The determinants of the rarity of nucleic and peptide short sequences in nature

The prevalence of nucleic and peptide short sequences across organismal genomes and proteomes has not been thoroughly investigated. We examined 45 785 reference genomes and 21 871 reference proteomes, spanning archaea, bacteria, eukaryotes and viruses to calculate the rarity of short sequences in them. To capture this, we developed a metric of the rarity of each sequence in nature, the rarity index. We find that the frequency of certain dipeptides in rare oligopeptide sequences is hundreds of times lower than expected, which is not the case for any dinucleotides. We also generate predictive regression models that infer the rarity of nucleic and proteomic sequences across nature or within each domain of life and viruses separately. When examining each of the three domains of life and viruses separately, the R² performance of the model predicting rarity for 5-mer peptides from mono- and dipeptides ranged between 0.814 and 0.932. A separate model predicting rarity for 10-mer oligonucleotides from mono- and dinucleotides achieved R² performance between 0.408 and 0.606. Our results indicate that the mono- and dinucleotide composition of nucleic sequences and the mono- and dipeptide composition of peptide sequences can explain a significant proportion of the variance in their frequencies in nature.