The structure of long RNA molecules, such as genomes of RNA viruses, cannot be reliably determined experimentally, and hence any study of it inevitably involves computational structure predictions. Although the prediction algorithms are more accurate for short RNAs, they can be used to compare the branching structure and spatial size between various long RNAs. Branching pattern and compactness are also the key determinants of RNA virus self-assembly. The main aim of the Thesis is to clarify how the global structure of RNA is encoded in its primary sequence. We explain the core ideas behind algorithms for thermodynamic prediction of secondary structure of RNA, and use branched polymers as a model to describe the RNA. We analyse more than 1700 viral RNA genomes, and use the predicted structures to calculate the graph-theoretical topological measures of compactness. Results are compared to the predictions for sets of random RNAs, which elucidates the presence of evolutionary pressure which keeps genomes of icosahedral viruses spatially compact. Furthermore, we use two different approaches on random RNAs to calculate their exponents $\rho$ and $\varepsilon$, which describe the scaling of average branch weights and average path lengths in large-size limit, and we show that $\rho \simeq \varepsilon \approx 0.67$. Compared to other models of polymers, the scaling exponents for random RNA are most compatible with those of three-dimensional self-avoiding trees. Finally, we assess the robustness of estimated scaling exponents by using different sets of energy parameters and random RNAs with non-uniform nucleotide compositions.
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