Quantum Information Flow in Microtubule Tryptophan Networks

Networks of aromatic amino acid residues within microtubules, particularly those formed by tryptophan, may serve as pathways for optical information flow. Ultraviolet excitation dynamics in these networks are typically modeled with effective non-Hermitian Hamiltonians. By extending this approach to a Lindblad master equation that incorporates explicit site geometries and dipole orientations, we track how correlations are generated, routed, and dissipated, while capturing both energy dissipation and information propagation among coupled chromophores. We compare localized injections, fully delocalized preparations, and eigenmode-based initial states. To quantify the emerging quantum-informational structure, we evaluate the $L_1$ norm of coherence, the correlated coherence, and the logarithmic negativity within and between selected chromophore sub-networks. The results reveal a strong dependence of both the direction and persistence of information flow on the type of initial preparation. Superradiant components drive the rapid export of correlations to the environment, whereas subradiant components retain them and slow their leakage. Embedding single tubulin units into larger dimers and spirals reshapes pairwise correlation maps and enables site-selective routing. Scaling to larger ordered lattices strengthens both export and retention channels, whereas static energetic and structural disorder suppresses long-range transport and reduces overall correlation transfer. These findings provide a Lindbladian picture of information flow in cytoskeletal chromophore networks and identify structural and dynamical conditions that transiently preserve nonclassical correlations in microtubules.

💡 Research Summary

The authors present a comprehensive open‑quantum‑systems study of ultraviolet excitation dynamics in the tryptophan (Trp) chromophore network embedded in microtubules. While previous works have modeled these systems with a non‑Hermitian effective Hamiltonian (H_eff = H₀ + Δ – i G/2) that captures coherent dipole‑dipole couplings (Δ) and collective radiative decay (G), such an approach does not preserve the trace of the density matrix and therefore cannot describe the full dissipative process. To overcome this limitation, the paper reformulates the problem in Lindblad form, retaining the same microscopic parameters (site positions, dipole orientations, transition frequency λ₀ = 280 nm) but adding explicit jump operators derived from the eigen‑decomposition of the decay matrix G. An auxiliary ground state |0⟩ is introduced so that radiative jumps transfer population from the single‑excitation manifold to |0⟩, guaranteeing complete positivity and trace preservation.

Five distinct initial conditions are examined on the basic eight‑Trp unit (the α‑β tubulin dimer): (i) the most super‑radiant eigenstate of H_eff, (ii) the most sub‑radiant eigenstate, (iii) a maximally coherent uniform superposition across all sites, (iv) a maximally mixed single‑excitation state, and (v) a site‑localized excitation mimicking a single‑photon absorption event. For each case the authors compute site‑resolved populations, the L₁‑norm of coherence (a basis‑dependent measure of delocalisation), a basis‑independent “correlated coherence” metric, and the logarithmic negativity as an entanglement witness. Simulations are performed with QuTiP over time windows ranging from picoseconds to tens of nanoseconds, reflecting the experimentally relevant radiative lifetimes of Trp.

The super‑radiant preparation exhibits a collective burst of emission: all site populations decay synchronously within ~1 ns, the L₁‑coherence drops sharply, and entanglement appears only fleetingly before vanishing. This demonstrates that the information carried by the excitation is rapidly exported to the electromagnetic environment, leaving little internal quantum correlation. In stark contrast, the sub‑radiant state shows strongly suppressed radiative loss; populations persist for tens of nanoseconds, coherence remains high, and logarithmic negativity stays sizable, indicating that the network can retain non‑classical correlations for biologically relevant timescales. The uniform coherent state initially carries large coherence but dephases on a similar timescale to the super‑radiant case, while the mixed state shows negligible coherence and a decay pattern dominated by site‑dependent radiative rates. The localized excitation spreads quickly through dipole couplings, generating a transient surge of pairwise coherence that again decays as the excitation radiates away.

Beyond the single dimer, the authors explore structural scaling. By assembling dimers into spirals (one circumferential turn of 13 dimers) and extending to larger ordered lattices, they find that geometry can steer correlation pathways: certain sites become hubs for sub‑radiant modes, enabling site‑selective routing of quantum information. Larger lattices amplify both the fast export channel (enhanced super‑radiance) and the retention channel (more pronounced sub‑radiant manifolds), suggesting that size alone can increase the diversity of information flow routes.

The impact of disorder is also investigated. Static energetic disorder (random site‑energy fluctuations) and structural disorder (geometrical variations sampled from molecular dynamics) both diminish long‑range coherence and reduce the lifetime of sub‑radiant states. Structural disorder, in particular, randomises dipole orientations, weakening Δ_nm and G_nm, and thereby suppresses the protective effect of sub‑radiance. Consequently, the network’s ability to sustain quantum correlations over nanometer distances is highly sensitive to the degree of order.

Finally, the paper quantifies non‑Markovianity by evaluating an information‑backflow measure based on trace‑distance dynamics of reduced subsystems. Significant backflow is observed only for sub‑radiant initial states in ordered large lattices, indicating temporary re‑injection of information from the environment. Super‑radiant and disordered scenarios remain essentially Markovian, with monotonic loss of correlations.

In summary, this work provides the first fully Lindbladian description of UV‑driven quantum dynamics in microtubule tryptophan networks. It shows that the direction and persistence of quantum information flow are dictated by the initial photonic preparation, the structural architecture (size, spiral vs. linear arrangement), and the level of energetic/structural disorder. Super‑radiant modes act as fast “broadcast” channels, rapidly exporting excitation and coherence, whereas sub‑radiant modes constitute slow “memory” channels that can retain entanglement for tens of nanoseconds. These findings suggest that, under appropriate conditions, microtubules could transiently host non‑classical correlations, offering a physically grounded mechanism for quantum‑inspired signaling pathways in neurons, albeit without claiming that such processes are directly responsible for computation. The study thus bridges collective radiative physics with quantum information theory in a biologically relevant macromolecular context.