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

Mohamad Toutounji; Muhammad Waqas Haseeb

arxiv: 2602.06469 · v2 · submitted 2026-02-06 · 🪐 quant-ph

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

Muhammad Waqas Haseeb , Mohamad Toutounji This is my paper

Pith reviewed 2026-05-16 07:11 UTC · model grok-4.3

classification 🪐 quant-ph

keywords vibrationally-assisted electron transfernon-Markovian dynamicsnon-Condon effectsACE2-Spike complexquantum coherenceopen quantum systemsSARS-CoV-2

0 comments

The pith

Vibrational assistance and quantum coherence may act as a molecular recognition mechanism in ACE2-Spike binding.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper simulates quantum dynamics of electron transfer at the SARS-CoV-2 Spike-ACE2 interface as an open quantum system. It uses a non-Markovian stochastic Schrödinger equation to show how a specific vibrational mode, combined with environmental memory and non-Condon coupling, produces non-exponential population decay and sustained coherence. These features deviate from classical Marcus-Jortner kinetics and support the possibility that vibrational assistance contributes to binding selectivity.

Core claim

Simulations reveal that beyond the Markovian Ohmic limit, non-Markovian dynamics and off-diagonal system-bath coupling allow nuclear motion to gate tunneling, sharpen frequency selectivity, and preserve electronic-vibrational coherence longer under a sub-Ohmic spectral density, indicating that ACE2-Spike binding may exploit vibrational assistance and quantum coherence.

What carries the argument

Non-Markovian Stochastic Schrödinger Equation (NMSSE) with diagonal and off-diagonal couplings to a Spike vibrational mode and a structured bath.

Load-bearing premise

A single chosen vibrational mode together with specific system-bath couplings and a sub-Ohmic spectral density captures the dominant physics of the real ACE2-Spike interface.

What would settle it

Observation of purely exponential transfer kinetics without coherent oscillations or sharpened frequency dependence at the modeled vibrational frequency would falsify the claimed non-Markovian enhancement.

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper runs NMSSE simulations with non-Condon coupling on a single-mode model of ACE2-Spike electron transfer and recovers semiclassical limits while showing coherence under sub-Ohmic memory, but the results depend on unvalidated parameter choices.

read the letter

The main thing to know is that this work takes the non-Markovian stochastic Schrödinger equation, adds off-diagonal system-bath coupling from one chosen Spike vibrational mode, and shows that memory effects plus non-Condon gating produce non-exponential population transfer and longer coherence times compared with the Markovian Ohmic case. In the appropriate limit the numerics match Marcus-Jortner rates, which is a useful check. The concrete combination applied to the ACE2-Spike interface is new relative to the cited literature, and the simulations cleanly illustrate how sub-Ohmic correlations can sharpen vibrational selectivity. That part is done competently. The soft spot is the lack of grounding for the model parameters. The abstract and stress-test note indicate a single frequency, specific coupling strengths, and sub-Ohmic spectral density are chosen without comparison to measured vibrational densities of states, multi-mode molecular-dynamics data for the interface, or experimental electron-transfer rates. No sensitivity analysis or error bars appear, so it is unclear how robust the deviations are once those choices vary. The central claim that the results support vibrational assistance and coherence as a recognition mechanism therefore rests on the assumption that the toy parameterization captures the dominant physics. Readers working on open quantum systems or quantum-biology models will find the numerical illustrations useful for seeing how non-Markovian and non-Condon terms interact at high temperature. The paper is not incoherent on its own terms and shows honest engagement with the method, so it deserves referee time even though the biological interpretation needs more anchoring. I would send it out for review and expect the referees to focus on validation steps.

Referee Report

2 major / 2 minor

Summary. The paper claims that simulations of vibrationally-assisted electron transfer (VA-ET) in the ACE2-Spike complex using the Non-Markovian Stochastic Schrödinger Equation (NMSSE) reveal non-exponential population dynamics, preserved electronic-vibrational coherence, and sharpened frequency selectivity when non-Markovian effects and non-Condon (off-diagonal) couplings are included; in the Markovian Ohmic limit the dynamics recover semiclassical Marcus-Jortner rates, supporting the proposition that vibrational assistance and quantum coherence may serve as a molecular recognition mechanism in ligand-receptor binding.

Significance. If the single-mode sub-Ohmic parameterization faithfully captures the dominant physics at the ACE2-Spike interface, the work would demonstrate how environmental memory and vibrational gating can produce observable deviations from semiclassical ET kinetics, offering a concrete theoretical framework for quantum effects in biological recognition. The explicit recovery of the expected Markovian limit and the demonstration of coherence amplification under non-Condon coupling are technically useful results for the open-quantum-systems community.

major comments (2)

