The relationship of protein conservation and sequence length

Background In general, the length of a protein sequence is determined by its function and the wide variance in the lengths of an organism's proteins reflects the diversity of specific functional roles for these proteins. However, additional evolutionary forces that affect the length of a protein may be revealed by studying the length distributions of proteins evolving under weaker functional constraints. Results We performed sequence comparisons to distinguish highly conserved and poorly conserved proteins from the bacterium Escherichia coli, the archaeon Archaeoglobus fulgidus, and the eukaryotes Saccharomyces cerevisiae, Drosophila melanogaster, and Homo sapiens. For all organisms studied, the conserved and nonconserved proteins have strikingly different length distributions. The conserved proteins are, on average, longer than the poorly conserved ones, and the length distributions for the poorly conserved proteins have a relatively narrow peak, in contrast to the conserved proteins whose lengths spread over a wider range of values. For the two prokaryotes studied, the poorly conserved proteins approximate the minimal length distribution expected for a diverse range of structural folds. Conclusions There is a relationship between protein conservation and sequence length. For all the organisms studied, there seems to be a significant evolutionary trend favoring shorter proteins in the absence of other, more specific functional constraints.


Introduction
Proteins evolve under a range of constraints. Probably the most studied constraints on proteins have to do with their specific function, for example, as enzymes, regulators or signaling molecules. In addition, more general constraints on protein evolution are apparent from studies showing a correlation between the base composition of a genome (i.e. GC content) and the overall amino acid composition of its proteins c.f. [1]. There can also be general constraints on protein length. For example, prokaryotes have shorter proteins on average than eukaryotes [2], and among the eukaryotes, the proteins of the microsporidium Encephalitozoon cuniculi, with an extremely compact genome, are smaller than the corresponding proteins in organisms with larger genomes [3].
The constraints due to specific protein function and these more general constraints might not always act in concert.
For example, Singer & Hickey [4] observed a weaker correlation between base composition and amino acid composition for conserved proteins as compared to rapidly evolving proteins. Thus, the more general constraints might be obscured for proteins, which evolve under intense specific functional constraints.
With this in mind, we studied the length distributions of rapidly and slowly evolving proteins from a range of organisms in an effort to detect general constraints on protein length.

