Excitonic Coupling and Photon Antibunching in Venus Yellow Fluorescent Protein Dimers: A Lindblad Master Equation Approach

TL;DR

This work develops a two-site open-quantum-system model for Venus YFP dimers using a Lindblad master equation with a Drude–Lorentz bath to reconcile strong excitonic coupling and photon antibunching observed experimentally. The excitonic Hamiltonian, with Δ and J, yields eigenenergies E± and a bright–dark basis that governs sub-ps decoherence and room-temperature thermalization; simulations predict rapid dephasing (T2*≈2.77 fs) and a bright-dominant mixed state at 293 K, along with a modest absorption redshift. Although the model captures AB coexisting with strong coupling, several Lindblad-approximation assumptions are violated in the chosen parameter regime, indicating the need for refined system–bath definitions and parameter choices. The findings suggest that antibunched emission and spectral shifts in Venus dimers can be explained without long-lived coherence, with implications for FP dimer design and photonic quantum platforms, and motivate extensions to non-Markovian/correlated baths and broader FP variants. Overall, the work integrates excitonic physics, spectral shifts, and photon statistics into a coherent framework that informs biological function and quantum technology prospects.

Abstract

Strong excitonic coupling and photon antibunching (AB) have been observed together in Venus yellow fluorescent protein dimers and currently lack a cohesive theoretical explanation. In 2019, Kim et al. demonstrated Davydov splitting in circular dichroism spectra, revealing strong J-like coupling, while antibunched fluorescence emission was confirmed by combined antibunching--fluorescence correlation spectroscopy (AB/FCS fingerprinting). To investigate the implications of this coexistence, Venus yellow fluorescent protein (YFP) dimer population dynamics are modeled within a Lindblad master equation framework, testing its ability to cope with typical, data-informed, Venus YFP dimer time and energy values. Simulations predict multiple-femtosecond (fs) decoherence, yielding bright/dark state mixtures consistent with antibunched fluorescence emission at room temperature. Thus, excitonic coupling and photon AB in Venus YFP dimers are reconciled without invoking long-lived quantum coherence. However, clear violations of several Lindblad approximation validity conditions appear imminent, calling for careful modifications to choices of standard system and bath definitions and parameter values.

Figures (4)

• Figure 1: Room-temperature, sub-ps thermal relaxation dynamics. Population dynamics of a Venus dimer at room temperature ($T = 293$ K) shown in the energy (exciton) basis, initialized in the bright state ($\rho_{++}$). In this true-homodimer case, $\Delta=0$, representing a timescale prior to vibrational relaxation. The exciton splitting $\Delta E=2|J|$, where the Coulombic coupling energy $J = -34$ meV (Appendix \ref{['sec:appendix_splitting']}). Inhomogeneous site decoherence occurs in $T_2^*\approx2.77$ fs, resulting in visibly overdamped, monotonic population decay.
• Figure 2: Room-temperature, ps thermal relaxation dynamics from an equal bright--dark mixture. Population dynamics of a Venus dimer at room temperature ($T = 293$ K) shown in the energy (exciton) basis, initialized in a 50:50 bright--dark mixed state ($\rho_{++}=\rho_{--}=0.5$), excluding pure dephasing. In this effective-heterodimer case, $\Delta = 59\ \mathrm{meV}$, representing the Venus Stokes shift following vibrational relaxation (Appendix \ref{['sec:appendix_site_energy_gap_stokes_shift']}). The exciton splitting becomes $\Delta E=\sqrt{\Delta^2+4J^2} \approx 90$ meV, where the Coulombic coupling energy $J = -34$ meV, favoring the bright exciton state, although, for a mixed state, both bright and dark exciton states should be optically accessible.
• Figure 3: Structural homology of Venus YFP and wild-type GFP. Global alignment of cartoon crystal structures of the Venus YFP subunit (yellow; PDB ID: 1MYW) and wild-type GFP dimer (marine blue; PDB ID: 1GFL) (RMSD: 0.323 Å, computed in PyMOL global alignment) highlights conserved chromophore orientation relative to the $\beta$-barrel scaffold and overall structural homology. (Chromophores are shown as sticks.) The roughly $C_2$-symmetric quaternary structure predicted by previous simulations of wild-type GFP dimerization Wang2019 is approximated by the corresponding crystal unit cell structure shown here.
• Figure 4: Heuristic cryogenic-temperature extrapolation of coherence half-life. Imaginary coherence Im[$\rho_{+-}$] is shown as a heuristic to highlight oscillatory decay and half-life, rather than to represent a “real” cryogenic observable in Venus dimers, both mathematically and physically. The system is initialized in the state $(|+\rangle+i|-\rangle)/\sqrt{2}$ to visualize coherence evolution. The case modeled here has identical system parameters to those used in Figure \ref{['fig:room-temperature_subps_dynamics']}. The high-temperature dephasing model used throughout this work is heuristically extrapolated to cryogenic temperatures (250--400 mK). Although this violates the $k_BT \gg \hbar\omega_0$ high-temperature modeling assumption, it provides a conservative lower bound: true coherence half-lives $t_{1/2}$ would be longer than shown, since vibrations are exponentially suppressed at low $T$. Even so, the extrapolation predicts $t_{1/2}\approx 1.04$ ps at 250 mK and $t_{1/2}\approx 0.651$ ps ($651$ fs) at 400 mK, placing FP dimers within a regime well-compatible with ultrafast optical gate times.