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RNA global alignment in the joint sequence-structure space using elastic shape analysis.

Laborde J, Robinson D, Srivastava A, Klassen E, Zhang J - Nucleic Acids Res. (2013)

Bottom Line: Comparison/alignment of RNA molecules provides an effective means to predict their functions and understand their evolutionary relationships.Means and covariances of full structures can be defined and computed, and probability distributions on spaces of such structures can be constructed for a group of RNAs.Our method was further applied to predict functions of RNA molecules and showed superior performance compared with previous methods when tested on benchmark datasets.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, Florida State University, FL, USA.

ABSTRACT
The functions of RNAs, like proteins, are determined by their structures, which, in turn, are determined by their sequences. Comparison/alignment of RNA molecules provides an effective means to predict their functions and understand their evolutionary relationships. For RNA sequence alignment, most methods developed for protein and DNA sequence alignment can be directly applied. RNA 3-dimensional structure alignment, on the other hand, tends to be more difficult than protein structure alignment due to the lack of regular secondary structures as observed in proteins. Most of the existing RNA 3D structure alignment methods use only the backbone geometry and ignore the sequence information. Using both the sequence and backbone geometry information in RNA alignment may not only produce more accurate classification, but also deepen our understanding of the sequence-structure-function relationship of RNA molecules. In this study, we developed a new RNA alignment method based on elastic shape analysis (ESA). ESA treats RNA structures as three dimensional curves with sequence information encoded on additional dimensions so that the alignment can be performed in the joint sequence-structure space. The similarity between two RNA molecules is quantified by a formal distance, geodesic distance. Based on ESA, a rigorous mathematical framework can be built for RNA structure comparison. Means and covariances of full structures can be defined and computed, and probability distributions on spaces of such structures can be constructed for a group of RNAs. Our method was further applied to predict functions of RNA molecules and showed superior performance compared with previous methods when tested on benchmark datasets. The programs are available at http://stat.fsu.edu/ ∼jinfeng/ESA.html.

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Structures, mean, variability and random Gaussian samples of a group of tRNA synthetase complexes. (a) RNA structures in tRNA synthetase complex class. (b) The mean structure of the structures in (a), which is the sample Karcher mean. (c) Samples from the directions of the three main variance components U1, U2 and U3. They represent the amount of variation in the set of structures. (d) Randomly sampled structures from Gaussian distributions with mean and variance estimated from the set of structures in (a).
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gkt187-F3: Structures, mean, variability and random Gaussian samples of a group of tRNA synthetase complexes. (a) RNA structures in tRNA synthetase complex class. (b) The mean structure of the structures in (a), which is the sample Karcher mean. (c) Samples from the directions of the three main variance components U1, U2 and U3. They represent the amount of variation in the set of structures. (d) Randomly sampled structures from Gaussian distributions with mean and variance estimated from the set of structures in (a).

Mentions: Mean shapes and probability distributions of RNA structure families/classes can be very useful in automatic classifications of new structures. For example, mean shapes can serve as filters to quickly narrow down the list of more likely RNA families, which can then be studied in more detail. We can also obtain confidence regions in the directions of main variability and apply likelihood ratio tests in structure classifications. Moreover, random RNA structures can be generated for a given class of structures. As an example of the latter application, Figure 3a shows the set of RNA structures in tRNA synthetase complexes family; Figure 3b is the mean shape calculated from the structures in 3a; Figure 3c shows five sampled structures on each of the top three variance components; and Figure 3d shows some randomly sampled structures from the distribution derived from the set of structures shown in Figure 3a.Figure 3.


RNA global alignment in the joint sequence-structure space using elastic shape analysis.

Laborde J, Robinson D, Srivastava A, Klassen E, Zhang J - Nucleic Acids Res. (2013)

Structures, mean, variability and random Gaussian samples of a group of tRNA synthetase complexes. (a) RNA structures in tRNA synthetase complex class. (b) The mean structure of the structures in (a), which is the sample Karcher mean. (c) Samples from the directions of the three main variance components U1, U2 and U3. They represent the amount of variation in the set of structures. (d) Randomly sampled structures from Gaussian distributions with mean and variance estimated from the set of structures in (a).
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3675459&req=5

gkt187-F3: Structures, mean, variability and random Gaussian samples of a group of tRNA synthetase complexes. (a) RNA structures in tRNA synthetase complex class. (b) The mean structure of the structures in (a), which is the sample Karcher mean. (c) Samples from the directions of the three main variance components U1, U2 and U3. They represent the amount of variation in the set of structures. (d) Randomly sampled structures from Gaussian distributions with mean and variance estimated from the set of structures in (a).
Mentions: Mean shapes and probability distributions of RNA structure families/classes can be very useful in automatic classifications of new structures. For example, mean shapes can serve as filters to quickly narrow down the list of more likely RNA families, which can then be studied in more detail. We can also obtain confidence regions in the directions of main variability and apply likelihood ratio tests in structure classifications. Moreover, random RNA structures can be generated for a given class of structures. As an example of the latter application, Figure 3a shows the set of RNA structures in tRNA synthetase complexes family; Figure 3b is the mean shape calculated from the structures in 3a; Figure 3c shows five sampled structures on each of the top three variance components; and Figure 3d shows some randomly sampled structures from the distribution derived from the set of structures shown in Figure 3a.Figure 3.

Bottom Line: Comparison/alignment of RNA molecules provides an effective means to predict their functions and understand their evolutionary relationships.Means and covariances of full structures can be defined and computed, and probability distributions on spaces of such structures can be constructed for a group of RNAs.Our method was further applied to predict functions of RNA molecules and showed superior performance compared with previous methods when tested on benchmark datasets.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, Florida State University, FL, USA.

ABSTRACT
The functions of RNAs, like proteins, are determined by their structures, which, in turn, are determined by their sequences. Comparison/alignment of RNA molecules provides an effective means to predict their functions and understand their evolutionary relationships. For RNA sequence alignment, most methods developed for protein and DNA sequence alignment can be directly applied. RNA 3-dimensional structure alignment, on the other hand, tends to be more difficult than protein structure alignment due to the lack of regular secondary structures as observed in proteins. Most of the existing RNA 3D structure alignment methods use only the backbone geometry and ignore the sequence information. Using both the sequence and backbone geometry information in RNA alignment may not only produce more accurate classification, but also deepen our understanding of the sequence-structure-function relationship of RNA molecules. In this study, we developed a new RNA alignment method based on elastic shape analysis (ESA). ESA treats RNA structures as three dimensional curves with sequence information encoded on additional dimensions so that the alignment can be performed in the joint sequence-structure space. The similarity between two RNA molecules is quantified by a formal distance, geodesic distance. Based on ESA, a rigorous mathematical framework can be built for RNA structure comparison. Means and covariances of full structures can be defined and computed, and probability distributions on spaces of such structures can be constructed for a group of RNAs. Our method was further applied to predict functions of RNA molecules and showed superior performance compared with previous methods when tested on benchmark datasets. The programs are available at http://stat.fsu.edu/ ∼jinfeng/ESA.html.

Show MeSH