Abstract
RNA molecules play crucial roles in various biological processes. Their three-dimensional configurations determine the functions and, in turn, influences the interaction with other molecules. RNAs and their interaction structures, the so-called RNA–RNA interactions, can be abstracted in terms of secondary structures, i.e., a list of the nucleotide bases paired by hydrogen bonding within its nucleotide sequence. Each secondary structure, in turn, can be abstracted into cores and shadows. Both are determined by collapsing nucleotides and arcs properly. We formalize all of these abstractions as arc diagrams, whose arcs determine loops. A secondary structure, represented by an arc diagram, is pseudoknot-free if its arc diagram does not present any crossing among arcs otherwise, it is said pseudoknotted. In this study, we face the problem of identifying a given structural pattern into secondary structures or the associated cores or shadow of both RNAs and RNA–RNA interactions, characterized by arbitrary pseudoknots. These abstractions are mapped into a matrix, whose elements represent the relations among loops. Therefore, we face the problem of taking advantage of matrices and submatrices. The algorithms, implemented in Python, work in polynomial time. We test our approach on a set of 16S ribosomal RNAs with inhibitors of Thermus thermophilus, and we quantify the structural effect of the inhibitors.
Highlights
Ribonucleic acid (RNA) is a linear polymer with a preferred 5–3′ direction, made of four different types of nucleotides, known as Adenine (A), Guanine (G), Cytosine (C), and Uracil (U)
RNA molecules play numerous roles in cellular processes. They do not act in isolation, but they express their biological roles by interacting with other molecules [1], including other RNAs that determine the so-called RNA–RNA interactions (RRIs)
RNA functions depend on their three-dimensional configuration
Summary
Ribonucleic acid (RNA) is a linear polymer with a preferred 5–3′ direction, made of four different types of nucleotides, known as Adenine (A), Guanine (G), Cytosine (C), and Uracil (U). Blin et al introduced an approach, called maximum arc-preserving common subsequence problem to compare arc-annotated sequences in [19], and Evans proposed an algorithm to find common structures excluding some classes of pseudoknots [20]. Based on our previous results [6, 25], we define three operators able to formalize the concatenation, nesting, and crossing between two loops Such operators are necessary and sufficient to describe any arc diagram in terms of relations among loops. Such description allows us to uniquely associate a matrix, called relation matrix, whose elements represent the relation between the two corresponding loops for each abstraction (secondary structure, core, or shadows) of RNA and RNA–RNA interactions structures.
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