BACKGROUND
cells and organisms show a remarkable robustness against loss of one or more genes, which has triggered an ongoing discussion on the factors promoting such robustness  <cit> .
one of the simplest and most obvious mechanism for buffering is redundancy produced by gene duplicates  <cit> .
indeed, gene duplication is a major factor shaping prokaryotic and eukaryotic genomes  <cit> .
duplicate genes diverge in their sequence and function  <cit>  and may or may not have the ability to buffer for loss of the respective homolog.
while processes other than buffering by duplicates play important roles in robustness against gene loss, e.g.
use of alternative pathways  <cit> , the relationship between essentiality and the existence of gene duplicates has attracted much attention, and previous work revealed an intricate picture.
for example, estimates of the role of duplicates as backups for gene loss vary widely within and across organisms.
most yeast genes are non-essential, i.e.
dispensable, in rich medium or under standard laboratory conditions .
a study by gu et al.
attributes 23–59% of the dispensability  to buffering by gene duplicates  <cit> , whereas other studies quote a much lower range   <cit> .
only 2% of gene pairs with a synthetic sick or lethal  mutant phenotype in yeast show detectable similarity  <cit> , and amongst the ~20% of mouse genes examined to-date no buffering by duplicates has been observed  <cit> .
several molecular causes may underlie buffering by duplicates, and their relative contributions are still debated.
for example, buffering duplicates lack functional redundancy that would be expected from their backup role.
buffering duplicates in yeast have only partially overlapping expression  <cit>  and genetic interaction profiles  <cit> , suggesting their functions have diverged.
alternative explanations for the bias against duplicates amongst essential genes have been suggested.
for example, it may be disadvantageous for the cell to retain duplicates for genes with severe  knockout phenotypes because this may disrupt their finely balanced expression dosage  <cit> .
further, the correlation between gene expression levels and existence of duplicates suggests buffering for gene loss may only be a by-product of processes that retain duplicates for dosage amplification  <cit> .
despite the availability of several large-scale datasets on single gene knockouts  or knock-downs  as well as double gene-kos for all of these organisms, previous studies mainly focused on single organisms like yeast  <cit> , worm  <cit>  and mouse  <cit> .
major hindrances of a cross-organism comparison are differences in experimental approaches and the specific definition of essentiality used.
the types and numbers of essential genes per organism are influenced by several factors: the mutational strategy  or knockdown), growth of the organism in clonal or mixed populations, life cycle stage of the organism, and, for multi-cellular organisms, whether the whole organism or simply a cell line was targeted.
selection pressure is more stringent in mixed than in clonal populations, and we expect lower survival rates in the former.
for example, a mutant bacterium of decreased fitness may be selected against in a mixed population, but still be able to form an isolated colony.
insertion experiments may result in leaky expression compared to knockout or deletion experiments, and thus identify fewer essential genes.
finally, while rnai experiments in worm have reasonably low false-positive and false-negative rates  <cit> , we would still expect lower degrees of gene essentiality from this knockdown technique than from gene deletions.
to gain further insights into general principles of buffering by gene duplicates, we conducted a comprehensive cross-organism comparison of essentiality and its relationship to gene duplication, analyzing eleven prokaryotic and eukaryotic organisms – m. genitalium, h. pylori, h. influenzae, m. tuberculosis, p. aeruginosa, b. subtilis, e. coli, s. cerevisiae , c. elegans , d. melanogaster , and m. musculus .
to do so, we addressed the above-mentioned challenges in several ways.
when selecting essentiality datasets, we aimed to minimize variation in experimental approaches, and, whenever possible, sampled several organisms for a specific technique .
we tested different definitions of gene duplication, measures of expression levels, and  robustness of the results against removal of genes of the whole-gene duplication  <cit>  and ribosomal genes .
when assessing the contribution of duplicates to survival upon gene-ko/kd, we normalized by the number of essential genes.
differences in technical approaches certainly influence the extent of essentiality detected amongst organisms; however, if duplicates have a buffering role against loss of gene function then this effect should be observable regardless of the exact number of genes identified to be essential.
the table summarizes properties of the eleven organisms in our analysis, such as  the names of the organims; the type of ko/kd experiment; the number of genes tested for their essentiality in gene-ko or kd experiments; the number of genes resulting in lethal phenotypes ; the number of genes with one or more duplicates  amongst the tested genes; the contribution of duplicates to buffering c = p/p - 1; the correlation between p and effective family size of the genes d ; and the correlation between p and distance of a gene to its nearest neighbor , bin size 5).
