Structural relation matching: an algorithm to identify structural patterns into RNAs and their interactions

RNA molecules play crucial roles in various biological processes. Their three-dimensional configurations determine the functions and, in turn, influences the interaction with other molecules. RNAs and their interaction structures, the so-called RNA-RNA interactions, can be abstracted in terms of secondary structures, i.e., a list of the nucleotide bases paired by hydrogen bonding within its nucleotide sequence. Each secondary structure, in turn, can be abstracted into cores and shadows. Both are determined by collapsing nucleotides and arcs properly. We formalize all of these abstractions as arc diagrams, whose arcs determine loops. A secondary structure, represented by an arc diagram, is pseudoknot-free if its arc diagram does not present any crossing among arcs otherwise, it is said pseudoknotted. In this study, we face the problem of identifying a given structural pattern into secondary structures or the associated cores or shadow of both RNAs and RNA-RNA interactions, characterized by arbitrary pseudoknots. These abstractions are mapped into a matrix, whose elements represent the relations among loops. Therefore, we face the problem of taking advantage of matrices and submatrices. The algorithms, implemented in Python, work in polynomial time. We test our approach on a set of 16S ribosomal RNAs with inhibitors of Thermus thermophilus, and we quantify the structural effect of the inhibitors

Genus Comparisons in the Topological Analysis of RNA Structures

RNA folding prediction remains challenging, but can be also studied using a topological mathematical approach. In the present paper, the mathematical method to compute the topological classification of RNA structures and based on matrix field theory is shortly reviewed, as well as a computational software, McGenus, used for topological and folding predictions. Additionally, two types of analysis are performed: the prediction results from McGenus are compared with topological information extracted from experimentally-determined RNA structures, and the topology of RNA structures is investigated for biological significance, in both evolutionary and functional terms. Lastly, we advocate for more research efforts to be performed at intersection of physics-mathematics and biology, and in particular about the possible contributions that topology can provide to the study of RNA folding and structure.Comment: 11 pages, 8 figure

RNA secondary structure factorization in prime tangles

Background: Due to its key role in various biological processes, RNA secondary structures have always been the focus of in-depth analyses, with great efforts from mathematicians and biologists, to find a suitable abstract representation for modelling its functional and structural properties. One contribution is due to Kauffman and Magarshak, who modelled RNA secondary structures as mathematical objects constructed in link theory: tangles of the Brauer Monoid. In this paper, we extend the tangle-based model with its minimal prime factorization, useful to analyze patterns that characterize the RNA secondary structure. Results: By leveraging the mapping between RNA and tangles, we prove that the prime factorizations of tangle-based models share some patterns with RNA folding’s features. We analyze the E. coli tRNA and provide some visual examples of interesting patterns. Conclusions: We formulate an open question on the nature of the class of equivalent factorizations and discuss some research directions in this regard. We also propose some practical applications of the tangle-based method to RNA classification and folding prediction as a useful tool for learning algorithms, even though the full factorization is not known

Hierarchical representation for PPI sites prediction

Background: Protein–protein interactions have pivotal roles in life processes, and aberrant interactions are associated with various disorders. Interaction site identification is key for understanding disease mechanisms and design new drugs. Effective and efficient computational methods for the PPI prediction are of great value due to the overall cost of experimental methods. Promising results have been obtained using machine learning methods and deep learning techniques, but their effectiveness depends on protein representation and feature selection. Results: We define a new abstraction of the protein structure, called hierarchical representations, considering and quantifying spatial and sequential neighboring among amino acids. We also investigate the effect of molecular abstractions using the Graph Convolutional Networks technique to classify amino acids as interface and no-interface ones. Our study takes into account three abstractions, hierarchical representations, contact map, and the residue sequence, and considers the eight functional classes of proteins extracted from the Protein–Protein Docking Benchmark 5.0. The performance of our method, evaluated using standard metrics, is compared to the ones obtained with some state-of-the-art protein interface predictors. The analysis of the performance values shows that our method outperforms the considered competitors when the considered molecules are structurally similar. Conclusions: The hierarchical representation can capture the structural properties that promote the interactions and can be used to represent proteins with unknown structures by codifying only their sequential neighboring. Analyzing the results, we conclude that classes should be arranged according to their architectures rather than functions

Automatic generation of pseudoknotted RNAs taxonomy

Background: The ability to compare RNA secondary structures is important in understanding their biological function and for grouping similar organisms into families by looking at evolutionarily conserved sequences such as 16S rRNA. Most comparison methods and benchmarks in the literature focus on pseudoknot-free structures due to the difficulty of mapping pseudoknots in classical tree representations. Some approaches exist that permit to cluster pseudoknotted RNAs but there is not a general framework for evaluating their performance. Results: We introduce an evaluation framework based on a similarity/dissimilarity measure obtained by a comparison method and agglomerative clustering. Their combination automatically partition a set of molecules into groups. To illustrate the framework we define and make available a benchmark of pseudoknotted (16S and 23S) and pseudoknot-free (5S) rRNA secondary structures belonging to Archaea, Bacteria and Eukaryota. We also consider five different comparison methods from the literature that are able to manage pseudoknots. For each method we clusterize the molecules in the benchmark to obtain the taxa at the rank phylum according to the European Nucleotide Archive curated taxonomy. We compute appropriate metrics for each method and we compare their suitability to reconstruct the taxa

An algebraic language for RNA pseudoknots comparison

Background RNA secondary structure comparison is a fundamental task for several studies, among which are RNA structure prediction and evolution. The comparison can currently be done efficiently only for pseudoknot-free structures due to their inherent tree representation. Results In this work, we introduce an algebraic language to represent RNA secondary structures with arbitrary pseudoknots. Each structure is associated with a unique algebraic RNA tree that is derived from a tree grammar having concatenation, nesting and crossing as operators. From an algebraic RNA tree, an abstraction is defined in which the primary structure is neglected. The resulting structural RNA tree allows us to define a new measure of similarity calculated exploiting classical tree alignment. Conclusions The tree grammar with its operators permit to uniquely represent any RNA secondary structure as a tree. Structural RNA trees allow us to perform comparison of RNA secondary structures with arbitrary pseudoknots without taking into account the primary structure