Quantum Dynamics of Vibrationally-Assisted Electron Transfer beyond Condon approximation in the Ligand-Receptor Complex

We investigate the quantum dynamics of ligand–receptor electron transfer and conformational response in a prototypical viral binding complex, using the SARS-CoV-2 Spike protein bound to the human ACE2 receptor as a model system. Treating the ACE2–Spike interface as an open quantum system embedded in a biological environment, we simulate how vibrational interactions and environmental memory reshape the coupled receptor–ligand dynamics and modulate vibrationally assisted electron transfer (VA-ET). Using a Non-Markovian Stochastic Schr"odinger Equation (NMSSE) approach, we simulate electron transfer between donor and acceptor states in ACE2 modulated by a specific vibrational mode of the Spike protein. The influence of environmental memory (non-Markovian dynamics) and non-Condon effects (vibrational modulation of electronic coupling) are analyzed in detail. In the Markovian limit with an Ohmic bath, population dynamics reduce to exponential kinetics, and extracted transfer rates agree with semiclassical Marcus–Jortner predictions in the appropriate regime. Beyond the Markovian, high-temperature limit, we observe clear deviations: non-exponential decay, coherent oscillatory features, and enhanced sensitivity to the vibrational frequency. Incorporating off-diagonal system–bath coupling alongside diagonal coupling shows that nuclear motion can dynamically gate electron tunneling, sharpening the frequency selectivity of the VA-ET mechanism. Finally, a structured (sub-Ohmic) environmental spectral density with long-lived correlations (``memory’’) preserves electronic–vibrational coherence over longer times, amplifying vibrational selectivity under non-Condon coupling. Our results support the proposition that ACE2–Spike binding may exploit vibrational assistance and quantum coherence as a molecular recognition mechanism.

💡 Research Summary

This paper presents a comprehensive quantum‑dynamical study of vibrationally‑assisted electron transfer (VA‑ET) at the interface of the SARS‑CoV‑2 Spike protein and the human ACE2 receptor. The authors model the ACE2 redox site as a two‑level system (donor |D⟩ and acceptor |A⟩) with energy bias ε and tunneling matrix element Δ. A single harmonic vibrational mode of the Spike protein, with frequency ω_v, is coupled linearly to the electronic population via a Holstein‑type term γσ_z(b + b†). The surrounding protein, membrane, and solvent are represented as a harmonic bath. Two distinct system‑bath couplings are included: (i) diagonal (Condon) coupling through σ_z, which modulates the donor‑acceptor energy gap, and (ii) off‑diagonal (non‑Condon) coupling through σ_x, which makes Δ time‑dependent. Two bath spectral densities are examined: an Ohmic Drude–Lorentz form (allowing a Markovian limit) and a structured sub‑Ohmic Lorentzian form that generates long‑lived correlations.

To treat the open‑system dynamics without perturbative approximations, the authors employ the Non‑Markovian Stochastic Schrödinger Equation (NMSSE), also known as Non‑Markovian Quantum State Diffusion (NMQSD). In this framework the reduced density matrix ρ(t) is obtained as an ensemble average over stochastic pure‑state trajectories |ψ_z(t)⟩ driven by a complex Gaussian noise z(t) whose two‑time correlation reproduces the bath correlation function C(t). The NMSSE contains a memory integral over the entire past noise history, thereby capturing non‑Markovian effects exactly for the chosen Hamiltonian.

Simulation results are organized into four regimes. In the Markovian limit (high temperature, fast bath cutoff, weak coupling) with only diagonal coupling, the population decay of the donor state is exponential and the extracted transfer rate matches the Marcus–Jortner expression, confirming the consistency of the method. When the bath is changed to a structured sub‑Ohmic form, the dynamics become non‑exponential: population decay exhibits revivals and coherent oscillations persisting for several hundred femtoseconds to picoseconds, indicating that environmental memory preserves electronic‑vibrational coherence. Introducing off‑diagonal (non‑Condon) coupling dramatically alters the picture: the tunneling element Δ becomes modulated by the vibrational coordinate, producing a sharp resonance condition. Near ω_v ≈ ε/ℏ the electron transfer rate is strongly enhanced, and the system behaves as a vibrational “gate” that selectively amplifies transfer at specific frequencies. When both non‑Condon coupling and a structured bath are present, the coherence time is further extended, and the frequency selectivity of the VA‑ET mechanism is amplified, leading to activation‑less transfer when the total reorganization energy λ_tot matches the driving force ε.

The authors interpret these findings as evidence that the ACE2‑Spike interaction may exploit quantum coherence and vibrational gating as part of its molecular recognition strategy. The combined effect of non‑Condon modulation and non‑Markovian environmental memory provides a mechanism for highly selective, rapid electron transfer that goes beyond classical lock‑and‑key affinity. The paper concludes by suggesting experimental validation via ultrafast 2D‑IR or femtosecond transient absorption spectroscopy, and by highlighting potential applications in drug design, where targeting specific vibrational modes could modulate viral binding.