Results and Discussion
To analyze the length distributions of proteins from a given organism, we start with a set of proteins from that organism chosen so as to minimize the number of partial proteins or sequences generated by ab initio gene prediction methods. We denote the subset of these proteins that share statistically significant similarity with proteins from organisms outside the given primary kingdom (Archaea, Eukaryota or Bacteria) the Conserved Set (i.e. slowly evolving proteins). We denote another subset the Nonconserved Set (i.e. rapidly evolving proteins) if they only match proteins from closely related organisms (e.g. human proteins to other mammals, or Drosophila proteins to other insects) or do not match proteins from any other organism (see Methods).
In addition to the length distributions of the Conserved and Nonconserved Set proteins, we also analyzed the length distribution of protein domains in a non-redundant set of protein structures derived from a range of eukaryotes and prokaryotes organisms, denoted the Minimal Structural Domain Set [5]. The Minimal Structural Domain Set contains 1882 domains defined purely on the basis of structural compactness. A chain is split between secondary structure elements whenever the ratio of intra-to inter-domain contacts exceeds a threshold [6]. This computational approach for determining domain boundaries splits multi-domain proteins into single domains and non-compact strands and loops are removed as well, thus even single-domain proteins may be shortened by this method. Given that the Minimal Structural Domain Set is derived from a non-redundant set of protein structures and that residues that are not compactly folded are removed, this set approximates the minimal length distribution possible for a diverse range of protein folds.
We computed the protein length histograms of the Conserved and Non-conserved Sets along with that of the Minimal Structural Domain Set for the bacterium Escherichia coli (Figure 1), the archaeon Archaeoglobus fulgidus (Figure 2), and the eukaryotes Saccharomyces cerevisiae (Figure 3), Drosophila melanogaster (Figure 4), and Homo sapiens ( Figure 5). Note that in these figures, the numbers for the Minimal Structural Domain Set were scaled to the total number of proteins in the respective Nonconserved Set. Because annotation artifacts of genomic sequence are likely to be more frequent among the shorter proteins [7,8], we computed an additional length distribution for a set of E. coli proteins (Figure 1) that share statistically significant similarity to proteins from the closely related bacterium Salmonella typhimurium but not proteins from more distant species. This group of proteins, denoted the Salmonella Set, approximated the Nonconserved Set but avoided potential artifacts associated with spurious short "proteins" in the latter. -the peaks of the Nonconserved Set histograms from yeast and Drosophila have shifted slightly to the right (i.e. the proteins tend to be longer) compared to the Minimal Structural Domain Set and the peak for the human proteins has shifted still more to the right; -the Conserved Set proteins from yeast, Drosophila, and human are, on average, longer than those from E. coli and A. fulgidus; -the right shoulder of the Nonconserved Set histograms from yeast, Drosophila, and human also diverge more from the Minimal Structural Domain Set histogram than do the E. coli and A. fulgidus histograms.
To evaluate the sensitivity of these observations to the cutoff expectation value used for the sequence comparisons (see Methods), we varied this cutoff over a range of six orders of magnitude for the E. coli proteins. The above conclusions held for all cut-off values ( Figure 6).
For purposes of clarity, Figures 1, 2, 3, 4, 5 only show histograms for the Conserved and Nonconserved Sets. However, one could generate a length distribution histogram for proteins whose evolutionary rate is intermediate between these two extremes, denoted the Intermediate Set. Thus, for yeast, the Intermediate Set includes proteins that, the Intermediate Set histogram was positioned between the histograms for the Conserved and Nonconserved Sets (data not shown). In addition, similar results were obtained for a variety of eukaryotic organisms for which a representative sample of known full-length proteins were available.
Although Figures 1,2,3,4,5 show that, with increasing length, an increasing fraction of the proteins contain regions that are highly conserved, they do not indicate the fraction of residues that is conserved in these proteins. In Figure 7, we show the fraction of all conserved residues for all E. coli and A. fulgidus proteins (conserved and nonconserved) of varying lengths. With increasing length, a greater fraction of the residues are conserved, converging at approximately 80-90% for proteins greater than 400 residues long. Also in Figure 7, we show the contact densitythe average number of contacts per amino acid residuefor known protein structures of varying lengths (see Methods). The curve for contact density shows good agreement with the curves corresponding to the fraction of conserved residues.