in the experimental descriptions, 'clones' refers to clonal outgrowth on plates or in cultures; 'population' refers to  population outgrowth in liquid culture.
p-value thresholds of  <dig> ,  <dig> , and  <dig>  are marked with *, **, and ***, respectively.
kd – knockdown; ko – knockout; p – probability of survival; d – effective gene family size
our study reveals heterogeneity of essentiality and the contribution of duplicates to survival that goes beyond what is accountable for by technical differences.
we show that organismal complexity and lifestyle, gene function, function similarity, sequence similarity or the number of duplicates per gene are only weak predictors of the buffering capacity – gene expression levels and related measures are the strongest correlates.
simple relationships with respect to essentiality and gene duplication hold true for some organisms, but not for others.
buffering by duplicates plays a significant but small and heterogeneous role.
RESULTS
the extent of essentiality varies widely amongst organisms
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  <cit>  and c. elegans  <cit> , 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  <cit>  sequence similarity search , and compared survival upon knockout  or knockdown  of genes from these gene families to survival upon ko/kd of singletons .
we estimate gene expression levels by use of the codon bias index .
we define the effective family size d of a target gene as the number of duplicates remaining after ko or kd.
d =  <dig> denotes singletons genes; d ≥  <dig> denotes genes with paralogs.
the probability p is derived from the fraction of genes in a genome which do have one or more duplicates .
we also use the probability p which describes for an organism chances of survival upon gene-deletion; p is derived from the fraction of genes identified as dispensable  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 ' is purely based on outcomes of experiments.
in accordance with the expectation that more complex organisms tend to have more duplicate genes, the fraction of genes with duplicates  increases from m. genitalium and the other bacteria, to yeast and the three animals .
compared to other organisms, mouse has a noticeable depletion of singleton genes  relative to genes with duplicates.
in five organisms, there is a significant increase in the fraction of duplicates  amongst highly expressed genes compared to other genes ; an exception is b. subtilis in which the trend is inverted.
when using codon adaptation index or experimental expression data we obtain similar results .
duplicates increase chances of survival – in some organisms more than in others
to assess the contribution of duplicates to survival following gene-ko/kd we define the buffering capacity c as c = p/p –  <dig>  where p is the probability of survival given the gene does not have additional duplicates, i.e.
is a singleton.
p 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 ; with contributions ranging from  <dig> to 13% .
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 , 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 .
however, only in five organisms , 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 ; 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 .
further correlates of buffering capacity
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  with both the number of duplicates available per gene and with the distance of the gene to the nearest homolog .
these correlations have been observed previously in worm  <cit> , but are not common amongst the organisms of our study.
yeast has a decent correlation with distance to the nearest homology , 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  <cit> , or when focusing on highly expressed genes .
yeast is particularly enriched in two-gene families  which buffer for each other .
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 .
two-gene families as model for buffering by duplicates
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 ~ <dig>  yeast gene pairs tested for double-ko phenotypes tested in large- and small-scale screens  <cit> , we identified  <dig> two-gene families with genetic interactions  and eight two-gene families with a viable double-ko phenotype .
these two-gene families represent prime candidates for comparing characteristics of buffering and non-buffering duplicates, respectively.
table  <dig> and additional file  <dig> describe their properties tested across and between the genes.
there are also another  <dig> two-gene families in yeast which have not been tested in double-ko experiments; additional file  <dig> describes their characteristics.
the table lists a selection of characteristics tested for the two sets of buffering and non-buffering yeast two-gene families, respectively.
also see table  <dig> for description of the data.
a small number of characteristics could also be tested for worm two-gene families, identified in published work  <cit> .
due to multiple hypothesis testing, a t-score >  <dig>  should be considered significant at an adjusted p-value of  <dig>  ; significant scores are marked with *.
an e-value of '0' signifies an e-value that is smaller than 10- <dig>
both buffering and non-buffering two-gene families are defined by the same e-value threshold ; however, buffering genes have significantly higher sequence identity between the members .
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  – 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  <cit> : buffering genes had slightly shorter paths between each other than non-buffering genes , 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  <cit> , 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 .
the lack of similarity of genetic interaction profiles between buffering genes is consistent with recent findings by ihmels et al.
