BACKGROUND
the discovery of rna interference  has been an important breakthrough in biology in the past years  <cit> .
although rnai-related phenomena have been described for decades  <cit> , it is only recently that the silencing mechanism has been understood at the molecular level  <cit> .
in caenorhabditis elegans, fire and colleagues described rnai as a sequence-specific gene-silencing event based on the introduction of a double-stranded rna  template having sequence similarity with the targeted messenger rna  <cit> .
since then, the rnai pathway has been shown to be conserved in a wide variety of eukaryotic organisms  <cit> .
the physiological functions of rnai range from immune response by degradation of exogenous genetic material  <cit>  to development by regulation of gene expression  <cit> .
in recent years, rnai has been extensively used as an experimental tool for the analysis of gene function  <cit> .
as our understanding of the underlying molecular machinery improves, the potential use of rnai for therapy is becoming more evident  <cit> .
in the rnai pathway, long dsrnas or short hairpin rnas are processed and digested into small interfering rnas  by dicer, an rnase iii family member  <cit> .
after incorporation of the sirna in the rna-induced silencing complex, the sirna-protein complex degrades mrnas having sequence complementarity to the sirna  <cit> .
interestingly, the rnai machinery has also been shown to mediate translational repression or induce chromatin modification  <cit> .
since interference is based on sequence recognition, targeting a gene by rnai can give rise to the silencing of another gene with similar sequence  <cit> .
this phenomenon is referred to as off-target effect or cross-reaction and can occur through mrna degradation or through translational repression  <cit> .
although rnai phenotypes are generally assumed to be due to the sole knock-down of the targeted gene, they can also be due to multi-gene silencing.
numerous genome-wide rnai analyses have been performed, e.g., for c. elegans  <cit>  and drosophila melanogaster  <cit> .
due to the issue of cross-reaction, rnai data should be filtered prior to their analysis.
in addition, accurate knowledge of rnai specificity is critical when considering the use of rnai as a therapeutic technology  <cit> .
in this context, it is crucial to know how much similarity is necessary to observe rnai off-target cross-reaction.
to assess identity requirements for rna interference in c. elegans, parrish et al.
<cit>  used a series of altered gfp coding regions with different degrees of similarity to the transgene target.
they found effective interference with dsrnas  that were 96% identical to the target sequence , less effective interference with a trigger that was 88% identical , and no interference with dsrna triggers that were 78% identical to the target .
different studies based on mrna expression profile analysis led to contradictory conclusions regarding rnai target specificity  <cit> .
for c. elegans rnai data, fraser et al.
<cit>  used  <dig> nt with 80% identity as a threshold.
interestingly, in silico examination of potential cross-reaction as a function of sirna length led to the conclusion that target specificity and low probability of off-target effects were optimally balanced for sirnas of  <dig> nucleotides  <cit> .
finally, for data repositories such as rnaidb  <cit> , tools have been developed for analysis and visualization of the rnai data as well as their potential risk of "contamination".
although these experiments give some indication of the sequence identity requirement, the question of how much similarity over how much length is necessary to observe off-target cross-reaction remains open.
RESULTS
using the rnai phenotypes of paralogous genes in c. elegans, we devised a strategy to estimate the minimum degree of similarity needed to observe off-target effects.
hereafter, any gene that exhibits any kind of rnai phenotype will be further referred to as a "ph gene" without further consideration of the phenotypic details.
similarly, any gene that was targeted by one or more rnai experiments and for which no phenotype is described will be defined as a "wt gene".
we extracted all  <dig> pairs of strict duplicates  for which both copies were targeted by rnai .
these pairs can be sorted according to the phenotypic class of both members:  <dig>  "wt/wt" pairs consist of two wt genes,  <dig>  "ph/ph" pairs of two ph genes and the remaining  <dig>  "wt/ph" pairs have one wt member and one ph member.
in order to predict whether these duplicates exhibit off-target cross-reaction, we elaborated a model where all duplicates are subject to off-target cross-reaction.
