The tryptophan residues in tubulin $αβ$-dimers form an ordered aromatic network that has been proposed to support quantum exciton transport even under physiological environmental noise. Existing studies of this system mostly assume white-noise dephasing, but the statistical properties of the protein-solvent bath coupled to tryptophan sites remain uncharacterised under physiological conditions. Here we characterise this fluctuation bath via all-atom molecular dynamics simulations of a solvated tubulin dimer at 310 K, combining high-frequency and long-time trajectories with 10 fs and 10 ps sampling intervals. The resulting autocorrelation of the site-energy fluctuations is tri-exponential, with three well-separated decay modes: sub-100-fs and picosecond fluctuations driven by water dynamics, and a nanosecond mode originating from protein conformational rearrangements. All three modes fall deep within the non-Markovian regime. We further demonstrate that the slow protein mode introduces strong quasi-static disorder, which results in Anderson localisation, while the two fast water modes frequently tune chromophore pairs through resonance, enabling environment-assisted quantum transport (ENAQT). On the full eight-site network, the coloured-noise bath confines excitons predominantly to strongly coupled proximal tryptophan pairs, in marked contrast to the more uniform delocalisation predicted by the standard white-noise Haken-Strobl model. Our workflow generalises to other pigment-protein systems with solvent-exposed chromophores.
Comments
15 pages, 5 main + 5 supplementary figures. Code: https://github.com/Varato/tubulin-bath-fluctuation v2: introduction tightened; citation and punctuation fixes; results unchanged. v3: added Fig. 1 fit-residual inset; clarified AIC model selection vs two-step parameter extraction; no scientific changes
The tryptophan residues in tubulin αβ-dimers form an ordered aromatic network that has been proposed to support quantum exciton transport even under physiological environmental noise. Existing studies of this system mostly assume white-noise dephasing, but the statistical properties of the protein-solvent bath coupled to tryptophan sites remain uncharacterised under physiological conditions. Here we characterise this fluctuation bath via all-atom molecular dynamics simulations of a solvated tubulin dimer at 310 K, combining high-frequency and long-time trajectories with 10 fs and 10 ps sampling intervals. The resulting autocorrelation of the site-energy fluctuations is tri-exponential, with three well-separated decay modes: sub-100-fs and picosecond fluctuations driven by water dynamics, and a nanosecond mode originating from protein conformational rearrangements. All three modes fall deep within the non-Markovian regime. We further demonstrate that the slow protein mode introduces strong quasi-static disorder, which results in Anderson localisation, while the two fast water modes frequently tune chromophore pairs through resonance, enabling environment-assisted quantum transport (ENAQT). On the full eight-site network, the coloured-noise bath confines excitons predominantly to strongly coupled proximal tryptophan pairs, in marked contrast to the more uniform delocalisation predicted by the standard white-noise Haken-Strobl model. Our workflow generalises to other pigment-protein systems with solvent-exposed chromophores.
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 L1 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.
The way in which energy is transported through an interacting system governs fundamental properties in nature such as thermal and electric conductivity or phase changes. Remarkably, environmental noise can enhance the transport, an effect known as environment-assisted quantum transport (ENAQT). In this Letter, we study ENAQT in a network of coupled spins subject to engineered static disorder and temporally varying dephasing noise. The interacting spin network is realized in a chain of trapped atomic ions, and energy transport is represented by the transfer of electronic excitation between ions. With increasing noise strength, we observe a crossover from coherent dynamics and Anderson localization to ENAQT and finally a suppression of transport due to the quantum Zeno effect. We find that in the regime where ENAQT is most effective, the transport is mainly diffusive, displaying coherences only at very short times. Further, we show that dephasing characterized by non-Markovian noise can maintain coherences longer than white noise dephasing, with a strong influence of the spectral structure on the transport efficiency. Our approach represents a controlled and scalable way to investigate quantum transport in many-body networks under static disorder and dynamic noise.
Excitation-energy transfer underpins the conversion of light into usable energy in photosynthetic organisms and serves as a paradigm for evolutionary optimized transport in open quantum systems. Although this process is often described as incoherent thermally assisted hopping, such descriptions become inadequate when electronic coupling, vibronic interactions and environmental fluctuations occur on comparable energy scales. Determining how the environment controls transport therefore remains a fundamental challenge. Here, we use temperature-dependent 2DES to investigate energy transfer in the photosynthetic antenna protein allophycocyanin over the range 10 - 296 K. The dominant β→α transfer step exhibits a pronounced non-monotonic temperature dependence: the transfer time decreases from 400 fs at 10 K to 200 fs near 30- 40 K before increasing again to 400 fs at 296 K. In contrast, the homogeneous optical dephasing time decreases monotonically across the same temperature range. To interpret these observations, we model APC as a vibronically coupled excitonic dimer interacting with a structured environment and solve the dynamics using hierarchical equations of motion. Conventional fixed-bath models, including Drude-Lorentz and explicit intermolecular-mode spectral densities, fail to reproduce the observed turnover. Quantitative agreement is obtained only when the low-frequency sector of the environmental spectral density is allowed to anharmonically evolve strongly with temperature, while the high-frequency bath remains essentially unchanged. More broadly, these findings demonstrate that transport efficiency is controlled not simply by the magnitude of environmental fluctuations, but by the distribution of environmental spectral weight across frequency space, providing new experimental constraints on theories of molecular transport in complex quantum environments.