<cit>  although these authors included epistatic interactions other than lethal double-ko phenotypes in their analysis.
two-gene families and their phenotypes in double-kos are a good model for buffering by gene duplicates.
we distinguish between 'buffering genes' , i. e. gene pairs resulting in a synthetic sick or lethal  phenotype upon double-ko; and 'non-buffering genes' , i. e. gene pairs that result in a viable phenotype upon double gene-ko, and which are thus unlikely to buffer for each other in single gene-ko.
tables  <dig> and  <dig> list the functions of a subset of buffering and all eight non-buffering gene pairs, respectively, with one pair per row.
the ten buffering gene pairs in this table originate from the same large-scale screens as the eight non-buffering pairs in table  <dig>  the remaining  <dig> buffering gene pairs originate from small-scale screens, and are listed in the additional file  <dig>  the descriptions of functions are taken from sgd  <cit> .
buffering genes  are more often described as having identical functions than non-buffering genes .
see table  <dig> for description.
tables  <dig> and  <dig> list the functions of a subset of buffering and all eight non-buffering gene pairs, respectively, with one pair per row.
the descriptions of functions are taken from sgd  <cit> .
buffering genes  are more often described as having identical functions than non-buffering genes .
buffering and non-buffering genes show clear differences in terms of transcriptional and translational regulation .
buffering genes have higher mrna and protein expression levels.
measures of translation efficiency, e.g.
protein length, molecular weight, codon adaptation index , or protein production rate, are significantly elevated in buffering genes compared to non-buffering ones ; protein degradation is slightly decreased.
interestingly, some of these measures  are significantly more different between members of a buffering gene pair than between members of a non-buffering gene pair .
we also extracted orthologs of the buffering and non-buffering yeast two-gene families in fly, worm and mouse using inparanoid  <cit> .
.
if a buffering gene pair in yeast has a single-gene ortholog in another organism , 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 .
there are several examples of essential single orthologs of buffering gene pairs: hmg <dig> and hmg <dig> are isozymes of hmg-coa reductase in yeast  and their double ko phenotype is lethal.
the genes have one ortholog in worm  and one in mouse  which both have embryonic lethal ko/kd phenotypes.
ssf <dig> and ssf <dig> are yeast proteins required for ribosomal large subunit maturation , and they have single essential orthologs in worm  and fly .
this table lists the number of instances in which for the buffering and non-buffering yeast two-gene families, respectively, single or multiple orthologs were found in fly, worm or mouse and their ko-phenotype if known.
also see table  <dig> for description of the data.
orthologs are divided into single-gene orthologs  and multi-gene orthologs .
single- or multi-gene orthologs can be essential or non-essential in the other organism.
for further validation, we extracted the  <dig> worm two-gene families tested in double-rnai knockdowns  <cit>  which consist of  <dig> pairs of synthetic sick or lethal  phenotypes, i.e.
buffering duplicates, and  <dig> 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 .
buffering genes are more efficiently translated than non-buffering genes.
noticeably, yeast is enriched for buffering gene pairs  vs. non-buffering gene pairs  compared to worm .
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  <cit> .
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.
CONCLUSIONS
our study provides a systematic and semi-quantitative assessment of essentiality and gene duplication across eleven prokaryotic and eukaryotic organisms revealing a heterogeneous picture.
to the best of our knowledge, this is the first such organism-wide comparison.
chances of survival upon gene deletion are very high in most organisms , i.e.
there are only few essential genes .
we observe some variation in survival that cannot be explained by experimental differences alone.
the bacteria in our dataset have been analyzed come from different experimental backgrounds .
for example, screens of mixed populations with random gene insertions identify more essential genes than clonal studies, e.g.
h. pylori, h. influenzae, and m. tuberculosis vs. p. aeruginosa, b. subtilis and e. coli ; however, there is no general trend.
the extremely high chances of survival in fly  can be  attributed to the use of a cell line rather than the whole organism and of rnai knockdowns instead of full gene deletion  <cit> , and may be an underestimate due to current technical limitations.
however, in worm, the same technique, rnai-kds, on the whole organism also produced high survival rates, but a much higher contribution of duplicates to survival .
the low chances of survival in mouse are likely due to the mouse dataset not originating from a large-scale screen, but from individual experiments that may have preferentially targeted and reported essential genes.
for example, the gene targets in the mouse dataset are strongly enriched for orthologs of human disease genes ; thus the dataset is biased.
the lack of buffering by duplicate genes in mouse has been demonstrated recently  <cit> ; however, with the availability of an unbiased large-scale essentiality screen in mouse these results may be refined.
the degree of gene essentiality  can be influenced by the experimental technique and the definition of essentiality that is used.
in contrast, if duplicates contribute to survival upon gene loss, then this effect should be detectable irrespective of the number of essential and non-essential genes identified .
in other words, we expect buffering by duplicates to be less dependent on technical differences than essentiality alone.
