A minimization principle for transition paths of maximum flux for collective variables

What is it about?

This article considers how to construct paths that describe how proteins and other macromolecules change from one conformation to another. In particular, it focuses on methods that do not require the generation of dynamics trajectories. There are, of course, a vast number of such paths, so the big question is how to define a {\em representative} path. If one limits the quest to finding a single path, the most attractive approach is (arguably) that proposed in a 1983 landmark paper by Berkowitz, Morgan, McCammon, and Northrup, which determines a path having the highest density of reactive trajectories. For many applications, it is desirable to describe transition paths using a much smaller number of {\em collective} variables.

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Why is it important?

The present article correctly generalizes the result of the 1983 article to the use of collective variables. It also demonstrates a flaw in the notion of a most probable path, which has been the dominant approach to this question.