Abstract
Reaction coordinates are of central importance for correct understanding of reaction dynamics in complex systems, but their counter-intuitive nature made it a daunting challenge to identify them. Starting from an energetic view of a reaction process as stochastic energy flows biased towards preferred channels, which we deemed the reaction coordinates, we developed a rigorous scheme for decomposing energy changes of a system, both potential and kinetic, into pairwise components. The pairwise energy flows between different coordinates provide a concrete statistical mechanical language for depicting reaction mechanisms. Application of this scheme to the C7eq → C7ax transition of the alanine dipeptide in vacuum revealed novel and intriguing mechanisms that eluded previous investigations of this well studied prototype system for biomolecular conformational dynamics. Using a cost function developed from the energy decomposition components by proper averaging over the transition path ensemble, we were able to identify signatures of the reaction coordinates of this system without requiring any input from human intuition.
Highlights
Many important biochemical processes, such as protein folding and enzymatic reactions, are rare activated processes that take place on a time scale orders of magnitude slower than that of elementary molecular motions
We proposed a framework of viewing an activated reaction process as stochastic energy flow biased towards preferred channels, which we deemed the reaction coordinates
To materialize this energetic view of reaction processes, we developed a scheme for projecting the changes in potential and kinetic energies of the system onto the motions of different degrees of freedom
Summary
Many important biochemical processes, such as protein folding and enzymatic reactions, are rare activated processes that take place on a time scale orders of magnitude slower than that of elementary molecular motions. It is important, for both practical and purely theoretical purposes, to understand the underlying mechanisms of such activated processes in complex biomolecular systems on a rigorous ground. The prevalent picture for an activated process is a transition between two meta-stable basins on the free energy landscape separated by a barrier that is high compared to thermal energy.[1] The slow time scale arises from the fact that the system can rarely accumulate enough energy in the relevant degrees of freedom (DOFs) to surpass the transition barrier. Du et al first adopted this rigorous definition of reaction coordinates in the context of protein folding;[9] Chandler and co-workers established its usage as a standard practice in the general context of activated processes.[8]
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