we introduced statistical tests to assess the significance of buffering by duplicates .
a small p-value implies that duplicates are significantly enriched amongst non-essential genes compared to random and vice versa.
thus, for example, h. pylori has only few genes with duplicates , but these duplicates exhibit a significant contribution to survival upon gene knockout .
likewise, b. subtilis and e. coli have similar degrees of gene essentiality , and similar fractions of duplicate genes, but very different contributions of these duplicates to survival.
duplicates significantly and positively contribute to survival in nine of the eleven organisms, but have noticeable effects only in six .
given that duplicates make up to 80% of eukaryotic genomes , the small contribution is surprising and points to dominant roles of other buffering processes, such as rerouting metabolic flux .
buffering by duplicates is uncorrelated with organismal complexity.
buffering capacity varies widely amongst bacteria and eukaryotes, even when accounting for differences in experimental approaches .
m. genitalium, h. influenzae, b. subtilis, fly and mouse show low or even negative contributions of duplicates to buffering; h. pylori, yeast and worm show the highest.
m. genitalium is a parasite with a small range of host- or tissue-specific living conditions  <cit>  and a very small genome  <cit> .
its low rate of survival upon gene-ko could be explained by the low number of duplicate genes and the lack of condition-specific dispensability of genes which boost survival rates under normal conditions  <cit> .
however, the same reasoning could apply to h. pylori and h. influenzae which have genome sizes similar to m. genitalium and restricted living conditions, but have much higher survival rates and different buffering capacities of duplicates.
mouse represents an exception in the analysis by having relatively low survival rates , a higher ratio of duplicates vs. singletons than other organisms , but a negative contribution of duplicates to survival .
as explained above, conclusions in mouse may be refined later.
next we examined gene characteristics which have been suggested to influence buffering capacity.
for example, we would expect duplicates of high sequence proximity  to be more likely to buffer for loss of function than duplicates that diverged in their sequence.
similarly, we would expect genes with many duplicates  to be more likely to be buffered for loss of function than genes of small families.
both expectations are fulfilled in only some of the organisms , e.g.
in the two most thoroughly studied organisms yeast and worm, but not in others.
related to sequence similarity is function, which is more dissimilar amongst buffering duplicates than naively expected, when measured in terms of expression regulation  <cit>  and genetic interactions  <cit> .
when evaluating function similarity in terms of verbal descriptions, shortest path length in a network of functional relationships, and in terms of similarity of their ko-phenotype and physical interaction vectors, buffering genes were slightly  more similar to each other in function than non-buffering genes .
thus, function similarity is also only a weak indicator of buffering capacity of duplicates.
the single best correlate of buffering capacity by gene duplicates  is expression level.
genes of high expression levels tend to have more duplicates, but these duplicates are also more likely to buffer for loss of the gene's function.
the trend holds true for all organisms with positive buffering capacity  and for different measures of expression levels .
for example, in highly expressed genes in e. coli, c increases to 23%.
likewise, buffering two-gene families in yeast have higher mrna and protein abundance than non-buffering two-gene families, higher transcription and translation rates and smaller protein degradation rates .
in sum, buffering by gene duplicates only plays a significant and visible role in robustness against gene loss in some organisms but not in others.
factors influencing such buffering are, in decreasing order of approximate importance, gene expression levels, sequence distance between duplicates, the number of duplicates available per gene, the gene's function and the type of organism and its lifestyle.
such ranking holds true despite differences in experimental approaches.
the lack of consistency across organisms, lack of strong correlates and low extent of buffering by duplicates suggests that buffering by duplicates is indeed merely a by-product of other processes.
genes with high expression levels are more likely to be essential  <cit>  and have increased duplicate retention rates  <cit> .
these duplicates thus likely function to amplify gene dosage  <cit> , which is supported by their tendency to be co-expressed  <cit> .
our analysis shows that only in relatively few cases these duplicates serve as backup for the loss of gene function.

