BACKGROUND
there has been great interest in understanding the role of amino acid covariation in protein evolution and function.
the importance of covariation goes beyond the linear contribution of amino acid coevolution to explain the stability of protein folds.
in fact not only conservation of amino acid positions may be important for maintaining protein folds but also the correlated variation of pairs of amino acid residues around these folds may have an important role in maintaining their stability  <cit> .
covariation may therefore reflect functional and/or structural constraints.
many parametric and non-parametric methods have been developed for such purpose .
methods based on the information theory are among the most used ones.
these methods measure the reduction in uncertainty in particular amino acid sites  achieved by considering the site's mutual information  with additional sites.
this measure accounts for the predictability of the composition of one amino acid column when the composition of another amino acid site is known.
however, the sensitivity of most of these methods has been always halted by the fact that true positive coevolutionary relationships between amino acid sites are swamped in a background of stochastic amino acid covariation.
consequently, studies using methods slightly different in their mathematical parameterisation have been dramatically affected by the properties of msas .
in addition to the problems of stochastic covariation between amino acid sites, no single pair of sites is unrelated in msas due to their historical  dependencies  <cit> .
finally, the coevolutionary relationships are due to many different links between amino acid sites including coevolution due to structural, functional or physical interactions  <cit> .
many authors have devised mathematically transformed models based on the mutual information of two amino acid sites to highlight true functional coevolutionary relationships between them.
some of these methods included a correction of mi values by the degree of amino acid variability at the amino acid sites  <cit> , using the phylogenetic information to remove phylogenetic coevolution  <cit> , limiting the size of groups of coevolving amino acid sites  <cit>  or quantitatively normalising the mi value by the content of information at the sites under test  <cit> .
even though most of these methods have improved the sensitivity to detect functional/structural relationships between coevolving amino acids, a realistic method accounting for some of the most obvious biological properties of amino acid sites is as yet to be performed.
for instance, most of the methods developed use qualitative approaches to remove the phylogenetic coevolutionary signal .
a formal or statistical method is then needed to conduct a more rigorous approach of removing the undesired historical coevolution.
introducing some biological parameters, such as the physico-chemical properties of amino acid sites may dramatically increase the sensitivity of mutual-information based methods to detect coevolution.
furthermore, these biological-information based methods may improve our ability in detecting compensatory mutations.
this is due to the fact that compensatory mutations usually occur proximal in the protein structure and they are produced to maintain internal volumes, preserve salt bridges, or retain optimal hydrogen bonding.
in summary, information-based coevolutionary analyses introducing biological information may indirectly aid at identifying pairs of three-dimensionally proximal residues.
few attempts have been made to relate coevolving pairs in a msa to biological information in order to shed light on the structural and functional reasons of such coevolution  <cit> .
these reports however, did not use this biological information as a filter for the coevolutionary analyses but rather as a criterion adopted a posteriori to performing the method to detect functionally important coevolving pairs.
also, no general approach was conducted to determine the relationships between such parameters and their biological meaning.
because of the growing interest in detecting molecular coevolution to infer biologically meaningful selective constraints, measuring the accuracy of such methods when varying the msas properties becomes crucial.
in this work we first examine the evolutionary and statistical behaviours of some of the properties of amino acid sites in proteins.
then we introduce this information in the coevolutionary analysis and test its effect on the sensitivity of mi-based methods.
because of the large amount of data examined in this study, we implemented these mi methods in in-house software .
we then examined the effect of msas with different properties.
finally, we apply our improved procedure to detect coevolution to several well-studied proteins, whose functional domains are known and examine the ability of the method to detect important functional sites.
RESULTS
filtering by the parsimony information criterion removes most of the stochastic coevolution
one of the pre-requisites to consider a site as valid for our analyses was when it presented enough information as to remove the effects of the phylogenetic asymmetry on the data.
for example, if one particular sequence were significantly distant from the root of the tree when compared to other sequences, then its effect on the amount of evolutionary information over the data would be more significant before any correction was applied.
to account for the asymmetric contribution of sequences to the coevolutionary analysis we used a parsimony criterion to filter down the number of pairs of sites considered in the analysis.
a site was considered parsimony informative if the number of amino acid states at that site was greater than two and if each state is present in at least two sequences .
this approach has previously been shown to reduce the false discovery rate  <cit> .
we first tested the effect of filtering by parsimony in mi values at different coevolutionary strengths, differently populated msas and at various amino acid distances.
one of the most important results obtained in this analysis was that the percentage of positive values  increases from a maximum value of approximately 20% in a previous work where no filter was applied  <cit>  to a maximum value of 82% when using  <dig> sequences, and 80% when using  <dig> and  <dig> sequences .
this important increase in ppv value suggests that amino acid distances per site are an important factor to take into account when performing this kind of approaches as previously suggested  <cit> .
the sensitivity values for this non-parametric method are also of the same order than that yielded by other parametric methods shown to be highly sensitive  <cit> .
a univariate analysis of variance shows significant effects of the number of sequences ; mean pairwise amino acid substitutions per site ; and strength of coevolution  on the ppv values.
the pairwise factors' interactions and the interaction between the three factors also showed significant effects on the ppv values.
inspection of the mean ppv values in msas with different sizes did not show a clear tendency when varying the number of sequences .
this result may be due to the fact that introducing the parsimony filter makes the mi based method more robust to variations in the msas sizes due to a lower effect of the stochastic and phylogenetic covariations.
increasing the pairwise divergence levels or the strength of coevolution increased the mean ppv values  .
comparison of coevolution data corresponding to the levels of 20% and 25% coevolution presented however no significant differences for both sets .
the interaction between the level of coevolution  and the variation of pairwise divergence levels also showed no effect on the detection of true coevolution .
neither the interaction between these three factors showed any significant variability levels in ppv .
however, pairwise distance as well as number of sequences still showed significant effects on the variance of ppv, with increasing pairwise distance being the only factor explaining a significant increase in ppv.
regarding the sensitivity  of the method when filtering by parsimonious variability per site, all three factors  as well as all possible combination of factors influenced the variance of sn.
