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

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 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 not captured by energetic models are leveraged for structure prediction and design, but the computational complexity has limited their study to local elements, loops, and recently to those covering pairs of SSEs. Systematically capturing recurrent patterns on a large scale is a main challenge in the study of RNA structures. In this paper, to automatically capture this topological information, we present a new general and efficient algorithm that leverages the fact that we can assign a proper edge coloring to graphs representing such structures. This allows to generalize previous approaches and systematically find for the first time modules over more than 2 SSEs, while improving speed a hundredfold. We then proceed to extract all recurrent base pairs networks between any RNA tertiary structures in our non-redundant dataset. We observed occurrences that are over 36 different SSEs, between the 23S ribosomes of E. Coli and of Thermus thermophilus. In addition to detecting them, our method organizes them into a network according to the similarities of their structures. Relaxing constraints, as not differentiating between local and distant interactions, reduces the number of isolated component in the network of structures. This behaviour can be leveraged to study the emergence of those intricate structures.