We quantify the excitonic coupling in the homodimer of the dimeric Venus fluorescent protein using a quantum-classical hybrid workflow. Because the anionic chromophore carries appreciable double-excitation character, we obtain its site energy from domain-based local-pair-natural-orbital similarity-transformed equation-of-motion coupled-cluster theory (DLPNO-STEOM-CCSD), which places the in-protein bright ππ∗ state at 523.90nm, in good agreement with the experimental absorption maximum near 515nm and validated against an explicit triples-corrected EOM-CCSD(fT) benchmark; single-excitation time-dependent density functional theory (TDDFT) blueshifts this state. Applying a transition-density coupling (TDC) formalism to the STEOM transition density and simulating the VenusA206 tandem-dimer construct (two β-barrels covalently joined by an inter-domain linker), the covalent tether holds the A206 interface docked throughout 1ns of room-temperature dynamics. We obtain a thermally averaged coupling of J=32.8±1.6cm−1 across the 1000-frame trajectory (Davydov splitting 2∣J∣=65.6±3.1cm−1), representing a 19% near-field enhancement over the ensemble point-dipole estimate (JPDA=27.6±1.3cm−1) at the 24.69±0.32A˚ chromophore centroid separation. Furthermore, we argue that a separation of timescales resolves the apparent theoretical tension between intermediate experimental excitonic couplings and the highly decoherent biological environment. While it has been hypothesised that the fluorescent protein β-barrel scaffold sustains coupling by shielding the chromophore from thermal fluctuations, we emphasise that the separation of timescales applies irrespective of the exact degree of environmental decoherence and dissipation.
Microtubules host dense ultraviolet-absorbing aromatic networks, suggesting an opportunity to engineer their optical response for biotechnology. Here we assess the feasibility of tuning microtubule fluorescence by combining an excitonic radiative-coupling model with molecular-dynamics-derived microtubule-like assemblies and steady-state absorbance and fluorescence measurements in microplate geometries. Simulations quantify how positional and orientational fluctuations reshape radiative rates and quantum yield, and predict how perturbing the tryptophan network by removing a specific site, adding an extra tryptophan at candidate binding pockets, or using mixed modification fractions can modulate emission. Experiments on porcine tubulin dimers and taxol-stabilized microtubules support these trends: polymerization enhances microtubule quantum yield at 280 nm and yields bounded changes at 295 nm due to scattering, while added L-tryptophan reproducibly quenches microtubules at both wavelengths. Together, theory and experiment provide evidence for chemically addressable tuning of microtubule quantum yield and motivate design rules for engineered microtubule photonics.
We investigate vibrationally assisted electron transfer in an effective ligand--receptor complex using finite-temperature non-Markovian quantum-state diffusion with explicitly colored environmental noise. The model comprises donor and acceptor electronic states, an explicit bound-ligand vibrational mode, and a Gaussian protein--solvent bath. Linearization of a coordinate-dependent diabatic Hamiltonian yields two distinct system--environment interactions: diagonal coupling, which modulates the donor--acceptor energy gap, and off-diagonal non-Condon coupling, which modulates the electronic tunneling matrix element. In the rapidly equilibrating diagonal-bath limit, the model recovers the expected Marcus--Levich--Jortner vibronic-transfer behavior. Persistent environmental correlations instead generate non-exponential dynamics characterized by transient oscillations, back-transfer, and memory-dependent damping. Under matched weak-tunneling conditions, off-diagonal coupling opens a direct transition pathway and produces a larger finite-time acceptor population throughout the investigated parameter space. Because these dynamics do not generally support a unique kinetic rate, the enhancement is quantified using a time-averaged transfer yield. Comparisons with exact closed-system and commuting pure-dephasing limits validate the deterministic propagator and colored-noise construction, respectively, while the noncommuting dynamics are evaluated within a declared first-order finite-memory closure. These results identify ligand vibration, environmental memory, and non-Condon tunneling modulation as cooperating mechanisms that can dynamically regulate electron transfer in receptor-like environments, while maintaining a clear distinction between a mechanistic coarse-grained model and an atomistically parameterized biological complex.