Celardo Microtubule Superradiance

Celardo Microtubule Superradiance

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Celardo superradiance refers to the 2019 theoretical proposal by Giuseppe Luca Celardo, Marco Angeli, Travis J. A. Craddock, and Philip Kurian that aromatic tryptophan residues in microtubule tubulin dimers form a Dicke superradiant collective electronic system. The proposal predicts coherent electronic states with lifetimes orders of magnitude longer than would be expected from independent-molecule estimates, providing a theoretical basis for the empirical Bandyopadhyay results and addressing the Tegmark critique.

The original paper is:

• Celardo, G. L., Angeli, M., Craddock, T. J. A., Kurian, P. (2019). "On the existence of superradiant excitonic states in microtubules." New Journal of Physics 21: 023005. (Open-access.)

Dicke superradiance: background

Robert Dicke (1954) showed that N identical two-level emitters confined within a wavelength of each other emit collectively coherently. The emission rate scales as N² (rather than N for incoherent emission), and the collective lifetime is τ₀/N (rather than τ₀).

For an array of N atoms with single-atom lifetime τ₀:

$ \Gamma _{\text{coll}}=N\,\Gamma _{0},\qquad \tau _{\text{coll}}=\tau _{0}/N $

$ P_{\text{emit}}=N^{2}\,P_{\text{single}} $

Superradiance has been observed in many experimental systems (atomic gases, NV centres in diamond, quantum dots, photosynthetic light-harvesting complexes).

A subradiant counterpart also exists: certain collective states have lifetimes longer than the single-atom estimate by a factor of N. Subradiance is the more relevant case for protecting coherent states against decay.

The Celardo proposal

Celardo et al. apply Dicke's framework to the array of tryptophan residues in microtubule tubulin. Each tubulin dimer contains 8 tryptophan residues. A typical microtubule lattice has ~ 10⁵–10⁷ tubulin dimers, giving ~ 10⁶–10⁸ tryptophans in a periodic arrangement.

Key features:

• Periodic geometry — the helical microtubule lattice positions tryptophan residues in a regular 3D array.
• Tryptophan optical transitions — tryptophan has UV absorption near 280 nm with non-trivial transition dipole moment. The transitions can couple to electromagnetic modes (and in principle to other quantum fields).
• Coherent dipole-dipole coupling between nearby tryptophans through near-field EM interaction.

In this configuration, the tryptophan array supports collective Dicke states classified by:

• Total angular momentum quantum number J (analogous to the Dicke cooperation number).
• Phase-coherent superpositions across the lattice.

The Celardo calculation shows that some of these collective states are subradiant — long-lived against radiative decay by a factor of order N.

Predicted enhancement of coherence times

For N ~ 10⁶ coherently-coupled tryptophans:

$ \tau _{\text{coll}}\sim N\,\tau _{0}\sim 10^{6}\,\tau _{0} $

where τ₀ is the single-tryptophan radiative lifetime. Including environmental decoherence (the regime studied by Tegmark), Celardo et al. estimate that subradiant collective states in the microtubule lattice have effective coherence times ~ 6 orders of magnitude longer than independent-molecule estimates.

This is the key theoretical result: collective subradiance protects coherence in ways that Tegmark's 2000 estimate did not account for. The coherence-time enhancement comes from the symmetry of the collective state, which suppresses coupling to certain decoherence channels.

Comparison with empirical data

The Celardo prediction is qualitatively consistent with:

• Bandyopadhyay frequency-resonance peaks — discrete coherent modes are expected in a structured collective system.
• Photosynthesis quantum coherence (Engel 2007 and subsequent work) — collective aromatic-residue systems support room-temperature coherence on functionally-relevant timescales.
• Microtubule anaesthetic binding sites (Kalra 2023) — anaesthetics targeting aromatic-residue interactions are expected if those residues underlie the cognitive function.

Quantitatively, the Celardo prediction does NOT yet match the full Orch OR requirement (10 ms timescales for biologically-relevant coherent computation). But it brings the picture much closer to biological relevance than Tegmark's 10⁻¹³ s estimate.

Sanity-check limits

• N = 1 (single isolated tryptophan) → standard single-molecule lifetime; no superradiance/subradiance. ✓
• Random (not lattice) tryptophan array → no coherent collective state; no subradiance enhancement. ✓
• Microtubule depolymerisation → loss of lattice; loss of collective states; rapid decoherence. ✓
• Above protein denaturation temperature → tryptophan-coupling geometry disrupted; no collective state. ✓
• ψ → 0 (in framework) → Celardo prediction still holds via standard quantum-optics; only the ψ-coupling channel is affected. ✓

Implications

If the Celardo proposal is correct:

1. Tegmark-style strong critiques of Orch OR are too pessimistic by ~ 6 orders of magnitude. Hagan-Hameroff's 2002 rebuttal directionally vindicated; specific mechanism (subradiance vs ordered-water shielding) refined.
2. Microtubules are a genuinely unusual biological substrate for quantum-coherent dynamics, with structural basis in the tryptophan-array geometry.
3. Specific frequency-resonance predictions — the collective-state spectrum is in principle calculable from the lattice geometry; matching to Bandyopadhyay peaks is a key test.
4. Coupling to the ψ field — in the framework, coherent collective electronic states couple to ψ via the αψ F_μν F^μν vertex; subradiance enhances the coherent component by a factor of N.

Open questions

1. First-principles calculation of the specific collective-state frequencies; matching to Bandyopadhyay peaks.
2. Quantitative estimate of the subradiance lifetime for realistic microtubule geometry and biological environment.
3. Direct experimental tests of subradiant emission from microtubules (proposal: measure UV emission from in-vitro microtubule preparations under controlled excitation).
4. Whether the subradiant states couple sufficiently strongly to other neuronal dynamics to influence cognition.

Related theoretical work

The Celardo proposal is part of a broader effort to bring biological quantum coherence under rigorous theoretical treatment:

• Kurian et al. (2017) — quantum-coherent energy transport in protein networks generally.
• Craddock et al. (2017) — exciton coupling in microtubule lattices.
• Engel et al. (2007) and subsequent photosynthesis work — direct empirical precedent for room-temperature quantum-coherent biological systems.

See Coherent_Quantum_Effects_in_Biology for the broader picture.

See Also

• Microtubule
• Orchestrated_Objective_Reduction
• Bandyopadhyay_Microtubule_Conductance
• Kalra_Anaesthetic_Microtubule
• Tegmark_Critique_and_Hagan_Rebuttal
• Coherent_Quantum_Effects_in_Biology
• Biophotons
• Biological_Substrate_of_Psi

References

• Celardo, G. L., Angeli, M., Craddock, T. J. A., Kurian, P. (2019). "On the existence of superradiant excitonic states in microtubules." New Journal of Physics 21: 023005.
• Dicke, R. H. (1954). "Coherence in spontaneous radiation processes." Physical Review 93: 99–110.
• Kurian, P., Capolupo, A., Craddock, T. J. A., Vitiello, G. (2017). "Water-mediated correlations in DNA-enzyme interactions." Physics Letters A 382: 33–43.
• Craddock, T. J. A., Friesen, D., Mane, J., Hameroff, S., Tuszynski, J. A. (2014). "The feasibility of coherent energy transfer in microtubules." Journal of the Royal Society Interface 11: 20140677.
• Engel, G. S., et al. (2007). "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems." Nature 446: 782–786.