Contribution
It extends the authors’ earlier single-microtubule superradiance model (Celardo et al. 2019, ref. 28) to tryptophan networks of 10⁴–10⁵ chromophores in centrioles, axonemes and hexagonal axon-like bundles. It adds a thermal, disorder-averaged prediction of the fluorescence quantum yield, and it reports a steady-state measurement of that yield in tryptophan, tubulin dimers and microtubules.
Key insight
Superradiance itself is fragile: static disorder of room-temperature size cuts the brightest state’s enhancement by two orders of magnitude. The quantum yield is not fragile. It depends on how much dipole strength sits within k_BT of the bottom of the exciton band, and disorder spreads that strength among neighbouring states without moving it far. So the quantum yield, not the peak decay rate, is the observable that can show cooperativity at room temperature.
Assumptions
- Two-level emitters, tryptophan only (SI S2): each tryptophan is its 1La transition dipole, λ = 280 nm (E₀ = 35 714 cm⁻¹), μ = 6 D, γ = 4μ²k₀³/3 = 2.73 × 10⁻³ cm⁻¹ (radiative lifetime about 1.9 ns). Tyrosine, phenylalanine, vibronic transitions and higher transitions are left out.
- Single-excitation manifold, justified by the weak intensity of biological ultraweak photon emission.
- Effective Hamiltonian (arXiv v1 Eqs. 5–8): H_eff = Σₙ(ħω₀ − iγ/2)|n⟩⟨n|
- Σ_{m≠n}(Ω_mn − iΥ_mn/2)|m⟩⟨n|, with the full retarded dipole–dipole couplings. The complex eigenvalues E_j − iΓ_j/2 give energies and decay rates.
- Geometry from PDB 1JFF: 8 tryptophans per dimer, 13 dimers per spiral, dimers rotated 27.69° and shifted 0.9 nm per step; bundles in hexagonal packing at 50 nm centre to centre; the centriole as nine microtubule triplets 100 nm from the axis.
- Thermal equilibrium within the excited manifold (Boltzmann weights over E_j), and a single, size-independent non-radiative rate per tryptophan, γ_nr ≈ 0.0193 cm⁻¹, fixed from the measured tryptophan QY in buffer. The authors say this neglects new non-radiative channels in large assemblies.
- Static disorder only: uniform on-site energy noise of width W, averaged over 10 realisations. No dynamic disorder or exciton–phonon coupling.
Key results
- Centriole (Fig. 5). max(Γ_j/γ) grows with length and saturates near 4000 at vertebrate centriole lengths. A 320 nm centriole has 112 320 dipoles, with its spectrum spanning about E₀ ± 100 cm⁻¹. At W = 200 cm⁻¹ the enhancement falls from about 3600 to about 20. Longer centrioles need larger W to lose the same fraction of enhancement (cooperative robustness).
- Axon-like bundles (Fig. 6). For 7, 19, 37, 61 and 91 microtubules, max(Γ_j/γ) is fitted by a two-variable curve (bundle size and length) with no free parameters. Extrapolation gives about 7000 for large bundles.
- Thermal quantum yield (Fig. 3). For one microtubule there are three regimes: a small (<10%) rise as one dimer forms, a plateau (to 0.1%) through the first spiral, then a sigmoid rise to saturation at a few wavelengths (about 800 nm, 10 400 tryptophans). For the centriole and the 91-microtubule bundle the yield is still rising at 10⁵ tryptophans, but in the bundle a tenfold increase from 10⁴ to 10⁵ adds only about 1%.
- Disorder (Fig. 4). QY is “almost unaffected” at W = 200 cm⁻¹, and some enhancement remains at W = 1000 cm⁻¹.
- Measurement (Table 1; SI Table S2). Tryptophan-weighted QY at 280 nm: tryptophan 12.4 ± 1.1%, tubulin dimer 10.6 ± 0.6%, microtubules 17.6 ± 2.1%. The last is the mean of 19.5 ± 2.8% (scattering-corrected) and 15.7 ± 1.3% (uncorrected). At 295 nm, where only tryptophan absorbs: 11.4 ± 1.1, 10.9 ± 1.3 and 14.7 ± 1.6%. Five freshly prepared solutions per sample were averaged. The microtubule emission is slightly sharper and its absorption peak slightly lower than the dimer’s, in the direction the model predicts.
