What limits the primary sequence space of natural proteins?

Number of naturally occurring primary sequences of proteins is an infinitesimally small subset of the possible number of primary sequences that can be synthesized using 20 amino acids. Prevailing views ascribe this to slow and incremental mutational/selection evolutionary mechanisms. However, considering the large number of avenues available in form of diversity of emerging/evolving and/or disappearing living systems for exploring the primary sequence space over the evolutionary time scale of ∼3.5 billion years, this remains a conjecture. Therefore, to investigate primary sequence space limitations, we carried out a systematic study for finding primary sequences absent in nature. We report the discovery of the smallest peptide sequence "Cysteine-Glutamine-Tryptophan-Tryptophan" that is not found in over half-a-million curated protein sequences in the Uniprot (Swiss-Prot) database. Additionally, we report a library of 83605 pentapeptides that are not found in any of the known protein sequences. Compositional analyses of these absent primary sequences yield a remarkably strong power relationship between the percentage occurrence of individual amino acids in all known protein sequences and their respective frequency of occurrence in the absent peptides, regardless of their specific position in the sequences. If random evolutionary mechanisms were responsible for limitations to the primary sequence space, then one would not expect any relationship between compositions of available and absent primary sequences. Thus, we conclusively show that stoichiometric constraints on amino acids limit the primary sequence space of proteins in nature. We discuss the possibly profound implications of our findings in both evolutionary and synthetic biology.Communicated by Ramaswamy H. Sarma.