Limits...
Tensor decomposition reveals concurrent evolutionary convergences and divergences and correlations with structural motifs in ribosomal RNA.

Muralidhara C, Gross AM, Gutell RR, Alter O - PLoS ONE (2011)

Bottom Line: We find, in support of our hypothesis that, first, the significant eigenpositions reveal multiple similarities and dissimilarities among the taxonomic groups.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.

View Article: PubMed Central - PubMed

Affiliation: Institute for Cellular and Molecular Biology, University of Texas at Austin, Austin, Texas, USA.

ABSTRACT
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.

Show MeSH
Sequence gaps exclusive to both Archaea and Microsporidia 16S rRNAs.The 100 positions identified in the gap segment of the third 16S eigenorganism                  with the largest decrease in relative nucleotide frequency map out entire                  substructures in the Bacteria 16S rRNAs that are convergently lost in the Archaea                  and the Microsporidia. (a) The 100 gaps conserved in both the                  Archaea and Microsporidia map to the entire substructures I–III in the                  secondary structure model of the bacterium E. coli                  [14].                     (b) Raster display of the 100 positions of conserved gaps in                  both the Archaea and Microsporidia across the alignment. (c)                  Raster display of the same 100 positions across an alignment of 858 mitochondrial                  16S rRNA sequences show gaps conserved in most Metazoa. The other groups of                  Eukarya represented in the mitochondrial alignment are Alveolata (1), Euglenozoa                  (2), Fungi (3) and Rhodophyta and Viridiplantae (4). The nucleotides are                  color-coded A (red), C (green), G (blue), U (yellow), unknown (gray) and gap                  (black). The color bars highlight the taxonomic groups.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC3094155&req=5

pone-0018768-g005: Sequence gaps exclusive to both Archaea and Microsporidia 16S rRNAs.The 100 positions identified in the gap segment of the third 16S eigenorganism with the largest decrease in relative nucleotide frequency map out entire substructures in the Bacteria 16S rRNAs that are convergently lost in the Archaea and the Microsporidia. (a) The 100 gaps conserved in both the Archaea and Microsporidia map to the entire substructures I–III in the secondary structure model of the bacterium E. coli [14]. (b) Raster display of the 100 positions of conserved gaps in both the Archaea and Microsporidia across the alignment. (c) Raster display of the same 100 positions across an alignment of 858 mitochondrial 16S rRNA sequences show gaps conserved in most Metazoa. The other groups of Eukarya represented in the mitochondrial alignment are Alveolata (1), Euglenozoa (2), Fungi (3) and Rhodophyta and Viridiplantae (4). The nucleotides are color-coded A (red), C (green), G (blue), U (yellow), unknown (gray) and gap (black). The color bars highlight the taxonomic groups.

Mentions: In both 16S and 23S alignments, the third most significant eigenposition captures the similarities among the two taxonomic groups and correlates with decreased nucleotide frequency across both the Archaea and Microsporidia relative to all other organisms with the P-values and , respectively. The 100 positions with largest nucleotide frequency decrease in the gap segment of the third 16S eigenorganism identify all six gaps exclusively conserved in both the Archaea and Microsporidia with the corresponding P-value . Mapped onto the secondary structure model of the bacterium E. coli, these 100 positions identify deletions of not only isolated nucleotides but entire substructures in the Archaea and Microsporidia with respect to the Bacteria (Figure 5a), indicating a convergent loss in both the Archaea and Microsporidia with respect to the Bacteria as well as the Eukarya. We observe that these same positions (Figure 5b) also identify nucleotides that are deleted in the metazoan mitochondrial 16S rRNA sequences (Figure 5c, and Dataset S7), suggesting that these similarities among the Archaea and Microsporidia may be explained by evolutionary forces that act to reduce the genome sizes of the Archaea and Microsporidia. Similarly, the 100 positions with largest nucleotide frequency decrease in the gap segment of the third 23S eigenorganism identify 41 of the 45 gaps and all 11 unpaired adenosines that are exclusively conserved in both the Archaea and Microsporidia with the corresponding P-values (Figures S10 and S11 in Appendix S1). Note that in the 16S alignment, the third eigenorganism also identifies positions of helices, i.e., base-paired nucleotides, that are exclusively conserved in both the Archaea and Microsporidia (Figure S12 in Appendix S1).


