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Download file# Propagation of Conformational Coordinates Across Angular Space in Mapping the Continuum of States from Cryo-EM Data by Manifold Embedding

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posted on 2020-04-02, 16:50 authored by Suvrajit Maji, Hstau Liao, Ali Dashti, Ghoncheh Mashayekhi, Abbas Ourmazd, Joachim FrankRecent
approaches to the study of biological molecules employ manifold
learning to single-particle cryo-EM data sets to map the continuum
of states of a molecule into a low-dimensional space spanned by eigenvectors
or “conformational coordinates”. This is done separately
for each projection direction (PD) on an angular grid. One important
step in deriving a consolidated map of occupancies, from which the
free energy landscape of the molecule can be derived, is to propagate
the conformational coordinates from a given choice of “anchor
PD” across the entire angular space. Even when one eigenvector
dominates, its sign might invert from one PD to the next. The propagation
of the second eigenvector is particularly challenging when eigenvalues
of the second and third eigenvector are closely matched, leading to
occasional inversions in their ranking as we move across the angular
grid. In the absence of a computational approach, this propagation
across the angular space has been done thus far “by hand”
using visual clues, thus greatly limiting the general use of the technique.
In this work we have developed a method that is able to solve the
propagation problem computationally, by using optical flow and a probabilistic
graphical model. We demonstrate its utility by selected examples.