If duplicate genes play a significant role in buffering against mutations, then genes with one or more paralogs should have higher chances of survival upon deletion than singletons. This simple relationship has been demonstrated for yeast 11 and C. elegans 24, but not yet for other organisms. To test the generality of this prediction, we estimated families of homologous genes for eleven bacterial and eukaryotic organisms based on a BLAST 29 sequence similarity search (E-value < 1.0e-10), and compared survival upon knockout (KO) or knockdown (KD) of genes from these gene families to survival upon KO/KD of singletons (Table 1). We estimate gene expression levels by use of the Codon Bias Index (Methods).

We define the effective family size D of a target gene as the number of duplicates remaining after KO or KD. D = 0 denotes singletons genes; D ≥ 1 denotes genes with paralogs. The probability P(D ≥ 1) is derived from the fraction of genes in a genome which do have one or more duplicates (paralogs). We also use the probability P(S) which describes for an organism chances of survival upon gene-deletion; P(S) is derived from the fraction of genes identified as dispensable (non-essential) in large-scale screens. When discussing 'buffering by duplicates' we mean the enrichment of duplicates amongst non-essential genes as inferred from statistical analysis. 'Essentiality/non-essentiality (survival)' is purely based on outcomes of experiments.

Table 1, Figure 1 and 2 summarize our results with respect to survival and gene duplication across whole genomes. Most genomes in our dataset have relatively few essential genes; chances for survival upon loss of a single gene are high in both prokaryotes and eukaryotes (P(S) > 0.80), except for M. genitalium, H. influenzae and mouse (Figure 1A). Genes of high expression levels are more likely to be essential than genes of low expression levels (smaller P(S)); in half (six) of the organisms the difference is significant (P-value ≤ 0.01).

In accordance with the expectation that more complex organisms tend to have more duplicate genes, the fraction of genes with duplicates (D ≥ 1) increases from M. genitalium and the other bacteria, to yeast and the three animals (Figure 1B). Compared to other organisms, mouse has a noticeable depletion of singleton genes (D = 0) relative to genes with duplicates. In five organisms, there is a significant increase in the fraction of duplicates (D ≥ 1) amongst highly expressed genes compared to other genes (P-value ≤ 0.01); an exception is B. subtilis in which the trend is inverted. When using Codon Adaptation Index or experimental expression data we obtain similar results (Additional file 1).

To assess the contribution of duplicates to survival following gene-KO/KD we define the buffering capacity C as C = P(S|D ≥ 1)/P(S|D = 0) – 1, where P(S|D = 0) is the probability of survival given the gene does not have additional duplicates, i.e. is a singleton. P(S|D ≥ 1) is the probability of survival given the gene has one or more additional duplicates. C is calculated for each organism and quantifies the increase in probability of survival upon gene-KO/KD for genes which have a duplicate in the genome.

In nine of the eleven organisms, duplicates contribute significantly and positively to survival (P-value ≤ 0.05); with contributions ranging from 1 to 13% (Table 1, Figure 2). The exceptions are M. genitalium and mouse in which duplicates appear to decrease chances of KO survival. The extent of buffering by duplicates, i.e. the value of C, does not correlate with the organisms' complexity or genome size. Total C is largest in yeast, worm and H. pylori and smallest in H. influenzae, B. subtilis and fly. While the total number and fraction of genes with duplicates increases from simpler to more complex organisms (Figure 1B), the propensity of duplicates to buffer against gene loss varies independently.

Next we ask whether amongst genes with duplicates chances for buffering upon gene loss increase with high expression levels compared to low expression levels. In most of the organisms, there are significant differences in buffering capacity C amongst genes of low and high expression levels (P-value ≤ 0.05). However, only in five organisms (H. pylori, P. aeruginosa, E. coli, yeast, and worm), genes of high expression levels and with duplicates have significantly improved chances of survival; with C reaching 23% in E. coli. In M. genitalium and M. tuberculosis, C is positive amongst highly expressed genes when examining experimental expression data (Additional file 1); in B. subtilis and fly survival is generally very high and a distinction between genes of high or low expression does not have any effect.

