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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Topological Coherence Domains in Microtubules: A Metriplectic and Non-Linear Sigma Model Approach

Authors: Návratil, Dávid;

Topological Coherence Domains in Microtubules: A Metriplectic and Non-Linear Sigma Model Approach

Abstract

Topological Coherence Domains in Microtubule Lattice Water: A Quantum Hall Ferromagnet Model (v8.2, Corrected and Extended) Description: This document presents a theoretical model of topological protection of quantum coherence in the lattice water domains of microtubules. The starting point is the Preparata and Del Giudice theory of coherence domains within the framework of condensed-phase quantum electrodynamics, which predicts the existence of coherent water regions approximately 50 nm in diameter where the electromagnetic field and molecular dipoles oscillate in phase. The model maps these coherence domains onto an effective quantum Hall ferromagnet on the cylindrical geometry of the microtubule. Each tubulin dimer carries an effective pseudospin derived from the conformational degrees of freedom of the GTP/GDP binding pocket, and the exchange interaction between neighbouring dimers is mediated by the coherent water field. In this formalism, topologically nontrivial excitations, specifically skyrmions with topological charge Q = +1, create an energy barrier against phase slips, thereby protecting the coherent state from thermal decoherence. Version 8.2 contains systematic corrections identified through an independent review. The principal corrections include: (i) a first-principles derivation of the inter-protofilament exchange coupling J_perp with explicit three-dimensional geometry and an angular factor, resolving an inconsistency of three different values present in the original text; (ii) a consistent distinction between the quantum (S_0 = 1/2) and classical (S_0 = 1) spin models when computing the macroscopic stiffness rho_s; (iii) correction of an arithmetic error in the effective damping rate gamma_eff; and (iv) the proper definition of the bare timescale tau_bare = hbar / k_B T instead of h / k_B T. All corrections are propagated through the entire computational chain and their impact on the final predictions is quantified. The corrected parameters lead to stronger topological protection than the original estimate. The macroscopic stiffness increases to rho_s = 0.044 eV, the topological barrier rises to E_v = 0.570 eV for a domain length of 150 nm, and the predicted coherence time extends from 0.38 ms to approximately 300 ms at physiological temperature (310 K). The ratio E_v / k_B T of approximately 20.7 ensures that thermal phase slips are exponentially suppressed. The document is extended with three native PGFPlots visualisations of the key scaling laws and with a numerical simulation of two entangled skyrmion qubits using the Lindblad master equation in the QuTiP framework. The simulation confirms that at the physical decoherence rate Gamma_ps of approximately 3.3 per second, quantum entanglement (concurrence C of approximately 0.14) and fidelity to the target Bell state (F of approximately 0.75) remain nonzero after 300 ms, which is a biologically relevant timescale. All derivations, calculations, and simulation code are included in the document and accompanying files to ensure full reproducibility. **Keywords:** coherence domains, microtubules, quantum Hall ferromagnet, topological protection, skyrmions, phase slip, Lindblad equation, QuTiP, quantum biology

Keywords

Microtubules Topological Insulator Quantum Hall Ferromagnet Quantum Biology Metriplectic Dynamics Theoretical Biophysics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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