in fact, univariate analyses showed significant effect of the size of the msa , amino acid substitutions per site  and strength of coevolution  on sn.
the tendency of sn with variations of each of the factors was however different .
even though an increase of the number of sequences from  <dig> to  <dig> influenced the sn and ppv values, further increasing to  <dig> sequences in the msa did not show any directional influence in sn as it remained within the same range of values .
when distances were greater than  <dig>  amino acid substitutions per site sn tended to increase with increasing coevolutionary signal and increasing pairwise amino acid distances .
as before, the effect was more pronounced when the signal of coevolution increased from 10% to 20% or to 25% coevolution.
in fact, significant differences were observed between the dataset belonging to the 10% of coevolution level and that belonging to the 20% coevolution level .
no differences were found however between the 20% and 25% datasets .
our results indicate that strong signals of coevolution ameliorate the effect of the number of sequences and pairwise amino acid distances.
this was especially notorious in the case of pairwise distance factor because its interaction with coevolution level factor shows no significant variability in sn .
finally, at high number of sequences, a direct relationship exists between the level of coevolution and the ppv values.
for instance the mean ppv value increased when we increased the strength of coevolution from 10% to 20% in msas comprising  <dig> sequences .
this increase is also significant when coevolution increases from 20% to 25% .
we obtained the same results when we tested the effect of the strength of coevolution on sn.
also, there was no proportionality at low number of sequences between the level of coevolution and the ppv and sn values .
biological filtering increases the robustness of the sensitivity of coevolution analyses
one of the main purposes of coevolutionary analyses is to highlight covariation produced by biologically meaningful relationships between sites.
two of such important biological properties influencing the distribution of sites in the protein structure are the hydrophobicity and the molecular weight of the corresponding amino acids.
we tested the relationships between amino acid sites in a set of  <dig>  proteins whose structures were available in the national center for biotechnology information  based on these two factors.
we then tested whether the correlation in these factors depends on the proximity of the pair of amino acid sites in the protein structure.
to test this hypothesis, we measured the euclidean atomic distance between all pairs of amino acids within a protein and categorised these distances into the following classes .
this classification includes amino acids that are in physical contact in the structure , those that interact through an intermediate amino acid  and so on and so forth.
we finally, obtained the average correlation values for the hydrophobicity and molecular weight variability for each category  and we analysed the variation in the correlation coefficients.
for each protein structure we used a minimum of  <dig> protein sequences isolated from phylogenetically related eukaryotic species.
the analysis of the  <dig> protein structures showed a strong negative correlation between atomic amino acid distance and covariation at these parameters .
these results clearly show that correlation between amino acid sites using these amino acid properties would be useful to identify proximity between sites and hence may aid in identifying the source of amino acid covariation .
when testing the effect of hydrophobicity and molecular weight compared to parsimony filtering criterion in simulated msa data, we found that introducing biological information increases the mean ppv and sn compared to parsimony filtering .
the mean ppv increases significantly when we compare hydrophobicity to parsimony  and when we compare molecular weight to parsimony   .
sn also increases significantly in both comparisons  .
the ppv values generated in the coevolution analyses filtered by the correlated hydrophobicity of the pairs of amino acid sites were influenced by all three factors: size of msas, mean pairwise distance and level of coevolution.
however, simultaneous variation of the coevolution levels and size of msas or mean amino acid pairwise distance showed no effect on the amount of true positive values detected, with high coevolution levels compensating for variations in the msa size  or mean pairwise amino acid distance .
the combination of the three factors did not have significant effect on the ppv values generated .
in examining the tendency of ppv at different coevolutionary levels, msas sizes and mean pairwise amino acid distance, ppv values increased with increasing amino acid distances  .
sn values in contrast decreased with increasing pairwise amino acid distances .
variation in the size of the msa had no effect on the sn values .
molecular weight also increased significantly the ppv and sn of the method to detect coevolution .
even though all three factors have significant effects on the ppv values, at high pairwise amino acid distances, ppv values are indistinguishable when using different coevolution levels  .
on the other hand, the ppv values increases with increasing msas sizes  and increasing mean pairwise distances .
in the case of sn values, these were highly affected by all three parameters, although the number of sequences had little effect on the sn outcome .
filtered coevolution analyses identify functional sites in the proteins groel, hsp <dig> and env
to test the performance of the method in detecting functionally important sites  or sites surrounding functional domains we used a msa for the heat-shock proteins groel and hsp <dig> and the envelope protein env from hiv- <dig>  we were interested in pairs of amino acid sites that are either functionally important themselves or that are alternatively surrounding important functional domains .
in the protein groel we identified  <dig> pairs of amino acid sites with significant mi values.
parsimony filtering reduced the number of pairs to  <dig> including sites organised into  <dig> groups of coevolution .
group g <dig> was the largest coevolution group and comprised  <dig> amino acid sites, each one of them coevolving with the rest of the sites in the group.
out of the  <dig> amino acid sites detected in the first group,  <dig> amino acids  were located in the equatorial domains,  <dig> amino acids  in the intermediate domain and  <dig> amino acids  in the apical domain .
here, all amino acid numbers refer to the amino acid position in the reference groel sequence from the bacterium escherichia coli k <dig>  although linearly scattered, these sites were concentrated in the three-dimensional structure of groel around three main functional domains .
two amino acid sites were surrounding  the atp binding region, one amino acid site  could not be assigned to any functional category or was not proximal to any functional domain in the three-dimensional structure and the rest of amino acid sites  were enveloping the substrate/groes binding domain .
in addition, we measured the atomic distances between any pair of proximal amino acids within group  <dig>  this measurement was done assuming that effects of amino acid changes would be transmitted from one amino acid to another with which would coevolve following the shortest amino acid pathway.
the shortest distances between any pair of coevolving amino acids within group  <dig> had as average  <dig>  Å and ranged between  <dig>  Å and  <dig>  Å, indicating very short distances between coevolving amino acids.
five other groups  each with a single pair of coevolving amino acid sites were also detected, with only g <dig> and g <dig> including a single amino acid  present in both groups and proximal to functional regions .
all these groups, except group g <dig>  presented very large atomic distances between the coevolving amino acids .