- Lifetimes (Table S3, arXiv v1). Superradiant lifetimes 0.43–0.94 ps for bundles, centrioles and the idealised axoneme, 2.6–3.9 ps for the 6U42 axoneme and a single microtubule. Subradiant lifetimes up to about 14 s.
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Ordered tryptophan networks in microtubule architectures have superradiant eigenmodes with enhancements of 10³–10⁴ γ in the absence of disorder | strong as a model result; it is diagonalisation of a standard quantum-optics Hamiltonian on PDB geometry | Figs. 5–6, SI Eqs. 5–8 |
| C2 | The thermal quantum yield rises with network size and is robust to static disorder of room-temperature size | moderate: model result under static disorder only, with a fixed per-site non-radiative rate | Figs. 3–4 |
| C3 | The measured rise in QY from tubulin dimers to microtubules is caused by superradiance | weak to moderate: the rise is statistically significant and in the predicted direction, but no lifetimes were measured, sample concentrations could not be fixed exactly, the microtubule value rests on a scattering correction, and the case against a change in non-radiative rate is an argument (“an unlikely scenario”), not a measurement | Table 1, pp. “Results” |
| C4 | Superradiance enhancement saturates once a structure is a few excitation wavelengths long | moderate: consistent across all structures simulated | Figs. 3, 5, 6; SI |
| C5 | Axons might act as waveguides between superradiant emitters, enabling ultrafast information transfer in the brain | speculation; no result in the paper supports it | Discussion, Conclusions |
| C6 | Enhanced QY in protein aggregates might be photoprotective in Alzheimer’s disease | speculation | Conclusions |
Concepts
- superradiance (single-excitation): a collective eigenmode of N coupled emitters whose decay rate exceeds the single emitter’s γ, up to about Nγ, because one excitation is coherently shared.
- subradiance: the paired long-lived, dark modes, with decay rates far below γ.
- superradiance enhancement factor: max(Γ_j)/γ, the structure’s brightest state.
- cooperative robustness: the disorder needed to suppress superradiance grows with system size, because the large decay width couples the system strongly to the field.
- thermal quantum yield: QY from the Boltzmann-averaged radiative rate ⟨Γ⟩_th against a fixed non-radiative rate.
Connections
- Derakhshani et al. (LIT-627). The other Orch OR evidence filed with this work, and its complement rather than its rival. That paper tests the gravity-related collapse that Orch OR’s “OR” names, using spontaneous radiation bounds. This paper says nothing about collapse. It bears only on whether ordered microtubule lattices support collective quantum states at room temperature. Neither cites the other.
- Chalmers (LIT-406, NOTE-336). Chalmers argues that quantum theories of consciousness explain at best more functions. Whatever this paper’s superradiant states do in cells, they are a function in that sense.
- Gao (LIT-121, NOTE-140) criticises Penrose’s gravity-collapse argument. That is unrelated to this paper’s physics, which uses no collapse.
Bearing on the record
- A THEORY on Orch OR would cite this paper only for the narrow claim it supports: collective electronic excitations in microtubule-scale tryptophan lattices are predicted to survive room-temperature static disorder, and the QY difference between dimers and microtubules is consistent with that. It cannot source any claim about neurons in vivo, cognition, consciousness or collapse.
- No ML instruction. Nothing here belongs in the anthology.
Limitations
- No time-resolved measurements, so neither the radiative rate nor superradiance itself was observed directly. The authors say the non-exponential decays would not give a reliable radiative rate even if measured.
- Only dimers and microtubules were measured. Centrioles, bundles and axonemes are simulation only; the larger assemblies had scattering and purity problems.
- In vitro, taxol-stabilised, lyophilised commercial microtubules, at concentrations the authors could not fix exactly because the vials contain sucrose and Ficoll.
- Dynamic disorder and exciton–phonon coupling are absent from the model.
- A size-independent non-radiative rate is assumed.
Open questions
- Do fluorescence lifetime measurements across dimers, microtubules and larger assemblies show the shortening the model predicts?
- Does the QY enhancement survive a model with dynamic disorder and vibronic coupling?
- Is there any physiological source of UV excitation, or consumer of it, at which a superradiant state would matter? The paper points to ultraweak photon emission but measures nothing in cells.