Simplicial Complexes and Graph Rewriting for Modelling RNA Folding

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Adane Letta Mamuye

Computational models are of interest as they are alternatives for understanding complex systems. A complex system is a system composed of many components whose collective behaviour emerges from non-linear interactions among them. Usually, the emerging behaviour can not be trivially inferred from the behaviours of the individual components, thus it can not be modelled by a compositional approach. However, it can be analysed by extracting the information hidden in the data that the system produces.
In this study we integrate in a unique modelling paradigm the structural elements obtained by simplicial complexes applied to data analysis and the behavioural dynamics of the system described by graph rewriting. The proposed approach is applied to a real biological complex system, the folding process of ribonucleic acid (RNA).
RNA is involved in a broad range of biological roles and its study is becoming more and more important in the research  eld of living organisms. The RNA secondary structure is invaluable in creating new drugs and understanding genetic diseases. Thus, numerous computational methods, such as comparative sequence analysis and dynamic programming based on thermodynamic models, have been established for dealing with the prediction of secondary structures.
Though comparative sequence analysis is the gold standard for predicting RNA secondary structures, it requires many multiple homologous sequences and is labour intensive. Thermodynamics based approaches can also be less accurate than comparative-based algorithms for long RNA sequences and are computationally expensive. Additionally, the number of possible secondary structures of a sequence in the folding space grows exponentially with its sequence length and corresponds to a multidimensional space. In terms of data volume, the folding space can be associated with a big dataset.