Free energy and kinetics of conformational transitions from voronoi tessellated milestoning with restraining potentials

Milestoning is a method aimed at reconstructing the statistical properties of the long-time dynamics of a system by exploiting the crossing statistics of a set of hypersurfaces, called the "milestones", placed along the reaction coordinate [Faradjian and Elber, J. Chem. Phys. 2004, 120, 10880]. Recently, Vanden-Eijnden and Venturoli [J. Chem. Phys. 2009, 130, 194101] showed that when a complete Voronoi tessellation of the configurational space is available, milestoning can be reformulated to utilize the statistics from a series of independent simulations, each confined within a single cell via strict reflections at the boundaries. As a byproduct, this "Voronoi tessellated milestoning" method also permits to compute the free energy of the tessellation. Here, the method is extended to support the usage of differentiable restraining potentials to confine the trajectories within each cell.