Mathematical modeling and comparison of protein size distribution in different plant, animal, fungal and microbial species reveals a negative correlation between protein size and protein number, thus providing insight into the evolution of proteomes

BACKGROUND: The sizes of proteins are relevant to their biochemical structure and for their biological function. The statistical distribution of protein lengths across a diverse set of taxa can provide hints about the evolution of proteomes. RESULTS: Using the full genomic sequences of over 1,302 prokaryotic and 140 eukaryotic species two datasets containing 1.2 and 6.1 million proteins were generated and analyzed statistically. The lengthwise distribution of proteins can be roughly described with a gamma type or log-normal model, depending on the species. However the shape parameter of the gamma model has not a fixed value of 2, as previously suggested, but varies between 1.5 and 3 in different species. A gamma model with unrestricted shape parameter described best the distributions in ~48% of the species, whereas the log-normal distribution described better the observed protein sizes in 42% of the species. The gamma restricted function and the sum of exponentials distribution had a better fitting in only ~5% of the species. Eukaryotic proteins have an average size of 472 aa, whereas bacterial (320 aa) and archaeal (283 aa) proteins are significantly smaller (33-40% on average). Average protein sizes in different phylogenetic groups were: Alveolata (628 aa), Amoebozoa (533 aa), Fornicata (543 aa), Placozoa (453 aa), Eumetazoa (486 aa), Fungi (487 aa), Stramenopila (486 aa), Viridiplantae (392 aa). Amino acid composition is biased according to protein size. Protein length correlated negatively with %C, %M, %K, %F, %R, %W, %Y and positively with %D, %E, %Q, %S and %T. Prokaryotic proteins had a different protein size bias for %E, %G, %K and %M as compared to eukaryotes. CONCLUSIONS: Mathematical modeling of protein length empirical distributions can be used to asses the quality of small ORFs annotation in genomic releases (detection of too many false positive small ORFs). There is a negative correlation between average protein size and total number of proteins among eukaryotes but not in prokaryotes. The %GC content is positively correlated to total protein number and protein size in prokaryotes but not in eukaryotes. Small proteins have a different amino acid bias than larger proteins. Compared to prokaryotic species, the evolution of eukaryotic proteomes was characterized by increased protein number (massive gene duplication) and substantial changes of protein size (domain addition/subtraction).