A Rigorous Method for Identifying a One-Dimensional Reaction Coordinate in Complex Molecules

Understanding the mechanism of functional protein dynamics is critical to understandingprotein functions. Reaction coordinate (RC) is a central topic in protein dynamics, and the grail is tofindthe one-dimensional RC (1D-RC) that can fully determine the value of a committor (i.e., the reactionprobability in configuration space) for any protein configuration. We present a new method that, for thefirst time, uses a fundamental mechanical operator, the generalized work functional, to identify the rigorous1D-RC in complex molecules. For a prototypical biomolecular isomerization reaction, the 1D-RC identifiedby the current method can determine the committor with an accuracy far exceeding what was achieved byprevious methods. This method only requires modest computational cost and can be readily applied tolarge molecules. Most importantly, the generalized work functional is the physical determinant of thecollectivity in functional protein dynamics and provides a tentative roadmap that connects the structure of a protein to its function