a amino acid sites included in each coevolution group.
all sites within the same group coevolve between each other.
numbers indicate the position of the site taking as reference the sequence of the bacterium escherichia coli k <dig>
b measure of mean uncertainty for the first site of the coevolving pair.
c measure of mean uncertainty for the second site of the coevolving pair.
d measure of the mean joined uncertainty for the pairs of sites within each group
e mutual information mean value for all the possible coevolving pairs within the group.
application of the filter of hydrophobicity reduced the number of groups from  <dig> to  <dig> groups, including g <dig> to g <dig> .
interestingly, all these groups included sites proximal to functionally important regions, although g <dig> and g <dig> only included one out of the two amino acid sites to be proximal  to functional regions.
finally, only g <dig> was detected when we applied the filter of correlation in the variance of the molecular weight or molecular weight and hydrophobicity between the coevolving amino acid sites .
once again, only the group sharing the greatest number of functionally/structurally important sites was identified.
in conclusion, the results show that application of variation in the biological properties of coevolving amino acids a priori identified removes most of the non-biologically relevant pairs of significant coevolving amino acids.
in the case of hsp <dig> and env proteins' analyses we have not used an illustrative figure for the sake of synthesis and because the structure for env protein was lacking.
hsp <dig> comprises  <dig> main functional domains, including the atp-binding domain , the flexible charged linker , the catalytic middle domain  and the c-terminal domain  involved in dimerisation  <cit> .
we identified  <dig> pairs  of amino acid sites with significant mi values at a significant level of  <dig>  in hsp <dig>  application of the parsimony filter reduced the number of pairs to  <dig> pairs of amino acid sites organised into  <dig> groups  of coevolution .
many of these groups  included amino acid sites  located in the charged linker domain involved in client protein binding or surrounding sites important for client protein binding   <cit> .
other amino acid sites were located in or three-dimensionally close to hsp <dig> dimerisation domains   <cit> .
here, all amino acid numbers refer to the amino acid position in the reference hsp <dig> sequence from saccharomyces cervisiae.
group g <dig> included  <dig> amino acid sites  that are close to the amphipathic loop involved in the protein client binding region  <cit> .
group g <dig> includes one amino acid in the charge linker domain .
groups g <dig>  g <dig>  g <dig> and g <dig> include amino acids close in the sequence and in the 3d structure to the dimerization domains  and one amino acid around l450-f <dig> that is surrounding the dimerization region.
the two coevolving amino acids of g <dig>  were three-dimensionally proximal to each other and to the dimerization domain as well.
application of the filter of hydrophobicity reduced the number of groups from the  <dig> groups identified under parsimony filtering to  <dig> groups, including g <dig>  g <dig>  g <dig>  g <dig>  g <dig>  g <dig> and g <dig>  interestingly, all these groups included sites proximal to functionally important regions, except g <dig>  finally, groups g <dig>  g <dig>  g <dig>  g <dig>  g <dig>  g <dig>  g <dig>  and g <dig> were detected when we applied the filter of correlation in the variances of molecular weights, with all the groups except g <dig> and g <dig> being involved or close to the dimerization domains or to the client protein binding domain.
a amino acid sites included in each coevolution group.
all sites within the same group coevolve between each other.
numbers indicate the position of the site taking as reference the sequence of saccharomyces cerevisae.
b measure of mean uncertainty for the first site of the coevolving pair.
c measure of mean uncertainty for the second site of the coevolving pair.
d measure of the mean joined uncertainty for the pairs of sites within each group
e mutual information mean value for all the possible coevolving pairs within the group.
regarding the env protein of hiv- <dig>  we identified  <dig> pairs of amino acid sites with significant mi values at the confidence level of  <dig> .
application of the parsimony criterion to filter coevolving pairs, reduced the number of pairs to  <dig> pairs of amino acid sites organised into  <dig> groups of coevolution .
g <dig> involved  <dig> amino acids  l <dig> is allocated in the protein gp <dig>  while the rest of the amino acids of the remaining groups are found in the gp <dig> protein.
position l <dig> is surrounding the cd <dig> and gp <dig> binding sites, while two out of the sites found in gp <dig>  are surrounding glycosylation site h564; we do not have relevant biological information for the position t <dig>  here, all amino acid numbers refer to the amino acid position in the env hxb <dig> reference sequence.
g <dig> include  <dig> amino acids , with s <dig> and v <dig> being located in gp <dig> close to the glycosylation site h <dig> and t <dig>  respectively.
the last group of coevolution, g <dig>  included  <dig> amino acids , one  is located in the gp <dig> protein close to the glycosylation site e <dig>  glycosilation consists on the covering of the surface of the molecule by carbohydrates shielding therefore the antigenic exposed sites of gp <dig> and enabling the virus to escape the immune response of the host  <cit> .
the other  <dig> amino acids, as explained before, belong to the gp <dig> protein and are surrounding gycosylation sites as well.
application of the filter of hydrophobicity reduced the number of groups from  <dig> to  <dig> group , which in this case just include the pair l <dig> and v <dig>  finally, the three groups were detected when we applied the filter of correlation in the variance of the molecular weight.
a amino acid sites included in each coevolution group.
all sites within the same group coevolve between each other.
numbers indicate the position of the site taking as reference the sequence of saccharomyces cerevisae.
b measure of mean uncertainty for the first site of the coevolving pair.
c measure of mean uncertainty for the second site of the coevolving pair.
d measure of the mean joined uncertainty for the pairs of sites within each group
e mutual information mean value for all the possible coevolving pairs within the group.
discusion
proteins evolve  under rules governed by the different selective constraints imposed over their constituent amino acids.
the magnitude of these constraints is a function of the relative contribution of proteins to the biological fitness of individuals in the population.
because different amino acids within a protein have different roles, they are usually under different selective pressures depending upon their importance on the protein's function or structure.
this differential relationship of amino acid sites to the protein's function is translated into different levels of within-protein amino acid conservation.
amino acids that contribute equally to the protein's function or structure should theoretically correlate in their evolutionary rates.
unraveling correlated evolution between amino acids is however generally swamped in a background of historical coevolution that makes difficult disentangling both types of covariation.