in this model:
a) the probability of occurrence of ph/ph duplicate pairs is the same as the probability of occurrence of ph genes within singletons .
the probability of a gene to be duplicated and further preserved being only very weakly correlated with the phenotypic class a gene , therefore, if at least one copy of the pair inherits the phenotypic class of their ancestral gene, we expect this first assumption to be true.
b) some ph genes are annotated as wt genes due to the important fraction of false negatives.
actually, the fraction of false negative in large-scale rnai experiments can be as high as  <dig>  but the fraction of false positive is extremely low.
in our dataset, we estimate the fraction of false negatives to be  <dig>  .
c) both genes in a duplicate pair give rise to the same rnai phenotype.
this last assumption seems reasonable when off-target cross-reaction happens, since the targeting of one copy would also knock down the other copy.
under such a model, we expect  <dig>  of ph/ph pairs,  <dig>  of wt/ph pairs and of  <dig>  wt/wt pairs.
we then computed the probability  of the entire set of  <dig> duplicate pairs to fit our model.
we observed that the fractions of wt/wt, wt/ph and ph/ph of the entire set of pairs do not fit our model .
from this result, we concluded that not all duplicates exhibit off-target effects.
this result is expected because only very similar duplicates should exhibit off-target cross-reaction.
accordingly, we sorted the pairs using the degree of sequence similarity between the genes and the corresponding rnai clones .
since we did not want to assume a sequence length for off-target cross-reaction, we chose to estimate the percentage identity over several lengths, i.e., over  <dig>   <dig>   <dig>   <dig> or  <dig> nucleotides.
sixteen out of the  <dig> pairs had at least one of their genes longer than  <dig> kb and identity were not estimated because of memory consumption.
for each selected length, we grouped the pairs according to their percentage identity.
for each group, we counted the number of wt/wt, wt/ph and ph/ph pairs and estimated the corresponding likelihood of these observed counts to fit the model of complete off-target cross-reaction.
the higher the likelihood, the higher the chance this group is sensitive to off-target effects.
results  show that only genes having high degree of sequence similarity with the rnai clones, i.e., 100% over  <dig> nt, ≥94% over  <dig> nt, ≥89% over  <dig> nt, ≥84% over  <dig> nt and ≥81% over  <dig> nt, fit well with the model .
this strongly suggests that off-target effects occur when the percentage identity exceeds these thresholds.
as sequence identity decreases, the likelihood of the data to fit the model decreases as well, illustrating the weaker effect of off-target.
to better understand sequence recognition requirements of the rnai machinery, we looked for the minimum length of high-similarity stretch between the dsrna and its target necessary to observe efficient rna interference.
more precisely, we calculated the minimal length over which sequence similarity is necessary to have a high likelihood to observe off-target cross-reaction.
this is not a trivial problem because pairs that are very similar to the rnai clone over  <dig> nt are usually also very similar over  <dig> nt .
consequently, to address this question of minimal length, we selected pairs whose maximum percentage identity with the rnai clones is above the threshold over  <dig> nt  and, in the same time, below the threshold over  <dig> nt .
if such pairs exhibit a high likelihood of off-target cross-reaction, it suggests that having 100% identity over  <dig> nt is sufficient to observe off-target effects.
on the other hand, if this likelihood is low, it suggests that having 100% identity over  <dig> nt is not sufficient to observe off-target effects.
out of  <dig> such pairs,  <dig> are wt/wt,  <dig> are wt/ph and none are ph/ph.
the corresponding likelihood is relatively low , suggesting that these pairs may be not subject to off-target cross-reaction and that the minimum length may be more than  <dig> nt.
to compute more precisely the minimum length on which a high identity is necessary to observe off-target cross-reaction, we applied the same strategy to compare  <dig> nt with  <dig> nt,  <dig> nt with  <dig> nt, etc.
results  show that the data fit well the model  for pairs with high identity on  <dig> nt only .
on the contrary, pairs with high identity on  <dig> nt only or on  <dig> nt only fit poorly the model .
