  Dynamics of reaction coordinates during barrier-crossing are key to
understand activated processes in complex systems such as proteins. The default
assumption from Kramers physical intuition is that of a diffusion process.
However, the dynamics of barrier-crossing in natural complex molecules are
largely unexplored. Here we investigate the transition dynamics of
alanine-dipeptide isomerization, the simplest complex system with a large
number of non-reaction coordinates that can serve as an adequate thermal bath
feeding energy into the reaction coordinates. We separate conformations along
the time axis and construct the dynamic probability surface of reaction. We
quantify its topological structure and rotational flux using persistent
homology and differential form. Our results uncovered a region with strong
reactive vortex in the configuration-time space, where the highest probability
peak and the transition state ensemble are located. This reactive region
contains strong rotational fluxes: Most reactive trajectories swirl multiple
times around this region in the subspace of the two most-important reaction
coordinates. Furthermore, the rotational fluxes result from cooperative
movement along the isocommitter surfaces and orthogonal barrier-crossing.
Overall, our findings offer a first glimpse into the reactive vortex regions
that characterize the non-diffusive dynamics of barrier-crossing of a naturally
occurring activation process.
