Quantifying the potential of thermal highways to facilitate long-range proton transport in enzymes

Proton transport in enzymes is often portrayed as a purely static, hydrogen-bond-mediated relay, yet this view neglects how ultrafast vibrational coherence within the protein fold can mechanically drive long-range transfer. Here, we introduce the vibrational entropy flux tensor to identify thermal highways-evolutionarily conserved networks of residues whose synchronized terahertz-frequency phonons transiently compress donor-acceptor distances. Using parameter-free coarse-grained elastic-network models of [Fe-Fe] hydrogenase, we show that these highways boost quantum-tunneling probabilities by 10-100 × (depending on mode frequency), directly linking picosecond-scale dynamics to increased proton flux. A single-value descriptor, T_lim, defined as the minimum entropy flux along a proton wire, explains 90% of the variance in H₂-production rates across ten enzyme variants (R=0.90). Crucially, mutations >10 Å from the active site that disrupt thermal highway connectivity proportionally attenuate both T_lim and catalytic turnover-evidence that long-range, fold-encoded phonon coherence is a mechanistic driver of proton transport. Our multiscale framework unifies static chemical models with dynamic phonon-mediated enhancement, offering a predictive route for engineering proton-coupled catalysts in bioenergy and beyond.