keeping in mind that our analysis is performed with limited amount of data, it suggests that dsrna having sequence similarity over  <dig> to  <dig> nucleotides  are optimal to observe efficient off-target cross-reaction and, by extrapolation, rnai in c. elegans.
it is important to distinguish between "the minimum length of the dsrna" and "the minimum length of high-similarity stretch between the dsrna and its target" necessary to observe an efficient rnai effect.
our analysis studies the later one.
our results do not imply that, overall, 30– <dig> nt dsrnas are the most efficient in an rnai experiment.
on the contrary, in c. elegans, long dsrna molecules tend to be much more efficient than small dsrna molecules for reasons not only related to the interaction with the target mrna but also to the initiation of the systemic effect and amplification of the rnai effect.
here our results suggest that a stretch of 30– <dig> nt of high similarity inside the dsrna molecule is sufficient to observe an efficient rnai.
a systematic experimental analysis of the minimum length of the dsrna molecule having a 30– <dig> nt stretch of high similarity with targeted gene would complement our study.
moreover, we would like to mention that our results are based on the assumption that only one stretch of high similarity is necessary to observe off-target reaction.
therefore, our method does not assess whether one or multiple stretches of high similarity are necessary.
our estimated range is in agreement with the current molecular model of the rnai machinery.
indeed, for each dsrna molecule having one fragment of  <dig> nucleotides identity with the targeted mrna, the chance to have an sirna of exactly  <dig> nucleotides identity with the same mrna after dicer processing is one out of  <dig>  however, for dsrna molecule having one fragment of  <dig> nucleotides identity with the targeted mrna, the chance to have an sirna of exactly  <dig> nucleotides identity with the same mrna after dicer processing is 100%.
to date, in mammalian cells, a typical rnai experiment is performed by using conventional 21-mer synthetic rna duplexes.
in addition to the limitation of using long dsrna triggers that can induce the non-specific interferon response, the choice of 21-mer long dsrnas as rnai triggers was mainly guided by the observation that 21-mer sirnas are key players in the rnai machinery   <cit> .
however, recent studies demonstrate that, in mammalian cells, synthetic rna duplexes 25– <dig> nucleotides in length can be up to 100-fold more potent than corresponding conventional 21-mer sirnas  <cit> .
the enhanced efficiency is attributed to the fact that longer dsrnas are substrates of dicer .
indeed, dicer would directly link the production of sirnas to their incorporation in the risc complex  <cit> .
likewise, although sirnas are ~ <dig> nucleotides long in c. elegans, our results suggest that sequences with similarity to the target mrna over a length of  <dig> to  <dig> nucleotides are more efficient for rnai.
we would like to mention that we are aware that the counts we used here can be sometimes low .
however, the trend seems clear enough that we think our results are meaningful.
corroborating our results with new data sets from other species will allow to explore whether the results we report here are a specificity of c. elegans or constitute a more general trend.
finally, we think that our predictions are ripe for experimental verifications using directed experiments.
for example, one can try to induce interference with a non-duplicated target gene with various sequences construction  and consequently analyze the rnai phenotype as well as the mrna expression level, possibly by real-time rt-pcr.
CONCLUSIONS
our analysis represents a novel approach to estimate the threshold of sequence identity susceptible to off-target cross-reaction in an rnai assay .
while enormous amounts of phenotypic data are being generated for many organisms using rnai, this strategy allows flagging potential false positive in rnai datasets.
the rnai data of genes  having greater than 95% identity over  <dig> nucleotides with another genes should be interpreted cautiously and tagged as potential false positives.
we propose that similar strategies and criteria should be applied for cautious interpretation of rnai data from any organisms.
it is noteworthy to mention that our approach may be extended to study additional features having impact on rnai cross-reaction.
those features include, for example, positional effect of mismatches, effects of utrs, thermodynamical stability, or prevalence/exclusion of certain nucleotides at different positions.
in addition, a better understanding of the off-target effect phenomenon should allow a better application of rnai as an experimental tool or as a therapeutic approach.

