Persistent Homology Analysis of RNA

Adane L Mamuye,Matteo Rucco,Emanuela Merelli,Luca Tesei

doi:10.1515/mlbmb-2016-0002

Adane L Mamuye, Matteo Rucco + Show 2 more

Open Access

https://doi.org/10.1515/mlbmb-2016-0002

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Abstract

Abstract Topological data analysis has been recently used to extract meaningful information frombiomolecules. Here we introduce the application of persistent homology, a topological data analysis tool, for computing persistent features (loops) of the RNA folding space. The scaffold of the RNA folding space is a complex graph from which the global features are extracted by completing the graph to a simplicial complex via the notion of clique and Vietoris-Rips complexes. The resulting simplicial complexes are characterised in terms of topological invariants, such as the number of holes in any dimension, i.e. Betti numbers. Our approach discovers persistent structural features, which are the set of smallest components to which the RNA folding space can be reduced. Thanks to this discovery, which in terms of data mining can be considered as a space dimension reduction, it is possible to extract a new insight that is crucial for understanding the mechanism of the RNA folding towards the optimal secondary structure. This structure is composed by the components discovered during the reduction step of the RNA folding space and is characterized by minimum free energy.

Highlights

Ribonucleic acid (RNA) is a biological molecule that plays a key role in various biological processes
In our setting we focus on the generators of the homological group H1 because the RNA folding space can be characterised by the value of Betti number 1 (β1), which counts the size of H1
The persistent loop is called irrelevant in two cases (1) when one nucleotide is involved in more than one base pair on a single persistent loop; and (2) whenever there is a cross-serial interaction in a loop

Summary

Introduction

Ribonucleic acid (RNA) is a biological molecule that plays a key role in various biological processes. Discoveries of the past decade witnessed that RNA is involved in catalytic activity, protein synthesis and gene regulation [22]. Understanding the recurrent interactions among RNA molecular components and their structures are vital to detect prominent information and insight on the RNA mechanism behind its roles. Base-pairing is the most specific interaction in RNA as it involves the hydrogen-bonding of nucleotides. Such interactions are fundamental for understanding RNA folding, function and evolution. RNA secondary structures are defined by list of base pairs in which each base pair appears at most once [10]. Understanding secondary structures is important for inferring structure-function relationships

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