The limited universe of exons

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).

Domain organization, genomic structure, evolution, and regulation of expression of the aggrecan gene family

Proteoglycans are complex macromolecules, consisting of a polypeptide backbone to which are covalently attached one or more glycosaminoglycan chains. Molecular cloning has allowed identification of the genes encoding the core proteins of various proteoglycans, leading to a better understanding of the diversity of proteoglycan structure and function, as well as to the evolution of a classification of proteoglycans on the basis of emerging gene families that encode the different core proteins. One such family includes several proteoglycans that have been grouped with aggrecan, the large aggregating chondroitin sulfate proteoglycan of cartilage, based on a high number of sequence similarities within the N- and C-terminal domains. Thus far these proteoglycans include versican, neurocan, and brevican. It is now apparent that these proteins, as a group, are truly a gene family with shared structural motifs on the protein and nucleotide (mRNA) levels, and with nearly identical genomic organizations. Clearly a common ancestral origin is indicated for the members of the aggrecan family of proteoglycans. However, differing patterns of amplification and divergence have also occurred within certain exons across species and family members, leading to the class-characteristic protein motifs in the central carbohydrate-rich region exclusively. Thus the overall domain organization strongly suggests that sequence conservation in the terminal globular domains underlies common functions, whereas differences in the central portions of the genes account for functional specialization among the members of this gene family.

The evolution of proteins from random amino acid sequences: II. Evidence from the statistical distributions of the lengths of modern protein sequences

This paper continues an examination of the hypothesis that modern proteins evolved from random heteropeptide sequences. In support of the hypothesis, White and Jacobs (1993, J Mol Evol 36:79-95) have shown that any sequence chosen randomly from a large collection of nonhomologous proteins has a 90% or better chance of having a lengthwise distribution of amino acids that is indistinguishable from the random expectation regardless of amino acid type. The goal of the present study was to investigate the possibility that the random-origin hypothesis could explain the lengths of modern protein sequences without invoking specific mechanisms such as gene duplication or exon splicing. The sets of sequences examined were taken from the 1989 PIR database and consisted of 1,792 "super-family" proteins selected to have little sequence identity, 623 E. coli sequences, and 398 human sequences. The length distributions of the proteins could be described with high significance by either of two closely related probability density functions: The gamma distribution with parameter 2 or the distribution for the sum of two exponential random independent variables. A simple theory for the distributions was developed which assumes that (1) protoprotein sequences had exponentially distributed random independent lengths, (2) the length dependence of protein stability determined which of these protoproteins could fold into compact primitive proteins and thereby attain the potential for biochemical activity, (3) the useful protein sequences were preserved by the primitive genome, and (4) the resulting distribution of sequence lengths is reflected by modern proteins. The theory successfully predicts the two observed distributions which can be distinguished by the functional form of the dependence of protein stability on length. The theory leads to three interesting conclusions. First, it predicts that a tetra-nucleotide was the signal for primitive translation termination. This prediction is entirely consistent with the observations of Brown et al. (1990a,b, Nucleic Acids Res 18:2079-2086 and 18: 6339-6345) which show that tetra-nucleotides (stop codon plus following nucleotide) are the actual signals for termination of translation in both prokaryotes and eukaryotes. Second, the strong dependence of statistical length distributions on sequence-termination signaling codes implies that the evolution of stop codons and translation-termination processes was as important as gene splicing in early evolution. Third, because the theory is based upon a simple no-exon stochastic model, it provides a plausible alternative to a limited universe of exons from which all proteins evolved by gene duplication and exon splicing (Dorit et al. 1990, Science 250:1377-1382).

Molecular cloning and analysis of the protein modules of aggrecans

The large aggregating chondroitin sulfate proteoglycan of cartilage, aggrecan, has served as a prototype of proteoglycan structure. Molecular cloning has elucidated its primary structure and revealed both known and unknown domains. To date the complete structures of chicken, rat and human aggrecans have been deduced, while partial sequences have been reported for bovine aggrecan. A related proteoglycan, human versican, has also been cloned and sequenced. Both aggrecan and versican have two lectin domains, one at the amino-terminus which binds hyaluronic acid and one at the carboxyl-terminus whose physiological ligand is unknown. Both lectins have homologous counterparts in other types of proteins. Within the aggrecans the keratan sulfate domain may be variably present and also has a prominent repeat in some species. The chondroitin sulfate domain has three distinct regions which vary in their prominence in different species. The complex molecular structure of aggrecans is consistent with the concept of exon shuffling and aggrecans serve as suitable prototypes for comprehending the evolution of multi-domain proteins.

The evolution of proteins from random amino acid sequences. I. Evidence from the lengthwise distribution of amino acids in modern protein sequences

We examine in this paper one of the expected consequences of the hypothesis that modern proteins evolved from random heteropeptide sequences. Specifically, we investigate the lengthwise distributions of amino acids in a set of 1,789 protein sequences with little sequence identify using the run test statistic (ro) of Mood (1940, Ann. Math. Stat. 11, 367-392). The probability density of ro for a collection of random sequences has mean = 0 and variance = 1 [the N(0,1) distribution] and can be used to measure the tendency of amino acids of a given type to cluster together in a sequence relative to that of a random sequence. We implement the run test using binary representations of protein sequences in which the amino acids of interest are assigned a value of 1 and all others a value of 0. We consider individual amino acids and sets of various combinations of them based upon hydrophobicity (4 sets), charge (3 sets), volume (4 sets), and secondary structure propensity (3 sets). We find that any sequence chosen randomly has a 90% or greater chance of having a lengthwise distribution of amino acids that is indistinguishable from the random expectation regardless of amino acid type. We regard this as strong support for the random-origin hypothesis. However, we do observe significant deviations from the random expectation as might be expected after billions years of evolution. Two important global trends are found: (1) Amino acids with a strong alpha-helix propensity show a strong tendency to cluster whereas those with beta-sheet or reverse-turn propensity do not. (2) Clustered rather than evenly distributed patterns tend to be preferred by the individual amino acids and this is particularly so for methionine. Finally, we consider the problem of reconciling the random nature of protein sequences with structurally meaningful periodic "patterns" that can be detected by sliding-window, autocorrelation, and Fourier analyses. Two examples, rhodopsin and bacteriorhodopsin, show that such patterns are a natural feature of random sequences.