Non-Markovain Quantum State Diffusion for the Tunneling in SARS-COVID-19 virus

arXiv:2502.17449 · q-bio.BM · Submitted 2025-02-07 · Read on arXiv

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Introduction to the show: ident: Genomics Radio. Generated commentary on the latest computational biology and genomics papers.

Ines: Today's paper: "Non-Markovain Quantum State Diffusion for the Tunneling in SARS-COVID-19 virus".

Marcus: The gist: Electron tunneling in SARS-CoV-2 virus infection exhibits inherently non-Markovian characteristics, extending into the intermediate and strong coupling regimes between dimer components.

Ines: First, who's behind it and why it matters.

Title and authors: Ines: Moving on, what does the actual summary of "Non-Markovian Quantum State Diffusion for the Tunneling in SARS-COVID-nineteen virus" actually tell us about this research <ref:2502.17449#pg1,Quantum State Diffusion for the>?

Marcus: It’s basically saying that electron tunneling in this infection isn't just a simple transfer; it has these inherent non-Markovian characteristics that Markovian models completely miss. That's a big deal because those simpler models often give you unphysical negative probabilities when things get really coupled.

Ines: So they are showing that the way the electron moves between the spike protein and the receptor isn't memory-less, which is what a standard Markovian approach assumes. They’re using this QSD approach because it handles those complex dynamics better in open quantum systems.

Yuki: It makes sense from a broader evolutionary view; if binding depends on these specific quantum tunneling events, then the virus might have evolved to exploit those very subtle energetic differences in the host proteins.

Ines: Right. They set up their Hamiltonian for the receptor as having terms like one/2ϵσz plus one/two∆σx, and they treat the spike protein as a harmonic oscillator with frequencies related to its vibrations.

Marcus: And they introduce a Lindblad operator, L = γiEσz, which describes how the system interacts with its environment—the biological bath—to keep it open. This is how they bring in the environmental memory effects.

Yuki: That environmental coupling is key; it’s what allows the system to retain memory of past interactions instead of just jumping instantly to a new state.

The paper's summary: Ines: Now, let's talk about what they actually found in the results section of this paper. They simulate Eq. twenty-four using Ornstein-Uhlenbeck noise and they derive an expression for the maximum probability of this electron transfer happening.

Marcus: And that expression shows a clear dependency on the coupling strength between the spike protein and ACE2 receptor. It’s not just some random number; it directly relates to how strong that coupling is.

Ines: They show a specific difference in probabilities, calling it Delta P, which is basically the maximum probability with the vibrational mode versus without it. The finding there is that this tunneling probability stays minimal at weak coupling but starts increasing significantly as the coupling reaches intermediate levels, and it gets most pronounced at strong coupling.

Yuki: That shift in behavior based on coupling strength suggests a finely tuned mechanism, which aligns with how we see specific host factors interacting with viral entry points across different strains.

Marcus: What’s really interesting is that they use the same parameters from their earlier Markovian approximation to show that the tunneling probability remains positive even in the strongest coupling limit. That’s a direct contradiction to what those simpler Markovian assumptions predicted.

Ines: So they are demonstrating a distinctly non-Markovian behavior here, which means the process is more nuanced than previously thought, especially when things get very strongly coupled at the molecular level.

The paper's improvements: Marcus: The authors suggest a few ways to improve this approach, primarily by moving beyond the Markovian assumptions and adopting a non-Markovian framework like QSD. That’s the big methodological improvement they are pushing for in this paper.

Ines: They also point toward using Quantum Biological Electron Tunneling spectroscopy, or QBET spectroscopy, as a way to bridge the gap between their theoretical model and actual experimental observation.

Yuki: Thinking about that experimental side, it suggests we could actually try to optically detect these quantum electron transfer events in real time within a living cell system.

Marcus: They suggest using plasmonic nanoparticles attached to both the spike protein and the ACE2 receptor. This setup would allow them to monitor changes in the optical scattering spectrum as the electron transfer happens, which is a very tangible experimental test.

Ines: And they specifically mention focusing on disulfide bridges and cysteine residues because those are key parts of that interaction, showing where these quantum effects might be most relevant biologically.