These results are robust to various methods of paralog estimation, although exact numbers change depending on parameter settings. We tested, for example, different E-value cutoffs, different length requirements on the match region or when using methods of homology estimation that are completely independent of particular E-value thresholds (Additional file 1).

Assuming that paralogs can take over the function of a deleted gene, one may hypothesize that chances of doing so increase i) with the number of paralogs present, and ii) their similarity to the mutant protein. We tested these predictions in the eleven organisms.

Only in three organisms, P. aeruginosa, E. coli, and worm, chances of survival correlate significantly (P-value ≤ 0.05) with both the number of duplicates available per gene and with the distance of the gene to the nearest homolog (R² ≥ 0.64 and R² ≥ 0.80, respectively; Table 1). These correlations have been observed previously in worm 24, but are not common amongst the organisms of our study. Yeast has a decent correlation with distance to the nearest homology (R² = 0.72), but not with the number of duplicates per gene. These results do not change even when removing ribosomal genes or gene pairs originating from the whole-genome duplication 28, or when focusing on highly expressed genes (Additional file 1). Yeast is particularly enriched in two-gene families (D = 1) which buffer for each other (Additional file 1). Figure 3A shows these distributions for E. coli, yeast and worm.

We further tested C for genes in different groups of gene function, without finding strong biases (Additional file 1).

To better understand buffering by duplicates, we compared the properties of a subset of duplicates which are likely to buffer for each other's function to those which do not buffer for each other. In particular, we analyzed two-gene families which had been tested for both single- and double gene-KOs. Of course, members of larger gene families can also buffer for each other – however, it is more difficult to distinguish buffering genes from those with other functions. For two-gene families, if the double-KO of two non-essential genes is lethal, the two genes are likely to buffer for each other's function in single-KOs, i.e. we call them buffering duplicates. Despite the generally low contribution of duplicates to survival upon gene knockout, these two-gene families are paramount candidates for buffering. If a double-KO is viable, reasons other than the presence of a duplicate should explain their viable single-KO phenotype. We call these pairs non-buffering duplicates.

Amongst the ~300,000 yeast gene pairs tested for double-KO phenotypes tested in large- and small-scale screens 30, we identified 50 two-gene families with genetic interactions (buffering) and eight two-gene families with a viable double-KO phenotype (non-buffering). These two-gene families represent prime candidates for comparing characteristics of buffering and non-buffering duplicates, respectively. Table 2 and Additional file 1 describe their properties tested across and between the genes. There are also another 551 two-gene families in yeast which have not been tested in double-KO experiments; Additional file 1 describes their characteristics.

Both buffering and non-buffering two-gene families are defined by the same E-value threshold (10^-10, Methods); however, buffering genes have significantly higher sequence identity between the members (P-value < 0.05; Table 2). Buffering genes are also more conserved than non-buffering genes, i.e. have slower rates of evolution and more orthologs across organisms.

We examined the functional similarity between genes in the sets of pairs, testing whether buffering duplicates are more similar in their function than non-buffering duplicates. We find that genes buffering two-gene families have mostly identical function descriptions, and descriptions for non-buffering genes are similar but not identical (Table 3, 4) – however, this finding is only qualitative. To quantify functional distance, we measured the average shortest path between the genes in a network of functional relationships 31: buffering genes had slightly shorter paths between each other than non-buffering genes (not significant, Table 2), i.e. their functions are closer to each other. Other quantitative measures of gene function can be derived from the number and types of physical protein-protein interactions, functional interactions 31, genetic interactions or gene-KO phenotypes under various conditions. Buffering genes are more similar to each other than non-buffering genes in all these measures except for genetic interactions, although the trends are not significant (Table 2). The lack of similarity of genetic interaction profiles between buffering genes is consistent with recent findings by Ihmels et al. 13 although these authors included epistatic interactions other than lethal double-KO phenotypes in their analysis.

