## 3 Results
### A Case Study on Chromosome 15  
The walking procedure and the surfing analysis were applied to chromosome 15, which contains the locus DYX1 on 15q21, one of the nine loci (DYX1-9) identified from Online Mendelian inheritance in man (OMIM, www.ncbi.nlm.nih.gov/omim (accessed on 16 February 2021)) for Developmental Dyslexia (DD). Because it has been reported that there is a link between the levels of some AA in brain and the reading abilities [11], and some proteins appear critical in the onset of the disorder (some proteins located within the loci and other proteins defined markers of dyslexia), we decided to verify whether in the proteins codified by the dyslexia locus there was a different distribution of AA. If so, we expected to find the proteins enriched in a selected AA in one of the peaks identified by our surfing analysis. Dyslexia is caused by multiple genetic and environmental risk factors [12; 13]. Based on the literature, we identified the following gene markers for dyslexia: CYP19A1, DCDC2, DYX1C1, CFAP36, S100B, MRPL19, GCFC2, FOXP2, ZNF280D, SLITRK2. For each gene/locus we annotated the cytogenetic position in order to identify them on chromosomes. The cytogenetic position was then converted to the molecular position using data from the University of California Santa Cruz ([[https://genome.ucsc.edu/index.html](https://genome.ucsc.edu/index.html)]([https://genome.ucsc.edu/index.html](https://genome.ucsc.edu/index.html))) (accessed on 16 February 2021), freely available online at [[http://hgdownload.cse.ucsc.edu/goldenPath/hg38/database/](http://hgdownload.cse.ucsc.edu/goldenPath/hg38/database/)]([http://hgdownload.cse.ucsc.edu/goldenPath/hg38/database/](http://hgdownload.cse.ucsc.edu/goldenPath/hg38/database/)) (accessed on 16 February 2021) for (GRCh38/hg38). We used the cytogenetic location, (column Cyto in Table 2) to identify the molecular position on Chromosome 15, using the transcoding file cytoBand.txt. Figure 2: Outline of the walking procedure and surfing analysis. (**A**) The frameshift throughout the ordered list of proteins (represented by squares) is carried out, and in each frame, the number of proteins having the amount of a selected AA (X) higher than the threshold (T) is counted. The frame most enriched in X is shown in red. (**B**) These numbers are plotted on graph, obtaining a peak that highlights the region of the chromosome codifying for proteins enriched in the chosen AA. We first applied the ordering procedure (step 2.1) to create the canonical table with genes and proteins of chromosome 15. Next, we selected the amino acid whose content could be possibly critical in dyslexia; based on literature search, our choice fell on glutamate (glu) and glutamine (gln) because high values of glutamate and low levels of glutamine have a positive correlation with reading ability [11] and because the availability of these AA could depend on local conditions, for example in hypoxia glutamate can be converted to glutamine [8]. We calculated the absolute content of glutamate and glutamine for each protein of chromosome 15, and we defined the threshold T and the length LB of the blocks necessary to carry out the Walking procedure. LB was established equal to 25 because it gave a reasonably deep frameshift (it allowed to obtain N = 533 values of walking steps) and a good compromise between precision and predictability of the model. In order to select one AA and to define the threshold needed in the walking procedure, we calculated the median value of glutamate (E) and glutamine (Q) of the proteins considered markers of dyslexia. The values are reported in Table 2.  
Of note, three markers were located in chromosome 15. We compared the median values of markers with the median values of the whole chromosome 15, as shown in Figure 3. We decided to consider only the relative frequencies and not the absolute content of Glu and Gln in each protein in order to ignore the differences in protein size, which would render the values extremely variable and barely comparable.