Thermodynamics of neutral sets and sequence length changes in the genotype-phenotype map of RNA secondary structure

The genotype-phenotype (GP) map of RNA secondary structure connects RNA sequences and the corresponding folded molecular structures. This relationship is required for modelling the evolution of functional RNA structures. In this thesis, we fill two gaps in the understanding of the RNA GP map: we analyse neutral sets, i.e. groups of sequences with the same structure, from the perspective of the thermodynamics of RNA folding. Moreover, we study insertions and deletions, two common types of mutations, which change the sequence length and have received little attention in the GP map literature. First, we focus on stability values in order to connect neutral set properties to the thermodynamics of the folding model. We study epistasis and the stability change through mutations to understand neutral mutations. Then we quantify differences between structures and find that not only their average stability, but also the typical change in stability through mutations, is linked to neutral set sizes. In the second chapter, we use a free-energy perspective to design a fast and accurate method of estimating neutral set sizes. In addition, we analyse more complex many-to-many GP map models, where multiple low-energy structures can fold for each sequence. We find that structures, which have large neutral sets in the more complex models tend to have large neutral sets in the simpler map, indicating that neutral set size differences are not contingent on the choice of GP map model. In the third chapter, we focus on mutational robustness in a more general GP map, which includes sequence length changes and is based on the RNAshapes concept. We find that robustness to insertions and deletions is correlated with robustness to substitutions. This holds both for genotype robustness variations within a neutral set and for differences in phenotype robustness. The fourth chapter compares structural changes obtained through insertions, deletions and substitutions: structural transitions that are a frequent result of substitutions are found to occur through insertions and deletions and we show that this is consistent with the known link between thermodynamically suboptimal structures and structural changes.