despite that most of the functionally important sites are generally restricted to change by selection, mutations studies have shown that non-conserved amino acid sites can be functionally important because of their contribution to maintain geometry-volume characteristics around important sites, their compensatory effects of mutations at important regions or their contribution to protein-protein interaction interfaces.
we have previously shown that indeed most of the significant coevolutionary relationships can affect regions surrounding functionally important domains  <cit> .
this implies that coevolving sites detected as not being proximal in the three-dimensional structure in other studies  <cit>  may be related through their contribution to the structural/functional equilibrium of important regions in the protein.
in such cases, introducing statistical filters based on biological information about the physico-chemical properties of the coevolving amino acids can significantly improve our ability to detect functionally important regions as shown in this study.
our results based on simulated msas demonstrate that the accuracy of mi based methods to detect coevolution can improve by introducing statistical and biological filters a priori to the identification of coevolving amino acid sites.
introducing statistical filters such as those proposed previously  <cit>  or using parsimony-informative amino acid sites as we show in this study increases sn and ppv values significantly.
as we show, despite the introduction of statistical filters to the analysis of coevolution, sn and ppv still depend on the size of msas, mean pairwise divergence levels and strength of the coevolution signal.
all these factors have intermingled effects and they should be considered prior to any coevolution analysis.
the effect of the interaction of all three factors in ppv and sn is however complex and differs significantly with specific combinations of values for these factors.
fares and travers  <cit>  highlighted the significant effect of amino acid divergence levels and size of the msas on the sn of the method.
they also showed that sn values of the mi based methods did not go beyond 20% when no filters were introduced.
martin and colleagues demonstrated using simulated msas that the contribution of background mi from finite column lengths is mitigated when msas comprise more than  <dig> sequences  <cit> .
when analysing real protein sequences, the number of sequences in msas is often limited to few sequences, which make the use of mi to detect coevolution prohibitive given the large expected number of false coevolutionary relationships.
we show that, the effect of the number of sequences on the variance of sn and ppv is significant but that parsimony filtering criterion employed in our coevolution analyses reduces the number of fp, increasing hence the ppv.
this procedure ameliorates hence the problem of low statistical power of mi coevolutionary analyses when the number of sequences in the msa is low.
the effect of the number of sequences in msas becomes less important when the strength of coevolution increases.
this is especially notorious when switching from msas comprising  <dig> sequences to those with  <dig> sequences.
these results support the fact that introducing stringent filters will increase the ability of avoiding fp in the coevolutionary analyses even when the msa sizes are limited.
furthermore, msas presenting high number of sequences  present proportional increase of ppv and sn when the coevolution level increases.
this means that our ability to classify sites with high mi values and their distinction from those with lower mi values is more feasible when the number of sequences is high.
consequently, these results suggest that the separation between the different types of coevolution may be more approachable in large msa.
parsimony criterion has been previously used successfully to identify pairs of coevolving residues involved in the interaction between two proteins  <cit> .
adding hydrophobicity and molecular weight as a priori filters for mi values we obtained significantly greater mi values compared to parsimony filtering.
in addition, the size of the msa did not have significant effects on ppv and sn.
moreover, increasing the level of coevolution did not involve a significant increase in ppv or sn when divergence levels were high.
although this approximation is similar to that performed previously  <cit> , their approach was uniquely based on the a posteriori qualitative use of the biological properties of amino acids to decide whether a coevolutionary pair was important biologically.
our approach however, considers the correlation in the hydrophobicity and/or molecular weight of coevolving amino acid sites a priori to statistically determine their biological significance.
in summary, taking into account this study for a given protein we can theoretically interpolate the values for the size of msas and mean pairwise amino acid distance and know at which level of coevolution we will be able to identify real coevolving pairs.
application of our method using the different filters to identify coevolving amino acid sites within the heat-shock proteins groel and hsp <dig> and the envelope protein env of hiv- <dig> clearly show the usefulness of these biological filters to identify functionally important amino acid regions.
this approach was performed previously using a parametric method to detect coevolution  <cit>  and applying it to the hsp70-hop-hsp <dig> system  <cit>  providing great sensitivity to detect functionally important regions.
in this study we show that these filters are very useful to ameliorate the limitations of non-parametric methods to detect functional coevolution as well.
CONCLUSIONS
the main conclusion derived from this study is that appropriate statistical as well as biological filters introduced in coevolutionary analyses can substantially reduce the false discovery rate.
the number of sequences, mean pairwise divergence levels and the strength of coevolution between amino acid sites in msas are strong parameters affecting the ability of non-parametric methods to detect coevolution.
as additional parameters affecting the accuracy of coevolution methods based on the mutual information criterion are the asymmetric phylogenies and the lack of biological filters.
the high correlation in the hydrophobicities and molecular weights of closely located amino acid sites in the protein structure is testament to the importance of the biological information in these kinds of analyses.
introduction of these amino acid properties as biological filters in mi based methods appears to equalise their sensitivity to a similar range of values determined by previous simulation studies of other parametric and highly sensitive methods  <cit> .