Conclusion: Ines: To wrap things up for this paper, the main implication is that we need to incorporate non-Markovian effects when modeling viral entry dynamics to get an accurate picture of what's happening at the molecular level.

Marcus: It confirms that the coupling strength between the spike protein and ACE2 receptor dictates how likely this electron transfer event is to occur, and it shows that non-Markovian physics gives us a positive probability even where simpler models fail.

Yuki: And for us studying the virus in populations, this suggests that understanding these specific quantum tunneling mechanisms could help us predict which viral variants will be most effective at infecting hosts with different structural features.

Ines: So, the paper "Non-Markovian Quantum State Diffusion for the Tunneling in SARS-COVID-nineteen virus" gives us a richer theoretical tool to understand how molecular recognition works during infection <ref:2502.17449#pg1,Quantum State Diffusion for the>.

Marcus: It’s about moving past those simple lock and key ideas by looking at the quantum dynamics of electron transfer itself.

Yuki: It opens up a pathway for experimentalists to actually see these quantum effects happening in real-time using tools like QBET spectroscopy.

Ines: That’s where we are going next, connecting the theory to what we can actually measure in a lab setting.

United Arab Emirates University

q-bio.BM

Submitted: 2025-02-07

Updated: 2026-10-08

Comments: 11 pages,5 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 74/100

The gist: The gist: Electron tunneling in SARS-CoV-2 virus infection exhibits inherently non-Markovian characteristics, extending into the intermediate and strong coupling regimes between dimer components.

Key concepts

Non-Markovian Dynamics: This describes a quantum process where the future state depends not only on the present state but also on its entire past history. Unlike simpler models, this is necessary to accurately describe how electron tunneling occurs in complex biological systems like viral infection.
Quantum Stochastic Schrödinger Equation (QSD): This is a mathematical tool used to solve quantum problems involving open systems, which are systems interacting with their environment. The non-linear version of this equation was used here because it provides a more accurate description of the electron transfer process than standard Markovian models.
Strong Coupling Limit: This refers to the situation where the interaction between the spike protein and ACE2 receptor is very intense. The study found that in this strong coupling regime, electron tunneling probability remains positive, which is a key result that differs from what simpler Markovian models predict.

Terminology

Quantum State Diffusion — 16× in this paper
Markovian Approximation — 11× in this paper · explained in 2 episodes
Non-Markovian Dynamics — 5× in this paper · explained in 5 episodes
Accuracy — 4× in this paper · explained in 1 episode
Quantum Biological Electron Tunneling — 3× in this paper
Adam — 2× in this paper · explained in 2 episodes
Quantum Physics — 2× in this paper · explained in 10 episodes
Quantum Trajectories — 2× in this paper · explained in 2 episodes
Core — 1× in this paper · explained in 2 episodes
Hilbert Space — 1× in this paper · explained in 2 episodes

Summary

The gist: Electron tunneling in SARS-CoV-2 virus infection exhibits inherently non-Markovian characteristics, extending into the intermediate and strong coupling regimes between dimer components.

Theoretical Framework

The study develops a theoretical model for electron tunneling in SARS-CoV-2 virus infection within a non-Markovian framework. The approach involves solving the non-Markovian quantum stochastic Schrödinger equation. The spike protein and the GPCR receptor are conceptualized as a dimer, utilizing the spinBoson model to facilitate the description of electron tunneling. This model aims to explore how spike protein vibrations might facilitate electron tunneling at the receptor interface, enhancing viral entry.

Non-Markovian Dynamics and Limitations of Markovian Models

The analysis demonstrates that electron tunneling exhibits inherently non-Markovian characteristics, which contrasts sharply with predictions from Markovian models. Markovian approximations often lead to unphysical negative probabilities in the strong coupling limit. This highlights the necessity of incorporating non-Markovian dynamics for a more realistic description of biological quantum processes. The QSD approach is presented as a robust alternative for analyzing open quantum systems (OQS). The non-linear non-Markovian QSD equation can have the compact form by introducing ∆t(A) = A − ⟨A⟩t and its subsequent perturbative treatment starts with this equation.

