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arXiv:2605.00027

Non-Equilibrium Dynamics of the Time-Dependent Excitonic Coupling in Fluorescent Protein Dimers

Robson Christie, Cerys Murray, Youngchan Kim, Jaewoo Joo

physics.chem-phphysics.bio-phquant-phSubmitted Apr 22, 2026• Announced Apr 23, 2026
v1 · Apr 22, 2026v2 · Sep 24, 2026
arXivHTMLPDF

Abstract

We quantify the excitonic coupling in the homodimer of dimeric Venus fluorescent protein using a quantum-classical hybrid workflow. Employing a transition-density coupling formalism, we calculate $J = 74.38~\mathrm{cm^{-1}}$, which is 5.6 times stronger than the far-field point-dipole estimate of $13.31~\mathrm{cm^{-1}}$. This disparity highlights the critical role of near-field multipolar effects at the 27.6~Å chromophore centroid separation. Furthermore, we argue that a separation of timescales resolves the apparent theoretical tension between robust experimental excitonic couplings and the highly decoherent biological environment. While it has been hypothesised that the fluorescent protein $β$-barrel scaffold sustains coupling by attenuating thermal fluctuations, we emphasise that the separation of timescales fundamentally applies irrespective of the exact degree of environmental noise suppression. Collective photoexcitation imprints the Davydov splitting under optical-limit dielectric screening upon absorption, preceding bulk solvent relaxation and sub-picosecond environmental dephasing. To characterise the subsequent post-absorption evolution, we employ stochastic simulations for quantum parts to model the transition from a delocalised exciton superposition to incoherent hopping between localised chromophore states.

Journal reference
Journal of Physical Chemistry B (2026)
DOI
10.1021/acs.jpcb.6c05048
Comments
11 pages, 3 figures

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We quantify the excitonic coupling in the homodimer of dimeric Venus fluorescent protein using a quantum-classical hybrid workflow. Employing a transition-density coupling formalism, we calculate J=74.38 cm−1J = 74.38~\mathrm{cm^{-1}}J=74.38 cm−1, which is 5.6 times stronger than the far-field point-dipole estimate of 13.31 cm−113.31~\mathrm{cm^{-1}}13.31 cm−1. This disparity highlights the critical role of near-field multipolar effects at the 27.6~Å chromophore centroid separation. Furthermore, we argue that a separation of timescales resolves the apparent theoretical tension between robust experimental excitonic couplings and the highly decoherent biological environment. While it has been hypothesised that the fluorescent protein βββ-barrel scaffold sustains coupling by attenuating thermal fluctuations, we emphasise that the separation of timescales fundamentally applies irrespective of the exact degree of environmental noise suppression. Collective photoexcitation imprints the Davydov splitting under optical-limit dielectric screening upon absorption, preceding bulk solvent relaxation and sub-picosecond environmental dephasing. To characterise the subsequent post-absorption evolution, we employ stochastic simulations for quantum parts to model the transition from a delocalised exciton superposition to incoherent hopping between localised chromophore states.
The tryptophan residues in tubulin αβαβαβ-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.
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→αβ\rightarrow αβ→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.
Understanding how quantum coherence is regulated by structured environments is essential for elucidating energy-transfer mechanisms in photosynthetic light-harvesting complexes. In this work, we present a trajectory-based computational analysis of the quantum-classical transition in asymmetrically coupled spin-boson models, motivated by exciton-phonon interactions in the phycobiliprotein PC645 complex. The model captures site-dependent environmental coupling that mimics pigment-specific dissipation pathways in biological systems. We employ three complementary approaches: a Redfield master equation in the Bloch-vector representation, numerically exact hierarchical equations of motion (HEOM), and a stochastic Schrödinger equation that generates ensembles of quantum trajectories. Within the stochastic framework, environmental backaction is interpreted as a continuous measurement process, giving rise to a time-dependent dynamical corridor on the Bloch sphere. The corridor width provides a quantitative measure of coherence loss and defines the quantum-classical crossover time. Our results show that moderate asymmetric coupling can sustain coherence and enhance directional population transfer, whereas strong coupling rapidly suppresses quantum trajectories. These findings offer mechanistic insight into environmentally assisted energy transfer and coherence regulation in photosynthetic pigment-protein complexes.
Excited electronic states are difficult to accurately and tractably model, particularly those exhibiting multiexcitonic character. Scalable single-reference excited state methods typically fail to describe such states as they suffer from the defects of the mean-field approximation and/or neglect higher-rank excitation operators. To address this, we derive the [T] perturbative correction to the quantum self-consistent equation-of-motion unitary coupled cluster singles and doubles (q-sc-EOM-UCCSD) method. The method captures triple excitation effects through a classical step of second-order in many-body perturbation theory following a q-sc-EOM-UCCSD calculation on a quantum computer. The perturbative correction developed has a O(N7)\mathcal{O}(N^7)O(N7) classical computational time scaling. We incorporate [T] into a hybrid compute strategy wherein eigenvectors of the effective Hamiltonian from the hybrid quantum-classical q-sc-EOM-UCCSD algorithm are relayed to a classical computer which performs the postprocessing required for the [T] correction. The benefits of [T] are quantified in a benchmark covering a variety of electronically excited states of the isoelectronic CH+^++ and BH molecules. We find that the addition of the [T] correction to both trotterized and full operator variants of q-sc-EOM-CCSD can offer dramatic improvements over baseline q-sc-EOM-UCCSD. Our assessment clearly demonstrates the importance of considering higher-rank excitation operators in q-sc-EOM-UCCSD, quantifies the overall success of the [T] correction, and discusses some of its limitations.
In this paper, we present a theoretical description to the quantum coherence and decoherence phenomena of energy transfer in photosynthesis observed in a recent experiment [see Science 316, 1462 (2007)]. As a successive two-color laser pulses with selected frequencies cast on a sample of the photosynthetic purple bacterium Rb. sphaeroides two resonant excitations of electrons in chromophores can be generated. However, this effective two-level subsystem will interact with its protein environment and decoherence is inevitable. We describe this subsystem coupled with its environment as a dynamical spin-boson model. The non-Markovian decoherence dynamics is described using a quasi-adiabatic propagator path integral (QUAPI) approach. With the photon-induced effective time-dependent level splitting energy and level flip coupling coefficient between the two excited states and the environment-induced non-Markovian decoherence dynamics, our theoretical result is in good agreement with the experimental data.
In this paper, we present a theoretical description to the quantum coherence and decoherence phenomena of energy transfer in photosynthesis observed in a recent experiment [Science 316, 1462 (2007)]. As a successive two-color laser pulses with selected frequencies cast on a sample of the photosynthetic purple bacterium Rb. sphaeroides two resonant excitations of electrons in chromophores can be generated. However, this effective two-level subsystem will interact with its protein environment and decoherence is inevitable. We describe this subsystem coupled with its environment as a dynamical spin-boson model. The non-Markovian decoherence dynamics is described using a quasiadiabatic propagator path integral (QUAPI) approach. With the photon-induced effective time-dependent level splitting energy and level flip coupling coefficient between the two excited states and the environment-induced non-Markovian decoherence dynamics, our theoretical result is in good agreement with the experimental data.