Tree graphs of RNA secondary structures and their comparisons
Computers and Biomedical Research
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Previously, it was shown that predicting selective mutations leading to topological transitions in the secondary structure of RNAs can be achieved by a coarse-grain Laplacian matrix tree graph representation using its second eigenvalue. When applying the coarse-grain tree graph representation, introduced by Shapiro and co-workers in the 80ýs, it is possible to predict mutations leading to conformational rearrangements in RNAs of around 50 nt and higher. However, for small RNAs, such representations at the level of stems, bulges, and loops become ineffective. Recently, there is an interest in investigating secondary structure rearrangements in small RNAs, following their structural probing by comparative imino proton NMR spectroscopy. For computational predictions of mutations leading to the structure rearrangements of small RNAs, it is necessary to use a fine-grain graph representation as introduced by Waterman in the 70ýs at the level of nucleotides. Each nucleotide becomes a node in the graph and its equivalent Laplacian matrix is of the size N 脳 N for a sequence of N nucleotides. Conformational rearrangements caused by mutations can be studied using measures to assess the differences between Laplacian matrices of fine-grain graph representations. The second eigenvalue of the Laplacian matrix can be used to filter mutations that lead to a structure similar to the wildtype but additional measures are needed. Image analysis techniques, by moving a sliding window over Laplacian matrices, can facilitate in differentiating between local rearrangements and global rearrangements.