Optimal Reaction Coordinates

The dynamic behavior of complex systems with many degrees of freedom is often analyzed by projection onto one or a few reaction coordinates. The dynamics is then described in a simple and intuitive way as diffusion on the associated free energy pro le. In order to use such a picture for a quantitative description of the dynamics one needs to select the coordinate in an optimal way so as to minimize non-Markovian effects due to the projection. For equilibrium dynamics between two boundary states (e.g., a reaction) the optimal coordinate is known as the committor or the pfold coordinate in protein folding studies. While the dynamics projected on the committor is not Markovian, many important quantities of the original multidimensional dynamics on an arbitrarily complex landscape can be computed exactly. Here we summarize the derivation of this result, discuss different approaches to determine and validate the committor coordinate and present three illustrative applications: protein folding, the game of chess, and patient recovery dynamics after kidney transplant.