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

Abstract

Context: Quantum mechanical proton tunneling is a recognized but often phenomenologically treated factor in enzymatic catalysis and transport. Its explicit role as a governing principle in drug-protein binding and pH-triggered release kinetics remains poorly understood, lacking a predictive theoretical framework that connects nanoscale cavity geometry to functional pharmacological outcomes. Method: We developed an analytical model for proton confinement in drug-protein cavities by solving the one-dimensional time-independent Schrödinger equation, reduced from a Nuclear Time Dependent Schrödinger equation for two fundamental potential classes viz an asymmetric double-well potentials representing localized enzymatic transfer and periodic Kronig-Penney potentials for delocalized conduction along proton wires. Analytical eigenproblems yield low-lying states and tunneling splittings, cross-checked by instanton/WKB estimates; KP/TB bands and a WKB bridge provide an effective hopping . Within the parameter ranges explored, our computations indicate that sub-ångström changes in donor–acceptor distance can modify tunneling probabilities and KIEs by factors on the order of ∼5−20, and produce apparent pKₐ shifts on the order of ∼0.3−0.5 units, leading to roughly one–to–two-order changes in and associated half-lives. In the extended sector, diagonal energetic disorder reduces localization length in a manner consistent with Anderson-type localization, and a modeled pH step on a proton wire can bias a confined cavity on ps–ns timescales, contingent on the adopted couplings. These results are model-based and meant to provide design implications not absolute predictions highlighting how cavity geometry and hydrogen-bond network order may be tuned to modulate tunneling-assisted kinetics.