 cells and organisms show a remarkable robustness against loss of one or more genes, which has triggered an ongoing discussion on the factors promoting such robustness. one of the simplest and most obvious mechanism for buffering is redundancy produced by gene duplicates. indeed, gene duplication is a major factor shaping prokaryotic and eukaryotic genomes. duplicate genes diverge in their sequence and function and may or may not have the ability to buffer for loss of the respective homolog. while processes other than buffering by duplicates play important roles in robustness against gene loss, e.g. use of alternative pathways, the relationship between essentiality and the existence of gene duplicates has attracted much attention, and previous work revealed an intricate picture. for example, estimates of the role of duplicates as backups for gene loss vary widely within and across organisms. most yeast genes are non-essential, i.e. dispensable, in rich medium or under standard laboratory conditions. a study by gu et al. attributes 23–59% of the dispensability to buffering by gene duplicates, whereas other studies quote a much lower range. only 2% of gene pairs with a synthetic sick or lethal mutant phenotype in yeast show detectable similarity, and amongst the ~20% of mouse genes examined to-date no buffering by duplicates has been observed. several molecular causes may underlie buffering by duplicates, and their relative contributions are still debated. for example, buffering duplicates lack functional redundancy that would be expected from their backup role. buffering duplicates in yeast have only partially overlapping expression and genetic interaction profiles, suggesting their functions have diverged. alternative explanations for the bias against duplicates amongst essential genes have been suggested. for example, it may be disadvantageous for the cell to retain duplicates for genes with severe knockout phenotypes because this may disrupt their finely balanced expression dosage. further, the correlation between gene expression levels and existence of duplicates suggests buffering for gene loss may only be a by-product of processes that retain duplicates for dosage amplification. despite the availability of several large-scale datasets on single gene knockouts or knock-downs as well as double gene-kos for all of these organisms, previous studies mainly focused on single organisms like yeast, worm and mouse. major hindrances of a cross-organism comparison are differences in experimental approaches and the specific definition of essentiality used. the types and numbers of essential genes per organism are influenced by several factors: the mutational strategy or knockdown), growth of the organism in clonal or mixed populations, life cycle stage of the organism, and, for multi-cellular organisms, whether the whole organism or simply a cell line was targeted. selection pressure is more stringent in mixed than in clonal populations, and we expect lower survival rates in the former. for example, a mutant bacterium of decreased fitness may be selected against in a mixed population, but still be able to form an isolated colony. insertion experiments may result in leaky expression compared to knockout or deletion experiments, and thus identify fewer essential genes. finally, while rnai experiments in worm have reasonably low false-positive and false-negative rates, we would still expect lower degrees of gene essentiality from this knockdown technique than from gene deletions. to gain further insights into general principles of buffering by gene duplicates, we conducted a comprehensive cross-organism comparison of essentiality and its relationship to gene duplication, analyzing eleven prokaryotic and eukaryotic organisms – m. genitalium, h. pylori, h. influenzae, m. tuberculosis, p. aeruginosa, b. subtilis, e. coli, s. cerevisiae, c. elegans, d. melanogaster, and m. musculus. to do so, we addressed the above-mentioned challenges in several ways. when selecting essentiality datasets, we aimed to minimize variation in experimental approaches, and, whenever possible, sampled several organisms for a specific technique. we tested different definitions of gene duplication, measures of expression levels, and robustness of the results against removal of genes of the whole-gene duplication and ribosomal genes. when assessing the contribution of duplicates to survival upon gene-ko/kd, we normalized by the number of essential genes. differences in technical approaches certainly influence the extent of essentiality detected amongst organisms; however, if duplicates have a buffering role against loss of gene function then this effect should be observable regardless of the exact number of genes identified to be essential. the table summarizes properties of the eleven organisms in our analysis, such as the names of the organims; the type of ko/kd experiment; the number of genes tested for their essentiality in gene-ko or kd experiments; the number of genes resulting in lethal phenotypes; the number of genes with one or more duplicates amongst the tested genes; the contribution of duplicates to buffering c = p/p - 1; the correlation between p and effective family size of the genes d; and the correlation between p and distance of a gene to its nearest neighbor, bin size 5). in the experimental descriptions,'clones' refers to clonal outgrowth on plates or in cultures;'population' refers to population outgrowth in liquid culture. p-value thresholds of,, and are marked with *, **, and ***, respectively. kd – knockdown; ko – knockout; p – probability of survival; d – effective gene family size our study reveals heterogeneity of essentiality and the contribution of duplicates to survival that goes beyond what is accountable for by technical differences. we show that organismal complexity and lifestyle, gene function, function similarity, sequence similarity or the number of duplicates per gene are only weak predictors of the buffering capacity – gene expression levels and related measures are the strongest correlates. simple relationships with respect to essentiality and gene duplication hold true for some organisms, but not for others. buffering by duplicates plays a significant but small and heterogeneous role.  the extent of essentiality