Tensor decomposition reveals concurrent evolutionary convergences and divergences and correlations with structural motifs in ribosomal RNA.

Muralidhara C, Gross AM, Gutell RR, Alter O - PLoS ONE (2011)

Sequence gaps exclusive to both Archaea and Microsporidia 16S rRNAs.The 100 positions identified in the gap segment of the third 16S eigenorganism                  with the largest decrease in relative nucleotide frequency map out entire                  substructures in the Bacteria 16S rRNAs that are convergently lost in the Archaea                  and the Microsporidia. (a) The 100 gaps conserved in both the                  Archaea and Microsporidia map to the entire substructures I–III in the                  secondary structure model of the bacterium E. coli                  [14].                     (b) Raster display of the 100 positions of conserved gaps in                  both the Archaea and Microsporidia across the alignment. (c)                  Raster display of the same 100 positions across an alignment of 858 mitochondrial                  16S rRNA sequences show gaps conserved in most Metazoa. The other groups of                  Eukarya represented in the mitochondrial alignment are Alveolata (1), Euglenozoa                  (2), Fungi (3) and Rhodophyta and Viridiplantae (4). The nucleotides are                  color-coded A (red), C (green), G (blue), U (yellow), unknown (gray) and gap                  (black). The color bars highlight the taxonomic groups.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3094155&req=5

pone-0018768-g005: Sequence gaps exclusive to both Archaea and Microsporidia 16S rRNAs.The 100 positions identified in the gap segment of the third 16S eigenorganism with the largest decrease in relative nucleotide frequency map out entire substructures in the Bacteria 16S rRNAs that are convergently lost in the Archaea and the Microsporidia. (a) The 100 gaps conserved in both the Archaea and Microsporidia map to the entire substructures I–III in the secondary structure model of the bacterium E. coli [14]. (b) Raster display of the 100 positions of conserved gaps in both the Archaea and Microsporidia across the alignment. (c) Raster display of the same 100 positions across an alignment of 858 mitochondrial 16S rRNA sequences show gaps conserved in most Metazoa. The other groups of Eukarya represented in the mitochondrial alignment are Alveolata (1), Euglenozoa (2), Fungi (3) and Rhodophyta and Viridiplantae (4). The nucleotides are color-coded A (red), C (green), G (blue), U (yellow), unknown (gray) and gap (black). The color bars highlight the taxonomic groups.
Mentions: In both 16S and 23S alignments, the third most significant eigenposition captures the similarities among the two taxonomic groups and correlates with decreased nucleotide frequency across both the Archaea and Microsporidia relative to all other organisms with the P-values and , respectively. The 100 positions with largest nucleotide frequency decrease in the gap segment of the third 16S eigenorganism identify all six gaps exclusively conserved in both the Archaea and Microsporidia with the corresponding P-value . Mapped onto the secondary structure model of the bacterium E. coli, these 100 positions identify deletions of not only isolated nucleotides but entire substructures in the Archaea and Microsporidia with respect to the Bacteria (Figure 5a), indicating a convergent loss in both the Archaea and Microsporidia with respect to the Bacteria as well as the Eukarya. We observe that these same positions (Figure 5b) also identify nucleotides that are deleted in the metazoan mitochondrial 16S rRNA sequences (Figure 5c, and Dataset S7), suggesting that these similarities among the Archaea and Microsporidia may be explained by evolutionary forces that act to reduce the genome sizes of the Archaea and Microsporidia. Similarly, the 100 positions with largest nucleotide frequency decrease in the gap segment of the third 23S eigenorganism identify 41 of the 45 gaps and all 11 unpaired adenosines that are exclusively conserved in both the Archaea and Microsporidia with the corresponding P-values (Figures S10 and S11 in Appendix S1). Note that in the 16S alignment, the third eigenorganism also identifies positions of helices, i.e., base-paired nucleotides, that are exclusively conserved in both the Archaea and Microsporidia (Figure S12 in Appendix S1).

Bottom Line: We find, in support of our hypothesis that, first, the significant eigenpositions reveal multiple similarities and dissimilarities among the taxonomic groups.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.

View Article: PubMed Central - PubMed

Affiliation: Institute for Cellular and Molecular Biology, University of Texas at Austin, Austin, Texas, USA.

ABSTRACT
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.

Show MeSH