Quantum Confinement of Proton Wavefunctions in Drug-Protein Cavities Governing Tunneling-Driven Catalysis and Controlled Drug Release

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.