varies widely amongst organisms 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 and c. elegans, 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 sequence similarity search, and compared survival upon knockout or knockdown of genes from these gene families to survival upon ko/kd of singletons. we estimate gene expression levels by use of the codon bias index. we define the effective family size d of a target gene as the number of duplicates remaining after ko or kd. d = denotes singletons genes; d ≥ denotes genes with paralogs. the probability p is derived from the fraction of genes in a genome which do have one or more duplicates. we also use the probability p which describes for an organism chances of survival upon gene-deletion; p is derived from the fraction of genes identified as dispensable 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' is purely based on outcomes of experiments. in accordance with the expectation that more complex organisms tend to have more duplicate genes, the fraction of genes with duplicates increases from m. genitalium and the other bacteria, to yeast and the three animals. compared to other organisms, mouse has a noticeable depletion of singleton genes relative to genes with duplicates. in five organisms, there is a significant increase in the fraction of duplicates amongst highly expressed genes compared to other genes; an exception is b. subtilis in which the trend is inverted. when using codon adaptation index or experimental expression data we obtain similar results. duplicates increase chances of survival – in some organisms more than in others to assess the contribution of duplicates to survival following gene-ko/kd we define the buffering capacity c as c = p/p – where p is the probability of survival given the gene does not have additional duplicates, i.e. is a singleton. p 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; with contributions ranging from to 13%. 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, 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. however, only in five organisms, 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; 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. further correlates of buffering capacity 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 with both the number of duplicates available per gene and with the distance of the gene to the nearest homolog. these correlations have been observed previously in worm, but are not common amongst the organisms of our study. yeast has a decent correlation with distance to the nearest homology, 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, or when focusing on highly expressed genes. yeast is particularly enriched in two-gene families which buffer for each other. 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. two-gene families as model for buffering by duplicates 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 ~ yeast gene pairs tested for double-ko phenotypes tested in large- and small-scale screens, we identified two-gene families with genetic interactions and eight two-gene families with a viable double-ko phenotype. these two-gene families represent prime candidates for comparing characteristics of buffering and non-buffering duplicates, respectively. table and additional file describe their properties tested across and between the genes. there are also another two-gene families in yeast which have not been tested in double-ko experiments; additional file describes their characteristics. the table lists a selection of characteristics tested for the two sets of buffering and non-buffering yeast two-gene families, respectively. also see table for description of the data. a small number of characteristics could also be tested for worm two-gene families, identified in published work. due to multiple hypothesis testing, a t-score > should be considered significant at an adjusted p-value of; significant scores are marked with *. an e-value of'0' signifies an e-value that is smaller than 10- both buffering and non-buffering two-gene families are defined by the same e-value threshold; however, buffering genes have significantly higher sequence identity between the members. 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 – 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: buffering genes had slightly shorter paths between each other than non-buffering genes, 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, 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. the lack of similarity of genetic interaction profiles between buffering genes is consistent with recent findings by ihmels et al. although these authors included epistatic interactions other than lethal double-ko phenotypes in their analysis. two-gene families and their phenotypes in double-kos are a good model for buffering by gene duplicates. we distinguish between'buffering genes', i. e. gene pairs resulting in a synthetic sick or lethal phenotype upon double-ko; and'non-buffering genes', i. e. gene pairs that result in a viable phenotype upon double gene-ko, and which are thus unlikely to buffer for each other in single gene-ko. tables and list the functions of a subset of buffering and all eight non-buffering gene pairs, respectively, with one pair per row. the ten buffering gene pairs in this table originate from the same large-scale screens as the eight non-buffering pairs in table the remaining buffering gene pairs originate from small-scale screens, and are listed in the additional file the descriptions of functions are taken from sgd. buffering genes are more often described as having identical functions than non-buffering genes. see table for description. tables and list the functions of a subset of buffering and all eight non-buffering gene pairs, respectively, with one pair per row. the descriptions of functions are taken from sgd. buffering genes are more often described as having identical functions than non-buffering genes. buffering and non-buffering genes show clear differences in terms of transcriptional and translational regulation. buffering genes have higher mrna and protein expression levels. measures of translation efficiency, e.g. protein length, molecular weight, codon adaptation index, or protein production rate, are significantly elevated in