Buffering and non-buffering genes show clear differences in terms of transcriptional and translational regulation (Table 2). Buffering genes have higher mRNA and protein expression levels. Measures of translation efficiency, e.g. protein length, molecular weight, Codon Adaptation Index (CAI), or protein production rate, are significantly elevated in buffering genes compared to non-buffering ones (P-value ≤ 0.05); protein degradation is slightly decreased. Interestingly, some of these measures (e. g. length, CAI) are significantly more different between members of a buffering gene pair than between members of a non-buffering gene pair (Additional file 1).

We also extracted orthologs of the buffering and non-buffering yeast two-gene families in fly, worm and mouse using InParanoid 32. (None of the yeast genes had orthologs in E. coli). If a buffering gene pair in yeast has a single-gene ortholog in another organism (without additional duplicates), we expect this ortholog to be essential – more often than single-gene orthologs of non-buffering gene pairs. If an ortholog of a buffering two-gene family has paralogs, we do not expect it to be essential. Indeed, buffering gene pairs are enriched for essential single orthologs compared to non-buffering gene pairs, although the trend is very weak and not significant due to small numbers in the dataset (Table 5, P-value = 0.19; Additional file 1, P-value = 0.07). There are several examples of essential single orthologs of buffering gene pairs: HMG1 and HMG2 are isozymes of HMG-CoA reductase in yeast (Table 3) and their double KO phenotype is lethal. The genes have one ortholog in worm (F08F8. 2) and one in mouse (HMG-CoAR, MGI96159) which both have embryonic lethal KO/KD phenotypes. SSF1 and SSF2 are yeast proteins required for ribosomal large subunit maturation (Table 3), and they have single essential orthologs in worm (K09H9. 6, lpd-6) and fly (CG5786, Peter Pan).

For further validation, we extracted the 143 worm two-gene families tested in double-RNAi knockdowns 33 which consist of 16 pairs of synthetic sick or lethal (SSL) phenotypes, i.e. buffering duplicates, and 127 non-buffering duplicate gene pairs. Unfortunately, there are no experimental data available for worm genes to test for measures of transcriptional and translational efficiency. When calculating CAI for the worm sequences, we found a significant bias confirming the trend in yeast (Table 2). Buffering genes are more efficiently translated than non-buffering genes.

Noticeably, yeast is enriched for buffering gene pairs (50) vs. non-buffering gene pairs (eight) compared to worm (16 and 143-16 = 127, respectively). This bias holds true even if only regarding the yeast gene pairs identified in large-scale screens: ten buffering and eight non-buffering pairs. Previous work has shown that yeast is enriched for buffering gene pairs which originate from the whole genome duplication 34. In addition, RNAi-based screens in worms may miss synthetically lethal interactions and thus have a high false-negative rate amongst gene pairs found to be non-buffering.

We obtained the amino acid sequences for ten genomes (Mycoplasma genitalium; Bacillus subtilis; Helicobacter pylori; Haemophilus influenzae; Mycobacterium tuberculosis; Pseudomonas aeruginosa; Escherichia coli; Saccharomyces cerevisiae (yeast); Caenorhabditis elegans (worm); Drosophila melanogaster (fly); Mus musculus (mouse)) from a collection in the SUPERFAMILY database 39. Information on gene essentiality (lethal phenotypes upon single gene-KO or KD) was taken from publications 25353640414243444546. Table 1 provides an overview of the number of genes in tested each organism (background set) and the number of genes identified to be essential. The table describes briefly the experimental strategy, as described in the publications and in the SEED database http://theseed.uchicago.edu. All screens were conducted in rich medium and on whole organisms except for fly (cell line). For mouse, data of ~4,000 individual knockout experiments were obtained from the Mouse Genome Database 47.