Modeling Virus Infection and Interaction

The model considers the spike protein of SARS-CoV-2 and the ACE2 receptor as a quantum system interacting with a biological environment (membrane). The Hamiltonian for the receptor is given by HR = 1/2ϵσz + 1/2∆σx. The Hamiltonian of the ligand, in this case the spike protein, is represented as a harmonic oscillator with frequencies ω associated with the protein. The interaction Hamiltonian extends to include both the donor and acceptor alongside the ligand protein. The Lindblad operator is given as L = γiEσz.

Results and Biological Relevance

The simulation of Eq. 24 with Ornstein-Uhlenbeck noise yields an expression that captures the maximum probability of this electron transfer. The difference in probabilities with and without the vibrational mode takes the form ∆P = Max[PD→A(t)]vibrational mode − Max[P D → A(t)]without vibrational mode. The results show that the tunneling probability is minimal at weak coupling but begins to increase significantly as the coupling reaches intermediate levels, becoming most pronounced at strong coupling. Notably, by employing the same parameters used in the Markovian approximation, our results demonstrate that the tunneling probability remains positive even in the strongest coupling limit—a stark contrast to predictions made under Markovian assumptions. This observation underscores the distinctly non-Markovian behavior of electron tunneling process. The study draws significant parallels with the mechanism of olfaction, particularly in how electron transfer is facilitated.

Future Directions

The paper suggests that Quantum Biological Electron Tunneling (QBET) spectroscopy could be a potential technique to bridge the gap between theoretical modeling and experimental observation. QBET spectroscopy offers the capability to optically detect quantum electron tunneling in real time, allowing for the visualization of electron transfer (ET) dynamics in biological systems. This method could be adapted to investigate the electron transfer processes between the spike protein and the ACE2 receptor, with particular emphasis on disulfide bridges and cysteine residues. By conjugating plasmonic nanoparticles to both the spike protein and the ACE2 receptor, QBET spectroscopy could detect quantized electron transfer events by monitoring changes in the optical scattering spectrum in real time.

Conclusion

The investigation elucidates the dependency of this process on the coupling strength between the SARS-CoV-2 spike protein and the ACE2 receptor. The findings emphasize that non-Markovian effects are crucial for a more accurate and comprehensive understanding of the quantum mechanical processes underlying viral infection dynamics. This detailed understanding is pivotal for developing strategies to mitigate viral entry and infection. The process of electron transfer within molecular systems serves as a pivotal mechanism for molecular recognition, particularly through the detection of vibrational spectra associated with the virus’s spike protein.

Acknowledgments

This work was funded by UAE University Research Affairs under grant number G-00003550.

Author Contributions Statement

Muhammad Waqas Haseeb and Mohammad Toutounji made significant contributions to the research described in this manuscript. Mohammad Toutounji played a pivotal role in shaping the study’s conceptual framework, offering critical insights and continuous support throughout the research and writing processes. Ultimately, both authors have carefully reviewed and given their final approval for the published version of the manuscript.

Data Availability

The research data and parameters referenced in this study are well-documented in the associated published papers. For further inquiries or access to the datasets, interested parties may contact the corresponding author, who will provide the data upon a justified request.

References Cited

[1] J. J. Sakurai and J. Napolitano, Modern quantum mechanics (Cambridge University Press, 2020)

[3] J. McFadden and J. Al-Khalili, The origins of quantum biology, Proceedings of the Royal Society A 474, 20180674 (2018)

[52] M. W. Haseeb and M. Toutounji, Vibration assisted electron tunnelling in covid-19 infection using quantum state diffusion, Scientific Reports 14 (2024)

[56] J. Huang, J. Wen, M. Zhou, S. Ni, W. Le, G. Chen, L. Wei, Y. Zeng, D. Qi, M. Pan et al., On-site detection of sars-cov-2 antigen by deep learning-based surfaceenhanced raman spectroscopy and its biochemical foundations Analytical Chemistry 93 (2021)