 the discovery of rna interference has been an important breakthrough in biology in the past years. although rnai-related phenomena have been described for decades, it is only recently that the silencing mechanism has been understood at the molecular level. in caenorhabditis elegans, fire and colleagues described rnai as a sequence-specific gene-silencing event based on the introduction of a double-stranded rna template having sequence similarity with the targeted messenger rna. since then, the rnai pathway has been shown to be conserved in a wide variety of eukaryotic organisms. the physiological functions of rnai range from immune response by degradation of exogenous genetic material to development by regulation of gene expression. in recent years, rnai has been extensively used as an experimental tool for the analysis of gene function. as our understanding of the underlying molecular machinery improves, the potential use of rnai for therapy is becoming more evident. in the rnai pathway, long dsrnas or short hairpin rnas are processed and digested into small interfering rnas by dicer, an rnase iii family member. after incorporation of the sirna in the rna-induced silencing complex, the sirna-protein complex degrades mrnas having sequence complementarity to the sirna. interestingly, the rnai machinery has also been shown to mediate translational repression or induce chromatin modification. since interference is based on sequence recognition, targeting a gene by rnai can give rise to the silencing of another gene with similar sequence. this phenomenon is referred to as off-target effect or cross-reaction and can occur through mrna degradation or through translational repression. although rnai phenotypes are generally assumed to be due to the sole knock-down of the targeted gene, they can also be due to multi-gene silencing. numerous genome-wide rnai analyses have been performed, e.g., for c. elegans and drosophila melanogaster. due to the issue of cross-reaction, rnai data should be filtered prior to their analysis. in addition, accurate knowledge of rnai specificity is critical when considering the use of rnai as a therapeutic technology. in this context, it is crucial to know how much similarity is necessary to observe rnai off-target cross-reaction. to assess identity requirements for rna interference in c. elegans, parrish et al. used a series of altered gfp coding regions with different degrees of similarity to the transgene target. they found effective interference with dsrnas that were 96% identical to the target sequence, less effective interference with a trigger that was 88% identical, and no interference with dsrna triggers that were 78% identical to the target. different studies based on mrna expression profile analysis led to contradictory conclusions regarding rnai target specificity. for c. elegans rnai data, fraser et al. used nt with 80% identity as a threshold. interestingly, in silico examination of potential cross-reaction as a function of sirna length led to the conclusion that target specificity and low probability of off-target effects were optimally balanced for sirnas of nucleotides. finally, for data repositories such as rnaidb, tools have been developed for analysis and visualization of the rnai data as well as their potential risk of "contamination". although these experiments give some indication of the sequence identity requirement, the question of how much similarity over how much length is necessary to observe off-target cross-reaction remains open.  using the rnai phenotypes of paralogous genes in c. elegans, we devised a strategy to estimate the minimum degree of similarity needed to observe off-target effects. hereafter, any gene that exhibits any kind of rnai phenotype will be further referred to as a "ph gene" without further consideration of the phenotypic details. similarly, any gene that was targeted by one or more rnai experiments and for which no phenotype is described will be defined as a "wt gene". we extracted all pairs of strict duplicates for which both copies were targeted by rnai. these pairs can be sorted according to the phenotypic class of both members: "wt/wt" pairs consist of two wt genes, "ph/ph" pairs of two ph genes and the remaining "wt/ph" pairs have one wt member and one ph member. in order to predict whether these duplicates exhibit off-target cross-reaction, we elaborated a model where all duplicates are subject to off-target cross-reaction. in this model: a) the probability of occurrence of ph/ph duplicate pairs is the same as the probability of occurrence of ph genes within singletons. the probability of a gene to be duplicated and further preserved being only very weakly correlated with the phenotypic class a gene, therefore, if at least one copy of the pair inherits the phenotypic class of their ancestral gene, we expect this first assumption to be true. b) some ph genes are annotated as wt genes due to the important fraction of false negatives. actually, the fraction of false negative in