buffering genes compared to non-buffering ones; protein degradation is slightly decreased. interestingly, some of these measures are significantly more different between members of a buffering gene pair than between members of a non-buffering gene pair. we also extracted orthologs of the buffering and non-buffering yeast two-gene families in fly, worm and mouse using inparanoid.. if a buffering gene pair in yeast has a single-gene ortholog in another organism, 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. there are several examples of essential single orthologs of buffering gene pairs: hmg and hmg are isozymes of hmg-coa reductase in yeast and their double ko phenotype is lethal. the genes have one ortholog in worm and one in mouse which both have embryonic lethal ko/kd phenotypes. ssf and ssf are yeast proteins required for ribosomal large subunit maturation, and they have single essential orthologs in worm and fly. this table lists the number of instances in which for the buffering and non-buffering yeast two-gene families, respectively, single or multiple orthologs were found in fly, worm or mouse and their ko-phenotype if known. also see table for description of the data. orthologs are divided into single-gene orthologs and multi-gene orthologs. single- or multi-gene orthologs can be essential or non-essential in the other organism. for further validation, we extracted the worm two-gene families tested in double-rnai knockdowns which consist of pairs of synthetic sick or lethal phenotypes, i.e. buffering duplicates, and 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. buffering genes are more efficiently translated than non-buffering genes. noticeably, yeast is enriched for buffering gene pairs vs. non-buffering gene pairs compared to worm. 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. 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.  our study provides a systematic and semi-quantitative assessment of essentiality and gene duplication across eleven prokaryotic and eukaryotic organisms revealing a heterogeneous picture. to the best of our knowledge, this is the first such organism-wide comparison. chances of survival upon gene deletion are very high in most organisms, i.e. there are only few essential genes. we observe some variation in survival that cannot be explained by experimental differences alone. the bacteria in our dataset have been analyzed come from different experimental backgrounds. for example, screens of mixed populations with random gene insertions identify more essential genes than clonal studies, e.g. h. pylori, h. influenzae, and m. tuberculosis vs. p. aeruginosa, b. subtilis and e. coli; however, there is no general trend. the extremely high chances of survival in fly can be attributed to the use of a cell line rather than the whole organism and of rnai knockdowns instead of full gene deletion, and may be an underestimate due to current technical limitations. however, in worm, the same technique, rnai-kds, on the whole organism also produced high survival rates, but a much higher contribution of duplicates to survival. the low chances of survival in mouse are likely due to the mouse dataset not originating from a large-scale screen, but from individual experiments that may have preferentially targeted and reported essential genes. for example, the gene targets in the mouse dataset are strongly enriched for orthologs of human disease genes; thus the dataset is biased. the lack of buffering by duplicate genes in mouse has been demonstrated recently; however, with the availability of an unbiased large-scale essentiality screen in mouse these results may be refined. the degree of gene essentiality can be influenced by the experimental technique and the definition of essentiality that is used. in contrast, if duplicates contribute to survival upon gene loss, then this effect should be detectable irrespective of the number of essential and non-essential genes identified. in other words, we expect buffering by duplicates to be less dependent on technical differences than essentiality alone. we introduced statistical tests to assess the significance of buffering by duplicates. a small p-value implies that duplicates are significantly enriched amongst non-essential genes compared to random and vice versa. thus, for example, h. pylori has only few genes with duplicates, but these duplicates exhibit a significant contribution to survival upon gene knockout. likewise, b. subtilis and e. coli have similar degrees of gene essentiality, and similar fractions of duplicate genes, but very different contributions of these duplicates to survival. duplicates significantly and positively contribute to survival in nine of the eleven organisms, but have noticeable effects only in six. given that duplicates make up to 80% of eukaryotic genomes, the small contribution is surprising and points to dominant roles of other buffering processes, such as rerouting metabolic flux. buffering by duplicates is uncorrelated with organismal complexity. buffering capacity varies widely amongst bacteria and eukaryotes, even when accounting for differences in experimental approaches. m. genitalium, h. influenzae, b. subtilis, fly and mouse show low or even negative contributions of duplicates to buffering; h. pylori, yeast and worm show the highest. m. genitalium is a parasite with a small range of host- or tissue-specific living conditions and a very small genome. its low rate of survival upon gene-ko could be explained by the low number of duplicate genes and the lack of condition-specific dispensability of genes which boost survival rates under normal conditions. however, the same reasoning could apply to h. pylori and h. influenzae which have genome sizes similar to m. genitalium and restricted living conditions, but have much higher survival rates and different buffering capacities of duplicates. mouse represents an exception in the analysis by having relatively low survival rates, a higher ratio of duplicates vs. singletons than other organisms, but a negative contribution of duplicates to survival. as explained above, conclusions in mouse may be refined later. next we examined gene characteristics which have been suggested to influence buffering capacity. for example, we would expect duplicates of