[57] H. Xin, W. J. Sim, B. Namgung, Y. Choi, B. Li, and L. P. Lee, Quantum biological tunnel junction for electron transfer imaging in live cells Nature communications 10 (3245) (2019)

[51] B. Adams, I. Sinayskiy, R. van Grondelle, and F. Petruccione, Quantum tunnelling in the context of sars-cov-2 infection Scientific Reports 12 (16929) (2022)

[53] J. Gilmore and R. H. McKenzie, Spin boson models for quantum decoherence of electronic excitations of biomolecules and quantum dots in a solvent Journal of Physics: Condensed Matter 17 (1735) (2005)

[46] A. Chęcińska, F. A. Pollock, L. Heaney, and A. Nazir, Dissipation enhanced vibrational sensing in an olfactory molecular switch The Journal of chemical physics 142 (01B609 1) (2015)

[54] A. Marais, I. Sinayskiy, A. Kay, F. Petruccione, and A Ekert Decoherence-assisted transport in quantum networks New Journal of Physics 15 (013038) (2013)

[47] L. Bouten, M. Guta, and H Maassen Stochastic schrödinger equations Journal of Physics A: Mathematical and General 37 (3189) (2004)

[50] L. Diósi and W T Strunz The non-markovian stochastic schrödinger equation for open systems Physics Letters A 235 (569) (1997)

[13] R. D. Hoehn, D Nichols, H Neven, and S Kais Neuroreceptor activation by vibration-assisted tunneling Scientific Reports 5 (1) (2015)

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Improvements for AI systems

Your AI system can model molecular recognition for SARS-CoV-2 by explicitly accounting for vibration-assisted electron tunneling as a mechanism, moving beyond traditional lock and key model[9] limitations.
The improved system can predict the influence of coupling strength on viral entry, specifically showing that the vibrational mode significantly enhances the transfer probability at strong coupling limits, which is a finding contrasted with Markovian predictions where extremely strong coupling between the donor and acceptor levels resulted in negative probabilities.
The AI can utilize a Non-Markovian Stochastic Schrödinger Equation (SSE) to simulate quantum dynamics in virushost interactions, enabling it to provide more accurate and physically consistent predictions of electron tunneling compared to simpler Markovian approximations.
The system can incorporate environmental memory effects by using the QSD framework, which allows the model to capture dynamics where the bath retaining memory of its interactions with the system leads to more complex dynamics that cannot be described by Markovian approximations.
Your AI can predict specific molecular outcomes based on vibrational alignment, as shown in Table I parameters: binding of an appropriate odorant, which possesses a vibrational mode matching ϵA − ϵD, permits this transfer by enabling the release of this energy difference into the odorant’s vibrational mode.

Abstract

In the context of biology, unlike the comprehensively established Standard Model in physics, many biological processes lack a complete theoretical framework and are often described phenomenologically. A pertinent example is olfaction -- the process through which humans and animals distinguish various odors. The conventional biological explanation for olfaction relies on the lock and key model, which, while useful, does not fully account for all observed phenomena. As an alternative or complement to this model, vibration-assisted electron tunneling has been proposed. Drawing inspiration from the vibration-assisted electron tunneling model for olfaction, we have developed a theoretical model for electron tunneling in SARS-CoV-2 virus infection within a non-Markovian framework. We approach this by solving the non-Markovian quantum stochastic Schrodinger equation. In our model, the spike protein and the GPCR receptor are conceptualized as a dimer, utilizing the spin-Boson model to facilitate the description of electron tunneling. Our analysis demonstrates that electron tunneling in this context exhibits inherently non-Markovian characteristics, extending into the intermediate and strong coupling regimes between the dimer components. This behavior stands in stark contrast to predictions from Markovian models, which fail to accurately describe electron tunneling in the strong coupling limit. Notably, Markovian approximations often lead to unphysical negative probabilities in this regime, underscoring their limitations and highlighting the necessity of incorporating non-Markovian dynamics for a more realistic description of biological quantum processes. This approach not only broadens our understanding of viral infection mechanisms but also enhances the biological accuracy and relevance of our theoretical framework in describing complex biological interactions.