large-scale rnai experiments can be as high as but the fraction of false positive is extremely low. in our dataset, we estimate the fraction of false negatives to be. c) both genes in a duplicate pair give rise to the same rnai phenotype. this last assumption seems reasonable when off-target cross-reaction happens, since the targeting of one copy would also knock down the other copy. under such a model, we expect of ph/ph pairs, of wt/ph pairs and of wt/wt pairs. we then computed the probability of the entire set of duplicate pairs to fit our model. we observed that the fractions of wt/wt, wt/ph and ph/ph of the entire set of pairs do not fit our model. from this result, we concluded that not all duplicates exhibit off-target effects. this result is expected because only very similar duplicates should exhibit off-target cross-reaction. accordingly, we sorted the pairs using the degree of sequence similarity between the genes and the corresponding rnai clones. since we did not want to assume a sequence length for off-target cross-reaction, we chose to estimate the percentage identity over several lengths, i.e., over or nucleotides. sixteen out of the pairs had at least one of their genes longer than kb and identity were not estimated because of memory consumption. for each selected length, we grouped the pairs according to their percentage identity. for each group, we counted the number of wt/wt, wt/ph and ph/ph pairs and estimated the corresponding likelihood of these observed counts to fit the model of complete off-target cross-reaction. the higher the likelihood, the higher the chance this group is sensitive to off-target effects. results show that only genes having high degree of sequence similarity with the rnai clones, i.e., 100% over nt, ≥94% over nt, ≥89% over nt, ≥84% over nt and ≥81% over nt, fit well with the model. this strongly suggests that off-target effects occur when the percentage identity exceeds these thresholds. as sequence identity decreases, the likelihood of the data to fit the model decreases as well, illustrating the weaker effect of off-target. to better understand sequence recognition requirements of the rnai machinery, we looked for the minimum length of high-similarity stretch between the dsrna and its target necessary to observe efficient rna interference. more precisely, we calculated the minimal length over which sequence similarity is necessary to have a high likelihood to observe off-target cross-reaction. this is not a trivial problem because pairs that are very similar to the rnai clone over nt are usually also very similar over nt. consequently, to address this question of minimal length, we selected pairs whose maximum percentage identity with the rnai clones is above the threshold over nt and, in the same time, below the threshold over nt. if such pairs exhibit a high likelihood of off-target cross-reaction, it suggests that having 100% identity over nt is sufficient to observe off-target effects. on the other hand, if this likelihood is low, it suggests that having 100% identity over nt is not sufficient to observe off-target effects. out of such pairs, are wt/wt, are wt/ph and none are ph/ph. the corresponding likelihood is relatively low, suggesting that these pairs may be not subject to off-target cross-reaction and that the minimum length may be more than nt. to compute more precisely the minimum length on which a high identity is necessary to observe off-target cross-reaction, we applied the same strategy to compare nt with nt, nt with nt, etc. results show that the data fit well the model for pairs with high identity on nt only. on the contrary, pairs with high identity on nt only or on nt only fit poorly the model. keeping in mind that our analysis is performed with limited amount of data, it suggests that dsrna having sequence similarity over to nucleotides are optimal to observe efficient off-target cross-reaction and, by extrapolation, rnai in c. elegans. it is important to distinguish between "the minimum length of the dsrna" and "the minimum length of high-similarity stretch between the dsrna and its target" necessary to observe an efficient rnai effect. our analysis studies the later one. our results do not imply that, overall, 30– nt dsrnas are the most efficient in an rnai experiment. on the contrary, in c. elegans, long dsrna molecules tend to be much more efficient than small dsrna molecules for reasons not only related to the interaction with the target mrna but also to the initiation of the systemic effect and amplification of the rnai effect. here our results suggest that a stretch of 30– nt of high similarity inside the dsrna molecule is sufficient to observe an efficient rnai. a systematic experimental analysis of the minimum length of the dsrna molecule having a 30– nt stretch of high similarity with targeted gene would complement our study. moreover, we would like to mention that our results are based on the assumption that only one stretch of high similarity is necessary to observe off-target