Quantum Tunneling-Gated Vesicle Fusion: Proton-Coupled Electron Transfer and Mechanical Barrier Softening Shape Neurotransmitter Release Latency

Neurotransmitter release in neurons requires synaptic vesicles to fuse rapidly with the presynaptic membrane after calcium entry, yet single-vesicle recordings show highly heterogeneous latency distributions with both fast events and long heavy tails. Most existing models fit these data empirically without mechanistic grounding. We introduce a \emph{quantum--mechanochemical model} in which an initial \emph{proton--coupled electron transfer} (PCET) step, governed by quantum tunneling, primes the vesicle for fusion, while a subsequent \emph{time-dependent mechanical barrier softening} drives the final membrane merger. The scheme consists of three states: a closed SNARE complex ($C$) that activates through PCET ($k_{1}^{\mathrm{H/D}}$), a primed intermediate ($P$) that undergoes mechanical gating with an aging rate $\eta$ and forward rate $k_{2}(t)$, and a reversible slip-back process ($k_{-1}(t)$) that sustains long-latency events. The PCET step is described by a Marcus-type tunneling expression with isotope-dependent mass terms, enabling direct prediction of the kinetic isotope effect (KIE) between protiated and deuterated conditions. Structural heterogeneity is included via a distribution of donor--acceptor distances. By calibrating the mechanochemical attempt frequency $\gamma$ to reproduce the typical early fusion probability ($P[0\!-\!5~\mathrm{ms}]^{\mathrm H} \approx 0.20$), the model generates latency probability density functions (PDFs), cumulative distributions (CDFs), and hazard rates consistent with experimental observations. Parameter sweeps show how tunneling decay ($\beta_\mathrm{tun}$) controls the KIE magnitude, while mechanical aging and back reaction redistribute early versus late events. This \emph{quantum--mechanical and force-activated framework} provides a physically interpretable, testable alternative to purely empirical fits for single-vesicle fusion latency in neurons.