high sequence proximity to be more likely to buffer for loss of function than duplicates that diverged in their sequence. similarly, we would expect genes with many duplicates to be more likely to be buffered for loss of function than genes of small families. both expectations are fulfilled in only some of the organisms, e.g. in the two most thoroughly studied organisms yeast and worm, but not in others. related to sequence similarity is function, which is more dissimilar amongst buffering duplicates than naively expected, when measured in terms of expression regulation and genetic interactions. when evaluating function similarity in terms of verbal descriptions, shortest path length in a network of functional relationships, and in terms of similarity of their ko-phenotype and physical interaction vectors, buffering genes were slightly more similar to each other in function than non-buffering genes. thus, function similarity is also only a weak indicator of buffering capacity of duplicates. the single best correlate of buffering capacity by gene duplicates is expression level. genes of high expression levels tend to have more duplicates, but these duplicates are also more likely to buffer for loss of the gene's function. the trend holds true for all organisms with positive buffering capacity and for different measures of expression levels. for example, in highly expressed genes in e. coli, c increases to 23%. likewise, buffering two-gene families in yeast have higher mrna and protein abundance than non-buffering two-gene families, higher transcription and translation rates and smaller protein degradation rates. in sum, buffering by gene duplicates only plays a significant and visible role in robustness against gene loss in some organisms but not in others. factors influencing such buffering are, in decreasing order of approximate importance, gene expression levels, sequence distance between duplicates, the number of duplicates available per gene, the gene's function and the type of organism and its lifestyle. such ranking holds true despite differences in experimental approaches. the lack of consistency across organisms, lack of strong correlates and low extent of buffering by duplicates suggests that buffering by duplicates is indeed merely a by-product of other processes. genes with high expression levels are more likely to be essential and have increased duplicate retention rates. these duplicates thus likely function to amplify gene dosage, which is supported by their tendency to be co-expressed. our analysis shows that only in relatively few cases these duplicates serve as backup for the loss of gene function. 
given that duplicates make up to 80% of eukaryotic genomes, the small contribution is surprising and points to dominant roles of other buffering processes, such as alternative metabolic pathways. this heterogeneity goes beyond what would be expected from differences in experimental approaches alone. the buffering capacity of duplicates appears to be independent of the degree of gene essentiality and tends to be higher for genes with high expression levels. one mechanism to account for robustness against gene knockouts or knockdowns is through buffering by gene duplicates, but the extent and general correlates of this process in organisms is still a matter of debate. sequence similarity and the number of duplicates per gene are weak predictors of the duplicate's buffering capacity. for example, buffering capacity increases to 23% amongst highly expressed genes in e. coli. in a case study we show that buffering gene duplicates in yeast and worm are somewhat more similar in their functions than non-buffering duplicates and have increased transcriptional and translational activity. to reveal general trends of this process, we provide a comprehensive comparison of gene essentiality, duplication and buffering by duplicates across seven bacteria, and four eukaryotes, caenorhabditis elegans, drosophila melanogaster, mus musculus ). in sum, the extent of gene essentiality and buffering by duplicates is not conserved across organisms and does not correlate with the organisms' apparent complexity. in nine of the eleven organisms, duplicates significantly increase chances of survival upon gene deletion, but only by up to 13%.
 one mechanism to account for robustness against gene knockouts or knockdowns is through buffering by gene duplicates, but the extent and general correlates of this process in organisms is still a matter of debate. to reveal general trends of this process, we provide a comprehensive comparison of gene essentiality, duplication and buffering by duplicates across seven bacteria, and four eukaryotes, caenorhabditis elegans, drosophila melanogaster, mus musculus ).  in nine of the eleven organisms, duplicates significantly increase chances of survival upon gene deletion, but only by up to 13%. given that duplicates make up to 80% of eukaryotic genomes, the small contribution is surprising and points to dominant roles of other buffering processes, such as alternative metabolic pathways. the buffering capacity of duplicates appears to be independent of the degree of gene essentiality and tends to be higher for genes with high expression levels. for example, buffering capacity increases to 23% amongst highly expressed genes in e. coli. sequence similarity and the number of duplicates per gene are weak predictors of the duplicate's buffering capacity. in a case study we show that buffering gene duplicates in yeast and worm are somewhat more similar in their functions than non-buffering duplicates and have increased transcriptional and translational activity.  in sum, the extent of gene essentiality and buffering by duplicates is not conserved across organisms and does not correlate with the organisms' apparent complexity. this heterogeneity goes beyond what would be expected from differences in experimental approaches alone. buffering by duplicates contributes to robustness in several organisms, but to a small extent – and the relatively large amount of buffering by duplicates observed in yeast and worm may be largely specific to these organisms. thus, the only common factor of buffering by duplicates between different organisms may be the by-product of duplicate retention due to demands of high dosage. 