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. Here we examined 45,785 reference genomes and 21,871 reference proteomes, spanning archaea, bacteria, viruses and eukaryotes 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 Anti-Kardashian 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 in nature. For six-mer peptide kmers the R2 performance of the regression models based on amino acid and dipeptide content is 0.816, whereas models based on physicochemical features achieve an R2 of 0.788. For twelve-mer nucleic kmers the R2 performance of our models based on mono and dinucleotides is 0.481. Our results indicate that the mono and dinucleotide composition of nucleic sequences and the amino acids, dipeptides and physicochemical properties of peptide sequences can explain a significant proportion of the variance in their frequencies between organisms in nature.