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To identify and deal with the various cases, some clustering and postprocessing were
needed, as follows.
Culling
As a preliminary step, we flagged all choices of i, j that resulted in
FoldX_energy < min(FoldX_energy) + (max(FoldX_energy) – min(FoldX_energy))⋅0.1
If this resulted in fewer than 30 fragment pairs, we instead flagged the 15% of pairs with
lowest energy. All the remaining (unflagged) elements were not considered to be
candidates for the hinge location.
Clustering
The next step was to identify and separate the local minima, for which we employed the
k-means clustering algorithm. Centroids were initially generated in a regular grid spaced
50 residues apart starting at i,j = 25,25. The pairs flagged in the culling step were each
assigned to the nearest centroid. The location of each centroid was then recomputed for
each resulting cluster, and the pairs were once again reassigned to the nearest recomputed
centroid. This process was repeated until all centroids stopped moving. The lowest-
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