 there has been great interest in understanding the role of amino acid covariation in protein evolution and function. the importance of covariation goes beyond the linear contribution of amino acid coevolution to explain the stability of protein folds. in fact not only conservation of amino acid positions may be important for maintaining protein folds but also the correlated variation of pairs of amino acid residues around these folds may have an important role in maintaining their stability. covariation may therefore reflect functional and/or structural constraints. many parametric and non-parametric methods have been developed for such purpose. methods based on the information theory are among the most used ones. these methods measure the reduction in uncertainty in particular amino acid sites achieved by considering the site's mutual information with additional sites. this measure accounts for the predictability of the composition of one amino acid column when the composition of another amino acid site is known. however, the sensitivity of most of these methods has been always halted by the fact that true positive coevolutionary relationships between amino acid sites are swamped in a background of stochastic amino acid covariation. consequently, studies using methods slightly different in their mathematical parameterisation have been dramatically affected by the properties of msas. in addition to the problems of stochastic covariation between amino acid sites, no single pair of sites is unrelated in msas due to their historical dependencies. finally, the coevolutionary relationships are due to many different links between amino acid sites including coevolution due to structural, functional or physical interactions. many authors have devised mathematically transformed models based on the mutual information of two amino acid sites to highlight true functional coevolutionary relationships between them. some of these methods included a correction of mi values by the degree of amino acid variability at the amino acid sites, using the phylogenetic information to remove phylogenetic coevolution, limiting the size of groups of coevolving amino acid sites or quantitatively normalising the mi value by the content of information at the sites under test. even though most of these methods have improved the sensitivity to detect functional/structural relationships between coevolving amino acids, a realistic method accounting for some of the most obvious biological properties of amino acid sites is as yet to be performed. for instance, most of the methods developed use qualitative approaches to remove the phylogenetic coevolutionary signal. a formal or statistical method is then needed to conduct a more rigorous approach of removing the undesired historical coevolution. introducing some biological parameters, such as the physico-chemical properties of amino acid sites may dramatically increase the sensitivity of mutual-information based methods to detect coevolution. furthermore, these biological-information based methods may improve our ability in detecting compensatory mutations. this is due to the fact that compensatory mutations usually occur proximal in the protein structure and they are produced to maintain internal volumes, preserve salt bridges, or retain optimal hydrogen bonding. in summary, information-based coevolutionary analyses introducing biological information may indirectly aid at identifying pairs of three-dimensionally proximal residues. few attempts have been made to relate coevolving pairs in a msa to biological information in order to shed light on the structural and functional reasons of such coevolution. these reports however, did not use this biological information as a filter for the coevolutionary analyses but rather as a criterion adopted a posteriori to performing the method to detect functionally important coevolving pairs. also, no general approach was conducted to determine the relationships between such parameters and their biological meaning. because of the growing interest in detecting molecular coevolution to infer biologically meaningful selective constraints, measuring the accuracy of such methods when varying the msas properties becomes crucial. in this work we first examine the evolutionary and statistical behaviours of some of the properties of amino acid sites in proteins. then we introduce this information in the coevolutionary analysis and test its effect on the sensitivity of mi-based methods. because of the large amount of data examined in this study, we implemented these mi methods in in-house software. we then examined the effect of msas with different properties. finally, we apply our improved procedure to detect coevolution to several well-studied proteins, whose functional domains are known and examine the ability of the method to detect important functional sites.  filtering by the parsimony information criterion removes most of the stochastic coevolution one of the pre-requisites to consider a site as valid for our analyses was when it presented enough information as to remove the effects of the phylogenetic asymmetry on the data. for example, if one particular sequence were significantly distant from the root of the tree when compared to other sequences, then its effect on the amount of evolutionary information over the data would be more significant before any correction was applied. to account for the asymmetric contribution of sequences to the coevolutionary analysis we used a parsimony criterion to filter down the number of pairs of sites considered in the analysis. a site was considered parsimony informative if the number of amino acid states at that site was greater than two and if each state is present in at least two sequences. this approach has previously been shown to reduce the false discovery rate. we first tested the effect of filtering by parsimony in mi values at different coevolutionary strengths, differently populated msas and at various amino acid distances. one of the most important results obtained in this analysis was that the percentage of positive values increases from a maximum value of approximately 20% in a previous work where no filter was applied to a maximum value of 82% when using sequences, and 80% when using and sequences. this important increase in ppv value suggests that amino acid distances per site are an important factor to take into account when performing this kind of approaches as previously suggested. the sensitivity values for this non-parametric method are also of the same order than that yielded by other parametric methods shown to be highly sensitive. a univariate analysis of variance shows significant effects of the number of sequences; mean pairwise amino acid substitutions per site; and strength of coevolution on the ppv values. the pairwise factors' interactions and the interaction between the three factors also showed significant effects on the ppv values. inspection of the mean ppv values in msas with different sizes did not show a clear tendency when varying the number of sequences. this result may be due to the fact that introducing the parsimony filter makes the mi based method more robust to variations in the msas sizes due to a lower effect of the stochastic and phylogenetic covariations. increasing the pairwise divergence levels or the strength of coevolution increased the mean ppv values. comparison of coevolution data corresponding to the levels of 20% and 25% coevolution presented however no significant differences for both sets. the interaction between the level of coevolution and the variation of pairwise divergence levels also showed no effect on the detection of true coevolution. neither the interaction between these three factors showed any significant variability levels in ppv. however, pairwise distance as well as number of sequences still showed significant effects on the variance of ppv, with increasing pairwise distance being the only factor explaining a significant increase in ppv. regarding the sensitivity of the method when filtering by parsimonious variability per site, all three factors as well as all possible combination of factors influenced the variance of sn. in fact, univariate analyses showed significant effect of the size of the msa, amino acid substitutions per site and strength of coevolution on sn. the tendency of sn with variations of each of the factors was however different. even though an increase of the number of sequences from to influenced the sn and ppv values, further increasing to sequences in the msa did not show any directional influence in sn as it remained within the same range of values. when distances were greater than amino acid substitutions per site sn tended to increase with increasing coevolutionary signal and increasing pairwise amino acid distances. as before, the effect was more pronounced when the signal of coevolution increased from 10% to 20% or to 25% coevolution. in fact, significant differences were observed between the dataset belonging to the 10% of coevolution level and that belonging to the 20% coevolution level. no differences were found however between the 20% and 25% datasets. our results indicate that strong signals of coevolution ameliorate the effect of the number of sequences and pairwise amino acid distances. this was especially notorious in the case of pairwise distance factor because its interaction with coevolution level factor shows no significant variability in sn. finally, at high number of sequences, a direct relationship exists between the level of coevolution and the ppv values. for instance the mean ppv value increased when we increased the strength of coevolution from 10% to 20% in msas comprising sequences. this increase is also significant when coevolution increases from 20% to 25%. we obtained the same results when we tested the effect of the strength of