  Enzymes speed up biochemical reactions at the core of life by as much as 15
orders of magnitude. Yet, despite considerable advances, the fine dynamical
determinants at the microscopic level of their catalytic proficiency are still
elusive. In this work, we use a powerful mathematical approach to show that
rate-promoting vibrations in the picosecond range, specifically encoded in the
3D protein structure, are localized vibrations optimally coupled to the
chemical reaction coordinates at the active site. The universality of these
features is demonstrated on a pool of more than 900 enzyme structures,
comprising a total of more than 10,000 experimentally annotated catalytic
sites. Our theory provides a natural microscopic rationale for the known subtle
structural compactness of active sites in enzymes.
