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

Version 10.0 – Final (Definitive Edition)

This manuscript presents Version 10.0 – Final, the definitive, complete and concluding edition of the theoretical framework for topological protection of quantum coherence in microtubules at physiological temperature (T = 310 K).

This is designated as the final version because it incorporates all major improvements and resolves every issue from previous iterations: explicit decoupling from Preparata–Del Giudice QED coherence domains, new sections on robustness against active biological noise and mechanical bending, full Monte Carlo validation with lattice regularization addressing Derrick’s theorem, refined QuTiP simulations with the correct topological barrier Ev ≈ 0.570 eV, and complete finite-size scaling for realistic defect-limited domains (L ≈ 150 nm).

The model treats ordered water domains in the tubulin lattice as an effective quantum Hall ferromagnet on a cylindrical geometry. Topologically nontrivial skyrmion excitations (winding number Q = +1) generate an energy barrier Ev ≈ 0.570 eV (≈ 21.3 kBT). Using Kramers-Grote-Hynes escape theory in the underdamped regime combined with metriplectic dynamics, the predicted coherence lifetime is τps ≈ 300 ms. This is quantitatively supported by Lindblad master-equation simulations in QuTiP (fidelity ≈ 0.81 and concurrence ≈ 0.65 at 300 ms for entangled skyrmion qubits).

Although historically inspired by the concept of coherence domains, the protection mechanism is fundamentally independent of QED coherence of water. Protection arises exclusively from the tubulin lattice topology (Q = +1 skyrmion) and the microscopic exchange interactions J∥ = 0.10 eV and J⊥ = 0.077 eV. Water enters the model only phenomenologically as a sub-Ohmic bath (s ≈ 0.6), justified by independent mainstream experiments (THz dielectric spectroscopy of protein hydration shells and molecular dynamics simulations – see Section 1.10.3).

The framework explicitly accounts for real biological conditions: structural defects and dynamic instability naturally define finite coherence domain lengths (L ≈ 150 nm), while skyrmions remain robust against continuous local perturbations (pH changes, MAP binding, mechanical strain) because they cannot change the topological invariant unless the full barrier Ev is overcome. The barrier also exceeds single ATP hydrolysis energy (Ev > ΔG_ATP ≈ 0.50 eV).

Six quantitative, falsifiable predictions are presented (including a clear D₂O isotope effect) together with detailed experimental protocols. Full QuTiP code, Monte Carlo scripts, scaling visualizations and sensitivity analysis are provided in the appendices for complete reproducibility.

Future extensions planned for Version 11 will include significantly improved and expanded QuTiP simulations (6-qubit and multi-qubit braiding protocols with full triple self-duality), additional Monte Carlo runs with larger system sizes, and complete PGFPlots-based visualisation suites for all scaling laws and sensitivity analyses.

Keywords: quantum biology, microtubules, topological protection, skyrmions, quantum Hall ferromagnet, metriplectic dynamics, Kramers escape, sub-Ohmic bath, topological time crystal, D2O isotope effect

We welcome experimental validation and collaboration from the quantum-biology and biophysics communities.

Author: Dávid Navrátil

I've aded few Visualization, no "Ad hoc" no "Toy models" everything derived from v10. 

Contact: david.navratil2016@gmail.com