Currently, there is a lack of bioinformatics approaches to identify highly divergent tandem repeats (TRs) in eukaryotic genomes. Here, we developed a new mathematical method to search for TRs, which uses a novel algorithm for constructing multiple alignments based on the generation of random position weight matrices (RPWMs), and applied it to detect TRs of 2 to 50 nucleotides long in the rice genome. The RPWM method could find highly divergent TRs in the presence of insertions or deletions. Comparison of the RPWM algorithm with the other methods of TR identification showed that RPWM could detect TRs in which the average number of base substitutions per nucleotide (x) was between 1.5 and 3.2, whereas T-REKS and TRF methods could not detect divergent TRs with x > 1.5. Applied to the search of TRs in the rice genome, the RPWM method revealed that TRs occupied 5% of the genome and that most of them were 2 and 3 bases long. Using RPWM, we also revealed the correlation of TRs with dispersed repeats and transposons, suggesting that some transposons originated from TRs. Thus, the novel RPWM algorithm is an effective tool to search for highly divergent TRs in the genomes.
A mathematical method for creating classes of promoter sequences has been developed. The method was used to calculate the classes of promoter sequences from the A.thaliana genome. A total of 16 statistically significant classes of promoter sequences were obtained with class sizes ranging from 8,000 to 100 promoters. The classes obtained allow us to identify potential promoter sequences in various genomes with the number of false positives not exceeding 103 per genome.
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