# Global Repeat Map (GRM) Application: Finding All DNA Tandem Repeat Units
## 3 Results
### Human Chromosome 19  
Let us consider three characteristic TRs in human chromosome 19. We start with No. 251 from Supplementary Table S1, TRs with repeat unit 19 bp (172 copies, RefSeq NC_000019.10 position 3,172,558-3,176,417 bp). In the GRM diagram for the subsequence containing these TRs (Figure 3a), prominent peaks appear for fragment lengths of 19 bp and its multiples. The multiples of the 19 bp peak in the GRM diagram and the points at the higher fragment lengths in the Fragment diagram (Figure 3b) occur due to different \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Loc** & **Type** & **Name** & **RefSeq** & **INSDC** & **Size** & **Offb** & **GC\%** & **Protein** & **rRNA** & **tRNA** & **Other** & **RNA** & **Gene** & **Pseudogene** \\ \hline _Homo sapiens_ & Chr & 19 & NC_000019.10 & CM000681.2 & 58.62 & 47.9 & 6944 & - & 6 & 2001 & 2494 & 527 \\ _Pan troglodytes_ & Chr & 19 & NC_000085.7 & CM001012.3 & 61.42 & 43.1 & 2718 & - & 9 & 1041 & 1380 & 229 \\ _Mus musculus_ & Chr & 19 & NC_00085.7 & CM001012.3 & 61.42 & 43.1 & 2718 & - & 9 & 1041 & 1380 & 229 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Case study genome information for reference and representative genomes. _Homo sapiens_ assembly GRCh38.p13, _Pan troglodytes_ assembly Clint_PTRv2 and _Mus musculus_ assembly GRCm39. Download sequences and annotation from GenBank ([[https://www.ncbi.nlm.nih.gov/genome/51](https://www.ncbi.nlm.nih.gov/genome/51)]([https://www.ncbi.nlm.nih.gov/genome/51](https://www.ncbi.nlm.nih.gov/genome/51)), [[https://www.ncbi.nlm.nih.gov/genome/52](https://www.ncbi.nlm.nih.gov/genome/52)]([https://www.ncbi.nlm.nih.gov/genome/52](https://www.ncbi.nlm.nih.gov/genome/52)), accessed on 1 November 2022). mutations (insertions, deletions, substitutions) in the components \(a_{2}^{i}\) (\"key string\") of the vectors \(a^{i}\). Due to these mutations, \"key string\" does not have its identical pair at a TR length distance but finds it on multiples of these lengths (Figure 3b). In the case of completely regular TRs, we would have all points at y = 39 bp in the Fragment graph (Figure 3b), which would result in only one peak in the GRM diagram (Figure 3a). During step four (Algorithm outline), we identify all major peaks, where the largest one defines TR for the observed subarray, and other peaks help in the decision on possible merging with the adjacent subarrays. At higher peaks for the observed 19 bp TRs there is a shift in one bp, which is the result of one nucleotide insertion in the basic repeat unit. By inspecting sequence No. 251 in Supplementary Data S1, we can confirm that 19 bp TR is repeated with lengths (19 bp, 19 bp, 20 bp, 19 bp, 20 bp, 20 bp, 19 bp, 19 bp, 19 bp, 20 bp, 19 bp, 20 bp, 19 bp, 20 bp, 19 bp, 20 bp, 19 bp, 19 bp, 20 bp,... ). The next example is No. 538, TRs with a basic repetitive unit of 7456 bp (three copies, RefSeq NC_000019.10 position 8,743,683-8,766,063 bp) from Supplementary Table S1. In the GRM diagram for THE subsequence containing these TRs (Figure 4a), there is only one prominent peak (fragment lengths of 7456 bp) due to the small number of copies of  
Figure 3: GRM diagram (**a**) and Fragment diagram (**b**) for 19 bp TR subarray in human chromosome 19 (Supplementary Table S1, repeat No. 254). (**a**) Pronounced GRM peaks at \(n\)-19 bp correspond to basic repeat unit of 19 bp and its multiples. Deviations from perfect multiples of the basic unit occur due to insertions and deletions. (**b**) Each dot in the Fragment diagram corresponds to fragment length (component \(a_{3}^{i}\) of vector \(a^{i}\)) at that position (component \(a_{1}^{i}\) of vector \(a^{i}\)). In the Fragment diagram, the density of the points decreases with increasing multiples of the basic repetitive unit, which corresponds to a decrease in the height of the peaks in corresponding GRM diagram. these TRs and due to the relatively small mutual deviation of the individual TR copies.