coevolution on sn. also, there was no proportionality at low number of sequences between the level of coevolution and the ppv and sn values. biological filtering increases the robustness of the sensitivity of coevolution analyses one of the main purposes of coevolutionary analyses is to highlight covariation produced by biologically meaningful relationships between sites. two of such important biological properties influencing the distribution of sites in the protein structure are the hydrophobicity and the molecular weight of the corresponding amino acids. we tested the relationships between amino acid sites in a set of proteins whose structures were available in the national center for biotechnology information based on these two factors. we then tested whether the correlation in these factors depends on the proximity of the pair of amino acid sites in the protein structure. to test this hypothesis, we measured the euclidean atomic distance between all pairs of amino acids within a protein and categorised these distances into the following classes. this classification includes amino acids that are in physical contact in the structure, those that interact through an intermediate amino acid and so on and so forth. we finally, obtained the average correlation values for the hydrophobicity and molecular weight variability for each category and we analysed the variation in the correlation coefficients. for each protein structure we used a minimum of protein sequences isolated from phylogenetically related eukaryotic species. the analysis of the protein structures showed a strong negative correlation between atomic amino acid distance and covariation at these parameters. these results clearly show that correlation between amino acid sites using these amino acid properties would be useful to identify proximity between sites and hence may aid in identifying the source of amino acid covariation. when testing the effect of hydrophobicity and molecular weight compared to parsimony filtering criterion in simulated msa data, we found that introducing biological information increases the mean ppv and sn compared to parsimony filtering. the mean ppv increases significantly when we compare hydrophobicity to parsimony and when we compare molecular weight to parsimony. sn also increases significantly in both comparisons. the ppv values generated in the coevolution analyses filtered by the correlated hydrophobicity of the pairs of amino acid sites were influenced by all three factors: size of msas, mean pairwise distance and level of coevolution. however, simultaneous variation of the coevolution levels and size of msas or mean amino acid pairwise distance showed no effect on the amount of true positive values detected, with high coevolution levels compensating for variations in the msa size or mean pairwise amino acid distance. the combination of the three factors did not have significant effect on the ppv values generated. in examining the tendency of ppv at different coevolutionary levels, msas sizes and mean pairwise amino acid distance, ppv values increased with increasing amino acid distances. sn values in contrast decreased with increasing pairwise amino acid distances. variation in the size of the msa had no effect on the sn values. molecular weight also increased significantly the ppv and sn of the method to detect coevolution. even though all three factors have significant effects on the ppv values, at high pairwise amino acid distances, ppv values are indistinguishable when using different coevolution levels. on the other hand, the ppv values increases with increasing msas sizes and increasing mean pairwise distances. in the case of sn values, these were highly affected by all three parameters, although the number of sequences had little effect on the sn outcome. filtered coevolution analyses identify functional sites in the proteins groel, hsp and env to test the performance of the method in detecting functionally important sites or sites surrounding functional domains we used a msa for the heat-shock proteins groel and hsp and the envelope protein env from hiv- we were interested in pairs of amino acid sites that are either functionally important themselves or that are alternatively surrounding important functional domains. in the protein groel we identified pairs of amino acid sites with significant mi values. parsimony filtering reduced the number of pairs to including sites organised into groups of coevolution. group g was the largest coevolution group and comprised amino acid sites, each one of them coevolving with the rest of the sites in the group. out of the amino acid sites detected in the first group, amino acids were located in the equatorial domains, amino acids in the intermediate domain and amino acids in the apical domain. here, all amino acid numbers refer to the amino acid position in the reference groel sequence from the bacterium escherichia coli k although linearly scattered, these sites were concentrated in the three-dimensional structure of groel around three main functional domains. two amino acid sites were surrounding the atp binding region, one amino acid site could not be assigned to any functional category or was not proximal to any functional domain in the three-dimensional structure and the rest of amino acid sites were enveloping the substrate/groes binding domain. in addition, we measured the atomic distances between any pair of proximal amino acids within group this measurement was done assuming that effects of amino acid changes would be transmitted from one amino acid to another with which would coevolve following the shortest amino acid pathway. the shortest distances between any pair of coevolving amino acids within group had as average Å and ranged between Å and Å, indicating very short distances between coevolving amino acids. five other groups each with a single pair of coevolving amino acid sites were also detected, with only g and g including a single amino acid present in both groups and proximal to functional regions. all these groups, except group g presented very large atomic distances between the coevolving amino acids. a amino acid sites included in each coevolution group. all sites within the same group coevolve between each other. numbers indicate the position of the site taking as reference the sequence of the bacterium escherichia coli k b measure of mean uncertainty for the first site of the coevolving pair. c measure of mean uncertainty for the second site of the coevolving pair. d measure of the mean joined uncertainty for the pairs of sites within each group e mutual information mean value for all the possible coevolving pairs within the group. application of the filter of hydrophobicity reduced the number of groups from to groups, including g to g. interestingly, all these groups included sites proximal to functionally important regions, although g and g only included one out of the two amino acid sites to be proximal to functional regions. finally, only g was detected when we applied the filter of correlation in the variance of the molecular weight or molecular weight and hydrophobicity between the coevolving amino acid sites. once again, only the group sharing the greatest number of functionally/structurally important sites was identified. in conclusion, the results show that application of variation in the biological properties of coevolving amino acids a priori identified removes most of the non-biologically relevant pairs of significant coevolving amino acids. in the case of hsp and env proteins' analyses we have not used an illustrative figure for the sake of synthesis and because the structure for env protein was lacking. hsp comprises main functional domains, including the atp-binding domain, the flexible charged linker, the catalytic middle domain and the c-terminal domain involved in dimerisation. we identified pairs of amino acid sites with significant mi values at a significant level of in hsp application of the parsimony filter reduced the number of pairs to pairs of amino acid sites organised into groups of coevolution. many of these groups included amino acid sites located in the charged linker domain involved in client protein binding or surrounding sites important for client protein binding. other amino acid sites were located in or three-dimensionally close to hsp dimerisation domains. here, all amino acid numbers refer to the amino acid position in the reference hsp sequence from saccharomyces cervisiae. group g included amino acid sites that are close to the amphipathic loop involved in the protein client binding region. group g includes one amino acid in the charge linker domain. groups g g g and g include amino acids close in the sequence and in the 3d structure to the dimerization domains and one amino acid around l450-f that is surrounding the dimerization region. the two coevolving amino acids of g were three-dimensionally proximal to each other and to the dimerization domain as well. application of the filter of hydrophobicity reduced the number of groups from the groups identified under parsimony filtering to groups, including g g g g g g and g interestingly, all these groups included sites proximal to functionally important regions, except g finally, groups g g g g g g g and g were detected when we applied the filter of correlation in the variances of molecular weights, with all the groups except g and g being involved or close to the dimerization domains or to the client protein binding domain. a amino acid sites included in each coevolution group. all sites within the same group coevolve between each other. numbers indicate the position of the site taking as reference the sequence of saccharomyces cerevisae. b measure of mean uncertainty for the first site of the coevolving pair. c measure of mean uncertainty for the second site of the coevolving pair. d measure