To-date, large-scale double-KO/KD data is only available for yeast and worm. For yeast we compiled in addition to the original data published by Tong et al. 1648 13 datasets identified as 'systematic screens' in the BioGRID database 30495051525354555657585960. In a parsimonious approach, we only included data on lethal phenotypes of double-KOs in our study and no other epistatic interactions. To calculate the background set of tested gene pairs, we paired the 204 bait genes identified in the 14 analyses with all non-essential yeast genes 42, resulting in ~300,000 tested pairs.

For worm we extracted data from two large-scale double KD screens 2661, which comprise 52781 tested gene-pairs and 3927 genetic interactions. Another study in worm specifically targeted two-gene families with a single ortholog in yeast 33, and we used these pairs to investigate properties of two-gene families.

We measured similarity between all sequences using a BLAST all-against-all search 29, and required an E-value < 10^-10 for two genes to be predicted homologs. This E-value threshold was established in yeast and adjusted accordingly in organisms of very different genome size, e.g. in M. genitatlium (10^-9) and worm (3.0*10^-10). This threshold identified 609 two-gene families in yeast. We tested several other methods of homology prediction including different E-value thresholds, E-value-independent methods and use of InParanoid 32, all with results qualitatively identical to those discussed here (Additional file 1).

As a surrogate for gene expression levels, we calculated the Codon Bias Index (CBI) for each gene using the CodonW server 62, with standard settings and parameters for the respective organism. We also calculated the Codon Adaptation Index (CAI). However, since it requires a reference dataset of expressed genes (which was not always available) we consider CAI less appropriate of a measure than CBI. Both measures are expected to work less well in multi-cellular organisms due to tissue-specific expression which may not be captured by these sequence features. For further validation, we extracted from literature experimental expression data for all organisms except H. pylori. Results for CAI and experimental expression data are in Additional file 1. For the results in Figure 1 and 2, we rank-ordered the CBI values within each genome and selected subsets of genes with the highest or lowest CBI; the sizes of the subsets varied according to the organism's genome size. See Additional file 1 for details.

In yeast, 50 two-gene families were identified as buffering (SSL phenotype) and eight two-gene families as non-buffering (viable phenotype). The buffering pairs consist of nine pairs identified in the 14 large-scale double-KO screens (see above), and 42 additional pairs identified in small-scale experiments and listed in BioGRID 30). The non-buffering pairs originate from pairs tested in 14 large-scale screens and found to have viable phenotypes. Table 2 describes characteristics between the two members of a gene family and characteristics of individual genes, averaged across the whole set. For vector comparisons, we constructed binary vectors (1 = observation, 0 = no observation) based on networks of functional interactions 31, genetic interactions (see description of datasets above), physical interactions (extracted from BioGRID 30), and single gene-KO phenotypes 63. The similarity between two vectors is measured as the percentage of shared positive interactions (Jaccard Index). More results are in Additional file 1.

As a control for the effects of WGD genes, we also compared some characteristics in all 609 yeast two-gene families split into 108 and 501 two-gene families with and without evidence for their origin in the WGD 28, respectively (Additional file 1). As another control, we extracted the 143 worm two-gene families, which were identified and tested by Tischler et al. 33 and calculated codon adaptation indices 64(Additional file 1). Results from these controls are consistent with those from the yeast analysis.

We used the FunSpec server 65 and SGD 66 for yeast protein function annotation. The SUPERFAMILY database 39 was used for annotation of ribosomal proteins in yeast. Genes originating from the whole-genome duplication were taken directly from the published paper 28. Characteristics described in Table 2 are obtained from the sources quoted in the table and in Additional file 1. For the ortholog analysis described in Table 5, we extracted information from InParanoid 32, and mapped that against the gene essentiality data described above. Information on yeast two-gene families is presented in Additional file 2.