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 [FeFe]-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, Tlim, defined as the minimum entropy-flux along a proton wire, explains 90% of the variance in H 2-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 Tlim 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.