cognition.

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Crossref · 10.3390/fractalfract4020011

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  • Functionally relevant quantum effects occur in microtubules at room temperature.

    “I also review experimental evidence that functionally relevant quantum effects occur in microtubules at room temperature”

    From A quantum microtubule substrate of consciousness is experimentally supported and solves the binding and epiphenomenalism problems (2025) · cites this paper as Saxena et al. 2020

    The Introduction (page unavailable) explicitly calls collisionless quantum transport along a microtubule at ambient conditions “non-physical.” The paper discusses microtubule electromagnetic resonance and its proposed role in neuronal firing, but does not present those functional effects as quantum effects at room temperature. (LLM, conf=0.79)

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  • Experiments have demonstrated nontrivial quantum effects in MTs at room temperature.

    “In any case, experiments have now demonstrated nontrivial quantum effects in MTs at room temperature.”

    From A quantum microtubule substrate of consciousness is experimentally supported and solves the binding and epiphenomenalism problems (2025) · cites this paper as Saxena et al. 2020

    The Introduction (page not available in our copy) calls purported quantum-like transport in microtubules non-physical at ambient conditions. The paper reports electromagnetic resonance measurements, but does not present them as a demonstration of quantum effects at room temperature. (LLM, conf=0.83)

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    Experimental — accuracy not yet measured

  • Stimulating MT resonances in cultured neurons produced an MT resonance state spanning across multiple neurons and controlling membrane voltage.

    “Similarly, Anirban Bandyopadhyay and colleagues stimulated MT resonances in cultured neurons and observed the MT resonance state “spanning across multiple neurons and controlling membrane voltage” (Saxena et al. 2020, Singh et al. 2021a, b).”

    From A quantum microtubule substrate of consciousness is experimentally supported and solves the binding and epiphenomenalism problems (2025) · cites this paper as Saxena et al. 2020

    Section 3.2 (page unavailable) reports stimulating cultured rat hippocampal neurons at microtubule resonance frequencies and observing changes in soma potential and nerve firing. It describes measurements in pairs of neurons, but does not report an MT resonance state spanning across multiple neurons; that part of the claim is unsupported. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • Anirban Bandyopadhyay and colleagues explored resonant responses of MTs at frequencies varying over many orders of magnitude in bare MTs and in cultured neurons.

    “Anirban Bandyopadhyay and colleagues explored resonant responses of MTs at frequencies varying over many orders of magnitude in “bare” MTs and in cultured neurons (Saxena et al., 2020; Singh et al., 2021a,b).”

    From Microtubule-stabilizer epothilone B delays anesthetic-induced unconsciousness in rats (2024) · cites this paper as Saxena et al., 2020

  • The prediction of quantum coherence in MTs at high temperatures (room temperature) has now been experimentally verified.

    “The prediction of quantum coherence in MTs at high temperatures (i.e., room temperature) has now been experimentally verified (Saxena et al., 2020; Babcock et al., 2024).”

    From Microtubule-stabilizer epothilone B delays anesthetic-induced unconsciousness in rats (2024) · cites this paper as Saxena et al., 2020

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Research works printed but not linked: 1

  1. Pizzi, R.; Strini, G.; Fiorentini, S.; Pappalardo, V.; Pregnolatio, M. Evidences of new biophysical properties of microtubule. In Artificial Neural Networks; Kwon, S.J., Ed.; Nova Science Publications: New York, NY, USA, 2010; pp. 1-17.

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Authors
Saxena, K., Singh, P., Sahoo, P., Sahu, S., Ghosh, S., Ray, K., Fujita, D., & Bandyopadhyay, A.
Affiliations
  • Dayalbagh Educational Institute (IN)
  • National Institute for Materials Science (JP)
  • Indian Institute of Technology Jodhpur (IN)
  • North East Institute of Science and Technology (IN)
  • Amity University Jaipur (IN)
Corresponding author
Bandyopadhyay, Anirban
ORCID
Venue
Fractal and Fractional
Publisher
MDPI AG
Published
2020-04-06
Volume
4
Issue
2
Pages
11
ISSN
2504-3110 (ISSN-L)
DOI
10.3390/fractalfract4020011
OpenAlex
W3014753675
Cited by
71
References
43
Citations by year
2026: 17 · 2025: 7 · 2024: 15 · 2023: 6 · 2022: 17 · 2021: 6 · 2020: 3
FWCI
4.80
Type
journal article
Language
en
Open access
Licence
Locations
  • Fractal and Fractional (publishedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
Asian office of Aerospace R&D (FA2386-16-1-0003)
Topics
  • Health Sciences › Medicine › Physiology › Biofield Effects and Biophysics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Mathematical Theories and Applications
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
Keywords
electromagnetic resonance, axon initial segment, neurons, self-similarity, vibrational symmetry, dielectric resonance, biomaterials, fractal resonance

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