Dimensionality
reduction is at the core of understanding and making intuitive sense of complex
dynamic phenomena in chemistry. It is
usually assumed that the slowest mode is the one of primary interest; however,
it is critical to realize that this is not always so! A conceptual example
hereof is a protein folding simulation (Lindorff-Larsen et al. Science 334, 517-520,
2011) where the slowest dynamical mode is not the folding itself (see Figure). What is the
influence, then, of “non-slowest” modes in this process and how can it most
appropriately be elucidated?

This work by Husic and Noé show how

*deflation*can provide an answer to these questions. Technically speaking deflation is a collection of methods for how to modify a matrix after the largest eigenvalue is known in order to find the rest. In their provided example of the folding simulation, the dominant Time-lagged Independent Component (TIC) encapsulates the "artifact" variation that we are not really interested in. Thus, a constructed kinetic (Markov-state) model will be contaminated in several undesirable ways as discussed by the authors in great detail.
In principle,
this should be a very common problem since chemical systems have complex
Hamiltonians. Perhaps the reason why we don’t see it discussed more is that ultra-rare
events – real or artifact – may not usually be sampled during conventional
simulations. So, with the increasing computational power available to us, and
simulations approaching ever-longer timescales, this is likely something that
we need to be able to handle. This preprint describes well how one can think
about attacking these potential difficulties.

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