RNA is crucial in life through both of its aspects, sequence and structure. In the beginning of this thesis, we study the statistical mechanics of RNA secondary structure formation. We first analytically describe the finite size effects. The crossover length, beyond which RNA stays in the thermodynamic limit, can be much longer than natural RNAs depending on the sequence pattern. Thus, one needs to consider the finite size effects whenever numerical or experimental results are to be interpreted within the framework in the thermodynamic limit. While this result holds only for homogeneous sequences, it might also hold for disordered RNA sequences.
Studying disordered RNA is itself a very interesting challenge in statistical mechanics. A solid analytical description is still lacking due to the difficulty in calculating the quenched average. An alternative approach, called annealed averaging, is more tractable. However, the differences between annealed and quenched averaging can be very large. We quantify these differences, which are then used to improve the annealed system. The resulting constrained annealed system can predict certain thermodynamic quantities very close to the quenched results.
We then switch to the study of RNA sequence as a genetic information carrier. An RNA sequence may undergo certain editing that can significantly alter its genetic information. Thus, usual computational approaches for gene search do not work when RNA editing occurs. We modify an algorithm to include the effects of editing, and predict three genes that have never been discovered before. Besides gene search, we also study certain feature of the editing sites.
Editing in many organisms usually occurs with a certain bias in choosing the editing positions. Currently, this position bias is a mystery since a clear editing mechanism is lacking. We propose an evolutionary model that quantitatively explains the position bias of editing in the organism Physarum . This suggests that in Physarum , editing is randomly acquired and the position bias is mainly a consequence of selection at the protein level.
This thesis covers the two important aspects of RNA, sequence and structure, and improves the overall picture of RNA.