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

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