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Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs.

ABSTRACT: RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary structure motif and submotif library using dual graph representation and partitioning. Dual graphs represent RNA helices as vertices and loops as edges. Unlike tree graphs, dual graphs can represent RNA pseudoknots (intertwined base pairs). For a representative set of RNA structures, we construct dual graphs from their secondary structures, and apply our partitioning algorithm to identify non-separable subgraphs (or blocks) without breaking pseudoknots. We report 56 subgraph blocks up to nine vertices; among them, 22 are frequently occurring, 15 of which contain pseudoknots. We then catalog atomic fragments corresponding to the subgraph blocks to define a library of building blocks that can be used for RNA design, which we call RAG-3Dual, as we have done for tree graphs. As an application, we analyze the distribution of these subgraph blocks within ribosomal RNAs of various prokaryotic and eukaryotic species to identify common subgraphs and possible ancestry relationships. Other applications of dual graph partitioning and motif library can be envisioned for RNA structure analysis and design.

SUBMITTER: Jain S

PROVIDER: S-EPMC6115904 | biostudies-other | 2018 Jul

REPOSITORIES: biostudies-other

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Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs.

Jain Swati S Bayrak Cigdem S CS Petingi Louis L Schlick Tamar T

Genes 20180725 8

RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary structure motif and submotif library using dual graph representation and partitioning. Dual graphs represent RNA helices as vertices and loops as edges. Unlike tree graphs, dual graphs can represent RNA pseudoknots (intertwined base pairs). For a repre ...[more]

PMID: 30044451

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Project description:Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG) framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2) corresponding to the second eigenvalues (?2) associated with the topology matrix defining the graph: ?2 describes the overall topology, and the sum of µ2's components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2's components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (? 220 nucleotides). While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs also suggest design strategies for novel RNA motifs.

Project description:BackgroundGene expression is regulated by transcription factors, cofactors, and epigenetic mechanisms. Coexpressed genes indicate similar functional categories and gene networks. Detecting gene-gene coexpression is important for understanding the underlying mechanisms of cellular function and human diseases. A common practice of identifying coexpressed genes is to test the correlation of expression in a set of genes. In single-cell RNA-seq data, an important challenge is the abundance of zero values, so-called "dropout", which results in biased estimation of gene-gene correlations for downstream analyses. In recent years, efforts have been made to recover coexpressed genes in scRNA-seq data. Here, our goal is to detect coexpressed gene pairs to reduce the "dropout" effect in scRNA-seq data using a novel graph-based k-partitioning method by merging transcriptomically similar cells.ResultsWe observed that the number of zero values was reduced among the merged transcriptomically similar cell clusters. Motivated by this observation, we leveraged a graph-based algorithm and develop an R package, scCorr, to recover the missing gene-gene correlation in scRNA-seq data that enables the reliable acquisition of cluster-based gene-gene correlations in three independent scRNA-seq datasets. The graphically partitioned cell clusters did not change the local cell community. For example, in scRNA-seq data from peripheral blood mononuclear cells (PBMCs), the gene-gene correlation estimated by scCorr outperformed the correlation estimated by the nonclustering method. Among 85 correlated gene pairs in a set of 100 clusters, scCorr detected 71 gene pairs, while the nonclustering method detected only 4 pairs of a dataset from PBMCs. The performance of scCorr was comparable to those of three previously published methods. As an example of downstream analysis using scCorr, we show that scCorr accurately identified a known cell type (i.e., CD4+ T cells) in PBMCs with a receiver operating characteristic area under the curve of 0.96.ConclusionsOur results demonstrate that scCorr is a robust and reliable graph-based method for identifying correlated gene pairs, which is fundamental to network construction, gene-gene interaction, and cellular omic analyses. scCorr can be quickly and easily implemented to minimize zero values in scRNA-seq analysis and is freely available at https://github.com/CBIIT-CGBB/scCorr .

Dataset Information

Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs.

Publications

Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs.

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