The first reference to long-range RNA structure appeared in the literature under the term “panhandle structure,” which was coined in by virologists in the 1980s to refer to a complementary base pairing between the 5′ end and 3′ end of the RNA genome of several segmented negative-stranded viruses119.

The PrePH utility uses a k-mer-based technique, which is similar to previously published IRBIS method29, to identify all pairs of nearly perfect complementary regions in a given pair of sequences. At the preparatory step, PrePH pre-computes a 4k × 4k table containing helix hybridization energies for all pairs of k-mers (default k = 5) that are either Watson–Crick complementary or contain a few GT base pairs (by default at most two) using energy tables from Vienna RNA package120. The dynamic programming matrix is computed by local Smith–Waterman algorithm using a limited set of structural rules: initiating a k-nt-long helix, extending a helix by a stacking base pair, and adding to a helix a short internal loop or bulge with up to m nucleotides in each strand (default m = 2), followed by another helix. To speed up back-tracking, PrePH uses auxiliary matrices to store intermediate structures, and reports nonintersecting pairs of complementary regions passing the energy threshold (by default −15 kcal/mol). Here, two pairs of complementary regions, x1 complementary to y1 and x2 complementary to y2, are referred to as intersecting if x1 has common nucleotides with x2 and also y1 has common nucleotides with y2. That is, two pairs of complementary regions may intersect by only one, not both interacting strands. The reduced scoring scheme, optimized back-tracking, and indexing of the initial sequences by k-mers result in a great improvement of computation speed. The detailed description of PrePH is exempt to Supplementary Methods. PrePH software is available at github (https://github.com/kalmSveta/PrePH) (codes are available at: 10.5281/zenodo.4601044).

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