# Global Repeat Map (GRM) Application: Finding All DNA Tandem Repeat Units
## 3 Results
### Human Chromosome 19
All nucleotide substitutions in these copies are visible as small peaks in the GRM diagram (Figure 4a) and as dispersed dots in the Fragment diagram (Figure 4b). The inserts in Figure 4a,b show that, in addition to nucleotide substitutions, there are also nucleotide deletions and insertions in different parts of the TR copies, which are manifested as smaller peaks around the main 7456 bp peak in the GRM diagram, and as points around y = 7456 bp in the Fragment diagram. The most interesting example is No. 1243, TRs with a repetitive unit 2896 bp (12 copies, RefSeq NC_000019.10 position 24,412,442-24,447,210 bp), from Supplementary Table S1. The GRM diagram (Figure 5a) and Fragment diagram (Figure 5b) reveal the basic monomer units of length 171 bp that are organized as TRs of 17 mer (17:171 bp \(\approx\) 2896 bp) into higher order repeats (HOR), each consisting of 17 monomers. In general, for monomeric arrays, frequencies of peaks at -(basic monomer length)-n bp gradually decrease with increasing n and a peak sizably above this background is an indication for HOR. In addition,  
Figure 4: GRM diagram (**a**) and Fragment diagram (**b**) for 7456 bp TR subarray in human chromosome 19 (Supplementary Table S1, repeat No. 538). (**a**) The pronounced GRM peak at 7456 bp corresponds to basic repeat unit of 7456 bp. Insert gives magnified presentation of weak peaks around 7456 bp, which are sizably screened by a 7456 bp peak. (**b**) Each dot in the Fragment diagram corresponds to the fragment length (component \(a_{3}^{i}\) of vector \(a^{i}\)) at that position (component \(a_{1}^{i}\) of vector \(a^{i}\)). Insert gives magnified presentation of points around 7456 bp, which are consequence of nucleotide mutation in TR copies. In the Fragment diagram, most points are located around y = 7456 bp, which corresponds to 7456 bp peak in the GRM diagram. The other points in the Fragment diagram create a small noise, which is visible in the GRM diagram as tiny peaks. due to the deletion and insertion of whole monomers in our 17 mer HOR copies, there are noticeable peaks at fragment lengths 2724 bp (\(\sim\)171\(\cdot\)16 bp) and 3067 bp (\(\sim\)171\(\cdot\)18 bp) (Figure 5a), respectively. The 171 bp monomers are known as alpha satellite monomers [9] and they are the most abundant constituent of centromeres in human and other primate chromosomes. In particular, the centromeric region of human chromosomes contains alpha satellite DNA composed of diverged monomers, some sections without, and some with a higher order repeat structure (HORs) [57; 58]. In pericentromeric regions, alpha satellite DNAs are surrounded by arrays of \"classical\" satellites (satDNA 1-4) [59; 60]. The GRM application confirms these findings and shows that the centromere of the human chromosome 19 is composed of 17 mer HOR (2746 bp), which is surrounded by a series of \(\sim\)171 bp TRs (Table 1, Supplementary Table S1 and Figure 6). In addition, as can be seen from Figure 6, some of the \(\sim\)171 bp alpha satellite arrays from Table 1 are organized into HORs, but their  
Figure 5: GRM diagram (**a**) and Fragment diagram (**b**) for alpha satellite 2896 bp HOR subarray in human chromosome 19 (Supplementary Table S1, repeat No. 1243). (**a**) Pronounced GRM peaks that correspond to alpha satellite HORs are denoted. The pronounced GRM peak at 2896 bp is a signature of 17 mer HOR (2896: 171 \(\approx\) 17). (**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, most points are located around y = \(n\):171 bp, which corresponds to multiples of alfa satellite lengths and peaks in GRM diagram. The highest concentration of points is at y = 2896 bp, which corresponds to 17 mer HOR length. There is also a smaller concentration of points at positions 5168 bp and 8513 bp, which are approximately multiples of 17 mer HOR length.