Discussion
The above results seem to indicate that conserved proteins are, in general, longer than non-conserved ones. It is highly unlikely that the above results are due to a detection bias given that these observations were unchanged when varying the cutoff expectation value used for the sequence comparisons (see Methods) between E < 10 -3 and E < 10 -9 . A possible explanation for the insensitivity of these results to varying similarity thresholds is that, e.g., for the E. coli Conserved Set, 80% of the proteins had conserved re- Salmonella Set gions (shared with protein from other kingdoms) over more than 75% of their length and thus would be easy to detect with most sequence comparison methods over a wide range of thresholds.
For the protein sequences determined by conceptual translation of genomic DNA, annotation artifacts would likely be more common among the shorter sequences and these would be classified into the Nonconserved Set. Thus, a possible explanation for the difference in the length distributions between the Nonconserved and Conserved Set proteins would be annotation artifacts for the proteins derived from genomic sequence. Skovgaard and colleagues [8] compared the length distribution of annotated microbial genome proteins matching known proteins with those that do not match a known protein. The sequences that did not have any matches were shorter and this was taken as evidence that too many short genes have been annotated in many genomes (i.e many of these short genes are artifacts). To test this possibility for the Escherichia coli proteins, we generated the length distribution for the Salmonella Set, a subset of E. coli proteins that match proteins from Salmonella but do not match proteins from more distant organisms. It is estimated that Salmonella and E. coli diverged about 100 million years ago [9] and thus a statistically significant similarity between sequences from these bacteria indicates that the corresponding genes evolve under purifying selection. Although this does not prove that all these genes encode proteins (i.e., some of them might encode heretofore uncharacterized regulatory RNAs), requiring a statistically significant similarity to Salmonella sequences greatly reduces the chance of retaining annotation artifacts. Although there are fewer proteins in the Salmonella Set, its length distribution is essentially the same as that of the Nonconserved Set ( Figure  1). Furthermore, although it is likely that there is a greater fraction of annotation artifacts among the Nonconserved set proteins derived from genome annotations, this is unlikely to be true for the human and Drosophila proteins analyzed here because they have been derived from cDNA sequences. To further reduce the chance of annotation errors, for the Drosophila set, we avoided cDNA sequences generated from high throughput cDNA projects. Thus, annotation artifacts are unlikely to explain the results shown in Figures 1,2,3,4,5.
A challenging problem for biologists trying to make sense of genomic sequence, particularly for the eukaryotes, is that shorter proteins are more difficult to predict on purely statistical grounds [8] and are also less likely to have confirmatory homologies in other organisms. Thus, without functionally cloned cDNA transcripts, it becomes hard to distinguish artifacts from rapidly evolving genes and a conservative approach may result in under representation of the shorter eukaryotic proteins in the databases. Consistent with this possibility is the rightward shift of the Nonconserved Set proteins of the eukaryotes as compared to that of the prokaryotes.
One generally assumes that the length of a protein is largely determined by its functions. The relatively wide variance in sequence length of the members of the Conserved set reflects the diverse range of specific functional roles for these proteins. The Nonconserved set proteins however are, on average, shorter than the conserved proteins, with the poorly conserved E. coli and A. fulgidus proteins closely approximating the minimal length distribution possible for globular proteins, as represented by the Minimal Structural Domain Set. In this sense, the poorly conserved proteins from these organisms appear to be as small as proteins can be and still fold into a stable globular structure.
Many biologists implicitly assume that functionally important proteins are more evolutionarily conserved than less vital proteins, and recent work has confirmed this belief [10,11]. Here, we identified another substantial difference between highly conserved and poorly conserved proteins: the less conserved (i.e. less important) proteins are, on average, smaller than more conserved (and more important) proteins. What global evolutionary forces would favor shorter proteins in the absence of other functional constraints? It seems logical to think of these potential forces in terms of minimizing the cost of having extra sequences that do not substantially affect fitness. Such costs might be associated with several distinct processes. One possibility is simply the cost of protein translation and another is the cost of the chaperones that are required to fold longer, particularly multidomain proteins [12]. Although perhaps less likely, yet another cost of longer proteins could be their increased risk of "side effects", i.e. deleterious interactions with other cellular components. For any given protein, the cost differential is likely to be almost negligible, but this difference becomes more significant when one considers the entire set of poorly conserved proteins. In a somewhat similar context, Akashi & Gojobori [13] have shown that highly expressed proteins in the proteomes of E. coli and B. subtilis have a greater abundance of less energetically costly amino acids than other proteins encoded in these genomes. Another related observation is that of Castillo-Davis and colleagues [14], Length who have shown that highly expressed genes have smaller introns on average than other genes presumably due to the cost of transcription and/or splicing.
The action of random genetic drift and selection pressure on genome size (c.f. [15]) could also favor shorter proteins. If deletions are more common than insertions for a given organism, then proteins that can tolerate more mutations (i.e. are evolving under weaker functional constraints) will tend to get smaller over time. Several studies in E. coli have indeed shown that, on average, deletions are eight times more frequent than insertions, c.f. [16]. Similarly, analysis of human mutations (A. Kondrashov, personal communication) has shown that deletions are approximately three times more frequent than insertions. It is reasonable to assume that evolutionary forces acting on genome size might be a more important factor favoring smaller proteins for prokaryotic and unicellular eukaryotic genomes because they are primarily composed of protein-coding sequence. This is less obvious for the larger eukaryotic genomes; in particular, the metazoan and plant genomes are primarily composed of noncoding DNA where reductions in protein length would tend to have far less impact on overall genome size.
All of the above constraints would tend to favor shorter proteins but do not seem to explain why the tendency to economize on unnecessary residues increases with greater sequence length, as seen in Figure 7. To have this effect, a constraint must initially have more than a linear increase in intensity with greater sequence length. Given the globular nature of a folded protein, the average number of intramolecular contacts per residue should grow with increasing sequence length (the volume of the globule grows faster than the surface with length increase) and these contacts would constrain the possible residues at any given site within a protein. However, the size of a single globular domain of a protein does not continue to grow with sequence length beyond a certain limit (~150 residues); rather, longer proteins typically have multiple  Figure 7, and the similarity of the contact density plot with that for the fraction of conserved residues is noteworthy. This similarity over a range of sequence lengths is consistent with an evolutionary force minimizing the cost of having extra sequences that do not substantially affect fitness.
The results presented here show that, for all the organisms studied, poorly conserved proteins are, on average, shorter than highly conserved ones. And, in general, there appears to be a significant trend towards shorter proteins in the absence of other, more specific functional constraints. This is compatible with the existence of an evolutionary force acting to minimize the costs associated with sequences that have no functional role. Thus, the size of the poorly conserved proteins seems to tend to minimal domain size, whereas the size of highly conserved proteins varies to a greater extent, reflecting the broad range of functions. It appears that analysis of functionally relatively unimportant proteins allows one to uncover general evolutionary trends that so far remain unnoticed.