of the mean joined uncertainty for the pairs of sites within each group e mutual information mean value for all the possible coevolving pairs within the group. regarding the env protein of hiv- we identified pairs of amino acid sites with significant mi values at the confidence level of. application of the parsimony criterion to filter coevolving pairs, reduced the number of pairs to pairs of amino acid sites organised into groups of coevolution. g involved amino acids l is allocated in the protein gp while the rest of the amino acids of the remaining groups are found in the gp protein. position l is surrounding the cd and gp binding sites, while two out of the sites found in gp are surrounding glycosylation site h564; we do not have relevant biological information for the position t here, all amino acid numbers refer to the amino acid position in the env hxb reference sequence. g include amino acids, with s and v being located in gp close to the glycosylation site h and t respectively. the last group of coevolution, g included amino acids, one is located in the gp protein close to the glycosylation site e glycosilation consists on the covering of the surface of the molecule by carbohydrates shielding therefore the antigenic exposed sites of gp and enabling the virus to escape the immune response of the host. the other amino acids, as explained before, belong to the gp protein and are surrounding gycosylation sites as well. application of the filter of hydrophobicity reduced the number of groups from to group, which in this case just include the pair l and v finally, the three groups were detected when we applied the filter of correlation in the variance of the molecular weight. a amino acid sites included in each coevolution group. all sites within the same group coevolve between each other. numbers indicate the position of the site taking as reference the sequence of saccharomyces cerevisae. b measure of mean uncertainty for the first site of the coevolving pair. c measure of mean uncertainty for the second site of the coevolving pair. d measure of the mean joined uncertainty for the pairs of sites within each group e mutual information mean value for all the possible coevolving pairs within the group. discusion proteins evolve under rules governed by the different selective constraints imposed over their constituent amino acids. the magnitude of these constraints is a function of the relative contribution of proteins to the biological fitness of individuals in the population. because different amino acids within a protein have different roles, they are usually under different selective pressures depending upon their importance on the protein's function or structure. this differential relationship of amino acid sites to the protein's function is translated into different levels of within-protein amino acid conservation. amino acids that contribute equally to the protein's function or structure should theoretically correlate in their evolutionary rates. unraveling correlated evolution between amino acids is however generally swamped in a background of historical coevolution that makes difficult disentangling both types of covariation. despite that most of the functionally important sites are generally restricted to change by selection, mutations studies have shown that non-conserved amino acid sites can be functionally important because of their contribution to maintain geometry-volume characteristics around important sites, their compensatory effects of mutations at important regions or their contribution to protein-protein interaction interfaces. we have previously shown that indeed most of the significant coevolutionary relationships can affect regions surrounding functionally important domains. this implies that coevolving sites detected as not being proximal in the three-dimensional structure in other studies may be related through their contribution to the structural/functional equilibrium of important regions in the protein. in such cases, introducing statistical filters based on biological information about the physico-chemical properties of the coevolving amino acids can significantly improve our ability to detect functionally important regions as shown in this study. our results based on simulated msas demonstrate that the accuracy of mi based methods to detect coevolution can improve by introducing statistical and biological filters a priori to the identification of coevolving amino acid sites. introducing statistical filters such as those proposed previously or using parsimony-informative amino acid sites as we show in this study increases sn and ppv values significantly. as we show, despite the introduction of statistical filters to the analysis of coevolution, sn and ppv still depend on the size of msas, mean pairwise divergence levels and strength of the coevolution signal. all these factors have intermingled effects and they should be considered prior to any coevolution analysis. the effect of the interaction of all three factors in ppv and sn is however complex and differs significantly with specific combinations of values for these factors. fares and travers highlighted the significant effect of amino acid divergence levels and size of the msas on the sn of the method. they also showed that sn values of the mi based methods did not go beyond 20% when no filters were introduced. martin and colleagues demonstrated using simulated msas that the contribution of background mi from finite column lengths is mitigated when msas comprise more than sequences. when analysing real protein sequences, the number of sequences in msas is often limited to few sequences, which make the use of mi to detect coevolution prohibitive given the large expected number of false coevolutionary relationships. we show that, the effect of the number of sequences on the variance of sn and ppv is significant but that parsimony filtering criterion employed in our coevolution analyses reduces the number of fp, increasing hence the ppv. this procedure ameliorates hence the problem of low statistical power of mi coevolutionary analyses when the number of sequences in the msa is low. the effect of the number of sequences in msas becomes less important when the strength of coevolution increases. this is especially notorious when switching from msas comprising sequences to those with sequences. these results support the fact that introducing stringent filters will increase the ability of avoiding fp in the coevolutionary analyses even when the msa sizes are limited. furthermore, msas presenting high number of sequences present proportional increase of ppv and sn when the coevolution level increases. this means that our ability to classify sites with high mi values and their distinction from those with lower mi values is more feasible when the number of sequences is high. consequently, these results suggest that the separation between the different types of coevolution may be more approachable in large msa. parsimony criterion has been previously used successfully to identify pairs of coevolving residues involved in the interaction between two proteins. adding hydrophobicity and molecular weight as a priori filters for mi values we obtained significantly greater mi values compared to parsimony filtering. in addition, the size of the msa did not have significant effects on ppv and sn. moreover, increasing the level of coevolution did not involve a significant increase in ppv or sn when divergence levels were high. although this approximation is similar to that performed previously, their approach was uniquely based on the a posteriori qualitative use of the biological properties of amino acids to decide whether a coevolutionary pair was important biologically. our approach however, considers the correlation in the hydrophobicity and/or molecular weight of coevolving amino acid sites a priori to statistically determine their biological significance. in summary, taking into account this study for a given protein we can theoretically interpolate the values for the size of msas and mean pairwise amino acid distance and know at which level of coevolution we will be able to identify real coevolving pairs. application of our method using the different filters to identify coevolving amino acid sites within the heat-shock proteins groel and hsp and the envelope protein env of hiv- clearly show the usefulness of these biological filters to identify functionally important amino acid regions. this approach was performed previously using a parametric method to detect coevolution and applying it to the hsp70-hop-hsp system providing great sensitivity to detect functionally important regions. in this study we show that these filters are very useful to ameliorate the limitations of non-parametric methods to detect functional coevolution as well.  the main conclusion derived from this study is that appropriate statistical as well as biological filters introduced in coevolutionary analyses can substantially reduce the false discovery rate. the number of sequences, mean pairwise divergence levels and the strength of coevolution between amino acid sites in msas are strong parameters affecting the ability of non-parametric methods to detect coevolution. as additional parameters affecting the accuracy of coevolution methods based on the mutual information criterion are the asymmetric phylogenies and the lack of biological filters. the high correlation in the hydrophobicities and molecular weights of closely located amino acid sites in the protein structure is testament to the importance of the biological information in these kinds of analyses. introduction of these amino acid properties as biological filters in mi based methods appears to equalise their sensitivity to a similar range of values determined by previous simulation studies of other parametric and highly sensitive methods. 