[Abstract] Abstract and Results sections: the central claim that the simulations support vibrational assistance and coherence as a possible recognition mechanism rests on the unvalidated choice of a single specific Spike vibrational mode together with chosen diagonal/off-diagonal couplings and a sub-Ohmic spectral density; no comparison is made to measured vibrational densities of states, multi-mode MD data, or experimental ET rates in the ACE2-Spike complex, leaving the reported frequency selectivity and coherence lifetime potentially model-specific rather than generic.
[Results] Results (Markovian vs. non-Markovian comparison): while the manuscript correctly recovers exponential kinetics and Marcus-Jortner rates in the Ohmic Markovian limit, the non-exponential and coherent features are shown only for the selected parameter set; the absence of a systematic parameter-sensitivity scan or error-bar quantification on the extracted rates undermines the robustness of the claim that non-Markovian memory amplifies vibrational selectivity.

minor comments (2)

[Abstract] Abstract: the phrase 'a specific vibrational mode of the Spike protein' is introduced without stating its frequency, symmetry, or structural origin, making it difficult for readers to assess biological relevance.
[Methods] Notation: the definition of the system-bath coupling operators (diagonal vs. off-diagonal) should be stated explicitly with an equation number in the methods section to allow direct reproduction of the non-Condon gating effect.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive report and detailed reading of our manuscript. We address the major comments point by point below, indicating where revisions will be incorporated.

read point-by-point responses

Referee: [Abstract] Abstract and Results sections: the central claim that the simulations support vibrational assistance and coherence as a possible recognition mechanism rests on the unvalidated choice of a single specific Spike vibrational mode together with chosen diagonal/off-diagonal couplings and a sub-Ohmic spectral density; no comparison is made to measured vibrational densities of states, multi-mode MD data, or experimental ET rates in the ACE2-Spike complex, leaving the reported frequency selectivity and coherence lifetime potentially model-specific rather than generic.

Authors: We agree that the single-mode sub-Ohmic parameterization and specific couplings constitute model assumptions rather than a direct fit to experiment. These choices are motivated by prior MD studies identifying relevant low-frequency Spike modes at the ACE2 interface, which we will cite explicitly. The work is a theoretical exploration demonstrating qualitative effects of non-Markovian memory and non-Condon coupling; we do not claim quantitative prediction of experimental rates, as such ET data for this complex are not available. In revision we will add a paragraph in the Discussion clarifying the illustrative scope of the frequency selectivity and coherence results, and we will expand the Methods section with additional justification for the chosen spectral density based on available literature. revision: partial
Referee: [Results] Results (Markovian vs. non-Markovian comparison): while the manuscript correctly recovers exponential kinetics and Marcus-Jortner rates in the Ohmic Markovian limit, the non-exponential and coherent features are shown only for the selected parameter set; the absence of a systematic parameter-sensitivity scan or error-bar quantification on the extracted rates undermines the robustness of the claim that non-Markovian memory amplifies vibrational selectivity.

Authors: We acknowledge that the main figures focus on a representative parameter set. To strengthen robustness, the revised manuscript will include a new supplementary section with a systematic scan over vibrational frequency, diagonal and off-diagonal couplings, and bath cutoff frequency. We will also report standard errors from the stochastic sampling on the extracted rates and coherence times, allowing quantitative assessment of how non-Markovian effects amplify selectivity across the scanned range. revision: yes

standing simulated objections not resolved

Direct comparison to measured vibrational densities of states, multi-mode MD data, or experimental ET rates in the ACE2-Spike complex, which would require new experimental or extensive multi-mode simulation work outside the scope of the present theoretical study.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper computes its central results by direct numerical integration of the NMSSE for an explicitly parameterized open-system model (single vibrational mode, chosen diagonal/off-diagonal couplings, sub-Ohmic spectral density). In the Markovian Ohmic limit the integrated dynamics recover exponential kinetics whose rates match the known semiclassical Marcus-Jortner formula; this is a consistency check, not a redefinition of the input as output. No quantity is fitted to a subset of the data and then relabeled a prediction, no ansatz is smuggled via self-citation, and no uniqueness theorem from the authors' prior work is invoked to force the model choice. The derivation therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The model rests on several adjustable parameters for vibrational frequency, diagonal and off-diagonal couplings, and bath spectral density shape that are introduced to represent the biological interface rather than derived from first principles.

free parameters (3)

vibrational frequency of chosen Spike mode
Specific frequency selected to modulate the donor-acceptor coupling
system-bath coupling strengths
Diagonal and off-diagonal values chosen to produce observable gating and non-Condon effects
bath spectral density parameters
Ohmic versus sub-Ohmic form and cutoff chosen to control memory time

axioms (2)

domain assumption The ACE2-Spike interface can be treated as an open quantum system whose environment is fully characterized by a spectral density
Foundation for the NMSSE approach
domain assumption Non-Condon effects arise from linear dependence of electronic coupling on nuclear coordinate
Standard extension beyond Condon approximation

pith-pipeline@v0.9.0 · 5609 in / 1451 out tokens · 83391 ms · 2026-05-16T07:11:18.475660+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We employ a non-perturbative Non-Markovian Stochastic Schrödinger Equation (NMSSE) framework... structured (sub-Ohmic) environmental spectral density
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

In the Markovian limit with an Ohmic bath... rates agree with semiclassical Marcus–Jortner predictions

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.