Abstract Context Proton transfer in drug–protein cavities is central to enzymatic catalysis and pH-responsive drug delivery, yet classical models often fail to capture the quantum mechanical behavior that governs these processes. The influence of nanoscale confinement on proton dynamics through quantum effects remains poorly understood, limiting our ability to design optimized therapeutic systems. We present a quantum theoretical framework that connects cavity geometry with measurable proton transfer properties, offering new insights for biocatalysis and nanomedicine. Method We developed an analytical model for proton confinement in biological cavities by solving the Schrödinger equation for two spherically symmetric potentials: finite square wells representing hydrophobic environments and Morse potentials for hydrogen-bonded systems. Our approach systematically calculates ground-state energies, wavefunctions, tunneling probabilities, and vibrational overtones. Results show confinement geometry exponentially modulates proton behavior, with tunneling probabilities spanning > 12 orders of magnitude under physiological conditions. Kinetic isotope effects (> 10¹¹) and catalytic enhancements (10³-fold) confirm quantum tunneling dominance. While finite wells promote classical localization, Morse potentials enable efficient proton transfer through delocalization. The model incorporates environmental decoherence and establishes design rules linking cavity parameters to spectroscopic and kinetic signatures, providing a bridge between quantum theory and structural biology.
Abstract Context Proton transfer in drug–protein cavities is central to enzymatic catalysis and pH-responsive drug delivery, yet classical models often fail to capture the quantum mechanical behavior that governs these processes. The influence of nanoscale confinement on proton dynamics through quantum effects remains poorly understood, limiting our ability to design optimized therapeutic systems. We present a quantum theoretical framework that connects cavity geometry with measurable proton transfer properties, offering new insights for biocatalysis and nanomedicine. Method We developed an analytical model for proton confinement in biological cavities by solving the Schrödinger equation for two spherically symmetric potentials: finite square wells representing hydrophobic environments and Morse potentials for hydrogen-bonded systems. Our approach systematically calculates ground-state energies, wavefunctions, tunneling probabilities, and vibrational overtones. Results show confinement geometry exponentially modulates proton behavior, with tunneling probabilities spanning > 12 orders of magnitude under physiological conditions. Kinetic isotope effects (> 10¹¹) and catalytic enhancements (10³-fold) confirm quantum tunneling dominance. While finite wells promote classical localization, Morse potentials enable efficient proton transfer through delocalization. The model incorporates environmental decoherence and establishes design rules linking cavity parameters to spectroscopic and kinetic signatures, providing a bridge between quantum theory and structural biology.
This work introduces a novel theoretical framework in which enzymatic tunnels are reinterpreted as quantum-fluid coherence channels rather than simple geometric pathways. Guided by π-field hydrodynamics, these tunnels support coherent, directed energy transport at the nanoscale, providing a unified explanation for ultrafast proton movement, long-range communication between protein sites, low-dissipation energy flow, and the remarkable sensitivity of catalytic efficiency to single-point mutations. In this article, I develop a quantum-hydrodynamic model incorporating coherence density, phase-field dynamics, and the π-induced quantum potential 𝑄𝜋. The resulting framework predicts: ballistic-like transport within enzymatic tunnels, π-gradient–driven directionality, coherence-supported reduction of effective energy barriers, mutation-induced π-defects disrupting transport, and the emergence of nanoscale quantum-fluid vortices. To the best of my knowledge, this is the first scientific work to formally characterize enzymatic tunnels as quantum-fluid conduits governed by π-field dynamics. This establishes a new research direction at the intersection of quantum biology, enzymology, and nanophysical modeling, which I refer to as Quantum Fluid Enzymology (QFE). The deposition includes conceptual figures, theoretical equations, and a computational π-fluid simulation approach for tunnel transport
Abstract The role of proton tunnelling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyses the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.
This analysis addresses the critical decoherence paradox in quantum biology, where observed microsecond coherence times in living cells vastly exceed the nanosecond predictions of standard open quantum systems theory. The study synthesizes theoretical and empirical advancements, establishing that the information geometry of biological macromolecules provides the mechanism for long-lived quantum states, where cellular structures function as optimized topological constraints that actively harness environmental noise. Key theoretical frameworks integrated include the Quantum Fisher Information (QFI) metric, which quantifies biological coherence and sets absolute limits on sensory precision (e.g., avian magnetoreception), and the Entanglement-Weighted Operator Geometry (EWOG). EWOG is empirically validated to resolve the decoherence discrepancy by demonstrating that quantum entanglement dynamically modifies the effective Hamiltonian, achieving a calculated 58% suppression of decoherence in proteins like MagLOV2. Furthermore, the study applies Quantum Geometrical Molecular Dynamics (QGMD) to show that the non-Abelian quantum geometric tensor drives nonadiabatic enzymatic catalysis, enabling quantum mechanical tunneling to provide profound energetic advantages, such as reducing the required energy for proton transport in mitochondrial Complex I by over 55%. Also available on Academia.edu: https://www.academia.edu/attachments/132032425/download_file?s=portfolio
Proton transfer plays a key role in the applications of advanced energy materials as well as in the functionalities of biological systems. In this work, based on the transfer matrix method, we study the quantum effects of proton transfer in a series of one-dimensional (1D) model potentials and numerically calculate the quantum probability of transferring across single and double barriers (wells). In the case of single barriers, when the incident energies of protons are above the barrier height, the quantum oscillations in the transmission coefficients depend on the geometric shape of the barriers. It is found that atomic resonant tunneling (ART) not only presents in the rectangular single well and rectangular double barriers as expected, but also exists in the other types of potential wells and double barriers. For hetero-structured double barriers, there is no resonant tunneling in the classical forbidden zone, i.e., in the case when the incident energy (E i) is lower than the barrier height (E b). Furthermore, we have provided generalized analysis on the characteristics of transmission coefficients of hetero-structured rectangular double barriers.
Quantum biology, at the intersection of quantum mechanics and biology, investigates the involvement of quantum phenomena in biological processes. A pivotal focus is quantum tunneling, wherein particles traverse energy barriers, a phenomenon with potential significance in various biological contexts. This article introduces a new class of linear potential functions for studying quantum tunneling in biological processes. The simplicity of linear potentials enables analytical solutions to the Schrödinger equation, offering efficiency compared to more complex numerical methods. The proposed linear potential functions are derived using parabolic curves, providing an analytical form with physical interpretations. The corresponding energy function and transmission coefficients are presented, facilitating a simplified understanding of tunneling behavior. Theoretical implications of the proposed model are discussed, emphasizing the ease of parameter variation and its applicability to diverse biological scenarios. In the numerical demonstration, two case studies are presented: (1) examining proton tunneling in DNA point mutations and (2) exploring electron tunneling in biological receptors, specifically the ACE2 receptor in the context of SARS-CoV-2.
This paper proposes a localized effective model of compressible vacuum medium to explain the anomalous long-lived quantum coherence observed in hydrophobic protein nanocavities. Four quantitative scaling relations are derived from geometry and density constraints of nanoscale confinement: coherence lifetime scales with cavity radius as τ=Arτ=Ar, decays quadratically with anesthetic concentration, increases quadratically with decreasing temperature, and exhibits a two-stage Gaussian-to-exponential decoherence transition. All predictions are directly testable by femtosecond ultrafast spectroscopy. The model introduces a saturation density bound for localized vacuum media, which also provides a physical cutoff preventing the stable formation of infinitely subdivided spatial structures analogous to abstract Kakeya sets.