2 research outputs found
Tensor Decomposition Reveals Concurrent Evolutionary Convergences and Divergences and Correlations with Structural Motifs in Ribosomal RNA
Evolutionary relationships among organisms are commonly described by using a
hierarchy derived from comparisons of ribosomal RNA (rRNA) sequences. We propose that
even on the level of a single rRNA molecule, an organism's evolution is composed
of multiple pathways due to concurrent forces that act independently upon different
rRNA degrees of freedom. Relationships among organisms are then compositions of
coexisting pathway-dependent similarities and dissimilarities, which cannot be
described by a single hierarchy. We computationally test this hypothesis in
comparative analyses of 16S and 23S rRNA sequence alignments by using a tensor
decomposition, i.e., a framework for modeling composite data. Each alignment is
encoded in a cuboid, i.e., a third-order tensor, where nucleotides, positions and
organisms, each represent a degree of freedom. A tensor mode-1 higher-order singular
value decomposition (HOSVD) is formulated such that it separates each cuboid into
combinations of patterns of nucleotide frequency variation across organisms and
positions, i.e., “eigenpositions” and corresponding nucleotide-specific
segments of “eigenorganisms,” respectively, independent of a-priori
knowledge of the taxonomic groups or rRNA structures. We find, in support of our
hypothesis that, first, the significant eigenpositions reveal multiple similarities
and dissimilarities among the taxonomic groups. Second, the corresponding
eigenorganisms identify insertions or deletions of nucleotides exclusively conserved
within the corresponding groups, that map out entire substructures and are enriched
in adenosines, unpaired in the rRNA secondary structure, that participate in tertiary
structure interactions. This demonstrates that structural motifs involved in rRNA
folding and function are evolutionary degrees of freedom. Third, two previously
unknown coexisting subgenic relationships between Microsporidia and Archaea are
revealed in both the 16S and 23S rRNA alignments, a convergence and a divergence,
conferred by insertions and deletions of these motifs, which cannot be described by a
single hierarchy. This shows that mode-1 HOSVD modeling of rRNA alignments might be
used to computationally predict evolutionary mechanisms
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Matrix and tensor decomposition methods as tools to understanding sequence-structure relationships in sequence alignments
textWe describe the use of a tensor mode-1 higher-order singular value decomposition (HOSVD) in the analyses of alignments of 16S and 23S ribosomal RNA (rRNA) sequences, each encoded in a cuboid of frequencies of nucleotides across positions and organisms. This mode-1 HOSVD separates the data cuboids into combinations of patterns of nucleotide frequency variation across the positions and organisms, i.e., "eigenorganisms"' and corresponding nucleotide-specific segments of "eigenpositions," respectively, independent of a-priori knowledge of the taxonomic groups and their relationships, or the rRNA structures. We show that this mode-1 HOSVD provides a mathematical framework for modeling the sequence alignments where the mathematical variables, i.e., the significant eigenpositions and eigenorganisms, are consistent with current biological understanding of the 16S and 23S rRNAs. First, the significant eigenpositions identify multiple relations of similarity and dissimilarity among the taxonomic groups, some known and some previously unknown. Second, the corresponding eigenorganisms identify positions of nucleotides exclusively conserved within the corresponding taxonomic groups, but not among them, that map out entire substructures inserted or deleted within one taxonomic group relative to another. These positions are also enriched in adenosines that are unpaired in the rRNA secondary structure, the majority of which participate in tertiary structure interactions, and some also map to the same substructures. This demonstrates that an organism's evolutionary pathway is correlated and possibly also causally coordinated with insertions or deletions of entire rRNA substructures and unpaired adenosines, i.e., structural motifs which are involved in rRNA folding and function. Third, this mode-1 HOSVD reveals two previously unknown subgenic relationships of convergence and divergence between the Archaea and Microsporidia, that might correspond to two evolutionary pathways, in both the 16S and 23S rRNA alignments. This demonstrates that even on the level of a single rRNA molecule, an organism's evolutionary pathway is composed of different types of changes in structure in reaction to multiple concurrent evolutionary forces.Institute for Cellular and Molecular Biolog