Initial Sequence Sets
The protein sequence sets were derived as follows: • 4279 Escherichia coli protein sequences from NCBI Genomes division, gi NC_002142; • 2420 Archaeoglobus fulgidus protein sequences from NCBI Genomes division gi NC_000917;

Figure 6
Protein Conservation versus Sequence Length for varying Similarity Thresholds. A. Histograms use similarity threshold of Evalue < 10 -3 to determine membership in Conserved Set or Nonconserved Set (see Methods). B. Histograms use Evalue < 10 -9 to determine membership. • 6305 Saccharomyces cerevisiae protein sequences from NCBI Genomes division, gi's NC_001133 -NC_001148, NC_001224, NC_001398; • 2390 Drosophila melanogaster protein sequences extracted from characterized mRNA sequences retrieved from the NCBI Entrez Nucleotides database, requiring a full-length coding sequence and excluding mRNAs generated from high-throughput cDNA projects to minimize partial proteins or proteins generated from ab initio gene predictions; • 14,538 Homo sapiens proteins derived from the NCBI Human RefSeq database, only including proteins encoded by characterized mRNAs and not ab initio gene predictions.
For each organism, protein sequences gained membership to their respective Conserved Sets if they had a BLASTP [17] match of Evalue < 10 -6 to any sequence in the NCBI nr database from an organism in a different kingdom (i.e. Archaea to Eubacteria, or, Eubacteria to Eukaryota). For the sensitivity tests of this cutoff value, we For each bin of 40 residues, the ratio of the total length of non-overlapping cross kingdom alignments divided by the total length of the proteins in that bin is plotted. Proteins that did not have cross kingdom matches contribute zero to the numerator but their lengths are added to the denominator. Error bars shown for Archaeoglobus fulgidus were computed as standard error of the mean and were essentially identical for Escherichia coli (not shown). Contact density: Plotted as green filled circles. For each bin of 50 residues, we plot contact density computed as described in Methods. Contact density repeated the analysis for the Escherichia coli proteins using Evalue < 10 -3 and Evalue < 10 -9 .
For each organism, protein sequences gained membership to their respective Nonconserved Sets if they had no BLASTP matches of Evalue < 10 -6 to any sequence in the NCBI nr database (other than within the same organism) or if the only sequence for which they had a BLASTP match was from an organism that was close evolutionarily. Close relatives were defined as follows: • Escherichia coli -Proteobacteria; • Archaeoglobus fulgidus -Euryarcheota; • Saccharomyces cerevisiae -Fungi; • Drosophila melanogaster -Insecta; • Homo sapiens -Mammalia.

Contact Density
A non-redundant set of chain sequences for protein structures from PDB was constructed by single-linkage clustering based on a BLASTP match of Evalue < 10 -7 or less, as described in Matsuo & Bryant [18]. Contact density was calculated as an average number of contacts per residue (for non-adjacent residues having side chain to side chain distances less than 8 Angstroms).