further, introducing statistical filters improves the sensitivity and increases the statistical power of the methods to detect functional coevolution. the application of this known biological information to the analysis of covariation greatly enhances the functional coevolutionary signal and removes historical covariation. application of these filters to three different proteins with known functional domains supports the importance of using biological filters to detect coevolution. using this biological information as filter in coevolutionary analyses minimises the false positive rate of these methods. coevolutionary analyses using non-parametric methods have proved difficult and highly prone to provide spurious results depending on the properties of msas and on the strength of coevolution between amino acid sites. the application of statistical filters to the number of pairs detected as coevolving reduces significantly the number of artifactual results. we test the effect that the size of the msa, mean pairwise amino acid distance per site and the strength of the coevolution signal have on the ability of non-parametric methods to detect coevolution. our results indicate that all three factors have significant effects on the accuracy of non-parametric methods. however, the difficulty in disentangling functional co-dependencies from historical covariation has fuelled the scepticism over their power to detect biologically meaningful results. non-parametric methods to detect coevolution have been reported to be especially susceptible to produce false positive results based on the properties of msas. results indicate a covariation trend in the hydrophobicities and molecular weight characteristics of amino acid sites when analysing a non-redundant set of protein structures. in addition, the biological parameters connecting linear sequence evolution to structure evolution remain elusive. the strength of selective constraints operating on amino acid sites of proteins has a multifactorial nature. in fact, amino acid sites within proteins coevolve due to their functional and/or structural relationships. different methods have been developed that attempt to account for the evolutionary dependencies between amino acid sites. statistical analysis of the physico-chemical properties of amino acid sites in the context of the protein structure reveals striking dependencies among amino acid sites. analysis of the physico-chemical properties of amino acid sites in the protein structure context reveals their structure-dependent covariation. simultaneous use of statistical and biological data is instrumental in the detection of functional amino acid sites dependencies and compensatory changes at the protein level. here we test the effect that variations on the msa properties have over the sensitivity of non-parametric methods to detect coevolution. researchers have invested a significant effort to increase the sensitivity of such methods. however, no formal statistical analysis has been performed to definitively test the differential effects of these properties on the sensitivity of such methods.
 the strength of selective constraints operating on amino acid sites of proteins has a multifactorial nature. in fact, amino acid sites within proteins coevolve due to their functional and/or structural relationships. different methods have been developed that attempt to account for the evolutionary dependencies between amino acid sites. researchers have invested a significant effort to increase the sensitivity of such methods. however, the difficulty in disentangling functional co-dependencies from historical covariation has fuelled the scepticism over their power to detect biologically meaningful results. in addition, the biological parameters connecting linear sequence evolution to structure evolution remain elusive. for these reasons, most of the evolutionary studies aimed at identifying functional dependencies among protein domains have focused on the structural properties of proteins rather than on the information extracted from linear multiple sequence alignments. non-parametric methods to detect coevolution have been reported to be especially susceptible to produce false positive results based on the properties of msas. however, no formal statistical analysis has been performed to definitively test the differential effects of these properties on the sensitivity of such methods.  here we test the effect that variations on the msa properties have over the sensitivity of non-parametric methods to detect coevolution. we test the effect that the size of the msa, mean pairwise amino acid distance per site and the strength of the coevolution signal have on the ability of non-parametric methods to detect coevolution. our results indicate that all three factors have significant effects on the accuracy of non-parametric methods. further, introducing statistical filters improves the sensitivity and increases the statistical power of the methods to detect functional coevolution. statistical analysis of the physico-chemical properties of amino acid sites in the context of the protein structure reveals striking dependencies among amino acid sites. results indicate a covariation trend in the hydrophobicities and molecular weight characteristics of amino acid sites when analysing a non-redundant set of protein structures. using this biological information as filter in coevolutionary analyses minimises the false positive rate of these methods. application of these filters to three different proteins with known functional domains supports the importance of using biological filters to detect coevolution.  coevolutionary analyses using non-parametric methods have proved difficult and highly prone to provide spurious results depending on the properties of msas and on the strength of coevolution between amino acid sites. the application of statistical filters to the number of pairs detected as coevolving reduces significantly the number of artifactual results. analysis of the physico-chemical properties of amino acid sites in the protein structure context reveals their structure-dependent covariation. the application of this known biological information to the analysis of covariation greatly enhances the functional coevolutionary signal and removes historical covariation. simultaneous use of statistical and biological data is instrumental in the detection of functional amino acid sites dependencies and compensatory changes at the protein level. 