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Review
. 2018 Jul 1;143:16-33.
doi: 10.1016/j.ymeth.2018.03.009. Epub 2018 Apr 3.

Adventures With RNA Graphs

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Free PMC article
Review

Adventures With RNA Graphs

Tamar Schlick. Methods. .
Free PMC article

Abstract

The structure of RNA has been a natural subject for mathematical modeling, inviting many innovative computational frameworks. This single-stranded polynucleotide chain can fold upon itself in numerous ways to form hydrogen-bonded segments, imperfect with single-stranded loops. Illustrating these paired and non-paired interaction networks, known as RNA's secondary (2D) structure, using mathematical graph objects has been illuminating for RNA structure analysis. Building upon such seminal work from the 1970s and 1980s, graph models are now used to study not only RNA structure but also describe RNA's recurring modular units, sample the conformational space accessible to RNAs, predict RNA's three-dimensional folds, and apply the combined aspects to novel RNA design. In this article, we outline the development of the RNA-As-Graphs (or RAG) approach and highlight current applications to RNA structure prediction and design.

Keywords: Coarse-grained modeling; Graphs; Mathematical biology; RNA design; RNA secondary structure; RNA structure.

Figures

Figure 1
Figure 1
RNA secondary (2D) and tertiary (3D) interactions. (a) The 2D and 3D structure of the P4-P6 Group I Ribozyme Domain is sketched. (b) Various types of possible 3D interactions are illustrated.
Figure 2
Figure 2
RNA pseudoknots. a) RNA pseudoknots are defined by an intertwined form of base pairing, which leads to crossing of base pairs in the circular representation. b) Examples of pseudoknotted RNAs are also shown.
Figure 3
Figure 3
History of RNA Graphs. See text for details.
Figure 4
Figure 4
RAG representations of RNA 2D structures as tree and dual graphs. The associated matrices (adjacency, diagonal, and Laplacian) are also shown, along with the eigenvalues {λi} and the second eigenvector, μ2
Figure 5
Figure 5
Examples of RAG 2D and 3D graphs: For RNAse P (top) and rRNA (bottom), shown are the experimentally determined 2D (left) and 3D (right) structures. The corresponding 2D RAG tree and dual graphs are also shown (middle), as well as the 3D tree graph superimposed on the experimental 3D structure.
Figure 6
Figure 6
RNA partitioning. a) Partitioning of tree graphs by the gap cut method [50], and b) partitioning of dual graphs by articulation points [51].
Figure 7
Figure 7
The in silico RAGPOOLS approach to simulate the experimental in vitro selection process for novel RNA motifs. Using ‘mixing matrices’ [61, 62] we can specify which graph motifs to blend into the selection pools to help obtain desired RNA motifs. The resulting sequences are ‘folded’ using available 2D algorithms and filtered to obtain the desired products.
Figure 8
Figure 8
Segments of RAG’s motif atlas, with classifications into existing, RNA-like and non-RNA-like motifs as determined by clustering [56].
Figure 9
Figure 9
RAG partitioning of the signal recognition particle into subgraphs.
Figure 10
Figure 10
Ten designed dual graphs [63].
Figure 11
Figure 11
Sketch of the fragment assembly approach.
Figure 12
Figure 12
Illustration of results from design of six RNA-like motifs by fragment assembly [64]. For each RNA-like motif, shown are the two fragments we piece together based on known RNAs, the yield of the intended motifs as determined by two in silico programs, and the trends we identified for obtaining that fold.
Figure 13
Figure 13
Sketch of the RAGTOP hierarchical sampling approach [49, 34, 50, 53]. 1. Initial junction topology prediction; 2. MC sampling of 3D graphs scored by a statistical scoring function with components for bend, twist, radius-of-gyration, and pseudoknot terms; 3. clustering of generated graphs to identify candidate graph; and 4. determination of atomic models from the candidate graph by our fragment assembly algorithm using RAG-3D subgraph partitioning.
Figure 14
Figure 14
Examples of RAGTOP results from graph models to full atomic models.

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