Quantum Information Flow in Microtubule Tryptophan Networks

Abstract

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.

Figures (14)

• Figure 1: Structure of the tubulin dimer from Protein Data Bank (PDB) entry 1JFF, rendered using PyMOL (molecular visualization software) DeLano2002PyMOL, highlighting the positions of the eight tryptophan residues. The $\alpha$-tubulin chain is shown in light gray and the $\beta$-tubulin chain in dark gray, with tryptophan residues displayed in green. Purple-labeled numbers correspond to specific tryptophan residues analyzed in the study: Trp1 ($\alpha$ 21), Trp2 ($\alpha$ 346), Trp3 ($\alpha$ 388), Trp4 ($\alpha$ 407), Trp5 ($\beta$ 21), Trp6 ($\beta$ 103), Trp7 ($\beta$ 346), and Trp8 ($\beta$ 407).
• Figure 2: Excitation dynamics for the initial state corresponding to the superradiant eigenstate of the non-Hermitian Hamiltonian. (a) shows rapid decay of excitation population across all tryptophan sites, characteristic of strong radiative coupling. (b) illustrates the rapid loss of coherence via the $L_1$ norm for the four most coherent chromophore pairs. (c) presents the logarithmic negativity, which peaks briefly before vanishing, indicating transient entanglement that dissipates alongside the excitation. Pairs $(i,j)$ denote tryptophan site indices (labels) defined in Fig. \ref{['fig:tub']}.
• Figure 3: Excitation dynamics for an initial state corresponding to the most subradiant eigenstate of the non-Hermitian Hamiltonian. (a) shows the site-resolved excitation population, which decays very slowly, indicating suppression of radiative losses. (b) illustrates the $L_1$ norm of coherence for the four most coherent chromophore pairs, remaining high throughout the evolution. (c) presents the logarithmic negativity between those pairs, showing sustained and robust bipartite entanglement over time. Pairs $(i,j)$ denote tryptophan site indices (labels) defined in Fig. \ref{['fig:tub']}. Time is reported in picoseconds (ps) in all panels.
• Figure 4: Excitation dynamics for a fully coherent initial state delocalized across all eight tryptophan sites. (a) Site-resolved excitation populations over time. (b) $L_1$ norm of coherence for selected chromophore pairs. (c) Logarithmic negativity showing entanglement dynamics. (d) Projection onto the eigenmodes of the effective non-Hermitian Hamiltonian $H_{\mathrm{eff}}$, classified by their collective radiative rates $\Gamma_j$ relative to the single-site rate $\gamma$ (superradiant/bright: $\Gamma_j/\gamma>1$; subradiant/dark: $\Gamma_j/\gamma<1$). The bright-to-dark crossover is identified when the total projected weight in modes with $\Gamma_j/\gamma<1$ exceeds that in modes with $\Gamma_j/\gamma>1$. Pairs $(i,j)$ denote tryptophan site indices (labels) defined in Fig. \ref{['fig:tub']}. Time is reported in picoseconds (ps) in all panels.
• Figure 5: Excitation dynamics for a fully incoherent mixed state uniformly distributed over all eight tryptophan sites. (a) Site-resolved excitation populations. (b) $L_1$ norm of coherence for selected chromophore pairs. (c) Logarithmic negativity reflecting lack of entanglement. (d) Projection onto eigenstates of the non-Hermitian Hamiltonian: the plotted weights indicate how population overlaps with eigenmodes $j$ of $H_{\mathrm{eff}}$, each characterized by a collective radiative rate $\Gamma_j$; modes with $\Gamma_j/\gamma>1$ are superradiant (bright) and those with $\Gamma_j/\gamma<1$ are subradiant (dark). For a fully mixed initial condition, the projection is broadly distributed and does not selectively target either sector, so the decay is effectively non-preferential across bright and dark channels. Pairs $(i,j)$ denote tryptophan site indices (labels) defined in Fig. \ref{['fig:tub']}. Time is reported in picoseconds (ps) in all panels.