Study of RNA structures with a connection to random matrix theory

This manuscript investigates the level of complexity and thermodynamic properties of the real RNA structures and compares the properties with the random RNA sequences. A discussion on the similarities of thermodynamical properties of the real structures with the non linear random matrix model of RNA folding is presented. The structural information contained in the PDB file is exploited to get the base pairing information. The complexity of an RNA structure is defined by a topological quantity called genus which is calculated from the base pairing information. Thermodynamic analysis of the real structures is done numerically. The real structures have a minimum free energy which is very small compared to the randomly generated sequences of the same length. This analysis suggests that there are specific patterns in the structures which are preserved during the evolution of the sequences and certain sequences are discarded by the evolutionary process. Further analyzing the sequences of a fixed length reveal that the RNA structures exist in ensembles i.e. although all the sequences in the ensemble have different series of nucleotides (sequence) they fold into structures that have the same pairs of hydrogen bonding as well as the same minimum free energy. The specific heat of the RNA molecule is numerically estimated at different lengths. The specific heat curve with temperature shows a bump and for some RNA, a double peak behavior is observed. The same behavior is seen in the study of the random matrix model with non linear interaction of RNA folding. The bump in the non linear matrix model can be controlled by the change in the interaction strength.