reaction. therefore, our method does not assess whether one or multiple stretches of high similarity are necessary. our estimated range is in agreement with the current molecular model of the rnai machinery. indeed, for each dsrna molecule having one fragment of nucleotides identity with the targeted mrna, the chance to have an sirna of exactly nucleotides identity with the same mrna after dicer processing is one out of however, for dsrna molecule having one fragment of nucleotides identity with the targeted mrna, the chance to have an sirna of exactly nucleotides identity with the same mrna after dicer processing is 100%. to date, in mammalian cells, a typical rnai experiment is performed by using conventional 21-mer synthetic rna duplexes. in addition to the limitation of using long dsrna triggers that can induce the non-specific interferon response, the choice of 21-mer long dsrnas as rnai triggers was mainly guided by the observation that 21-mer sirnas are key players in the rnai machinery. however, recent studies demonstrate that, in mammalian cells, synthetic rna duplexes 25– nucleotides in length can be up to 100-fold more potent than corresponding conventional 21-mer sirnas. the enhanced efficiency is attributed to the fact that longer dsrnas are substrates of dicer. indeed, dicer would directly link the production of sirnas to their incorporation in the risc complex. likewise, although sirnas are ~ nucleotides long in c. elegans, our results suggest that sequences with similarity to the target mrna over a length of to nucleotides are more efficient for rnai. we would like to mention that we are aware that the counts we used here can be sometimes low. however, the trend seems clear enough that we think our results are meaningful. corroborating our results with new data sets from other species will allow to explore whether the results we report here are a specificity of c. elegans or constitute a more general trend. finally, we think that our predictions are ripe for experimental verifications using directed experiments. for example, one can try to induce interference with a non-duplicated target gene with various sequences construction and consequently analyze the rnai phenotype as well as the mrna expression level, possibly by real-time rt-pcr.  our analysis represents a novel approach to estimate the threshold of sequence identity susceptible to off-target cross-reaction in an rnai assay. while enormous amounts of phenotypic data are being generated for many organisms using rnai, this strategy allows flagging potential false positive in rnai datasets. the rnai data of genes having greater than 95% identity over nucleotides with another genes should be interpreted cautiously and tagged as potential false positives. we propose that similar strategies and criteria should be applied for cautious interpretation of rnai data from any organisms. it is noteworthy to mention that our approach may be extended to study additional features having impact on rnai cross-reaction. those features include, for example, positional effect of mismatches, effects of utrs, thermodynamical stability, or prevalence/exclusion of certain nucleotides at different positions. in addition, a better understanding of the off-target effect phenomenon should allow a better application of rnai as an experimental tool or as a therapeutic approach. 
we use a novel strategy based on phenotypic analysis of paralogs and predict that, in caenorhabditis elegans, off-target effects occur when an mrna sequence shares more than 95% identity over nucleotides with the dsrna. interestingly, our results suggest that the minimum length necessary of a high-similarity stretch between a dsrna and its target in order to observe an efficient rnai effect varies from to nucleotides rather than nucleotides, which is the length of sirnas in c. elegans. the rnai mechanism, which is based on the introduction of a double-stranded rna trigger whose sequence is similar to that of the targeted messenger rna, is subject to off-target cross-reaction.
 in the few years since its discovery, rnai has turned into a very powerful tool for the study of gene function by allowing post-transcriptional gene silencing. the rnai mechanism, which is based on the introduction of a double-stranded rna trigger whose sequence is similar to that of the targeted messenger rna, is subject to off-target cross-reaction.  we use a novel strategy based on phenotypic analysis of paralogs and predict that, in caenorhabditis elegans, off-target effects occur when an mrna sequence shares more than 95% identity over nucleotides with the dsrna. interestingly, our results suggest that the minimum length necessary of a high-similarity stretch between a dsrna and its target in order to observe an efficient rnai effect varies from to nucleotides rather than nucleotides, which is the length of sirnas in c. elegans.  our predictive methods would improve the design of dsrna and ultimately the use of rnai as a therapeutic tool upon experimental verification. 