Finding recurrent RNA structural networks with fast maximal common subgraphs of edge-colored graphs.

Antoine Soulé,Alain Denise,Jérôme Waldispühl,Vladimir Reinharz,Roman Sarrazin-Gendron,Tamar Schlick

doi:10.1371/journal.pcbi.1008990

Abstract

RNA tertiary structure is crucial to its many non-coding molecular functions. RNA architecture is shaped by its secondary structure composed of stems, stacked canonical base pairs, enclosing loops. While stems are precisely captured by free-energy models, loops composed of non-canonical base pairs are not. Nor are distant interactions linking together those secondary structure elements (SSEs). Databases of conserved 3D geometries (a.k.a. modules) not captured by energetic models are leveraged for structure prediction and design, but the computational complexity has limited their study to local elements, loops. Representing the RNA structure as a graph has recently allowed to expend this work to pairs of SSEs, uncovering a hierarchical organization of these 3D modules, at great computational cost. Systematically capturing recurrent patterns on a large scale is a main challenge in the study of RNA structures. In this paper, we present an efficient algorithm to compute maximal isomorphisms in edge colored graphs. We extend this algorithm to a framework well suited to identify RNA modules, and fast enough to considerably generalize previous approaches. To exhibit the versatility of our framework, we first reproduce results identifying all common modules spanning more than 2 SSEs, in a few hours instead of weeks. The efficiency of our new algorithm is demonstrated by computing the maximal modules between any pair of entire RNA in the non-redundant corpus of known RNA 3D structures. We observe that the biggest modules our method uncovers compose large shared sub-structure spanning hundreds of nucleotides and base pairs between the ribosomes of Thermus thermophilus, Escherichia Coli, and Pseudomonas aeruginosa.

Highlights

Functional Ribonucleic Acids (RNAs) tertiary structures are stabilized by a collection of base pairs and base stackings often referred to as the secondary structure
First are the results obtained from the dataset used in CaRNAval [28] that aim at validating our method, at illustrating the flexibility of the method in regards of defining families of substructures and at evaluating the impact of consecutive relaxations of constraints over the same dataset
Our motivations in using two datasets instead of just using the more recent dataset 3.137 lie in that dataset 2.92 was the one used in CaRNAval [28]

Summary

Introduction

Functional RNA tertiary structures are stabilized by a collection of base pairs and base stackings often referred to as the secondary structure The latter forms a planar structure made of stems of canonical base pairs (i.e. Watson-Crick and Wobble) connected by loops. These loops do not feature regular canonical base pairs patterns, they are often characterized by complex non-canonical base pair networks that create sophisticated 3D motifs used to shape the molecular structure. These loops occasionally interact with distant parts of the structure (i.e. other loops or stems) to form bridges stabilizing the global architecture of the RNA. This information can be used to infer the 3D structure of the whole molecule [1,2,3,4,5,6,7]

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Results

Conclusion